Exergy evolution of the mineral capital on earth - circe

Mechanical Engineering 

Ph.D. Thesis 

EXERGY EVOLUTION OF THE MINERAL CAPITAL 

ON EARTH 

By Alicia Valero Delgado 

July 2008 

Directed by: 

Antonio Valero Capilla, Ph.D. 

Department <strong>of</strong> Mechanical Engineering 

Centro Politécnico Superior 

University <strong>of</strong> Zaragoza

<strong>Exergy</strong> <strong>evolution</strong> <strong>of</strong> <strong>the</strong> <strong>mineral</strong> <strong>capital</strong> on earth 

Alicia Valero Delgado 

Thesis submitted in partial fulfilment <strong>of</strong> <strong>the</strong> requirements for 

<strong>the</strong> degree <strong>of</strong> Doctor <strong>of</strong> Philosophy 

University <strong>of</strong> Zaragoza, Spain 

Abstract 

The 20th century has been characterized by <strong>the</strong> economic growth <strong>of</strong> many industrialized 

countries. This growth was mainly sustained by <strong>the</strong> massive extraction 

and use <strong>of</strong> <strong>the</strong> earth’s <strong>mineral</strong> resources. The tendency observed worldwide in <strong>the</strong> 

present, is that consumption will continue increasing, especially due to <strong>the</strong> rapid 

development <strong>of</strong> Asia, <strong>the</strong> desire for a higher living standard <strong>of</strong> <strong>the</strong> developing world 

and <strong>the</strong> technological progress. But <strong>the</strong> physical limitations <strong>of</strong> our planet might 

seriously restrain world economies. In fact, many <strong>mineral</strong> commodities such as oil 

or copper are already showing signs <strong>of</strong> scarcity problems, and consequently <strong>the</strong>ir 

prices are increasing sharply. 

Our society is based on an inefficient use <strong>of</strong> energy and materials, since <strong>the</strong>re is a 

lack <strong>of</strong> awareness <strong>of</strong> <strong>the</strong> limit. If resources are limited, <strong>the</strong>ir management must be 

carefully planned. But it is impossible to manage efficiently <strong>the</strong> resources on earth, 

if we do not know what is available and at which rate it is being depleted. 

Therefore, <strong>the</strong> aim <strong>of</strong> this PhD has been <strong>the</strong> assessment <strong>of</strong> <strong>the</strong> physical stock on 

earth and <strong>the</strong> degradation velocity <strong>of</strong> our <strong>mineral</strong> resources due to human action. 

This has been accomplished through <strong>the</strong> exergy analysis under <strong>the</strong> exergoecological 

approach. This way, <strong>the</strong> resources are physically assessed as <strong>the</strong> energy required 

to replace <strong>the</strong>m from a complete degraded state to <strong>the</strong> conditions in which <strong>the</strong>y 

are currently presented in nature. The main advantage <strong>of</strong> its use with respect to 

o<strong>the</strong>r physical indicators is that in a single property, all <strong>the</strong> physical features <strong>of</strong> a 

resource are accounted for. Fur<strong>the</strong>rmore, exergy has <strong>the</strong> capability <strong>of</strong> aggregating 

heterogeneous energy and material assets. Unlike standard economic valuations, 

<strong>the</strong> exergy analysis gives objective information since it is not subject to monetary 

policy, or currency speculation. 

i

Accordingly, in this work three imperative activities were carried out: 

• A systematic analysis <strong>of</strong> <strong>the</strong> main chemical components and <strong>the</strong> <strong>mineral</strong> resources 

on earth has been accomplished. Fur<strong>the</strong>rmore, <strong>the</strong> first composition in 

terms <strong>of</strong> <strong>mineral</strong>s <strong>of</strong> <strong>the</strong> upper continental crust has been developed, through 

a procedure that assures chemical coherence between species and elements. 

The integration <strong>of</strong> all <strong>the</strong>se data has provided a global overview <strong>of</strong> <strong>the</strong> geochemistry 

<strong>of</strong> our planet with special attention to <strong>the</strong> substances that compose 

<strong>the</strong> earth’s outer spheres and to that part <strong>of</strong> <strong>the</strong> substances useful to man: <strong>the</strong> 

<strong>mineral</strong> resources. 

• The <strong>the</strong>rmodynamic tools required for <strong>the</strong> physical assessment <strong>of</strong> natural resources 

and particularly for <strong>mineral</strong>s have been provided. This way, <strong>the</strong> standard 

<strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> earth and its constituents (enthalpy, 

Gibbs free energy and exergy) have been calculated. Additionally, <strong>the</strong> exergy 

<strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources <strong>of</strong> <strong>the</strong> earth (<strong>of</strong> fuel and non-fuel origin) has been 

obtained and compared to that <strong>of</strong> o<strong>the</strong>r energy resources. 

• With <strong>the</strong> help <strong>of</strong> different scarcity indicators developed in this PhD, an analysis 

<strong>of</strong> <strong>the</strong> state <strong>of</strong> our <strong>mineral</strong> resources has been accomplished. For that purpose 

<strong>the</strong> <strong>mineral</strong> exergy degradation throughout <strong>the</strong> 20th century has been studied. 

This has allowed to estimate when <strong>the</strong> peak <strong>of</strong> production <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> 

commodities is reached. Additionally, an outlook <strong>of</strong> <strong>the</strong> scarcity degree <strong>of</strong> our 

<strong>mineral</strong> <strong>capital</strong> in <strong>the</strong> 21st century has been undertaken. 

The results <strong>of</strong> this study reveal that <strong>the</strong> exergy analysis <strong>of</strong> <strong>mineral</strong>s could constitute 

a universal and transparent prediction tool for assessing <strong>the</strong> degradation degree <strong>of</strong> 

non-renewable resources, with dramatic consequences for <strong>the</strong> future management 

<strong>of</strong> <strong>the</strong> earth’s physical stock. 

ii

To my beloved grandfa<strong>the</strong>r 

iii

‘‘In <strong>the</strong> end we will conserve only what we 

love; we will love only what we understand; 

we will understand only what we have been 

taught” 

v 

Baba Dioum. Senegalese Environmentalist

Acknowledgements 

The work with this dissertation has been exciting, instructive, and fun, although 

moments <strong>of</strong> hardship and frustration have also existed. Without help, support, and 

encouragement from a great number persons, I would never have been able to 

finish this PhD. In this long ride <strong>of</strong> almost 5 years, I have had <strong>the</strong> opportunity to 

meet exceptional people around <strong>the</strong> world. 

In <strong>the</strong> scientific field, many researchers have unselfishly supported me. I should 

start to acknowledge <strong>the</strong> Russian geochemist N.A. Grigor’ev, that I discovered by 

chance investigating <strong>the</strong> literature about <strong>the</strong> geochemistry <strong>of</strong> <strong>the</strong> earth. Through 

a quite complicated communication procedure (via ordinary post and in Russian 

language), Grigor’ev generously shared with me his not yet published results about 

<strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> earth’s crust. Thanks to <strong>the</strong> translations <strong>of</strong> 

<strong>the</strong> Russian teacher in <strong>the</strong> University <strong>of</strong> Zaragoza Helena Moradell, Grigor’ev’s 

exceptional and pioneer work has been <strong>the</strong> base <strong>of</strong> <strong>the</strong> model <strong>of</strong> continental crust 

developed in this PhD. 

A deep debt <strong>of</strong> thanks is also owed to Gavin Mudd from <strong>the</strong> Institute for Sustainable 

Water Resources in Monash University (Australia), who kindly made available and 

prior to publication, his excellent and also pioneer study about average <strong>mineral</strong> ore 

grades in his country. Thanks to Mudd’s work, a comprehensive case study <strong>of</strong> <strong>the</strong> 

<strong>mineral</strong> exergy degradation <strong>of</strong> a nation was possible. 

This <strong>the</strong>sis has required a high level <strong>of</strong> geological and geochemical knowledge. 

Therefore, my chemical engineering background had to be reinforced with earth 

science’s fundamentals. Of essential help was <strong>the</strong> continued support <strong>of</strong> Javier 

Gómez, from <strong>the</strong> department <strong>of</strong> petrology in <strong>the</strong> University <strong>of</strong> Zaragoza. From 

<strong>the</strong> very beginning, he became my un<strong>of</strong>ficial advisor in <strong>the</strong> geological field and his 

point <strong>of</strong> view has been very valued for this work. I should also thank <strong>the</strong> “Instituto 

Geológico y Minero de España - IGME”, and in particular Miguel Ángel Zapatero, 

for making available IGME’s information and <strong>mineral</strong> statistics. 

Decisive for <strong>the</strong> accomplishment <strong>of</strong> this PhD, was my 3-month stay at <strong>the</strong> British 

Geological Survey (BGS), one <strong>of</strong> <strong>the</strong> most renowned geological institutions in 

Europe. Not only <strong>the</strong> exceptional library and data bases <strong>of</strong> BGS were crucial for this 

work, but also <strong>the</strong> good advice <strong>of</strong> many <strong>of</strong> its premium researchers. I would like to 

express my deepest gratitude to <strong>the</strong> BGS’s director, John Ludden, who immediately 

accepted me in <strong>the</strong> organization and gave me access with no exception to all BGS 

available information. Thanks go also to Andrew Bloodworth, head <strong>of</strong> <strong>the</strong> Mineral’s 

UK department and to all his team, for <strong>the</strong>ir warm welcome and for treating me as 

one more <strong>of</strong> <strong>the</strong> group. I cannot forget Tim Colman, who was always willing to help 

me and from which I learnt so many things. I have met at BGS many good friends 

that surely will remain in <strong>the</strong> future. 

vii

The <strong>the</strong>rmochemistry part <strong>of</strong> this PhD was strongly reinforced with <strong>the</strong> reviews 

<strong>of</strong> Philippe Vieillard, probably <strong>the</strong> best European expert in <strong>the</strong> field <strong>of</strong> geo<strong>the</strong>rmochemistry, 

from <strong>the</strong> University <strong>of</strong> Poitiers. In <strong>the</strong>se few lines, I want to express 

my gratitude for <strong>the</strong> many hours that Vieillard spent in teaching me patiently <strong>the</strong> 

different estimation methods for <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> 

<strong>mineral</strong>s and in reviewing <strong>the</strong> results obtained. 

I would like to thank pr<strong>of</strong>. Jan Szargut and Wojciech Stanek from <strong>the</strong> Institute <strong>of</strong> 

Thermal Technology in <strong>the</strong> Silesian University <strong>of</strong> Technology. It has been an honor 

to interact and discuss with my Polish friends <strong>the</strong> different exergy approaches used. 

Very useful were also <strong>the</strong> advices <strong>of</strong> <strong>the</strong> Spanish renowned economist José Manuel 

Naredo. He has been and is being a fundamental piece in <strong>the</strong> integration <strong>of</strong> 

<strong>the</strong> exergoecological approach used and fur<strong>the</strong>r developed in this PhD, into <strong>the</strong> 

economic thinking. 

I should not forget Juan Ignacio Pardo, from <strong>the</strong> department <strong>of</strong> physical chemistry 

and M a Cruz López de Silanes, from <strong>the</strong> department <strong>of</strong> applied ma<strong>the</strong>matics, both 

in <strong>the</strong> University <strong>of</strong> Zaragoza, who were always willing to help me. 

If Javier Gómez was my geology advisor, César Torres, expert <strong>of</strong> <strong>the</strong>rmoeconomics 

and collaborator <strong>of</strong> <strong>the</strong> CIRCE Foundation, was doubtless my ma<strong>the</strong>matics and L ATEX 

advisor. When I got stuck in a ma<strong>the</strong>matical problem, he was <strong>the</strong> one in finding <strong>the</strong> 

best solution. In <strong>the</strong> same way, he has solved most <strong>of</strong> my numerous doubts with 

L ATEX. In fact, he is <strong>the</strong> author <strong>of</strong> <strong>the</strong> layout <strong>of</strong> this PhD. Thank you very much indeed 

for your invaluable help and time. 

I wish to acknowledge <strong>the</strong> CIRCE Foundation for its financial support and for <strong>the</strong> 

excellent working environment. All its members, starting from <strong>the</strong> administration 

staff, teachers, students and researchers make <strong>the</strong> work very pleasant. Special 

thanks are owed to my managers and fellows Javier Uche, Luis Miguel Romeo and 

Inmaculada Arauzo, who have giving me every facility in <strong>the</strong> accomplishment <strong>of</strong> 

this PhD. Thanks to <strong>the</strong>ir generosity and that <strong>of</strong> my CIRCE friends Amaya Martínez 

and Francisco Barrio, I could dedicate most <strong>of</strong> my time in <strong>the</strong> last year in finishing 

this work. 

I would also like to thank all my friends from Zaragoza, and from o<strong>the</strong>r parts <strong>of</strong> 

Spain for <strong>the</strong> great moments that I have shared with <strong>the</strong>m. 

viii

This PhD is dedicated to my beloved grandfa<strong>the</strong>r, who has always believed in me 

and has supported and encouraged me. As you see I finally finished <strong>the</strong> work that 

you were impatiently waiting for. In <strong>the</strong> same way, I want to deeply thank my 

grandmo<strong>the</strong>r, for her endless care and affection. And <strong>of</strong> course I cannot forget my 

uncles, aunts and cousins, which all constitute an important part <strong>of</strong> my life. 

I am totally indebted to Stefan, who left family, friends and work in Germany 

for living with me in Spain. Probably I will never be able to reward <strong>the</strong> huge 

sacrifice you have made for me. I just hope that in some way, it has been worth. 

Thanks for your love, patience and understanding. Thanks also for helping me in 

<strong>the</strong> programming <strong>of</strong> <strong>the</strong> calculation tools used in this PhD, which has resulted in 

<strong>the</strong> first scientific web portal devoted to exergoecology. The great success <strong>of</strong> <strong>the</strong> 

"Exergoecology Portal", which every day gains supporters around <strong>the</strong> world, is due 

to your effort and your well-doing. You are not only a good pr<strong>of</strong>essional, but an 

excellent person and I am very lucky to have you by my side. 

My beloved mo<strong>the</strong>r, your wise advise, love and care are an essential support in my 

personal and pr<strong>of</strong>essional life. Your firm and sincere personality has affected me to 

be steadfast and never bend to difficulty. You have taught me many indispensable 

things <strong>of</strong> life that have helped me to face fearlessly important challenges and 

decisions in my life. 

I reserve my most grateful thanks to my fa<strong>the</strong>r and supervisor Antonio Valero. To 

be honest, at <strong>the</strong> beginning I was not sure whe<strong>the</strong>r this combination would work. 

Today I am sure that it was worth and that you have been <strong>the</strong> best PhD director that 

I could ever had. Obviously you have been very demanding with me, probably more 

than with o<strong>the</strong>r <strong>of</strong> your students. But you have also been <strong>the</strong>re many evenings, 

week-ends and holidays, motivating me to work harder and to do my best. You are 

an inspiration for me as a scientist, teacher, entrepreneur and most importantly as a 

fa<strong>the</strong>r. It has been a great pleasure to work with you. When <strong>the</strong> next one? 

ix

Contents 

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x 

1 Starting point, objectives and scope . . . . . . . . . . . . . . . . . . . . . 1 

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 

1.2 Economic growth and <strong>the</strong> consumption <strong>of</strong> natural resources . . . . 1 

1.3 Scarcity indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 

1.4 <strong>Exergy</strong> and <strong>the</strong> assessment <strong>of</strong> natural resources . . . . . . . . . . . . 7 

1.5 The Exergoecology approach . . . . . . . . . . . . . . . . . . . . . . . . 9 

1.6 Scope, objectives and structure <strong>of</strong> this PhD . . . . . . . . . . . . . . . 12 

1.7 Scientific papers derived from this PhD . . . . . . . . . . . . . . . . . 14 

I The earth and its resources 17 

2 The geochemistry <strong>of</strong> <strong>the</strong> earth. Known facts . . . . . . . . . . . . . . . . 19 


2.2 The bulk earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 

2.2.1 The composition <strong>of</strong> <strong>the</strong> earth . . . . . . . . . . . . . . . . . . . 19 

2.3 The atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 

2.3.1 The composition <strong>of</strong> <strong>the</strong> atmosphere . . . . . . . . . . . . . . . 22 

2.4 The hydrosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 

2.4.1 Seawater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 

2.4.1.1 The composition <strong>of</strong> <strong>the</strong> sea . . . . . . . . . . . . . . 26 

2.4.2 Renewable water resources: surface and ground waters . . 30 

2.4.2.1 Stream, river and lake waters . . . . . . . . . . . . 30 

2.4.2.2 Ground waters . . . . . . . . . . . . . . . . . . . . . . 33 

2.4.3 Ice caps, ice sheets and glaciers . . . . . . . . . . . . . . . . . 33 

2.4.3.1 The composition <strong>of</strong> glacial run<strong>of</strong>f . . . . . . . . . . 35 

2.5 The continental crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 

2.5.1 The chemical composition <strong>of</strong> <strong>the</strong> upper continental crust . . 37 

2.6 Summary <strong>of</strong> <strong>the</strong> chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 

3 The <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> upper continental crust . . . . 43 

x


3.2 The classification <strong>of</strong> <strong>mineral</strong>s . . . . . . . . . . . . . . . . . . . . . . . . 43 

3.2.1 The silica <strong>mineral</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . 44 

3.2.2 The feldspar group . . . . . . . . . . . . . . . . . . . . . . . . . 44 

3.2.3 The pyroxene group . . . . . . . . . . . . . . . . . . . . . . . . 45 

3.2.4 The amphibole group . . . . . . . . . . . . . . . . . . . . . . . . 45 

3.2.5 The olivine group . . . . . . . . . . . . . . . . . . . . . . . . . . 45 

3.2.6 The mica group . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 

3.2.7 The chlorite group . . . . . . . . . . . . . . . . . . . . . . . . . 46 

3.3 Grigor’ev’s <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> crust . . . . . . . . . . . 46 

3.4 A new model <strong>of</strong> <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> earth’s crust . 54 

3.4.1 The mass balance . . . . . . . . . . . . . . . . . . . . . . . . . . 54 

3.4.2 The mass balance applied to <strong>the</strong> continental crust . . . . . . 55 

3.4.3 Aluminium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 

3.4.4 Antimony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 

3.4.5 Arsenic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 

3.4.6 Barium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

3.4.7 Beryllium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 

3.4.8 Bismuth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 

3.4.9 Boron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 

3.4.10 Bromine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 

3.4.11 Cadmium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 

3.4.12 Calcium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 

3.4.13 Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 

3.4.14 Cerium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 

3.4.15 Cesium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 

3.4.16 Chlorine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 

3.4.17 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 

3.4.18 Cobalt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 

3.4.19 Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 

3.4.20 Dysprosium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 

3.4.21 Erbium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 

3.4.22 Europium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 

3.4.23 Fluorine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 

3.4.24 Gadolinium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 

3.4.25 Gallium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 

3.4.26 Germanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 

3.4.27 Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 

3.4.28 Hafnium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 

3.4.29 Holmium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 

3.4.30 Indium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 

3.4.31 Iodine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 

3.4.32 Iridium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 

3.4.33 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 

xi

3.4.34 Lanthanum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 

3.4.35 Lead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 

3.4.36 Lithium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 

3.4.37 Lutetium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 

3.4.38 Magnesium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 

3.4.39 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 

3.4.40 Mercury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 

3.4.41 Molybdenum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 

3.4.42 Neodymium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 

3.4.43 Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 

3.4.44 Niobium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 

3.4.45 Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 

3.4.46 Osmium and Iridium . . . . . . . . . . . . . . . . . . . . . . . . 75 

3.4.47 Palladium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 

3.4.48 Phosphorous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 

3.4.49 Platinum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 

3.4.50 Potassium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 

3.4.51 Praseodymium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 

3.4.52 Rare Earth Elements: Praseodymium, Samarium, Europium, 

Gadolinium, Terbium, Dysprosium, Holmium, Erbium, 

Thulium and Lutetium . . . . . . . . . . . . . . . . . . . 77 

3.4.53 Rhenium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 

3.4.54 Rhodium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 

3.4.55 Rubidium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 

3.4.56 Ru<strong>the</strong>nium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 

3.4.57 Samarium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 

3.4.58 Scandium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 

3.4.59 Selenium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 

3.4.60 Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 

3.4.61 Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 

3.4.62 Sodium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 

3.4.63 Strontium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 

3.4.64 Sulfur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 

3.4.65 Tantalum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 

3.4.66 Tellurium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 

3.4.67 Terbium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 

3.4.68 Thallium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 

3.4.69 Thorium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 

3.4.70 Thulium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 

3.4.71 Tin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 

3.4.72 Titanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 

3.4.73 Uranium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 

3.4.74 Vanadium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 

3.4.75 Wolfram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 

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3.4.76 Ytterbium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 

3.4.77 Yttrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 

3.4.78 Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 

3.4.79 Zirconium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 

3.5 Ma<strong>the</strong>matical representation . . . . . . . . . . . . . . . . . . . . . . . . 88 

3.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 

3.6.1 Discussion <strong>of</strong> <strong>the</strong> most abundant <strong>mineral</strong>s . . . . . . . . . . . 99 

3.6.2 Discussion <strong>of</strong> <strong>the</strong> most relevant <strong>mineral</strong>s . . . . . . . . . . . . 100 

3.6.3 Discussion <strong>of</strong> <strong>the</strong> aggregated composition . . . . . . . . . . . 101 

3.6.4 Drawbacks <strong>of</strong> <strong>the</strong> model . . . . . . . . . . . . . . . . . . . . . . 102 


4 The resources <strong>of</strong> <strong>the</strong> earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 


4.2 Natural resources: definition, classification and early assessment . 105 

4.3 The energy balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 

4.4 Energy from <strong>the</strong> solid earth . . . . . . . . . . . . . . . . . . . . . . . . . 107 

4.4.1 The Geo<strong>the</strong>rmal energy . . . . . . . . . . . . . . . . . . . . . . 108 

4.4.2 Nuclear energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 

4.5 Tidal energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 

4.6 Energy from <strong>the</strong> sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 

4.6.1 Solar power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 

4.6.2 Water power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 

4.6.3 Wind power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 

4.6.4 Ocean power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 

4.6.4.1 Ocean <strong>the</strong>rmal gradient . . . . . . . . . . . . . . . . 116 

4.6.4.2 Ocean Waves . . . . . . . . . . . . . . . . . . . . . . . 117 

4.6.5 Biomass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 

4.6.6 Fossil fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 

4.6.6.1 Coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 

4.6.6.2 Oil and natural gas . . . . . . . . . . . . . . . . . . . 121 

4.6.6.3 Unconventional fossil fuels . . . . . . . . . . . . . . 124 

4.7 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> energy resources . . . . . . . . . . . . . . . 127 

4.8 Non-fuel <strong>mineral</strong> resources . . . . . . . . . . . . . . . . . . . . . . . . . 127 

4.8.1 The economic classification <strong>of</strong> <strong>mineral</strong>s . . . . . . . . . . . . 129 

4.8.2 Mineral’s average ore grades . . . . . . . . . . . . . . . . . . . 130 

4.8.3 Mineral’s abundance . . . . . . . . . . . . . . . . . . . . . . . . 136 


xiii

II The <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> earth and its exergy 

<strong>evolution</strong> 139 

5 Thermodynamic models for <strong>the</strong> exergy assessment <strong>of</strong> natural resources 

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 


5.2 The reference environment . . . . . . . . . . . . . . . . . . . . . . . . . 141 

5.2.1 Selection <strong>of</strong> <strong>the</strong> best suitable reference environment . . . . 142 

5.2.1.1 Partial reference environments . . . . . . . . . . . . 142 

5.2.1.2 Comprehensive reference environments . . . . . . 143 

5.2.1.3 Abundance criterion . . . . . . . . . . . . . . . . . . 146 

5.2.2 Calculation methodology: standard chemical exergy <strong>of</strong> <strong>the</strong> 

chemical elements . . . . . . . . . . . . . . . . . . . . . . . . . 146 

5.2.2.1 Standard chemical exergy <strong>of</strong> chemical compounds 146 

5.2.2.2 Gaseous reference substances . . . . . . . . . . . . 147 

5.2.2.3 Solid reference substances . . . . . . . . . . . . . . 147 

5.2.2.4 Reference substances dissolved in seawater . . . . 148 

5.2.3 Update <strong>of</strong> Szargut’s R.E. . . . . . . . . . . . . . . . . . . . . . . 150 

5.2.3.1 Update <strong>of</strong> <strong>the</strong> standard chemical exergy <strong>of</strong> chemical 

compounds . . . . . . . . . . . . . . . . . . . . . . 150 

5.2.3.2 Update <strong>of</strong> <strong>the</strong> gaseous reference substances . . . . 150 

5.2.3.3 Update <strong>of</strong> <strong>the</strong> solid reference substances . . . . . . 150 

5.2.3.4 Update <strong>of</strong> <strong>the</strong> liquid reference substances . . . . . 152 

5.2.3.5 The updated reference environment. Results . . . 153 

5.2.4 Drawbacks <strong>of</strong> Szargut’s R.E. methodology . . . . . . . . . . . 156 

5.3 The exergy <strong>of</strong> <strong>mineral</strong> resources . . . . . . . . . . . . . . . . . . . . . . 157 

5.3.1 The energy involved in <strong>the</strong> process <strong>of</strong> formation <strong>of</strong> a <strong>mineral</strong> 

deposit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 

5.3.2 The exergy <strong>of</strong> non-fuel <strong>mineral</strong> resources . . . . . . . . . . . 159 

5.3.3 The chemical energy and exergy <strong>of</strong> fossil fuels . . . . . . . . 160 

5.3.4 The exergy costs . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 

5.4 Prediction <strong>of</strong> Enthalpy and Gibbs free energy <strong>of</strong> formation <strong>of</strong> <strong>mineral</strong>s 172 

5.4.1 Calculation <strong>of</strong> ∆H 0 or ∆G0 

f f from s0 5.4.2 

. . . . . . . . . . . . . . . 

The ideal mixing model . . . . . . . . . . . . . . . . . . . . . . 

172 

173 

5.4.3 Assuming ∆Gr and ∆Hr constant . . . . . . . . . . . . . . . . 174 

5.4.3.1 Thermochemical approximations for sulfosalts and 

complex oxides . . . . . . . . . . . . . . . . . . . . . 174 

5.4.3.2 The method <strong>of</strong> corresponding states . . . . . . . . 176 

5.4.4 The method <strong>of</strong> Chermak and Rimstidt for silicate <strong>mineral</strong>s . 177 

5.4.5 The ∆O−2 method . . . . . . . . . . . . . . . . . . . . . . . . . 178 

5.4.5.1 The ∆O−2 method for hydrated clay <strong>mineral</strong>s and 

for phyllosilicates . . . . . . . . . . . . . . . . . . . . 180 

5.4.5.2 The ∆O−2 method for different compounds with 

<strong>the</strong> same cations . . . . . . . . . . . . . . . . . . . . 181 

xiv

5.4.6 Assuming ∆S r zero . . . . . . . . . . . . . . . . . . . . . . . . . 181 

5.4.7 Assuming ∆G r and ∆H r zero . . . . . . . . . . . . . . . . . . . 181 

5.4.7.1 The element substitution method . . . . . . . . . . 181 

5.4.7.2 The addition method for hydrated <strong>mineral</strong>s . . . . 182 

5.4.7.3 The decomposition method . . . . . . . . . . . . . . 183 

5.4.8 Summary <strong>of</strong> <strong>the</strong> methodologies . . . . . . . . . . . . . . . . . 184 


6 The <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> earth and its <strong>mineral</strong> resources 187 


6.2 The properties <strong>of</strong> <strong>the</strong> earth . . . . . . . . . . . . . . . . . . . . . . . . . 187 

6.2.1 The <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> atmosphere . . . . . . 188 

6.2.2 The <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> hydrosphere . . . . . 190 

6.2.3 The <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> upper continental crust 195 

6.2.4 The chemical exergy <strong>of</strong> <strong>the</strong> earth . . . . . . . . . . . . . . . . 205 

6.3 An approach to <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> crepuscular earth . 205 

6.4 The exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources . . . . . . . . . . . . . . . . . . . 207 

6.4.1 The exergy contained in fossil fuels . . . . . . . . . . . . . . . 207 

6.4.1.1 Coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 

6.4.1.2 Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 

6.4.1.3 Natural gas . . . . . . . . . . . . . . . . . . . . . . . . 215 

6.4.2 The exergy <strong>of</strong> non-fuel <strong>mineral</strong> resources . . . . . . . . . . . 218 

6.4.3 The exergy <strong>of</strong> <strong>the</strong> natural resources on earth . . . . . . . . . 221 


7 The time factor in <strong>the</strong> exergy assessment <strong>of</strong> <strong>mineral</strong> resources . . . . 227 


7.2 The exergy distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 

7.3 The tons <strong>of</strong> <strong>mineral</strong> equivalent . . . . . . . . . . . . . . . . . . . . . . . 230 

7.4 The R/P ratio applied to exergy . . . . . . . . . . . . . . . . . . . . . . 232 

7.5 The Hubbert peak applied to exergy . . . . . . . . . . . . . . . . . . . 232 

7.6 The exergy loss <strong>of</strong> <strong>mineral</strong> deposits due to <strong>mineral</strong> extraction. The 

case <strong>of</strong> copper in <strong>the</strong> US . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 

7.6.1 Copper mining features . . . . . . . . . . . . . . . . . . . . . . 235 

7.6.2 Chemical exergy . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 

7.6.3 Concentration exergy . . . . . . . . . . . . . . . . . . . . . . . . 238 

7.6.4 Total exergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 

7.6.5 <strong>Exergy</strong> costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 

7.6.6 The R/P ratio and <strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> deposits . . . 242 

7.6.7 The Hubbert peak model . . . . . . . . . . . . . . . . . . . . . 242 

7.6.8 Summary <strong>of</strong> <strong>the</strong> results . . . . . . . . . . . . . . . . . . . . . . 244 

7.7 The exergy loss <strong>of</strong> a country due to <strong>mineral</strong> extraction. The case <strong>of</strong> 

Australia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 

7.7.1 Non-fuel <strong>mineral</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . 246 

xv

7.7.1.1 Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 

7.7.1.2 Copper . . . . . . . . . . . . . . . . . . . . . . . . . . 249 

7.7.1.3 Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 

7.7.1.4 Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 

7.7.1.5 Lead . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 

7.7.1.6 Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 

7.7.1.7 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 

7.7.2 Fuel <strong>mineral</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 

7.7.2.1 Coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 

7.7.2.2 Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 

7.7.2.3 Natural gas . . . . . . . . . . . . . . . . . . . . . . . . 266 

7.7.3 Summary and discussion <strong>of</strong> <strong>the</strong> results . . . . . . . . . . . . . 269 

7.8 Conversion <strong>of</strong> exergy costs into monetary costs . . . . . . . . . . . . 275 


8 The exergy <strong>evolution</strong> <strong>of</strong> planet earth . . . . . . . . . . . . . . . . . . . . . 281 


8.2 The exergy loss <strong>of</strong> world’s <strong>mineral</strong> reserves in <strong>the</strong> 20th century . . . 281 

8.2.1 Non-fuel <strong>mineral</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . 282 

8.2.2 Fuel <strong>mineral</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 

8.3 The exergy loss <strong>of</strong> world’s fossil fuel reserves due to <strong>the</strong> greenhouse 

effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 

8.3.1 The carbon cycle and <strong>the</strong> greenhouse effect . . . . . . . . . . 297 

8.3.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 

8.3.3 The fossil fuel exergy decrease . . . . . . . . . . . . . . . . . . 302 

8.4 A prediction <strong>of</strong> <strong>the</strong> exergy loss <strong>of</strong> world’s <strong>mineral</strong> reserves in <strong>the</strong> 

21st century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 

8.4.1 Hubbert scenario . . . . . . . . . . . . . . . . . . . . . . . . . . 307 

8.4.2 The IPCC’s B1 scenario . . . . . . . . . . . . . . . . . . . . . . . 309 

8.4.3 The IPCC’s A1T scenario . . . . . . . . . . . . . . . . . . . . . . 310 

8.4.4 The IPCC’s B2 scenario . . . . . . . . . . . . . . . . . . . . . . . 311 

8.4.5 The IPCC’s A1B scenario . . . . . . . . . . . . . . . . . . . . . . 314 

8.4.6 The IPCC’s A2 scenario . . . . . . . . . . . . . . . . . . . . . . . 315 

8.4.7 The IPCC’s A1FI scenario . . . . . . . . . . . . . . . . . . . . . 315 

8.4.8 Summary <strong>of</strong> <strong>the</strong> scenarios . . . . . . . . . . . . . . . . . . . . . 317 

8.5 Final reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 

8.5.1 The Limits to Growth to be reconsidered? . . . . . . . . . . . 320 

8.5.2 The need for global agreements on <strong>the</strong> extraction and use 

<strong>of</strong> natural resources . . . . . . . . . . . . . . . . . . . . . . . . . 322 

8.5.3 The need for an accountability <strong>the</strong>ory <strong>of</strong> <strong>mineral</strong> resources. 

The Physical Geonomics . . . . . . . . . . . . . . . . . . . . . . 325 


9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 

xvi


9.2 Syn<strong>the</strong>sis <strong>of</strong> <strong>the</strong> PhD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 

9.3 Scientific contributions <strong>of</strong> <strong>the</strong> PhD . . . . . . . . . . . . . . . . . . . . 340 

9.4 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 

A Additional calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 

A.1 Input data. Mineralogical composition <strong>of</strong> <strong>the</strong> earth’s crust . . . . . . 351 

A.2 Calculation <strong>of</strong> average <strong>mineral</strong> ore grades . . . . . . . . . . . . . . . . 376 

A.3 Calculation <strong>of</strong> <strong>the</strong> R.E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 

A.4 Calculation <strong>of</strong> <strong>the</strong> chemical exergy <strong>of</strong> gaseous fuels . . . . . . . . . . 386 

A.5 Estimation <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>mineral</strong>s . . . . . . . 386 

A.5.1 Chermak’s methodology . . . . . . . . . . . . . . . . . . . . . . 386 

A.5.2 Vieillard’s methodology for hydrated clay <strong>mineral</strong>s . . . . . 387 

A.5.3 Estimated values <strong>of</strong> <strong>the</strong> enthalpy and Gibbs free energy <strong>of</strong> 

<strong>mineral</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 

A.6 <strong>Exergy</strong> calculation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources . . . . . . . . . . . . . . . 397 

A.7 Australian fossil fuel production . . . . . . . . . . . . . . . . . . . . . . 402 

A.7.1 Coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 

A.7.2 Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 

A.7.3 Natural gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 

A.8 World’s fuel production . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 

A.8.1 Uranium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 

A.8.2 Coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 

A.8.3 Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 

A.8.4 Natural gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 

A.9 The Hubbert peak applied to world production <strong>of</strong> <strong>the</strong> main non-fuel 

<strong>mineral</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 

A.10 Fuel consumption in <strong>the</strong> 21st century . . . . . . . . . . . . . . . . . . 410 

Nomenclature, Figures, Tables and References 413 

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 

List <strong>of</strong> Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 

List <strong>of</strong> Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 

xvii

1.1 Introduction 

Chapter 1 

Starting point, objectives and 

scope 

The aim <strong>of</strong> this first introductory chapter is to provide an overview <strong>of</strong> <strong>the</strong> fundamentals 

on which this PhD is based and to outline <strong>the</strong> main objectives and scope <strong>of</strong> <strong>the</strong> 

study. 

Since this work is focused on <strong>the</strong> assessment <strong>of</strong> earth’s resources, <strong>the</strong> most relevant 

studies concerned with <strong>the</strong> depletion <strong>of</strong> natural resources are reviewed. The former 

studies reveal <strong>the</strong> urgent need for information about our natural <strong>capital</strong> and for 

appropriate indicators for its assessment. Accordingly, <strong>the</strong> most common scarcity indicators 

are outlined and compared to <strong>the</strong> indicator used in this PhD: <strong>the</strong> exergy indicator, 

based on <strong>the</strong> second law <strong>of</strong> <strong>the</strong>rmodynamics. Subsequently, an overview <strong>of</strong> <strong>the</strong> 

different existing approaches connecting <strong>the</strong> entropy law with <strong>the</strong> consumption <strong>of</strong> 

resources is provided. The latter are compared to <strong>the</strong> exergoecology approach, which 

is <strong>the</strong> methodology applied in this PhD for <strong>the</strong> assessment <strong>of</strong> <strong>mineral</strong> resources. 

Finally, <strong>the</strong> specific questions that this work tries to answer are outlined, toge<strong>the</strong>r 

with its scope. 

1.2 Economic growth and <strong>the</strong> consumption <strong>of</strong> natural 

resources 

The earth’s continental crust is <strong>the</strong> source <strong>of</strong> <strong>the</strong> main goods essential for industrial 

civilization. Fuels, metals and non-metallic <strong>mineral</strong>s are <strong>the</strong> fundamental basis for 

<strong>the</strong> technological development <strong>of</strong> any country. As Dunham [78] states, although <strong>the</strong> 

whole continental crust is composed by rocks as solid solutions <strong>of</strong> <strong>mineral</strong>s, <strong>the</strong>se 

1

2 STARTING POINT, OBJECTIVES AND SCOPE 

are not in practice recoverable. Only when a combination <strong>of</strong> natural processes has 

worked toge<strong>the</strong>r to produce an enrichment, is an ore to be found. And <strong>the</strong>se complex 

processes operate very slowly when compared with <strong>the</strong> whole life-span <strong>of</strong> our species 

so far. Hence, it is clear <strong>the</strong> non-renewable nature <strong>of</strong> <strong>mineral</strong> resources, at least from 

a human perspective. 

The 20 th century was marked by great technological innovations leading to <strong>the</strong> consumption 

and fur<strong>the</strong>r dispersion <strong>of</strong> huge amounts <strong>of</strong> <strong>mineral</strong> resources previously 

concentrated in natural deposits. This fact pushed up <strong>the</strong> economies <strong>of</strong> industrialized 

countries, but also raised <strong>the</strong> concern about resources scarcity. Probably, <strong>the</strong> 

possibility <strong>of</strong> running out <strong>of</strong> energy resources has provoked <strong>the</strong> most worries, especially 

due to <strong>the</strong> sharp rise <strong>of</strong> fuel prices. However non-fuel resources are also being 

exhausted very rapidly, as shown by Morse [230]: only in <strong>the</strong> US, over <strong>the</strong> span <strong>of</strong> 

<strong>the</strong> last century, <strong>the</strong> demand for metals grew from a little over 160 million tons to 

about 3,3 billion tons. 

The general attitude that has governed in <strong>the</strong> past was that <strong>the</strong> earth is nothing 

more than resources to be used. Adam Smith’s invisible hand [321] has been a 

guiding principle for those who believe that free trade or market will ultimately lead 

to a natural order <strong>of</strong> things. Never<strong>the</strong>less, in <strong>the</strong> early seventies <strong>the</strong> first Arab oil 

embargo, <strong>the</strong> peaking <strong>of</strong> oil production, toge<strong>the</strong>r with <strong>the</strong> studies <strong>of</strong> <strong>the</strong> Club <strong>of</strong> 

Rome (Forrester [96] and Meadows et al. [218]), started <strong>the</strong> alarm bells ringing 

regarding resources scarcity as <strong>the</strong> limit to economic growth [221]. 

In fact, <strong>the</strong> <strong>the</strong>ory that economic growth is irrevocably constrained by <strong>the</strong> finiteness 

<strong>of</strong> natural resources came at least 1 a century before with <strong>the</strong> British economist 

Thomas Malthus [206]. The <strong>the</strong>ory <strong>of</strong> Malthus was that <strong>the</strong> efforts <strong>of</strong> an expanding 

population to produce food on a limited land base would suffer diminishing returns, 

and if reproduction was not checked through moral restraint it would be checked 

by famine, war and pestilence. Malthus contemporary David Ricardo relativized <strong>the</strong> 

Malthusian’s absolute scarcity <strong>of</strong> land. He showed that an expanding competitive 

economy could always turn to lower-quality land, <strong>the</strong>reby increasing <strong>the</strong> required 

labor to produce food and driving up its cost [302]. 

But classical economists were mainly focused on land and did not really faced <strong>the</strong> 

problem <strong>of</strong> depletion <strong>of</strong> <strong>mineral</strong>s and o<strong>the</strong>r non-renewable resources. It was not 

until <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> 20 th century, that <strong>the</strong> US conservation movement feared 

that progress would end because <strong>the</strong> rapacious present generation would consume 

<strong>the</strong> next <strong>of</strong> its needed natural resources. In <strong>the</strong> 1930s, Harold Hotelling [145] put 

numbers to <strong>the</strong> not very rigorous statements <strong>of</strong> <strong>the</strong> conservationists. According to 

Hotelling, resources would be depleted at a declining rate, and <strong>the</strong>ir price would rise 

at a rate equal to <strong>the</strong>ir owners’ opportunity rate <strong>of</strong> interest. 

In <strong>the</strong> seventies, <strong>the</strong> Club <strong>of</strong> Rome came into being and <strong>the</strong> first attempt at a global 

model by J. Forrester was pubilshed in World Dynamics [96]. The limits to Growth 

wealth. 

1 The French physiocrats came to <strong>the</strong> conclusion in <strong>the</strong> XVIII century that land is <strong>the</strong> source <strong>of</strong> all

Economic growth and <strong>the</strong> consumption <strong>of</strong> natural resources 3 

by Meadows et al. [218] followed in 1972, receiving great publicity. The works <strong>of</strong> 

Meadows et al. in 1972 and later updates in 1993 [217] and 2004 [219], argue that 

<strong>the</strong> current exponential growth cannot longer be supported as natural goods become 

depleted. Through <strong>the</strong> World3 computer model, different scenarios <strong>of</strong> resources 

consumption, pollution, population, policy, etc. were developed. The study claimed 

that if no immediate actions are undertaken, an economical collapse is foreseeable 

in <strong>the</strong> near future. 

The truth is that even if <strong>the</strong> consumption <strong>of</strong> natural <strong>capital</strong> has increased dramatically, 

evidence until to date has not really supported <strong>the</strong> idea that natural resources 

depletion has stopped economic growth. Some authors such as Barnett and Morse 

[20] or Scott and Pearse [302] appealed to <strong>the</strong> role <strong>of</strong> technological progress in 

improving <strong>the</strong> efficiency <strong>of</strong> extractive processes and redefining available resources. 

They stated that <strong>the</strong>re is no evidence for <strong>the</strong> hypo<strong>the</strong>sis that natural resources will 

lead to reduction <strong>of</strong> economic growth. Solow [326] argued that substitution <strong>of</strong> 

<strong>capital</strong> goods <strong>of</strong> natural resources in production processes reduces resource requirements 

and, in general, technical change may overcome limits imposed on economic 

activities in <strong>the</strong> environment. 

On <strong>the</strong> contrary, Costanza and Daly [65], Ayres and Nair [17] or Cleveland and Ruth 

[59], believe that technology will not overcome resource scarcity and environmental 

degradation, since human <strong>capital</strong> ultimately is derived from and sustained by energy, 

materials and ecological services. Until now, natural <strong>capital</strong> has been treated as a 

free good, but nowadays it is becoming <strong>the</strong> limiting factor in development. Champan 

and Roberts [53] argue also that resource substitution might be valid in <strong>the</strong> short 

term, but will fail in <strong>the</strong> long term when <strong>the</strong>re is equal resource scarcity on all 

substitutable materials. 

Some attempts have been made to measure <strong>the</strong> economic costs <strong>of</strong> depletion and 

degradation and use <strong>the</strong>m to correct standard measures <strong>of</strong> economic welfare such as 

GDP (see for instance Ahmad, El Serafy and Lutz [2]; Daly and Cobb [70]; Costanza 

[64]; Van Dieren [75]). Although <strong>the</strong> debate on how national accounting should be 

extended towards environmental accounting is still open, all approaches reflect that 

when depletions <strong>of</strong> natural <strong>capital</strong>, pollution costs, and income distribution effects 

are accounted for, <strong>the</strong> improving <strong>of</strong> <strong>the</strong> economy is seriously questioned. 

As we face <strong>the</strong> new century, <strong>the</strong> question <strong>of</strong> whe<strong>the</strong>r resource scarcity will constrain 

economy is still in <strong>the</strong> air. But <strong>the</strong> rapid economic development <strong>of</strong> Asia and <strong>the</strong> desire 

for a higher living standard in <strong>the</strong> developing world demands an even greater 

consumption <strong>of</strong> natural resources toge<strong>the</strong>r with rapid technological progress to prevent 

increasing scarcity <strong>of</strong> <strong>the</strong> different commodities. Our society is based on an 

inefficient use <strong>of</strong> energy and materials, since <strong>the</strong>re is a lack <strong>of</strong> awareness <strong>of</strong> <strong>the</strong> 

limit. If resources are limited, <strong>the</strong>ir management must be carefully planned in order 

to be consistent with <strong>the</strong> sustainability doctrine. But for that purpose, we need to 

know how many resources are available on earth and at which rate <strong>the</strong>y are being 

consumed. A responsible management can only be based thus on a comprehensive


information source. As Faber [91] claimed, <strong>the</strong> true intertemporal scarcity <strong>of</strong> environmental 

goods must be analyzed and appropriate indicators for <strong>the</strong> scarcity <strong>of</strong> 

<strong>the</strong>se goods must be found. 

In this PhD, we have dived in data bases <strong>of</strong> many different institutions, organizations, 

universities and journals, searching for global numbers <strong>of</strong> <strong>the</strong> <strong>mineral</strong> <strong>capital</strong> on 

earth. For someone that never faced that task, it is surprising <strong>the</strong> lack <strong>of</strong> existing 

information about our resources not only in <strong>the</strong> past, but also in <strong>the</strong> present. This is 

a clear indicator <strong>of</strong> <strong>the</strong> little importance that humankind has placed in investigating 

<strong>the</strong> resources that nature gives us for free. 

Generally, <strong>the</strong> institutions owning information about resources do not interpret <strong>the</strong> 

compiled values. And ironically, many studies claiming <strong>the</strong> end <strong>of</strong> natural resources 

are rarely based on <strong>the</strong> physical statistics provided by <strong>the</strong> formers. 

More resources data bases, better global statistics, <strong>the</strong> opening <strong>of</strong> global information 

channels and impartial and serious interpretations <strong>of</strong> <strong>the</strong> information are key factors 

for transformation to sustainability. And <strong>the</strong> data interpretation must be undertaken 

with <strong>the</strong> help <strong>of</strong> appropriate indicators. 

This PhD has tried to fill with physical content some <strong>of</strong> <strong>the</strong> sociological messages 

about resource scarcity published elsewhere. This has been accomplished by making 

a rigorous analysis <strong>of</strong> <strong>the</strong> global <strong>mineral</strong>s on earth through an indicator based on 

<strong>the</strong> second law <strong>of</strong> <strong>the</strong>rmodynamics. The next section provides an overview <strong>of</strong> <strong>the</strong> 

different available scarcity indicators with its capabilities and drawbacks, so as to 

compare <strong>the</strong>m to <strong>the</strong> indicator chosen in this PhD. 

1.3 Scarcity indicators 

Consideration <strong>of</strong> scarcity and its measurement requires clarification <strong>of</strong> what we mean 

by scarcity. As Zwartendyk et al. [414] argue, physical scarcity refers to <strong>the</strong> relative 

rarity <strong>of</strong> an element or <strong>mineral</strong> substance in nature; it has nothing to do with 

human effort. Economic scarcity has very much to do with <strong>the</strong> interests and needs 

<strong>of</strong> humans. It reflects that work is required to obtain <strong>mineral</strong> products and that we 

are willing to pay a price for <strong>the</strong>m. Generally, <strong>the</strong> greater <strong>the</strong> physical scarcity <strong>of</strong> a 

<strong>mineral</strong>, <strong>the</strong> costlier it will be to obtain, so its economic scarcity may be greater as 

well. 

The scientific community has already started to study this issue and some physical 

and economic indicators have been proposed. 

In <strong>the</strong> renowned work Scarcity and Growth 2 (1963) <strong>of</strong> Barnet and Morse [20], extraction 

costs were used as scarcity indicators. Extraction cost is computed as <strong>the</strong> 

amount <strong>of</strong> labor and <strong>capital</strong> required to produce a unit <strong>of</strong> output. The same indicator 

2 Scarcity and Growth was <strong>the</strong> first systematic empirical examination <strong>of</strong> historical trends.

Scarcity indicators 5 

was used until <strong>the</strong> update <strong>of</strong> that work: Scarcity and Growth Reconsidered [325]. This 

measure is founded on <strong>the</strong> classical economics view that with diminishing marginal 

returns and finite natural resources, <strong>the</strong> cost <strong>of</strong> natural resource extraction should 

increase as demand increases and depletion occurs. Krautkraemer [188] argued in 

Scarcity and Growth Reconsidered that extraction cost is an inherently static measure; 

it does not capture future effects that are important for indicating natural resource 

scarcity. In addition, extraction cost captures information about only <strong>the</strong> supply side 

<strong>of</strong> <strong>the</strong> market. If demand is growing more rapidly than extraction cost is declining, 

<strong>the</strong>n extraction cost will give a false indication <strong>of</strong> decreasing scarcity (<strong>the</strong> opposite 

is also possible). 

Probably <strong>the</strong> most used indicator nowadays is price. Price incorporates information 

about <strong>the</strong> demand for <strong>the</strong> resource and possible expectations about future demand 

and availability. According to Fisher [95], <strong>the</strong> resource price would “summarize <strong>the</strong> 

sacrifices, direct and indirect, made to obtain a unit <strong>of</strong> <strong>the</strong> resource”. 

Naredo [237] claims though that standard economy is only concerned with what 

being directly useful to man, is also acquirable, valuable and produce-able. For this 

reason, most <strong>of</strong> <strong>the</strong> natural resources, remain outside <strong>the</strong> object <strong>of</strong> analysis <strong>of</strong> <strong>the</strong> 

economic system. And <strong>the</strong> price-fixing mechanisms, rarely take into account <strong>the</strong> 

concrete physical characteristics which make <strong>the</strong>m valuable. 

Ruth [294] states that for prices to subsume all required information to make an intertemporally 

optimal choice about material and energy and <strong>the</strong> level <strong>of</strong> production, 

markets must be efficient, and preferences <strong>of</strong> current and future generations have to 

be anticipated. Additionally, current and future technologies must be fully described. 

In contrast, prices ra<strong>the</strong>r reflect <strong>the</strong> incomplete description <strong>of</strong> current technologies, 

preferences <strong>of</strong> present generations, and current institutional settings. 

Though non renewable resources are becoming more and more scarce, prices have 

not followed <strong>the</strong> same trend. According to Hotelling [145], prices should raise with 

scarcity, since low cost resources normally would be used first and quantities <strong>of</strong> 

extraction normally would decrease over time. On <strong>the</strong> contrary, historical statistics 

show that costs <strong>of</strong> extraction and prices have mostly decreased over time [313]. 

This apparent contradiction is due to technological innovation but also to <strong>the</strong> lack <strong>of</strong> 

information about scarcity. Reynolds [277] states that true scarcity is only revealed 

through prices towards <strong>the</strong> end <strong>of</strong> exhaustion. 

Physical indicators are usually based ei<strong>the</strong>r on mass or energy. Generally, all energy 

resources are assessed in terms <strong>of</strong> its energy content, what allows a direct comparison 

between <strong>the</strong>m. On <strong>the</strong> o<strong>the</strong>r hand, non-fuel <strong>mineral</strong>s are usually physically and 

individually assessed in terms <strong>of</strong> tonnage and grade. It is obvious that <strong>mineral</strong> resources 

evaluated in that way cannot be easily compared, and a global number for 

<strong>the</strong> <strong>mineral</strong>’s <strong>capital</strong> on earth cannot be given, as mass and grade are not additive. 

Fur<strong>the</strong>rmore, assimilating such a great amount <strong>of</strong> information for each resource is 

not always easy and not very useful for decision makers.


Odum [245], [246] proposed an original physical unit <strong>of</strong> measure for assessing resources 

and products based on <strong>the</strong> solar emergy joule (sej). Emergy analysis is a 

technique <strong>of</strong> quantitative analysis which determines <strong>the</strong> values <strong>of</strong> resources, services 

and commodities in common units <strong>of</strong> <strong>the</strong> solar energy it took to make <strong>the</strong>m. One 

<strong>of</strong> its fundamental organizing principles is <strong>the</strong> maximum empower principle. It is 

stated as “systems that will prevail in competition with o<strong>the</strong>rs, develop <strong>the</strong> most 

useful work with inflowing emergy sources by reinforcing productive processes and 

overcoming limitations through system organization”. To derive solar emergy <strong>of</strong> a 

resource or commodity, it is necessary to trace back through all <strong>the</strong> resources and 

energy that are used to produce it and express <strong>the</strong>m in <strong>the</strong> amount <strong>of</strong> solar energy 

that went into <strong>the</strong>ir production [42]. The solar emergy per unit product or output 

flow is called “solar transformity”, with units <strong>of</strong> seJ/J. Solar transformities have to be 

obtained for each commodity. Most transformities cannot be considered as universal, 

as <strong>the</strong> processes involved in <strong>the</strong> formation <strong>of</strong> <strong>the</strong> commodities differ, depending 

on <strong>the</strong> period <strong>of</strong> time and place considered. 

The emergy analysis owns two fundamental capabilities that we think are required 

to be used as a scarcity indicator: 1) it is based on <strong>the</strong> physical characteristics <strong>of</strong> <strong>the</strong> 

resource and 2) all resources are measured with a single unit. 

Generally, <strong>the</strong> emergy analysis can be successfully applied for renewable resources. 

However it is very questioned <strong>the</strong> applicability <strong>of</strong> this approach for <strong>mineral</strong> resources, 

where <strong>the</strong> sun has not played a central role in <strong>the</strong>ir creation. No matter 

how much solar energy is received from <strong>the</strong> sun, <strong>the</strong> quantity <strong>of</strong> gold or iron for 

instance on earth, will not change. Consequently, <strong>the</strong> rigorousness <strong>of</strong> <strong>the</strong> transformities 

for <strong>mineral</strong> resource assessment is doubtful. Hence, <strong>the</strong> emergy analysis is not 

suitable for <strong>the</strong> purpose <strong>of</strong> this PhD, which is <strong>the</strong> assessment <strong>of</strong> <strong>mineral</strong> resources. 

The physical features that make <strong>mineral</strong> resources valuable are: a particular composition 

which differentiates <strong>the</strong>m from <strong>the</strong> surrounding environment, and a distribution 

which places <strong>the</strong>m in a specific concentration. And <strong>the</strong>se intrinsic properties can 

be in fact evaluated from a second law <strong>of</strong> <strong>the</strong>rmodynamics point <strong>of</strong> view in terms <strong>of</strong> 

a single property: exergy. 

As it happens to emergy and unlike standard economic valuations, <strong>the</strong> exergy analysis 

gives objective information since it is not subject to monetary policy, or currency 

speculation. Fur<strong>the</strong>rmore, all natural resources can be assessed in terms <strong>of</strong> exergy 

and can be summed up. <strong>Exergy</strong> is a property <strong>of</strong> <strong>the</strong> resource and as such, <strong>the</strong> calculation 

methods are physically and ma<strong>the</strong>matically supported, as opposed to emergy. 

As explained in <strong>the</strong> next section, exergy is based on <strong>the</strong> notion <strong>of</strong> a reference environment, 

in which <strong>the</strong> quality and quantity <strong>of</strong> substances is fixed. Hence <strong>the</strong> analysis 

places value to resources depending on <strong>the</strong> level <strong>of</strong> departure from <strong>the</strong> defined reference 

environment. And, as opposed to <strong>the</strong> emergy analysis, whe<strong>the</strong>r <strong>the</strong> substances 

in it were created through <strong>the</strong> energy <strong>of</strong> <strong>the</strong> sun or through o<strong>the</strong>r processes is irrelevant 

and does not affect <strong>the</strong> final results.

<strong>Exergy</strong> and <strong>the</strong> assessment <strong>of</strong> natural resources 7 

The exergy method is chosen in this PhD for assessing <strong>the</strong> <strong>evolution</strong> <strong>of</strong> <strong>mineral</strong> 

scarcity. In <strong>the</strong> next section, an overview <strong>of</strong> <strong>the</strong> different existing approaches connecting 

<strong>the</strong> entropy law with <strong>the</strong> consumption <strong>of</strong> resources is provided. 

1.4 <strong>Exergy</strong> and <strong>the</strong> assessment <strong>of</strong> natural resources 

A fundamental law <strong>of</strong> nature (<strong>the</strong> first law <strong>of</strong> <strong>the</strong>rmodynamics), tells us that energy 

and matter can be nei<strong>the</strong>r created nor destroyed. The second law places additional 

limits on energy transformations and reflects qualitative characteristics. It states that 

energy can only be transformed by <strong>the</strong> consumption <strong>of</strong> quality. Locally, <strong>the</strong> quality 

can be improved, but this can only occur at <strong>the</strong> expense <strong>of</strong> a greater deterioration 

<strong>of</strong> <strong>the</strong> quality elsewhere. The level <strong>of</strong> quality deterioration or disorder is measured 

through <strong>the</strong> property entropy. Hence, <strong>the</strong> second law <strong>of</strong> <strong>the</strong>rmodynamics can be formulated 

as follows. In all real processes <strong>of</strong> energy transformation <strong>the</strong> total entropy 

<strong>of</strong> all involved bodies can only be increased or, in an ideal case, unchanged. Beyond 

<strong>the</strong>se conditions, <strong>the</strong> process is impossible even if <strong>the</strong> first law is fulfilled [39]. 

The combination <strong>of</strong> both laws indicates that it is not a question <strong>of</strong> <strong>the</strong> existent 

amount <strong>of</strong> mass or energy, but on <strong>the</strong> quality <strong>of</strong> that mass or energy, or in o<strong>the</strong>r 

words on its exergy content. Technically, exergy is defined as <strong>the</strong> maximum amount 

<strong>of</strong> work that may <strong>the</strong>oretically be performed by bringing a resource into equilibrium 

with its surroundings by a sequence <strong>of</strong> reversible processes. The exergy <strong>of</strong> a system 

gives an idea <strong>of</strong> its <strong>evolution</strong> potential for not being in <strong>the</strong>rmodynamic equilibrium 

with <strong>the</strong> environment. Unlike mass and energy, exergy is not a conserved property. It 

is an extensive property, with <strong>the</strong> same unit as energy. In all physical transformations 

<strong>of</strong> matter or energy, it is always exergy that is lost. 

<strong>Exergy</strong> analysis is a powerful tool for improving <strong>the</strong> efficiency <strong>of</strong> processes and systems. 

This leads to less resources to be used and <strong>the</strong> emission <strong>of</strong> less wastes to 

<strong>the</strong> environment. However it is a much more useful concept, and can be applied 

for resource accounting. All materials have a definable and calculable exergy content, 

with respect to a defined external environment. The consumption <strong>of</strong> natural 

resources implies destruction <strong>of</strong> organized systems and pollution dispersion, which 

is in fact generation <strong>of</strong> entropy or exergy destruction. Fur<strong>the</strong>rmore, exergy has <strong>the</strong> 

capability <strong>of</strong> aggregating heterogeneous energy and material assets. This is why <strong>the</strong> 

exergy analysis can describe perfectly <strong>the</strong> degradation <strong>of</strong> natural <strong>capital</strong>. For that 

reason, an increasing number <strong>of</strong> scientists, such as Szargut and coworkers [344], 

[338], [339], Brodianski [39], Wall [393], [394], [395], Rosen [289], [290], Dincer 

[76], Sciubba [299] or Ayres et al. [14] believe that exergy provides useful 

information within resource accounting and can adequately address certain environmental 

concerns. 

Additionally, different renowned studies have shown up <strong>the</strong> connection between 

economic scarcity and <strong>the</strong> entropy law. Some notable examples are briefly outlined 

next.


Georgescu-Roegen was one <strong>of</strong> <strong>the</strong> first authors in realizing <strong>the</strong> links between <strong>the</strong> 

economic process and <strong>the</strong> second law <strong>of</strong> <strong>the</strong>rmodynamics. In his seminal work The 

Entropy Law and <strong>the</strong> Economic Process [111], he states that “<strong>the</strong> entropy law itself 

emerges as <strong>the</strong> most economic in nature <strong>of</strong> all natural laws [...] and this law is <strong>the</strong> 

basis <strong>of</strong> <strong>the</strong> economy <strong>of</strong> life at all levels”. Georgescu-Roegen stresses <strong>the</strong> importance 

<strong>of</strong> <strong>the</strong> variable time in economic activity, which is clearly shown in <strong>the</strong> irreversibility 

<strong>of</strong> <strong>the</strong> exploitation <strong>of</strong> resources. This author even postulated <strong>the</strong> Fourth Law <strong>of</strong> Thermodynamics, 

<strong>the</strong> entropy law <strong>of</strong> matter. According to this law, matter and not energy 

is <strong>the</strong> limiting factor in economic growth. Georgescu-Roegen’s Fourth Law has been 

criticized by a number <strong>of</strong> analysts in economics and physical sciences. It has been 

pointed out that on a fundamental physical level, <strong>the</strong>re is no such law. In principle, 

it is always possible to use high quality energy to trace, collect and reassemble <strong>the</strong> 

dissipated elements [59]. The <strong>the</strong>oretical flaws <strong>of</strong> <strong>the</strong> Fourth Law, have lead some 

to dismiss Georgescu-Roegen’s ideas or deny <strong>the</strong>ir significance. 

Faber et al. [92] developed a model integrating <strong>the</strong>rmodynamic considerations into 

a model <strong>of</strong> optimal resource use and environmental management. They analyzed <strong>the</strong> 

relationship among resource use in <strong>the</strong> economic system, <strong>capital</strong> formation, resource 

concentration and entropy production. 

Ayres and Nair [17] state that <strong>the</strong> second law <strong>of</strong> <strong>the</strong>rmodynamics has certain consequences 

for <strong>the</strong> production process which are not adequately reflected in <strong>the</strong> standard 

economic model. Among <strong>the</strong>se consequences are that <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> total 

output <strong>of</strong> a sector must be less than <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> inputs and overall entropy 

is increased through <strong>the</strong> production <strong>of</strong> waste materials and heat. Ayres and Miller 

[16] developed a model that treats natural resources, physical <strong>capital</strong> and knowledge 

(measured in terms <strong>of</strong> negative entropy or negentropy) as mutually substitutable 

inputs into <strong>the</strong> production process. In 1988, Ayres [13] used <strong>the</strong> model for 

<strong>the</strong> calculation <strong>of</strong> optimal investment policies and simulation <strong>of</strong> optimal time paths 

and substitution pattern for <strong>the</strong> world primary energy sources from <strong>the</strong> year 1869 

to 2050. Recently, Ayres [15], calculated <strong>the</strong> exergy performed in <strong>the</strong> US economy 

during <strong>the</strong> twentieth century. One <strong>of</strong> <strong>the</strong> conclusions <strong>of</strong> his study was that growth in 

exergy consumption have had an enormous impact on past economic growth. The 

increasing efficiency <strong>of</strong> <strong>the</strong> production in primary work tended to result in lower 

costs, which triggered increasing demand that <strong>of</strong>ten resulted in greater exergy consumption. 

This fact is known as “Jevons paradox”. 

Ruth [294] stated that use in economic production processes must consider <strong>the</strong>rmodynamic 

limits on material and energy use in order to be optimal in <strong>the</strong> long-run. 

And economic decisions must consider <strong>the</strong> finiteness <strong>of</strong> <strong>the</strong> resources available, <strong>the</strong> 

interconnectedness <strong>of</strong> <strong>the</strong> economic system with o<strong>the</strong>r ecosystem components, <strong>the</strong> 

time preference <strong>of</strong> consumers and producers and <strong>the</strong> technologies with which materials 

and energy are transformed in <strong>the</strong> production process. He developed a model 

<strong>of</strong> nonrenewable resource use. As an example, Ruth determined <strong>the</strong> optimal extraction 

path and production <strong>of</strong> iron ore at each period <strong>of</strong> time, taking into account 

<strong>the</strong>rmodynamic limits on material and energy efficiency, <strong>the</strong> treatment <strong>of</strong> endoge-

The Exergoecology approach 9 

nous technical change through <strong>the</strong> <strong>the</strong>ory <strong>of</strong> learning curves and <strong>the</strong> evaluation <strong>of</strong> 

alternative time paths from an economic and <strong>the</strong>rmodynamic perspective. 

In this PhD <strong>the</strong>sis, exergy has been used as a global scarcity indicator from <strong>the</strong> point 

<strong>of</strong> view <strong>of</strong> <strong>the</strong> exergoecology paradigm. In <strong>the</strong> next section, exergoecology will be 

explained in detail, and compared to o<strong>the</strong>r approaches, where exergy is also used as 

an accounting tool. 

1.5 The Exergoecology approach 

Generally, <strong>the</strong> studies based on exergy and natural resources are focused on calculating 

<strong>the</strong> amount <strong>of</strong> exergy required for <strong>the</strong> production <strong>of</strong> a certain good. Probably, 

<strong>the</strong> better known one is <strong>the</strong> <strong>the</strong>rmo-ecological cost analysis proposed by Szargut and 

coworkers [341], [344], [328]. The <strong>the</strong>rmo-ecological cost analysis accounts for <strong>the</strong> 

cumulative consumption <strong>of</strong> non-renewable exergy connected with <strong>the</strong> fabrication <strong>of</strong> 

a particular product including <strong>the</strong> additional exergy consumption needed for <strong>the</strong> 

compensation <strong>of</strong> environmental losses caused by <strong>the</strong> disposal <strong>of</strong> harmful substances 

to <strong>the</strong> environment. 

A similar approach is also used by Ayres and coworkers. For example, in [14], Ayres 

et al. applied <strong>the</strong> exergy concept for accounting for <strong>the</strong> materials and energy use 

and waste residuals <strong>of</strong> five basic metal industries in <strong>the</strong> US. This allowed to compare 

systems on a common basis, to identify major loss streams that may correspond to 

inefficiencies and to provide a first evaluation <strong>of</strong> <strong>the</strong>ir environmental burden. 

O<strong>the</strong>r exergy-based approaches are for instance those from Sciubba [300], Connely 

and Koshland [61] or Cornelissen and Hirs [63]. Sciubba [300] extended Szargut’s 

<strong>the</strong>ory, including non-energetic quantities like <strong>capital</strong>, labor and environmetal impact 

on <strong>the</strong> calculation. Connely and Koshland [61], discussed <strong>the</strong> ties between 

exergy and industrial ecology and proposed exergy-based definitions and methods 

for addressing resource depletion. Cornelissen and Hirs [63] applied <strong>the</strong> exergy analysis 

to <strong>the</strong> Life Cycle Assessment (LCA) methodology and proposed <strong>the</strong> exergetic life 

cycle assessment, which should account for <strong>the</strong> depletion <strong>of</strong> natural resources. 

All <strong>the</strong>se approaches provide very useful information for <strong>the</strong> optimization <strong>of</strong> processes, 

as <strong>the</strong>y obtain <strong>the</strong> exergy costs <strong>of</strong> production, allowing a reduction in energy, 

materials and harmful emissions. 

The Exergoecology method proposed by Valero [365], which derives from <strong>the</strong> general 

<strong>the</strong>ory <strong>of</strong> exergy cost developed by <strong>the</strong> same author [370], uses also <strong>the</strong> property 

exergy as an accounting tool, but differs radically from <strong>the</strong> approaches explained 

above in <strong>the</strong> point <strong>of</strong> how resources are assessed. Exergoecology is defined as <strong>the</strong> 

exergy assessment <strong>of</strong> natural resources, from a defined R.E. It allows to value <strong>the</strong>se 

resources, according to <strong>the</strong> physical cost that would require to obtain <strong>the</strong>m from 

<strong>the</strong> materials contained in a hypo<strong>the</strong>tical earth that has reached <strong>the</strong> maximum level


<strong>of</strong> deterioration. In o<strong>the</strong>r words, it quantifies <strong>the</strong> physical cost <strong>of</strong> replacing natural 

resources from a degraded state in <strong>the</strong> so called reference environment to <strong>the</strong> 

conditions in which <strong>the</strong>y are currently presented in nature. Its aim is to determine 

<strong>the</strong> physical stock available in <strong>the</strong> current continental crust, how that stock is being 

degraded and dispersed by mankind and at which rate. As Naredo [238] states, if 

life came up and evolved from a primitive soup, human species pushes now strongly 

towards a sort <strong>of</strong> crepuscular planet, whose composition would be hypo<strong>the</strong>tically 

equivalent to <strong>the</strong> R.E. This methodology allows to quantify <strong>the</strong> loss <strong>of</strong> <strong>the</strong> natural resource’s 

potential as <strong>the</strong> human effect pushes it towards that sort <strong>of</strong> entropic planet. 

One <strong>of</strong> <strong>the</strong> questions that opens <strong>the</strong> exergoecology paradigm is <strong>the</strong> determination 

<strong>of</strong> <strong>the</strong> degraded planet (or entropic planet) towards which civilization is moving. 

The entropic planet could be assimilated to a dead planet where all materials have 

reacted, dispersed and mixed and are in a hypo<strong>the</strong>tical chemical equilibrium. A degraded 

earth would still have an atmosphere, hydrosphere and continental crust. 

Never<strong>the</strong>less, <strong>the</strong>re would not be any <strong>mineral</strong> deposits, all fossil fuels would have 

been burned and consequently, <strong>the</strong> CO 2 concentration in <strong>the</strong> atmosphere would be 

much higher than it now is. Similarly, all water available in <strong>the</strong> hydrosphere would 

be in <strong>the</strong> form <strong>of</strong> salt-water, due to <strong>the</strong> mixing processes. So far, <strong>the</strong> assessment <strong>of</strong> 

<strong>mineral</strong> resources has been carried out from R.E. models designed for <strong>the</strong> optimization 

<strong>of</strong> industrial processes. It is open to question whe<strong>the</strong>r <strong>the</strong>se kinds <strong>of</strong> models fit 

<strong>the</strong> characteristics <strong>of</strong> <strong>the</strong> degraded planet that we are searching for. This topic will 

be addressed in chapter 5 <strong>of</strong> this report. 

Note <strong>the</strong> difference between extraction costs and replacement costs. The former 

assesses <strong>the</strong> resource from <strong>the</strong> mine to market. However, <strong>the</strong> latter assesses <strong>the</strong> resource 

from <strong>the</strong> entropic planet to <strong>the</strong> mine. As Carpintero [50] and Naredo [238] 

argue, economy puts value to natural goods considering its extraction costs and not 

its replacement costs. Therefore, extraction and not recovery or recycling is promoted, 

thus enhancing <strong>the</strong> efficiency <strong>of</strong> <strong>the</strong> extraction processes ra<strong>the</strong>r than saving 

those resources for future generations. Moreover, extraction implies more emissions 

and more degradation. The exergoecological approach quantifies <strong>the</strong> physical costs, 

both in minimum exergy terms and in actual exergy terms, required to replace <strong>the</strong> 

resources with <strong>the</strong> best available technology. Thereby <strong>the</strong> anthropogenic view <strong>of</strong> 

<strong>the</strong> value <strong>of</strong> resources is shifted to <strong>the</strong> nature’s point <strong>of</strong> view. This way, <strong>the</strong> earth 

is not consider as an infinite reservoir <strong>of</strong> <strong>mineral</strong>s. On <strong>the</strong> contrary, it is seen as a 

warehouse with a finite number <strong>of</strong> exergy resources, whose extraction implies <strong>the</strong> 

use <strong>of</strong> o<strong>the</strong>r exergy resources. Fur<strong>the</strong>rmore, as <strong>the</strong> warehouse becomes depleted, 

<strong>the</strong> quantity <strong>of</strong> exergy resources required to extract more goods increases following 

an exponential behavior. In exergoecology, conservation ra<strong>the</strong>r than efficiency is <strong>the</strong> 

point. 

Exergoecology has been developed so far for its application to inorganic substances, 

focusing mainly on <strong>the</strong> <strong>mineral</strong> <strong>capital</strong>. Never<strong>the</strong>less, Jorgensen [176], [175] applies 

similar concepts for ecosystems, and introduces <strong>the</strong> term Eco-exergy. According 

to this author, eco-exergy is defined as “<strong>the</strong> exergy <strong>of</strong> an ecosystem but with <strong>the</strong> same

The Exergoecology approach 11 

Solar energy 

NATURE 

Resources 

<strong>Exergy</strong> 

THERMO-ECOLOGICAL COST 

Life cycle <strong>of</strong> 

<strong>the</strong> product 

Services <strong>of</strong> 

products 

Emissions 

Technological 

abatement process 

Residues 

<strong>Exergy</strong> distance 

Technological process <strong>of</strong> 

replacement <strong>of</strong> materials from 

<strong>the</strong> Reference Environment 


EXERGOECOLOGICAL COST 


Zero <strong>Exergy</strong> 

Wastes, effluents 

and emissions 

Reference 

Environment 

Figure 1.1. Conceptual diagram <strong>of</strong> <strong>the</strong> terms exergoecology and <strong>the</strong>rmo-ecology 

system at <strong>the</strong> same temperature and pressure but consisting <strong>of</strong> dead inorganic material 

as reference”. Eco-exergy becomes <strong>the</strong>n a measure <strong>of</strong> how far <strong>the</strong> ecosystem is 

from <strong>the</strong>rmodynamic equilibrium, or how developed <strong>the</strong> ecosystem is. 

Let us outline <strong>the</strong> difference between <strong>the</strong> exergoecological method and <strong>the</strong> o<strong>the</strong>r 

exergy approaches (leaded by <strong>the</strong> <strong>the</strong>rmo-ecological method) through an example. 

In <strong>the</strong> production <strong>of</strong> copper from a deposit, Szargut’s <strong>the</strong>rmo-ecological analysis 

would account for <strong>the</strong> exergy input <strong>of</strong> all industrial processes involved in <strong>the</strong> production 

<strong>of</strong> pure copper from <strong>the</strong> mine, including <strong>the</strong> abatement processes <strong>of</strong> <strong>the</strong> 

emissions and wastes (see Fig. 1.1). The exergoecology approach closes <strong>the</strong> cycle <strong>of</strong> 

Fig. 1.1, because it is concerned about <strong>the</strong> exergy needed to return <strong>the</strong> copper from 

<strong>the</strong> depleted state <strong>of</strong> <strong>the</strong> R.E. to <strong>the</strong> conditions <strong>of</strong> <strong>the</strong> mine where it was found. The 

exergy distance between <strong>the</strong> R.E. and <strong>the</strong> mine increases with <strong>the</strong> mine’s quality. 

This means that as <strong>the</strong> <strong>mineral</strong> deposits become exhausted, <strong>the</strong> exergy difference 

between <strong>the</strong> R.E. and <strong>the</strong> mine becomes lower. In <strong>the</strong> limit, when all natural resources 

have been extracted and dispersed, this distance is equal to zero or, what is 

<strong>the</strong> same, <strong>the</strong> planet has lost all its natural exergy. 

The exergoecology paradigm and its ideas were developed by Valero in <strong>the</strong> book <strong>of</strong> 

Naredo and Valero [239] “Desarrollo económico y deterioro ecológico” (Economical 

development and ecological degradation). In that book, <strong>the</strong> basis for a general <strong>the</strong>ory 

<strong>of</strong> <strong>the</strong> physical cost <strong>of</strong> economic processes is proposed, and some examples <strong>of</strong> 

<strong>the</strong> exergy replacement costs <strong>of</strong> <strong>mineral</strong>s are provided.


Additionally, two PhD <strong>the</strong>sis accomplished in <strong>the</strong> CIRCE institute <strong>of</strong> <strong>the</strong> University <strong>of</strong> 

Zaragoza and directed by Antonio Valero, have applied and have fur<strong>the</strong>r developed 

<strong>the</strong> exergoecology approach. The first one entitled “Análisis De Los Costes Exergéticos 

De La Riqueza Mineral Terrestre. Su Aplicación Para La Gestión De La Sostenibilidad” 

[276] (<strong>Exergy</strong> cost analysis <strong>of</strong> <strong>the</strong> <strong>mineral</strong> wealth on earth. Applicaton for <strong>the</strong> 

management <strong>of</strong> sustainability), was carried out by Lidia Ranz in 1999. The second 

one was written by Edgar Botero one year later: “Valoración Exergética De Recursos 

Naturales, Minerales, Agua y Combustibles Fósiles” [34] (<strong>Exergy</strong> assessment <strong>of</strong> 

natural resources, <strong>mineral</strong>s, water and fossil fuels). 

Ranz developed an approximation <strong>of</strong> <strong>the</strong> R.E., based on <strong>the</strong> methodology proposed 

by Szargut [336] and calculated <strong>the</strong> chemical exergy <strong>of</strong> some important <strong>mineral</strong> 

commodities. Her reference environment was chosen according to <strong>the</strong> abundance 

criterion, i.e. <strong>the</strong> components <strong>of</strong> <strong>the</strong> R.E. should be <strong>the</strong> most abundant ones found 

currently in nature. For that purpose, she carried out a comprehensive and systematic 

analysis <strong>of</strong> <strong>the</strong> most abundant <strong>mineral</strong>s on earth for each chemical element. An 

important message <strong>of</strong> her study was that exergoecology is irrevocably connected to 

geology. A problem with Ranz’s proposed R.E. is that if we assign zero exergy to <strong>the</strong> 

most abundant substances, we are decreasing arbitrarily <strong>the</strong> natural <strong>capital</strong>, because 

many abundant <strong>mineral</strong>s like sulfides naturally evolute to <strong>the</strong> most stable species. 

Botero extended <strong>the</strong> exergy analysis to o<strong>the</strong>r natural resources such as water and 

fossil fuels. In his PhD, <strong>the</strong> concept <strong>of</strong> exergy replacement costs was fur<strong>the</strong>r developed, 

and <strong>the</strong> exergy abatement costs, were firstly applied. The exergy replacement cost 

was first calculated as <strong>the</strong> exergy required for replacing a resource from <strong>the</strong> R.E. 

to <strong>the</strong> current conditions found in nature, with <strong>the</strong> best available technology. The 

exergy abatement cost was proposed as a physical way to measure <strong>the</strong> exergy cost for 

avoiding <strong>the</strong> environmental externalities associated to <strong>the</strong> use <strong>of</strong> fossil fuels, with 

<strong>the</strong> best available technology. 

Both PhD <strong>the</strong>sis, <strong>the</strong> book <strong>of</strong> Naredo and Valero [239], and <strong>the</strong> first paper describing 

<strong>the</strong> exergoecological method (Valero [365]), constitute <strong>the</strong> basis and starting point 

<strong>of</strong> <strong>the</strong> present study. The fundamental concepts described in <strong>the</strong> previous works are 

used in this <strong>the</strong>sis and are fur<strong>the</strong>r developed. 

1.6 Scope, objectives and structure <strong>of</strong> this PhD 

The aim <strong>of</strong> this PhD is <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> state <strong>of</strong> <strong>the</strong> <strong>mineral</strong>’s exergy on earth and 

its degradation velocity, due to <strong>the</strong> human action. As opposed to Botero’s and Ranz’s 

PhDs, where <strong>the</strong> exergoecological analysis was applied in a static way, in this <strong>the</strong>sis 

<strong>the</strong> time factor constitutes a fundamental variable. For that purpose, an exhaustive 

analysis <strong>of</strong> <strong>the</strong> geochemistry <strong>of</strong> our planet and its past, current and future declining 

resources needs to be carried out.

Scope, objectives and structure <strong>of</strong> this PhD 13 

Although an exergy analysis <strong>of</strong> <strong>the</strong> entropic earth remains outside <strong>the</strong> scope <strong>of</strong> this 

PhD, a previous step for modeling it, is <strong>the</strong> assessment <strong>of</strong> <strong>the</strong> composition <strong>of</strong> <strong>the</strong> 

atmosphere, hydrosphere and continental crust. While <strong>the</strong> atmosphere and hydrosphere 

are well studied and its main components are reasonably known, <strong>the</strong> composition 

<strong>of</strong> <strong>the</strong> continental crust in terms <strong>of</strong> <strong>mineral</strong>s has been barely studied. In fact, 

only <strong>the</strong> chemical composition <strong>of</strong> it in terms <strong>of</strong> elements is approximately known, 

and nowadays it is still being improved and updated. Therefore, an important milestone 

<strong>of</strong> this PhD, is to develop a model <strong>of</strong> <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> 

upper continental crust. With <strong>the</strong> upper crust’s model, an approach to <strong>the</strong> chemical 

composition <strong>of</strong> <strong>the</strong> crepuscular earth can be provided. 

Once <strong>the</strong> composition <strong>of</strong> <strong>the</strong> main components <strong>of</strong> <strong>the</strong> earth is known, a closer look 

can be taken at its resources useful to man. The aim is to make a thorough analysis 

<strong>of</strong> <strong>the</strong> abundance and physical characteristics <strong>of</strong> renewable and non renewable 

resources on earth, stressing <strong>the</strong> <strong>mineral</strong> <strong>capital</strong>. The whole physical stock on earth 

will be later assessed with a single unit <strong>of</strong> measure in terms <strong>of</strong> exergy. 

The use <strong>of</strong> exergy as an accounting tool, requires <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> 

<strong>the</strong> substances under analysis. We have dealt with more than 330 substances, for 

which a little more than 50% empirical <strong>the</strong>rmodynamic values are available from 

<strong>the</strong> literature. Therefore, ano<strong>the</strong>r milestone <strong>of</strong> this <strong>the</strong>sis is <strong>the</strong> semi-<strong>the</strong>oretical 

estimation <strong>of</strong> <strong>the</strong> lacking properties. 

With this information, <strong>the</strong> enthalpy, Gibbs free energy and exergy <strong>of</strong> each <strong>of</strong> <strong>the</strong> 

components included in <strong>the</strong> three outer layers <strong>of</strong> <strong>the</strong> earth will be obtained for <strong>the</strong> 

first time. In <strong>the</strong> same way, <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> resources <strong>of</strong> fuel and 

non-fuel origin will be calculated and compared to <strong>the</strong> o<strong>the</strong>r physical resources on 

earth. 

The accomplishment <strong>of</strong> a dynamic analysis <strong>of</strong> <strong>the</strong> resources on earth, requires <strong>the</strong> 

time factor to be introduced. The final aim is to analyze <strong>the</strong> degradation <strong>of</strong> <strong>mineral</strong> 

resources due to <strong>the</strong> human action, from <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> industrialization period 

to nowadays. For that purpose, a comprehensive review <strong>of</strong> historical statistics <strong>of</strong> 

fuel and non-fuel <strong>mineral</strong> extraction from different institutions needs to be carried 

out. Additionally, with <strong>the</strong> help <strong>of</strong> scenarios, <strong>the</strong> possible degradation <strong>of</strong> <strong>mineral</strong> 

resources in <strong>the</strong> future can be provided. The representation <strong>of</strong> <strong>the</strong> exergy degradation 

throughout history, will allows us to introduce new concepts and to apply 

degradation models for assessing global <strong>mineral</strong> scarcity. An example <strong>of</strong> that is <strong>the</strong> 

application <strong>of</strong> <strong>the</strong> Hubbert peak model, for determining <strong>the</strong> peak <strong>of</strong> production <strong>of</strong> all 

kinds <strong>of</strong> <strong>mineral</strong>s. 

The objectives <strong>of</strong> this PhD cannot be accomplished only with a <strong>the</strong>rmodynamic perspective. 

We have stated throughout this work, that o<strong>the</strong>r disciplines such as geology, 

geochemistry and economy are also crucial. Hence, for <strong>the</strong> completion <strong>of</strong> <strong>the</strong> 

studies, interaction with experts from different knowledge areas was required. In 

<strong>the</strong> geological field, <strong>the</strong> interaction with experts from <strong>the</strong> British Geological Survey 

and <strong>the</strong> department <strong>of</strong> Petrology in <strong>the</strong> University <strong>of</strong> Zaragoza were decisive. In


<strong>the</strong> same way, <strong>the</strong> geochemistry part <strong>of</strong> this PhD was reinforced with <strong>the</strong> reviews <strong>of</strong> 

Dr. Vieillard, from <strong>the</strong> “Laboratoire d’Hydrogéologie, Argiles, Sols et Altérations” in 

<strong>the</strong> University <strong>of</strong> Poitiers. In <strong>the</strong> economic field, <strong>the</strong> point <strong>of</strong> view <strong>of</strong> <strong>the</strong> Spanish 

economist J.M. Naredo was especially taken into account. 

This PhD is structured into two differentiated parts. Part 1, which includes chapters 

2, 3 and 4, describes <strong>the</strong> geochemistry <strong>of</strong> <strong>the</strong> earth and its resources. Part 2 contains 

chapters 5, 6, 7, and 8 and is focused on calculating <strong>the</strong> <strong>the</strong>rmodynamic properties 

<strong>of</strong> <strong>the</strong> earth and its exergy <strong>evolution</strong>. 

Summarizing, this PhD tries to answer <strong>the</strong> following questions: 

• Chapter 2: What is <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> layers <strong>of</strong> <strong>the</strong> earth? 

• Chapter 3: What is <strong>the</strong> average <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> continental 

crust? 

• Chapter 4: What are <strong>the</strong> available, potential and currently in use energy resources 

<strong>of</strong> <strong>the</strong> earth? What are <strong>the</strong> non-fuel <strong>mineral</strong> resources on earth and 

which is <strong>the</strong>ir average ore grade? 

• Chapter 5: Which is <strong>the</strong> R.E. and <strong>the</strong> <strong>the</strong>rmodynamic models required for <strong>the</strong> 

calculation <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> earth? 

• Chapter 6: What is <strong>the</strong> enthalpy, Gibbs free energy and exergy <strong>of</strong> <strong>the</strong> planet 

and its resources? What is <strong>the</strong> exergy replacement cost <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources 

on earth? 

• Chapter 7: How can we measure <strong>the</strong> level and <strong>the</strong> velocity <strong>of</strong> degradation <strong>of</strong> 

<strong>mineral</strong> resources? How are <strong>the</strong>se concepts applied to a specific nation? 

• Chapter 8: How fast is humankind degrading <strong>the</strong> <strong>mineral</strong> exergy resources <strong>of</strong> 

<strong>the</strong> earth? Have we reached <strong>the</strong> peak <strong>of</strong> production <strong>of</strong> <strong>mineral</strong>s? 

In short, <strong>the</strong> aim <strong>of</strong> this PhD is to improve <strong>the</strong> knowledge <strong>of</strong> <strong>the</strong> earth and its resources, 

from <strong>the</strong> exergoecological point <strong>of</strong> view. Because, as stated before, it is 

impossible to manage efficiently <strong>the</strong> resources on earth, if we do not know what is 

available and at which rate it is being depleted. 

1.7 Scientific papers derived from this PhD 

Some <strong>of</strong> <strong>the</strong> results obtained in this PhD have been presented in different conferences 

and published in international journals. Here is a list <strong>of</strong> <strong>the</strong> papers developed from 

<strong>the</strong> work carried out in this PhD ([343], [368],[377], [378], [375], [376], [374], 

[373]).

Scientific papers derived from this PhD 15 

1. J. Szargut, A. Valero, W. Stanek, and A. Valero D. Towards an international 

legal reference environment. In Proceedings <strong>of</strong> ECOS 2005, pages 409–420, 

Trondheim, Norway, June 2005. 

2. A. Valero, E. Botero, and A. Valero D. <strong>Exergy</strong> accounting <strong>of</strong> natural resources. 

<strong>Exergy</strong>, Energy System Analysis, and Optimization., from Encyclopedia <strong>of</strong> Life 

Support Systems (EOLSS), Developed under <strong>the</strong> Auspices <strong>of</strong> <strong>the</strong> UNESCO Eolss 

Publishers, Oxford, UK; Online encyclopedia: http://www.eolss.net, Retrieved 

May 19, 2005. 

3. A. Valero D., A. Valero, and A. Martinez. <strong>Exergy</strong> evaluation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> 

<strong>capital</strong> on Earth. Influence <strong>of</strong> <strong>the</strong> reference environment. In Proceedings <strong>of</strong> 

IMECE 2005, Orlando, USA, 5-11 November 2005. ASME. 

4. A. Valero D., A. Valero, A. Martínez, and G. Mudd. A physical way to assess <strong>the</strong> 

decrease <strong>of</strong> <strong>mineral</strong> <strong>capital</strong> through exergy. The Australian case. In Proceedings 

<strong>of</strong> ISEE 2006, New Delhi, India, 15-18 December 2006. Ninth Biennial Conference 

on <strong>the</strong> International Society for Ecological Economics (ISEE). “Ecological 

Sustainability and Human Well-being”. 

5. A. Valero D., A. Valero, and I. Arauzo. <strong>Exergy</strong> as an indicator for resources 

scarcity. The exergy loss <strong>of</strong> Australian <strong>mineral</strong> <strong>capital</strong>, a case study. In Proceedings 

<strong>of</strong> IMECE2006, Chicago, USA, 5-10 November 2006. ASME. 

6. A. Valero D., A. Valero, and I. Arauzo. Evolution <strong>of</strong> <strong>the</strong> decrease in <strong>mineral</strong> 

exergy throughout <strong>the</strong> 20th century. The case <strong>of</strong> copper in <strong>the</strong> US. Energy, 

33(2):107–115, 2008. 

7. A. Valero D. Assessing world <strong>mineral</strong> deposits through <strong>the</strong> second law <strong>of</strong> <strong>the</strong>rmodynamics. 

In Inproceedings <strong>of</strong> <strong>the</strong> Mineral Deposit Studies Group (MDSG) 

conference, Nottingham (UK), 2-4 January 2008. 

8. A. Valero, A. Valero D., and C. Torres. <strong>Exergy</strong> and <strong>the</strong> Hubbert peak. An extended 

analysis for <strong>the</strong> assessment <strong>of</strong> <strong>the</strong> scarcity <strong>of</strong> <strong>mineral</strong>s on earth. In Proceedings 

<strong>of</strong> IMECE 2008, Boston, USA, 31 October - 6 November 2008. ASME.

Part I 

The earth and its resources 

17

Chapter 2 

The geochemistry <strong>of</strong> <strong>the</strong> earth. 

Known facts 


In this chapter a comprehensive analysis <strong>of</strong> <strong>the</strong> geochemistry <strong>of</strong> <strong>the</strong> earth is undertaken 

as <strong>the</strong> starting point for assessing its <strong>the</strong>rmodynamic properties. The geochemical 

features <strong>of</strong> each layer <strong>of</strong> <strong>the</strong> earth are described: <strong>the</strong> atmosphere; hydrosphere 

with <strong>the</strong> oceans, surface and ground waters as well as ice sheets; and <strong>the</strong> crust, focusing 

mainly on <strong>the</strong> upper part <strong>of</strong> it. 

2.2 The bulk earth 

The earth is an approximately spherical body, 12.756 km <strong>of</strong> diameter and 5, 98×10 24 

kg [23]. Its physical and chemical peculiarities have allowed <strong>the</strong> existence <strong>of</strong> life on 

earth. The solid earth is divided into <strong>the</strong> crust (continental and oceanic), mantle and 

core. The external layers above <strong>the</strong> crust are <strong>the</strong> hydrosphere and <strong>the</strong> atmosphere. 

From all layers, <strong>the</strong> mantle and core are <strong>the</strong> largest, accounting for 67 and 33% <strong>of</strong> 

<strong>the</strong> total mass <strong>of</strong> <strong>the</strong> earth [169]. The crust, hydrosphere and atmosphere toge<strong>the</strong>r 

make up less than 1% by mass. Only that small fraction <strong>of</strong> <strong>the</strong> mass <strong>of</strong> <strong>the</strong> earth is 

available for direct study and analysis, and so it is necessary to use indirect methods 

to estimate <strong>the</strong> earth’s inner composition. The continental crust, in concert with 

<strong>the</strong> atmosphere and hydrosphere provides <strong>the</strong> nurturing and nourishing habitat in 

which our species lives. 

2.2.1 The composition <strong>of</strong> <strong>the</strong> earth 

The earth can be considered as a closed system with a finite number <strong>of</strong> substances 

in it, except for <strong>the</strong> very occasional and insignificant matter contribution <strong>of</strong> mete- 

19

20 THE GEOCHEMISTRY OF THE EARTH. KNOWN FACTS 

orites [209]. The spheres are large reservoirs and between <strong>the</strong> reservoirs <strong>the</strong>re are 

flows <strong>of</strong> materials that balance out and keep <strong>the</strong> reservoir compositions nearly constant. 

Hence <strong>the</strong> composition <strong>of</strong> <strong>the</strong> atmosphere, hydrosphere and continental crust 

is practically constant. 

Table 2.1 shows <strong>the</strong> composition <strong>of</strong> <strong>the</strong> main layers on earth based on Javoy’s [169] 

study. Only four elements constitute nearly 95% <strong>of</strong> <strong>the</strong> earth’s mass. In order <strong>of</strong> 

abundance, <strong>the</strong>se are O, Fe, M g and Si. The relative importance <strong>of</strong> M g relies on 

<strong>the</strong> geochemistry <strong>of</strong> <strong>the</strong> mantle, ra<strong>the</strong>r than on <strong>the</strong> o<strong>the</strong>r layers <strong>of</strong> <strong>the</strong> solid earth, 

where Si and Fe predominate in <strong>the</strong> upper crust and core, respectively. O<strong>the</strong>r estimations 

were done by Mason [209], Ringwood [280], Ganapathy and Anders [105] 

and Smith [322]. As Javoy [169] states, <strong>the</strong> only significant discrepancy between 

chemical models <strong>of</strong> <strong>the</strong> earth lies in <strong>the</strong> lower mantle. All primary upper mantle 

compositions agree to within a few percent relative for major and minor elements. 

For <strong>the</strong> core, <strong>the</strong> composition is not so strictly defined but <strong>the</strong> dominant agreement 

is on Fe − N i − Co − C r − M n − Si − O − S combinations. 

If we only take into account <strong>the</strong> outer layers <strong>of</strong> <strong>the</strong> earth, i.e. <strong>the</strong> continental crust, 

hydrosphere and atmosphere, <strong>the</strong>se constitute 92,87%, 3,15% and 0,0712% by volume, 

respectively. 

In <strong>the</strong> next sections, <strong>the</strong> geochemistry <strong>of</strong> <strong>the</strong> atmosphere, hydrosphere and upper 

continental crust are explained in detail. 

2.3 The atmosphere 

The atmosphere is <strong>the</strong> colorless, odorless and tasteless gaseous layer surrounding 

<strong>the</strong> earth and retained by it through <strong>the</strong> earth’s gravity. Its relative mass compared 

to <strong>the</strong> o<strong>the</strong>r spheres <strong>of</strong> <strong>the</strong> earth is minuscule (see table 2.1). Never<strong>the</strong>less, it is a 

crucial geochemical reservoir, providing conditions essential for sustaining life, such 

as supplying O 2, CO 2, moisture and many nutrients. The atmosphere plays also a 

very direct role in controlling <strong>the</strong> earth’s climate via <strong>the</strong> absorption and scattering 

<strong>of</strong> sunlight and infrared radiation and reducing temperature extremes between day 

and night. 

The atmosphere is made up <strong>of</strong> several layers with different qualities [359], [182] 

[331] (see figure 2.1): 

• The troposphere is <strong>the</strong> lowest atmospheric layer. It begins at <strong>the</strong> surface and 

extends between 7 to 17 km. It contains over 75% <strong>of</strong> all <strong>the</strong> atmospheric gases 

and vast quantities <strong>of</strong> water and dust. Almost all phenomena <strong>of</strong> wea<strong>the</strong>r and 

climate that physically affect man take place within <strong>the</strong> troposphere, caused by 

<strong>the</strong> churning <strong>of</strong> its mass. The troposphere is <strong>the</strong> region in which <strong>the</strong> infrared 

radiation is absorbed mainly by water vapor to raise <strong>the</strong> surface temperature.

The atmosphere 21 

Table 2.1. Composition <strong>of</strong> <strong>the</strong> main envelopes derived from direct sampling or from 

a chemical translation <strong>of</strong> a direct measurement (density), in <strong>the</strong> case <strong>of</strong> <strong>the</strong> core, 

and <strong>the</strong> corresponding whole earth composition [169]. 

Mantle Oceanic Continental Core Oceans Atmosphere Whole 

crust crust 

earth 

% vol 81,89 0,085 0,44 17,56 0,033 1,48E-08 100 

% mass 67 0,072 0,36 32,54 0,023 0,842 ppm 100 

O 44,12 44,33 47,25 3 88,889 23,16 30,76 

Si 20,89 23,1 27,58 7 16,39 

Mg 25,09 4,66 2,65 0,0053 16,82 

Al 1,24 8,47 8,36 0,87 

Ca 1,49 8,07 4,57 0,0412 1,02 

Fe 6,53 8,17 5,13 80 30,43 

Ni 0,17 0,3 4,65 1,63 

Ti 0,058 0,9 0,42 0,04 

Cr 0,169 0,2 0,77 0,36 

Mn 0,081 0,11 0,09 0,57 0,24 

Na 0,14 2,08 2,37 1,0764 0,10 

S 0,01 4 0,0902 1,31 

K 0,03 0,12 1,58 0,0398 2,59E-02 

U 5E-12 2E-11 1,00E-06 6,96E-12 

Th 1,2E-11 4,4E-11 3,50E-06 2,07E-11 

Cl 

Br 

1,9383 4,46E-04 

B 0,0005 1,15E-07 

C 0,04 0,0028 2,68E-02 

N 75,56 6,36E-08 

Rare 

gases 

1,28 1,08E-09 

• The stratosphere extends from <strong>the</strong> troposphere to about 50 km. In this thin 

layer, <strong>the</strong>re is 19% <strong>of</strong> <strong>the</strong> atmospheric gases and a small quantity <strong>of</strong> water vapor. 

Temperature increases with height because <strong>of</strong> <strong>the</strong> absorption <strong>of</strong> ultraviolet 

light by ozone. The ozone layer is contained in <strong>the</strong> stratosphere. 

• The mesosphere extends from about 50 km to <strong>the</strong> range <strong>of</strong> 80 to 85 km. The 

gases in <strong>the</strong> mesosphere are too thin to absorb much <strong>of</strong> <strong>the</strong> sun’s radiation, but 

<strong>the</strong> air is thick enough to slow down meteorites. In this case, <strong>the</strong> temperature 

decreases with height. 

• The <strong>the</strong>rmosphere ranges from 80-85 km to more than 640 km.The gases <strong>of</strong> 

this sphere are even thinner than in <strong>the</strong> mesosphere, but <strong>the</strong>y absorb ultraviolet 

light from <strong>the</strong> sun and as a consequence, temperature increases with 

height. 

• The ionosphere is part <strong>of</strong> <strong>the</strong> <strong>the</strong>rmosphere and is made <strong>of</strong> electrically charged 

gas particles ionized by solar radiation. It plays an important role since it


Figure 2.1. The atmospheric layers. Source: http://www.atmosphere.mpg.de (Max 

Plank Institute) 

influences radio propagation to distant places on earth. Fur<strong>the</strong>rmore, it is 

responsible for auras. 

• And finally <strong>the</strong> exosphere, it is <strong>the</strong> outermost layer <strong>of</strong> <strong>the</strong> atmosphere and 

extends from 500 to 1000 km up to 10.000 km. It is composed <strong>of</strong> free-moving 

particles that may migrate into and out <strong>of</strong> <strong>the</strong> magnetosphere. In this layer, 

gases get thinner and thinner and drift <strong>of</strong>f into space. 

The stability <strong>of</strong> <strong>the</strong> physical and geochemical conditions <strong>of</strong> <strong>the</strong> atmosphere is being 

altered by <strong>the</strong> action <strong>of</strong> man through air pollution. The greatest source <strong>of</strong> emissions 

are <strong>the</strong> burning <strong>of</strong> fossil fuels, emitting huge quantities <strong>of</strong> carbon dioxide, methane 

and fluorocarbons, believed to contribute to global warming. Ano<strong>the</strong>r man-made 

consequence <strong>of</strong> <strong>the</strong> use <strong>of</strong> chlor<strong>of</strong>luorocarbons is <strong>the</strong> stratospheric ozone depletion, 

which lowers <strong>the</strong> effectiveness <strong>of</strong> <strong>the</strong> atmosphere to protect us against UV radiation. 

2.3.1 The composition <strong>of</strong> <strong>the</strong> atmosphere 

In terms <strong>of</strong> its constituent gases, <strong>the</strong> atmosphere presents a notably uniform chemical 

composition to heights <strong>of</strong> about 100 km [100], except for water which varies with 

location and season as well as with elevation. Above this altitude, <strong>the</strong> atmosphere 

becomes layered and non uniform in chemical composition.

The hydrosphere 23 

The atmosphere is composed roughly by (volume content) 78% <strong>of</strong> usually inert nitrogen 

1 , around 21% <strong>of</strong> oxygen, 0,93% argon, 380 ppm <strong>of</strong> carbon dioxide, a variable 

amount <strong>of</strong> water vapor (average around 1%) and trace amounts <strong>of</strong> o<strong>the</strong>r gases. 

That mixture <strong>of</strong> gases is commonly known as air. The latest atmospheric geochemical 

advances are compiled in Keeling [181]. Next, <strong>the</strong> main components <strong>of</strong> <strong>the</strong> 

troposphere and <strong>the</strong>ir origin are explained basing on <strong>the</strong> information provided by 

Turekian [359]. 

Nitrogen in <strong>the</strong> presence <strong>of</strong> oxygen at <strong>the</strong> surface <strong>of</strong> <strong>the</strong> oceans combines to form 

nitrate in solution as <strong>the</strong> stable form. Both nitrogen and oxygen are maintained 

at <strong>the</strong>ir levels by biological processes. Oxygen is more biologically controlled than 

nitrogen but both are dependent on <strong>the</strong> chemical actions <strong>of</strong> life. 

The argon in <strong>the</strong> atmosphere is believed to have been produced by <strong>the</strong> radioactive 

decay <strong>of</strong> potassium-40 in <strong>the</strong> earth and released to <strong>the</strong> atmosphere by degassing <strong>of</strong> 

<strong>the</strong> earth. It is not certain whe<strong>the</strong>r most <strong>of</strong> <strong>the</strong> argon was supplied from <strong>the</strong> argon 

produced in <strong>the</strong> earth by potassium-40 decay at some major degassing epoch in <strong>the</strong> 

earth’s early history or by <strong>the</strong> continuously generated argon in <strong>the</strong> earth’s crust and 

mantle. 

Methane and carbon dioxide are closely tied to biological activity. Methane oxidized 

carbon dioxide and its presence is directly sustained by production by bacteria and 

animals. 

Man-made impurities such as sulphur dioxide and carbon monoxide, which are responsible 

for <strong>the</strong> physical discomforts <strong>of</strong> smog, are also sometimes highly concentrated 

in urban areas. 

A summary <strong>of</strong> <strong>the</strong> composition <strong>of</strong> <strong>the</strong> atmosphere at <strong>the</strong> start <strong>of</strong> <strong>the</strong> twenty-first 

century done by Prinn [272], from Brasseur et al. [36] and Prinn et al. [271] is 

given in table 2.2. 

2.4 The hydrosphere 

The hydrosphere is <strong>the</strong> liquid water component <strong>of</strong> <strong>the</strong> earth. It includes oceans, seas, 

lakes, rivers, rain, underground water, ice and atmospheric water vapor as in clouds. 

It covers about 70% <strong>of</strong> <strong>the</strong> surface <strong>of</strong> <strong>the</strong> earth and is <strong>the</strong> home for many plants and 

animals. 

The hydrosphere is in continuous motion through <strong>the</strong> hydrologic cycle, which is a 

conceptual model that describes <strong>the</strong> storage and movement <strong>of</strong> water between <strong>the</strong> 

biosphere, atmosphere, lithosphere and <strong>the</strong> hydrosphere (see section 4.6.2 for more 

details). 

1 Normally inert except upon electrolysis by lightning and in certain biochemical processes <strong>of</strong> ni- 

trogen fixation.


Table 2.2. Gaseous chemical composition <strong>of</strong> <strong>the</strong> atmosphere [272]. 

Substance Chemical 

formula 

Mole fraction in dry air Major sources 

Nitrogen N2 78,084 % Biological 

Oxygen O2 20,948 % Biological 

Argon Ar 0,934 % Inert 

Carbon dioxide CO2 360 ppm Combustion, 

sphere 

ocean, bio- 

Neon N e 18,18 ppm Inert 

Helium He 5,24 ppm Inert 

Methane CH 4 1,7 ppm Biogenic, anthropogenic 

Hydrogen H2 0,55 ppm Biogenic, anthropogenic, 

Nitrous oxide N2O 0,31 ppm 

photochemical 

Biogenic, anthropogenic 

Carbon monoxide CO 50-200 ppb Photochemical, 

pogenicanthro- 

Ozone (troposphere) O3 10-500 ppb Photochemical 

Ozone (stratosphere) O3 0,5-10 ppm Photochemical 

NMHC Cx H y 5,0-20 ppb Biogenic, anthropogenic 

Chlor<strong>of</strong>luorocarbon 12 C F2Cl2 540 ppt Anthropogenic 

Chlor<strong>of</strong>luorocarbon 11 C F Cl 3 265 ppt Anthropogenic 

Methylchlor<strong>of</strong>orm CH 3CCl 3 65 ppt Anthropogenic 

Carbon tetrachloride CCl 4 98 ppt Anthropogenic 

Nitrogen oxides NOx 0,01-1 ppm Soils, 

pogenic 

lightning, anthro- 

Ammonia N H3 0,01-1 ppb Biogenic 

Hydroxyl radical OH 0,05 ppt Photochemical 

Hydroperoxyl radical HO2 2 ppt Photochemical 

Hydrogen peroxide H2O2 0,1-10 ppb Photochemical 

Formaldehyde CH 2O 0,1-1 ppb Photochemical 

Sulfur dioxide SO2 0,01-1 ppb Photochemical, 

anthropogenic 

volcanic, 

Dimethyl sulfide CH 3SCH 3 10-100 ppt Biogenic 

Carbon disulfide CS2 1-300 ppt Biogenic, anthropogenic 

Carbonyl sulfide OCS 500 ppt Biogenic, volcanic, anthropogenic 

Hydrogen sulfide H2S 5-500 ppt Biogenic, volcanic


Table 2.3. Inventory <strong>of</strong> water at <strong>the</strong> earth’s surface [263]. 

Reservoir Volume, M km 3 % 

Oceans 1370 97,25 

Ice Caps and Glaciers 29 2,05 

Groundwater 9,5 0,68 

Lakes 0,125 0,01 

Soil Moisture 0,065 0,005 

Atmosphere 0,013 0,001 

Streams and Rivers 0,0017 0,0001 

Biosphere 0,0006 0,00004 

Sum 1408,71 100,00 

The planetary water supply is dominated by <strong>the</strong> oceans (see table 2.3). Approximately 

97% <strong>of</strong> all water on <strong>the</strong> earth is <strong>the</strong> oceans. The o<strong>the</strong>r 3% is held as freshwater 

in glaciers and icecaps, groundwater, lakes, soil, <strong>the</strong> atmosphere and biosphere 

[263]. The greater portion <strong>of</strong> <strong>the</strong> fresh water (75%) is in <strong>the</strong> shape <strong>of</strong> ice and permanent 

snow cover in <strong>the</strong> Antarctic, Arctic and mountainous regions. Next 25% are 

fresh and ground waters. Only 0,33% <strong>of</strong> <strong>the</strong> total amount <strong>of</strong> fresh waters on <strong>the</strong> 

earth are concentrated in lakes, reservoirs and river systems (surface waters), which 

are most accessible for economic needs and very important for water ecosystems. 

Considered as a whole, <strong>the</strong> earth has a comparatively stable water budget. The major 

problem is that most <strong>of</strong> it is overwhelmingly salty. Additionally, fresh water is not 

evenly distributed over <strong>the</strong> lands. Fur<strong>the</strong>rmore, industrialization and unsustainable 

land uses are increasing dramatically water pollution and <strong>the</strong>reby threatening world 

water supply. 

Next, <strong>the</strong> main water reservoirs <strong>of</strong> <strong>the</strong> earth are analyzed, stressing out <strong>the</strong>ir abundances, 

economic uses and chemical compositions. 

2.4.1 Seawater 

The oceans account for a little over 70% <strong>of</strong> <strong>the</strong> earth’s surface and comprise more 

than 97% <strong>of</strong> <strong>the</strong> hydrosphere. The volume <strong>of</strong> ocean water is about 1, 37 · 10 9 km 3 

[263]. The Pacific ocean is by far <strong>the</strong> biggest in <strong>the</strong> world, followed by <strong>the</strong> Atlantic 

and <strong>the</strong> Indian oceans (see table 2.4). 

Oceans represent a relatively well-mixed system <strong>of</strong> considerable mass and potential 

economic use. The prime functions <strong>of</strong> <strong>the</strong> oceans are those related to atmospheric 

behavior. The oceans constitute <strong>the</strong> only major source <strong>of</strong> atmospheric moisture for 

<strong>the</strong> lands, and <strong>the</strong>y serve as gigantic “energy cells” for <strong>the</strong> receipt, storage, and release 

<strong>of</strong> <strong>the</strong> radiant sun energy that fuels <strong>the</strong> earth’s climatic and wea<strong>the</strong>r systems. 

Besides <strong>of</strong> being a huge food reservoir, <strong>the</strong>y have o<strong>the</strong>r uses such as pure water


Table 2.4. Volume <strong>of</strong> Oceans and Seas. Adapted from [85] 

Name Volume, M km 3 

Atlantic Ocean 

without marginal seas 324,6 

with marginal seas 354,7 

Pacific Ocean 

without marginal seas 707,6 


Indian Ocean 

without marginal seas 291 


Arctic Ocean 17 

Mediterranean Sea and Black Sea 4,2 

Gulf <strong>of</strong> Mexico and Caribbean Sea 9,6 

Australasian Central Sea 9,9 

Hudson Bay 0,16 

Baltic Sea 0,02 

North Sea 0,05 

English Channel 0,004 

Irish Sea 0,006 

Sea <strong>of</strong> Okhotsk 1,3 

Bering Sea 3,33 

The world ocean 1.370 

sources after <strong>the</strong> process <strong>of</strong> desalination and as chlorine and bromine sources 2 . Never<strong>the</strong>less, 

its salinity avoids seawater to have more economic uses than <strong>the</strong> o<strong>the</strong>r 

types <strong>of</strong> water reservoirs mentioned before. In fact it is frequently considered to be 

a drain ra<strong>the</strong>r than a resource. 

2.4.1.1 The composition <strong>of</strong> <strong>the</strong> sea 

Despite <strong>the</strong>ir overall size, <strong>the</strong> oceans are sufficiently uniform to make description 

<strong>of</strong> <strong>the</strong>ir chemical nature relatively straightforward. Studies have shown that <strong>the</strong> 

relative compositions <strong>of</strong> major components: N a + , M g2+ , Ca2+ , K + , Cl − , SO −2 

4 , 

Sr 2+ , HBO − 

3 , CO2− 

3 , B(OH) 3, B(OH) − 

4 , F − <strong>of</strong> seawater were constant [69], [37], 

[264] and [224]. The first six ions make up 99,4% <strong>of</strong> <strong>the</strong> dissolved salts (see table 

2.5). Most <strong>of</strong> <strong>the</strong> chemicals in <strong>the</strong> ocean are brought from <strong>the</strong> water <strong>of</strong> rivers, 

which in turn receive <strong>the</strong>m from rocks <strong>of</strong> <strong>the</strong> crust that have suffered <strong>the</strong> process 

<strong>of</strong> wea<strong>the</strong>ring. An average composition <strong>of</strong> river waters given by Livingstone [197] is 

listed in table 2.8. It is remarkable <strong>the</strong> difference between river and ocean chemical 

compositions. The explanation <strong>of</strong> that relies on <strong>the</strong> residence time <strong>of</strong> <strong>the</strong> ions. Most 

abundant ions found in seawater have residence times <strong>of</strong> above one million years 

[137]. The salinity <strong>of</strong> ocean water is about 35 parts per thousand by mass, but 

2 See sections 3.4.16 and 3.4.10 for more details.


Table 2.5. The composition <strong>of</strong> average seawater. Adapted from [224] 

Substance Concentration, mg/g 

Cl − 19,351 

N a + 10,784 

M g2+ 1,284 

SO2− 4 

Ca 

2,713 

2+ 0,412 

K + 0,399 

HCO − 

3 

Br 

0,107 

− 0,067 

Sr 2+ 0,008 

CO2− 3 

B(OH) 

0,048 

− 

4 

F 

0,003 

− 0,013 

B(OH) 3 

0,009 

Sum 35,198 

variations from about 33 to 38 parts per thousand are observed in <strong>the</strong> open oceans. 

The variation in salinity results from a number <strong>of</strong> physical processes that control <strong>the</strong> 

salt content <strong>of</strong> seawater such as temperature, rainfall, ice melting or land run<strong>of</strong>f. 

But not all seawater substances have a crustal origin. In fact, <strong>the</strong> sea is a huge reservoir 

for many atmospheric substances such as carbon dioxide, a major contributor 

to climate change. Through <strong>the</strong> air-sea interaction processes, all <strong>the</strong> components <strong>of</strong> 

air can be expected to find <strong>the</strong>ir way into <strong>the</strong> ocean. Additionally, <strong>the</strong>re are o<strong>the</strong>r 

sources and mechanisms producing gases within <strong>the</strong> ocean that supplement those 

supplied from <strong>the</strong> atmosphere. The dissolved gases in seawater are classified into 

four general groups [148]. The first group contains <strong>the</strong> inert gases: nitrogen, argon, 

helium, neon, xenon, and krypton. These gases enter <strong>the</strong> oceans through <strong>the</strong> 

air-sea interface or through <strong>the</strong> introduction <strong>of</strong> aerated water by land run<strong>of</strong>f. The 

second group is composed by solely oxygen, coming from <strong>the</strong> same sources than <strong>the</strong> 

o<strong>the</strong>r group plus from photosyn<strong>the</strong>sis by <strong>the</strong> plants that exist in <strong>the</strong> ocean. The third 

group also contains only one member, carbon dioxide. This gas is introduced into 

<strong>the</strong> sea through <strong>the</strong> large chemical equilibrium system. Specific sources <strong>of</strong> carbon 

dioxide include <strong>the</strong> atmosphere, land run<strong>of</strong>f and <strong>the</strong> ocean floor. The fourth group 

is simply <strong>the</strong> collection <strong>of</strong> all <strong>the</strong> remaining gaseous ingredients found in seawater, 

and its sources are air pollution, usually from industry, and chemical reactions o<strong>the</strong>r 

than photosyn<strong>the</strong>sis. Hydrogen sulfide resulting from <strong>the</strong> reduction <strong>of</strong> sulfate in <strong>the</strong> 

absence <strong>of</strong> oxygen is one member <strong>of</strong> this fourth group. 

Wilhelm Dittmar’s complete analysis <strong>of</strong> <strong>the</strong> seventy-seven seawater samples collected 

in 1884 stood for almost a century. Nowadays, one <strong>of</strong> <strong>the</strong> most accepted composition 

<strong>of</strong> minor species in seawater is <strong>the</strong> compilation <strong>of</strong> Quinby-Hunt and Turekian [273], 

listed in table 2.6.


Table 2.6: Predicted Mean Oceanic Concentrations. Adapted from [273]. 

Element Species Concentration 

Hydrogen H 2 

Helium 1,9 nmol/kg 

Lithium 178 µg/kg 

Beryllium 0,2 ng/kg 

Boron Inorganic Boron 4,4 mg/kg 

Carbon ΣCO 2 2200 µg/kg 

Nitrogen N 2 590 µg/kg 

NO 3 30 µg/kg 

Oxygen Dissolved O 2 150 µg/kg 

Fluorine 1,3 mg/kg 

Neon 8 nmol/kg 

Sodium 10,781 g/kg 

Magnesium 1,28 g/kg 

Aluminum 1 µg/kg 

Silicon Silicate 110 µmole/kg 

Phosphorous Reactive Phosphate 2 µmole/kg 

Sulfur Sulfate 2,712 g/kg 

Chlorine Chloride 19,353 g/kg 

Argon 15,6 µmole/kg 

Potassium 399 mg/kg 

Calcium 415 mg/kg 

412 mg/kg 

Scandium < 1 ng/kg 

Titanium < 1 ng/kg 

Vanadium < 1 µg/kg 

Chromium C r (tot) 330 ng/kg 

330 ng/kg 

250 ng/kg 

Manganese Dissolved M n 10 ng/kg 

Iron 40 ng/kg 

Cobalt 2 ng/kg 

Nickel 480 ng/kg 

Copper 120 ng/kg 

Zinc 390 ng/kg 

Gallium 10 20 ng/kg 

Germanium < 5 ng/kg 

Arsenic As (V) 2 µg/kg 

Dimethylarsenate 

Selenium Se (tot) 170 ng/kg 

Se (IV) < 

Se (VI) 

Bromine Bromide 67 mg/kg 

Krypton 3,7 nmol/kg 

Rubidium 124 mug/kg 

Strontium 7,8 mg/kg 

7,7 mg/kg 

Yttrium 13 ng/kg 

Zirconium 1 µg/kg 

Niobium < 1 ng/kg 

Molybdenum 11 µg/kg 

Continued on next page . . .


Table 2.6: Predicted Mean Oceanic Concentrations. Adapted from [273]. – 

continued from previous page. 

Element Species Concentration 

Ru<strong>the</strong>nium 0,5 ng/kg 

Rhodium 

Palladium 

Silver 3 ng/kg 

Cadmium 70 ng/kg 

Indium 0,5 ng/kg 

Tin 0,5 ng/kg 

Antimony 0,2 µg/kg 

Tellurium 

Iodine 59 µg/kg 

60 µg/kg 

Xenon 0,5 nmol/kg 

Cesium 0,3 ng/kg 

Barium 11,7 µg/kg 

Lanthanum 4 ng/kg 

Cerium 4 ng/kg 

Praeseodymium 0,6 ng/kg 

Neodymium 4 ng/kg 

Promethium 

Samarium 0,6 ng/kg 

Europeum 0,1 ng/kg 

Gadolinium 0,8 ng/kg 

Terbium 0,1 ng/kg 

Dysprosium 1 ng/kg 

Holmium 0,2 ng/kg 

Erbium 0,9 ng/kg 

Thulium 0,2 ng/kg 

Ytterbium 0,9 ng/kg 

Lutetium 0,2 ng/kg 

Hafnium ≪ 8 ng/kg 

Tantalum ≪ 2,5 ng/kg 

Tungsten ≪ 1 ng/kg 

Rhenium 4 ng/kg 

Osmium 

Iridium 

Platinum 

Gold 11 ng/kg 

Mercury 6 ng/kg 

Thallium 12 ng/kg 

Lead 1 ng/kg 

Bismuth 10 ng/kg 

Polonium 

Radon 

Radium 

Actinium 

Thorium ≪ 0,7 ng/kg 

Proactinium 

Uranium 3,2 µg/kg 

End <strong>of</strong> <strong>the</strong> table


2.4.2 Renewable water resources: surface and ground waters 

The renewable water resources are <strong>the</strong> total amount <strong>of</strong> a country’s water resources, 

both surface water and ground water, which are generated through <strong>the</strong> hydrological 

cycle. It is mainly <strong>the</strong> river run<strong>of</strong>f estimated in <strong>the</strong> volume referred to a unit <strong>of</strong> 

time (as for instance km 3 /year) and formed in <strong>the</strong> region at issue or incoming from 

outside, including <strong>the</strong> ground water inflow to <strong>the</strong> river network. This kind <strong>of</strong> water 

resources includes also <strong>the</strong> yearly renewable upper aquifer ground water not drained 

by <strong>the</strong> river systems. 

Despite <strong>of</strong> <strong>the</strong>ir relative low abundance, renewable water resources on earth (see 

table 2.3) in forms <strong>of</strong> lakes, streams 3 , rivers and ground water play an important 

role for life and especially for human-beings, since <strong>the</strong>y are <strong>the</strong> main sources <strong>of</strong> 

freshwater. They are also an important source <strong>of</strong> water for agricultural and industrial 

consumption. Rivers and flows are comparatively small but essential source <strong>of</strong> 

energy. Many rivers are avenues <strong>of</strong> transportation. They have also a great scenic and 

recreational value. 

The mean renewable global water resources are estimated at 42.785 km 3 /year, and 

<strong>the</strong>y are very variable with space and time. Table 2.7 presents <strong>the</strong> distribution <strong>of</strong> water 

resources and availability by <strong>the</strong> earth’s continents. This information is based on 

a water balance approach by Shiklomanov [311], who provided country data for 51 

countries on available water resources. O<strong>the</strong>r comprehensive world renewable publications 

are <strong>the</strong> early work <strong>of</strong> L’vovich [204], Gleick [115] and <strong>the</strong> World Resources 

Institute [410]. By an absolute value <strong>the</strong> largest water resources are characteristic 

<strong>of</strong> Asia and South America. The smallest are typical for Europe and Australia with 

Oceania. Due to rapid earth’s population, growth since 1970 to 1994, <strong>the</strong> potential 

water availability <strong>of</strong> earth’s population decreased form 12,9 to 7,6 km 3 per year and 

person. 

2.4.2.1 Stream, river and lake waters 

The nature <strong>of</strong> aqueous solutions that are produced or modified by <strong>the</strong> processes 

<strong>of</strong> wea<strong>the</strong>ring is determined by several factors, including chemical controls such as 

reaction rate, solubility and interface reactions, as well as environmental controls 

such as climate, geology and <strong>the</strong> hydrologic cycle. The solutions from wea<strong>the</strong>ring 

may mix with o<strong>the</strong>r waters that effectively have not been involved in a wea<strong>the</strong>ring 

process. In turn, <strong>the</strong> mixed waters may be modified by fur<strong>the</strong>r reactions such as by 

some cation exchange with clay or o<strong>the</strong>r <strong>mineral</strong> phases, or by <strong>the</strong> activities <strong>of</strong> man. 

3 Stream is defined as a body <strong>of</strong> water that carries rock particles and dissolved substances, and 

flows down a slope along a clearly defined path.


Table 2.7. Renewable water resources and potential water availability by continents 

[311]. 

Continent Area, Population, Water resources, Water availability, 

M km2 Millions 

1995 

km3 /year 1000m3 /year 

Average Max. Min. per km2 per 

capita 

Europe 10,46 685 2900 3410 2254 277 4,23 

North 

America 

24,3 453 7890 8917 6895 324 17,4 

Africa 30,1 708 4050 5082 3073 134 5,72 

Asia 43,5 3445 13510 15008 11800 311 3,92 

South 

America 

17,9 315 12030 14350 10320 672 38,2 

Australia 8,95 28,7 2404 2880 1891 269 83,7 

and 

niaOcea- 

World 135 5633 42785 44751 39775 317 7,6 

There is <strong>the</strong>refore a great variation in <strong>the</strong> concentrations <strong>of</strong> dissolved materials in 

lake, stream and river water. None<strong>the</strong>less an extensive amount <strong>of</strong> available data 

allowed Livingstone [197] to estimate <strong>the</strong> mean composition <strong>of</strong> world river water 

(see table 2.8). 

Table 2.8. Mean chemical contents <strong>of</strong> world river water [197] 

Substance Concentration µg/g 

HCO − 

3 

SO 

58,4 

2− 

4 

Cl 

11,2 

− 7,8 

1 

NO− 3 

Ca 2+ 15 

M g2+ 4,1 

N a + 6,3 

K + 2,3 

Fe2+ 0,67 

SiO2 13,1 

Sum 120 

Different compilations <strong>of</strong> <strong>the</strong> average concentration <strong>of</strong> <strong>the</strong> main trace elements found 

in rivers were later done by Li [196] and Gaillardet et al. [102]. The composition <strong>of</strong> 

Li is lited in table 2.9. 

Lake waters also vary greatly in composition, not only from lake to lake but <strong>of</strong>ten 

within a lake where marked temperature and compositional stratifications can occur. 

Reducing conditions <strong>of</strong>ten exist in <strong>the</strong> lower, more saline level <strong>of</strong> stratified lakes and


Table 2.9. The average concentrations <strong>of</strong> elements in filtered river water. Concentration 

in ppb. Adapted from Li [196]. 

Element Concentration Element Concentration 

Li 3 M o 0,6 

Be 0,01 Ag 0,3 

B 10 Cd 0,01 

F 100 In 

N a 6300 Sn 0,04 

M g 4100 S b 0,07 

Al 50 I 7 

Si 6500 Cs 0,02 

P 20 Ba 20 

S 3700 La 0,05 

Cl 7800 Ce 0,08 

K 2300 P r 0,007 

Ca 15000 N d 0,04 

Sc 0,004 Sm 0,008 

T i 3 Eu 0,001 

V 0,9 Gd 0,008 

C r 1 T b 0,001 

M n 7 Ho 0,001 

Fe 40 Er 0,004 

Co 0,1 T m 0,001 

N i 0,3 Y b 0,004 

Cu 7 Lu 0,001 

Zn 20 H f 

Ga 0,09 Ta 

Ge 0,005 W 0,03 

As 2 Re 

Se 0,06 Au 0,002 

Br 20 H g 0,07 

Rb 1 T l 

Sr 70 P b 1 

Y Bi 

Z r Th 0,1 

N b U 0,04


<strong>the</strong>se give rise to relatively high concentrations <strong>of</strong> nitrite ammonia and Fe 2+ in <strong>the</strong> 

water. The reducing conditions may also lead to <strong>the</strong> production <strong>of</strong> hydrogen sulphide 

gas and <strong>the</strong> precipitation <strong>of</strong> some metal sulphides (including iron sulphides). Silica 

and phosphorous may be released from <strong>the</strong> sediments. The <strong>the</strong>rmocline zone, which 

separates <strong>the</strong> upper and lower levels <strong>of</strong> a lake by a large change in temperature, 

prevents <strong>the</strong> diffusion <strong>of</strong> atmospheric oxygen to go into <strong>the</strong> reduction layer [137]. 

2.4.2.2 Ground waters 

As seen from table 2.3, less than 1% <strong>of</strong> <strong>the</strong> water on earth is ground water. Although 

<strong>the</strong> total volume <strong>of</strong> ground water is small, it is about 35 times greater than <strong>the</strong> volume 

<strong>of</strong> water lying in fresh-water lakes <strong>of</strong> flowing in streams on <strong>the</strong> earth’s surface. 

Nearly all <strong>the</strong> earth’s groundwater has its origin in rainfall. It is always slowly moving 

on its way back to <strong>the</strong> ocean, ei<strong>the</strong>r directly through <strong>the</strong> ground or by flowing 

out onto <strong>the</strong> surface and joining stream. 

The hydrogeochemistry <strong>of</strong> ground waters reflects <strong>the</strong> source <strong>of</strong> <strong>the</strong> water, <strong>the</strong> lithology 

<strong>of</strong> <strong>the</strong> aquifer and <strong>the</strong> local chemical conditions such as temperature, pressure 

and redox potential. White et al. [405] classified <strong>the</strong> source <strong>of</strong> ground waters as: 

• magmatic, 

• meteoric (e.g. precipitated and surface water), 

• connate (i.e. water trapped in <strong>the</strong> pore spaced <strong>of</strong> a sediment at <strong>the</strong> time <strong>of</strong> 

deposition), 

• oceanic. 

Extensive compilations <strong>of</strong> ground water compositions were recorded by White et al. 

[405]. Table 2.10 shows examples <strong>of</strong> constituents <strong>of</strong> ground waters in Maryland and 

New York from different rock types. 

2.4.3 Ice caps, ice sheets and glaciers 

Glaciers, ice sheets and ice caps are huge masses <strong>of</strong> ice, formed on land by <strong>the</strong> 

compaction and re-crystallization <strong>of</strong> snow, that move very slowly down slopes or 

move outward due to <strong>the</strong>ir own weight. If <strong>the</strong> rate <strong>of</strong> melting is greater than <strong>the</strong> 

rate <strong>of</strong> accumulation, <strong>the</strong> glacier recedes; if it is less, <strong>the</strong> glacier advances. Many 

recent studies on glacier run<strong>of</strong>f around <strong>the</strong> world have shown that <strong>the</strong> first tendency 

is ra<strong>the</strong>r happening presumably due to climate change. 

Around 10% <strong>of</strong> <strong>the</strong> earth’s surface is covered by glaciers (∼ 15, 9 × 10 6 km 2 glacierized 

vs 148, 8 × 10 6 <strong>of</strong> total land surface [185]). Approximately 91% <strong>of</strong> <strong>the</strong> earth’s 

land ice covers Antarctica, 8% Greenland and glaciers in o<strong>the</strong>r regions contribute


Table 2.10. Constituents <strong>of</strong> ground waters from different rock types. Concentrations 

in µg/g [405]. 

Substance Granite Serpentinite Shale 

Cations or oxide 

SiO 2 39 31 5,5 

Al 9 0,2 0 

Fe 1,6 0,06 3,5 

Ca 27 9,5 227 

M g 6,2 51 29 

N a 9,5 4 12 

K 1,4 2,2 2,7 

Anions 

HCO 3 93 276 288 

CO 3 0 0 0 

SO 4 32 2,6 439 

Cl 5,2 12 24 

F 0 0 0 

NO 3 7,5 6,8 0,9 

PO 4 0 0 0 

to around 1% (see table 2.11). Current annual global glacial run<strong>of</strong>f range from 

0,3×10 3 km 3 to 1×10 3 km 3 [173]. Glaciers are estimated to contribute to 0,6 to 

1% to <strong>the</strong> global annual run<strong>of</strong>f. 

There are two types <strong>of</strong> glaciers, those that are unconstrained by topography and 

blanket <strong>the</strong> topography, including ice sheets and ice caps, and those that are constrained 

by topography, mainly valley glaciers. Ice sheets cover areas which are 

typically > 5 × 10 4 km 2 (mostly found in Antarctica and Greenland), whereas ice 

caps cover smaller areas < 5×10 4 km 2 . Ice masses constrained by topography cover 

areas between 1 and 100 km 2 . Most research on <strong>the</strong> geochemical wea<strong>the</strong>ring <strong>of</strong> 

glaciers has been conducted mainly on valley glaciers. Fortunately it seems that to 

a first approximation, <strong>the</strong> biochemical processes inferred from <strong>the</strong> small systems are 

similar to those occurring in large systems [357]. 

Glaciers are very important to <strong>the</strong> stability <strong>of</strong> <strong>the</strong> environment. Changes in heat and 

atmosphere can cause glaciers to melt, change shape and move more rapidly and 

as a consequence, more land is reformed in its movement. Glaciers exert a direct 

influence on <strong>the</strong> hydrologic cycle by slowing <strong>the</strong> passage <strong>of</strong> water through <strong>the</strong> cycle. 

Like ground water, glaciers are considered to be key natural reservoirs <strong>of</strong> freshwater. 

They are <strong>the</strong>refore extremely important sources <strong>of</strong> water for human consumption, 

irrigation, electric power and o<strong>the</strong>r industrial uses, especially during <strong>the</strong> summer, 

when <strong>the</strong> highest rate <strong>of</strong> melting is reached and precipitation is more scarce.


Table 2.11. Area <strong>of</strong> land surface covered by glaciers in different regions <strong>of</strong> <strong>the</strong> world, 

toge<strong>the</strong>r with estimates <strong>of</strong> volume and <strong>the</strong> equivalent sea level rise that <strong>the</strong> volume 

implies [185]. 

Region Area, km 2 Volume, km 3 Sea level equivalent, 

m 

Antarctica 13600000 25600000 64 

Greenland 1730000 2600000 6 

North America 276000 

Asia 185000 

Europe 54000 200000 0,5 

South America 25900 

Australasia 860 

Africa 10 

Total 15900000 28400000 70,5 

2.4.3.1 The composition <strong>of</strong> glacial run<strong>of</strong>f 

The main source <strong>of</strong> water in most glacier systems is snow and/or ice melt. Some 

water is also derived from rain, and a little is derived from geo<strong>the</strong>rmal melting and 

internal deformation [257]. Table 2.12 shows <strong>the</strong> chemical composition <strong>of</strong> glacial 

run<strong>of</strong>f compiled by Brown [43] for different regions <strong>of</strong> <strong>the</strong> world. It also includes an 

estimation on <strong>the</strong> average composition <strong>of</strong> glaciers on earth, which is <strong>the</strong> weighted 

sum <strong>of</strong> <strong>the</strong> average compositions in each region. Glacial run<strong>of</strong>f is a dilute solution 

containing ions Ca2+ , HCO − 

3 , SO2− 

4 , with variable N a+ and Cl − . Glacial run<strong>of</strong>f is 

usually more dilute than global mean river4 . 

4 See table 2.8 for comparisons between river and glacier compositions.


Table 2.12. The concentration <strong>of</strong> major ions in glacial run<strong>of</strong>f from different regions <strong>of</strong> <strong>the</strong> world. Concentrations are reported in 

mg/l. Adapted from [43] 

Cl − 

SO 2− 

4 

Region Ca2+ M g2+ N a + K + HCO − 

3 

Greenland 2,60-3,40 0,82-1,19 1,79-2,53 0,20-0,35 13,42-20,74 4,32-9,60 0,27-0,51 

Antarctica 1,44-26,01 1,45-4,07 8,28-32,2 0,03-4,30 5,55-97,62 1,63-57,61 0,01-17,01 

Iceland 2,20-7,00 0,36-1,45 0,69-11,0 0,11-0,47 11,59-34,78 1,25-6,24 0,51 

Alaska 11,00 0,44 0,57 2,39 26,24 12,48 0,03 

Canadian high Arctic 5,20-52,01 0,25-7,75 0,02-4,37 0,0039-1,53 12,81-42,1 2,83-187,2 

Canadian rockies 19,20-22,0 3,51-3,75 0,09-0,83 0,23-0,36 54,3-56,13 18,24-24,96 0,03-0,43 

Cascades 0,70-1,60 0,10-0,24 0,06-0,39 0,38-1,45 5,06-6,10 0,38-1,39 

European alps 0,40-12,8 0,07-1,69 0,11-2,11 0,23-1,29 0,67-24,41 0,48-11,52 0,02-1,56 

Himalayas 1,50-11,8 0,08-2,78 0,57-1,49 0,86-1,99 12,20-44,54 7,68-19,68 0,02-0,37 

Norway 0,18-12,5 0,02-0,80 0,19-4,83 0,04-1,13 0,09-41,49 0,34-6,72 0,02-3,23 

Svalbard 2,40-20,0 1,20-6,54 2,53-6,21 0,20-1,60 6,71-57,35 4,61-36,49 0,09-5,27 

Average 12,69 2,59 18,44 1,98 48,15 27,38 7,71

The continental crust 37 

2.5 The continental crust 

The solid earth is composed by several layers. These can be classified into: core, 

mantle and crust. Figure 2.2 shows an earth cutaway with its different layers. The 

inner part <strong>of</strong> <strong>the</strong> earth is <strong>the</strong> core and is about 2900 km below <strong>the</strong> earth’s surface. 

The core is fur<strong>the</strong>r divided into <strong>the</strong> inner and outer core. The inner core, or center <strong>of</strong> 

<strong>the</strong> earth is solid and about 1250 km thick. The outer core (approx. 2200 km thick) 

is composed <strong>of</strong> high-density molten metals, highly concentrated in iron [403]. 

The core is surrounded by a solid mantle <strong>of</strong> iron-magnesium silicates and oxides. It 

contains <strong>the</strong> inner mantle (between 300 and 2890 km below <strong>the</strong> earth’s surface) and 

<strong>the</strong> outer mantle (between 10 and 300 km below <strong>the</strong> earth’s surface). 

The outer shell covering <strong>the</strong> mantle is called <strong>the</strong> crust. According to Rudnick [291], 

it constitutes only 0,6% <strong>of</strong> <strong>the</strong> silicate earth and is covered by geological rock formations 

and <strong>the</strong> oceans. It is made up <strong>of</strong> <strong>the</strong> oceanic and continental crust. The oceanic 

crust is 7 km on average thick and is composed <strong>of</strong> relatively rock types such as 

basalt. The continental crust is about 40 km thick and contains virtually every rock 

type known on earth. The structure <strong>of</strong> <strong>the</strong> continental crust is defined to consist <strong>of</strong> 

upper-, middle- and lower crustal layers. The deep continental crust is composed 

<strong>of</strong> granulite-facies rocks and begins at 23 km depth on average. The middle crust 

extends from 8 to 17 km depth. Estimates indicate that it is composed <strong>of</strong> rocks in 

<strong>the</strong> amphibolite facies. 

The upper continental crust is <strong>the</strong> reservoir <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s and o<strong>the</strong>r natural 

resources useful for mankind. Therefore, it will be our object <strong>of</strong> study. Fur<strong>the</strong>rmore, 

being <strong>the</strong> most accessible part <strong>of</strong> our planet, <strong>the</strong> upper crust has long been <strong>the</strong> target 

<strong>of</strong> geochemical investigations. According to Yoder [411], <strong>the</strong> mass <strong>of</strong> <strong>the</strong> upper 

continental crust is about half <strong>the</strong> mass <strong>of</strong> <strong>the</strong> total crust, this corresponds to a 

volume <strong>of</strong> 6, 55 × 10 20 cm 3 and thus a sphere with a radius <strong>of</strong> about 54±4 km as an 

upper limit. 

2.5.1 The chemical composition <strong>of</strong> <strong>the</strong> upper continental crust 

There are two basic methods employed to determine <strong>the</strong> composition <strong>of</strong> <strong>the</strong> upper 

crust [291]: 

• establishing weighted averages <strong>of</strong> <strong>the</strong> compositions <strong>of</strong> rocks exposed at <strong>the</strong> 

surface and, 

• determining averages <strong>of</strong> <strong>the</strong> composition <strong>of</strong> insoluble elements in fine-grained 

clastic sedimentary rocks or glacial deposits and using <strong>the</strong>se to infer uppercrust 

composition. 

The determination <strong>of</strong> <strong>the</strong> major-element composition <strong>of</strong> <strong>the</strong> upper continental crust 

relies on <strong>the</strong> first method. It has been used by a variety <strong>of</strong> authors starting with


Figure 2.2. Earth’s cutaway. Source: USGS [397] 

Clarke et al. in 1889 [58] and continuing with Ronov and Yaroshevsky [287], Shaw 

et al. [306], [308], Eade and Fahring [80], Condie [60] and Gao et al. [106]. The 

results <strong>of</strong> <strong>the</strong>se independent studies show a very similar composition for most majorelement 

averages, but not insignificant differences for rare earth elements (REEs). 

Estimates <strong>of</strong> <strong>the</strong> trace-element composition <strong>of</strong> <strong>the</strong> upper crust rely on <strong>the</strong> natural 

sampling processes <strong>of</strong> sedimentation and glaciation. This method was suggested by 

Goldschmidt [116], [117], using <strong>the</strong> idea that glacial clays are compositionally representative 

<strong>of</strong> <strong>the</strong> crust from which <strong>the</strong>y were derived. Elements that are insoluble 

during wea<strong>the</strong>ring are transported from <strong>the</strong> site <strong>of</strong> wea<strong>the</strong>ring/glacial erosion to deposition 

and <strong>the</strong>ir concentrations in sedimentary rocks may provide robust estimates 

<strong>of</strong> <strong>the</strong> average composition <strong>of</strong> <strong>the</strong>ir source regions. Relevant studies <strong>of</strong> <strong>the</strong> composition 

<strong>of</strong> <strong>the</strong> crust through <strong>the</strong>se methods are: Taylor and McLennan [353], [354], 

Plank and Langmuir [267] and <strong>the</strong> recent work <strong>of</strong> McLennan [215]. 

Table 2.13 shows average upper crustal compositions from <strong>the</strong> compilation works 

done by Wedepohl [404], McLennan [215] and <strong>the</strong> latest recommended composition 

<strong>of</strong> Rudnick et al. [292]. Rudnick et al. presented <strong>the</strong>ir best estimate for <strong>the</strong> chemical 

composition <strong>of</strong> <strong>the</strong> upper continental crust based mainly on averages <strong>of</strong> <strong>the</strong> different 

surface-exposure studies such as Shaw et al. [306], Fahring and Eade [93], Plank 

and Langmuir [267], Taylor and McLennan [353], McLennan [215], Sims et al. 

[314], Gao et al. [106], Teng et al. [355] or Newson et al. [243]. In <strong>the</strong> upper 

crust, only eight elements account for 99% <strong>of</strong> <strong>the</strong> weight; <strong>the</strong> most prominent among 

<strong>the</strong>se is O, accounting for almost 50% <strong>of</strong> <strong>the</strong> weight.

The continental crust 39 

Table 2.13: Average composition <strong>of</strong> <strong>the</strong> upper continental crust according 

to different studies. Elements in g/g. 

Element Wedepohl [404] McLennan [215] Rudnick et. al. [292] 

O 4,72E-01 4,72E-01 

Si 2,88E-01 3,08E-01 3,09E-01 

Al 7,96E-02 8,04E-02 8,15E-02 

Fe 4,32E-02 3,50E-02 3,92E-02 

Ca 3,85E-02 3,00E-02 2,57E-02 

Na 2,36E-02 2,89E-02 2,73E-02 

Mg 2,20E-02 1,33E-02 1,50E-02 

K 2,14E-02 2,80E-02 2,32E-02 

Ti 4,01E-03 4,10E-03 3,84E-03 

C 1,99E-03 

P 7,57E-04 7,00E-04 6,55E-04 

Mn 7,16E-04 6,00E-04 7,74E-04 

S 6,97E-04 6,20E-05 

Ba 5,84E-04 5,50E-04 6,28E-04 

F 5,25E-04 5,57E-04 

Cl 4,72E-04 3,70E-04 

Sr 3,33E-04 3,50E-04 3,20E-04 

Zr 2,03E-04 1,90E-04 1,93E-04 

Cr 1,26E-04 8,30E-05 9,20E-05 

V 9,80E-05 1,07E-04 9,70E-05 

Rb 7,80E-05 1,12E-04 8,40E-05 

Zn 6,50E-05 7,10E-05 6,70E-05 

Ce 6,00E-05 6,40E-05 6,30E-05 

N 6,00E-05 8,30E-05 

Ni 5,60E-05 4,40E-05 4,70E-05 

La 3,00E-05 3,00E-05 3,10E-05 

Nd 2,70E-05 2,60E-05 2,70E-05 

Cu 2,50E-05 2,50E-05 2,80E-05 

Co 2,40E-05 1,70E-05 1,73E-05 

Y 2,40E-05 2,20E-05 2,10E-05 

Nb 1,90E-05 1,20E-05 1,20E-05 

Li 1,80E-05 2,00E-05 2,40E-05 

Sc 1,60E-05 1,36E-05 1,40E-05 

Ga 1,50E-05 1,70E-05 1,75E-05 

Pb 1,48E-05 1,70E-05 1,70E-05 

B 1,10E-05 1,50E-05 1,70E-05 

Th 8,50E-06 1,07E-05 1,05E-05 

Pr 6,70E-06 7,10E-06 7,10E-06 

Sm 5,30E-06 4,50E-06 4,70E-06 

Hf 4,90E-06 5,80E-06 5,30E-06 

Gd 4,00E-06 3,80E-06 4,00E-06 

Dy 3,80E-06 3,50E-06 3,90E-06 

Cs 3,40E-06 4,60E-06 4,90E-06 

Be 2,40E-06 3,00E-06 2,10E-06 



Table 2.13: Average composition <strong>of</strong> <strong>the</strong> upper continental crust according 

to different studies. Elements in g/g. – continued from previous 

page. 

Element Wedepohl [404] McLennan [215] Rudnick et. al. [292] 

Sn 2,30E-06 5,50E-06 2,10E-06 

Er 2,10E-06 2,30E-06 2,30E-06 

Yb 2,00E-06 2,20E-06 1,96E-06 

As 1,70E-06 1,50E-06 4,80E-06 

U 1,70E-06 2,80E-06 2,70E-06 

Ge 1,40E-06 1,60E-06 1,40E-06 

Eu 1,30E-06 8,80E-07 1,00E-06 

Mo 1,10E-06 1,50E-06 1,10E-06 

Ta 1,10E-06 1,00E-06 9,00E-07 

Br 1,00E-06 1,60E-06 

W 1,00E-06 2,00E-06 1,90E-06 

Ho 8,00E-07 8,00E-07 8,30E-07 

I 8,00E-07 1,40E-06 

Tb 6,50E-07 6,40E-07 7,00E-07 

Tl 5,20E-07 7,50E-07 9,00E-07 

Lu 3,50E-07 3,20E-07 3,10E-07 

Sb 3,00E-07 2,00E-07 4,00E-07 

Tm 3,00E-07 3,30E-07 3,00E-07 

Se 1,20E-07 5,00E-05 9,00E-08 

Cd 1,00E-07 9,80E-08 9,00E-08 

Bi 8,50E-08 1,27E-07 1,60E-07 

Ag 7,00E-08 5,00E-08 5,30E-08 

In 5,00E-08 5,00E-08 5,60E-08 

Hg 4,00E-08 5,00E-08 

Te 5,00E-09 

Au 2,50E-09 1,80E-09 1,50E-09 

Pd 4,00E-10 5,00E-10 5,20E-10 

Pt 4,00E-10 5,00E-10 

Re 4,00E-10 4,00E-10 1,98E-10 

Ru 1,00E-10 3,40E-10 

Rh 6,00E-11 

Ir 5,00E-11 2,00E-11 2,20E-11 

Os 5,00E-11 5,00E-11 3,10E-11 

End <strong>of</strong> <strong>the</strong> table 

Although a lot <strong>of</strong> effort has been placed in determining <strong>the</strong> chemical composition 

<strong>of</strong> <strong>the</strong> upper continental crust, <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> it has been barely 

studied. This is due mainly to <strong>the</strong> complexity and heterogeneity <strong>of</strong> <strong>the</strong> earth’s crust. 

The <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> earth are related to <strong>the</strong> species contained in it 

and not to <strong>the</strong>ir elements, as we will see in later chapters. Therefore, a model <strong>of</strong> <strong>the</strong>

Summary <strong>of</strong> <strong>the</strong> chapter 41 

<strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> crust needs to be developed. This will be <strong>the</strong> aim 

<strong>of</strong> chapter 3. 

2.6 Summary <strong>of</strong> <strong>the</strong> chapter 

In order to determine <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> earth, <strong>the</strong> geochemistry 

<strong>of</strong> it must be analyzed in detail. For that purpose, <strong>the</strong> composition <strong>of</strong> each layer: 

atmosphere, hydrosphere and continental crust has to be studied in terms <strong>of</strong> substances. 

A comprehensive analysis <strong>of</strong> <strong>the</strong> physical and geochemical properties <strong>of</strong> <strong>the</strong> earth 

has been undertaken in this chapter. 

First, a coarse composition <strong>of</strong> <strong>the</strong> bulk earth with <strong>the</strong> relative mass proportions <strong>of</strong> 

each sphere has been presented. This overview has given way to <strong>the</strong> more detailed 

explanation <strong>of</strong> <strong>the</strong> geochemistry <strong>of</strong> <strong>the</strong> atmosphere, hydrosphere and upper continental 

crust. 

The atmosphere is <strong>the</strong> gaseous layer surrounding <strong>the</strong> earth. It is fur<strong>the</strong>r divided into 

different parts. The troposphere, being <strong>the</strong> lowest <strong>of</strong> all, is <strong>the</strong> layer with which 

human beings have more interaction. The chemical composition <strong>of</strong> <strong>the</strong> atmosphere 

is ra<strong>the</strong>r uniform to heights up to 100 km. Apart from <strong>the</strong> natural occurring gases, 

<strong>the</strong>re are traces <strong>of</strong> anthropogenic substances in <strong>the</strong> atmosphere that may alter <strong>the</strong> 

conditions on earth. 

The hydrosphere is <strong>the</strong> liquid water component <strong>of</strong> <strong>the</strong> earth and includes seas (constituting 

over 97% <strong>of</strong> it); renewable water resources (rivers, lakes and underground 

water); ice; and atmospheric water. The continuous motion <strong>of</strong> <strong>the</strong> hydrosphere is 

governed by <strong>the</strong> hydrological cycle. The composition <strong>of</strong> seawater is, as it happened 

to <strong>the</strong> atmosphere, quite uniform. Many components <strong>of</strong> <strong>the</strong> sea have a crustal origin. 

Never<strong>the</strong>less, it contains dissolved atmospheric gases such as CO 2, what makes 

oceans to be huge and crucial reservoirs <strong>of</strong> GhG gases. Although <strong>the</strong> relative small 

weight proportion, renewable water resources are essential for life on earth, as <strong>the</strong>y 

are <strong>the</strong> main sources <strong>of</strong> freshwater. No uniform composition can be applied to <strong>the</strong>m, 

but some examples and averages have been provided. Glaciers, ice sheets and ice 

caps are huge amounts <strong>of</strong> frozen freshwater, and as a consequence <strong>the</strong>y are important 

water suppliers for human beings. The composition <strong>of</strong> glacial run<strong>of</strong>f from <strong>the</strong> 

different regions <strong>of</strong> <strong>the</strong> world has been presented. 

The solid earth is composed by <strong>the</strong> core, mantle and crust. The crust is fur<strong>the</strong>r 

divided into <strong>the</strong> lower, middle and upper crust. The upper crust is <strong>the</strong> reservoir 

<strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s and o<strong>the</strong>r natural resources for mankind and being <strong>the</strong> most 

accessible, it is <strong>the</strong> best well studied part. Its chemical composition in terms <strong>of</strong> 

elements is well known. However, <strong>the</strong> <strong>mineral</strong>ogical composition has been barely 

studied.


In <strong>the</strong> next chapter, <strong>the</strong> only unknown composition <strong>of</strong> <strong>the</strong> earth’s outer spheres, 

<strong>the</strong> upper continental crust, will be analyzed in detail and a new methodology for 

obtaining its <strong>mineral</strong>ogical composition will be developed.

Chapter 3 

The <strong>mineral</strong>ogical composition <strong>of</strong> 

<strong>the</strong> upper continental crust 


In this chapter, a model <strong>of</strong> <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> earth’s crust is developed. 

The starting point <strong>of</strong> <strong>the</strong> model is <strong>the</strong> composition given by <strong>the</strong> Russian 

geochemist Grigor’ev. The new <strong>mineral</strong>ogical composition is constrained by <strong>the</strong> conservation 

<strong>of</strong> mass statement, which must be satisfied not only in <strong>the</strong> crust, but in <strong>the</strong> 

entire earth. Additionally, <strong>the</strong> model is given geological consistence, by introducing 

a series <strong>of</strong> assumptions based on geological observations. This information, will allow 

to obtain in fur<strong>the</strong>r chapters, <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> earth’s upper 

crust and to propose an approximation <strong>of</strong> <strong>the</strong> entropic planet. 

3.2 The classification <strong>of</strong> <strong>mineral</strong>s 

Minerals can be defined as natural occurring inorganic solids that possess an orderly 

internal structure and a definite chemical composition, whereas rocks are indefinite 

mixtures <strong>of</strong> naturally occurring substances, mainly <strong>mineral</strong>s. According to <strong>the</strong> International 

Mineralogical Association 1 <strong>the</strong>re are more than 4000 known <strong>mineral</strong>s. Of 

<strong>the</strong>se, around 150 can be called “common”, 50 are occasional and <strong>the</strong> rest are “rare” 

or “extremely rare”. 

Minerals can be classified according to different criteria including hardness, crystal 

structure, specific gravity, color, luster or cleavage. Table 3.1 shows one <strong>of</strong> <strong>the</strong> most 

commonly used <strong>mineral</strong> classifications based on <strong>the</strong> chemical composition. The most 

1 The International Mineralogical Association (IMA) is responsible for <strong>the</strong> approval <strong>of</strong> and naming 

<strong>of</strong> new <strong>mineral</strong> species found in nature. 

43

44 THE MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST 

Table 3.1. Mineral classification based on Dana’s New Mineralogy [103] 

I Native Elements 

II Sulfides 

III Oxides 

Hydroxides 

IV Halides 

V Carbonates 

Nitrates 

Borates 

VI Sulfates 

Chromates 

VII Phosphates 

Arsenates 

Vanadates 

Tungstates 

Molybdates 

VIII Silicates: 

- Nesosilicates 

- Sorosilicates 

- Cyclosilicates 

- Ionosilicates 

- Phyllosilicates 

- Tectosilicates 

IX Organic Minerals 

common <strong>mineral</strong>s are <strong>the</strong> silicates, accounting for more than 90% <strong>of</strong> <strong>the</strong> earth’s crust, 

whereas <strong>the</strong> most common non-silicates are carbonates, oxides and sulfides. 

Minerals can be fur<strong>the</strong>r classified into groups. Some <strong>of</strong> <strong>the</strong> main groups found in 

nature are now briefly discussed, indicating <strong>the</strong> principal <strong>mineral</strong>s included in each 

group. The information has been primarily extracted from Mason [209]. 

3.2.1 The silica <strong>mineral</strong>s 

Silica (SiO 2) occurs in nature as five different <strong>mineral</strong>s: quartz (including chalcedony), 

tridymite, cristobalite, opal and lechatelierite or silica glass. Of <strong>the</strong>se, 

quartz is very common, tridymite and cristobalite are widely distributed in volcanic 

rocks and can hardly be called rare; opal is not uncommon and lechatelierite is very 

rare. 

3.2.2 The feldspar group 

The feldspar are <strong>the</strong> most common <strong>of</strong> all <strong>mineral</strong>s. They are closely related in form 

and physical properties, but <strong>the</strong>y fall into two groups: <strong>the</strong> potassium and barium 

feldspars, which are monoclinic or very nearly monoclinic in symmetry, and <strong>the</strong>

The classification <strong>of</strong> <strong>mineral</strong>s 45 

sodium and calcium feldspars (plagioclases), which are triclinic. The general formula 

<strong>of</strong> feldspars can be stated as XAl(Al, Si)Si 2O 8, being X elements N a, K, Ca, 

and Ba. The barium-containing feldspars are very rare and <strong>of</strong> no importance as rockforming 

<strong>mineral</strong>s. The main K-feldspars are orthoclase, sanidine and microcline. In 

<strong>the</strong> plagioclase subgroup, albite, oligoclase, andesine, labradorite, bytownite and 

anorthite are <strong>the</strong> most important <strong>mineral</strong>s. 

3.2.3 The pyroxene group 

The pyroxenes are a group <strong>of</strong> <strong>mineral</strong>s closely related in crystallographic and o<strong>the</strong>r 

principal properties, as well as in chemical composition, although <strong>the</strong>y crystallize in 

two different systems, orthorhombic and monoclinic. Pyroxenes have <strong>the</strong> general 

formula X Y (Si, Al) 2O 6 (where X represents Ca, N a, Fe +2 and M g and more rarely 

Zn, M n and Li and Y represents ions <strong>of</strong> smaller size, such as C r, Al, Fe +3 , M g, 

M n, Sc, T i, V and even Fe +2 ). On <strong>the</strong> basis <strong>of</strong> chemical composition and crystal 

structure, <strong>the</strong> following species are recognized: enstatite and hyperstene (both orthorhombic), 

augite, clinoenstatite, clinohypers<strong>the</strong>ne, aegirine, diopside, pegeonite, 

jadeite, spodumene, pigeonite or hedenbergite (all monoclinic). 

3.2.4 The amphibole group 

The amphibole group comprises a number <strong>of</strong> species, which, although falling both 

in <strong>the</strong> orthorhombic and monoclinic systems, are closely related in crystallographic 

and o<strong>the</strong>r physical properties, as well as in chemical composition. They form isomorphous 

series, and extensive replacement <strong>of</strong> one ion by o<strong>the</strong>rs <strong>of</strong> similar size can take 

place, giving rise to very complex chemical compositions. The difference in chemical 

composition between compounds <strong>of</strong> <strong>the</strong> amphibole type and corresponding 

compounds <strong>of</strong> <strong>the</strong> pyroxene type is not great. A general formula for all members 

<strong>of</strong> <strong>the</strong> amphibole group can be written (W, X , Y ) 7−8(Z 4O 11) 2(O, OH, F) 2, in which 

symbols W, X, Y, Z indicate elements having similar ionic radii and capable <strong>of</strong> replacing 

each o<strong>the</strong>r. W stands for Ca, N a and K; X stands for M g and Fe +3 (sometimes 

M n); Y for T i, Al and Fe +3 ; and Z for Si and Al. The main amphibole <strong>mineral</strong>s 

are tremolite, actinolite, cummingtonite, hornblende, glaucophane, arfvedsonite or 

riebeckite. 

3.2.5 The olivine group 

The <strong>mineral</strong>s <strong>of</strong> <strong>the</strong> olivine group are silicates <strong>of</strong> bivalent metals and crystallize in 

<strong>the</strong> orthorhombic system. The composition <strong>of</strong> olivine generally corresponds closely 

to (M g, Fe) 2SiO 4, <strong>the</strong>re being little replacement by o<strong>the</strong>r elements. Minerals included 

in <strong>the</strong> olivine group are: forsterite, fayalite, olivine, tephroite, monticellite, 

glaucochroite and larsenite.


3.2.6 The mica group 

The <strong>mineral</strong>s <strong>of</strong> <strong>the</strong> mica group have in common <strong>the</strong> perfect basal cleavage easily 

recognizable. The composition <strong>of</strong> individual specimens may be very complex, but a 

general formula <strong>of</strong> <strong>the</strong> type W (X , Y ) 2−3Z 4O 10(OH, F) 2 can be written for <strong>the</strong> group 

as a whole. In this formula W is generally K or N a, X and Y represent Al, Li, M g, 

Fe 2+ , and Fe 3+ ; Z represents Si and Al, <strong>the</strong> Si:Al ratio being generally about 3:1. 

Some <strong>of</strong> <strong>the</strong> main mica <strong>mineral</strong>s are biotite, muscovite, paragonite, phologipte and 

lepidolite. 

3.2.7 The chlorite group 

The chlorites are a group <strong>of</strong> phyllosilicate <strong>mineral</strong>s. Chlorites can be described 

by <strong>the</strong> following four endmembers based on <strong>the</strong>ir chemistry via substitution <strong>of</strong> 

M g, Fe, N i, and M n in <strong>the</strong> silicate lattice: clinochlore (M g 5Al)(AlSi 3)O 10(OH) 8, 

chamosite (Fe 5Al)(AlSi 3)O 10(OH) 8, nimite (N i 5Al)(AlSi 3)O 10(OH) 8 and pennantite 

(M n, Al) 6(Si, Al) 4O 10(OH) 8. The formula that emphasizes <strong>the</strong> group is (M g, Fe) 3 

(Si, Al) 4O 10(OH) 2 · (M g, Fe) 3(OH) 6. And <strong>the</strong> main chlorite <strong>mineral</strong>s are besides 

<strong>of</strong> <strong>the</strong> ones mentioned above, clinochlore, ripidolite, pennantite, orthochamosite, 

thuringite or penninite. 

3.3 Grigor’ev’s <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> crust 

As explained in <strong>the</strong> previous chapter, a lot <strong>of</strong> effort has been placed in determining 

<strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> upper continental crust. The composition has been 

refined and improved with <strong>the</strong> studies <strong>of</strong> many different authors throughout <strong>the</strong> last 

century. Never<strong>the</strong>less, <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> it has been barely studied, 

because <strong>of</strong> <strong>the</strong> complexity and heterogeneity <strong>of</strong> <strong>the</strong> earth’s crust. 

A very general average <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> crust was obtained by 

Wedepohl 2 [402], [403], and Nesbitt and Young [242] (table 3.2). According to 

<strong>the</strong>se studies, only ten types <strong>of</strong> <strong>mineral</strong>s are <strong>the</strong> main constituents <strong>of</strong> <strong>the</strong> upper 

crust. 

A more comprehensive study <strong>of</strong> <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> upper crust 

was recently carried out by Grigor’ev [127]. He calculated <strong>the</strong> average contents 

<strong>of</strong> rock forming and accessory <strong>mineral</strong>s in <strong>the</strong> upper part <strong>of</strong> <strong>the</strong> continental crust 

through <strong>the</strong> model <strong>of</strong> Ronov et al. [288]. The average composition <strong>of</strong> 208 <strong>mineral</strong>s 

in <strong>the</strong> rocks <strong>of</strong> <strong>the</strong> upper crust was already calculated by <strong>the</strong> same author for <strong>the</strong> 

first time in year 2000 [124]. The calculations were based on <strong>the</strong> quantitatively 

analysis published in <strong>the</strong> literature <strong>of</strong> more than 3000 rock samples published mainly 

2 The <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> crust given by Wedepohl was calculated using <strong>the</strong> <strong>mineral</strong> 

composition <strong>of</strong> magmatic rocks.

Grigor’ev’s <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> crust 47 

Table 3.2. Crustal abundance <strong>of</strong> <strong>mineral</strong>s. Data in percent volume. 

Mineral Wedepohl [402] Nesbitt and Young [242] 

Quartz 21,0 23,2 

Plagioclase 41,0 39,9 

Orthoclase 21,0 12,9 

Biotite 4,0 8,7 

Muscovite 5,0 

Chlorite 2,2 

Amphiboles 6,0 2,1 

Pyroxenes 4,0 1,4 

Olivines 0,6 0,2 

Oxides 2,0 1,6 

O<strong>the</strong>rs 0,5 3,0 

in <strong>the</strong> USSR and USA. In Grigor’ev’s 2007 [127] publication, additional data was 

considered. The average content in rocks <strong>of</strong> 265 <strong>mineral</strong>s, <strong>the</strong>ir varieties and <strong>the</strong>ir 

non-<strong>mineral</strong> materials were calculated. The content <strong>of</strong> 80 fundamental <strong>mineral</strong>s 

<strong>of</strong> <strong>the</strong> list was corrected, in order to ensure <strong>the</strong> mass balance with <strong>the</strong> chemical 

composition <strong>of</strong> <strong>the</strong> elements in <strong>the</strong> rocks. The output is <strong>the</strong> result <strong>of</strong> a partiallyquantitative 

<strong>mineral</strong>ogical analysis. His main bibliographical sources were [38], 

[119], [126], [228] and [301]. 

Table 3.3: Average <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> upper continental crust 

according to Grigor’ev [127]. Results are given in mass percentage. 

Mineral Abundance, mass % 

Native Elements 

Copper 4,10E-07 

Silver 1,20E-07 

Gold 1,80E-08 

Lead 1,80E-07 

Polixene 3,00E-10 

I-Platinum 3,00E-10 

Zinc 4,70E-08 

Bismuth 4,90E-08 

Tin 4,40E-08 

Graphite 1,20E-01 

Moissonite 7,00E-07 

Sulphur 9,00E-05 

Sulphides 

Tetradymite 1,60E-08 

Chalcocite 1,80E-07 

Bornite 2,20E-06 

Acanthite 3,90E-08 

Argentite 7,10E-08 

Pentlandite 8,40E-05 

Sphalerite 4,60E-05 




according to Grigor’ev [127]. Results are given in mass percentage. – continued 

from previous page. 


Metacinnabar 7,60E-10 

Chalcopyrite 1,10E-04 

Tetrahedrite 5,70E-08 

Freibergite 3,90E-08 

Fahlerz Group 

Cubanite 6,00E-06 

Pyrrhotite 2,90E-02 

Troilite 2,00E-07 

Nickeline 5,10E-06 

Galena 1,90E-05 

Cinnabar 5,90E-08 

Covellite 3,60E-06 

Cooperite 3,00E-10 

Antimonite/ Stibnite 4,40E-09 

Bismuthinite 9,20E-08 

Stephanite 3,50E-08 

Samsonite 2,80E-09 

Boulangerite 4,00E-10 

Pyrargirite 7,40E-08 

Violarite 7,60E-06 

Pyrite 6,30E-02 

Marcasite 1,20E-03 

Vaesite 7,60E-06 

Cobaltite 8,40E-07 

Gersdorffite 3,00E-06 

Lollingite 5,00E-10 

Arsenopyrite 8,80E-06 

Molybdenite 1,20E-05 

Realgar 2,80E-08 

Orpiment 8,50E-07 

Halides 

Halite 1,90E-01 

Chlorargyrite 4,50E-09 

Sylvite 6,60E-04 

Fluorite 2,20E-03 

Bisch<strong>of</strong>ite 2,60E-05 

Carnallite 1,30E-04 

Oxides 

Periclase 2,40E-08 

Spinel 2,40E-03 

Pleonaste 1,10E-05 

Magnetite 6,50E-01 

Ulvöspinel 6,60E-02 

Jacobsite 3,00E-04 

Chromite 1,90E-04 

Iotsite 1,40E-06 

Corundum 3,80E-03 

Hematite 7,90E-02 







Ilmenite 1,90E-01 

Perovskite 2,80E-05 

Loparite 1,00E-06 

Pyrochlore 1,00E-06 

Microlite 7,60E-09 

Quarz 2,40E+01 

Tridymite 6,60E-05 

Cristobalite 1,30E-03 

Opal 1,30E+00 

Pyrolusite 5,40E-04 

Rutile 1,10E-02 

Cassiterite 2,50E-06 

Hollandite 6,40E-04 

Ilmenorutile 2,50E-05 

Cryptomelane 2,50E-04 

Psilomelane 3,10E-04 

Todorokite 8,60E-05 

Vernadite 2,60E-05 

Anatase 1,80E-03 

Brookite 1,70E-05 

Columbite 6,60E-06 

Ferrotantalite 2,60E-07 

Delorenzite/ Tanteuxenite 6,60E-09 

Polycrase 4,00E-11 

Euxenite 6,60E-06 

Blomstrandite/ Betafite 9,00E-07 

Fergusonite 2,40E-06 

Baddeleyite 3,10E-07 

Thorianite 3,40E-08 

Uraninite 6,60E-06 

Hydroxides 

Hydragillite/ Gibbsite 4,30E-02 

Diaspore 5,50E-02 

Brucite 2,50E-04 

Goethite 8,50E-02 

Manganite 1,50E-04 

Boehmite 1,80E-02 

Carbonates 

Magnesite 1,50E-02 

Smithsonite 3,70E-08 

Siderite 1,20E-01 

Mg-Siderite 5,90E-03 

Rhodochrosite 1,20E-03 

Calcite 3,98E+00 

Dolomite 7,00E-01 

Ankerite 3,10E-02 

Aragonite 3,80E-02 

Strontianite 2,00E-07 







Cerussite 6,30E-07 

Azurite 2,50E-06 

Malachite 2,00E-06 

Dawsonite 1,80E-04 

Bastnasite 3,20E-04 

Bismutite 1,10E-07 

Sulphates 

Anhydrite 4,50E-02 

Celestine 1,70E-04 

Anglesite 3,30E-07 

Barite 7,30E-04 

Alunite 7,60E-09 

Jarosite 4,00E-04 

Kieserite 6,70E-04 

Gypsum 2,40E-02 

Wolframates 

Wolframite 7,80E-07 

Powellite 4,00E-08 

Scheelite 6,50E-06 

Wulfenite 4,00E-09 

Phosphates 

Xenotime 3,70E-05 

Monazite 1,30E-03 

Rhabdophane 3,30E-07 

Amblygonite 4,90E-08 

Apatite 1,30E-01 

Francolite 8,30E-03 

Britholite 2,10E-06 

Vivianite 1,30E-07 

Weinschenkite/ Churchite 3,70E-08 

Metatorbenite 7,40E-09 

Nesosilicates (single tetrahedrons) 

Phenakite 4,00E-06 

Forsterite 1,10E-02 

Olivine 3,70E-02 

Fayalite 3,90E-03 

Tephroite 1,40E-03 

Almandine 8,50E-01 

Spessartine 2,60E-03 

Grossular 2,50E-03 

Andradite 1,20E-03 

Zircon 1,00E-02 

Naegite 3,30E-08 

Tsirtolite 1,90E-06 

Thorite 5,70E-05 

Uranium-Thorite 8,60E-08 

Sillimanite 3,10E-01 







Andalusite 6,30E-02 

Distene/ Kyanite 2,20E-02 

Topaz 4,60E-04 

Staurolite 5,10E-02 

Sapphirine 2,20E-03 

Kornerupine 6,00E-04 

Chondrodite 2,20E-05 

Humite 1,00E-03 

Clinohumite 1,50E-03 

Braunite 2,70E-03 

Gadolinite 4,00E-06 

Titanite 1,80E-01 

Leucoxene 1,50E-02 

Murmanite 1,70E-05 

Dumortierit 7,60E-09 

Thortveitite 7,60E-09 

Yttrialite 1,60E-05 

Wohlerite 1,30E-11 

Lovenite/ Lavenite 2,50E-07 

Rinkolite/ Mosandrite 5,30E-09 

Lamprophyllite 5,00E-06 

Bertrandite 4,00E-06 

Lawsonite 2,40E-01 

Clinozoisite 4,10E-02 

Epidote 1,17E+00 

Zoisite 3,10E-02 

Orthite/ Allanite 4,80E-03 

Chevkinite 4,20E-07 

Pumpellyite 1,50E-02 

Vesubianite/ Idocrase 2,70E-02 

Prehnite 1,70E-01 

Cyclosilicates 

Eudialyte 1,10E-05 

Neptunite 2,50E-06 

Axinite -Fe 1,10E-05 

Beryl 1,60E-04 

Nordite 5,50E-08 

Cordierite 8,80E-03 

Tourmaline 4,30E-03 

Chrysocolla 2,70E-09 

Inosilicates (single and double chains) 

Pigeonite 6,90E-02 

Diopside 4,80E-01 

Hedenbergite 8,20E-03 

Ferrosilite 5,00E-02 

Spodumene 9,60E-07 

Jadeite 2,90E-03 

Aegirine 9,00E-02 







Omphacite 2,50E-04 

Augite 1,21E+00 

Enstatite 4,40E-02 

Bronzite 6,50E-02 

Hypers<strong>the</strong>ne 4,30E-01 

Cummingtonite 4,60E-01 

Tremolite 5,50E-02 

Actinolite 3,90E-01 

Riebeckite 1,70E-01 

Arfvedsonite 3,10E-03 

Glaucophane 1,50E-03 

Crossite 5,10E-02 

Hastingsite 3,10E-01 

Hornblende 3,16E+00 

Anthophyllite 3,30E-03 

Gedrite 5,10E-03 

Aenigmatite 1,10E-04 

Wollastonite 5,70E-04 

Rhodonite 3,30E-04 

Miserite 1,80E-07 

Ramsayite/ Lorenzenite 5,00E-06 

Phyllosilicates (sheets) 

Talc 4,60E-02 

Pyrophyllite 1,00E-03 

Paragonite 5,60E-01 

Muscovite 1,99E+00 

Glaukonite 1,30E-01 

Phengite 3,90E-02 

Phlogopite 1,30E-02 

Biotite 7,49E+00 

Lepidomelane/ Annite 7,60E-02 

Hydromuscovite/ Illite 2,51E+00 

Hydrobiotite 4,80E-01 

Stilpnomelane 2,80E-02 

Montmorillonite 4,30E-01 

Beidellite 1,60E-01 

Nontronite 5,70E-01 

Vermiculite 5,40E-02 

Pennine 2,70E-01 

Clinochlore 6,90E-01 

Ripidolite/ Cinochlore 1,89E+00 

Sepiolite 5,50E-01 

Thuringite/ Chamosite 1,20E-01 

Clementite 4,00E-03 

Chloritoid 3,30E-04 

Kaolinite 2,60E-01 

Serpentine/ Clinochrysotile 7,20E-02 

Garnierite/ Falcondoite 1,30E-05 







Hisingerite 1,80E-04 

Palygorskite 1,80E-04 

Tectosilicates (framework) 

Nepheline 6,20E-03 

Analcime 6,60E-03 

Anorthite 3,30E-02 

Bytownite 3,00E-01 

Labradorite 3,02E+00 

Andesine 6,56E+00 

Oligoclase 1,43E+01 

Albite 4,00E+00 

Orthoclase 9,81E+00 

Sanidine 6,10E-02 

Cancrinite 2,20E-05 

Sodalite 6,40E-05 

Hydrosodalite 2,50E-05 

Nosean 2,50E-04 

Helvine/ Helvite 4,00E-06 

Scapolite 1,80E-02 

Natrolite 8,80E-02 

Thomsonite 6,00E-02 

Palagonite 1,70E-02 

Basic Crystal 3,10E-01 

Acid Crystal 3,10E-02 

C org 1,10E-01 

Sum 99,51 


According to Grigor’ev’s composition, <strong>the</strong> molecular weight <strong>of</strong> <strong>the</strong> earth’s upper crust 

is 142,1 g/mole 3 . This value is important, because it will be required for <strong>the</strong> calculation 

<strong>of</strong> <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> elements, discussed in chapter 5. 

Grigor’ev’s <strong>mineral</strong>ogical composition, although comprehensive, does not satisfy <strong>the</strong> 

mass balance <strong>of</strong> <strong>the</strong> earth. In <strong>the</strong> next section, a methodology for obtaining <strong>the</strong> average 

composition <strong>of</strong> <strong>the</strong> earth’s crust is developed, assuring that all species comprising 

<strong>the</strong> analysis are ma<strong>the</strong>matically, chemically and geologically consistent. 

3 The calculation <strong>of</strong> <strong>the</strong> average molecular weight <strong>of</strong> <strong>the</strong> crust is carried out through <strong>the</strong> weighted 

sum <strong>of</strong> <strong>the</strong> molecular weights <strong>of</strong> each <strong>mineral</strong> considered. The chemical composition and molecular 

weights <strong>of</strong> <strong>the</strong> substances listed in table 3.3 are given in table 3.5.


3.4 A new model <strong>of</strong> <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> 

earth’s crust 

3.4.1 The mass balance 

As explained in section 2.2, <strong>the</strong> earth can be assumed to be a closed system, with 

a fixed number <strong>of</strong> substances contained in it. Hence, it will always be true that <strong>the</strong> 

total mass <strong>of</strong> <strong>the</strong> earth is constant. 

As an example, let us consider a very simplified earth containing ξ i species (CO 2, 

H 2O, O 2, N 2, CaSO 4 · 2H 2O and CaCO 3), composed by ε j chemical elements 

(C, H, O, N, S, Ca), where ξ i and ε j are expressed in moles <strong>of</strong> <strong>the</strong> substance per 

gram <strong>of</strong> earth (mole/g). Then, <strong>the</strong> system <strong>of</strong> equations defined in Eq. 3.1 has to be 

satisfied [369]: 

Σr j,i · ξ i = ε j 

(3.1) 

being R <strong>the</strong> stoichiometric coefficient matrix <strong>of</strong> <strong>the</strong> species <strong>of</strong> dimensions [ j × i], as 

in <strong>the</strong> next table. 

i→ 1 2 3 4 5 6 j 

CO 2 H 2O O 2 N 2 CaSO 4 · 2H 2O CaCO 3 ↓ 

1 0 0 0 0 1 C 1 

0 2 0 0 4 0 H 2 

R[j × i] = 4 1 2 0 6 1 O 3 

0 0 0 2 0 1 N 4 

0 0 0 0 1 0 S 5 

0 0 0 0 1 0 Ca 6 

The resolution <strong>of</strong> <strong>the</strong> system <strong>of</strong> equations for vector ξ gives <strong>the</strong> general expression 

<strong>of</strong> ξi = εj · r −1 

j,i . In our particular case, this is: 

(i=1) CO 2 ξ 1 = C + S − Ca 

(i=2) H 2O ξ 2 = H/2 − 2S 

(i=3) O 2 ξ 3 = −C + O/2 − H/4 − 3S/2 − Ca/2 

(i=4) N 2 ξ 4 = N/2 

(i=5) CaSO 4 · 2H 2O ξ 5 = S 

(i=6) CaCO 3 ξ 6 = Ca − S 

As it happens to <strong>the</strong> entire earth, <strong>the</strong> substances contained in each sphere <strong>of</strong> our 

planet can be considered to be constant. Therefore, <strong>the</strong> same methodology is applied 

for <strong>the</strong> components <strong>of</strong> <strong>the</strong> atmosphere, hydrosphere and continental crust.

A new model <strong>of</strong> <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> earth’s crust 55 

3.4.2 The mass balance applied to <strong>the</strong> continental crust 

If <strong>the</strong> continental crust is assumed to be a closed system, <strong>the</strong> elements contained in 

<strong>the</strong> <strong>mineral</strong>s <strong>of</strong> <strong>the</strong> crust, must be equal to <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> crust. If 

we assume to be correct <strong>the</strong> chemical composition defined by Rudnick et al. [292] 

given in table 2.13, <strong>the</strong> application <strong>of</strong> Eq. 3.1 to Grigor’ev’s analysis, should give as 

result Rudnick’s values. 

However, <strong>the</strong> output <strong>of</strong> <strong>the</strong> mass balance between species and elements for Grigorev’s 

analysis does not correspond to <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> upper earth’s 

crust determined by Rudnick et al. [292], i.e. ˆε j = ε j (see table 3.4) 4 . Additionally, 

not all <strong>the</strong> elements compiled in <strong>the</strong> chemical composition are taken into account in 

<strong>the</strong> <strong>mineral</strong>s <strong>of</strong> Grigor’ev’s analysis (Grigor’ev accounts for 56 elements, as opposed 

to <strong>the</strong> 78 included in Rudnick et al. study). The reason for which many elements 

are missing in Grigor’ev’s analysis is because many <strong>of</strong> <strong>the</strong>m are minor elements not 

appearing with enough concentration in <strong>the</strong> crust in order to form by <strong>the</strong>mselves 

<strong>mineral</strong> phases. They usually replace major elements in crystal structures. The ability 

<strong>of</strong> certain different elements to exist in place <strong>of</strong> each o<strong>the</strong>r in certain points <strong>of</strong> a 

space lattice is called Diadochy. 

Table 3.4: Comparison <strong>of</strong> Rudnick and Gao’s [292] chemical composition <strong>of</strong> 

<strong>the</strong> upper earth’s crust and <strong>the</strong> one generated by Grigor’ev [127] according 

to Eq. 3.1. 

Element Rudnick and Gao [292] From Grigorev [127] Difference 

ˆε j · MW j, g/g ε j · MW j, g/g (ˆε j-ε j)/ˆε j, % 

O 4,72E-01 4,76E-01 -0,76 

Si 3,09E-01 2,86E-01 7,18 

Al 8,15E-02 7,02E-02 13,86 

Fe 3,92E-02 3,58E-02 8,59 

Na 2,73E-02 1,99E-02 27,08 

Ca 2,57E-02 3,86E-02 -50,54 

K 2,32E-02 2,43E-02 -4,68 

Mg 1,50E-02 2,25E-02 -50,18 

Ti 3,84E-03 1,50E-03 60,95 

C 1,99E-03 8,22E-03 -313,26 

Mn 7,74E-04 6,02E-05 92,22 

P 6,55E-04 2,53E-04 61,43 

Ba 6,28E-04 5,84E-06 99,07 

S 6,20E-04 6,13E-04 1,19 

F 5,57E-04 1,09E-03 -95,46 

Cl 3,70E-04 1,19E-03 -222,54 

Sr 3,20E-04 8,13E-07 99,75 

Zr 1,93E-04 4,98E-05 74,18 

Continued on next page . . . 

4 In table 3.4, <strong>the</strong> values are expressed in g <strong>of</strong> substance per g <strong>of</strong> crust, since this is <strong>the</strong> usual 

way found in <strong>the</strong> literature <strong>of</strong> expressing <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> crust. This means that ε j is 

multiplied by <strong>the</strong> molecular weight <strong>of</strong> <strong>the</strong> substance MW j.




to Eq. 3.1. – continued from previous page. 



V 9,70E-05 

Cr 9,20E-05 8,83E-07 99,04 

Rb 8,40E-05 

N 8,30E-05 100,00 

Zn 6,70E-05 3,11E-07 99,54 

Ce 6,30E-05 8,18E-06 87,01 

Ni 4,70E-05 4,07E-07 99,13 

La 3,10E-05 3,91E-06 87,39 

Cu 2,80E-05 4,64E-07 98,34 

Nd 2,70E-05 1,57E-06 94,20 

Li 2,40E-05 5,66E-10 100,00 

Y 2,10E-05 9,98E-07 95,25 

Ga 1,75E-05 

Co 1,73E-05 2,98E-09 99,98 

B 1,70E-05 1,45E-06 91,48 

Pb 1,70E-05 4,84E-07 97,15 

Sc 1,40E-05 1,83E-11 

Nb 1,20E-05 1,19E-07 99,01 

Th 1,05E-05 1,09E-06 89,66 

Pr 7,10E-06 

Hf 5,30E-06 

Cs 4,90E-06 

As 4,80E-06 9,24E-08 98,07 

Sm 4,70E-06 1,22E-09 99,97 

Gd 4,00E-06 

Dy 3,90E-06 

U 2,70E-06 5,97E-08 97,79 

Er 2,30E-06 

Be 2,10E-06 9,64E-08 95,41 

Sn 2,10E-06 2,01E-08 99,04 

Yb 1,96E-06 2,39E-07 87,82 

W 1,90E-06 4,63E-08 97,56 

Br 1,60E-06 

Ge 1,40E-06 

I 1,40E-06 

Mo 1,10E-06 7,22E-08 93,44 

Eu 1,00E-06 

Ta 9,00E-07 1,60E-08 98,22 

Tl 9,00E-07 

Ho 8,30E-07 

Tb 7,00E-07 

Sb 4,00E-07 5,04E-10 99,87 

Lu 3,10E-07 

Tm 3,00E-07 

Bi 1,60E-07 2,23E-09 98,60 

Se 9,00E-08 

Cd 9,00E-08 





to Eq. 3.1. – continued from previous page. 



In 5,60E-08 

Ag 5,30E-08 3,04E-09 94,26 

Hg 5,00E-08 5,16E-10 98,97 

Te 5,00E-09 5,79E-11 98,84 

Au 1,50E-09 1,80E-10 88,00 

Pd 5,20E-10 5,14E-13 99,90 

Pt 5,00E-10 4,89E-12 99,02 

Ru 3,40E-10 

Re 1,98E-10 

Rh 6,00E-11 

Os 3,10E-11 

Ir 2,20E-11 

SUM 1,00 0,98 


Assuming that <strong>the</strong> average chemical composition <strong>of</strong> Rudnick and Gao [292] is correct, 

if <strong>the</strong> difference between <strong>the</strong> mass content <strong>of</strong> a specific element given by Rudnick 

(ˆε j) and that included in <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> crust given by 

Grigor’ev (ε j) is positive, i.e. ˆε j − ε j > 0, <strong>the</strong>n it can be due to two factors: 

1. The quantity <strong>of</strong> one or more <strong>mineral</strong>s containing <strong>the</strong> specific element under 

consideration is greater than <strong>the</strong> assumption done by Grigor’ev. 

2. There are o<strong>the</strong>r <strong>mineral</strong>s not included in Grigorev’s analysis or ores containing 

not insignificant quantities <strong>of</strong> <strong>the</strong> element under consideration. 

On <strong>the</strong> o<strong>the</strong>r hand, if <strong>the</strong> difference is negative (ˆε j −ε j < 0), it is clear that Grigor’ev 

overestimated <strong>the</strong> quantity <strong>of</strong> <strong>the</strong> <strong>mineral</strong> or <strong>mineral</strong>s containing <strong>the</strong> element under 

consideration. 

Basing on Grigorev’s analysis, a new <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> upper continental 

crust m i=1 ˆ ξi will be calculated. The model will be optimized so that it 

complies with <strong>the</strong> following requirements: 

1. The mass balance between species and elements must be satisfied. 

j r j,i · 

ˆξ i = ˆε j, being ˆε j <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> upper crust determined by 

Rudnick et al. [292]. 

2. The mass content <strong>of</strong> every <strong>mineral</strong> in <strong>the</strong> crust must be always greater than 

zero, i.e. ˆ ξ i > 0.


3. Generally, <strong>the</strong> relative proportions <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s in Grigorev’s model will be 

kept if constraints 1 and 2 are satisfied. 

4. If an important 5 <strong>mineral</strong> <strong>of</strong> a certain element is not considered in Grigor’ev 

analysis, it will be included in our model, making reasonable assumptions on 

its abundance based on <strong>the</strong> literature. 

Next, <strong>the</strong> <strong>mineral</strong>s <strong>of</strong> each element found in <strong>the</strong> upper continental crust will be 

briefly described, stressing out <strong>the</strong>ir main uses, terrestrial abundance and distribution. 

The specific optimization method for each element will be also outlined 6 . The 

information about uses and main <strong>mineral</strong>s and ores <strong>of</strong> <strong>the</strong> different elements has 

been extracted mainly from geochemical books: Wedepohl [402], [403] and Greenwood 

and Earnshaw [122]; <strong>mineral</strong> books and databases: Hey [140], Duda [77], 

<strong>the</strong> Geochemical Earth Reference Model [329], [114], Jolyon [172] and Bar<strong>the</strong>lmy 

[21]; and from commodity databases: US Geological Survey (USGS) [363] and 

British Geological Survey (BGS) [28]. 

The descriptive procedure for obtaining <strong>the</strong> <strong>mineral</strong>ogical composition shown next, 

is represented in a ma<strong>the</strong>matical way in section 3.5. 

3.4.3 Aluminium 

Aluminium is a light, malleable, ductile, easily machined and strong metal used 

for many different applications. It has excellent corrosion resistance and durability. 

Some <strong>of</strong> <strong>the</strong> many uses for aluminium are in transportation (automobiles, aircraft, 

trucks railcars, marine vessels, etc.), packaging (cans, foil, etc.), transmission lines, 

machinery, mirrors, cooking utensils, water treatment, etc. 

Aluminium is <strong>the</strong> most abundant metal in <strong>the</strong> earth’s crust. It is a major constituent 

<strong>of</strong> many common igneous <strong>mineral</strong>s, including feldspars and micas. Aluminim is a 

very reactive metal and it requires a lot <strong>of</strong> energy to extract it from its ore bauxite, 

which is composed mainly <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s gibbsite Al(OH) 3, diaspore AlO(OH) and 

boehmite AlO(OH). Therefore, recovery <strong>of</strong> this metal from scrap has become so 

important and about 50% <strong>of</strong> its production comes from recycled Al. 

In our model <strong>of</strong> continental crust, we have considered 84 Al-containing <strong>mineral</strong>s, 

one more than in Grigorev’s analysis. Their abundance in <strong>the</strong> earth’s crust will be 

determined applying <strong>the</strong> constraints explained above. 

5A <strong>mineral</strong> is considered to be important here, especially when it constitutes an ore <strong>of</strong> a certain 

element. 

6Note that when we refer to percentages in <strong>the</strong> optimization process, <strong>the</strong>y are always based on a 

volume basis.


3.4.4 Antimony 

Antimony is a semimetallic chemical element increasingly being used in <strong>the</strong> semiconductor 

industry. As an alloy, it increases lead’s durability and mechanical strength. 

Antimony compounds are used to make flame-pro<strong>of</strong>ing materials, paints, glass and 

pottery. 

Stibnite S b 2S 3 is <strong>the</strong> most important ore <strong>of</strong> antimony and it occurs in large quantities 

in China, South Africa, Mexico, Bolivia and Chile. O<strong>the</strong>r sulfide ores include 

ullmanite N iS bS, livingstonite H gS b 4S8, boulangerite P b 5S b 4S 11 or jamesonite 

FeP b 4S b 6S 14 and small amounts <strong>of</strong> oxide <strong>mineral</strong>s formed by wea<strong>the</strong>ring are also 

known. Considerable amounts <strong>of</strong> S b are also obtained as a byproduct in lead and 

copper refining, especially from galena. 

Grigorev’s S b <strong>mineral</strong>s are stibnite, boulangerite, tetrahedrite and <strong>the</strong> silver <strong>mineral</strong>s 

samsonite, freibergite, stephanite and pyrargirite. Since stibnite is by far <strong>the</strong> 

most important <strong>mineral</strong> <strong>of</strong> S b, <strong>the</strong> quantity <strong>of</strong> that <strong>mineral</strong> on earth should presumably 

account for a very important part <strong>of</strong> S b in <strong>the</strong> crust. The quantity <strong>of</strong> antimony 

in stibnite considered by Grigor’ev is about four orders <strong>of</strong> magnitude smaller than 

Rudnick’s S b estimations in <strong>the</strong> upper crust. Therefore, we will ignore Grigorev’s 

estimations about stibnite and assume that most S b comes at equal rates from stibnite 

and in solution with galena P bS. Grigorev’s estimation for boulangerite and 

tetrahedrite will be assumed to be correct. The quantity <strong>of</strong> <strong>the</strong> Sb-Ag-containing 

<strong>mineral</strong>s are fixed by <strong>the</strong>ir silver content. 

3.4.5 Arsenic 

Arsenic is a semi-metallic poisonous element. Its compounds are used as insecticides 

<strong>of</strong> fruit trees, as wood preservatives, in making special types <strong>of</strong> glass and lately, in 

<strong>the</strong> semiconductor gallium arsenade, which has <strong>the</strong> ability to convert electric current 

to laser light. Many o<strong>the</strong>r arsenic compounds used in <strong>the</strong> past have fallen out <strong>of</strong> use 

due to <strong>the</strong>ir toxicity and reactivity. 

Arsenic <strong>mineral</strong>s are widely distributed throughout <strong>the</strong> world and small amounts <strong>of</strong> 

<strong>the</strong> free element have also been found. Most arsenic is found in conjunction with 

sulphur such as realgar As 4S 4 and orpiment As 2S 3, and <strong>the</strong> oxidized form arsenolite 

As 2O 3. But non is mined as such because it is produced as a byproduct <strong>of</strong> refining 

ores <strong>of</strong> o<strong>the</strong>r metals such as iron, copper, cobalt or nickel. The main economic 

source <strong>of</strong> As is arsenopyrite FeAsS. But it can be also recovered from loellingite 

FeAs 2, safflorite CoAs, nickeline N iAs, cobaltite CoAsS, gersd<strong>of</strong>fite N iAsS, enargite 

Cu 3AsS 4, etc. 

The arsenic-containing <strong>mineral</strong>s considered by Grigor’ev are: <strong>the</strong> sulphides arsenopyrite, 

orpimnet, realgar, freibergite and <strong>the</strong> sulfosalt group “fahlerz group”, 

which will be assumed to be represented by <strong>the</strong> <strong>mineral</strong> tennantite Cu 11Fe 2+ As 4S 13.


Less abundant N i, Fe and Co arsenides recorded in his model are nickeline, gersdorffite, 

loellingite and cobaltite. In addition to <strong>the</strong> <strong>mineral</strong>s considered by Grigor’ev, 

<strong>the</strong> cobalt arsenide smaltite 7 is also included. Due to <strong>the</strong> importance <strong>of</strong> its oxidized 

form, arsenolite will be also taken into account, assuming that it is responsible for <strong>the</strong> 

same quantity <strong>of</strong> As on earth as realgar. The relative proportions given by Grigor’ev 

will be kept in our model. The abundance <strong>of</strong> cobaltite, smaltite and freibergite are 

fixed by <strong>the</strong>ir Co and Ag contents. 

3.4.6 Barium 

Barium is an alkaline-earth metal that is chemically similar to calcium. Barium and 

its compounds have many industrial uses. For instance barite BaSO 4 is extremely important 

for <strong>the</strong> petroleum industry, which accounts for more than 85% <strong>of</strong> <strong>the</strong> barite 

consumption in <strong>the</strong> world. It is used as a weighting agent in petroleum well-drilling 

mud. Barium-nickel alloys are used for spark-plug electrodes and in vacuum tubes 

as drying and oxygen-removing agents. Barium nitrate and chlorate give fireworks 

a green color. O<strong>the</strong>r compounds <strong>of</strong> barium are used to make bricks, tiles, glass or 

rubber. 

Barium is ra<strong>the</strong>r abundant in <strong>the</strong> earth’s crust. The chief mined ore is barite. A 

subsidiary <strong>mineral</strong> is barium carbonate wi<strong>the</strong>rite, BaCO 3. 

Barium-containing <strong>mineral</strong>s analyzed by Grigor’ev are barite, psilomenane, hollandite 

and lamprophyllite. We take into account in our model all four <strong>mineral</strong>s given 

by Grigorev’s analysis and include additionally wi<strong>the</strong>rite, for being an important Ba 

ore. It will be assumed that wi<strong>the</strong>rite accounts for about 10% <strong>of</strong> <strong>the</strong> Ba content <strong>of</strong> 

all barite in <strong>the</strong> crust. The relative concentrations <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s in Grigor’ev model 

will be kept. Never<strong>the</strong>less, <strong>the</strong> quantity <strong>of</strong> lamprophyllite is fixed as a result <strong>of</strong> <strong>the</strong> 

strontium mass balance 8 . 

3.4.7 Beryllium 

Beryllium is a light alkaline-earth metal and has one <strong>of</strong> <strong>the</strong> highest melting points <strong>of</strong> 

any light metal. It is used as an alloying agent in <strong>the</strong> production <strong>of</strong> beryllium-copper. 

Thanks to <strong>the</strong>ir electrical and <strong>the</strong>rmal conductivity, high strength and hardness, good 

stability over a wide temperature range, Be − Cu alloys are used in many applications. 

Some <strong>of</strong> <strong>the</strong>m are in <strong>the</strong> defense and aerospace industries, in <strong>the</strong> field <strong>of</strong> X-ray 

detection diagnostic and in <strong>the</strong> manufacture <strong>of</strong> computer equipment. 

Beryllium is relatively unabundant in <strong>the</strong> earth’s crust. It occurs as bertrandite 

Be 4Si 2O 7(OH) 2, beryl Be 3Al 2Si 6O 18, chrysoberyl BeAl 2O 4 and phenakite Be 2SiO 4. 

Precious forms <strong>of</strong> beryl are aquamarine and emerald. 

7 See section 3.4.18 for details about <strong>the</strong> assumptions done for cobaltite and smaltite. 

8 See section 3.4.63 for details about <strong>the</strong> optimization procedure for lamprohyllite


Grigor’ev accounted in his model for beryl, phenakite, bertrandite and helvite 

M n 4Be 3(SiO4) 3. In addition to those <strong>mineral</strong>s, chrysoberyl is included in our model, 

assuming that it has <strong>the</strong> same Be content as beryl. The relative proportions <strong>of</strong> <strong>the</strong> 

<strong>mineral</strong>s given by Grigor’ev will be kept and <strong>the</strong> concentrations <strong>of</strong> each <strong>mineral</strong> will 

be obtained assuring that constraint 1 is satisfied. 

3.4.8 Bismuth 

Bismuth is a metal used for metallurgical additives for castings and galvanizing, in 

<strong>the</strong> manufacture <strong>of</strong> low melting solders and fusible alloys as well as low toxicity bird 

shot and fishing sinkers. Additionally, it finds some application in <strong>the</strong> pharmaceutical 

industry. 

The most important ores <strong>of</strong> bismuth are bismuthinite Bi 2S 3, bismutite (BiO) 2CO 3 

and bismite B 2O 3. It occurs naturally also as <strong>the</strong> metal itself and is found as crystals 

in <strong>the</strong> sulphide ores <strong>of</strong> nickel, cobalt, silver and tin. The main commercial source <strong>of</strong> 

<strong>the</strong> element is as a byproduct from lead-zinc and copper plants. 

Grigor’ev takes into account four <strong>mineral</strong>s containing bismuth: bismutite, bismuthinite, 

native bismuth and tetradymite. Because <strong>of</strong> its importance, we include in our 

model bismite as well, assuming that it accounts for <strong>the</strong> same quantity <strong>of</strong> Bi as 

bismuthinite. Never<strong>the</strong>less, <strong>the</strong> relative proportions <strong>of</strong> bismutite, bismuthinite and 

native bismuth as well as <strong>the</strong> quantity <strong>of</strong> tetradymite 9 given by Grigor’ev will be kept 

in our model. 

3.4.9 Boron 

Boron is a non metallic element and <strong>the</strong> only non-metal <strong>of</strong> <strong>the</strong> group 13 <strong>of</strong> <strong>the</strong> periodic 

table. The most economically important compound <strong>of</strong> boron is borax, used for 

insulating fiberglass and sodium perborate bleach. Boric acid is also an important 

compound used in textile products. O<strong>the</strong>r uses <strong>of</strong> boron are in syn<strong>the</strong>tic herbicides 

and fertilizers, porcelain enamels, detergents, soaps, cleaners and cosmetics, catalysts 

or corrosion control. 

More than 200 <strong>mineral</strong>s contain boron, but only a few <strong>of</strong> commercial importance. 

Boron is usually found combined in tincal N a 2B 4O 7·10H 2O (natural borax), sassolite 

H 3BO 3 (natural boric acid), colemanite Ca 2B 6O 11 · 5H 2O, kernite N a 2B 4O 7 · 4H 2O, 

ulexite N aCaB 5O 9 · 8H 2O and boracite M g 3B 7O 13Cl. Only four <strong>mineral</strong>s make up 

almost 90% <strong>of</strong> <strong>the</strong> borates used by industry worldwide: borax, kernite, colemanite 

and ulexite. 

Non <strong>of</strong> <strong>the</strong>se <strong>mineral</strong>s are included in Grigorev’s model. However, boron element 

is present in his analysis as <strong>the</strong> borate silicates tourmaline, kornerupine, axinite 

9 See section 3.4.66 for <strong>the</strong> derivation <strong>of</strong> <strong>the</strong> assumption for tetradymite.


and dumortierite. Never<strong>the</strong>less, we cannot forget <strong>the</strong> four most important boroncontaining 

<strong>mineral</strong>s for industrial applications. Therefore, we keep in our model <strong>the</strong> 

concentrations <strong>of</strong> <strong>the</strong> borates given by Grigor’ev and assume that <strong>the</strong> rest quantity 

<strong>of</strong> boron in <strong>the</strong> crust is in form <strong>of</strong> borax, kernite, colemanite and ulexite having all 

<strong>of</strong> <strong>the</strong>m <strong>the</strong> same boron content. 

3.4.10 Bromine 

Bromine is a brownish-red liquid at ambient temperature and is used in industry to 

make organobromo compounds. These compounds find application as insecticides, 

fire extinguishers, water purification, flame retardants, pharmaceuticals, fumigants, 

dyes or photography. 

Like chlorine, <strong>the</strong> largest amount <strong>of</strong> bromine is <strong>the</strong> oceans. Salt lakes and brine wells 

are also rich sources <strong>of</strong> bromine, and <strong>the</strong>se are usually richer in bromine than <strong>the</strong> 

oceans. It occurs in nature as bromide salts in very diffuse amounts in crustal rock, 

which are accumulated in sea water after leaching processes. 

Grigor’ev does not include any bromine-containing <strong>mineral</strong>s. We will account for 

<strong>the</strong>m in our model as “dispersed Br”. 

3.4.11 Cadmium 

Cadmium is used as a protective coating for iron and steel, as a pigment, and as a 

stabilizer for plastics. But its main application (about three-fourths <strong>of</strong> its production) 

is used in Ni-Cd batteries. 

No cadmium ore is mined for <strong>the</strong> metal, because more than enough is produced as a 

byproduct <strong>of</strong> <strong>the</strong> smelting <strong>of</strong> zinc from its ore, sphalerite (ZnS), in which greenockite 

CdS is a significant impurity making up as much as 3%. 

No cadmium ores are recorded by Grigor’ev. We will assume in our model that 

greenockite is <strong>the</strong> only ore containing Cd. 

3.4.12 Calcium 

Calcium is a silvery white metal belonging to <strong>the</strong> alkaline earth group. The metal is 

used as a reducing agent in <strong>the</strong> extraction <strong>of</strong> o<strong>the</strong>r metals, as a deoxidizer, desulfurizer 

and decarbonizer in <strong>the</strong> manufacture <strong>of</strong> many steels, as separating material for 

gaseous mixtures, as an alloying agent used in <strong>the</strong> production <strong>of</strong> aluminium, beryllium, 

copper, lead and magnesium alloys as well as in <strong>the</strong> making <strong>of</strong> cements and 

mortars to be used in construction. Calcium compounds are used in a wide variety 

<strong>of</strong> applications such as insecticides, manufacture <strong>of</strong> plastics, as an additive in food 

and vitamin pills, as a disinfectant, as a fertilizer, in paints lights and X-rays, etc.


Calcium is <strong>the</strong> fifth most abundant element in <strong>the</strong> earth’s crust and <strong>the</strong> third most 

abundant metal after Al and Fe. Vast sedimentary deposits <strong>of</strong> CaCO 3, which represent 

<strong>the</strong> fossilized remains <strong>of</strong> earlier marine life, occur over large parts <strong>of</strong> <strong>the</strong> earth’s 

surface. O<strong>the</strong>r important <strong>mineral</strong>s are gypsum CaSO 4 · 2H 2O, anhydrite CaSO 4, 

fluorite CaF 2 and apatite Ca 5(PO 4) 3F. 

Sixty-six <strong>mineral</strong>s contain Ca in our model. The mass balance between elements 

and species for carbon in Grigorev’s model gives a quantity <strong>of</strong> Ca greater than <strong>the</strong> 

accepted value for Ca in <strong>the</strong> earth’s crust in Rudnick et al. [292]. Probably, Grigor’ev 

overestimated <strong>the</strong> quantity <strong>of</strong> some calcium-containing <strong>mineral</strong>s in <strong>the</strong> upper crust. 

3.4.13 Carbon 

Carbon is a non metallic element that forms more chemical compounds than any 

o<strong>the</strong>r element except hydrogen. The major economic use <strong>of</strong> carbon not in living 

material or organisms is in <strong>the</strong> form <strong>of</strong> hydrocarbons. The free element has a lot 

<strong>of</strong> uses, including jewelry (as diamonds), as a black fume pigment in automobile’s 

rims, printer’s ink, for pencil tips, dry cell and arch electrodes and as a lubricant. 

Carbon compounds have also plenty <strong>of</strong> uses. Carbon dioxide is used in drinks, in fire 

extinguishers and in solid state, as a cooler. Carbon monoxide is used as a reduction 

agent in many metallurgic processes. O<strong>the</strong>r carbon compounds are used as solvents, 

cooling systems, for welding and cutting materials. 

Carbon occurs both as <strong>the</strong> free element (graphite, diamond) and in combined form 

mainly as <strong>the</strong> carbonates <strong>of</strong> Ca, M g, and o<strong>the</strong>r electropositive elements. It also 

occurs as CO 2, a minor but very important constituent <strong>of</strong> <strong>the</strong> atmosphere, because 

<strong>of</strong> its important contribution to <strong>the</strong> greenhouse effect. Additionally, carbon is widely 

distributed in <strong>the</strong> organic form <strong>of</strong> coal and petroleum. 

The carbon-containing substances included in Grigorev’s model are graphite, organic 

carbon, moissonite and <strong>the</strong> carbonates calcite, dolomite, siderite, aragonite, magnesite, 

dawsonite, cancrinite, strontianite, bismutite, bastnasite, smithsonite cerussite, 

azurite, malachite, ankerite and rhodocrossite. Additionally, we have included in 

our model <strong>the</strong> barium carbonate wi<strong>the</strong>rite, for being an important Ba ore. It must 

be pointed out, that <strong>the</strong> mass balance between elements and species for carbon in 

Grigorev’s model gives a quantity <strong>of</strong> C greater than <strong>the</strong> accepted value for C in <strong>the</strong> 

earth’s crust in Rudnick et al. [292]. Probably, Grigor’ev overestimated <strong>the</strong> quantity 

<strong>of</strong> some carbon-containing <strong>mineral</strong>s in <strong>the</strong> upper crust. 

3.4.14 Cerium 

Cerium is a silvery metallic element, belonging to <strong>the</strong> lanthanide group. The metal 

is used as a core for <strong>the</strong> carbon electrodes <strong>of</strong> arc lamps, in incandescent mantles for 

gas lighting, in aluminium and iron alloys, in stainless steel as a hardening agent 

and to make permanent magnets.


Although cerium is part <strong>of</strong> <strong>the</strong> REE, it is not rare at all. In fact it is <strong>the</strong> most common 

rare earth and is more abundant than lead. It is commonly found in orthite, 

monazite, bastnaesite, rhabdophane or in zircon. 

Fur<strong>the</strong>r Ce-containing <strong>mineral</strong>s considered in Grigor’ev model are miserite, loparite, 

rhabdophane, chevkinite, tanteuxenite, euxenite rinkolite, polycrase, gadolinite, 

nordite britholite and fergusonite. In addition to those <strong>mineral</strong>s, <strong>the</strong> cerium included 

in <strong>the</strong> crystal structure <strong>of</strong> o<strong>the</strong>r <strong>mineral</strong>s such as zircon, gadolinite or bastnasite is 

accounted in our model as “diadochic Ce”. The quantity <strong>of</strong> it will be calculated 

as <strong>the</strong> difference between <strong>the</strong> cerium content in <strong>the</strong> crust and <strong>the</strong> cerium content 

<strong>of</strong> <strong>the</strong> <strong>mineral</strong>s included in <strong>the</strong> model. Except for miserite, which will be assumed 

to have <strong>the</strong> same concentration on earth than <strong>the</strong> one given by Grigor’ev, all o<strong>the</strong>r 

Ce-containing <strong>mineral</strong>s are fixed by <strong>the</strong>ir REE, U, Z r, Ba and Ta contents. 

3.4.15 Cesium 

Cesium is <strong>the</strong> most electropositive and least abundant <strong>of</strong> <strong>the</strong> five naturally occurring 

alkali metals. The most important use for cesium has been in research and 

development, primarily in chemical and electrical applications. 

Cesium occurs as <strong>the</strong> hydrated aluminosilicate pollucite, Cs 0.6N a 0.2Rb 0.04Al 0.9Si 2.1O 6· 

(H 2O), but <strong>the</strong> world’s only commercial source is at Bernic Lake, Manitoba. Cesium 

is mainly obtained as a byproduct <strong>of</strong> <strong>the</strong> Li industry. 

Cesium is not included in any <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s given by Grigor’ev. We will account for 

it in our model in <strong>the</strong> form <strong>of</strong> pollucite, assuming that it is <strong>the</strong> only main Cs ore. 

3.4.16 Chlorine 

Chlorine is <strong>the</strong> most common element <strong>of</strong> <strong>the</strong> halogens. In pure form, it is a greenyellow 

diatomic gas. Chlorine is very reactive and combines with nearly all o<strong>the</strong>r 

elements. It is used in water purification, disinfectants, in bleach and in mustard 

gas. Chlorine is also used extensively in <strong>the</strong> manufacture <strong>of</strong> many products directly 

or indirectly, i.e. in paper product production, antiseptics, food, insecticides, paints, 

petroleum products, plastics, medicines, etc. 

In nature it <strong>the</strong> upper continental crust it is found in <strong>the</strong> form <strong>of</strong> halite N aCl, but 

also in carnallite KCl and sylvite K M gCl 3 · 6(H 2O). Never<strong>the</strong>less, it is so abundant 

in <strong>the</strong> ocean, that it is extracted mainly from <strong>the</strong> sea and underground brine deposits 

for commercial uses. 

In addition to <strong>the</strong> <strong>mineral</strong>s mentioned above, Grigor’ev considers also <strong>the</strong> following 

Cl-containing <strong>mineral</strong>s: apatite, scapolite, sodalite, bisch<strong>of</strong>ite, eudialyte and chlorargirite. 

The mass balance between elements and species for chlorine in Grigorev’s 

model gives a quantity <strong>of</strong> Cl grater than <strong>the</strong> accepted value for Cl in <strong>the</strong> earth’s crust 

in Rudnick et al. [292]. Probably, Grigor’ev overestimated <strong>the</strong> quantity <strong>of</strong> halite. All


<strong>of</strong> <strong>the</strong>m are included in our model keeping <strong>the</strong>ir relative proportions. The quantity 

<strong>of</strong> eudyalite and chlorargirite are however fixed by <strong>the</strong> Z r and Ag mass balance. 

3.4.17 Chromium 

Chromium is a hard transition metal. In iron, steel and nonferrous alloys it imparts 

hardness and resistance to corrosion and oxidation. The use <strong>of</strong> chromium to produce 

stainless steel and nonferrous alloys are two <strong>of</strong> its more important applications. It 

finds also applications as dyes and paints to produce syn<strong>the</strong>tic rubies, as a catalyst 

in dyeing and in <strong>the</strong> tanning <strong>of</strong> lea<strong>the</strong>r or to make molds for <strong>the</strong> firing bricks. 

The only ore <strong>of</strong> chromium <strong>of</strong> any commercial importance is chromite FeC r 2O 4. O<strong>the</strong>r 

less plentiful sources are crocoite P bC rO 4 and chrome ochre C r 2O 3, while <strong>the</strong> gemstones 

emerald and ruby owe <strong>the</strong>ir colors to traces <strong>of</strong> chromium. Like in Grigorev’s 

analysis, we include chromite as <strong>the</strong> main chromium-containing <strong>mineral</strong>, since <strong>the</strong> 

o<strong>the</strong>r C r ores can be assumed to be insignificant when compared to chromite. Dietzeite 

Ca 2(IO 3) 2(C rO 4) is <strong>the</strong> o<strong>the</strong>r C r-containing <strong>mineral</strong> considered but its concentration 

is fixed by its iodine content. 

It must be pointed out that <strong>the</strong>re are big discrepancies between chromite concentration 

in Grigorev’s model and in our model. Never<strong>the</strong>less, we leave chromite as <strong>the</strong> 

sole chromium <strong>mineral</strong> for <strong>the</strong> reasons explained before. 

3.4.18 Cobalt 

Cobalt is a hard ferromagnetic, silver-white transition metal. The largest use <strong>of</strong> 

cobalt is in superalloys, which are used to make parts <strong>of</strong> gas turbine aircraft engines. 

Cobalt is also used in corrosion resistant alloys, high-speed steels, cemented 

carbides, in magnets and magnetic recording media, as catalysts for <strong>the</strong> petroleum 

and chemical industries and as drying agent for paints and inks. 

More than 200 ores are known to contain cobalt but only a few are <strong>of</strong> commercial 

value. The more important are arsenides and sulfides such as smaltite, CoAs 2, 

cobaltite CoAsS and linnaeite Co 3S 4.These are invariably associated with nickel and 

also with copper and lead, so that Co is usually obtained as a byproduct or coproduct 

<strong>of</strong> <strong>the</strong>se metals. 

The only cobalt-containing <strong>mineral</strong> considered in Grigorev’s analysis is cobaltite. In 

our model, we take also into account <strong>the</strong> o<strong>the</strong>r two <strong>mineral</strong>s mentioned before, assuming 

that all three contribute with <strong>the</strong> same amount <strong>of</strong> Co to <strong>the</strong> cobalt content 

<strong>of</strong> <strong>the</strong> upper earth’s crust. Although important, only those three <strong>mineral</strong>s are not 

responsible for <strong>the</strong> whole Co on earth 10 . Therefore, we will assume that <strong>the</strong> concentration 

<strong>of</strong> cobaltite given by Grigor’ev is correct and will account for <strong>the</strong> rest Co in 

<strong>the</strong> earth crust as “dispersed Co”. 

10 If cobaltite, smaltite and linnaeite would be assumed to be <strong>the</strong> only cobalt-carriers in <strong>the</strong> earth’s 

crust, <strong>the</strong> mass balance for arsenic would not be satisfied.


3.4.19 Copper 

Copper is one <strong>of</strong> <strong>the</strong> coinage metals with gold and silver because <strong>of</strong> its former usage. 

It is an excellent conductor <strong>of</strong> heat and electricity and <strong>the</strong>refore is a key metal 

in <strong>the</strong> electric and electronic industry. Electrical uses <strong>of</strong> copper, including power 

transmission and generation, building wiring, telecommunication and electrical and 

electronic products account for about three quarters <strong>of</strong> total copper use. Fur<strong>the</strong>r 

applications <strong>of</strong> copper are in construction, such as ro<strong>of</strong>ing and plumbing, industrial 

machinery such as heat exchangers. It is also commonly used in <strong>the</strong> manufacture <strong>of</strong> 

brass and o<strong>the</strong>r alloys with zinc, tin, nickel, lead aluminium, etc. 

Copper is found mainly as <strong>the</strong> sulfide, oxide or carbonate, its major ores being copper 

pyrite (chalcopyrite) CuFeS 2, which is estimated to account for about 50% <strong>of</strong> 

all Cu deposits; copper glance (chalcocite), Cu 2S; cuprite, Cu 2O, and malachite 

Cu 2CO 3(OH) 2. Bornite Cu 5FeS 4, azurite Cu 3(CO 3) 2(OH) 2, and covellite CuS are 

o<strong>the</strong>r minor ores <strong>of</strong> Cu. Native copper is found as well occasionally. 

In addition to <strong>the</strong> <strong>mineral</strong>s explained above, o<strong>the</strong>r Cu-containing <strong>mineral</strong>s in Grigorev’s 

model are chrysocolla, metatorbenite, tennantite, freibergite and tetrahedrite. 

No additional <strong>mineral</strong>s will be taken into account in our model, since <strong>the</strong> most important 

are already ga<strong>the</strong>red in Grigorev’s analysis. The quantities for metatorbenite 

and tennantite have been fixed by <strong>the</strong>ir uranium and arsenium content, while for 

freibergite and tetrahedrite by <strong>the</strong>ir silver content. For <strong>the</strong> rest substances, <strong>the</strong> relative 

proportions given by Grigor’ev will be maintained, assuring <strong>the</strong> compliance <strong>of</strong> 

constraint 1. 

3.4.20 Dysprosium 

See section 3.4.52. 

3.4.21 Erbium 


3.4.22 Europium 


3.4.23 Fluorine 

Fluorine is <strong>the</strong> lightest and most reactive element <strong>of</strong> <strong>the</strong> halogens. Atomic and molecular 

fluorine are used for plasma etching in semiconductor manufacturing, flat panel


display production and microelectromechanical systems fabrication. Sodium hexafluoroaluminate 

(cryolite), is used in <strong>the</strong> electrolysis <strong>of</strong> aluminium. It is indirectly 

used for <strong>the</strong> production <strong>of</strong> plastics such as teflon and halons such as freon. Fluorides 

are added to toothpaste to prevent dental cavities. O<strong>the</strong>r components <strong>of</strong> fluorine 

are used in pharmaceuticals as antibiotics, antidepressants and for <strong>the</strong> prevention <strong>of</strong> 

infections. 

The three most important <strong>mineral</strong>s <strong>of</strong> fluorine are fluorite CaF 2, cryolite N a 3Al F 6 

and flourapatite Ca 5(PO 4) 3F. Of <strong>the</strong>se, however, only fluorite is extensively <strong>the</strong> 

only commercial deposit. Cryolite is a rare <strong>mineral</strong>, <strong>the</strong> only commercial deposit 

being in Greenland, and most <strong>of</strong> it is used in <strong>the</strong> aluminium industry. But by far <strong>the</strong> 

largest amount <strong>of</strong> fluorine in <strong>the</strong> earth’s crust is in <strong>the</strong> form <strong>of</strong> <strong>of</strong> fluorapatite. Minor 

occurrences <strong>of</strong> fluorine are also in <strong>the</strong> rare elements topaz or bastanesite. 

The fluorine-containing <strong>mineral</strong>s taken into account by Grigor’ev are: apatite, fluorite, 

topaz, bastnaesite, lamprophyllite, amblygonite, britholite, lavenite, rinkolite, 

wohlerite, microlite, apatite, bastnasite, francolite, pyrochlore, miserite, biotite, 

muscovite, hydrobiotite, phlogopite, clinohumite, fluorite, humite and chondrodite. 

In addition to those, we include in our model cryolite because <strong>of</strong> its industrial relevance, 

assuming that it contributes to <strong>the</strong> same F content to <strong>the</strong> earth than topaz. 

3.4.24 Gadolinium 

See section 3.4.52 

3.4.25 Gallium 

Gallium is a rare element and found little use until its properties as a semiconductor 

were discovered. Analog integrated circuits are <strong>the</strong> largest application for gallium 

with optoelectronic devices (mostly laser diodes and light-emitting diodes) as <strong>the</strong> 

second largest end use. 

The highest concentrations (0,1-1%) are found in <strong>the</strong> rare <strong>mineral</strong> germanite 

(Cu 26Fe 4Ge 4S 32); concentrations in sphalerite (ZnS), bauxite or coal are a hundredfold 

less. It was formerly recovered from flue dusts emitted during sulfide roasting or 

coal burning (up to 1,5% Ga), but is now obtained as a byproduct <strong>of</strong> <strong>the</strong> Al industry. 

Grigor’ev does not explicitly include any <strong>mineral</strong> containing Ga. It will be included 

in our model as “dispersed Ga”. 

3.4.26 Germanium 

Germanium is a semiconductor and was used for transistors, diodes and rectifiers 

until it was replaced by pure silicon in <strong>the</strong> early 1970’s. Meanwhile germanium


is used in fiber optics communication networks, infrared night vision systems and 

polymerization catalysts. 

Germanium <strong>mineral</strong>s are extremely rare, but <strong>the</strong> element is widely distributed in 

trace amounts among <strong>the</strong> silicates <strong>of</strong> rocks, igneous as well as sedimentary and 

metamorphic ones. Recovery is achieved normally from <strong>the</strong> flue dusts <strong>of</strong> smelters 

processing Zn ores. Germanite is <strong>the</strong> only commercial <strong>mineral</strong> <strong>of</strong> Germanium 

(Cu 26Fe 4Ge 4S 32), but it is not considered in Grigorev’s analysis. 

In order to account for Ge in our model, it will be included as “dispersed Ge”, which 

will represent all germanium included in <strong>the</strong> different ores where it is found. 

3.4.27 Gold 

Gold is mostly used in <strong>the</strong> manufacture <strong>of</strong> jewelry. However, because <strong>of</strong> its superior 

electrical conductivity and resistance to corrosion, it has also emerged in <strong>the</strong> late 

20th century as an essential industrial metal in computers, communication equipment, 

spacecraft, etc. 

Gold is widely but sparsely distributed both native and in tellurides. Grigo’ev considers 

native gold as <strong>the</strong> only carrier <strong>of</strong> Au in <strong>the</strong> upper crust. 

Since tellurides are also important ores for gold, we will include in our model <strong>the</strong> 

tellurides calaverite AuTe 2 and sylvanite Au 0.75Ag 0.25Te 2, assuming that 15% in volume 

<strong>of</strong> Au in <strong>the</strong> upper continental crust comes from <strong>the</strong>m at equal rates and <strong>the</strong> 

rest from native gold. 

3.4.28 Hafnium 

Hafnium is a transition metal similar to zirconium. It resists corrosion and has a high 

melting point. Its major end uses are in nuclear control rods because <strong>of</strong> its excellent 

properties in absorbing neutrons, nickel-based superalloys, nozzles for plasma arc 

metal cutting and high-temperature ceramics. 

Hafnium ores are rare, but two are known: hafnon and alvite. However, H f is 

mostly found in quantities <strong>of</strong> about 2% <strong>of</strong> <strong>the</strong> Z r content in zirconium ores such as 

zircon Z rSiO 4 and baddeleyite Z rO 2. 

H f will be considered in our model only as a diadochic element in zirconium ores, 

since Grigor’ev did not provide any information about <strong>the</strong> hafnium ores explained 

before. 

3.4.29 Holmium 

See section 3.4.52.


3.4.30 Indium 

Indium is a rare metal used in low-melting fusible alloys, solders and electronics. 

Large-scale application for indium was also as a protective coating for bearings and 

o<strong>the</strong>r metal surfaces in high-performance aircraft engines. Nowadays, its main application 

is in <strong>the</strong> manufacture <strong>of</strong> indium-tin-oxide thin films for Liquid Crystal Displays 

(LCD). 

Indium tends to associate with <strong>the</strong> similarly sized Zn in its sulfide <strong>mineral</strong>s, hence 

it is mainly produced from residues generated during zinc and lead sulfide ore processing, 

mainly from sphalerite ZnS. The indium metal indite Fe 2+ In 2S 4 has been 

found in Siberia but it is very rare. 

We will include In in our model as being in <strong>the</strong> crystal lattice <strong>of</strong> sphalerite (“diadochic 

In in sphalerite”). 

3.4.31 Iodine 

Iodine is <strong>the</strong> most electropositive halogen and is used in medical treatment as tincture 

and iod<strong>of</strong>orm. It is employed in <strong>the</strong> preparation <strong>of</strong> certain drugs, and in <strong>the</strong> 

manufacture <strong>of</strong> printing inks and dyes. Silver iodine is used in photography and 

iodine is added to table salt and is used as a supplement to animal feed. It is also an 

ingredient <strong>of</strong> water purification tablets. 

Iodine is considerably less abundant than <strong>the</strong> lighter halogens. It can be found 

naturally in air, water and soil. But <strong>the</strong> most important sources are <strong>the</strong> oceans. It 

occurs but rarely as iodide <strong>mineral</strong>s. Commercial deposits are usually iodates, e.g. 

lautarite Ca(IO 3) 2 and dietzeite Ca 2(IO 3) 2(C rO 4). 

None <strong>of</strong> <strong>the</strong>se <strong>mineral</strong>s or o<strong>the</strong>r iodine-containing <strong>mineral</strong>s were considered by 

Grigor’ev. We will assume that <strong>the</strong> <strong>mineral</strong>s above account for all I in <strong>the</strong> upper 

continental crust in <strong>the</strong> same proportion. 

3.4.32 Iridium 


3.4.33 Iron 

Iron is <strong>the</strong> most used <strong>of</strong> all <strong>the</strong> metals, including 95% <strong>of</strong> all <strong>the</strong> metal tonnage 

produced worldwide. Thanks to <strong>the</strong> combination <strong>of</strong> low cost and high strength it is 

indispensable. Its applications go from food containers to cars, from screwdrivers to 

washing machines, from cargo ships to paper staples. Steel is <strong>the</strong> best known alloy 

<strong>of</strong> iron and some <strong>of</strong> <strong>the</strong> forms that iron takes include pig iron, cast iron, carbon steel, 

wrought iron, alloy steels and iron oxides.


Iron is <strong>the</strong> most abundant element in <strong>the</strong> universe and on earth. widely distributed 

as oxides and carbonates, <strong>of</strong> which <strong>the</strong> chief ones are haematite Fe 2O3, magnetite 

Fe 3O 4 and siderite FeCO 3. 

Eighty-two Fe-containing <strong>mineral</strong>s are included in our model. 

3.4.34 Lanthanum 

Lanthanum is a rare earth element (REE) and gives its name to <strong>the</strong> lanthanide group. 

It can be found in domestic equipment such as in color televisions, fluorescent and 

energy-saving lamps and optical glasses. If added in small amounts, it improves <strong>the</strong> 

malleability and resistance <strong>of</strong> steel. Lanthanum is also used as <strong>the</strong> core material in 

carbon arc electrodes and in zeolite catalysts for <strong>the</strong> petroleum industry. 

Lanthanum is one <strong>of</strong> <strong>the</strong> most abundant REE. Its major ores are <strong>mineral</strong>s monazite 

and bastnasite, in percentages <strong>of</strong> up to 25 to 38 percent <strong>of</strong> <strong>the</strong> total lanthanide 

content. 

In addition to monazite and bastnasite, Grigor’ev considers in his analysis <strong>the</strong> Lacontaining 

<strong>mineral</strong>s britholite, chevkinite, loparite, rhabdophane and nordite. All 

<strong>the</strong>se <strong>mineral</strong>s with <strong>the</strong>ir respective proportions are included in our model assuring 

<strong>the</strong> satisfaction <strong>of</strong> constraint number 1. The abundance <strong>of</strong> nordite is however fixed 

by its Ba content. 

3.4.35 Lead 

Lead is a very corrosion-resistant, malleable and toxic bluish-white metal that has 

been known for at least 5000 years. Ancient romans used lead as drains from <strong>the</strong> 

baths. Nowadays lead is a major constituent <strong>of</strong> <strong>the</strong> lead-acid battery, it is used as a 

coloring element in ceramic glazes, as projectiles, as electrodes for electrolysis and 

in <strong>the</strong> glass <strong>of</strong> computer and television screens, shielding <strong>the</strong> viewer from radiation. 

Lead alloys include pewter and solder. The toxicity <strong>of</strong> lead leaded in <strong>the</strong> twentieth 

century to strong environmental regulations that significantly reduced or eliminated 

its use in nonbattery products including gasoline, paints, solders and water systems. 

Lead is <strong>the</strong> most abundant <strong>of</strong> <strong>the</strong> heavy elements. It can be found native, but its most 

important ore is <strong>the</strong> heavy black <strong>mineral</strong> galena P bS. O<strong>the</strong>r important <strong>mineral</strong>s are 

anglesite P bSO 4 and cerussite P bCO 3. It is usually found in zinc, silver and copper 

ores and it is extracted toge<strong>the</strong>r with <strong>the</strong>se <strong>mineral</strong>s. However, <strong>the</strong> largest current 

source <strong>of</strong> lead is recycling, primarily <strong>of</strong> automobile batteries. 

In addition to galena, anglesite and cerussite, Grigor’ev takes into account <strong>mineral</strong>s 

boulangerite P b 5S b 4S 11, native lead P b and wulfenite P bM oO 4. All <strong>the</strong>se are included 

in our model keeping <strong>the</strong> relative proportions <strong>of</strong> galena, cerussite, anglesite


and native lead given by Grigor’ev. The concentrations <strong>of</strong> wulfenite and boulangerite 

are fixed by <strong>the</strong>ir M o and S b contents respectively 11 . 

3.4.36 Lithium 

Lithium is an alkali metal <strong>of</strong> very high chemical reactivity. As a consequence, it takes 

part in a huge number <strong>of</strong> reactions. The carbonate can be used in <strong>the</strong> pottery industry 

and in medicine as antidepressant. Low-density alloys are used for armor plate 

and for aerospace components. The bromine and chloride both form concentrated 

brine, which have <strong>the</strong> property <strong>of</strong> absorbing humidity in a wide temperature range; 

<strong>the</strong>se brines are also used for air conditioning systems. Lithium finds additional use 

in nuclear breeder reactors as a coolant and as a source for tritium. O<strong>the</strong>r important 

uses for lithium are as lubricants, in porcelain glaze, as an additive to extend <strong>the</strong> life 

and performance <strong>of</strong> alkaline storage batteries and in welding. 

Lithium is a moderately abundant element. Its most important <strong>mineral</strong> commercially 

is spodumene LiAsSi 2O 6, followed by lepidolite K Li 2AlSi 4O 10F(OH). It is 

commonly found in nature as silicates and phosphates. However it is usually recovered 

from brines. 

Grigor’ev has included in his model spodumene, <strong>the</strong> silicate neptunite and <strong>the</strong> phosphate 

amblygonite. Additionally, we will include lepidolite in our model because <strong>of</strong> 

its industrial importance, assuming that <strong>the</strong> Li quantity coming from it in <strong>the</strong> crust is 

10% <strong>of</strong> that <strong>of</strong> spodumene. Our model keeps <strong>the</strong> relative proportions <strong>of</strong> <strong>the</strong> different 

lithium <strong>mineral</strong>s considered by Grigor’ev, but assuring <strong>the</strong> satisfaction <strong>of</strong> <strong>the</strong> mass 

balance. 

3.4.37 Lutetium 


3.4.38 Magnesium 

Magnesium is a light, chemically reactive metal, belonging to <strong>the</strong> alkaline earth 

group. It is known as <strong>the</strong> lighter structural metal in <strong>the</strong> industry, due to its low 

weight and its capability <strong>of</strong> forming mechanically resistant alloys. Magnesium alloys 

are used in beverage cans, as structural components <strong>of</strong> automobiles and machinery. 

Magnesium compounds, primarily magnesium oxide, are used mainly as refractory 

material in furnace linings for producing iron and steel, nonferrous metals, glass 

and cement. Magnesium oxide and o<strong>the</strong>r compounds are also used in agricultural, 

chemical and construction industries. 

11 See sections 3.4.41 and 3.4.4 for details about <strong>the</strong> assumptions done for wulfenite and boulan- 

gerite, respectively.


Magnesium is among <strong>the</strong> eight most abundant elements. It usually occurs in crustal 

rocks mainly as <strong>the</strong> insoluble carbonates and sulfates and less accessibly as silicates. 

Important magnesium-containing <strong>mineral</strong>s are dolomite CaM g(CO 3) 2, magnesite 

M gCO 3, carnallite K 2M gCl 4 · 6H 2O, olivine (M g, Fe) 2SiO 4, talc M g 3Si 4O 10(OH) 2 

or spinel M gAl 2O 4. 

Fifty-five magnesium-containing <strong>mineral</strong>s have been considered in our model. 

3.4.39 Manganese 

Manganese is a grey-white chemically active metal. It resembles iron and is essential 

in <strong>the</strong> iron and steel production by virtue <strong>of</strong> its sulfur-fixing, deoxidizing and alloying 

properties. It is also widely used in aluminium alloys. Fur<strong>the</strong>r applications for 

manganese and its compounds are as additive in gasoline to boost octane rating, as 

a reagent in organic chemistry, as a colorizing and decolorizing agent for glass, as a 

paint, as a disinfectant and in batteries. 

Manganese is found over 300 different and widely distributed <strong>mineral</strong>s <strong>of</strong> which 

about twelve are commercially important. It occurs in primary deposits as <strong>the</strong> silicate 

metal. Of more commercial importance are <strong>the</strong> secondary deposits <strong>of</strong> oxides 

and carbonates such as pyrolusite M nO 2 and to a lesser extent as rhodochrosite 

M nCO 3. Vast quantities <strong>of</strong> manganese exist in manganese nodules (manganese, iron 

and o<strong>the</strong>r metal-containing agglomerates) <strong>of</strong> <strong>the</strong> ocean floor. But no economically 

viable methods <strong>of</strong> harvesting manganese nodules have been found yet. 

The M n-containing <strong>mineral</strong>s included in Grigorev’s model are: rhodochrosite, pyrolusite, 

chloritoid, ankerite, todorokite, vernadite, spessartine, wolframite, jacobsite, 

cryptomelane, manganite, tephroite, braunite, rhodonite, samsonite, psilomelane, 

hollandite, neptunite, helvite, eudyalite, lavenite and nordite. The quantity <strong>of</strong> <strong>the</strong> 

nine latter <strong>mineral</strong>s is fixed by <strong>the</strong>ir W , Ag, Ba, Li, Be, Z r and Sr contents. The 

rest <strong>mineral</strong>s are assumed to have in our model <strong>the</strong> relative proportions given by 

Grigor’ev. 

3.4.40 Mercury 

Mercury is <strong>the</strong> only common metal which is liquid at ordinary temperatures. Because 

<strong>of</strong> its high density it is used in barometers and manometers. It is extensively used in 

<strong>the</strong>rmometers thanks to its high rate <strong>of</strong> <strong>the</strong>rmal expansion that is fairly constant over 

a wide temperature range. Amalgams <strong>of</strong> silver, gold and tin (alloys <strong>of</strong> mercury) are 

used in dentistry. Most mercury is used for <strong>the</strong> manufacture <strong>of</strong> industrial chemicals 

and form electrical and electronic applications. 

Cinnabar, H gS is <strong>the</strong> only important ore and source <strong>of</strong> mercury, being <strong>the</strong> deposits 

at Almaden in Spain <strong>the</strong> most famous and extensive ones. 

Grigor’ev records two <strong>mineral</strong>s <strong>of</strong> mercury: cinnabar and metacinnabar. Both <strong>mineral</strong>s 

will be kept in our model, maintaining <strong>the</strong>ir respective proportions.


3.4.41 Molybdenum 

Molybdenum is a refractory metal able to withstand extreme temperatures without 

significantly expanding or s<strong>of</strong>tening. Those properties make M o useful in applications 

that involve intense heat, including aircraft parts, electrical contacts and filaments. 

Molybdenum is used in alloys, mainly in steel, cast iron and superalloys. It is 

also used in electrodes, lubricants, pigments and catalysts. 

The most important ore <strong>of</strong> molybdenum is <strong>the</strong> sulphide molybdenite M oS 2, which 

can be found in tungsten and copper ores, being molybdenite a byproduct <strong>of</strong> W and 

Cu production. Less important ores are wulfenite P bM oO 4 and powellite CaM oO 4. 

All three <strong>mineral</strong>s are considered in Grigorev’s model and will be considered in our 

model, keeping Grigorev’s relative proportions. 

3.4.42 Neodymium 

Neodymium is a member <strong>of</strong> <strong>the</strong> lanthanide series and hence has few properties 

which distinguish it from <strong>the</strong> o<strong>the</strong>r members <strong>of</strong> <strong>the</strong> series. Like lanthanum and o<strong>the</strong>r 

REE, it can be found in houses equipment such as televisions, lamps and glasses. 

Neodymium forms an important alloy (neodybium), found to produce very high 

magnetic field strengths with small masses. 

Neodymium is <strong>the</strong> second most abundant <strong>of</strong> <strong>the</strong> REE after cerium. It is found in 

<strong>mineral</strong>s that include o<strong>the</strong>r lanthanide elements such as monazite and bastnasite. 

N d is included in <strong>the</strong> empirical formula <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s fergusonite, britholite and 

monazite given by Grigor’ev. In addition to those <strong>mineral</strong>s, we include <strong>the</strong> rest <strong>of</strong> 

N d in <strong>the</strong> upper continental crust as “diadochic N d” in our model, which should 

account mainly for N d found as an ion solution in bastnaesite. 

3.4.43 Nickel 

Nickel is a transition metal that belongs to <strong>the</strong> iron group. It is mainly used in 

<strong>the</strong> preparation <strong>of</strong> alloys, giving to <strong>the</strong>m good strength, ductility and resistance to 

corrosion properties. About 65% <strong>of</strong> <strong>the</strong> nickel consumed in <strong>the</strong> western world is used 

to make stainless steel. The remaining is divided between alloy steels, rechargeable 

batteries, catalysts, coinage, foundry products and plating. 

The bulk <strong>of</strong> <strong>the</strong> nickel mined comes from two types <strong>of</strong> ore deposits. The first are 

laterites where <strong>the</strong> principal ore <strong>mineral</strong>s are nickeliferous limonite 12 and garnierite 

N i 3M gSi 6O 15(OH) 2 · 6(H 2O). The second are magmatic sulfide deposits where <strong>the</strong> 

principal ore <strong>mineral</strong> is pentlandite Fe 2+ 

4.5 N i 4.5S 8. Arsenide ores such as nickeline 

12 Nickeliferous limonite is <strong>the</strong> term used to describe poorly crystalline nickel-bearing ferric oxides 

<strong>of</strong> which <strong>the</strong> main constituent is goethite Fe 3+ O · OH.


N iAs or gersdorffite N iAsS can be also found. N i appears as well in <strong>the</strong> crystalline 

structure <strong>of</strong> many o<strong>the</strong>r <strong>mineral</strong>s including pyrrhotite, chalcopyrite, pyrite, ilmenite 

or magnetite. 

The laterites group is represented in Grigorev’s model by garnierite, while <strong>the</strong> second 

by pentlandite. O<strong>the</strong>r arsenides and sulphides <strong>of</strong> N i considered are violarite 

Fe2+ N i 3+ 

2 S4, vaesite N iS2, cooperite P t0.6Pd 0.3N i0.1S, nickeline and gersdorffite. 

Additionally to those, we will include in our model “diadochic N i”, which should 

account for <strong>the</strong> whole N i appearing in small quantities in <strong>the</strong> crystal lattice <strong>of</strong> <strong>the</strong> 

<strong>mineral</strong>s mentioned before. It will be assumed that diadochic N i contributes to <strong>the</strong> 

same N i amount than pentlandite. The relative proportions given by Grigor’ev will 

be maintained, although cooperite13 , nickeline and gersdorffite14 are fixed by <strong>the</strong>ir 

Pd, and As contents. 

3.4.44 Niobium 

Niobium, sometimes called columbium, is a rare s<strong>of</strong>t transition metal, used mainly 

for <strong>the</strong> production <strong>of</strong> high-temperature resistant alloys and special stainless steels. 

Small amounts <strong>of</strong> niobium impart greater strength to o<strong>the</strong>r metals. The applications 

<strong>of</strong> those alloys are in nuclear reactors, jets, missiles, cutting tools, pipelines, super 

magnets, surgical implants and welding rods. Niobium is additionally used as a 

superconductor when lowered to cryogenic temperatures. 

Niobium has been mainly mined as columbite FeN b 2O 6. Two o<strong>the</strong>r important N bcontaining 

<strong>mineral</strong>s are euxenite (Y, Ca, Ce, U, Th)(N b, Ta, T i) 2O 6 and pyrochlore 

N a 1.5Ca 0.5N b 2O 6(OH) 0.75F 0.25 <strong>the</strong> latter is now its most important ore. Due to its 

similarities to tantalum, <strong>mineral</strong>s that contain niobium also contain tantalum, so 

that columbite gets <strong>the</strong> name <strong>of</strong> tantalite when tantalum preponderates. 

Besides <strong>of</strong> columbite, pyrochlore and tantalite, o<strong>the</strong>r N b-containing <strong>mineral</strong>s included 

in Grigorev’s model are ilmenorutile, murmanite, loparite, tanteuxenite, 

lavenite rinkolite, wohlerite, polycrase, blomstrandite and fergusonite. No additional 

<strong>mineral</strong>s will be included in our model. It will be assured <strong>the</strong> satisfaction <strong>of</strong> 

<strong>the</strong> mass balance, keeping <strong>the</strong> relative proportions <strong>of</strong> <strong>the</strong> different <strong>mineral</strong>s given by 

Grigor’ev. 

3.4.45 Nitrogen 

Nitrogen is a common inert gas and an essential element in most <strong>of</strong> <strong>the</strong> substances 

that make up living organisms, including proteins. Its main application is as a component 

in <strong>the</strong> manufacture <strong>of</strong> ammonia, subsequently used as fertilizer and to produce 

nitric acid. It can be used also as a refrigerant for freezing and transporting 

food products. 

13 See section 3.4.47 for details about <strong>the</strong> optimization method used for cooperite. 

14 see section 3.4.5 for details about <strong>the</strong> optimization method used for nickeline and gersdorffite.


Despite its ready availability in <strong>the</strong> atmosphere, constituting 78% <strong>of</strong> <strong>the</strong> air by volume, 

nitrogen is relatively unabundant in <strong>the</strong> continental crust. The only major 

<strong>mineral</strong>s are KNO 3 (nitre, salpetre) and N aNO 3 (sodanitre, nitratine). Both occur 

widespread. 

Grigor’ev did not consider any <strong>of</strong> both <strong>mineral</strong>s. We will assume that <strong>the</strong>y are <strong>the</strong> 

only carriers <strong>of</strong> Nitrogen in <strong>the</strong> upper continental crust at equal relative proportions. 

3.4.46 Osmium and Iridium 

Osmium is a silvery metal <strong>of</strong> <strong>the</strong> platinum group metals. It has <strong>the</strong> distinction <strong>of</strong> 

being <strong>the</strong> most dense <strong>of</strong> all <strong>the</strong> naturally occurring elements. Its main application is 

as an alloy with o<strong>the</strong>r platinum metals. 

Iridium is a transition metal <strong>of</strong> <strong>the</strong> platinum family and it is notable for being <strong>the</strong> 

most corrosion resistant element known. Demand for iridium comes mainly from <strong>the</strong> 

electronic, automotive and chemical industry, where it is used to coat <strong>the</strong> electrodes 

in <strong>the</strong> chlor-alkali process and in catalysts. 

Osmium and iridum are very rare metals. Osmium is usually found in combination 

with iridium and ru<strong>the</strong>nium. The most important ores are iridosmine and osmiridium. 

The same main ores are found for iridium. 

Grigor’ev did not account for any <strong>of</strong> both substances. We will include both <strong>mineral</strong>s 

in <strong>the</strong> proportions so that <strong>the</strong>y comply with <strong>the</strong> mass balance for elements osmium 

and iridium. 

3.4.47 Palladium 

Palladium is a silver-white metal belonging to <strong>the</strong> platinum group metals. Because 

<strong>of</strong> its corrosion resistance, a major use <strong>of</strong> palladium is in alloys used in low voltage 

electrical contacts. It is also used as a catalyst, replacing platinum for reducing 

car exhaust emissions and it is alloyed with certain metals in jewelry. Palladium is 

nowadays being more and more used in electrical appliances in <strong>the</strong> form <strong>of</strong> multilayer 

ceramic capacitors. 

Palladium is usually associated with <strong>the</strong> o<strong>the</strong>r platinum metals and occur ei<strong>the</strong>r native 

or as sulfides or arsenides in N i, Cu and Fe sulfide ores. However, much <strong>of</strong> it 

is extracted as a by-product from copper-nickel ores such as chalcopyrite, pyrrhotite 

and pentlandite or chromite. 

The only <strong>mineral</strong> considered by Grigor’ev in his model is cooperite P t 0.6Pd 0.3N i 0.1S. 

The rest <strong>of</strong> palladium found in nature will be considered in our model to be included 

dispersed in <strong>the</strong> copper-nickel ores mentioned before.


3.4.48 Phosphorous 

Phosphorous is a nonmetal <strong>of</strong> <strong>the</strong> nitrogen group. Concentrated acids are used in fertilizers 

for agriculture and farm production. Phosphates are used for special glasses, 

sodium lamps, in steel production, in military applications and in o<strong>the</strong>r applications 

such as pyrotechnics, pesticides, toothpaste or detergent. 

Phosphorous is an abundant <strong>mineral</strong> on earth. All its known terrestrial <strong>mineral</strong>s are 

orthophosphates. Some 200 crystalline phosphate <strong>mineral</strong>s have been described, 

but by far <strong>the</strong> major amount <strong>of</strong> P occurs in <strong>the</strong> family <strong>of</strong> apatites, and <strong>the</strong>se are <strong>the</strong> 

only ones <strong>of</strong> industrial importance. Common members are fluorapatite Ca 5(PO 4) 3F, 

chlorapatite Ca 5(PO 4) 3Cl and hydroxylapatite Ca 5(PO 4) 3OH. In addition, <strong>the</strong>re 

are vast deposits <strong>of</strong> amorphous phosphate rock phosphorite, which approximates in 

composition to fluoroapatite. 

The phosphates taken into account in Grigorev’s model are: apatite, xenotime, 

rhabdophane, amblygonite, metatorbernite, monazite, weinschenkite, francolite, vivianite. 

All three kinds <strong>of</strong> apatite are included in <strong>the</strong> general formula Ca 5(PO 4) 3 

(OH) 0.3333F 0.3333Cl 0.3333. No o<strong>the</strong>r <strong>mineral</strong>s are taken into account in our model. 

Except for weinschenkite and vivianite, which are assumed to have <strong>the</strong> same concentration 

than <strong>the</strong> given by Grigor’ev, <strong>the</strong> quantity <strong>of</strong> all those <strong>mineral</strong>s are fixed 

by <strong>the</strong> mass balance <strong>of</strong> Cl,Y b, Li, U, Y , F and La. Additionally, <strong>the</strong> amorphous 

phosphate rock phosphorite is included in our model due to its abundance. It will 

be assumed to have <strong>the</strong> composition Ca 3(PO 4) 2. 

3.4.49 Platinum 

Platinum gives <strong>the</strong> name to <strong>the</strong> platinum-group metals (PGM), which comprise platinum, 

palladium, rhodium, ru<strong>the</strong>nium, iridium and osmium. It has outstanding 

catalytic properties and its resistance is well suited for making fine jewelry. Platinum 

and its alloys are used also in surgical tools, laboratory utensils, electrical 

resistance wires, etc. The glass industry uses platinum for optical fibers and liquid 

crystal display glass. 

Platinum occurs generally associated with <strong>the</strong> o<strong>the</strong>r platinum metals and occur 

also in native form or as sulfides or arsenides in N i, Cu and Fe sulfide ores. 

Three-quarters <strong>of</strong> <strong>the</strong> world’s platinum comes from South Africa, where it occurs 

as cooperite. It is also extracted as a by-product from copper-nickel ores such as 

chalcopyrite, pyrrhotite and pentlandite or with chromite. 

Platinum is included in three <strong>mineral</strong>s <strong>of</strong> Grigorev’s model: cooperite, ferroplatinum 

and native platinum. We will maintain <strong>the</strong> concentrations given by Grigor’ev for <strong>the</strong> 

latter two and assume that <strong>the</strong> rest platinum in <strong>the</strong> upper crust is equally distributed 

in cooperite and in <strong>the</strong> copper-nickel ores mentioned before.


3.4.50 Potassium 

Potassium is a s<strong>of</strong>t, silvery-white metal, member <strong>of</strong> <strong>the</strong> alkali group. Most potassium 

goes into fertilizers. Potassium carbonate is used in <strong>the</strong> glass manufacture for 

making televisions. Potassium hydroxide is used to make liquid soaps and detergents. 

Fur<strong>the</strong>r application <strong>of</strong> o<strong>the</strong>r potassium compounds are in <strong>the</strong> pharmaceutical 

industry, photography and to make iodize salts. 

Potassium is a very abundant element on earth. Most <strong>of</strong> it occurs as <strong>mineral</strong>s such as 

feldspars and clays. Potassium is leached from <strong>the</strong>se by wea<strong>the</strong>ring, which explains 

why <strong>the</strong>re is quite a lot <strong>of</strong> this element in <strong>the</strong> sea. Important ores for potassium are 

sylvite KCl, carnallite K M gCl 3 · 6(H 2O) and alunite KAl 3(SO 4) 2(OH) 6. 

Potassium-containing <strong>mineral</strong>s in Grigor’ev analysis are: orthoclase, hydromuscovite, 

glauconite, lepidomelane, nepheline, sanidine, stilpnomelane, jarosite, alunite, 

neptunite, sylvite, carnallite, miserite, biotite, muscovite, hydrobiotite, phlogopite, 

todoroskite and cryptomelane. In addition to those, niter, carnotite and lepidomelane 

are o<strong>the</strong>r potasium-containing <strong>mineral</strong>s included in our model, because 

<strong>of</strong> its nitrogen, uranium and lithium contents 15 . The quantity <strong>of</strong> <strong>the</strong> latter 9 <strong>mineral</strong>s 

mentioned above <strong>of</strong> Grigorev’s analysis is fixed by <strong>the</strong>ir Li, U, Cl, F and M n 

content. For <strong>the</strong> remaining <strong>mineral</strong>s, <strong>the</strong>ir respective proportions given by Grigor’ev 

are kept in our model. It must be pointed out, that <strong>the</strong> mass balance between elements 

and species for potassium in Grigorev’s model gives a quantity <strong>of</strong> K greater 

than <strong>the</strong> accepted value for K in <strong>the</strong> earth’s crust in Rudnick et al. [292]. Probably, 

Grigor’ev overestimated <strong>the</strong> quantity <strong>of</strong> some potassium-containing <strong>mineral</strong>s in <strong>the</strong> 

earth’s crust. 

3.4.51 Praseodymium 


3.4.52 Rare Earth Elements: Praseodymium, Samarium, Europium, 

Gadolinium, Terbium, Dysprosium, Holmium, Erbium, Thulium 

and Lutetium 

All fourteen members <strong>of</strong> <strong>the</strong> lanthanide series have very similar geochemical properties. 

Many applications <strong>of</strong> rare earth elements (REE) are characterized by high 

specificity and high unit value. For example, europium is used for color cathoderay 

tubes and liquid crystal displays used in monitors and televisions. A major use 

<strong>of</strong> praseodymium is in misch metal, used in making cigarette lighters. Samarium 

is used as a catalyst in certain organic reactions. Erbium finds extensive use in 

15 See sections 3.4.73, 3.4.36 and 3.4.39 for more details about <strong>the</strong> optimization process for ura- 

nium, lithium and manganese.


laser repeaters for fiber-optic telecommunication cables. Permanent magnet technology 

has been r<strong>evolution</strong>ized by alloys containing gadolinium, dysprosium and o<strong>the</strong>r 

REE. Terbium, gadolinium or europium are used in new energy-efficient fluorescent 

lamps. Lutetium can be used as a catalyst in petroleum cracking in refineries and in 

alkylation, hydrogenation and polymerization applications. Holmium and thulium 

are being used in lasers for medical applications. 

There are over 100 <strong>mineral</strong>s known to contain lanthanides but <strong>the</strong> only two <strong>of</strong> commercial 

importance are monazite, a mixed La, Th, Ln phosphate and bastnaesite, a 

La, Ln fluorocarbonate. Tamarium, terbium and erbium are also found in xenotime 

and euxenite, while gadolinite is also an important source for Holmium, Terbium 

and Thulium. 

Grigor’ev accounted for <strong>the</strong> <strong>mineral</strong> fergusonite in his model, which contains <strong>the</strong> 

REE Sm and traces <strong>of</strong> P r. We will keep in our model <strong>the</strong> same concentration <strong>of</strong> fergusonite 

on earth given by Grigor’ev. Not being specifically in <strong>the</strong> empirical formula 

<strong>of</strong> <strong>the</strong> <strong>mineral</strong>s explained above, <strong>the</strong> REE Gd, T b, D y, Ho, Er, T l and Lu will be 

considered in our model as diadochical elements. 

3.4.53 Rhenium 

Rhenium was <strong>the</strong> last naturally-occurring element to be discovered. Its main 

applications in industry are found in <strong>the</strong> manufacture <strong>of</strong> tungsten-rhenium and 

molybdenum-rhenium alloys. O<strong>the</strong>r important uses <strong>of</strong> rhenium are in platinumrhenium 

catalysts, used primarily in producing lead-free, high octane gasoline and 

in high-temperature superalloys used for jet engine components. 

The concentration <strong>of</strong> rhenium in <strong>the</strong> earth’s crust is extremely low and it is also very 

diffuse. Being chemically akin to molybdenum it is in molybdenites that its highest 

concentrations (0,2%) are found. 

No Re <strong>mineral</strong> is included in Grigorev’s model. We will account for it as “diodochic 

Re”. 

3.4.54 Rhodium 

Rhodium is part <strong>of</strong> <strong>the</strong> platinum group metals. Most part <strong>of</strong> its production goes into 

catalytic converters for cars and in some industrial processes. It is used in alloys with 

platinum and iridium, giving improved high-temperature strength and oxidation resistance 

to furnace windings, high-temperature <strong>the</strong>rmocouple and resistance wires, 

spark plugs, bearings, electrical contacts, etc. 

Rhodium occurs as rare deposits <strong>of</strong> <strong>the</strong> native element and in rare <strong>mineral</strong>s associated 

with o<strong>the</strong>r metals <strong>of</strong> <strong>the</strong> platinum group. But usually, <strong>the</strong> commercially available 

metal comes as a by product <strong>of</strong> <strong>the</strong> refining <strong>of</strong> copper and nickel ores which 

contain up to 0,1% rhodium.


There is no rhodium <strong>mineral</strong> in Grigorev’s analysis. We will account for it as being 

included in <strong>the</strong> ores mentioned before. 

3.4.55 Rubidium 

Rubidium is a silvery white, very active metal as are <strong>the</strong> o<strong>the</strong>r alkali metals. Rubidium 

and its salts have few commercial uses. The metal is used in <strong>the</strong> manufacture 

<strong>of</strong> photocells and in <strong>the</strong> removal <strong>of</strong> residual gases from vacuum tubes. Rubidium 

salts are used in glasses and ceramics and in fireworks to give <strong>the</strong>m a purple color. 

Although very abundant, no purely Rb-containing <strong>mineral</strong> is known and much <strong>of</strong> 

<strong>the</strong> commercially available material is obtained as a byproduct <strong>of</strong> lepidolite processing 

for Li. It occurs also naturally in <strong>the</strong> <strong>mineral</strong>s pollucite, lepodite, carnallite, 

zinnwaldite and leucite. 

All Rb on earth will be accounted in our model as “diadochic Rb”. 

3.4.56 Ru<strong>the</strong>nium 

Ru<strong>the</strong>nium is one <strong>of</strong> <strong>the</strong> six platinum metals. It finds use in <strong>the</strong> electronic and chemical 

industry, with smaller amounts being used in alloying for increasing hardness 

and corrosion resistance. It is used in electrical contact alloys and filaments, in jewelry, 

in pen nibs and in instrument pivots. Like <strong>the</strong> o<strong>the</strong>r metals <strong>of</strong> its group, it is a 

versatile catalyst used in different industrial processes. 

Ru<strong>the</strong>nium is one <strong>of</strong> <strong>the</strong> rarest metals on earth. It is found native and sometimes 

associated with platinum, osmium and iridium. Like <strong>the</strong> o<strong>the</strong>r platinum metals, it is 

commercially extracted from nickel and copper deposits. 

In addition to osmiridium, we will assume that most part <strong>of</strong> ru<strong>the</strong>nium is found in 

nickel and copper ores. 

3.4.57 Samarium 


3.4.58 Scandium 

The transition metal scandium is mainly used in aluminium alloys for sporting equipment, 

metallurgical research, high-intensity metal halide lamps, analytical standards, 

electronics, oil well tracers and lacers. 

Scandium occurs in many ores in trace amounts, but has not been found in sufficient 

quantities to be considered as a reserve. Therefore, scandium has been produced


exclusively as a byproduct during processing <strong>of</strong> various ores or recovered from previously 

processed tailings or residues. Considerable amounts <strong>of</strong> scandium oxide 

Sc 2O 3 can be obtained as a byproduct <strong>of</strong> <strong>the</strong> extraction <strong>of</strong> uranium. Its only rich 

<strong>mineral</strong> is <strong>the</strong> rare thortveitite Sc 2Si 2O 7. 

We will keep <strong>the</strong> value given by Grigor’ev for thortveitite, and assume that <strong>the</strong> rest <strong>of</strong> 

it is widely dispersed in o<strong>the</strong>r <strong>mineral</strong>s. The latter is called in our model “Diodochic 

Sc”. 

3.4.59 Selenium 

Selenium is a non metallic chemical element, resembling sulfur and tellurium in its 

chemical activity and physical properties. It has good photovoltaic and photoconductive 

properties, and it is used extensively in electronics, such as photocells, light 

meters and solar cells. The second largest use <strong>of</strong> selenium is <strong>the</strong> glass industry, used 

to remove color from glass. It finds also extensive application as animal feeds and 

food supplements. Additionally, it can be used in photocopying, in <strong>the</strong> toning <strong>of</strong> 

photographs, in metal alloys and to improve <strong>the</strong> abrasion resistance in vulcanized 

rubbers. 

Selenium is among <strong>the</strong> rarer elements on <strong>the</strong> earth’s crust. It is occasionally found 

native, but it is usually associated with sulfur, copper, zinc and lead, such as in <strong>the</strong> 

form <strong>of</strong> clausthalite CuSe or klockmanite P bSe. Selenium is recovered commercially 

as a byproduct <strong>of</strong> <strong>the</strong> electrolytic refining <strong>of</strong> copper where it accumulates in anode 

residues. 

There is no selenium <strong>mineral</strong> considered in Grigorev’s analysis. We will account for 

<strong>the</strong> element as being part <strong>of</strong> copper ores, since <strong>the</strong>y are its main sources. 

3.4.60 Silicon 

Silicon is a brittle steel-gray metalloid. It has many industrial uses. It is <strong>the</strong> main 

component <strong>of</strong> glass, cement, ceramics, most semiconductor devices and silicones. 

Silicon is also an important constituent <strong>of</strong> some steels and a major ingredient in 

bricks. It is also used as an alloy to provide resistance to aluminium, magnesium, 

copper and o<strong>the</strong>r metals. Metallurgic silicon is used as a raw material in <strong>the</strong> manufacture 

<strong>of</strong> organosilic and silicon resins, seals and oils. Silicon chips are used in 

integrated circuits and photovoltaic cells are made <strong>of</strong> thin cut slices <strong>of</strong> simple silicon 

crystals. 

Silicon is <strong>the</strong> most abundant element in <strong>the</strong> earth’s crust after oxygen. It never 

occurs free, it occurs invariably combined with oxygen and with trivial exceptions 

is always 4-coordinate in nature. Sand is used as a source <strong>of</strong> <strong>the</strong> silicon produced 

commercially. A few silicate <strong>mineral</strong>s are mined, e.g. talc and mica. O<strong>the</strong>r mined 

silicates are feldspars, nepheline, olivine, vermiculite, perlite, kaolinite, etc. 

Our model accounts for 136 Si-containing <strong>mineral</strong>s.


3.4.61 Silver 

In addition to coinage, silver is used mainly in tableware, mirrors, electronic products, 

photography, jewelry and as a catalyst in oxidation reactions. 

Silver is widely distributed in sulfide ores <strong>of</strong> which argentite (Ag 2S) is <strong>the</strong> most 

important. Silver can be also found native in nature and associated to chlorine as 

AgCl. Only about 10% <strong>of</strong> all silver mined is won from deposits primarily exploited 

for <strong>the</strong> metal; 90% or more represents a by-product <strong>of</strong> copper, lead, zinc and gold 

mining. 

Grigor’ev accounted in his model for <strong>the</strong> most important compounds <strong>of</strong> silver found 

in nature, namely native silver, argentite, acanti<strong>the</strong>, stephanite, pyrargirite, chlorargirite, 

freibergite and samsonite. In addition to those, we take into account <strong>the</strong> 

gold-silver telluride sylvanite. 

3.4.62 Sodium 

Sodium is a white-silvery metal, belonging to <strong>the</strong> alkali group, and hence <strong>of</strong> high 

reactivity. Sodium in its metallic form is very important in making esters and in <strong>the</strong> 

manufacture <strong>of</strong> organic compounds. Sodium is also a component <strong>of</strong> sodium chloride 

N aCl, a very important compound found everywhere in <strong>the</strong> living environment. 

O<strong>the</strong>r applications <strong>of</strong> sodium are: in alloys to improve <strong>the</strong>ir structure, in soap, to purify 

molten metals, in sodium vapor lamps, as a heat transfer fluid and as a desiccant 

for drying solvents. 

Sodium is a very abundant element in <strong>the</strong> earth’s crust. After chloride, sodium is 

also <strong>the</strong> second most abundant element dissolved in seawater. Sodium occurs as 

rock-salt (N aCl) and as <strong>the</strong> carbonate, nitrate, sulfate, borate, etc. 

Fifty N a-containing <strong>mineral</strong>s have been considered in our model. 

3.4.63 Strontium 

Strontium is a bright silvery alkaline-earth metal. Principal uses <strong>of</strong> strontium compounds 

are in pyrotechnics, vacuum tubes to remove <strong>the</strong> last traces <strong>of</strong> air and as <strong>the</strong> 

carbonate in special glass for television screens and visual display units. Fur<strong>the</strong>r uses 

<strong>of</strong> strontium and its compounds are in toothpastes, in aerosol paint or for medical 

treatment <strong>of</strong> osteoporosis. 

Strontium commonly occurs in nature, averaging about 0,034% <strong>of</strong> all igneous rocks. 

It is found chiefly in <strong>the</strong> form <strong>of</strong> <strong>the</strong> sulfate <strong>mineral</strong> celestine SrCO 4 and <strong>the</strong> carbonate 

strontianite SrCO 3. 

Grigorev’s strontium-containing <strong>mineral</strong>s are celestine, strontianite and <strong>the</strong> rare <strong>mineral</strong>s 

lamprophyllite and nordite. Our model will keep <strong>the</strong> relative proportions <strong>of</strong>


celestine and strontianite given by Grigor’ev, but assuring that <strong>the</strong>y satisfy <strong>the</strong> mass 

balance for strontium in <strong>the</strong> upper crust. The abundance <strong>of</strong> nordite and lamprophyllite 

given by Grigor’ev is assumed to be correct. Although <strong>the</strong> Sr content in Grigorev’s 

analysis does not fulfill constraint number 4 on page 57, no more strontiumcontaining 

<strong>mineral</strong>s will be included in our model because celestine and strontianite 

are <strong>the</strong>ir most important ores should account for almost all Sn in <strong>the</strong> earth’s upper 

crust. 

3.4.64 Sulfur 

Sulfur is a yellow solid nonmetal. Its main compound is sulfuric acid H 2SO 4, one 

<strong>of</strong> <strong>the</strong> most important substance in industrial and fertilizer complexes. In fact, <strong>the</strong> 

yearly consumption <strong>of</strong> sulfuric acid is an index <strong>of</strong> industrial development <strong>of</strong> a country. 

Sulfur is also used in batteries, detergents, fungicides, manufacture <strong>of</strong> fertilizers, 

gun power, matches and fireworks. It finds also application in <strong>the</strong> manufacture <strong>of</strong> 

corrosion-resistant concrete. 

Sulfur is widely distributed in nature. The three most important commercial sources 

are: 1) elemental sulfur in <strong>the</strong> caprock salt domes in <strong>the</strong> USA and Mexico and <strong>the</strong> 

sedimentary evaporite deposits in eastern Poland and western Asia; 2) as H 2S in sour 

natural gas and as organosulfur compounds in crude oil. They represent currently 

<strong>the</strong> main commercial source <strong>of</strong> <strong>the</strong> element. 3) from pyrites FeS 2 and o<strong>the</strong>r metalsulfide 

<strong>mineral</strong>s. Common naturally occurring sulfur compounds include <strong>the</strong> sulfide 

<strong>mineral</strong>s cinnabar H gS, galena P bS, sphalerite ZnS, stibnite S b 2S 3 and <strong>the</strong> sulfates 

gypsum CaSO 4 · 2H 2O, alunite KAl 3(SO 4) 2(OH) 6 and barite BaSO 4. 

Our model accounts for 47 S-containing <strong>mineral</strong>s. 

3.4.65 Tantalum 

Tantalum is a hard transition metal highly corrosion-resistant and a good conductor 

<strong>of</strong> heat and electricity. The major use for tantalum is in <strong>the</strong> manufacture <strong>of</strong> electronic 

components, mainly capacitors. Additionally, it is used in high-temperature 

applications such as aircraft engines and for handling corrosive chemicals. 

Tantalum occurs invariably toge<strong>the</strong>r with niobium. The chief <strong>mineral</strong> for Ta is 

known as tantalite FeTa 2O 6. Deposits are widespread but rarely very concentrated. 

Microlite and euxenite are o<strong>the</strong>r minor ores for Ta. 

Grigor’ev accounts for Ta in <strong>mineral</strong>s ferrotantalite, microlite, tanteuxenite and euxenite, 

as well as in polycrase and blomstrandite. The relative proportions <strong>of</strong> <strong>the</strong> 

four <strong>mineral</strong>s given by Grigor’ev are kept in our model, while <strong>the</strong> quantities <strong>of</strong> <strong>the</strong> 

last two are fixed by <strong>the</strong> uranium mass balance 16 . 

dite. 

16 See section 3.4.73 for details about <strong>the</strong> optimization procedure used for polycrase and blomstran


3.4.66 Tellurium 

Tellurium is a semiconductor. Its chemistry is similar to that <strong>of</strong> sulfur and has properties 

both <strong>of</strong> metals and non metals. It is used as an additive to steel and it is <strong>of</strong>ten 

alloyed to aluminium, copper, lead or tin. It can be used for cast iron, ceramics, 

blasting caps, solar panels or rubber. 

Tellurium is a relatively rare element. Commercial tellurium comes mainly as a 

byproduct <strong>of</strong> copper processing. Samples <strong>of</strong> tellurium can be found uncombined 

in nature, but <strong>the</strong>y are extremely rare. There are some tellurium <strong>mineral</strong>s such as 

calaverite, sylvanite or tellurite, but none is mined as a source <strong>of</strong> <strong>the</strong> element. 

The only <strong>mineral</strong> containing tellurium considered by Grigore’ev is tetradymite. We 

will keep <strong>the</strong> concentration given by Grigor’ev for tetradymite and include tellurite 

(assuming that it has <strong>the</strong> same Te concentration as sylvanite and calaverite) and “dispersed 

Te”, which should account for <strong>the</strong> rest <strong>of</strong> tellurium in <strong>the</strong> crust found mostly 

in copper ores. Remember that sylvanite and calaverite were already accounted for 

gold-containing <strong>mineral</strong>s. 

3.4.67 Terbium 


3.4.68 Thallium 

Thallium is a s<strong>of</strong>t and malleable heavy metal that is used in a wide variety <strong>of</strong> applications. 

Some <strong>of</strong> <strong>the</strong>m are as a semiconductor material for selenium rectifiers, in 

gamma radiation detection equipment, in infrared radiation detection and transmission 

equipment, in crystalline filters for light diffraction, in medical diagnostic tests 

to detect heart diseases, etc. 

Although thallium is reasonable abundant in <strong>the</strong> crust, it exists mostly in association 

with potassium <strong>mineral</strong>s such as sylvite and pollucite and is not generally considered 

to be commercially recoverable from those forms. Very rare <strong>mineral</strong>s <strong>of</strong> thallium 

occur in nature as sulfide or selenide complexes with antimony, arsenic, copper, 

lead and silver such as hutchingsonite P bT lAs 5S 9, but <strong>the</strong>y have no commercial 

importance as sources ei<strong>the</strong>r. Thallium is commercially recovered as a byproduct 

from <strong>the</strong> flue dust and residues generated during <strong>the</strong> roasting and smelting <strong>of</strong> Zn 

and P b sulfide ores. 

No thallium <strong>mineral</strong> has been recorded by Grigor’ev. We will include T l in our model 

as “dispersed T l”, which should account for all T l in <strong>the</strong> crust in <strong>the</strong> forms <strong>of</strong> <strong>the</strong> 

sources mentioned above.


3.4.69 Thorium 

Thorium is a silver-grey heavy metallic element <strong>of</strong> <strong>the</strong> actinide series. Thorium 

demand worldwide is relatively small. Some <strong>of</strong> its applications are as an alloying 

element in magnesium, as a coating for wolfram wire used in electronic equipment, 

to control grain size <strong>of</strong> plutonium used for electric lamps, as a catalyst, in <strong>the</strong> manufacture 

<strong>of</strong> refractory materials for <strong>the</strong> metallurgical industries, or as a fertile material 

for producing nuclear fuel. 

Thorium is very abundant in <strong>the</strong> earth’s crust (three times more abundant than uranium). 

Thorium occurs naturally in <strong>the</strong> <strong>mineral</strong>s thorite, uranothorite, thorianite 

and is a major component <strong>of</strong> monazite, where it is usually commercially extracted 

as a byproduct. It is present also in significant amounts as diodochic element in <strong>the</strong> 

<strong>mineral</strong>s zircon, titanite, gadolinite and blomstrandite. 

Grigor’ev records all <strong>the</strong> main thorium-containing <strong>mineral</strong>s in his model explained 

above, as well as britholite, polycrase, yttrialite and chevkinite. They are all included 

in our model, maintaining <strong>the</strong> relative proportions provided by Grigor’ev. 

3.4.70 Thulium 


3.4.71 Tin 

Tin is a silvery-white metal that finds extensive use as a protective layer for mild 

steel. Alloys <strong>of</strong> tin are used in many ways, such as solder for joining pipes or electronic 

circuits, bell and babbit metal, dental amalgams, etc. The principal alloys <strong>of</strong> 

tin are bronzite (tin and copper), s<strong>of</strong>t solder (tin and lead), pewter (75% tin and 

25% lead) and britannia metal (tin with small amounts <strong>of</strong> antimony and copper). 

There are few tin-containing <strong>mineral</strong>s, but only one is <strong>of</strong> commercial significance 

and that is cassiterite SnO 2. 

Grigor’ev accounts for Sn in cassiterite as well as native tin. We keep <strong>the</strong> relative 

proportions <strong>of</strong> both <strong>mineral</strong>s given by Grigor’ev in our model but assuring that <strong>the</strong>y 

fulfill <strong>the</strong> mass balance <strong>of</strong> Sn on earth. No more tin-containing <strong>mineral</strong>s will be 

included because cassiterite is its most important ore and should account for almost 

all Sn in <strong>the</strong> earth’s upper crust. 

3.4.72 Titanium 

Titanium is a light, strong transition metal, well known for corrosion resistance and 

for its high strength-to-weight ratio. Most <strong>of</strong> it is consumed in <strong>the</strong> form <strong>of</strong> titanium


dioxide T iO 2, a white pigment in paints, paper and plastics. Titanium alloys are 

used in aircraft, pipes for power plants, armor plating, naval ships and missiles. In 

medicine, titanium is used to make hip and knee replacements, pace-makers, boneplates 

and screws. 

Titanium is an abundant element on earth and is found in <strong>mineral</strong>s rutile T iO 2, 

brookite T iO 2, anatase T iO 2, illmenite Fe 2+ T iO 3, leucoxene CaT iSiO 5 and titanite 

CaT iSiO 5. The chief mined ore is ilmenite, but leucoxene and rutile are also 

important economic ores for titanium. 

Titanium-containing <strong>mineral</strong>s considered by Grigor’ev are: ilmenite, leucoxene, rutile, 

brookite, titanite, augite, ulvöspinel, anatase, aenigmatite, perovskite, ramsayite, 

lamprophyllite, neptunite, blomstrandite, polycrase, lavenite, rinkolite, delorenzite, 

loparite, chevkinite, murmanite, ilmenorutile and euxenite. No additional 

<strong>mineral</strong>s are included in our model. 

3.4.73 Uranium 

Uranium is a silvery metallic radioactive element <strong>of</strong> <strong>the</strong> actinide group. It gained 

importance with <strong>the</strong> development <strong>of</strong> practical uses <strong>of</strong> nuclear energy. Depleted uranium 

is used as shielding to protect tanks and also in bullets and missiles. However, 

<strong>the</strong> main use <strong>of</strong> uranium is to fuel commercial nuclear power plants. 

Uranium is widely distributed, being <strong>the</strong> most important ores uraninite UO 2 and 

carnotite K 2(UO 2) 2(VO 4)2 · 3H 2O. However, even <strong>the</strong>se are usually dispersed so 

that typical ores contain only about 0,1%, and many <strong>of</strong> <strong>the</strong> more readily exploited 

deposits are nearing exhaustion. Significant concentrations <strong>of</strong> uranium occur in 

some <strong>mineral</strong>s such as monazite sands or lignite. 

Grigor’ev considers five uranium-containing <strong>mineral</strong>s: uraninite, betafite, metatorbenite 

and polycrase. In addition to those <strong>mineral</strong>s, we include also carnotite in 

our model, assuming that it has <strong>the</strong> same U content as uraninite. The relative proportions 

<strong>of</strong> all <strong>mineral</strong>s accounted by Grigor’ev are kept and <strong>the</strong>ir quantities are 

obtained by satisfying constraint 1. 

3.4.74 Vanadium 

Vanadium is a transition metal and finds extensive use in <strong>the</strong> manufacture <strong>of</strong> special 

steels with exceptional strength and toughness. Steel alloys are used in axles, 

crankshafts, gears and o<strong>the</strong>r critical components. Mixed with aluminium in titanium 

alloys, it is used in jet engines and high speed air-frames. 

Vanadium is widely, though sparsely distributed; thus although more than 60 different 

<strong>mineral</strong>s <strong>of</strong> vanadium have been characterized, <strong>the</strong>re are few concentrated 

deposits and most <strong>of</strong> it is obtained as a byproduct <strong>of</strong> iron, uranium, phosphor, copper, 

lead, zinc or titanium ores. Most important vanadium <strong>mineral</strong>s are patronite


V S 4, vanadinite P b 5(VO 4) 3Cl and carnotite K 2(UO 2) 2(VO 4) 2 · (H 2O). Vanadium is 

also found in some crude oils, coal, oil shale and tar sands. 

No vanadium-containing <strong>mineral</strong>s are registered by Grigor’ev. We take into account 

in our model carnotite, for being an uranium important ore. The rest vanadium is 

assumed to come from dispersed sources. 

3.4.75 Wolfram 

Wolfram, also known as Tungsten, is a transition metal, having <strong>the</strong> highest melting 

point <strong>of</strong> any metal. Hence, it is used in filaments in incandescent light bulbs, in 

electric contacts and arc-welding electrodes. It imparts great strength to alloys such 

as steel. Tungsten is also used in X-ray tubes and in microchip technology. Its most 

important application though is in <strong>the</strong> manufacture <strong>of</strong> cement carbide, since its main 

component is wolfram carbide (W C). 

There are several <strong>mineral</strong>s <strong>of</strong> wolfram, <strong>the</strong> most important ones are scheelite and 

wolframite. 

Both <strong>mineral</strong>s have been considered by Grigor’ev and will be taken into account in 

our model, keeping <strong>the</strong> relative proportions <strong>of</strong> Grigorev’s analysis. The quantity <strong>of</strong> 

both <strong>mineral</strong>s in our model almost exceeds two orders <strong>of</strong> magnitude <strong>the</strong> values given 

by Grigorev. However, all references consulted coincide in giving most relevance 

only to those two substances. Therefore, no additional <strong>mineral</strong>s are going to be 

considered. 

3.4.76 Ytterbium 

Ytterbium is a rare earth element used in certain steels for improving <strong>the</strong> grain refinement, 

strength and o<strong>the</strong>r mechanical properties <strong>of</strong> stainless steel. Some ytterbium 

alloys have been used in dentistry. Like o<strong>the</strong>r REE, it can be used to dope phosphors, 

or for ceramic capacitors and o<strong>the</strong>r electronic devices. 

Ytterbium is found with o<strong>the</strong>r rare earth elements in several rare <strong>mineral</strong>s as gadolinite, 

monazite and xenotime. It is most <strong>of</strong>ten recovered commercially from monazite 

sand. 

The latter <strong>mineral</strong>s have been considered by Grigor’ev. We will assume that Grigorev’s 

quantity for xenotime is correct and will account for Y b in monazite as <strong>the</strong> 

difference between <strong>the</strong> contents in <strong>the</strong> earth’s crust and in xenotime. 

3.4.77 Yttrium 

Yttrium is a silver-metallic rare earth metal. The largest use <strong>of</strong> <strong>the</strong> element is as its 

oxide yttria Y 2O 3, which is used in making red phosphors for color television picture


tubes. It is also used in small amounts to increase <strong>the</strong> strength <strong>of</strong> aluminium and 

magnesium alloys. Additional uses <strong>of</strong> yttrium are in camera lenses and to make 

superconductors. 

Yttrium, like lanthanum is invariably associated with lanthanide elements in <strong>mineral</strong>s 

such as xenotime, monazite, fergusonite or gadolinite. 

Yttrium-containing <strong>mineral</strong>s in Grigorev’s model are: fergusonite, thortveitite, polycrase, 

gadolinite, rinkolite, euxenite, tanteuxenite, ytriallite, orthite and weinschenkite. 

The concentration <strong>of</strong> all those <strong>mineral</strong>s on earth, except for weinschenkite 

are fixed by <strong>the</strong>ir content in o<strong>the</strong>r elements in our model. For weinschenkite, we will 

assume that it has <strong>the</strong> concentration given by Grigor’ev. Additionally, “diodochic Y ” 

is included in our model in order to account for <strong>the</strong> Y found in <strong>the</strong> crystalline structure 

<strong>of</strong> o<strong>the</strong>r lanthanide <strong>mineral</strong>s. 

3.4.78 Zinc 

Zinc is a bluish-white transition metal. It is <strong>the</strong> fourth metal mostly consumed in <strong>the</strong> 

world. The main use <strong>of</strong> zinc is for <strong>the</strong> galvanizing <strong>of</strong> iron sheets or wires. Zinc is 

used in making alloys such as brass or bronze. Zinc oxide is used as a white pigment 

in plastics, cosmetics, paper, printing inks, etc. and as an activator in <strong>the</strong> rubber 

industry. 

The major ores <strong>of</strong> zinc are sphalerite ZnS and smithsonite ZnCO 3. Less important 

ores are franklinite Zn0.6M n 2+ 

0.3Fe2+ 0.1M n3+ 

0.5O4, hemimorphite Zn4Si 2O7(OH) 2 

and wurtzite Zn0.9Fe 2+ 

0.1S. Grigorev’s Zn-containing <strong>mineral</strong>s are sphalerite, smithsonite, nordite and native 

zinc. In our model we will assume that all those four <strong>mineral</strong>s account for <strong>the</strong> majority 

<strong>of</strong> <strong>the</strong> zinc found in <strong>the</strong> upper crust and hence we will omit <strong>the</strong> less important 

ores mentioned above. The abundance <strong>of</strong> nordite is fixed by its Sr content. 

3.4.79 Zirconium 

Zirconium is a silver-gray metal with chemical and physical properties similar to 

those <strong>of</strong> titanium. It is extremely resistant to heat and corrosion. Zircon is its most 

used compound and is used in refractories, ceramic opacification and foundry sands. 

It is also considered as a semi-precious gemstone used in jewelry. Fur<strong>the</strong>r uses for 

zirconium are in alloys such as zircaloy, which is used in nuclear applications since 

it does not absorb neutrons. It is also used in catalytic converters. 

Zirconium is not particularly a rare element and occurs in nature mainly as <strong>the</strong> 

silicate <strong>mineral</strong> zircon Z rSiO 4. Baddeleyite Z rO 2 is also an important ore for Z r. 

Grigorev’s model includes eight different zirconium-containing <strong>mineral</strong>s: zircon, 

naegite (a variety <strong>of</strong> zircon that contains U, Th, Y and o<strong>the</strong>r REE in its lattice),


sirtolite (a variety <strong>of</strong> zircon that contains Th and H f in its lattice), eudialyte, baddeleyite, 

lavenite, mosandrite and wohlerite. An interesting aspect about his analysis is 

that eudialyte is a more abundant <strong>mineral</strong> than baddeleyite, which is more common. 

All eight <strong>mineral</strong>s are also included in our analysis. Grigorev’s relative proportions 

are kept, but assuring <strong>the</strong> satisfaction <strong>of</strong> <strong>the</strong> constraints described before. 

3.5 Ma<strong>the</strong>matical representation 

The problem described in a qualitatively way in <strong>the</strong> last section, can be represented 

ma<strong>the</strong>matically according to Eq. 3.2. The objective is to minimize (M in) with a 

least squares procedure <strong>the</strong> difference between <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> 

our model ( ˆ ξi) and that <strong>of</strong> Grigor’ev’s analysis ( ξ i). This optimization must be 

constrained by physical and geological restrictions. 

The physical restrictions are constraints 1 and 2 defined in section 3.4, namely <strong>the</strong> 

satisfaction <strong>of</strong> <strong>the</strong> mass balance and <strong>the</strong> positiveness requirement for all <strong>mineral</strong>s. 

The geological restrictions are based on reasonable assumptions and, as opposed to 

<strong>the</strong> physical ones, may change with new <strong>mineral</strong> discoveries and with <strong>the</strong> point <strong>of</strong> 

view <strong>of</strong> <strong>the</strong> analyst. Hence, <strong>the</strong> model that we have developed must not be considered 

as final and closed. On <strong>the</strong> contrary, it is <strong>the</strong> first step for obtaining a comprehensive, 

physically and geologically coherent <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> 

upper earth’s crust. Remember that <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> crust has been 

improved throughout decades and is still under research. 

Vector ˆε j, containing <strong>the</strong> elements that compose <strong>the</strong> <strong>mineral</strong>s in our model are 

showed in table A.1 (page 351). Vector ξ i, containing <strong>the</strong> <strong>mineral</strong>s described by 

Grigor’ev’s analysis is represented in table A.2 (page 352). Finally, <strong>the</strong> matrix <strong>of</strong> 

coefficients R[ j × i] is showed in tables A.3 and A.4 17 (page 360). 

The objective function is showed in equation 3.2: 

M in ˆ ξ i − ξ i 2 

The physical restrictions to be applied are: 

• Σr j,i · ˆ ξ i = ˆε j 

• ˆ ξ i > 0 

(3.2) 

The geological restrictions based on reasonable assumptions and described in sections 

3.4.3 through 3.4.79 for each substance are <strong>the</strong> following: 

17 For <strong>the</strong> sake <strong>of</strong> a more flexible representation <strong>of</strong> matrix R[ j × i], its transposed is given R ′ [i × j].

Ma<strong>the</strong>matical representation 89 

• Gold: ˆ ξ 1 = ˆε 1 · 0, 85/r 1,1 

• Calaverite: ˆ ξ 2 = ˆε 1 · 0, 075/r 1,2 

• Sylavanite: ˆ ξ 3 = ˆε 1 · 0, 075/r 1,3 

• Thortveitite: ˆ ξ 6 = ξ 6 

• Lautarite: ˆ ξ 22 = ˆε 28/(r 28,22 + r 28,23) 

• Dietzeite: ˆ ξ 23 = ˆε 28/(r 28,22 + r 28,23) 

• Nitratine: ˆ ξ 25 = ˆε 31/(r 31,25 + r 31,26) 

• Niter: ˆ ξ 26 = ˆε 31/(r 31,25 + r 31,26) 

• Xenotime: ˆ ξ 31 = ξ 31 

• Tetradymite: ˆ ξ 35 = ξ 35 

• Tellurite: ˆ ξ 36 = (r 2,2 · ˆ ξ 2)/(r 2,36) 

• Polixene: ˆ ξ 40 = ξ 40 

• I-Platinum: ˆ ξ 41 = ξ 41 

• Cooperite: ˆ ξ 42 = (ˆε 46 − r 46,40 · ˆ ξ 40 − r 46,41 · ˆ ξ 41)/(2 · r 46,42) 

• P t in N i-Cu ores ˆ ξ 43 = (ˆε 46 − r 46,40 · ˆ ξ 40 − r 46,41 · ˆ ξ 41)/(2 · r 46,43) 

• Fergusonite: ˆ ξ 47 = ξ 47 

• Stibnite: ˆ ξ 50 = (ˆε 41 − r 41,34 · ˆ ξ 34 − r 41,51 · ˆ ξ 51 − r 41,309 · ˆ ξ 309 − r 41,310 · ˆ ξ 310 − 

r 41,312 · ˆ ξ 312)/(2 · r 41,50) 

• Boulangerite: ˆ ξ 51 = ξ 51 

• S b in galena: ˆ ξ 52 = (ˆε 41 − r 41,34 · ˆ ξ 34 − r 41,51 · ˆ ξ 51 − r 41,309 · ˆ ξ 309 − r 41,310 · 

ˆξ 310 − r 41,312 · ˆ ξ 312)/(2 · r 41,52) 

• Lamprophyllite: ˆ ξ 55 = ξ 55 

• Tourmaline: ˆ ξ 58 = ξ 58 

• Kornerupine: ˆ ξ 59 = ξ 59 

• Axinite - Fe: ˆ ξ 60 = ξ 60 

• Dumortierite: ˆ ξ 61 = ξ 61 

• Sassolite: ˆ ξ 62 = (ˆε 62−r 62,58· ˆ ξ 58−r 62,59· ˆ ξ 59−r 62,60· ˆ ξ 60−r 62,61· ˆ ξ 61)/(4·r 62,62)


• Colemanite: ˆ ξ 63 = (ˆε 62 − r 62,58 · ˆ ξ 58 − r 62,59 · ˆ ξ 59 − r 62,60 · ˆ ξ 60 − r 62,61 · ˆ ξ 61)/(4 · 

r 62,63) 

• Kernite: ˆ ξ 64 = (ˆε 62−r 62,58· ˆ ξ 58−r 62,59· ˆ ξ 59−r 62,60· ˆ ξ 60−r 62,61· ˆ ξ 61)/(4·r 62,64) 

• Ulexite: ˆ ξ 65 = (ˆε 62−r 62,58· ˆ ξ 58−r 62,59· ˆ ξ 59−r 62,60· ˆ ξ 60−r 62,61· ˆ ξ 61)/(4· r 62,65) 

• Wi<strong>the</strong>rite: ˆ ξ 68 = 0, 1 · ˆ ξ 67 

• Bismutite: ˆ ξ 72 = (r 42,70 · ˆ ξ 70)/(r 42,72) 

• Carnotite: ˆ ξ 85 = (r 66,81 · ˆ ξ 81)/(r 66,85) 

• Chyroberyl: ˆ ξ 90 = (r 71,86 · ˆ ξ 86)/(r 71,90) 

• Cobaltite: ˆ ξ 125 = ξ 125 

• Smaltite: ˆ ξ 126 = ˆ ξ 125 

• Linnaeite: ˆ ξ 127 = (r 76,125 · ˆ ξ 125)/(r 76,127) 

• Arsenolite: ˆ ξ 136 = (r 77,131 · ˆ ξ 131)/(r 77,136) 

• Diadochic N i: ˆ ξ 141 = (r 48,137 · ˆ ξ 137)/(r 48,141) 

• Miserite: ˆ ξ 151 = ξ 151 

• Weinschenkite: ˆ ξ 153 = ξ 153 

• Vivianite: ˆ ξ 155 = ξ 155 

• Cryotile: ˆ ξ 165 = (r 60,163 · ˆ ξ 163)/(r 60,165) 

• Lepidolite: ˆ ξ 179 = (r 64,73 · ξ 73 · 0, 1)/r 64,179 

• Tetrahedrite: ˆ ξ 313 = ξ 313 

• Nordite: ˆ ξ 314 = ξ 314 

The problem described above was not able to be solved with a ma<strong>the</strong>matical s<strong>of</strong>tware 

18 . The reasons for which <strong>the</strong> ma<strong>the</strong>matical applications could not solve it 

might have been: 

• Matrix R [ j × i] is a sparce matrix, composed mainly by zeros. 

• There are differences between <strong>the</strong> orders <strong>of</strong> magnitude <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s <strong>of</strong> a 

factor <strong>of</strong> up to 10 12 . 

18 The problem was tried to be solved with <strong>the</strong> s<strong>of</strong>tware Matlab 7.0. The function used was lsqlin 

with <strong>the</strong> constraints described previously.

Results 91 

• The orders <strong>of</strong> magnitude are very small (down to 10 −15 ) and may be below 

<strong>the</strong> significant figures <strong>of</strong> <strong>the</strong> programmes. 

The resolution <strong>of</strong> <strong>the</strong> system through a ma<strong>the</strong>matical application is open for fur<strong>the</strong>r 

studies. Probably, more powerful s<strong>of</strong>tware will be required. 

3.6 Results 

Fortunately, <strong>the</strong> optimization problem was solved in a manual way through a trial 

and error procedure. For that purpose, <strong>the</strong> relative proportions <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s in 

Grigorev’s model were always tried to be kept. The fitting <strong>of</strong> <strong>the</strong> elements, i.e. 

assuring that ˆε j −ε j = 0, was carried out gradually in increasing order <strong>of</strong> appearance 

in <strong>the</strong> <strong>mineral</strong>s recorded by Grigor’ev. This way, element Au was <strong>the</strong> first to be 

fitted, since native gold is <strong>the</strong> only Au-containing <strong>mineral</strong> in Grigor’ev’s model. The 

last element to be adjusted was Si, since it is <strong>the</strong> element mostly contained in <strong>the</strong> 

<strong>mineral</strong>s <strong>of</strong> <strong>the</strong> crust. It must be pointed out that elements O and H have been left 

free, i.e. without constraints. 

Table 3.5 shows <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> earth’s crust obtained in order 

<strong>of</strong> abundance. The abundance <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s in mass terms, is calculated with Eq. 

3.3. 

ˆξ i · MWi Abundance(%) = m i=1 (ˆ · 100 (3.3) 

ξi · MWi) In table A.2 in page 352, <strong>the</strong> difference between our <strong>mineral</strong>ogical composition and 

that <strong>of</strong> Grigor’ev is shown. It contains 324 species, 57 more than in Grigor’ev’s 

model 19 . Of <strong>the</strong> 324 substances, 292 are <strong>mineral</strong>s and <strong>the</strong> rest are mainly diadochic 

elements included in <strong>the</strong> crystal structure <strong>of</strong> o<strong>the</strong>r <strong>mineral</strong>s. That is <strong>the</strong> case for 

elements Ce, N d, N i, Y , Rb, Co, D y, Er, Eu, Ga, Gd, Ge, Ho, Lu, Re, Sc, T b, T l, 

T m, V , H f , In, Pd, P r, P t, Rh, Ru, S b, Se, Sm, Te, Y b. The resulting molecular 

weight <strong>of</strong> <strong>the</strong> upper continental crust according to this model is 157,7 g/mole 20 . 

Next, <strong>the</strong> results obtained are discussed, stressing out <strong>the</strong> differences for <strong>the</strong> most 

abundant and relevant <strong>mineral</strong>s with Grigor’ev’s model. Additionally, <strong>the</strong> <strong>mineral</strong>s 

are aggregated into <strong>the</strong> main groups explained in section 3.2 and are compared to 

<strong>the</strong> values given by Wedepohl [402], [403] and Nesbitt and Young [242]. Finally 

<strong>the</strong> drawbacks <strong>of</strong> <strong>the</strong> model are also explained. 

19 The non-<strong>mineral</strong> materials <strong>of</strong> Grigor’ev’s model have not been taken into account. 

20 Remember that <strong>the</strong> molecular weight <strong>of</strong> <strong>the</strong> crust in Grigor’ev’s model was MWcr = 142, 1 g/mole.


Table 3.5: Mineralogical composition <strong>of</strong> <strong>the</strong> earth’s crust according to <strong>the</strong> 

calculations <strong>of</strong> this study 

Mineral Formula MW Abundance 

g/mole mass, % 

Quarz SiO2 60,08 2,29E+01 

Albite N aAlSi 3O8 263,02 1,35E+01 

Oligoclase N a0.8Ca 0.2Al1.2Si2.8O8 265,42 1,19E+01 

Orthoclase KAlSi 3O8 278,33 1,18E+01 

Andesine N a0.6Ca 0.4Al1.4Si2.6O8 268,62 5,46E+00 

Paragonite 

Biotite 

N aAl3Si 3O10(OH) 2 

K M g2.5Fe 800,00 3,96E+00 

2+ 

0.5AlSi Hydromuscovite/ 

Illite 

3O10(OH) 1.75F0.25 K0.6(H3O) 0.4Al2M g0.4Fe 433,53 3,82E+00 

2+ 

0.1Si3.5O10(OH) 2 392,65 3,03E+00 

Augite Ca0.9N a0.1M g0.9Fe 2+ 

0.2Al Hornblende 

(Fe) 

0.4T i0.1Si1.9O6 Ca2Fe 236,35 3,00E+00 

2+ 

4 Al0.75Fe 3+ 

0.25 (Si7AlO 22)(OH) 2 947,32 2,63E+00 

Labradorite 

Nontronite 

N a0.5Ca 0.5Al1.5Si2.5O8 N a0.3Fe 270,21 2,50E+00 

3+ 

2 Si Opal 

Ripidolite 

3.7Al0.3O10(OH) 2 · 4(H2O) SiO2 · 1.5(H2O) M g3.75Fe 496,67 

87,11 

1,93E+00 

1,24E+00 

2+ 

1.25Si Almandine 

3Al2O10(OH) 8 

Fe 

595,22 1,20E+00 

2+ 

3 Al Muscovite 

2(SiO 4) 3 

KAl3Si 3O10(OH) 1.8F0.2 497,75 

398,71 

1,04E+00 

1,01E+00 

Sillimanite 

Epidote 

Al2SiO 5 

Ca2Fe 162,05 9,97E-01 

3+ Al2(SiO 4) 3(OH) 483,23 9,06E-01 

Kaolinite Al2Si 2O5(OH) 4 258,16 8,36E-01 

Calcite 

Magnetite 

CaCO 3 

Fe 

100,09 8,00E-01 

3+ 

2 Fe2+ Riebeckite 

O4 N a2Fe 231,54 7,95E-01 

2+ 

3 Fe3+ 

2 (Si Beidellite 

Ilmenite 

8O22)(OH) 2 

N a0.33Al2.33Si3.67O10(OH) 2 

Fe 

935,90 

367,54 

5,74E-01 

5,10E-01 

2+ T iO3 151,73 4,71E-01 

Titanite 

Clinochlore 

CaT iSiO 5 

M g3.75Fe 196,04 4,46E-01 

2+ 

1.25Si Sepiolite 

Aegirine 

3Al2O10(OH) 8 

M g4Si6O 15(OH) 2 · 6(H2O) N aFe 

595,22 

613,82 

4,37E-01 

3,48E-01 

3+ Si2O6 231,00 3,04E-01 

Diopside CaM gSi2O6 216,55 3,04E-01 

Natrolite N a2Al2Si 3O10 · 2(H2O) 380,22 2,97E-01 

Cummingtonite 

Ankerite 

M g7(Si8O 22)(OH) 2 

CaFe 

780,82 2,91E-01 

2+ 

0.6M g0.3M n2+ 0.1 (CO Phosphate rock 

Hypers<strong>the</strong>ne 

3) 2 

Ca3(PO 4) 2 

M gFe 

206,39 

310,00 

2,82E-01 

2,79E-01 

2+ Hastingsite 

Si2O6 N aCa 2Fe 

232,32 2,72E-01 

2+ 

4 Fe3+ Bytownite 

Actinolite 

(Si6Al 2O22)(OH) 2 

N a0.2Ca 0.8Al1.8Si2.2O8 Ca2M g3Si8O 22(OH) 2Fe 

990,86 

275,01 

2,58E-01 

2,50E-01 

2+ 

Hydrobiotite 

2 

M g2.3Fe 875,45 2,47E-01 

3+ 

0.6K Montmorillonite 

0.3Ca 0.1Si2.8Al1.3O10(OH) 1.8F0.2· 3(H2O) N a0.165Ca 0.0835Al2.33Si3.67O10(OH) 2 

463,51 

367,09 

2,44E-01 

2,39E-01 

Andalusite Al2SiO 5 162,05 2,03E-01 

Lawsenite CaAl 2Si2O 7 314,24 2,00E-01 

Diaspore AlO(OH) 59,99 1,77E-01 

Pennine M g3.75Fe 2+ 

1.25Si Glauconite 

3Al2O10(OH) 8 

K0.6N a0.05Fe 595,22 1,71E-01 

3+ 

1.3M g0.4Fe 2+ 

0.2Al Prehnite 

0.3Si3.8O10(OH) 2 

Ca2Al2Si 3O10(OH) 2 

426,93 

395,38 

1,56E-01 

1,41E-01 

Dolomite CaM g(CO 3) 2 


184,40 1,41E-01

Results 93 


calculations <strong>of</strong> this study. – continued from previous page. 



Hydragillite/ 

Gibbsite 

Al(OH) 3 78,00 1,38E-01 

Ulvöspinel T iFe 2+ 

2 O Goethite 

4 

Fe 

223,57 1,16E-01 

3+ O(OH) 88,85 1,04E-01 

Neptunite KN a2 LiFe 2+ M n2+ 

1.5 0.5T i Hematite 

Lepidomelane/ 

Annite 

2Si8O 24 

Fe2O3 K Fe 

907,69 

159,69 

9,97E-02 

9,66E-02 

2+ 

2.5M g0.5Fe 3+ 

0.75Al0.25Si3O 10(OH) 2 512,40 9,11E-02 

Sanidine K0.75N a0.25AlSi 3O8 274,30 7,31E-02 

Barite BaSO4 233,39 7,09E-02 

Distene/ Kyanite 

Al2SiO 5 162,05 7,08E-02 

Celestine 

Staurolite 

SrSO 4 

Fe 

183,68 6,70E-02 

2+ Thuringite/ 

Chamosite 

Al9Si 4O23(OH) Fe 

851,86 6,54E-02 

2+ 

3 M g2Al 3+ 

0.5 Fe3+ 

0.5Si3AlO 10(OH) 2 562,80 6,43E-02 

Ferrosilite Fe2+ M gSi2O 6 263,86 6,11E-02 

Halite N aCl 58,44 5,89E-02 

Boehmite AlO(OH) 59,99 5,79E-02 

Thomsonite N aCa 2Al5Si 5O20 · 6(H2O) 806,56 4,99E-02 

Serpentine/ 

Clinochrysotile 

M g3Si2O 5(OH) 4 277,11 4,56E-02 

Pigeonite M g1.35Fe 2+ 

0.55Ca Bronzite 

0.1Si2O 6 

M gFe 

219,70 4,37E-02 

2+ Si2O6 232,32 4,11E-02 

Apatite Ca5(PO 4) 3(OH) 0.33F0.33Cl 0.33 509,12 4,03E-02 

Zircon 

Stilpnomelane 

Z rSiO 4 

K0.8Fe 183,31 3,88E-02 

2+ 

8 Al Spodumene 

Psilomelane 

0.8Si11.1O21(OH) 8.6 · 6(H2O) LiAlSi 2O6 Ba2M n 

1391,50 

186,09 

3,85E-02 

3,83E-02 

3+ 

5 O Leucoxene 

10 · H2O CaT iSiO 5 

745,37 

196,04 

3,80E-02 

3,72E-02 

Tremolite Ca2M g5Si8O 22(OH) 2 812,37 3,48E-02 

Clinozoisite 

Crossite 

Ca2Al3(SiO 4) 3(OH) 

N a2M g2Fe 454,36 3,41E-02 

2+ Al2(Si 8O22)(OH) 2 815,09 3,31E-02 

Pyrite FeS?2 119,98 3,30E-02 

Niter KNO 3 101,10 3,00E-02 

Talc M g3Si4O 10(OH) 2 379,27 2,91E-02 

Vermiculite M g3Si4O 10(OH) 2 · 2(H2O) 415,30 2,81E-02 

Enstatite M g2Si2O 6 200,78 2,78E-02 

Anorthite CaAl 2Si2O 8 277,41 2,75E-02 

Rutile T iO2 79,88 2,73E-02 

Zoisite Ca2Al3Si 3O12(OH) 454,36 2,58E-02 

Nitratine 

Braunite 

N aNO3 M n 

84,99 2,52E-02 

2+ M n 3+ 

6 SiO Siderite 

12 

Fe 

604,64 2,45E-02 

2+ CO3 115,86 2,41E-02 

Graphite C 12,01 2,41E-02 

Spessartine M n2+ 3Al2(SiO4)3 495,03 2,36E-02 

Anhydrite 

Olivine 

CaSO 4 

M g1.6Fe 136,14 2,36E-02 

2+ 

0.4 (SiO4) Continued on next page . . . 

153,31 2,34E-02






Hollandite Ba0.8P b0.2N a0.125M n 4+ 

6 Fe3+ M n2+ 

1.3 0.5Al Analcime 

0.2Si0.1O16 N aAlSi2O6 · (H2O) 848,06 

220,15 

2,23E-02 

2,23E-02 

C org C 12,01 2,21E-02 

Chromite Fe2+ C r2O4 223,84 1,98E-02 

Vesuvianite/ 

Idocrase 

Ca10M g2Al4(SiO 4) 5(Si2O 7) 2(OH) 4 1422,09 1,71E-02 

Pyrrhotite Fe2+ S 87,91 1,57E-02 

Tephroite M n2+ 2 (SiO Gypsum 

4) 

CaSO 4 · 2H2O 201,96 

158,14 

1,27E-02 

1,26E-02 

Corundum Al2O3 101,96 1,22E-02 

Rhodochrosite 

Arfvedsonite 

M nCO3 N a3Fe 114,95 1,09E-02 

2+ 

4 Fe3+ Monazite (Ce) 

(Si8O22)(OH) 2 

Ce0.5 La0.25N d0.2Th 0.05(PO 4) 

958,89 

240,21 

1,05E-02 

1,03E-02 

Sphalerite ZnS 97,44 9,96E-03 

Jadeite N aAl0.9Fe 3+ 

0.1 (Si Dispersed V 

2O6) V 

205,03 

51,00 

9,80E-03 

9,71E-03 

Pumpellyite Ca2M gAl2(SiO 4)(Si2O7)(OH) 2 · (H2O) 502,25 9,49E-03 

Diodochic Rb Rb 85,00 8,30E-03 

Aragonite CaCO 3 100,09 7,64E-03 

Nepheline N a0.75K0.25Al(SiO 4) 146,08 7,43E-03 

Forsterite 

Hedenbergite 

M g2SiO 4 

CaFe 

140,69 6,96E-03 

2+ Si2O6 248,09 6,82E-03 

Chalcopyrite CuFeS 2 183,53 6,64E-03 

Phlogopite K M g3AlSi 3O10F(OH) 419,25 6,62E-03 

Wi<strong>the</strong>rite 

Pentlandite 

BaCO 3 

Fe 

197,34 5,99E-03 

2+ 

4.5N i Cordierite 

4.5S8 M g2Al4Si 5O18 771,94 

584,95 

5,75E-03 

5,57E-03 

Pyrolusite 

Fayalite 

M nO2 Fe 

86,94 4,90E-03 

2+ 

2 SiO Anatase 

4 

T iO2 203,78 

79,88 

4,77E-03 

4,46E-03 

Francolite 

Tourmaline 

Ca5(PO 4) 2.63(CO 3) 0.5F1.11 N aFe 

501,26 4,35E-03 

2+ 

3 Al Orthite-Ce/ Allanite 

6(BO3) 3Si6O 18(OH) 4 

Ca1.2Ce 0.4Y0.133Al2Fe 1053,38 4,30E-03 

3+ (Si3O12)(OH) 519,03 4,05E-03 

Lepidolite K Li2AlSi 4O10F(OH) 388,30 3,99E-03 

Gedrite M g5Al2(Si 6Al2O22)(OH) 2 783,97 3,23E-03 

Beryl Be3Al 2Si6O 18 537,50 3,22E-03 

Pyrophyllite 

Rhodonite 

Al2Si 4O10(OH) 2 

M n 

360,31 3,22E-03 

2+ SiO3 131,02 3,04E-03 

Magnesite 

Chloritoid 

M gCO 3 

Fe 

84,31 3,02E-03 

2+ 

1.2M g0.6M n2+ 0.2Al Ilmenorutile 

4Si2O 10(OH) 4 

T i0.7N b0.15Fe 484,71 3,00E-03 

2+ 

0.225O Ulexite 

2 

N aCaB 5O9 · 8H2O 92,01 

405,23 

2,96E-03 

2,92E-03 

Diadochic Ce Ce 140,00 2,83E-03 

Jacobsite M n 2+ 

0.6Fe2+ 0.3M g0.1Fe 3+ M n3+ 

1.5 0.5O Clementite 

4 

Fe 

227,38 2,72E-03 

2+ 

3 M g1.5AlFe 3+ Kernite 

Si3AlO 12(OH) 6 

N a2B4O7 · 4H2O 692,09 

290,28 

2,64E-03 

2,61E-03 

Bastnaesite La(CO 3)F 


219,12 2,54E-03

Results 95 





Colemanite Ca2B6O11 · 5H2O 411,09 2,46E-03 

Sassolite (natural 

boric acid) 

H3BO 3 61,83 2,22E-03 

Cryptomelane K M n 4+ 

7.5 

M n2+ 

0.5 O 16 707,12 2,19E-03 

Murmanite N a 4T i 3.6N b 0.4(Si 2O 7) 2O 4 · 4(H 2O) 773,84 2,15E-03 

Anthophyllite M g 7Si 8O 22(OH) 2 780,82 2,09E-03 

Grossular Ca 3Al 2(SiO 4) 3 450,45 2,08E-03 

Diadochic Ni N i 59,00 1,98E-03 

Amblygonite Li 0.75N a 0.25Al(PO 4)F 0.75(OH) 0.25 151,41 1,95E-03 

Diadochic Y Y 89,00 1,86E-03 

Scapolite N a 2Ca 2Al 3Si 9O 24Cl 287,93 1,83E-03 

Pollucite Cs 0.6N a 0.2Rb 0.1Al 0.9Si 2.1O 6 · (H 2O) 290,16 1,78E-03 

Dispersed Ga Ga 70,00 1,76E-03 

Dispersed Co Co 59,00 1,73E-03 

Spinel M gAl 2O 4 142,27 1,52E-03 

Diadochic Nd N d 144,00 1,46E-03 

Sapphirine M g 4Al 6.5Si 1.5O 20 689,23 1,40E-03 

Dispersed Sc Sc 45,00 1,40E-03 

Manganite M nO(OH) 87,94 1,36E-03 

Cristobalite SiO 2 60,08 1,24E-03 

Fluorite CaF 2 78,07 1,12E-03 

Andradite Ca3Fe 2+ 

2 (SiO4) 3 508,18 9,99E-04 

Glaucophane N a2(M g3Al2)Si 8O22(OH) 2 783,54 9,49E-04 

Todorokite N a 2M n 4+ 

4 

M n3+ 

2 O 12 · 3(H 2O) 621,65 8,33E-04 

Ferrocolumbite Fe 2+ N b 2O 6 337,66 8,10E-04 

Clinohumite M g6.75Fe 2+ 

2.25 (SiO Pr in Monazite 

and Bastnasite 

4) 4F1.5(OH) 0.5 

P r 

695,05 

141,00 

7,64E-04 

7,10E-04 

Thorite ThSiO 4 324,12 6,91E-04 

Galena P bS 239,27 6,67E-04 

Marcasite FeS2 119,98 6,29E-04 

Kornerupine M g3.5Fe 2+ 

0.2Al Hf in Zr ores 

5.7(SiO 4) 3.7(BO4) 0.3O1.2(OH) H f 

649,39 

178,00 

6,00E-04 

5,29E-04 

Vaesite 

Violarite 

N iS2 Fe 

122,82 5,20E-04 

2+ Humite 

N i2S4 M g5.25Fe 301,49 5,20E-04 

2+ 

1.75 (SiO Jarosite 

4) 3F1.5(OH) 0.5 

K Fe 

538,58 5,09E-04 

3+ 

3 (SO Wollastonite 

4) 2(OH) 6 

CaSiO 3 

500,81 

116,16 

4,79E-04 

4,74E-04 

Arsenopyrite FeAsS 162,83 4,71E-04 

Sm in Monazite 

and Bastnasite 

Sm 150,00 4,69E-04 

Kieserite M gSO4 · (H2O) 138,38 4,24E-04 

Garnierite N i2M gSi2O 5(OH) 4 345,92 4,10E-04 

Euxenite Y0.7Ca 0.2Ce 0.1(Ta0.2) 2(N b0.7) 2(T i0.025)O6 385,10 3,93E-04 

Dispersed Dy D y 163,00 3,91E-04 

Cubanite CuFe 2S3 271,44 3,62E-04 

Dispersed Gd Gd 157,00 3,19E-04 

Nickeline N iAs 


133,61 2,73E-04






Aenigmatite N a2Fe 2+ 

5 T iSi Scheelite 

6O20 CaW O4 861,60 

287,93 

2,73E-04 

2,67E-04 

Cassiterite SnO2 150,71 2,61E-04 

Carnotite 

Vernadite 

K2(UO 2) 2(VO 4) 2 · 3H2O M n 

902,18 2,52E-04 

4+ 

0.6Fe3+ 0.2Ca Topaz 

0.2N a0.1O1.5(OH) 0.5 · 1.4(H2O) Al2(SiO 4)F1.1(OH) 0.9 

112,17 

182,25 

2,45E-04 

2,34E-04 

Dispersed Er Er 167,00 2,30E-04 

Chrysoberyl 

Hisingerite 

BeAl2O 4 

Fe 

126,97 2,28E-04 

3+ 

2 Si Covellite 

2O5(OH) 4 · 2(H2O) CuS 

351,92 

95,61 

2,20E-04 

2,17E-04 

Sylvite KCl 74,55 2,05E-04 

Yttrialite Y1.5Th 0.5Si2O 7 417,54 1,94E-04 

Molybdenite M oS2 160,07 1,83E-04 

Yb in monazite Y b 173,00 1,72E-04 

Gersdorffite N iAsS 165,68 1,61E-04 

Dispersed Br Br 80,00 1,60E-04 

Omphacite Ca0.6N a0.4M g0.6Al0.3Fe 2+ 

0.1Si Brucite 

2O6 M g(OH) 2 

213,67 

58,32 

1,60E-04 

1,58E-04 

Uraninite UO2 270,03 1,51E-04 

Azurite Cu3(CO 3) 2(OH) 2 344,67 1,51E-04 

Dietzeite Ca2(IO 3) 2(C rO4) 545,96 1,51E-04 

Sb in galena Sb 879,29 1,42E-04 

Dispersed Ge Ge 73,00 1,41E-04 

Bornite Cu5FeS 4 501,84 1,33E-04 

Nosean N a8Al6Si 6O24(SO4) 1012,38 1,31E-04 

Pyrochlore N a1.5Ca 0.5N b2O6(OH) 0.75F0.25 362,38 1,26E-04 

Malachite Cu2(CO 3)(OH) 2 221,12 1,21E-04 

Palygorskite M gAlSi 4O10(OH) · 4(H2O) 412,69 1,14E-04 

Lautarite Ca(IO 3) 2 389,88 1,08E-04 

Dispersed Eu Eu 152,00 1,00E-04 

Dispersed Tl T l 204,00 8,98E-05 

Hydrosodalite N a8(AlSiO 4) 6(OH) 2 932,00 8,44E-05 

Dispersed Ho Ho 165,00 8,30E-05 

Gadolinite Y2Fe 2+ Be2(Si 2O10) 569,31 8,05E-05 

Phenakite Be2SiO 4 110,11 8,05E-05 

Bertrandite Be4Si 2O7(OH) 2 238,23 8,05E-05 

Helvine/ 

Helvite 

M n4Be3(SiO 4) 3S 555,10 8,05E-05 

Strontianite SrCO 3 147,63 7,88E-05 

Dispersed Tb T b 159,00 7,00E-05 

Perovskite CaT iO3 135,96 6,94E-05 

Tridymite SiO2 60,08 6,30E-05 

Cryolite N a3AlF 6 209,94 4,95E-05 

Sulphur S8 256,53 4,72E-05 

Orpiment As2S3 246,04 4,55E-05 

Brookite T iO2 79,88 4,21E-05 

Eudialyte N a 4Ca 2Ce 0.5Fe 2+ 

0.7 

M n2+ 

0.3 Y 0.1Z rSi 8O 22(OH) 1.5Cl 0.5 938,82 4,04E-05 

Carnallite K M gCl 3 · 6(H 2O) 277,85 4,03E-05 


Results 97 





Xenotime Y bPO4 268,01 3,70E-05 

Dawsonite N aAl(CO 3)(OH) 2 144,00 3,62E-05 

Wolframite Fe 2+ 

0.5 

M n2+ 

0.5 (W O 4) 303,24 3,21E-05 

Dispersed Lu Lu 175,00 3,10E-05 

Dispersed Tm T m 169,00 3,00E-05 

Stibnite Sb 2S 3 339,70 2,75E-05 

Copper Cu 63,55 2,48E-05 

Cerussite 

Blomstrandite/ 

Betafite 

P bCO3 U0.3Ca 0.2N b0.9T i0.8Al0.1Fe 267,21 2,21E-05 

3+ 

0.1Ta0.5O6(OH) 413,09 2,05E-05 

Sodalite N a8Al6Si 6O24Cl 2 969,21 1,98E-05 

Britholite 

Ferrotantalite 

Ca2.9Ce 0.9Th 0.6 La0.4N d0.2Si2.7P0.5O12(OH) 1.8F0.2 Fe 

783,69 1,71E-05 

2+ Ta2O6 513,74 1,58E-05 

Ramsayite/ 

Lorenzenite 

N a2T i2Si2O 9 341,91 1,24E-05 

Anglesite P bSO4 303,26 1,16E-05 

Greenockite CdS 144,48 1,16E-05 

Chondrodite M g3.75Fe 2+ 

1.25 (SiO Axinite -Fe 

4) 2F1.5(OH) 0.5 

Ca2Fe 382,12 1,12E-05 

2+ Al2BO 3Si4O 12(OH) 570,12 1,10E-05 

Chalcocite Cu2S 159,16 1,09E-05 

Zinc Zn 65,39 1,01E-05 

Se 

ores 

in copper Se 79,00 9,00E-06 

Loparite (Ce) N a0.6Ce 0.22 La0.11Ca 0.1T i0.8N b0.2O3 168,78 8,13E-06 

Bisch<strong>of</strong>ite M gCl 2 · 6(H2O) 203,30 8,06E-06 

Smithsonite ZnCO 3 125,40 7,98E-06 

Sirtolite 

Pleonaste/ 

Magnesi<strong>of</strong>errite 

Z rSiO 4 

M gFe 

183,31 7,37E-06 

3+ 

2 O4 158,04 6,96E-06 

Lead P b 207,20 6,32E-06 

Bismutite Bi2(CO 3)O2 509,97 6,09E-06 

Cinnabar H gS 232,66 5,73E-06 

In in ZnS In 115,00 5,61E-06 

Arsenolite As2O3 197,84 5,55E-06 

Bismuthinite Bi2S3 514,16 5,10E-06 

Bismite Bi2O3 465,96 4,62E-06 

Tin Sn 118,69 4,59E-06 

Cancrinite 

Chevkinite 

N a6Ca 2Al6Si 6O24(CO 3) 2 

Ce1.7 La1.4Ca 0.8Th 0.1Fe 

1052,50 4,42E-06 

2+ 

1.8M g0.5T i2.5Fe 3+ 

0.5Si Bismuth 

4O22 Bi 

1212,52 

208,98 

3,35E-06 

2,71E-06 

Rhabdophane- 

Ce 

Ce0.75 La0.25(PO 4) · (H2O) 252,80 2,62E-06 

Fergusonite N d0.4Ce 0.4Sm0.1Y0.1N bO4 294,57 2,38E-06 

Native silver Ag 107,87 2,09E-06 

Iotsite FeO 71,80 1,71E-06 

Realgar As4S4 106,99 1,50E-06 

Pyrargirite Ag3SbS 3 541,55 1,29E-06 

Argentite Ag2S Continued on next page . . . 

247,80 1,24E-06






Baddeleyite Z rO2 123,22 1,20E-06 

Uranium- Thorite 

ThSiO 4 327,12 1,04E-06 

Lavenite N a0.5Ca 0.5M n2+ 0.5Fe2+ 0.5Z r0.8T i0.1 388,58 1,01E-06 

N b 0.1(Si 2O 7)O 0.6(OH) 0.3F 0.1 

Cobaltite CoAsS 165,92 8,40E-07 

Acanthite 

Freibergite 

Ag2S Ag7.2Cu 3.6Fe 

247,80 6,79E-07 

2+ 

1.2Sb Smaltite 

3AsS13 CoAs 2 

1929,46 

125,40 

6,79E-07 

6,35E-07 

Powellite CaM oO4 200,02 6,10E-07 

Stephanite Ag5SbS 4 789,36 6,09E-07 

Linnaeite Co3S4 305,06 5,15E-07 

Microlite N a0.4Ca 1.6Ta2O 6.6(OH) 0.3F0.1 547,81 4,77E-07 

Lamprophyllite N a2SrBaT i3Si4O 16(OH)F 818,87 4,59E-07 

Te in Cu ores Te 128,00 4,47E-07 

Thorianite ThO2 264,04 4,12E-07 

Delorenzite/ 

Tanteuxenite 

Y0.7Ca 0.2Ce 0.12(Ta0.7) 2(N b0.2) 2(T i0.1)O5.5(OH) 0.5 480,83 4,00E-07 

Miserite 

Fahlerz Group: 

Tennantite 

KCa 2Ce 3Si8O 22(OH) 1.5F0.5 Cu11Fe 1151,28 2,30E-07 

2+ As4S13 1471,40 1,82E-07 

Metatorbenite Cu(UO 2)2(PO 4)2 · 8(H2O) 937,67 1,69E-07 

Moissanite SiC 40,10 1,41E-07 

Vivianite Fe3+ 3 (PO Naegite 

4) 2 · 8(H2O) Z rSiO 4 

501,61 

183,31 

1,30E-07 

1,28E-07 

Gold Au 196,97 1,28E-07 

Chrysocolla Cu2Si 2O6 · (H2O) 4 351,32 1,25E-07 

Troilite FeS 87,91 1,05E-07 

Chlorargirite AgCl 143,32 7,83E-08 

Metacinnabar H gS 232,66 7,38E-08 

Wulfenite P bM oO4 367,14 6,10E-08 

Tetrahedrite 

Nordite 

Cu9Fe 3Sb 4S13 N a2.8M n 

1643,31 5,70E-08 

2+ 

0.2Sr Samsonite 

0.5Ca 0.5 La0.33Ce 0.6Zn 0.6 M g0.4Si6O 17 

Ag4M nSb2S 6 

758,57 

922,31 

5,46E-08 

4,87E-08 

Pd 

ores 

in Ni-Cu Pd 106,00 4,51E-08 

Cooperite P t0.6Pd 0.3N i0.1S 186,91 3,95E-08 

Weinschenkite Y PO4 · 2(H2O) 219,91 3,70E-08 

Ru 

ores 

in Ni-Cu Ru 101,00 3,37E-08 

Sylvanite Au0,75Ag0,25Te2 429,89 3,27E-08 

Lollingite FeAs2 205,69 2,68E-08 

Calaverite AuTe2 452,17 2,58E-08 

Pt in Ni-Cu ores P t 195,00 2,47E-08 

Rinkolite/ 

Mosandrite 

N a2Ca 3Ce 1.5Y0.5T i0.4N b0.5Z r0.1(Si2O 7) 2O1.5F3.5 922,39 2,07E-08 

Dispersed Re Re 186,00 1,98E-08 

Tellurite TeO2 Continued on next page . . . 

159,60 1,82E-08

Results 99 





Tetradymite Bi2Te 2S 705,23 1,60E-08 

Periclase M gO 40,30 1,52E-08 

Alunite KAl3(SO 4)2(OH) 6 414,21 9,11E-09 

Thortveitite Sc1.5Y0.5Si2O 7 280,05 7,60E-09 

Dumortierite Al6.9(BO3)(SiO 4) 3O2.5(OH) 0.5 569,73 7,60E-09 

Rh 

ores 

in Ni-Cu Rh 103,00 6,01E-09 

Osmium Os0.75I r0.25 190,71 3,00E-09 

Iridium I r0.5Os0.3Ru0.2 173,39 2,61E-09 

Polycrase (Y) Y0.5Ca 0.1Ce 0.1U0.1Th 0.1T i1.2N b0.6Ta0.2O6 354,85 8,71E-10 

Boulangerite P b5Sb 4S11 1887,90 4,00E-10 

I-Platinum P t 195,08 3,00E-10 

Polixene/ Tetraferroplatinum 

P t Fe 167,00 2,00E-10 

Wohlerite N aCa 2Z r0.6N b0.4Si2O 8.4(OH) 0.3F0.3 396,41 5,05E-11 

Sum 


155,2 105,0 

3.6.1 Discussion <strong>of</strong> <strong>the</strong> most abundant <strong>mineral</strong>s 

The 10 most abundant <strong>mineral</strong>s according to our calculations are: quartz, albite, 

oligoclase, orthoclase, andensine, paragonite, biotite, hydromuscovite, augite, and 

hornblende. Grigor’ev’s 10 most abundant <strong>mineral</strong>s are quartz, oligoclase, orthoclase, 

biotite, andesine, albite, calcite, hornblende, labradorite and hydromuscovite. 

From <strong>the</strong> top ten most abundant <strong>mineral</strong>s in Grigor’ev’s model, calcite and labradorite 

do not appear in <strong>the</strong> 1 to 10 ranking <strong>of</strong> abundance in our model. They appear in 

positions 20 and 11, respectively. On <strong>the</strong> contrary, <strong>mineral</strong>s paragonite and augite 

appearing in our model as most abundant, are in Grigor’ev’s composition in positions: 

15 and 14. The difference for labradorite in both models is very small, around 

17%. However, <strong>the</strong> significant difference between <strong>the</strong> concentration <strong>of</strong> calcite in 

both models (75%) is because its quantity is fixed by element C. The quantity <strong>of</strong> 

carbon generated by Grigor’ev’s model in <strong>the</strong> upper earth’s crust is much greater 

than <strong>the</strong> one given by Wedepohl 21 [404] (see table 3.4). According to Grigor’ev’s 

composition, calcite would account for around 50% <strong>of</strong> all carbon in <strong>the</strong> earth’s crust, 

what seems to be very unlikely, due to <strong>the</strong> vast amount <strong>of</strong> o<strong>the</strong>r important substances 

containing that element 22 . It could also be possible, that Wedepohl’s concentration 

21 Rudnick and Gao [292] or McLennan [215] did not provide any number for element C and hence, 

<strong>the</strong> value <strong>of</strong> Wedepohl [404] was considered. 

22 For instance all carbonates.


for element C was underestimated. In that case, calcite would occupy a more relevant 

position in <strong>the</strong> ranking <strong>of</strong> abundance <strong>of</strong> <strong>mineral</strong>s in <strong>the</strong> crust, according to our 

model. 

Paragonite and augite are about 2,5 and 1,5 times more abundant in our model 

than in Grigor’ev’s, respectively. This is due to <strong>the</strong> fact that <strong>the</strong>ir contents are fixed 

by elements N a and M g. The discrepancy between both models for M g and N acontaining 

<strong>mineral</strong>s is explained in <strong>the</strong> next section. 

3.6.2 Discussion <strong>of</strong> <strong>the</strong> most relevant <strong>mineral</strong>s 

Next, <strong>the</strong> abundances <strong>of</strong> some <strong>of</strong> <strong>the</strong> most important <strong>mineral</strong>s for industrial uses 

are discussed and compared to Grigor’ev’s analysis. Those are <strong>the</strong> <strong>mineral</strong>s <strong>of</strong> gold, 

silver, copper, iron, aluminium, titanium, magnesium, calcium, sodium, sulfur, mercury, 

zinc, lead and uranium. 

The abundance <strong>of</strong> gold obtained in our model is around one order <strong>of</strong> magnitude 

greater than that <strong>of</strong> Grigor’ev’s. As explained in section 3.4.27, it is widely found as 

native gold and in <strong>the</strong> form <strong>of</strong> tellurides. The number given by Grigor’ev for gold, 

would imply that only 12% <strong>of</strong> Au comes from native gold, instead <strong>of</strong> <strong>the</strong> 85% that 

we assumed. It is believed that <strong>the</strong> main source <strong>of</strong> element Au is native gold and not 

tellurides, and <strong>the</strong>refore we keep <strong>the</strong> assumptions made. 

Grigorev’s silver <strong>mineral</strong>’s concentration are also about one order <strong>of</strong> magnitude 

greater than in our model. It is considered, that most important Ag-containing <strong>mineral</strong>s 

are included in both models. Hence, <strong>the</strong> mass balance indicates that <strong>the</strong> 

concentration for <strong>the</strong>m should be around one order <strong>of</strong> magnitude greater. 

We have assumed that <strong>the</strong> <strong>mineral</strong>s for copper considered in Grigor’ev’s model are 

<strong>the</strong> most important and no additional substances were taken into account. The mass 

balance for Cu brought <strong>the</strong> result that <strong>the</strong> Cu-containing <strong>mineral</strong>s in our model are 

around two orders <strong>of</strong> magnitude greater than in Grigor’ev’s analysis. 

A great amount <strong>of</strong> Fe-containing <strong>mineral</strong>s was considered in both models. The differences 

between <strong>the</strong>m are usually less than 25% for <strong>the</strong> oxides and <strong>the</strong> most important 

silicates, being <strong>the</strong> numbers given by Grigor’ev greater. For sulfates, Grigorev’s 

iron-containing <strong>mineral</strong>s are around 50% greater. 

The most important Al-containing <strong>mineral</strong>s show a difference between both models 

<strong>of</strong> around 220%, such as for sillimanite or boehmite. 

The concentration <strong>of</strong> T i-containing <strong>mineral</strong>s in our model is about 1,5 times greater 

than in Grigor’ev’s composition. Since most important titanium <strong>mineral</strong>s have been 

considered, <strong>the</strong> mass balance for T i indicates that <strong>the</strong> values estimated by Grigor’ev 

are slightly low. 

The difference between <strong>the</strong> main M g and Ca-containing <strong>mineral</strong>s in both models 

is around 37% and 17% respectively, being <strong>the</strong> concentrations <strong>of</strong> our study smaller

Results 101 

Table 3.6. Crustal abundance <strong>of</strong> <strong>mineral</strong>s according to this and Grigor’ev’s model in 

mass % [127] 

Mineral This study Grigor’ev [127] 

Quartz 56,7 58,8 

Plagioclase 18,9 15,6 

O<strong>the</strong>rs 6,5 11,6 

Orthoclase 6,3 5,2 

Oxides 4,3 3,2 

Micas 3,7 2,9 

Pyroxene 2,5 1,4 

Amphibole 0,6 0,6 

Chlorite 0,5 0,7 

than in Grigor’ev’s model, since <strong>the</strong> latter overestimated <strong>the</strong> abundance <strong>of</strong> <strong>the</strong> magnesium 

and calcium <strong>mineral</strong>s, as revealed by <strong>the</strong> value <strong>of</strong> ε j, greater than ˆε j. 

Sodium-containing <strong>mineral</strong>s in our model are around 2,5 times greater than in 

Grigor’ev’s analysis for <strong>mineral</strong>s like albite, nontronite, riebeckite or aegirine, where 

<strong>the</strong> limiting element is N a, but are around 17% smaller for those <strong>mineral</strong>s that also 

contain Ca. That is <strong>the</strong> case for oligoclase, andesine or labradorite. 

The abundance <strong>of</strong> sulfur <strong>mineral</strong>s in our model differ from Grigor’ev’s study in less 

than 50% for native sulfur, gypsum or pyrite, but in two orders <strong>of</strong> magnitude in 

o<strong>the</strong>rs, such as cinnabar. The differences depend on <strong>the</strong> limiting element that contain 

<strong>the</strong> substance. For <strong>the</strong> case <strong>of</strong> cinnabar, <strong>the</strong> limiting element is H g and not S. The 

discrepancy for <strong>the</strong> latter <strong>mineral</strong> and that for metacinnabar is because only two 

H g-containing <strong>mineral</strong>s were considered (<strong>the</strong> most important ones). 

Zinc-containing <strong>mineral</strong>s in our model are more than two orders <strong>of</strong> magnitude 

greater than in Grigor’ev’s studies. This is due to <strong>the</strong> fact that only a few zinc <strong>mineral</strong>s 

were considered: sphalerite, smithsonite, nordite and native zinc. Probably, 

o<strong>the</strong>r <strong>mineral</strong>s <strong>of</strong> zinc should be taken into account, such as franklinite, hemimorphite 

or wurtzite. 

We have considered only 6 uranium and 6 lead-containing <strong>mineral</strong>s and that might 

be <strong>the</strong> reason why <strong>the</strong>ir concentrations in our model are around one and two orders 

<strong>of</strong> magnitude greater than in Grigor’ev’s study, respectively. As in <strong>the</strong> case <strong>of</strong> zinc, 

o<strong>the</strong>r <strong>mineral</strong>s <strong>of</strong> uranium and lead are likely to be taken into account. 

3.6.3 Discussion <strong>of</strong> <strong>the</strong> aggregated composition 

A comparison between <strong>the</strong> aggregated composition <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s in <strong>the</strong> crust (as 

carried out by Wedepohl [402], [403] and Nesbitt and Young [242], table 3.2) 

obtained in this and in Grigor’ev’s study, is shown in table 3.6.


The most significant differences between <strong>the</strong>se two new models and <strong>the</strong> older ones 

from Wedepohl and Nesbitt and Young are <strong>the</strong> abundances <strong>of</strong> quartz and plagioclase. 

According to <strong>the</strong> recent models, quartz accounts for nearly 60% <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s 

on <strong>the</strong> upper earth’s crust. Plagioclase occupies <strong>the</strong> second position in abundance 

(representing more than 15%) and not <strong>the</strong> first, like in <strong>the</strong> older models. All four 

studies agree in that orthoclase is <strong>the</strong> third group <strong>of</strong> importance, although <strong>the</strong> new 

calculated values are significantly lower than <strong>the</strong> older ones, especially between 

Wedepohl’s and Grigor’ev’s. The relative proportion <strong>of</strong> micas (including biotite and 

muscovite) are much lower than in <strong>the</strong> older analysis. The same thing happens to 

chlorites, amphiboles and olivine, <strong>the</strong> latter with imperceptible abundance. However 

oxides are more abundant in <strong>the</strong> recent models, while <strong>the</strong> abundance <strong>of</strong> pyroxenes 

is close to <strong>the</strong> analysis <strong>of</strong> Nesbitt and Young. 

3.6.4 Drawbacks <strong>of</strong> <strong>the</strong> model 

The first thing to me noted in <strong>the</strong> composition <strong>of</strong> table 3.5 is that <strong>the</strong> total mass 

<strong>of</strong> <strong>the</strong> <strong>mineral</strong>s contained in <strong>the</strong> upper crust is greater than 100%. As mentioned 

above, <strong>the</strong> oxygen and hydrogen quantities in <strong>the</strong> crust have been left free. In <strong>the</strong> 

chemical compositions <strong>of</strong> <strong>the</strong> crust given by Rudnick et al. [292], Wedepohl [404] 

or McLennan [215], no H or O values are provided. However <strong>the</strong> value for O can 

be determined from <strong>the</strong> first two authors, as some <strong>of</strong> <strong>the</strong> elements are given as <strong>the</strong> 

corresponding oxides. That is <strong>the</strong> case for SiO 2, T iO 2, Al 2O 3, FeO, M nO, M gO, 

CaO, N a 2O, K 2O and P 2O 5. The oxygen concentration resulting from those oxides 

gives in Rudnick’s and Wedepohl’s models <strong>of</strong> <strong>the</strong> crust 2, 95 × 10 −2 mole/g. In <strong>the</strong> 

model developed in this PhD, <strong>the</strong> concentration <strong>of</strong> oxygen is 4,8% greater: 3, 10 × 

10 −2 mole/g, while in Grigor’ev’s 0,7% greater: 2, 97 × 10 −2 mole/g. Hence, if 

<strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> crust is right, <strong>the</strong>n <strong>the</strong>re is an excess <strong>of</strong> oxygen in 

<strong>the</strong> <strong>mineral</strong>s <strong>of</strong> our model and that <strong>of</strong> Grigor’ev. This oxygen could be in <strong>the</strong> form 

<strong>of</strong> molecules O 2 or H 2O, which would be in <strong>the</strong> concentration <strong>of</strong> 1, 5 × 10 −2 and 

1, 1 × 10 −3 mole/g, respectively. An excess <strong>of</strong> oxygen could be attributed to <strong>the</strong> fact 

that <strong>the</strong> <strong>mineral</strong>s considered may not be electronegatively neutral. Never<strong>the</strong>less, we 

have assured <strong>the</strong> neutrality <strong>of</strong> <strong>the</strong> charges <strong>of</strong> every <strong>mineral</strong> considered. If <strong>the</strong> oxygen 

quantity is fixed in our model, <strong>the</strong>n <strong>the</strong> Si content is significantly smaller than <strong>the</strong> 

one given by Rudnick: 1, 01×10 −2 instead <strong>of</strong> 1, 10×10 −2 g/mole. With <strong>the</strong> chemical 

composition <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s given in table 3.5, <strong>the</strong>re is no possible solution to Eq. 3.2 

if <strong>the</strong> concentration <strong>of</strong> oxygen is also fixed. Hence, it seems that <strong>the</strong> problem comes 

from <strong>the</strong> chemical formulae used. It must be pointed out, that many <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s 

given by Grigor’ev do not have a fixed chemical composition. They represent a 

variety <strong>of</strong> <strong>mineral</strong>s with changing concentrations <strong>of</strong> certain elements. That is <strong>the</strong> 

case for biotite, apatite, phosphate rock, etc. We have tried to take into account an 

average chemical formula, given by <strong>the</strong> empirical formula recorded under [172], 

but assuring <strong>the</strong> neutrality <strong>of</strong> <strong>the</strong> charges and <strong>the</strong> general molecular structure <strong>of</strong> <strong>the</strong>


<strong>mineral</strong>. Never<strong>the</strong>less, many different formulas are possible. Therefore, this aspect 

should be checked in fur<strong>the</strong>r developments <strong>of</strong> <strong>the</strong> model. 

Ano<strong>the</strong>r aspect that should be taken into account, is that <strong>the</strong> chemical composition 

<strong>of</strong> <strong>the</strong> earth in terms <strong>of</strong> elements has been assumed to be correct and not <strong>the</strong> one 

generated by Grigor’ev. The decision to do so was because <strong>the</strong> first one has been 

subject <strong>of</strong> many research studies throughout history, while <strong>the</strong> last one has just begun 

to be analyzed. Never<strong>the</strong>less, in some cases <strong>the</strong> procedure developed in this PhD 

could serve as a tool for assuring <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> crust. The low 

concentration <strong>of</strong> calcite obtained in our model for example, has set <strong>the</strong> alarms for 

<strong>the</strong> concentration value <strong>of</strong> C in <strong>the</strong> crust, which might have been underestimated by 

Wedepohl. 


In this chapter, a revision <strong>of</strong> <strong>the</strong> studies concerning <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> 

<strong>the</strong> earth’s crust has been carried out. It has been verified, that <strong>the</strong> literature about 

this topic is very limited and inaccurate, due to <strong>the</strong> heterogeneity and complexity 

<strong>of</strong> <strong>the</strong> crust. Never<strong>the</strong>less, one single author, <strong>the</strong> Russian geochemist Grigor’ev has 

been very recently <strong>the</strong> first one in giving a comprehensive <strong>mineral</strong>ogical composition 

<strong>of</strong> <strong>the</strong> upper crust. 

With <strong>the</strong> help <strong>of</strong> Eq. 3.1, we were able to check <strong>the</strong> satisfaction <strong>of</strong> <strong>the</strong> mass balance 

between <strong>the</strong> <strong>mineral</strong>s proposed by Grigor’ev and <strong>the</strong> better known chemical composition 

in terms <strong>of</strong> elements <strong>of</strong> <strong>the</strong> crust. The no satisfaction <strong>of</strong> <strong>the</strong> mass balance, lead 

us to propose a new composition, based on <strong>the</strong> Grigor’ev’s semi-empirical analysis. 

The methodology used minimizes <strong>the</strong> difference between Grigor’ev’s and our proposed 

compositions under <strong>the</strong> constraint <strong>of</strong> assuring chemical coherence with <strong>the</strong> 

average chemical composition <strong>of</strong> <strong>the</strong> earth’s crust in terms <strong>of</strong> elements. We have 

made assumptions based on <strong>the</strong> literature for those important <strong>mineral</strong>s not taken 

into account in Grigor’ev’s analysis, and included <strong>the</strong>m in our model. As a result, 

we have obtained a mean <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> upper crust, consisting 

<strong>of</strong> <strong>the</strong> 292 most abundant <strong>mineral</strong>s. 

This composition does not have to be taken as final and closed, since many assumptions 

had to be made. Never<strong>the</strong>less, it is <strong>the</strong> first step for obtaining a coherent 

<strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> crust. 

In chapters 2 and 3, we have tried to describe <strong>the</strong> composition <strong>of</strong> <strong>the</strong> earth as a 

whole. From <strong>the</strong> global components <strong>of</strong> <strong>the</strong> earth, only a few are used by man. The 

next chapter is focused on describing that part <strong>of</strong> <strong>the</strong> earth useful to man: <strong>the</strong> natural 

resources.


Chapter 4 

The resources <strong>of</strong> <strong>the</strong> earth 

In this chapter, a deeper look at <strong>the</strong> earth’s components useful to man is undertaken. 

For that purpose, a revision <strong>of</strong> energy and non-energy resources is carried out. The 

energy resources have been divided into energy coming from <strong>the</strong> solid earth, i.e. 

nuclear and geo<strong>the</strong>rmal energy; tidal energy; and energy coming from <strong>the</strong> sun, including 

solar, water, wind, ocean power and hydrocarbons. 

In addition to <strong>the</strong> energy resources, <strong>mineral</strong> resources are also studied, stressing out 

<strong>the</strong>ir abundance and average crustal concentration. 

4.2 Natural resources: definition, classification and early 

assessment 

A natural resource can be defined as any form <strong>of</strong> matter or energy obtained from <strong>the</strong> 

environment that meets human needs. Therefore water, air, oil, biomass or <strong>mineral</strong>s 

are classified as natural resources. On <strong>the</strong> o<strong>the</strong>r hand, Costanza [65], defines <strong>the</strong> 

natural <strong>capital</strong> as a stock that yields a flow <strong>of</strong> variable goods in <strong>the</strong> future. 

Natural resources are frequently classified as renewable or non-renewable. Renewable 

resources are defined as resources that are regenerated on a human time scale. 

Examples <strong>of</strong> renewable resources are water, biomass or <strong>the</strong> energy from <strong>the</strong> sun. 

Non-renewable resources can be considered as a stock that has a regeneration rate 

<strong>of</strong> zero over a relatively long period. That is <strong>the</strong> case for <strong>mineral</strong>s [203]. 

Minerals can be fur<strong>the</strong>r classified as fuel and non-fuel <strong>mineral</strong> resources. Fuel resources 

are those from which energy can be potentially extracted. That is <strong>the</strong> case 

for coal, fuel or uranium. The rest are non-fuel <strong>mineral</strong>s, including construction 

materials, metals, etc. 

105

106 THE RESOURCES OF THE EARTH 

Table 4.1. World energy use in 1984 [130] 

Fuel source Current use Proven re- Resources Resource un- 

(EJ/y) 

serves (EJ) (EJ) 

certainty 

Coal 97,6 21500 238000 ±20% 

Oil 127,3 4300 10000 -30% + 60% 

Gas 63,1 3700 10000 -40% + 70% 

Uranium 12,6 813 1324 ±50 

Tar sands+Oil shale - 550+ 1600+ highly 

tainuncer- 

Approx. total 300,6 30850+ 260900+ 

Fluxes (EJ/year) Practical Ultimate potential 

Hydro 21,7 100 200 little 

taintyuncer- 

Biomass 47 80 720 highly 

tainuncer- 

Wind v. small 30 100 speculative 

Photovoltaic v. small infinite infinite rapidly 

ing price 

reduc- 

Geo<strong>the</strong>rmal 0,1 large large 

Approx. total 63,8 210 1020+ 

Overall total 368,4 

An early assessment <strong>of</strong> <strong>the</strong> renewable and nonrenewable energy resources on earth 

was done by Hall et al. [130] and can be seen in table 4.1. 

The degree <strong>of</strong> knowledge about resources and technological development has improved 

notably since <strong>the</strong> eighties, what has lead to better estimations <strong>of</strong> <strong>the</strong> available 

resources on earth. 

In <strong>the</strong> next sections, <strong>the</strong> numbers given in table 4.1 are updated and new figures are 

provided for o<strong>the</strong>r types <strong>of</strong> resources. The results are summarized in section 4.7, 

table 4.8. 

4.3 The energy balance 

The sun is <strong>the</strong> main source <strong>of</strong> energy sustaining life on earth. According to Skinner 

[317], [318] <strong>the</strong> sun sends around 17, 3 × 10 16 W <strong>of</strong> power in form <strong>of</strong> shortwavelength 

solar radiation towards <strong>the</strong> earth. From this, approximately 30% is directly 

reflected by clouds and by <strong>the</strong> earth’s surface, but most rays pass through <strong>the</strong> 

atmosphere, heating <strong>the</strong> layers <strong>of</strong> <strong>the</strong> earth and causing winds, rains, snowfalls and 

ocean currents. These transformations lead to progressive depreciation <strong>of</strong> energy 

quality, and <strong>the</strong>refore, to exergy losses. The devaluated energy in form <strong>of</strong> heat is 

however sent back to space and <strong>the</strong> earth’s surface remains in <strong>the</strong>rmal balance. One 

part <strong>of</strong> solar radiation is used for photosyn<strong>the</strong>sis and is temporarily stored in <strong>the</strong> bio-

Energy from <strong>the</strong> solid earth 107 

Short wavelength 

solar radiation 

17,3x10 16 W 

Direct reflection 

5,2x1016 W 

Common 

sedimentary rocks 

10 26 J 

Direct conversion to heat 

8,1x1016 W 

Evaporation and precipitation 

4x10 16 W 

Recoverable 

fossil fuels 

2,5x1023 J 

Short wavelength 

radiation 

Winds, ocean currents, waves, etc. 

0,035x10 16 W 

Water 

storage 

bank 

Photosyn<strong>the</strong>sis 

Plant 

storage 

0,004x10 bank 

16 W Decay 

Organic matter 

Thermal energy 

1,3x10 27 J to 10 

km depth 

Long wavelength 

radiation 

Conduction 21x10 12 W 

Submarine volcanism 

11x1012 W 

Spontaneous 

nuclear decay 

Tidal energy 

27,3x10 12 

Tides, tidal energy, currents, etc. 

2,7x1012 W 

Volcanoes, hot springs on land 

0,3x1012 W 

Earth’s <strong>the</strong>rmal energy 

32,3x1012 W 

GEOTHERMAL ENERGY 

Uranium and 

Thorium withing 1 

km <strong>of</strong> surface 

5x10 29 J 

Figure 4.1. Energy flow sheet for <strong>the</strong> surface <strong>of</strong> <strong>the</strong> earth [317] 

sphere as organic matter and eventually as coal, oil and natural gas. Ano<strong>the</strong>r small 

fraction <strong>of</strong> <strong>the</strong> solar-derived energy is stored in water reservoirs such as lakes and 

rivers. But <strong>the</strong> sun is not <strong>the</strong> solely source <strong>of</strong> energy on earth, geo<strong>the</strong>rmal energy is 

<strong>the</strong> second most powerful source <strong>of</strong> energy, at 23 TW or 0,013 % <strong>of</strong> <strong>the</strong> total. This 

energy reaches <strong>the</strong> surface in <strong>the</strong> form <strong>of</strong> volcanoes, hot springs or conduction and 

plays an important role in <strong>the</strong> rock cycle. The third and smallest source <strong>of</strong> energy 

on earth is <strong>the</strong> tidal energy produced by <strong>the</strong> interaction <strong>of</strong> gravitational potential 

energy <strong>of</strong> <strong>the</strong> moon and <strong>the</strong> earth’s rotation. The transfer <strong>of</strong> tidal energy accounts 

for about 3 TW or 0,002 % <strong>of</strong> <strong>the</strong> total energy budget. Figure 4.1 shows <strong>the</strong> energy 

cycle on earth according to Skinner [317], which was adapted in part from Hubbert 

[147]. 

4.4 Energy from <strong>the</strong> solid earth 

Two different sources <strong>of</strong> energy come from <strong>the</strong> solid earth. The first one is geo<strong>the</strong>rmal 

energy, which is considered as a renewable resource, but it has found less applicability 

on a global scale. The second one is <strong>the</strong> non-renewable nuclear energy, 

coming from <strong>the</strong> mining <strong>of</strong> radioactive <strong>mineral</strong>s found on earth, mainly from uranium 

isotopes. The latter, although socially and politically controversial constitutes


nowadays a key source <strong>of</strong> energy for many countries. Next, both sources <strong>of</strong> energy 

will be explained in detail. 

4.4.1 The Geo<strong>the</strong>rmal energy 

The temperature <strong>of</strong> <strong>the</strong> earth’s interior increases with depth. The geo<strong>the</strong>rmal gradient 

varies in different parts <strong>of</strong> <strong>the</strong> world from 15 to 75 o C/km. The geo<strong>the</strong>rmal 

gradient creates obviously a heat flow leading to a heat loss escaping <strong>the</strong> crust. The 

amount <strong>of</strong> heat that escapes through <strong>the</strong> earth’s surface is due to <strong>the</strong> superposition 

<strong>of</strong> four components [168]: 

Q = Q C + Q L + Q B + Q T 

(4.1) 

where Q B is <strong>the</strong> heat input at <strong>the</strong> base <strong>of</strong> <strong>the</strong> lithosphere 1 due to mantle convection, 

Q T is a long-term transient due to cooling after a major tectonic or magmatic perturbation, 

Q L is <strong>the</strong> radiogenic heat production in <strong>the</strong> mantle part <strong>of</strong> <strong>the</strong> lithosphere, 

and Q C is <strong>the</strong> radiogenic heat production <strong>of</strong> <strong>the</strong> crust. 

The radiogenic heat production is due to <strong>the</strong> decay <strong>of</strong> <strong>the</strong> radioactive elements 

238 U, 235 U, 232 U and 40 K ei<strong>the</strong>r in <strong>the</strong> crust or in <strong>the</strong> upper mantle. For geological 

provinces older than ∼100 million years, Q L, Q B and Q T are lumped toge<strong>the</strong>r 

into a single parameter called mantle heat flow Q M. There are different ways to 

estimate <strong>the</strong> bulk crustal heat flow <strong>of</strong> <strong>the</strong> earth. Some estimates [251], [7], [104] 

are obtained by redistributing <strong>the</strong> heat producing elements in <strong>the</strong> bulk silicate earth 

between <strong>the</strong> continental crust and various reservoirs in <strong>the</strong> mantle. They require 

assumptions regarding <strong>the</strong> structure <strong>of</strong> <strong>the</strong> convecting mantle, <strong>the</strong> composition and 

<strong>the</strong> homogeneity <strong>of</strong> <strong>the</strong> reservoirs. O<strong>the</strong>r estimates are based on measurements ei<strong>the</strong>r 

from representative rock types and <strong>the</strong>ir proportions in crustal columns derived 

from geophysical pr<strong>of</strong>iles [129], [60], [404], [32] or on large-scale production data 

sets [81], [307] [106]. 

Jaupart [168] suggested to estimate <strong>the</strong> bulk crustal heat production directly from 

<strong>the</strong> heat flow data and local studies <strong>of</strong> crustal structure and estimating <strong>the</strong> mantle 

heat flow Q M with different ways. He obtained <strong>the</strong> values <strong>of</strong> heat production for 

three age groups: Archean, Proterozoic, and Phanerozoic (see table 4.2). The average 

<strong>of</strong> heat production was estimated to be between 0,79 and 0,95 µW m −3 and <strong>the</strong> 

crustal heat flow component ranges from 32 to 38 mW m −2 , considering an average 

crustal thickness <strong>of</strong> 40 km. According to <strong>the</strong>se numbers, <strong>the</strong> continental crust contributes 

to 5,8 to 6,9 TW to <strong>the</strong> total energy budget <strong>of</strong> <strong>the</strong> earth 2 . Active provinces 

and continental margins now represent 30% <strong>of</strong> <strong>the</strong> total volume <strong>of</strong> <strong>the</strong> crust; 50% 

error on <strong>the</strong>ir heat production would lead to a 15% error in <strong>the</strong> global budget. These 

1The lithosphere is <strong>the</strong> rigid strong outer layer <strong>of</strong> <strong>the</strong> earth, consisting <strong>of</strong> <strong>the</strong> crust and upper 

mantle, approximately 100 km thick. 

2 18 3 For a total volume <strong>of</strong> <strong>the</strong> continental crust <strong>of</strong> 7,3×10 m .

Energy from <strong>the</strong> solid earth 109 

Table 4.2. Estimates <strong>of</strong> bulk continental crust heat production from heat flow data 

[168]. 

Age group Range <strong>of</strong> heat production 

µW m−3 Range <strong>of</strong> crustal heat Fraction <strong>of</strong> total con- 

flow, mW m−2 tinental surface, % 

Archean 0,56-0,73 23-30 9 

Proterozoic 0,73-0,90 30-37 56 

Phanerozoic 0,95-1,10 37-43 35 

Total continents 0,79-0,95 32-38 

numbers differ from <strong>the</strong> values given by Skinner [317], in which <strong>the</strong> <strong>the</strong> flow is estimated 

to be 63 mW m −2 or 32,3 TW across <strong>the</strong> entire earth’s surface (not only <strong>the</strong> 

crust). It seems though that <strong>the</strong> numbers given by Jaupart are more updated and in 

consonance with <strong>the</strong> order <strong>of</strong> magnitude <strong>of</strong> <strong>the</strong> geo<strong>the</strong>rmal studies mentioned before. 

Extrapolating Jaupart’s values to <strong>the</strong> entire surface <strong>of</strong> <strong>the</strong> earth, would lead to 

an average geo<strong>the</strong>rmal energy contribution 3 <strong>of</strong> 17,9 TW. 

Geo<strong>the</strong>rmal energy constitutes a renewable source <strong>of</strong> energy. However, its reserves 

represent only a tiny fraction <strong>of</strong> all geo<strong>the</strong>rmal heat. Besides, like tidal energy, 

geo<strong>the</strong>rmal energy can be important locally but will be minor on a global scale. According 

to <strong>the</strong> Renewables Global Status Report [208], <strong>the</strong> 2005 worldwide geo<strong>the</strong>rmal 

capacity was 28 GWth for direct <strong>the</strong>rmal use and 9,3 GW for electricity production. 

The Geo<strong>the</strong>rmal Energy Association [109] reports that geo<strong>the</strong>rmal resources 

using today’s technology have <strong>the</strong> potential to support between 35.448 and 72.392 

MW <strong>of</strong> electrical generation capacity. Using enhanced technology currently under 

development (permeability enhancement, drilling improvements), <strong>the</strong> geo<strong>the</strong>rmal 

resources could support between 65.576 and 138.131 MW <strong>of</strong> electrical generation 

capacity. Assuming a 90% availability factor, which is well within <strong>the</strong> range experienced 

by geo<strong>the</strong>rmal power plants, this electric capacity could produce as much as 

1, 09 × 10 9 MWh <strong>of</strong> electricity annually (124 GW) (Table 4.8). Never<strong>the</strong>less, <strong>the</strong>se 

values need to be taken with precaution, until <strong>the</strong> USGS submits its geo<strong>the</strong>rmal 

energy report updating <strong>the</strong>se numbers. 

4.4.2 Nuclear energy 

Nuclear energy derives from <strong>the</strong> huge binding force <strong>of</strong> <strong>the</strong> nucleus <strong>of</strong> elements. Theoretically, 

<strong>the</strong>re are two kinds <strong>of</strong> processes that can release nuclear energy: fusion 

and fission. 

Fusion consists in binding light elements, such as hydrogen and lithium, and <strong>the</strong>reby 

forming heavier elements. This is <strong>the</strong> process that goes on in <strong>the</strong> sun. Fusion has not 

yet been achieved in <strong>the</strong> laboratory under conditions such that <strong>the</strong> energy produced 

3 For a total surface <strong>of</strong> <strong>the</strong> earth <strong>of</strong> 5,12×10 14 m 2


exceeds <strong>the</strong> energy used. Never<strong>the</strong>less, many scientists believe that it might be <strong>the</strong> 

solution <strong>of</strong> future energy supply. Hermann [138] estimated <strong>the</strong> exergy reservoir 

for <strong>the</strong> fusion cycle between deuterium (coming from <strong>the</strong> ocean) and tritium (bred 

from an isotope <strong>of</strong> lithium) as around 74 Ttoe. Fur<strong>the</strong>rmore, if deuterium, <strong>the</strong> 

isotope <strong>of</strong> 1 in every 5000 hydrogen atoms, is fused with ano<strong>the</strong>r deuterium nucleus 

at higher temperatures, <strong>the</strong> resulting resource contained in <strong>the</strong> ocean is on <strong>the</strong> order 

<strong>of</strong> magnitude <strong>of</strong> 10 million YJ. 

Fission nuclear energy is produced during controlled transformation <strong>of</strong> suitable radioactive 

isotopes, when neutrons are fired into <strong>the</strong> nucleus, making <strong>the</strong> atoms 

unstable and subject to spontaneous disintegration. Uranium is <strong>the</strong> crucial fission 

energy raw material due to <strong>the</strong> fact that as mined it contains 0,71% <strong>of</strong> 235 U (<strong>the</strong> 

only naturally occurring fissionable atom). Thorium, beryllium, lithium and zirconium 

are o<strong>the</strong>r low-demand raw materials with potential or specific uses in nuclear 

power production [71]. When 235 U undergoes fission, it releases heat and forms 

new elements and ejects some neutrons from its nucleus. These neutrons are <strong>the</strong>n 

used to induce more 235 U to fission. According to Skinner [317], once separated 

235 U from 238 U (an energy intensive process), <strong>the</strong> disintegration <strong>of</strong> a single atom releases 

3, 2×10 −11 J; because one gram <strong>of</strong> 235 U contains 2, 56×10 21 atoms, fission <strong>of</strong> 

a gram <strong>of</strong> uranium produces 8, 19 × 10 10 J (equivalent to <strong>the</strong> energy released when 

2,7 metric tons <strong>of</strong> coal are burned). Eq. 4.2 shows a representative fission process 

<strong>of</strong> 235 U. 

1 

0n +235 

92 U →137 

37 Cs +95 

37 Rb + 3n + 3, 2 × 10−11J (4.2) 

Estimated uranium resources in <strong>the</strong> continental crust amounted in year 1986 to 

3.457 kton [317] (see table 4.3), representing an exergy reservoir <strong>of</strong> 2, 8×10 14 GJ or 

6.741 Gtoe. More recent estimations <strong>of</strong> uranium sources indicate that <strong>the</strong>se amount 

to about 13 Mt according to Grubler [128] and 14,8 Mt according to <strong>the</strong> OECD 

[247], which represent an exergy reservoir <strong>of</strong> around 23.800 and 27.100 Gtoe, respectively. 

With current state <strong>of</strong> technology, which makes use <strong>of</strong> only 0,7% <strong>of</strong> <strong>the</strong> 

natural fuel in a “once-through” fuel cycle, <strong>the</strong> reserves would last only a few hundred 

years (174 Gtoe). With fast spectrum reactors operated in a “closed” fuel cycle 

by reprocessing <strong>the</strong> spent fuel and extracting <strong>the</strong> un-utilized uranium and plutonium 

produced, <strong>the</strong> reserves <strong>of</strong> natural uranium may exceed 5.200 Gtoe (Table 4.8). 

However, if advanced breeder reactors could be designed in <strong>the</strong> future to efficiently 

utilize recycled or depleted uranium and all actinides, <strong>the</strong>n <strong>the</strong> reserves <strong>of</strong> natural 

uranium may be extended to several thousand years at current consumption levels 

[249]. 

Additionally, Hermann [138], estimated <strong>the</strong> exergy reserves <strong>of</strong> thorium as around 

7.500 Gtoe and <strong>of</strong> seawater uranium as around 8.350 Ttoe. 

At <strong>the</strong> end <strong>of</strong> year <strong>of</strong> 2006, 6% <strong>of</strong> <strong>the</strong> world’s primary energy consumption was 

derived from nuclear power plants (see figure 4.4), and amounted to 635,5 Mtoe. In

Tidal energy 111 

Table 4.3. Estimated uranium resources in ores rich enough to be mined for use 

in 235 U power plants [317], toge<strong>the</strong>r with estimated rates <strong>of</strong> production for 2005 

according to <strong>the</strong> BGS [139]. Data reported as ktons <strong>of</strong> metal content. No distinctions 

are drawn between reserves and resources, and no data for resources are reported 

by <strong>the</strong> former URSS countries. 

Country Reasonably assured Production rate in 

resources, kton 2005, kton 

Australia 1357 9,516 

USA 758 1,034 

Rep. Of South Africa 332 0,674 

Canada 199 11,627 

Niger 136 3,093 

Namibia 113 3,08 

France 47 - 

O<strong>the</strong>r 516 12,876 

Total 3457 42 

France, more than half <strong>of</strong> all <strong>the</strong> electrical power comes from nuclear plants and in 

o<strong>the</strong>r European countries and Japan, <strong>the</strong> fraction is high too. Nuclear power capacity 

forecasts out to 2030 vary between 279 - 740 GWe when proposed new plants and 

<strong>the</strong> decommissioning <strong>of</strong> old plants are both considered [163]. Nuclear energy has 

<strong>the</strong> advantage against fossil fuels that it does not emit greenhouse gases and its 

reserves are greater (see table 4.3). Some renowned scientists such as Lovelock 

[200] claim that: “<strong>the</strong>re is no alternative but nuclear fission energy until fusion 

energy and sensible forms <strong>of</strong> renewable energy arrive as a truly long-term provider”. 

However, o<strong>the</strong>r problems are associated with nuclear energy. The isotopes used in 

power plants are <strong>the</strong> same used in atomic weapons, so a political problem exists. The 

possibility <strong>of</strong> a power plant failing in some unexpected way creates a safety problem 

as it happened in <strong>the</strong> Chernobyl disaster in 1986. Finally, <strong>the</strong> problem <strong>of</strong> safe burial 

<strong>of</strong> dangerous radioactive waste matter must be faced, since some <strong>of</strong> <strong>the</strong> waste matter 

will retain dangerous levels <strong>of</strong> radioactivity for thousand years. 

4.5 Tidal energy 

Tidal energy is <strong>the</strong> smallest source <strong>of</strong> energy on earth. Tides result from <strong>the</strong> gravitational 

attraction exerted upon <strong>the</strong> earth by <strong>the</strong> moon and to a lesser extent by <strong>the</strong> 

sun [346]. As <strong>the</strong> earth spins on its axis, <strong>the</strong> bulges move and produce two high 

and two low tides everywhere each day. Tidal heights are not uniform everywhere. 

They rarely exceed a meter in <strong>the</strong> deep ocean, but over continental shelves, <strong>the</strong>y may 

reach 20 meters. Movement <strong>of</strong> such vast masses <strong>of</strong> water requires a great deal <strong>of</strong> 

exergy, which is estimated to be 2,7 TW. Through a year, this amounts to 0, 85×10 20 

J, according to Skinner [317].


Tidal electricity generation involves <strong>the</strong> construction <strong>of</strong> a barrage across a delta, estuaries, 

beaches, or o<strong>the</strong>r places that are affected by <strong>the</strong> tides. Like in a hydraulic 

power plant, normal turbines will produce electricity as <strong>the</strong> water flows out. However, 

tidal stations differ from hydraulic ones in <strong>the</strong> two-dimensional flow. They 

are able to produce electricity when both water enters <strong>the</strong> basin and when it leaves 

[54]. Tidal energy provides a non-polluting and inexhaustible supply <strong>of</strong> energy and 

assures <strong>the</strong> regularity <strong>of</strong> power production from year to year with less than 5% annual 

variation. The specific tidal exergy is about 10 kJ for each m 2 <strong>of</strong> reservoir and 

each meter <strong>of</strong> height difference, according to Hermann [138]. The high <strong>capital</strong> cost 

for construction and <strong>the</strong> limited number <strong>of</strong> potential sites (about 20) are its main 

drawbacks. Tidal heights <strong>of</strong> 5 meters or more and easily dammed bays or estuaries 

are needed in order for tidal plants to operate effectively. To date, relatively few 

tidal power plants have been constructed. Of <strong>the</strong>se, <strong>the</strong> oldest and by far <strong>the</strong> largest 

is <strong>the</strong> La Rance 240 megawatt barrage located near St. Malo, in Brittany, Nor<strong>the</strong>rn 

France. The worldwide tidal power production is about 300 MW [208]. Tidal 

projects worldwide have been estimated to have a potential energy output <strong>of</strong> around 

166 GW, according to <strong>the</strong> World Energy Council. 

4.6 Energy from <strong>the</strong> sun 

According to Skinner [317], solar radiation is <strong>the</strong> largest energy input <strong>of</strong> <strong>the</strong> earth, 

accounting for about 99,985 % <strong>of</strong> <strong>the</strong> total. From <strong>the</strong> 173.000 TW <strong>of</strong> incoming solar 

radiation, about 30% is directly reflected unchanged, back into space, by <strong>the</strong> clouds, 

sea, continents, and ice and snow. Around 350 TW are used for causing winds, 

ocean currents, waves, etc. Evaporation and precipitation use approximately 4.000 

TW <strong>of</strong> sun’s energy, which will lead to <strong>the</strong> storage <strong>of</strong> water and ice. Only 40 TW 

are effectively used in <strong>the</strong> process <strong>of</strong> photosyn<strong>the</strong>sis, leading to <strong>the</strong> production <strong>of</strong> 

biomass and eventually <strong>of</strong> fossil fuels. 

4.6.1 Solar power 

The exergy flow <strong>of</strong> solar radiation heating <strong>the</strong> land and oceans amounts to 43.200 

TW (Szargut [337]), that is about three thousand times more than <strong>the</strong> present power 

needs <strong>of</strong> <strong>the</strong> whole world: 14 TW in 2006 and 17 TW in 2010. Energy supplied by 

<strong>the</strong> sun in one minute is enough to meet <strong>the</strong> global power need for one year (Khan 

[184]). Unfortunately, technology is not developed enough to make use <strong>of</strong> this huge 

amount <strong>of</strong> energy provided directly by <strong>the</strong> sun. 

Solar power density at <strong>the</strong> earth’s surface is 125-375 W/m 2 and an average photovoltaic 

panel, with 15% efficiency, may deliver 15-60 W/m 2 . But solar cell conversion 

efficiency has increased from 6% in 1954 to 40% in 2006 and thus <strong>the</strong> size 

<strong>of</strong> solar power stations has exponentially increased form 500 kW in 1977 to more 

than 3 GW in 2005 [208]. Electricity generated directly by utilizing solar photons to

Energy from <strong>the</strong> sun 113 

create free electrons in a PV cell is estimated to have a technical potential <strong>of</strong> at least 

450.000 TWh/year or around 51 TW [170], [297] (Table 4.8). 

In addition to <strong>the</strong> direct use <strong>of</strong> solar radiation through photovoltaic panels, solar 

heating collectors use <strong>the</strong> sun’s energy to heat water. Solar <strong>the</strong>rmal power capacity 

was 88 GWth in 2005 [208] and is expected to increase dramatically due to new 

building regulations, especially in Europe 4 . 

Additionally, promising experiences with concentrating solar <strong>the</strong>rmal power plants 

(CSP) show that this technology could be an alternative way <strong>of</strong> producing clean 

electricity from <strong>the</strong> sun. In CSPs, <strong>the</strong> solar flux is concentrated by parabolic troughshaped 

mirror reflectors (30 - 100 suns concentration), central tower receivers requiring 

numerous heliostats (500 - 1000 suns), or parabolic dish-shaped reflectors 

(1000 - 10.000 suns) to heat a working fluid, which in turn transfers <strong>the</strong> heat to a 

<strong>the</strong>rmal power conversion system. According to Philibert [261], 1 km 2 <strong>of</strong> land sited 

at lower latitudes in areas receiving high levels <strong>of</strong> direct insolation, such as desserts 

is enough to generate around 125 GWh/year from a 50 MW plant at 10% conversion 

<strong>of</strong> solar energy to electricity. Thus about 1% <strong>of</strong> <strong>the</strong> world’s desert areas (240.000 

km 2 ), if linked to demand centers by high voltage DC cables, could in <strong>the</strong>ory be 

sufficient to meet total global electricity demand as forecast out to 2030. Installed 

capacity is 354 MWe from nine plants in California. New projects totalling over 1400 

MW are being constructed in different parts <strong>of</strong> <strong>the</strong> world [208]. Technical potential 

estimates for global CSP vary widely from 630 GWe installed by 2040 [10] to 4700 

GWe by 2030 [149] (Table 4.8). 

4.6.2 Water power 

About 23% <strong>of</strong> <strong>the</strong> incoming solar radiation (around 40 PW) is <strong>the</strong> driving force <strong>of</strong> <strong>the</strong> 

hydrologic cycle, which is a conceptual model that describes <strong>the</strong> storage and movement 

<strong>of</strong> water between <strong>the</strong> biosphere, atmosphere, lithosphere and <strong>the</strong> hydrosphere 

(see figure 4.2). About 320.000 km 3 <strong>of</strong> water are evaporated each year form <strong>the</strong> 

oceans, while evaporation from <strong>the</strong> land (including lakes and streams) contributes 

to 60.000 km 3 <strong>of</strong> water. Of this total, about 284.000 km 3 fall back to <strong>the</strong> ocean 

and <strong>the</strong> remaining 96.000 km 3 fall on <strong>the</strong> earth’s land surface. Since 60.000 km 3 

<strong>of</strong> water evaporate from <strong>the</strong> land, 36.000 km 3 <strong>of</strong> water remain to erode <strong>the</strong> land 

during <strong>the</strong> journey back to <strong>the</strong> oceans [346]. 

According to Szargut [337], <strong>the</strong> exergy flow used for <strong>the</strong> evaporation <strong>of</strong> water is 

around 38.100 TW. This exergy is transformed into <strong>the</strong> potential exergy <strong>of</strong> clouds 

(300 TW) and only a small part (5 TW) is transformed into <strong>the</strong> potential exergy <strong>of</strong> 

rivers. Additionally, he calculated <strong>the</strong> chemical exergy <strong>of</strong> fresh water reaching <strong>the</strong> 

land with <strong>the</strong> rain and snow as about 6 TW. Hence, <strong>the</strong> total water power is 11 TW, 

if <strong>the</strong> potential and chemical exergy components are summed (Table 4.8). Valero et 

4 See <strong>the</strong> Directive 2002/91/EC on <strong>the</strong> energy performance <strong>of</strong> buildings.


al. [371] calculated <strong>the</strong> exergy replacement costs <strong>of</strong> renewable water resources and 

world’s ice sheets 5 considering <strong>the</strong>ir chemical and potential components as between 

3.592 and 53.304 Mtoe/year for freshwater and 3, 84 × 10 8 and 7.210 × 10 9 Mtoe 

for ice sheets. 

Humans use only part <strong>of</strong> <strong>the</strong> renewable exergy <strong>of</strong> water. That is <strong>the</strong> potential exergy 

<strong>of</strong> rivers in form <strong>of</strong> hydropower. The chemical and <strong>the</strong>rmal exergy <strong>of</strong> <strong>the</strong> freshwater 

in rivers or ice sheets cannot be transformed into useful energy yet, at least with <strong>the</strong> 

current state <strong>of</strong> technology. 

Hydropower is <strong>the</strong> most highly developed renewable energy resource. The power 

present in water that runs <strong>of</strong>f continents was calculated in 1962 as 2,9 TW [317]. 

The International Water Power & Dam Construction (IWP&DC) classified and calculated 

more recently <strong>the</strong> world hydroelectric potentials according to <strong>the</strong> following 

criteria [166]: 

• Gross Hydroelectric Potential: <strong>the</strong> hydroelectric potential <strong>of</strong> a country if all 

its water flows were turbined until sea level or to <strong>the</strong> country borders (if <strong>the</strong> 

flow continues into o<strong>the</strong>r countries) under 100% system efficiency. It has been 

estimated as 4.200 GW. 

• Technically Useful Hydroelectric Potential: <strong>the</strong> hydroelectric energy obtained 

from all <strong>the</strong> exploitable or exploited places under existing technological limits, 

without taking into account environmental, economic or o<strong>the</strong>r restrictions. It 

has been estimated as 1.800 GW (Table 4.8). 

• Economically Exploitable Hydroelectric Potential: part <strong>of</strong> technically feasible 

potential that can be or that has been developed under <strong>the</strong> local economic 

conditions and in a competitive way with o<strong>the</strong>r energy supply sources. Some 

<strong>of</strong> <strong>the</strong> places that can be exploited economically can have restrictions from 

<strong>the</strong> environmental point <strong>of</strong> view. None<strong>the</strong>less, this limitation is not taken into 

account when determining this potential. It has been estimated as around 

1.200 GW. 

At <strong>the</strong> end <strong>of</strong> 2006, worldwide hydropower consumption was 688,1 Mtoe, accounting 

for about 6% <strong>of</strong> <strong>the</strong> total energy consumption [35]. 

4.6.3 Wind power 

According to Skinner [317], around 350 TW <strong>of</strong> solar energy is used for driving winds 

and ocean waves. Wind is horizontal air movement arising from differences in air 

pressure created by <strong>the</strong> uneven heating <strong>of</strong> <strong>the</strong> atmosphere. It always flows from a 

5 <strong>Exergy</strong> replacement costs are defined as <strong>the</strong> energy required by <strong>the</strong> best available technologies to 

return a resource to <strong>the</strong> same conditions as it was delivered by <strong>the</strong> ecosystem(s).


Figure 4.2. The hydrologic cycle. Source: http://www.ec.gc.ca/water (Environment 

Canada) 

place <strong>of</strong> high pressure to one <strong>of</strong> low pressure. Wind’s speed and direction are also 

affected by <strong>the</strong> Coriolis effect 6 and friction occurring between wind and solid objects 

<strong>of</strong> any kind such as <strong>the</strong> ground, trees, etc. Most places around <strong>the</strong> world have wind 

speeds that average between 10 and 30 km/h [318]. The average global wind speed 

at 50 m is 6,6 m/s (23,7 km/h) [240] and with an exergy content <strong>of</strong> about 336 

W /m 2 perpendicular to <strong>the</strong> wind direction, according to Hermann [138]. 

Estimates <strong>of</strong> <strong>the</strong> total global wind power are very large (on <strong>the</strong> order <strong>of</strong> 10 15 W) but 

much <strong>of</strong> <strong>the</strong> power is in high altitude winds and is not recoverable by devices on <strong>the</strong> 

land surface [317]. Global wind power generated at locations with mean annual 

wind speeds ≥ 6,9 m/s at 80 m is found to be ∼ 72 TW [9]. A technical potential 

<strong>of</strong> 72 TW installed global capacity at 20% average capacity factor would generate 

126.000 TWh/yr or around 14,5 TW (Table 4.8). In 2005, <strong>the</strong> existing exergy power 

capacity worldwide was 59 GW [208]. 

4.6.4 Ocean power 

The sun is responsible for three effects occurring in <strong>the</strong> oceans: an ocean <strong>the</strong>rmal 

gradient, from which <strong>the</strong>rmal energy could be eventually extracted; <strong>the</strong> <strong>the</strong>rmohaline 

circulation, which is in part caused by <strong>the</strong> <strong>the</strong>rmal gradient and causing vast 

6 The Coriolis effect is <strong>the</strong> deviation from a straight line in <strong>the</strong> path <strong>of</strong> a moving body due to <strong>the</strong> 

earth’s rotation.


volumes <strong>of</strong> water to move around <strong>the</strong> globe; and ocean waves, indirectly generated 

by <strong>the</strong> sun through blowing <strong>of</strong> winds. 

4.6.4.1 Ocean <strong>the</strong>rmal gradient 

The sun heats <strong>the</strong> surface <strong>of</strong> <strong>the</strong> ocean, generating a <strong>the</strong>rmal gradient that varies 

from around 22 ◦ C to 2 ◦ C in <strong>the</strong> deep ocean. This temperature difference gives 

a specific exergy <strong>of</strong> about 800 J/kg seawater [138]. Considering <strong>the</strong> mass <strong>of</strong> <strong>the</strong> 

oceans equal to 1, 37 × 10 23 kg, this gives an absolute exergy <strong>of</strong> 1, 13 × 10 8 Gtoe 

(Table 4.8). Theoretically, this <strong>the</strong>rmal gradient could be used for drawing energy 

from <strong>the</strong> oceans. However, <strong>the</strong> small temperature difference involved makes ocean 

<strong>the</strong>rmal power to be unpracticable with current technology and no commercial plant 

exists. However, if this source <strong>of</strong> energy would be used with an efficiency <strong>of</strong> less than 

1%, <strong>the</strong> ocean’s <strong>the</strong>rmal energy potential would exceed <strong>the</strong> potential <strong>of</strong> fossil fuels 

[317]. 

Ano<strong>the</strong>r consequence <strong>of</strong> <strong>the</strong> <strong>the</strong>rmal gradient <strong>of</strong> oceans is <strong>the</strong> so called <strong>the</strong>rmohaline 

circulation (THC) or “<strong>the</strong> great ocean conveyor belt” [40]. This global ocean circulation 

is driven by density differences, which depend on temperature and salinity. The 

salinity and temperature differences arise from heating/cooling at <strong>the</strong> sea surface 

and from <strong>the</strong> surface freshwater fluxes (evaporation and sea ice formation enhance 

salinity; precipitation, run<strong>of</strong>f and ice-melt decrease salinity). It transports enormous 

volumes <strong>of</strong> cold, salty water from <strong>the</strong> North Atlantic to <strong>the</strong> Nor<strong>the</strong>rn Pacific, and 

brings warmer, fresher water in return. 

In <strong>the</strong> North Atlantic warm and salty water that has been transported north from 

tropical regions is cooled, forming frozen water without salts, and <strong>the</strong>reby, increasing 

<strong>the</strong> salinity <strong>of</strong> <strong>the</strong> remaining, unfrozen water. The dense, saline waters drop to 

<strong>the</strong> floor <strong>of</strong> <strong>the</strong> ocean. This water begins a great circuit through <strong>the</strong> world’s oceans 

(see <strong>the</strong> path <strong>of</strong> this circuit in fig. 4.3). In <strong>the</strong> Pacific, <strong>the</strong> current mixes with warmer 

water, where it undergoes upwelling and warming once again. When this warmer, 

saltier water reaches again <strong>the</strong> high nor<strong>the</strong>rn latitudes, it chills, and eventually becomes 

North Atlantic deep water, completing <strong>the</strong> circuit. 

The volume transport <strong>of</strong> <strong>the</strong> overturning circulation at 24 N has been estimated 

from hydrographic section data as around 17 × 10 16 m 3 /s [286], its heat transport 

as 1.200 TW. The heat transport was estimated as well by Munk et al. [235] as 

2.000 TW. The corresponding exergy flow assuming a difference <strong>of</strong> 20 K is about 

100 TW transferred to <strong>the</strong> <strong>the</strong>rmal gradient [138]. Unfortunately, <strong>the</strong>re is currently 

no energy-conversion technology <strong>of</strong> this nature. 

The climatic effect <strong>of</strong> <strong>the</strong> THC is still to some extent under discussion, and is due to 

<strong>the</strong> heat transport <strong>of</strong> this circulation [274]. This amount <strong>of</strong> heat transported into <strong>the</strong> 

nor<strong>the</strong>rn North Atlantic (north <strong>of</strong> 24 N) should warm this region by around 5 o C (<strong>the</strong> 

difference sea surface temperature in <strong>the</strong> North Atlantic as compared to <strong>the</strong> North 

Pacific at similar latitudes). Global surface air temperatures show that over <strong>the</strong> three


Figure 4.3. A simplified summary <strong>of</strong> <strong>the</strong> path <strong>of</strong> <strong>the</strong> Thermohaline Ocean Circulation 

[274] 

main deep water formation regions <strong>of</strong> <strong>the</strong> world ocean, air temperatures are warmer 

by up to around 10 o C compared to <strong>the</strong> latitudinal mean. 

The concerns about <strong>the</strong> possible collapse <strong>of</strong> <strong>the</strong> THC through <strong>the</strong> anthropogenic 

greenhouse effect have increased recently. When <strong>the</strong> strength <strong>of</strong> <strong>the</strong> haline forcing 

increases due to excess precipitation, run<strong>of</strong>f, or ice melt, <strong>the</strong> conveyor belt will 

weaken or even shut down. The variability in <strong>the</strong> strength <strong>of</strong> <strong>the</strong> conveyor belt will 

lead to climate change in Europe (decreasing <strong>the</strong> temperatures down to 9 o C) and it 

could also influence o<strong>the</strong>r areas <strong>of</strong> <strong>the</strong> global ocean. 

4.6.4.2 Ocean Waves 

Waves are ano<strong>the</strong>r expression <strong>of</strong> solar energy. They are formed from winds blowing 

over <strong>the</strong> ocean, and <strong>the</strong>ir energy content is many thousands <strong>of</strong> times greater than 

that in tides. The momentum to currents and surface gravity waves transferred by 

<strong>the</strong> wind is estimated as 60 TW [396], but <strong>the</strong> wave breaking and internal friction 

reduces <strong>the</strong> wave exergy flow to 3 TW breaking on <strong>the</strong> world’s coast [138]. For 

example, a single wave that is 1,8 meters high and moving in water 9 meters deep 

generates around 10 kW for each meter <strong>of</strong> wave front [317]. Different wave energy 

conversion schemes have been developed, but none are currently in large-scale use. 

The only two commercial wave power projects total 750 kW [163].


Table 4.4. Specific exergy on a dry basis <strong>of</strong> representative biomass samples [138] 

Biomass type <strong>Exergy</strong> (dry), 

MJ/kg 

Eucalyptus 19,9 

Poplar 19,2 

Corn stover 18,2 

Bagasse 17,8 

Water hyacinth 15,2 

Brown kelp 10,9 

The best wave energy climates have deep water power densities <strong>of</strong> 60-70 kW/m but 

fall to about 20 kW/m at <strong>the</strong> foreshore. Around 2% <strong>of</strong> <strong>the</strong> world’s 800.000 km <strong>of</strong> 

coastline exceeds 30kW/m giving a technical potential <strong>of</strong> around 500 GW assuming 

<strong>of</strong>f-shore wave energy devices have 40% efficiency [163]. 

4.6.5 Biomass 

Plants depend on sunlight <strong>of</strong> photosyn<strong>the</strong>sis and hence biomass is ano<strong>the</strong>r expression 

<strong>of</strong> solar power. The radiation flow absorbed by <strong>the</strong> vegetation has an energy <strong>of</strong> 

about 40 TW according to Skinner [317] and an exergy about 37 TW, according to 

Szargut [337]. 

Biomass is a term used for plant and animal derived material and includes wood, 

energy crops, crop residues and animal dung. It consists mostly <strong>of</strong> cellulose, lignin, 

protein and ash. Specific exergy <strong>of</strong> biomass ranges form 15 to 20 MJ/kg on a dry 

basis depending on carbon and ash content. Woody biomass tends to have a higher 

carbon content, as opposed to marine biomass [138] (see table 4.4). 

The photosyn<strong>the</strong>tic efficiency <strong>of</strong> converting solar energy into energy-rich organic 

compounds averages around 1%. And only 2,5 TW <strong>of</strong> energy and 2,9 TW <strong>of</strong> exergy is 

transformed into <strong>the</strong> chemical exergy <strong>of</strong> plants [337]. Estimates <strong>of</strong> <strong>the</strong> dry weight <strong>of</strong> 

all living plant matter on earth’s land surface vary but average about 2×10 12 metric 

tons [317]. Considering a specific exergy <strong>of</strong> biomass <strong>of</strong> 17 MJ/kg, <strong>the</strong> exergy content 

<strong>of</strong> dry biomass on earth is around 810 Gtoe 7 The <strong>the</strong>oretical biomass potential was 

estimated by Johansson [170] as around 92 TW, what implies an available exergy 

capacity <strong>of</strong> 70 Gtoe each year (Table 4.8). 

Humans own about 16 TW <strong>of</strong> <strong>the</strong> land productivity. From <strong>the</strong>se, about 5 TW contributes 

to <strong>the</strong> consumption <strong>of</strong> 1,5 TW in <strong>the</strong> form <strong>of</strong> wood fuel and around 0,2 TW 

goes into <strong>the</strong> production <strong>of</strong> 20 GW <strong>of</strong> ethanol [138]. The world biomass production 

energy potential vary greatly depending on <strong>the</strong> assumptions taken into account. Fulton 

and Howes [98] compiled <strong>the</strong> different estimates <strong>of</strong> world biomass production. 

7 This number represents <strong>the</strong> total exergy we could extract from biomass, if it were not renewable.


The IPCC [161] estimates a raw biomass energy potential <strong>of</strong> 10,4 Gtoe/year (14 

TW) and a liquid bi<strong>of</strong>uels energy potential <strong>of</strong> 3,6 Gtoe/year (4,8 TW), while Moreira 

[229] 31,2 Gtoe/year (41,5 TW) and 10,8 Gtoe/year (14,4 TW), respectively 

(Table 4.8). 

4.6.6 Fossil fuels 

Fossil fuels represent <strong>the</strong> remains <strong>of</strong> plants or animals that ga<strong>the</strong>red <strong>the</strong>ir energy 

from <strong>the</strong> sun millions <strong>of</strong> years ago and constitute reservoirs <strong>of</strong> chemical exergy. 

Around 40 GW <strong>of</strong> biological matter are buried under sediments and will eventually 

form fossil fuels [26]. Like <strong>the</strong> o<strong>the</strong>r <strong>mineral</strong>s, <strong>the</strong>y are nonrenewable resources, 

since <strong>the</strong>y cannot be replenished at least in our lifetime. The main commercial types 

<strong>of</strong> fossil fuels are coal, oil and natural gas. O<strong>the</strong>r unconventional fossil fuels include 

tight gas sands, coal bed methane, clathrate hydrates, shale and heavy oil and tar 

sands, but no commercial way <strong>of</strong> extraction has been discovered yet. 

The specific exergies <strong>of</strong> fossil fuels vary with <strong>the</strong> carbon content and <strong>the</strong> percentage 

<strong>of</strong> inert components. Different authors such as Shieh and Fan [310] or Stepanov 

[330] have derived expressions for <strong>the</strong> exergy estimation <strong>of</strong> fuels. In many cases, 

especially for substances containing mainly C, H, O and N, <strong>the</strong> High Heating Value 

(HHV) is essentially identical to <strong>the</strong> specific exergy. 

Fossil fuels are by far <strong>the</strong> most important sources <strong>of</strong> energy nowadays, accounting for 

87,8% <strong>of</strong> world energy consumption. Production <strong>of</strong> fossil fuels reached at <strong>the</strong> end <strong>of</strong> 

2006 over 9.500 Mtoe [35]. The remaining 12% is distributed at almost equal rates 

into nuclear and hydroelectrical power. See figure 4.4 for <strong>the</strong> world distribution <strong>of</strong> 

energy consumption. 

4.6.6.1 Coal 

Coal is a sedimentary and metamorphic rock. It is formed from plants that grew in 

ancient swamps. The remains <strong>of</strong> <strong>the</strong> plants accumulated in a nonoxidizing environment 

and were eventually buried by o<strong>the</strong>r sediments, usually sand or mud, which are 

now <strong>the</strong> sandstone and shale typically associated with coal beds. The coal deposits 

start <strong>of</strong>f as organic materials made chiefly <strong>of</strong> carbon, oxygen and hydrogen. With 

rising <strong>the</strong> temperature and pressure, due to <strong>the</strong> burial <strong>of</strong> <strong>the</strong> deposits, <strong>the</strong> hydrogen 

and oxygen are gradually lost [195]. 

In addition to carbon, oxygen and hydrogen, coal contains many o<strong>the</strong>r elements in 

small amounts. Sulfur is one <strong>of</strong> its most common impurities, making coal a dangerous 

pollutant <strong>of</strong> air and water. Table 4.5 shows <strong>the</strong> ASTM D388 coal-rank classification 

according to <strong>the</strong> high heating value (HHV). Coal’s specific exergy varies from 

about 20 to 30 MJ/kg [138], although some low-carbon coals such as lignites may 

have specific exergies as low as 15 MJ/kg.


Coal; 3090,1; 

28% 

Oil; 3889,8; 36% 

Nuclear Energy; 

688,1; 6% 

Natural Gas; 

2574,9; 24% 

Hydroelectric; 

688,1; 6% 

Figure 4.4. Primary world energy consumption by fuel type at <strong>the</strong> end <strong>of</strong> 2006. 

Values in Mtoe [35]. 

Coal accounts for about 28% <strong>of</strong> <strong>the</strong> energy consumption in <strong>the</strong> world. World proved 8 

reserves <strong>of</strong> coal at <strong>the</strong> end <strong>of</strong> 2006 were estimated by British Petroleum [35] to 

be 909.064 millions <strong>of</strong> tons (see figure 4.5) and by <strong>the</strong> WEC [401], 847.488 Mt. 

Considering an average heating value <strong>of</strong> 25 MJ/kg, <strong>the</strong> world’s coal proven reserves 

are about 523 Gtoe, taking <strong>the</strong> average reserves given by BP and <strong>the</strong> WEC. The exact 

exergy <strong>of</strong> <strong>the</strong> coal reserves will be calculated later in chapter 6. 

The WEC [401] estimates additional resources amount in place as around 1770 

Mtons or 1100 Gtoe. From <strong>the</strong>se, additional recoverable reserves are estimated at 

180 Mtons or 110 Gtoe. 

Unlike oil or natural gas, coal is more evenly distributed worldwide and consumption 

and production rates are ra<strong>the</strong>r equilibrated (see figure 4.6). At <strong>the</strong> end <strong>of</strong> 2006, 

world coal consumption was 3.090,1 Mtoe [35]. The demand for coal is expected 

to more than double by 2030 and <strong>the</strong> IEA has estimated that more than 4.500 GW 

<strong>of</strong> new power plants (half in developing countries) will be required in this period 

[150]. 

8 Proved reserves <strong>of</strong> coal - Generally taken to be those quantities that geological and engineering 

information indicates with reasonable certainty can be recovered in <strong>the</strong> future from known deposits 

under existing economic and operating conditions.


Table 4.5. Rank <strong>of</strong> coal according to <strong>the</strong> norm ASTM D388. 

Class rank Fix carbon limits Volatile limits HHV Limits, MJ/kg 

≥ < ≥ < ≥ < 

Anthracite 

Anthracite 98 2 

Meta-anthracite 92 98 2 8 

Semianthracite 86 92 8 14 

Bituminous 

Low-volatile 78 86 14 22 

Medium volatile 69 78 22 31 

High-volatile A - 69 31 - 32,56 

High-volatile B 30,24 32,56 

High-volatile C 26,75 30,24 

Subbituminous 

Subbituminous A 24,42 26,75 

Subbituminous B 22,1 24,42 

Subbituminous C 19,31 22,1 

Lignite 

Lignite A 14,65 19,31 

Lignite B 14,65 

Ano<strong>the</strong>r young form <strong>of</strong> coal, peat, (partially decayed plant matter toge<strong>the</strong>r with <strong>mineral</strong>s) 

has been used as a fuel for thousands <strong>of</strong> years and is still in use, particularly 

in Nor<strong>the</strong>rn Europe. The reserves <strong>of</strong> peat have not been estimated but are very large. 

4.6.6.2 Oil and natural gas 

Oil and natural gas have proved to be economical, efficient and relative clean fuels. 

As a result, by 1950, <strong>the</strong>y had overtaken coal as <strong>the</strong> primary source <strong>of</strong> energy. 

Almost without exception, petroleum and natural gas are associated with sedimentary 

rocks <strong>of</strong> marine origin. Both are mixtures <strong>of</strong> hydrocarbon compounds (composed 

largely <strong>of</strong> hydrogen and carbon) with minor amounts <strong>of</strong> sulphur, nitrogen and 

oxygen. Hydrocarbon production takes place in two stages [195]. First, biological, 

chemical and physical processes begin to break down <strong>the</strong> organic matter into 

what is called kerogen, a precursor <strong>of</strong> oil and gas. The second stage is marked by 

<strong>the</strong> <strong>the</strong>rmal alteration <strong>of</strong> kerogen to hydrocarbons as <strong>the</strong> deposit is buried deeper 

by younger, overlying sediments. The production <strong>of</strong> hydrocarbons begins at a temperature 

<strong>of</strong> about 50 to 60 o C and a depth <strong>of</strong> 2 to 2,5 km. Hydrocarbon formation 

continues to depths <strong>of</strong> 6 to 7 km and temperatures <strong>of</strong> 200 to 250 o C. Formation <strong>of</strong> oil 

dominates in <strong>the</strong> lower range <strong>of</strong> temperature and burial and gas in <strong>the</strong> higher range. 

The British standard BS2869:1998 classifies fuel oil into six classes according to its 

boiling temperature, composition and purpose. No. 1 and No. 2 are referred to as 

distillate fuel oils, while No. 4, No. 5 and No. 6 are labelled residual fuel oils. In


Figure 4.5. Coal proved reserves at <strong>the</strong> end 2006. Values in thousand millions tonnes 

(share <strong>of</strong> anthracite and bituminous coal in brackets) [35]. 

Table 4.6. Rank <strong>of</strong> oil according to <strong>the</strong> British standard BS2869:1998 

Class rank No. 1 No. 2 No. 4 No .5 No. 6 

Density (kg/l) 0,824 0,864 0,927 0,952 1 

Residual carbon (%) Traces Traces 2,5 5 12 

Sulphur (%) 0,1 0,4-0,7 0,4-1,5 2,0 max. 2,8 max. 

Oxygen and Nitrogen (%) 0,2 0,2 0,48 0,7 0,92 

Hydrogen (%) 13,2 12,7 11,9 11,7 10,5 

Carbon (%) 86,5 86,4 86,1 85,55 85,7 

Water and sediments (%) Traces Traces 0,5 max. 1,0 max. 2,0 max. 

Ashes (%) Traces Traces 0,02 0,05 0,08 

HHV (kJ/kg) 46.365 45.509 43.920 43.353 42.467 

a more commercial sense: No. 1 fuel oil is kerosene; No. 2 is diesel oil and No. 4, 

5 and 6 are heavy fuel oils. Table 4.6 shows <strong>the</strong> chemical composition, density and 

high heating value <strong>of</strong> classes 1, 2, 4, 5 and 6. Low molecular weight petroleum has 

an exergy content between 40 to 46 MJ/kg. Higher molecular weight petroleum and 

<strong>the</strong> hydrocarbon portion <strong>of</strong> <strong>the</strong> inorganic mixtures have a chemical exergy close to 

40 MJ/kg [138]. 

Natural gas consists primarily <strong>of</strong> methane but including significant quantities <strong>of</strong> 

ethane, butane, propane, carbon dioxide, nitrogen, helium and hydrogen sulfide.


2000 

1500 

1000 

500 

0 

Mtoe 

Total North 

America 

Total S. & 

Cent. 

America 

Total Europe 

& Eurasia 

Total Middle 

East 

Coal: Production Coal: Consumption 

Total Africa Total Asia 

Pacific 

Figure 4.6. Coal production and consumption at <strong>the</strong> end <strong>of</strong> 2006. Elaborated from 

data included in [35]. 

Table 4.7. Physical properties <strong>of</strong> different compositions <strong>of</strong> natural gas [34] 

Composition Density HHV 

CO 2 N 2 H 2S CH 4 C 2H 6 C 3H 8 C 4H 10 C 5H 12 kg/N m 3 kJ/N m 3 kJ/kg 

5,5 - 7 77,7 5,5 2,4 1,18 0,63 0,9 39.575 43.915 

3,51 32 0,5 52,5 3,7 2,2 2,02 3,44 1,06 32.600 30.750 

26,2 0,7 - 59,2 13,9 - - - 1,08 31.668 29.261 

0,17 87,7 - 10,5 1,6 - - - 1,14 5.073 2.552 

0,2 0,6 - 99,2 - - - - 0,72 37.524 52.126 

- 0,6 - - 79,4 20 - - 1,41 72.176 51.079 

- 0,5 - - 21,8 77,7 - - 1,77 89.110 50.049 

The main properties <strong>of</strong> natural gas are listed in table 4.7. The specific exergy <strong>of</strong> 

natural gas is around 50 MJ/kg [138]. 

Oil accounts for 36% <strong>of</strong> world energy consumption, while natural gas for about 24%. 

World proved reserves <strong>of</strong> oil and gas are much smaller than those <strong>of</strong> coal. At <strong>the</strong> end 

<strong>of</strong> 2006, <strong>the</strong>y were estimated as 1.208,2 thousand million barrels or 164,8 Gtons 

and <strong>of</strong> gas 181,46 trillion <strong>of</strong> cubic meters or 163,4 Gtoe, considering <strong>the</strong> conversion 

factor given in <strong>the</strong> BP report [35] (see figures 4.7 and 4.9).


In terms <strong>of</strong> exploration, <strong>the</strong> oil industry is relatively mature and <strong>the</strong> quantity <strong>of</strong> additional 

reserves that remain to be discovered is unclear. The general and ra<strong>the</strong>r 

pessimistic believe concerning oil discoveries is that few new oil fields are being 

discovered, and that most <strong>of</strong> <strong>the</strong> increases in reserves results from revisions <strong>of</strong> underestimated 

existing reserves (Ivanhoe and Leckie [165], Laherre [190], Campbell 

[45] or Hatfield [133]). The optimistic views appeal to improvements in technology, 

such as 3D seismic surveys and extended reach (e.g. horizontal) drilling, that 

have improved recovery rates from existing reservoirs and made pr<strong>of</strong>itable <strong>the</strong> development 

<strong>of</strong> fields previously regarded as uneconomic (Smith and Robinson [324]). 

Masters et al. [211] reflect <strong>the</strong> current state <strong>of</strong> knowledge as to <strong>the</strong> uncertainties in 

future potentials for conventional oil resources. These estimates assess in addition 

to <strong>the</strong> conventional oil reserves a corresponding range <strong>of</strong> additionally recoverable 

resources between 38 and 141 Gtoe. 

Estimates <strong>of</strong> gas reserves and resources are being revised continuously. The International 

Gas Union (IGU) estimates that additional reserves, including gas yet to be 

discovered could be as high as 200 Gtoe [156]. Gregory and Rogner [123] suggest 

an optimistic estimate for ultimately recoverable reserves <strong>of</strong> additional 500 Gtoe . 

World major oil suppliers are by far middle-east countries. Except <strong>of</strong> <strong>the</strong>m, south 

and central America and Africa, <strong>the</strong> rest <strong>of</strong> <strong>the</strong> world is a net importer <strong>of</strong> oil, even if 

some countries like north America produce considerable amounts <strong>of</strong> <strong>the</strong> resource as 

well (see figure 4.8). Oil world consumption at <strong>the</strong> end <strong>of</strong> 2006 was 3889,8 Mtons 

[35]. 

Major natural gas consumers in <strong>the</strong> world are Asian-Pacific countries, and most part 

<strong>of</strong> it has to be imported. The largest producers in <strong>the</strong> world are <strong>the</strong> Russian federation, 

followed by north America, Iran, Norway and Algeria (see figure 4.10). Natural 

gas world consumption at <strong>the</strong> end <strong>of</strong> 2006 was 2574,9 Mtoe [35]. 

4.6.6.3 Unconventional fossil fuels 

Besides <strong>of</strong> <strong>the</strong> fossil fuels mentioned before, <strong>the</strong>re is a great quantity and variety <strong>of</strong> 

unconventional fossil fuel resources, not on a large-scale commercially recoverable. 

Oil that requires extra processing such as from shales, heavy oils, and oil (tar) sands, 

is classified as unconventional. Toge<strong>the</strong>r contributed around 3% <strong>of</strong> world oil production 

in 2005 (66 Mtoe) and could reach 110 Mtoe by 2020 [230] and up to 140 Mtoe 

by 2030 [151]. Resource estimates are uncertain but could have a potential <strong>of</strong> over 

830 Gtoe [163]. 

Methane stored in a variety <strong>of</strong> geologically complex, unconventional reservoirs, such 

as tight gas sands, fractured shales, coal beds and hydrates, is even more abundant 

than conventional gas. Worldwide coal bed methane may be larger than 190,5 Gtoe 

but a scarcity <strong>of</strong> basic information on <strong>the</strong> gas content <strong>of</strong> coal resources makes this 

number highly speculative [163]. A similar quantity is estimated to be in <strong>the</strong> form <strong>of</strong>


Figure 4.7. Oil proved reserves at <strong>the</strong> end 2006. Values in thousand millions <strong>of</strong> 

barrels [35]. 

1400 

1200 

1000 

800 

600 

400 

200 

0 

Mtoe 

Total North 

America 

Total S. & 

Cent. 

America 

Total Europe 

& Eurasia 

Total Middle 

East 

Oil: Production Oil: Consumption 


Pacific 

Figure 4.8. Oil production and consumption at <strong>the</strong> end <strong>of</strong> 2006. Elaborated from 

data included in [35].


Figure 4.9. Natural gas proved reserves at <strong>the</strong> end 2006. Values in trillion cubic 

meters [35]. 

2000 

1500 

1000 

500 

0 

Mtoe 

Total North 

America 

Total S. & 

Cent. 

America 

Total Europe 

& Eurasia 

Total Middle 

East 


Pacific 

Natural Gas: Production Natural Gas: Consumption 

Figure 4.10. Natural gas production and consumption at <strong>the</strong> end <strong>of</strong> 2006. Elaborated 

from data included in [35].

Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> energy resources 127 

tight sands. Methane clathrate is a solid form <strong>of</strong> water that contains a large amount 

<strong>of</strong> methane within its crystal structure. It is usually found in vast quantities under 

sediments on <strong>the</strong> ocean floor. According to <strong>the</strong> IPCC [160], technologies to recover 

<strong>the</strong>se resources economically could be developed in <strong>the</strong> future, if demand for natural 

gas continues to grow in <strong>the</strong> longer run, in which case gas resource availability would 

increase enormously. The reserves are estimated by <strong>the</strong> USGS [360] to be greater 

than 1.400 Gtoe. 

The great drawback <strong>of</strong> <strong>the</strong>se kinds <strong>of</strong> unconventional fuels is <strong>the</strong> elevated quantity <strong>of</strong> 

energy required for <strong>the</strong>ir extraction. The refinement <strong>of</strong> oil shale for instance, needs 

two or three times more energy than <strong>the</strong> production <strong>of</strong> conventional fuel oil. Fur<strong>the</strong>rmore, 

<strong>the</strong> associated environmental footprint is huge, since usually vast forest 

areas need to be destroyed and <strong>the</strong> important amount <strong>of</strong> water used and emissions 

produced threatens <strong>the</strong> biodiversity <strong>of</strong> <strong>the</strong> surroundings. 

4.7 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> energy resources 

Table 4.8 summarizes <strong>the</strong> results discussed in <strong>the</strong> previous sections. It shows <strong>the</strong> 

available energy, potential energy use and current energy consumption <strong>of</strong> most important 

energy resources on earth. With potential energy, we mean probable energy 

capacity using advanced technology, not necessarily developed nowadays. Consumption 

values are referred to <strong>the</strong> end <strong>of</strong> 2006, except for geo<strong>the</strong>rmal, PV, wind, biomass 

and tidal energy, which are 2005 values. 

It must be pointed out that <strong>the</strong> data must be still considered as an approximation 

and in any case, it might increase, as technology allows to make a more efficient use 

<strong>of</strong> <strong>the</strong> resources and to exploit non currently recoverable fuels. 

The detailed analysis <strong>of</strong> <strong>the</strong> results will be carried out in chapter 6, when all resources, 

including non-fuel <strong>mineral</strong>s are assessed with <strong>the</strong> same unit <strong>of</strong> measure. 

In <strong>the</strong> next section <strong>the</strong> remaining type <strong>of</strong> natural resources will be studied. Namely, 

<strong>the</strong> non-fuel <strong>mineral</strong> resources. 

4.8 Non-fuel <strong>mineral</strong> resources 

In addition to energy resources, non-fuel <strong>mineral</strong>s are <strong>the</strong> o<strong>the</strong>r kind <strong>of</strong> resources 

essential for civilization. The quantity <strong>of</strong> <strong>mineral</strong>s on earth is finite and hence <strong>the</strong>y 

are classified as non-renewable. The physical and chemical properties <strong>of</strong> <strong>mineral</strong>s 

are directly influenced by <strong>the</strong> two major energy sources <strong>of</strong> <strong>the</strong> earth: <strong>the</strong> sun and 

<strong>the</strong> geo<strong>the</strong>rmal power. They are responsible for <strong>the</strong> movement <strong>of</strong> materials from <strong>the</strong> 

earth’s interior, to <strong>the</strong> crust, from <strong>the</strong>se to <strong>the</strong> sea or to rivers through currents and 

from <strong>the</strong> sea to form rocks in <strong>the</strong> so called geochemical cycle. The resulting dynamic 

equilibrium is called <strong>the</strong> geochemical balance [68].


Table 4.8. Available energy, potential energy use and current consumption <strong>of</strong> natural 

resources on earth. 

Resource Available energy Potential energy Current energy 

use 

consumption 

Geo<strong>the</strong>rmal 17,9 TW 59 - 124 GWe 9,3 GWe / 28 

Uranium - fission 27.100 Gtoe 5.200 Gtoe 

GWth 

635,5 Mtoe 

Thorium - fission 7.500 Gtoe - - 

Deutorium + Tritium (fusion) 74 Ttoe - - 

Tidal power 2,7 TW 166 GW 300 MW 

Solar PV 43,2 PW 51,4 TW 3 GWe 

Solar <strong>the</strong>rmal power 43,2 PW 630 - 4700 GWe 354 MWe 

Water power 11 TW 1.800 GW 688,1 Mtoe 

Wind power 1000 TW 14,5 TW 59 GW 

Ocean <strong>the</strong>rmal gradient 1, 4 × 108 Gtoe - - 

Ocean conveyor belt 1.200 - 2.000 TW - - 

Ocean waves 3 TW 500 GW 750 kW 

Biomass 92 TW 19 - 56 TW 1,7 TW 

Coal 1615 Gtoe 523 Gtoe 3090 Mtoe 

Natural gas 365-665 Gtoe 163,4 Gtoe 2574,9 Mtoe 

Oil 200-300 Gton 164,8 Gton 3889,8 Mton 

Unconventional fuels ∼ 2600 Gtoe - 66 Mtoe 

In chapter 3 we obtained an estimation <strong>of</strong> <strong>the</strong> average <strong>mineral</strong>ogical composition <strong>of</strong> 

<strong>the</strong> crust. The figures given in table 3.3 show <strong>the</strong> relative abundance <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s 

on earth. Of course <strong>mineral</strong>s are not found in <strong>the</strong> same concentration everywhere 

in <strong>the</strong> crust. Fortunately for mankind, nature provides us with areas accounting for 

high-concentrated deposits, that allow us to extract <strong>the</strong>m in a relatively cost-effective 

way. Minerals become concentrated in five ways [318]: 

1. Concentration by hot, aqueous solutions flowing through fractures and pore 

spaces in crustal rock to form hydro<strong>the</strong>rmal <strong>mineral</strong> deposits. 

2. Concentration by magmatic processes within a body <strong>of</strong> igneous rock to form 

magmatic <strong>mineral</strong> deposits. 

3. Concentration by precipitation from lake water or seawater to form sedimentary 

<strong>mineral</strong> deposits. 

4. Concentration by flowing surface water in streams or along <strong>the</strong> shore to form 

placers. 

5. Concentration by wea<strong>the</strong>ring processes to form residual <strong>mineral</strong> deposits. 

Besides <strong>of</strong> <strong>the</strong> physical way <strong>of</strong> classifying <strong>mineral</strong> concentrations, <strong>the</strong>re is an economical 

way <strong>of</strong> classifying <strong>the</strong>m. This is explained in <strong>the</strong> following section.

Non-fuel <strong>mineral</strong> resources 129 

4.8.1 The economic classification <strong>of</strong> <strong>mineral</strong>s 

Concentrations <strong>of</strong> <strong>mineral</strong>s can be classified as resources, reserves and reserve base, 

depending on <strong>the</strong> different factors explained next. 

The US Bureau <strong>of</strong> Mines defines a resource as a concentration <strong>of</strong> naturally occurring 

solid, liquid, or gaseous material in or on <strong>the</strong> earth’s crust in such form and amount 

that economic extraction <strong>of</strong> a commodity from <strong>the</strong> concentration is currently or potentially 

feasible. 

Reserve base is defined as that part <strong>of</strong> an identified resource 9 that meets specified 

minimum physical and chemical criteria related to current mining and production 

practices, including those for grade, quality, thickness, and depth. And reserves are 

that part <strong>of</strong> <strong>the</strong> reserve base which could be economically extracted or produced at 

<strong>the</strong> time <strong>of</strong> determination. Reserve base and reserves are subdivided in order <strong>of</strong> increasing 

confidence into demonstrated and inferred. The latter are estimates based 

on an assumed continuity beyond indicated resources, for which <strong>the</strong>re is geologic 

evidence. There may be no samples or measurements. Demonstrated reserves are 

<strong>the</strong> sum <strong>of</strong> measured and indicated. If <strong>the</strong> quantity is computed from dimensions 

revealed in outcrops, trenches, workings or drill holes; grade and or quality are computed 

from <strong>the</strong> results <strong>of</strong> detailed sampling; <strong>the</strong> sites <strong>of</strong> inspection are spaced closely 

and <strong>the</strong> geologic character is so well defined that size, shape, depth and <strong>mineral</strong> 

content <strong>of</strong> <strong>the</strong> resource are well established, <strong>the</strong>n we talk about measured resources. 

Indicated resources are those in which <strong>the</strong> grade and or quality are computed from 

information similar to that used for measured resources, but <strong>the</strong> sites for inspection, 

sampling, measurement are far<strong>the</strong>r apart or are o<strong>the</strong>rwise less adequately spaced. 

It is clear <strong>the</strong>n, that all <strong>the</strong> classifications listed above are related to economy, especially 

reserves. Figure 4.11 shows <strong>the</strong> <strong>mineral</strong> resources and reserves classification 

after McKelvey [214]. Increasing geological information expands <strong>the</strong> amount <strong>of</strong> reserves. 

So do commodity prices and development <strong>of</strong> efficient technologies, as lower 

grades become economically pr<strong>of</strong>itable. 

Hence, nei<strong>the</strong>r reserve base, nor reserves are good indicators for assessing <strong>the</strong> earth’s 

<strong>mineral</strong> <strong>capital</strong>. In fact, total world reserves <strong>of</strong> most <strong>mineral</strong> commodities are larger 

now than at any time in <strong>the</strong> past [141] due to wider geological information, more 

efficient technologies and price changes. The best approximation <strong>of</strong> numbers compiling 

<strong>the</strong> <strong>mineral</strong> <strong>capital</strong> would be using resources data. However, for being indeed <strong>the</strong> 

most comprehensive classification, <strong>the</strong> information is <strong>of</strong>ten scarce, inaccurate and 

incomplete as it can be seen in table 4.10. Estimates <strong>of</strong> resources are necessarily dynamic. 

For example, <strong>the</strong> realization that it was economic to mine copper porphyry 

deposits for <strong>the</strong>ir ore in <strong>the</strong> early part <strong>of</strong> <strong>the</strong> 20th century increased <strong>the</strong> world’s 

known copper reserves, and <strong>the</strong>refore resources, by several hundred per cent [121]. 

Too little is known about <strong>the</strong> earth’s crust, since exploration costs are extremely high. 

9 Identified resources: resources whose location, grade, quality and quantity are known or esti- 

mated from specific geologic evidence.


Figure 4.11. A classification <strong>of</strong> <strong>mineral</strong> resources and reserves [141]. 

Most <strong>of</strong> <strong>the</strong> deposits worked at present are close to <strong>the</strong> surface but <strong>the</strong> earth’s crust 

is on average 40 km thick and <strong>the</strong> deepest open-pit mine is less than 1 km deep, 

while <strong>the</strong> deepest underground mine goes down to 3,5 km to <strong>the</strong> surface and few 

exceed 2 km [29]. Thus only approximately <strong>the</strong> outer one-tenth <strong>of</strong> <strong>the</strong> continental 

crust is <strong>of</strong> present interest [78]. Besides, <strong>the</strong>re are many <strong>mineral</strong>s and metals such 

as bismuth, cesium, germanium, gallium, etc. that are just byproducts <strong>of</strong> o<strong>the</strong>r more 

demanded metals such as gold, copper, zinc, lead, etc. No exploration efforts will be 

undertaken for those specific <strong>mineral</strong>s until demand significantly increases. 

4.8.2 Mineral’s average ore grades 

For some time, many geologists have assumed that <strong>the</strong> amount <strong>of</strong> less common 

metals existing at different grades in <strong>the</strong> crust could be represented by lognormal 

or similar unimodal frequency distributions. This assumption was questioned by 

Skinner [316] for <strong>the</strong> metals that make up less than 0,1% <strong>of</strong> <strong>the</strong> earth’s crust. He 

suggested that for <strong>the</strong>se scarce metals <strong>the</strong> distribution might be bimodal and that 

<strong>the</strong> small mode at higher grades would represent metal concentrations <strong>of</strong> nonsilicate 

<strong>mineral</strong>s localized in <strong>mineral</strong> deposits [73] (see fig. 4.12). 

There are ma<strong>the</strong>matical procedures that correlate <strong>the</strong> tonnage <strong>of</strong> <strong>the</strong> ore with its 

mean grade. Much <strong>of</strong> <strong>the</strong> original work on this problem was carried out by Lasky 

[193]. He argued that a linear relation is obtained if <strong>the</strong> logarithm <strong>of</strong> <strong>the</strong> tonnage 

<strong>of</strong> ore with grades above a specified value is plotted against grade. Cargill et al. 

[48] suggested that a linear relation was obtained if <strong>the</strong> logarithm <strong>of</strong> <strong>the</strong> tonnage


Tonnage 

Tonnage 

a. Unimodal 

Grade 

b. Bimodal 

Grade 

Figure 4.12. Two possible relationships between ore grade and <strong>the</strong> metal, <strong>mineral</strong>, 

or energy content <strong>of</strong> <strong>the</strong> resource base [316]. 

was plotted against <strong>the</strong> logarithm <strong>of</strong> <strong>the</strong> grade. Later on, <strong>the</strong> fractal relationship, 

exhibited by a variety <strong>of</strong> natural processes, was proved to be better applicable to 

<strong>mineral</strong> deposits. Turcotte [358], showed that <strong>the</strong> tonnage <strong>of</strong> ore with a mean 

grade was proportional to <strong>the</strong> mean grade raised to a power for mercury, copper 

and uranium deposits in <strong>the</strong> US. This fractal relationship follows <strong>the</strong> expression <strong>of</strong> 

Eq. 4.3. 

¯x m 

= 

x c 

Mc 

M 

F 

3 

(4.3) 

Where ¯x m is <strong>the</strong> average concentration in <strong>the</strong> deposit; x c <strong>the</strong> concentration in <strong>the</strong> 

earth’s crust; M <strong>the</strong> tonnage <strong>of</strong> <strong>the</strong> deposit; M c <strong>the</strong> tonnage <strong>of</strong> <strong>the</strong> piece <strong>of</strong> land 

under consideration and F <strong>the</strong> fractal relationship to be determined. 

These <strong>the</strong>oretical methodologies have mainly <strong>the</strong> objective to determine <strong>the</strong> tonnage 

<strong>of</strong> ore with grades above a specified value, providing thus a basis for estimating 

ore reserves. But <strong>the</strong>y require as input for estimating F, information about already 

existing deposits with ore grades and tonnage, which is what we are searching for. 

A comprehensive study <strong>of</strong> average ore grades was undertaken by Cox and Singer 

[66]. In <strong>the</strong>ir study, a compendium <strong>of</strong> geologic models was presented, includ-


ing 85 descriptive models identifying attributes <strong>of</strong> <strong>the</strong> deposit type and 60 gradetonnage 

models giving estimated pre-mining tonnage’s grades from over 3900 wellcharacterized 

deposits all over <strong>the</strong> world. 

We have calculated with Eq. 4.4 <strong>the</strong> weighted average grades (¯x m) <strong>of</strong> <strong>the</strong> different 

<strong>mineral</strong> models <strong>of</strong> Cox and Singer [66], considering <strong>the</strong> average tonnage (M) and 

grade (x m) <strong>of</strong> <strong>the</strong> different deposits containing <strong>the</strong> particular <strong>mineral</strong> (see section 

A.2 in <strong>the</strong> appendix). The <strong>mineral</strong>s under consideration in Cox and Singer’s study 

were: rare earths, uranium oxide, zircon, niobium oxide, barite, alumina, phosphorous, 

potash, titanium, chromium, manganese, iron, cobalt, nickel, copper, molybdenum, 

wolfram, palladium, platinum, rhodium, iridium, ru<strong>the</strong>nium, osmium, silver, 

gold, zinc, mercury, tin, lead and antimony. Table 4.9 shows <strong>the</strong> final average grade 

obtained. 

¯x m = 

M 

0 x md M 

M 

0 

d M 

(4.4) 

Some <strong>of</strong> <strong>the</strong> values may appear to be quite low. Never<strong>the</strong>less, it must be pointed 

out that <strong>the</strong> figures are averages <strong>of</strong> <strong>mineral</strong> extraction <strong>of</strong> deposits. Most deposits 

extract many <strong>mineral</strong>s as byproducts, with a relatively low grade which would not 

be cost-effective if <strong>the</strong>y were to be extracted alone. 

Table 4.9: Summary statistics <strong>of</strong> grade-tonnage models. After [66] 

Deposit ¯x m Deposit ¯x m 

RE 2O 5 (%) 0,10 Cu (%) 0,58 

Monazite (%) 0,03 M o (%) 0,03 

U 3O 8 (%) 0,33 W O 3 (%) 0,72 

Zircon (% Z rO 2) 0,27 Pd (ppb) 158,51 

N b 2O 5 (%) 0,64 P t (ppb) 802,39 

Barite (%) 83,02 Rh (ppb) 12,92 

Al 2O 3(%) 45,97 I r (ppb) 20,62 

P (%) 0,11 Ru (ppb) 220,02 

P 2O 5 (%) 24,01 Os (ppb) 82,22 

Ilmenite (% T iO 2) 1,27 Ag (g/t) 4,27 

Rutile (% T iO 2) 0,21 Au (g/t) 0,22 

Leucocite (% T iO 2) 0,23 Zn (%) 4,06 

C r 2O 3 (%) 43,52 H g (%) 0,38 

M n (%) 31,49 Sn (%) 0,48 

Fe (%) 51,05 P b (%) 2,05 

Co (%) 0,11 S b (%) 3,78 

N i (%) 1,30


No average numbers have been found in <strong>the</strong> literature for <strong>the</strong> rest <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s 

not included in Cox and Singer [66]. Most <strong>of</strong> those <strong>mineral</strong>s are not mined as <strong>the</strong> 

principal product and are only commercially produced in <strong>the</strong> case <strong>the</strong>y are found 

as reasonable byproducts <strong>of</strong> o<strong>the</strong>r important <strong>mineral</strong>s. In those cases, values found 

in <strong>the</strong> literature (as in Carr [51]) <strong>of</strong> certain deposits have been taken as reference. 

We are aware that those figures cannot be considered as global <strong>mineral</strong> ore grades. 

Never<strong>the</strong>less, <strong>the</strong>y are good enough for giving an order <strong>of</strong> magnitude. 

The following assumptions have been made in order to estimate <strong>the</strong> average <strong>mineral</strong> 

ore grades not included in Cox and Singer: 

• Arsenic: Northparkes copper-gold ore grade for arsenic is 0,11% [323]; Mt 

Piper Gold Project in Victoria (Australia) contains 3% [252]. We will assume 

an average grade <strong>of</strong> 1%. 

• Beryllium: ore grades range from 0,2 to 3,5 % <strong>of</strong> beryllium oxide [260]. We 

will assume an average grade <strong>of</strong> 1%. 

• Bismuth: Bonfim W-Au-Bi-Te Skarn deposit (Brazil) contains 475 to > 2000 

ppm [327]. We assume <strong>the</strong> value <strong>of</strong> 2000 ppm. 

• Boron: According to <strong>the</strong> USGS [363], average grades <strong>of</strong> boron oxide mined 

all over <strong>the</strong> world range from 11 to 39%. We will assume an average grade <strong>of</strong> 

20%. 

• Bromine: an important source <strong>of</strong> bromine is <strong>the</strong> Dead Sea. Its bromine concentration 

is around 5000 ppm [406]. 

• Cadmium: cadmium is usually found in zinc ores. According to <strong>the</strong> Mineral 

Information Institute 10 , zinc ores around <strong>the</strong> world average about 1/400 th as 

much cadmium as zinc. Hence, if Zn average grade is 4,06%, Cd grade is 

estimated to be around 100 ppm. 

• Cesium: it is usually found in <strong>the</strong> <strong>mineral</strong> pollucite. The world largest pollucite 

deposit is in a zoned pegmatite at Bernic Lake, Canada, grading 23,3% cesium 

oxide 11 . 

• Feldspar: <strong>the</strong> major commercial feldspar deposits occur in pegmatites, granitic 

rocks, granitic rock types known as alaskite and aplite and certain river, dune 

and beach sands. The feldspar content <strong>of</strong> <strong>the</strong>se deposits range from 15 to up 

to 75% <strong>of</strong> <strong>the</strong> different feldspar <strong>mineral</strong>s [180]. We will assume an average <strong>of</strong> 

45%. 

10 Mineral Information Institute: http://www.mii.org/Minerals/photocad.html 

11 Source: Houston Lake Mining Inc. http://www.houstonlakemining.com


• Fluorite (fluorspar): The compilation <strong>of</strong> Fulton and Montgomery [99], gives 

averages for <strong>the</strong> different types <strong>of</strong> deposits where fluorite is found: fissure 

veins (from 25 to 80%), statiform deposits (from 15% upward), stockworks 

(about 14%), gangue <strong>mineral</strong> (from 10 to 20%), lake sediments (50 to 60% 

<strong>of</strong> <strong>the</strong> clayey parts and 15% <strong>of</strong> <strong>the</strong> sandy parts). Specific examples <strong>of</strong> fluorite 

deposits are for example in <strong>the</strong> southwestern United States, deposits <strong>of</strong>ten 

assay less than 10% fluorite [131] and in <strong>the</strong> Pöhrenk deposit <strong>of</strong> Turkey ore 

grades range from a few to more than 40% CaF 2 [110]. We will assume an 

average fluorite grade <strong>of</strong> 25%. 

• Gallium: <strong>the</strong> most important ore in which gallium is found as a trace element 

is bauxite in an average <strong>of</strong> 50 ppm, according to <strong>the</strong> Mineral Information Institute. 

Assuming that <strong>the</strong> average grade <strong>of</strong> alumina alumina in laterite bauxite 

is 45,97% [66], gallium grade is estimated here as about 23 ppm. 

• Germanium: grades <strong>of</strong> a few tens to several hundred ppm Ge are known in 

sulphide deposits [142], [220]. We will assume an average grade <strong>of</strong> 50 ppm. 

• Graphite: economic deposits <strong>of</strong> graphite include five main geological types: 

flake graphite disseminated in metamorphosed (with an average deposit <strong>of</strong> 10 

to 12%), silica-rich sedimentary rocks (1-10%), flake graphite disseminated in 

marble amorphous deposits formed by metamorphism <strong>of</strong> coal or carbon-rich 

sediments (50-95%), veins filling fractures (85-98%) and contact metasomatic 

or hydro<strong>the</strong>rmal deposits in marble (irregular concentrated). We will assume 

an average grade <strong>of</strong> 50%. 

• Gypsum: it is usually found in very high grades, ranging from 45 to 95% 

[174]. We will assume an average grade <strong>of</strong> 80%. 

• Hafnium: it is always present in 1,5 to 3,0 % in zirconium compounds [315]. 

Assuming an average <strong>of</strong> zinc <strong>of</strong> 0,27% [66], <strong>the</strong> hafnium average grade ranges 

from 40,5 to 81 ppm. We will assume an average <strong>of</strong> 60 ppm. 

• Helium: it is recovered usually as a byproduct in natural gas production. Some 

natural gas deposits have as much as 7% helium, found in Texas, Russia, 

Poland, Algeria, China and Canada 12 . 

• Indium: <strong>the</strong> average value in ore deposits varies drastically up to percent levels. 

In <strong>the</strong> Kuroko deposits <strong>of</strong> Japan, <strong>the</strong> In-content <strong>of</strong> Cu-concentrates had 

been reported at about 10 ppm and in Zn concentrates is 100 ppm. Some 

skarn deposits and Pb-Zn veins have ranges <strong>of</strong> In concentration similar to 

<strong>the</strong>se. Atypical maximum concentrations <strong>of</strong> In are up to 3000 ppm. We will 

assume an average content <strong>of</strong> 140 g/t which is reported for one <strong>of</strong> <strong>the</strong> most 

well known In deposits in Japan, <strong>the</strong> Toyoha mine in Hokkaido [236]. 

12 Source: Mineral Information Institute (http://www.mii.org/Minerals/photohelium.html


• Iodine: iodine is primarily retrieved from underground brines. Dried seaweeds, 

particularly those <strong>of</strong> <strong>the</strong> Liminaria family, contain as much as 0,45% 

iodine. Japan is <strong>the</strong> largest iodine producing country. The maximum iodine 

content <strong>of</strong> <strong>the</strong> brines is about 160 ppm [171]. 

• Lithium: some lithium is recovered from <strong>the</strong> <strong>mineral</strong> spodumene with an Li 

grade <strong>of</strong> 1 to 4%. But most lithium is recovered from brine. Lithium grades in 

brine range from 0,015 to 0,06% [260]. We will assume an average grade <strong>of</strong> 

0,04%. 

• Magnesium compounds: one <strong>of</strong> <strong>the</strong> most important magnesium <strong>mineral</strong>s is 

magnesite, M gCO 3, which represents <strong>the</strong> world’s largest source <strong>of</strong> magnesia, 

M gO. The next most used sources for magnesia are magnesia-rich brines and 

seawater. Dolomite is ano<strong>the</strong>r important source for industrial magnesium. The 

crude ore <strong>of</strong> magnesite contains typically around 45% <strong>of</strong> magnesia. 

• Potash: potash oxide grades in Canada, <strong>the</strong> most important producer in <strong>the</strong> 

world, range from 14 to 32% [407]. In Saskatchewan, ore grades range between 

23 and 27% 13 . We assume an average grade <strong>of</strong> K 2O <strong>of</strong> 25%. 

• Rhenium is a very rare element produced mainly as a byproduct in <strong>the</strong> processing 

<strong>of</strong> porphyry copper-molybdenum ores. The Re contents in <strong>the</strong> majority <strong>of</strong> 

<strong>the</strong> concentrates range from 6 to 460 ppm [27]. We assume an average <strong>of</strong> 233 

ppm. 

• Selenium: it is widely distributed within <strong>the</strong> earth’s crust and does not occur 

in concentrations high enough to justify solely for <strong>the</strong>ir content. It is recovered 

as byproduct <strong>of</strong> nonferrous metal mining, mostly from <strong>the</strong> anode slimes 

associated with electrolytic refining copper. The economic concentration 14 is 

2,5% [34]. 

• Strontium: celestine and strontianite are <strong>the</strong> only Sr-containing <strong>mineral</strong>s having 

sufficient quantities to make its recoveral practical. From <strong>the</strong>se, only celestine 

has been found to occur in deposits <strong>of</strong> sufficient size. Celestine is mined 

in many countries all over <strong>the</strong> world. Reported average ore grades <strong>of</strong> SrSO 4 

range from 54% in Cyprus to more than 90% in Iran [244]. We will assume 

an average grade <strong>of</strong> 70% <strong>of</strong> celestine or 34% <strong>of</strong> Sr content. 

• Tantalum: it is recovered from tantalite and columbite ores. The average ore 

grades are similar to those <strong>of</strong> niobium, since it is recovered from <strong>the</strong> same ores. 

Therefore, we assume that <strong>the</strong> average grade <strong>of</strong> tantalum oxide is 0,64%, <strong>the</strong> 

same as <strong>the</strong> grade <strong>of</strong> niobium oxide recorded by Cox and Singer [66]. 

13 Source: <strong>the</strong> Canadian Encyclopedia (http://<strong>the</strong>canadianencyclopedia.com) 

14 Economic concentration: concentration at which a <strong>mineral</strong> is economically producible


• Tellurium: it is widely distributed within <strong>the</strong> earth’s crust and does not occur 

in concentrations high enough to justify solely for <strong>the</strong>ir content. It is recovered 

as byproduct <strong>of</strong> nonferrous metal mining, mostly from <strong>the</strong> anode slimes 

associated with electrolytic refining copper. The economic concentration is 1 

ppm [34]. 

• Thorium: it has been mined at an average grade <strong>of</strong> nearly 3% <strong>of</strong> ThO 2 in <strong>the</strong> 

Bokan Mountain in Alaska [356]. 

• Vanadium: average ore grades for vanadium range from 0,3 to 5% [260]. We 

will assume an average <strong>of</strong> 2%. 

4.8.3 Mineral’s abundance 

Table 4.10 shows world reserves, reserve base, and resources <strong>of</strong> <strong>the</strong> main naturaloccurring 

non-fuel <strong>mineral</strong>s <strong>of</strong> economic importance according to <strong>the</strong> USGS [362]. 

It shows also <strong>the</strong> average ore grades obtained in <strong>the</strong> previous section. The most 

abundant ores in <strong>the</strong> crust are those <strong>of</strong> iron, followed by phosphate rock, potash, 

manganese and aluminium. On <strong>the</strong> contrary, <strong>the</strong> ores <strong>of</strong> <strong>the</strong> platinum group metals, 

thallium, tellurium and rhenium are <strong>the</strong> scarcest in <strong>the</strong> world. 

Table 4.10: Mineral world reserves, reserve base and world resources in 2006 

Production Reserves Reserve base World 

sourcesre- 

Ore grades 

Resource tons tons tons tons % 

Aluminium 3,37E+07 4,55E+09 5,82E+09 1,36E+10 45,97 

Antimony 1,34E+05 2,10E+06 4,30E+06 N.A. 3,78 

Arsenic 5,98E+04 1,20E+06 1,20E+06 > 11000000 1,00 

Barite 7,96E+06 1,90E+08 8,80E+08 2,00E+09 83,02 

Beryllium 1,79E+02 N.A. N.A. > 8E+04 1,00 

Bismuth 5,70E+03 3,20E+05 6,80E+05 N.A. 0,50 

Boron 

B2O3) (as 4,26E+06 1,70E+08 4,10E+08 N.A. 20,00 

Bromine 5,45E+05 Large Large Unlimited 0,50 

(dead sea 

contains 1 

Cadmium 1,93E+04 4,90E+05 1,20E+06 

billion tons <strong>of</strong> 

bromine) 

6,00E+06 100 ppm 

Cesium N.A. 7,00E+04 1,10E+05 N.A. 23,30 

Chromium 5,85E+06 N.A. N.A. 3,80E+09 43,52 

Cobalt 6,75E+04 7,00E+06 1,30E+07 1,50E+07 0,11 

Copper 1,51E+07 4,90E+08 9,40E+08 > 3,00E+09 0,58 

Feldspar 1,54E+07 Large Large Large 45,00 

Fluorspar 5,33E+06 2,40E+08 4,80E+08 5,00E+08 25,00 

Gallium 7,30E+01 N.A. N.A. 1,00E+06 23 ppm 

Germanium 9,00E+01 N.A. N.A. N.A. 50 ppm 




– continued from previous page. 

Production Reserves Reserve base World re- Ore grades 

(year 2006) 

sources 


Gold 2,46E+03 4,20E+04 9,00E+04 N.A. 0,22 g/t 

Graphite 1,03E+06 8,60E+07 2,10E+08 > 8,00E+08 50,00 

Gypsum 1,25E+08 Large Large Large 80,00 

Hafnium 

H f O2) (as N.A. 6,10E+05 1,10E+06 N.A. 60 ppm 

Helium 2,81E+04 N.A. 6,47E+06 N.A. 7,00 

Indium 5,81E+02 1,10E+04 1,60E+04 N.A. 140 g/t 

Iodine 2,50E+04 1,50E+07 2,70E+07 3,40E+07 160 ppm 

Iridium N.A. N.A. N.A. N.A. 20,6 ppb 

Iron ore 8,66E+08 7,30E+10 1,60E+11 2,30E+11 51,05 

Lead 3,47E+06 7,90E+07 1,70E+08 > 1,50E+09 2,05 

Lithium 3,33E+05 4,10E+06 1,10E+07 >1,3E+07 0,04 (Lithium 

Magnesium 6,89E+05 N.A. N.A. Large to unlimited 

brines) 

45 as MgO 

Manganese 1,19E+07 4,60E+08 5,20E+09 Large 31,49 

Mercury 1,48E+03 4,60E+04 2,40E+05 6,00E+05 0,38 

Molybdenum 1,84E+05 8,60E+06 1,90E+07 1,30E+07 0,03 

Nickel 1,58E+06 6,70E+07 1,50E+08 N.A. 1,30 

Niobium 4,45E+04 2,70E+06 3,00E+06 N.A. 0,64 

Osmium N.A. N.A. N.A. N.A. 82,2 ppb 

Palladium 2,24E+02 N.A. N.A. N.A. 158,5 ppb 

Phosphate 

rock 

1,42E+08 1,80E+10 5,00E+10 N.A. 0,11 

Platinum 5,18E+02 7,10E+04 8,00E+04 > 1,00E+05 See Pt, Pd, Rh, 

group metals 

Ru, Ir and Os 

Platinum 2,21E+02 N.A. N.A. N.A. 802,4 ppb 

Potash 2,91E+07 8,30E+09 1,80E+10 2,50E+11 25,00 

Rare Earths 1,23E+05 8,80E+07 1,50E+08 Undiscovered 

resources 

0,10 

are thought 

to be very 

large relative 

to expected 

Rhenium 4,72E+01 2,50E+03 1,00E+04 

demand 

1,10E+04 223 ppm 

Ru<strong>the</strong>nium N.A. N.A. N.A. N.A. 220,0 ppb 

Selenium 1,54E+03 8,20E+04 1,70E+05 N.A. 2,50 

Silicon 3,87E+06 N.A. N.A. N.A. N.A. 

Silver 2,02E+04 2,70E+05 5,70E+05 Large 4,3 g/t 

Strontium 5,85E+05 6,80E+06 1,20E+07 > 1,00E+09 34,00 

Tantalum 1,39E+03 1,30E+05 1,80E+05 N.A. 0,65 

Tellurium 1,32E+02 2,10E+04 4,70E+04 N.A. 1 ppm 

Thallium 1,00E+01 3,80E+02 6,50E+02 6,47E+05 N.A. 

Thorium N.A. 1,05E+06 1,23E+06 N.A. 3,00 

Tin 3,02E+05 6,10E+06 1,10E+07 N.A. 0,48 





Production Reserves Reserve base World re- Ore grades 

(year 2006) 

sources 


Titanium 

T iO2) (as 5,80E+06 7,30E+08 1,50E+09 N.A. 0,69 

Vanadium 5,63E+04 1,30E+07 3,80E+07 > 6,30E+07 2,00 

Wolfram 9,08E+04 2,90E+06 6,30E+06 N.A. 0,72 

Yttrium 

Y2O3) (as 8,90E+03 5,40E+05 6,10E+05 N.A. N.A. 

Zinc 1,00E+07 1,80E+08 4,80E+08 1,90E+09 4,06 

Zirconium 

Z rO2) (as 1,18E+06 3,80E+07 7,20E+07 N.A. 0,27 



This chapter closes <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> earth’s components (Part I <strong>of</strong> this report), by 

undertaking a review <strong>of</strong> <strong>the</strong> different natural resources, useful to man. 

With <strong>the</strong> most updated information sources, <strong>the</strong> available energy, potential energy 

use and current energy consumption <strong>of</strong> all known renewable and non-renewable 

energy resources has been obtained. That is for geo<strong>the</strong>rmal, nuclear, tidal, solar, 

wind and ocean power, as well as for biomass, coal, natural gas, oil and unconventional 

fuels. 

In addition to energy resources, non-fuel <strong>mineral</strong>s have been analyzed. As opposed 

to fossil fuels, <strong>the</strong> abundance <strong>of</strong> <strong>mineral</strong>s is not important if <strong>the</strong>se are dispersed 

throughout <strong>the</strong> crust. Hence, besides <strong>of</strong> <strong>the</strong> available resources registered, which 

are very uncertain, average ore grades for <strong>the</strong> main <strong>mineral</strong> resources have been 

provided. Both figures (abundance and concentration), will allow us to calculate <strong>the</strong> 

exergy <strong>of</strong> non-fuel <strong>mineral</strong>s. 

With <strong>the</strong> next chapter, begins Part II <strong>of</strong> this report, whose aim is to assess <strong>the</strong> exergy 

<strong>of</strong> <strong>the</strong> earth and its resources. Chapter 5, provides <strong>the</strong> <strong>the</strong>rmodynamic tools required 

for calculating <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> earth, including <strong>the</strong> <strong>mineral</strong> resources (<strong>of</strong> fuel and 

non-fuel nature) just reviewed. Consequently, all resources will be able to be evaluated 

with a single unit <strong>of</strong> measure, allowing us to compare <strong>the</strong>m and to analyze 

<strong>the</strong>ir scarcity.

Part II 

The <strong>the</strong>rmodynamic properties <strong>of</strong> 

<strong>the</strong> earth and its exergy <strong>evolution</strong> 

139

Chapter 5 

Thermodynamic models for <strong>the</strong> 

exergy assessment <strong>of</strong> natural 

resources 


This aim <strong>of</strong> this chapter is to provide <strong>the</strong> <strong>the</strong>rmodynamic tools for <strong>the</strong> exergy assessment 

<strong>of</strong> natural resources and particularly for <strong>mineral</strong>s. 

The exergy <strong>of</strong> any substance or process is always fixed by <strong>the</strong> so called reference 

environment (R.E.). Therefore, for calculating <strong>the</strong> exergy <strong>of</strong> any natural resource, 

an appropriate R.E. should be defined. In section 5.2, <strong>the</strong> different reference environments 

proposed in <strong>the</strong> literature are reviewed and <strong>the</strong> best suitable R.E. so far, 

for assessing <strong>the</strong> natural <strong>capital</strong> is chosen. 

Once <strong>the</strong> R.E. is fixed, <strong>the</strong> exergy <strong>of</strong> <strong>mineral</strong> resources can be calculated with <strong>the</strong> 

help <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic models provided in section 5.3. For that purpose, <strong>the</strong> 

energy involved in <strong>the</strong> process <strong>of</strong> formation <strong>of</strong> a <strong>mineral</strong> deposit is described. Next, 

<strong>the</strong> formulas for obtaining <strong>the</strong> exergy and exergy cost <strong>of</strong> <strong>mineral</strong> resources (including 

fossil fuels) are provided. And finally, 12 models for estimating <strong>the</strong> Gibbs free energy 

values <strong>of</strong> <strong>mineral</strong> resources, required for <strong>the</strong> calculations, is shown. 

5.2 The reference environment 

The R.E. can be assumed as being a <strong>the</strong>rmodynamically dead planet where all materials 

have reacted, dispersed and mixed. This R.E. must be determined by <strong>the</strong> 

natural environment and is fixed by its chemical composition. In past years, <strong>the</strong>re 

141

142 THERMODYNAMIC MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES 

have been many contributions to <strong>the</strong> determination <strong>of</strong> <strong>the</strong> best suitable R.E. The divergences 

between standard chemical exergies <strong>of</strong> <strong>the</strong> elements obtained from different 

R.E. conceptions can be very significant. Each R.E. definition generate different 

exergies, what implies that <strong>the</strong> determination <strong>of</strong> <strong>the</strong> natural <strong>capital</strong>’s exergy is necessarily 

linked to <strong>the</strong> definition and <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> R.E. In order 

to correctly evaluate <strong>the</strong> natural resources, it is necessary to know how does <strong>the</strong> modification 

<strong>of</strong> reference substances or physical variables <strong>of</strong> <strong>the</strong> R.E. change <strong>the</strong> exergy 

calculation <strong>of</strong> a system. Most <strong>of</strong> <strong>the</strong> contributions concerned with that topic deal 

with <strong>the</strong> exergy variation <strong>of</strong> processes according to physical parameters <strong>of</strong> <strong>the</strong> environment 

such as pressure or temperature (see for instance Brodianski et al. [304] 

[39]). O<strong>the</strong>r authors have studied <strong>the</strong> influence <strong>of</strong> environment CO 2 or temperature 

on <strong>the</strong> exergy <strong>of</strong> fossil fuels (Valero and Arauzo [366]) and hydrocarbons (Rivero 

et al. [282]). Never<strong>the</strong>less, it is crucial to analyze <strong>the</strong> influence <strong>of</strong> <strong>the</strong> reference 

environment’s chemical composition if <strong>the</strong> point is to evaluate <strong>the</strong> natural <strong>capital</strong>’s 

exergy. 

Next, <strong>the</strong> different models <strong>of</strong> reference environments are reviewed, and <strong>the</strong> best 

suitable R.E. is selected and improved for <strong>the</strong> evaluation <strong>of</strong> natural resources. 

5.2.1 Selection <strong>of</strong> <strong>the</strong> best suitable reference environment 

The different R.E. conceptions can be divided into two main groups: 

• Partial reference environments 

• Comprehensive reference environments 

5.2.1.1 Partial reference environments 

Some authors such as Bosjankovich [33], Gaggioli and Petit [101] and Sussman 

[332] established that <strong>the</strong> R.E. should be defined according to <strong>the</strong> specific characteristics 

<strong>of</strong> <strong>the</strong> analyzed process. This criterion is based on that being <strong>the</strong> exergy a 

parameter that quantifies <strong>the</strong> <strong>the</strong>oretical <strong>evolution</strong> <strong>of</strong> a system with respect to <strong>the</strong> 

R.E., some <strong>of</strong> <strong>the</strong> possible <strong>evolution</strong>s <strong>of</strong> <strong>the</strong> system, cannot be attained because <strong>of</strong> 

process limitations. Hence, only possibilities <strong>of</strong> <strong>evolution</strong> that <strong>the</strong> system can practically 

attain are analyzed. The conception <strong>of</strong> <strong>the</strong>se R.E. are very far removed from 

<strong>the</strong> idea <strong>of</strong> degraded earth. For computing exergy changes <strong>of</strong> variable composition 

or chemically reactive steady flow processes, a Comprehensive reference environment 

is generally unnecessary. 

However, this is not <strong>the</strong> case when <strong>the</strong> point is to evaluate <strong>the</strong> natural <strong>capital</strong> on 

earth. In that case, <strong>the</strong>re are no process limitations and <strong>the</strong> resources can follow an 

<strong>evolution</strong> process towards <strong>the</strong> dead state. Thus a comprehensive R.E. is required.

The reference environment 143 

5.2.1.2 Comprehensive reference environments 

Within <strong>the</strong> known Comprehensive reference environments, all authors agree in dividing 

<strong>the</strong> Reference Substances (R.S.) that compose <strong>the</strong> R.E. into gaseous components 

<strong>of</strong> <strong>the</strong> atmospheric air, solid components <strong>of</strong> <strong>the</strong> external layer <strong>of</strong> <strong>the</strong> earth’s 

crust, and molecular components <strong>of</strong> seawater. Never<strong>the</strong>less, <strong>the</strong>re are also criterion 

differences between <strong>the</strong> different authors. They can be classified into environments 

based on: 

• Szargut’s criterion 

• Chemical equilibrium 

• Abundance 

Szargut’s R.E. could be considered as an environment based on partial abundance, 

even though Szargut itself regards his R.E. as based only on abundance. We will 

show next, that his R.E. is not only based on abundance, as opposed to <strong>the</strong> criterion 

taken by Ranz [276]. 

According to Szargut’s criterion, among a group <strong>of</strong> reasonable abundant substances, 

<strong>the</strong> most stable will be chosen if <strong>the</strong>y also fulfill <strong>the</strong> “earth similarity criterion”. That 

is, if <strong>the</strong> stability <strong>of</strong> <strong>the</strong> possible different reference substances for a specific element 

(measured in terms <strong>of</strong> <strong>the</strong> formation Gibbs energy) is within a certain threshold, <strong>the</strong>n 

<strong>the</strong> most abundant R.S. will be chosen. If <strong>the</strong> differences exceed this threshold, <strong>the</strong> 

most stable substance will be taken as R.S. as long as <strong>the</strong> “earth similarity criterion” 

is not contradicted. The stability threshold has not a fix value and depends on each 

element considered, since it is subject to geological uncertainties. Thus for example 

in <strong>the</strong> case <strong>of</strong> S b, <strong>the</strong> substance S b 2S 3 is more abundant than S b 2O 5, never<strong>the</strong>less, 

according to Szargut’s criterion, S b 2O 5, which is much more stable, will be taken 

as reference substance. This happens also with <strong>the</strong> substances listed in table 5.1. 

Never<strong>the</strong>less nitrates such as Ca(NO 3) 2, N aNO 3, KNO 3 are discarded, because being 

most stable but not abundant in <strong>the</strong> natural environment, <strong>the</strong>y would break <strong>the</strong> 

similarity criterion if <strong>the</strong>y are taken as R.S. Therefore, Szargut’s [333] dead environment 

is similar to <strong>the</strong> real physical environment and should represent <strong>the</strong> products 

<strong>of</strong> an interaction between <strong>the</strong> components <strong>of</strong> <strong>the</strong> natural environment and <strong>the</strong> waste 

products <strong>of</strong> <strong>the</strong> processes. The most probable products <strong>of</strong> this interaction should 

be chosen as reference species. Section 5.2.2 explains purposively <strong>the</strong> well known 

Szargut’s methodology for obtaining <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> elements from <strong>the</strong> 

R.E.


Table 5.1: <strong>Exergy</strong> difference <strong>of</strong> selected elements considering ei<strong>the</strong>r as reference 

species <strong>the</strong> most abundant or <strong>the</strong> most stable substances in <strong>the</strong> R.E. 

[367] 

Element Most abundant 

species 

Most stable 

species 

Sb Sb2S 3 S b2O5 1235,58 

As 

S 

FeAsS 

FeS2 As2O5 SO 

1201,32 

−2 

4 

963,63 

Bi Bi BiO + 228,88 

Cd CdS CdCl 2 745,75 

Ce 

Zn 

CePO 4 

ZnS 

CeO2 Zn 

258,33 

+2 717,22 

Co 

Cu 

Co3S 4 

CuFeS 2 

Co3O4 Cu 

967,70 

+2 1423,18 

M o M oS2 M oO−2 Os 

Ag 

Os 

Ag2S 4 

OsO4 AgCl 

1675,9 

306,81 

− 

P t P t 

2 

P tO2 330,65 

84,59 

P b P bS P bCl 2 710,34 

Re ReS2 Re2O7 1556,65 

Ru Ru RuO2 254,82 

U UO2 UO3.H 2O 127,49 

<strong>Exergy</strong> difference 

between both 

R.E. (kJ/mole) 

Ano<strong>the</strong>r group <strong>of</strong> authors derive <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> elements from <strong>the</strong> hypo<strong>the</strong>tical 

chemical equilibrium that could be attained on earth in a very distant future. 

Ahrendts [3], [4] and Diederichsen [74] for example, stated that if <strong>the</strong> amount <strong>of</strong> 

different elements in <strong>the</strong> reference system is known and <strong>the</strong> temperature <strong>of</strong> <strong>the</strong> 

system is fixed, <strong>the</strong> quantity <strong>of</strong> each chemical compound and <strong>the</strong> value <strong>of</strong> each chemical 

potential is uniquely determined by <strong>the</strong> condition <strong>of</strong> chemical equilibrium. This 

criterion is <strong>the</strong>rmodynamically consistent and thus does not generate any negative 

exergies as it happens with <strong>the</strong> o<strong>the</strong>r two comprehensive R.E. classifications. 

Ahrendt’s R.E. relied on <strong>the</strong> model <strong>of</strong> Ronov and Yaroshevsky [287] to ascertain 15 

elements, making up more than 99% <strong>of</strong> <strong>the</strong> earth’s crust: H, C, N, O, N a, M g, 

Al, Si, P, S, Cl, Ar, K, Ca, T i, M n and Fe. These elements were allowed to react 

until chemical equilibrium was attained. The composition <strong>of</strong> this environment in 

chemical equilibrium, had as a variable parameter <strong>the</strong> thickness <strong>of</strong> <strong>the</strong> crust layer 

(between δ = 1 m and δ = 1000 m). The resulting equilibrium reference system 

based on an earth’s crust <strong>of</strong> δ = 1000 m, showed that <strong>the</strong> exergy <strong>of</strong> oxygen was even 

smaller than that <strong>of</strong> fuels. He found that <strong>the</strong> exergy <strong>of</strong> oxygen increased, when <strong>the</strong> 

considered thickness <strong>of</strong> <strong>the</strong> crust was smaller. In order to overcome this paradox, 

Ahrendts considered a crust layer on only 1 m. 

Szargut criticizes Ahrendt’s model, stressing that it is not possible to attain an equilibrium 

with <strong>the</strong> system being not in <strong>the</strong> state <strong>of</strong> internal equilibrium (and <strong>the</strong> natural


environment is far removed from such equilibrium). Valero, Ranz and Botero [371], 

explained already why Ahrendt’s R.E. was not suitable to evaluate <strong>the</strong> natural <strong>capital</strong> 

on earth. Most <strong>of</strong> <strong>the</strong> metals cannot be evaluated because <strong>the</strong>y form part <strong>of</strong> <strong>the</strong> 1% 

<strong>of</strong> <strong>the</strong> earth’s crust neglected by Ahrendts. His obtained R.E. is very different from 

<strong>the</strong> real environment and it is very unlikely an eventual <strong>evolution</strong> towards it, since 

some processes are kinetically, biologically and/or geologically blocked. 

Diederichsen updated and extended Ahrendt’s model with new geochemical data 

and obtained among o<strong>the</strong>rs, a R.E. including 75 elements. Fur<strong>the</strong>rmore, he allowed 

<strong>the</strong> composition <strong>of</strong> this environment to change with two variable parameters: thickness 

<strong>of</strong> <strong>the</strong> earth’s crust and ocean’s depth. The final chosen environment should 

fulfill <strong>the</strong> “earth similarity criterion”. The similarity with <strong>the</strong> earth was measured 

with <strong>the</strong> equilibrium pressure, <strong>the</strong> oxygen and nitrogen content in <strong>the</strong> gas-phase 

and <strong>the</strong> equilibrium salt content in <strong>the</strong> oceans. 

Even though Diederichsen [74] added more elements than Ahrendts [4] and included 

a new variable parameter, <strong>the</strong> composition <strong>of</strong> his new reference environment 

was still too different from <strong>the</strong> real earth. According to <strong>the</strong> “earth similarity criterion”, 

<strong>the</strong> R.E. that best fits with <strong>the</strong> earth’s environment takes a crust thickness <strong>of</strong> 

only 0,1 m and an ocean’s depth <strong>of</strong> 100 m. Greater values would move fur<strong>the</strong>r away 

<strong>the</strong> R.E. from <strong>the</strong> real earth, and would have among o<strong>the</strong>r features, reduced pressures 

and oxygen contents. As it happened with Ahrendt’s model before, Diederichsen 

obtained high exergy values for oxygen. This happens because nearly all <strong>the</strong> 

oxygen <strong>of</strong> <strong>the</strong> air is consumed basically by <strong>the</strong> formation <strong>of</strong> nitrates and only in <strong>the</strong> 

limit, for a crustal thickness <strong>of</strong> 0 m, <strong>the</strong> mean earth pressure matches with that <strong>of</strong> <strong>the</strong> 

model. It seems <strong>the</strong>refore that achieving a R.E. in chemical equilibrium is in disagreement 

with <strong>the</strong> “earth similarity criterion” and is not appropriate for <strong>the</strong> evaluation <strong>of</strong> 

natural <strong>capital</strong> on earth. This idea fully fits with Lovelock’s Gaia hypo<strong>the</strong>sis [199]: 

“<strong>the</strong> earth is a life being and fights against <strong>the</strong>rmodynamic stable equilibrium.” 

Van Gool’s methodology [379] assures as well a R.E. in which all <strong>the</strong> substances 

have positive exergy values. However as he discards <strong>the</strong> geological information <strong>of</strong> 

<strong>mineral</strong> abundance, his R.E. does not guarantee a good model for a dissipated earth, 

which is critical in our research. 

Kameyama et al. [177] proposed a reference environment with <strong>the</strong> criterion <strong>of</strong> chemical 

stability. The references are <strong>the</strong> most stable compounds among those with 

<strong>the</strong>rmo-chemical data and can be integrated in <strong>the</strong> solid, liquid and gaseous environments. 

As Szargut stated in [336], some <strong>of</strong> <strong>the</strong> most stable compounds selected 

by Kameyama et al. like nitrates, compounds between rare elements (e.g. P tBr 2) or 

compounds with F r as <strong>the</strong> reference species for <strong>the</strong> elements F, Cl, Br or I should 

not be recommended, because <strong>the</strong> probability <strong>of</strong> <strong>the</strong>ir formation in <strong>the</strong> environment 

is very small. Therefore, Kameyama et al. R.E. is not very suitable ei<strong>the</strong>r to evaluate 

<strong>the</strong> scarcity <strong>of</strong> <strong>the</strong> natural <strong>capital</strong>.


5.2.1.3 Abundance criterion 

According to Ranz [276], lots <strong>of</strong> <strong>mineral</strong>s are compounds with <strong>the</strong> most common 

components <strong>of</strong> <strong>the</strong> upper continental crust, but are not very stable and do not represent 

<strong>the</strong> products <strong>of</strong> an interaction between <strong>the</strong> components <strong>of</strong> <strong>the</strong> natural environment 

and <strong>the</strong> waste products <strong>of</strong> industrial processes. Hence, Ranz [276] proposes 

a new R.E. very close to <strong>the</strong> real environment based on abundance and following 

Szargut’s methodology. The solid phase <strong>of</strong> this new R.E. reproduces accurately <strong>the</strong> 

earth’s upper continental crust, since <strong>the</strong> solid reference species that make up this 

environment are <strong>the</strong> same as <strong>the</strong> most abundant types found in <strong>the</strong> earth’s upper 

continental crust. A problem with Ranz’s proposed R.E. is that if we assign zero 

exergy to <strong>the</strong> most abundant substances, we are decreasing arbitrarily <strong>the</strong> natural 

<strong>capital</strong>, because many abundant <strong>mineral</strong>s like sulfides naturally evolute to <strong>the</strong> most 

stable oxides. Therefore, as proposed by Valero, Ranz and Botero [371], we must return 

to Szargut’s criterion <strong>of</strong> using <strong>the</strong> most stable substance, within <strong>the</strong> limits fixed 

by <strong>the</strong> “earth similarity criterion”. 

Hence, our first goal is to obtain a reference state for evaluating <strong>the</strong> natural resources 

on earth, based on Szargut’s criterion and methodology and using <strong>the</strong> more 

precise data used by Ranz and o<strong>the</strong>r authors such as Rivero [281], as well as new 

geochemical updates. 

In <strong>the</strong> next section, Szargut’s methodology for obtaining <strong>the</strong> standard chemical 

exergy <strong>of</strong> <strong>the</strong> chemical elements is explained and <strong>the</strong> variables used are discussed. 

5.2.2 Calculation methodology: standard chemical exergy <strong>of</strong> <strong>the</strong> 

chemical elements 

5.2.2.1 Standard chemical exergy <strong>of</strong> chemical compounds 

The chemical exergy expresses <strong>the</strong> exergy <strong>of</strong> a substance at ambient temperature 

and pressure. It is defined as <strong>the</strong> maximum work which can be obtained when 

<strong>the</strong> considered substance is brought in a reversible way to <strong>the</strong> state <strong>of</strong> reference 

substances present in <strong>the</strong> environment, using <strong>the</strong> environment as a source <strong>of</strong> heat 

and <strong>of</strong> reference substances necessary for <strong>the</strong> realization <strong>of</strong> <strong>the</strong> described process. 

Standard chemical exergy results from a conventional assumption <strong>of</strong> a standard ambient 

temperature and pressure and standard concentration <strong>of</strong> reference substances 

in <strong>the</strong> natural environment. 

The chemical exergy <strong>of</strong> any chemical compound (b ch i), can be calculated by means 

<strong>of</strong> <strong>the</strong> exergy balance <strong>of</strong> a reversible formation reaction;. 

 

bch i = ∆G f i + r j,i bch j 

j 

(5.1)


where: 

∆G f i 

r j,i 

bch j 

Gibbs free energy <strong>of</strong> substance i 

amount <strong>of</strong> mole <strong>of</strong> element j per mole <strong>of</strong> substance i 

standard chemical exergy <strong>of</strong> element j contained in substance i. 

If <strong>the</strong> chemical element does not belong to <strong>the</strong> reference substances, its standard 

chemical exergy can also be calculated from Eq. 5.1. The standard chemical exergy 

<strong>of</strong> <strong>the</strong> reference substances are calculated prior to <strong>the</strong> standard chemical exergy <strong>of</strong> 

<strong>the</strong> element. 

5.2.2.2 Gaseous reference substances 

Free chemical elements present in <strong>the</strong> atmospheric air (O 2, N 2, Ar, He, N e, K r, X e) 

and <strong>the</strong> compounds H 2O, CO 2 are assumed as reference substances. Their standard 

chemical exergy results from <strong>the</strong> conventional standard concentration in <strong>the</strong> 

atmosphere. 

bch i = −¯R T 0 ln P0 

i 

P0 = −¯R T 0 ln xi where: 

¯R universal gas constant (8,314E-3 kJ/(mole K)), 

T 0 standard ambient temperature (298,15 K), 

P0 i 

P 

conventional mean ideal gas partial pressure in <strong>the</strong> atmosphere (kPa), 

0 standard pressure (101,325 kPa), 

xi molar fraction in <strong>the</strong> environment. 

(5.2) 

The values <strong>of</strong> standard chemical exergy <strong>of</strong> gaseous reference substances O 2, H 2O, 

CO 2, N 2 are calculated before o<strong>the</strong>r values because <strong>the</strong>y are necessary in <strong>the</strong> calculation 

<strong>of</strong> standard chemical exergy <strong>of</strong> non-gaseous reference substances. 

5.2.2.3 Solid reference substances 

For a prevailing part <strong>of</strong> chemical elements, solid R.S. commonly appearing in <strong>the</strong> 

external layer <strong>of</strong> <strong>the</strong> continental part <strong>of</strong> earth’s crust, are assumed. However, <strong>the</strong> 

earth’s crust is a very complicated mixture <strong>of</strong> solid solutions and an exact calculation 

<strong>of</strong> <strong>the</strong> chemical exergy <strong>of</strong> its components is impossible. We can only approximately 

evaluate that exergy, assuming that <strong>the</strong> reference species behave as components <strong>of</strong> 

an ideal solution. Hence, Eq. 5.2 can be applied also in this case. 

The evaluation <strong>of</strong> <strong>the</strong> standard molar concentration <strong>of</strong> solid R.S. in <strong>the</strong> external 

layer <strong>of</strong> <strong>the</strong> earth’s crust is difficult and as stated in chapter 3, <strong>the</strong>re wasn’t any 

average <strong>mineral</strong>ogical composition until <strong>the</strong> recent publications <strong>of</strong> Grigor’ev [124], 

[127] arrived. In past geochemical publications (such as Allègre [6], [8], Shan Gao 

[106], Rudnick [291], Condie [60], Javoy [169], McDonough [212], Taylor and


McLennan [353], [216], [215], or Wedepohl [404]) one can only find mean mass 

concentrations <strong>of</strong> particular chemical elements and <strong>the</strong> most common oxides found 

in <strong>the</strong> continental crust, namely SiO 2, T iO 2, Al 2O 3, FeO, M nO, M gO, CaO, N a 2O, 

K 2O and P 2O 5. Hence, <strong>the</strong> best considered way so far to obtain <strong>the</strong> standard molar 

concentration <strong>of</strong> R.S. in <strong>the</strong> solid environment, has been with <strong>the</strong> following equation 

suggested by Szargut in [336]. 

where: 

ε j 

l j 

c j 

MWcr xi = 1 

εj c j MWcr l j 

(5.3) 

mean molar concentration <strong>of</strong> <strong>the</strong> j-th element in <strong>the</strong> continental part <strong>of</strong> <strong>the</strong> 

earth’s crust (mole/g), 

number <strong>of</strong> <strong>the</strong> atoms <strong>of</strong> j-th element in <strong>the</strong> molecule <strong>of</strong> <strong>the</strong> reference 

species, 

fraction <strong>of</strong> <strong>the</strong> j-th element appearing in <strong>the</strong> form <strong>of</strong> reference species, 

mean molecular weight <strong>of</strong> <strong>the</strong> upper continental crust (g/mole). 

The reference reactions <strong>of</strong> <strong>the</strong> elements having solid reference substances contain 

usually gaseous reference substances such as O for example. Sometimes <strong>the</strong>re appear 

also solid or liquid reference species. In such case <strong>the</strong> standard chemical exergy 

<strong>of</strong> <strong>the</strong> appearing solid or liquid reference substance should be calculated prior to <strong>the</strong> 

calculation <strong>of</strong> <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> considered element. 

5.2.2.4 Reference substances dissolved in seawater 

Assumption <strong>of</strong> ionic or molecular R.S. dissolved in seawater ensures in many cases 

more exact determination <strong>of</strong> standard chemical exergy <strong>of</strong> chemical elements when 

compared with solid R.S. The calculation methods <strong>of</strong> <strong>the</strong>rmodynamic functions <strong>of</strong> 

monocharged and bicharged ions are relatively exact. This is <strong>the</strong> case also when 

<strong>the</strong> reference substance is dissolved in molecular form with a very small degree <strong>of</strong> 

ionization. 

The method <strong>of</strong> calculation <strong>of</strong> standard chemical exergy <strong>of</strong> elements with R.S. dissolved 

in seawater was developed by Morris [340]: 

 

bch j = −∆ Gf i + 0, 5 z + 

bch H2 − rk,i bch k − 

− ¯R T 0 [2, 303 z + (pH) + ln m i γ i] 

k 

 

(5.4)


where: 

∆G f i Gibbs free energy <strong>of</strong> <strong>the</strong> R.S., 

z + number <strong>of</strong> elementary positive charges <strong>of</strong> <strong>the</strong> reference ion, 

rk,i number <strong>of</strong> molecules <strong>of</strong> additional elements k present in <strong>the</strong> molecule <strong>of</strong> 

reference substance i, 

bch H2 , bch k standard chemical exergy <strong>of</strong> hydrogen gas and <strong>of</strong> <strong>the</strong> k-th additional element. 

mi conventional standard molarity <strong>of</strong> <strong>the</strong> reference substance i in seawater, 

γi activity coefficient (molarity scale) <strong>of</strong> <strong>the</strong> reference substance in seawater, 

pH exponent <strong>of</strong> <strong>the</strong> concentration <strong>of</strong> hydrogen ion in seawater (=8,1) 

Eq. 5.4 should be multiplied by 2 for <strong>the</strong> diatomic elements Br 2, Cl 2 and I 2. 

The activity coefficient <strong>of</strong> a single ion can be calculated by means <strong>of</strong> <strong>the</strong> Debye- 

Huckel equation: 

− log γi = A1 (z + ) 2 I 

 

1 + ai A2 I 

(5.5) 

where: 

A1 A2 ai = 0,51 kg1/2 mole−1/2 for water at 25oC, = 3,287 * 109 kg1/2 m−1 mole−1/2 for water at 25oC, effective diameter <strong>of</strong> <strong>the</strong> ion, 

I ionic strength <strong>of</strong> <strong>the</strong> electrolyte. 

The ionic strength <strong>of</strong> <strong>the</strong> electrolyte results from <strong>the</strong> following equation: 

I = 1 

mi (z 

2 

i 

+ ) 2 

where: 

mi molarity <strong>of</strong> <strong>the</strong> ion, mole/kg H2O, z + number <strong>of</strong> elementary electric charges <strong>of</strong> <strong>the</strong> ion. 

(5.6) 

The ion Cl − prevails among <strong>the</strong> negative ions in seawater. Therefore, <strong>the</strong> data <strong>of</strong> 

chlorides can be assumed for activity coefficients <strong>of</strong> <strong>the</strong> positive ions N a + and K + . 

The activity coefficients <strong>of</strong> <strong>the</strong> negative ions Cl − and SO −2 

4 can be estimated in reference 

to <strong>the</strong> predominant positive ion N a + . The positive ionic reference substances 

were assumed for <strong>the</strong> elements from <strong>the</strong> first column <strong>of</strong> <strong>the</strong> periodic system and 

for <strong>the</strong> monocharged and bicharged negative ions formed from acids. The elements 

from <strong>the</strong> second column <strong>of</strong> <strong>the</strong> periodic system appear in seawater in <strong>the</strong> form <strong>of</strong> 

positive bicharged ions, however, <strong>the</strong>y are not recommended as R.S., because <strong>the</strong> 

so calculated standard chemical exergy <strong>of</strong> <strong>the</strong> elements leads to negative values <strong>of</strong> 

chemical exergy <strong>of</strong> some solid compounds common in <strong>the</strong> earth’s crust.


5.2.3 Update <strong>of</strong> Szargut’s R.E. 

Next, Szargut’s R.E. will be updated with <strong>the</strong> help <strong>of</strong> new geochemical data and <strong>the</strong> 

information provided by o<strong>the</strong>r authors such as Ranz [276] or Rivero [281]. 

5.2.3.1 Update <strong>of</strong> <strong>the</strong> standard chemical exergy <strong>of</strong> chemical compounds 

The only variable included in Eq. 5.1 that is subject to be updated is ∆G f . The Gibbs 

free energy used by Szargut [336] was revised by Rivero [281] using [258], [391], 

[194], [19] and [399]. No substantial differences were found, except for sillimanite 

(Al 2SiO 5), whose new value was ∆G f = 2440, 9 kJ/mole. The information source 

<strong>of</strong> Ranz [276] for obtaining ∆G f , was Faure [94], which is a compilation <strong>of</strong> <strong>the</strong> 

literature from several authors. This source corroborates Rivero’s revision and thus, 

it will be considered for <strong>the</strong> calculation <strong>of</strong> this particular R.E. 

5.2.3.2 Update <strong>of</strong> <strong>the</strong> gaseous reference substances 

Rivero and Garfias [281] accepted <strong>the</strong> reference pressure <strong>of</strong> Eq. 5.2 according to <strong>the</strong> 

conventional unit “physical atmosphere”, thus 101,325 kPa. We are assuming <strong>the</strong> 

mean partial pressure calculated by Szargut and used by Ranz [276], which is <strong>the</strong> 

really appearing mean value and is equal to 99,31 kPa. 

5.2.3.3 Update <strong>of</strong> <strong>the</strong> solid reference substances 

The mean molar concentration <strong>of</strong> <strong>the</strong> elements in <strong>the</strong> upper continental crust ε j <strong>of</strong> 

Eq. 5.3 used in Szargut [336], was <strong>the</strong> recommended by Polanski and Smulikowski 

[268]. Ranz [276] used updated values mainly from Taylor and McLennan [354], 

[353]. For <strong>the</strong> elements: Br, C, Cl, F, S, P t, Pu, Ra, Rh, Ru, Te, I, H g and N, 

Taylor and McLennan did not provide any information, <strong>the</strong>refore, Ranz used <strong>the</strong> 

values given by Wedepohl [404] for S, Br, C, F, I, H g, N and for <strong>the</strong> remaining 

elements, <strong>the</strong> values used by Szargut [336]. Some authors like Plank and Langmuir 

[267] basing on <strong>the</strong>ir studies on marine sediments, suggested already in 1998 some 

revisions <strong>of</strong> <strong>the</strong> estimated values by Taylor and McLennan [354], [353] for N b, 

Cs,T i, Ta. As a consequence, McLennan [215] published in year 2001 new mean 

molar concentrations <strong>of</strong> <strong>the</strong> upper continental crust for <strong>the</strong> elements: Sc, T i, V , Co, 

N i, N b, Cs, P b, Ta. The most recent data about <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> 

upper continental crust has been published by Rudnick and Gao [292], taking into 

account <strong>the</strong> studies published so far. 

The recent values provided by Rudnick and Gao will be used for <strong>the</strong> update <strong>of</strong> 

Szargut’s R.E. Never<strong>the</strong>less, values for Pu and Ra that are not provided in <strong>the</strong>ir 

tables, will be assumed to be <strong>the</strong> ones given by Polanski [268].


As explained in chapter 3, Grigor’ev published in year 2000 [125] <strong>the</strong> average <strong>mineral</strong> 

content <strong>of</strong> <strong>the</strong> upper continental crust obtained through a great number <strong>of</strong> 

quantitative <strong>mineral</strong>ogical analysis <strong>of</strong> important rocks. In 2007, Grigor’ev updated 

this information; <strong>the</strong> new analysis comprises 265 <strong>mineral</strong>s, <strong>the</strong>ir varieties and <strong>the</strong>ir 

non-<strong>mineral</strong> materials, corresponding to 99,13% <strong>of</strong> <strong>the</strong> total <strong>mineral</strong> content <strong>of</strong> <strong>the</strong> 

upper continental crust. With this valuable information, we have been able to propose 

a new model <strong>of</strong> <strong>the</strong> continental crust, based on Grigor’ev’s composition, but 

assuring <strong>the</strong> mass balance <strong>of</strong> <strong>the</strong> earth. This information allows to obtain directly 

<strong>the</strong> standard molar concentration <strong>of</strong> <strong>the</strong> following 14 reference substances in <strong>the</strong> 

solid environment without using Eq. 5.3: Al 2SiO 5, BaSO 4, Be 2SiO 4, CaCO 3, Au, 

Fe 2O 3, M g 3Si 4O 10(OH) 2, M nO 2, SiO 2, SrCO 3, ThO 2, SnO 2, T iO 2, Z rSiO 4. For <strong>the</strong> 

rest substances, Eq. 5.3 must be used, taking ε j from <strong>the</strong> latest geochemical publications 

explained before. 

For <strong>the</strong> fraction <strong>of</strong> <strong>the</strong> j-th element appearing in <strong>the</strong> form <strong>of</strong> reference species (coefficient 

c j), Szargut [335] associates values comprised between 0,5 for more abundant 

substances and 0,001 for less frequent substances from geochemical data given by 

Polanski and Smulikowski [268]. Ranz [276] obtained more accurate c j coefficients 

for solid R.S. containing <strong>the</strong> most abundant elements in <strong>the</strong> upper continental crust. 

For this purpose, she used <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> earth’s upper layer 

obtained with <strong>the</strong> CIPW norm before and updated geochemical information, mainly 

from Taylor and McLennan [354]. For minority elements, due to <strong>the</strong> lack <strong>of</strong> information, 

Szargut’s [335] values were used. As long as a better <strong>mineral</strong>ogical composition 

<strong>of</strong> <strong>the</strong> earth’s crust is not developed and <strong>the</strong> c j coefficients are recalculated with this 

information, we will assume <strong>the</strong> c j values obtained by Ranz [276]. 

The mean molecular mass <strong>of</strong> <strong>the</strong> upper layer <strong>of</strong> <strong>the</strong> continental part <strong>of</strong> <strong>the</strong> earth’s 

crust, was first estimated by Szargut [334]. The obtained value was MW cr= 135,5 

kg/kmole, applying <strong>the</strong> following estimation method: according to <strong>the</strong> geochemical 

data, <strong>the</strong> mean concentration values (in mole/kg) <strong>of</strong> particular chemical groups 

or elements in <strong>the</strong> external layer <strong>of</strong> <strong>the</strong> continental earth’s crust and <strong>the</strong> chemical 

compound formed from <strong>the</strong>se groups were assumed. The first considered group was 

CO 2, which appears in <strong>the</strong> earth’s crust mainly as <strong>the</strong> carbonates <strong>of</strong> Ca, M g and Fe. 

Per 1 mole <strong>of</strong> (CaO + M gO + FeO) 0,035 mole <strong>of</strong> CO 2 is present. The group CO 2 

was partitioned between <strong>the</strong> mentioned groups and elements Zn, Cu, P b and Cd, 

appearing also in <strong>the</strong> form <strong>of</strong> carbonates. The group SO 3 was partitioned between 

CaO and M gO forming sulphates. It was assumed that a prevailing part <strong>of</strong> metals 

(Sn, Co, M n, Fe, N i) appears in <strong>the</strong> form <strong>of</strong> different oxides (Co 2O 3, Co 3O 4, Fe 2O 3, 

Fe 3O 4). It was also assumed that 8% <strong>of</strong> Fe appears in <strong>the</strong> form <strong>of</strong> <strong>the</strong> free oxide 

Fe 2O 3. The remaining part appears in <strong>the</strong> form <strong>of</strong> FeT iO 3, FeC r 2O 3 and silicates. For 

example, <strong>the</strong> following silicates were assumed: N aAlSi 3O 8, KAlSi 3O 8, N aFeSi 2O 6, 

M gSiO 3, CaO.Al 2Si 2O 7. Because <strong>of</strong> <strong>the</strong> large content <strong>of</strong> SiO 2, a considerable part <strong>of</strong> 

it was assumed in <strong>the</strong> free form. After estimating <strong>the</strong> composition <strong>of</strong> a mean sample 

<strong>of</strong> <strong>the</strong> lithosphere, its molecular mass was calculated.


Ranz [276] updated <strong>the</strong> molecular mass <strong>of</strong> <strong>the</strong> upper continental crust using more 

recent geochemical information and adopting not only a geochemical approach, but 

also a geological one. The methodology used was as follows: <strong>the</strong> international accepted 

norm CIPW [262] was applied to <strong>the</strong> mass fractions <strong>of</strong> <strong>the</strong> principal oxide 

groups obtained by Carmichael [49] for <strong>the</strong> cratonic and sedimentary layers, in order 

to redistribute <strong>the</strong> chemical components from <strong>the</strong> oxides to <strong>the</strong> <strong>mineral</strong> molecules 

that are representative in real <strong>mineral</strong>s appearing in a rock. Next, <strong>the</strong> <strong>mineral</strong>s <strong>of</strong> 

<strong>the</strong> norm and <strong>the</strong>ir respective relative masses were modified to adjust <strong>the</strong>m to <strong>the</strong> 

real volumes <strong>of</strong> <strong>the</strong> principal groups <strong>of</strong> each rock. Finally, <strong>the</strong>ir molar fractions were 

calculated and <strong>the</strong> mean molecular mass <strong>of</strong> <strong>the</strong> whole was obtained. The resulting 

MW cr was equal to 145,5 g/mole. Even though this methodology used better 

geochemical values than <strong>the</strong> ones in Szargut [334], and included <strong>the</strong> geological 

approach, we cannot forget that <strong>the</strong> CIPW norm is an artificial way to obtain <strong>the</strong> 

possible <strong>mineral</strong>s that can appear in a rock. It is <strong>the</strong>refore only an approximation as 

well. 

In <strong>the</strong> light <strong>of</strong> Grigor’ev’s analysis, a more accurate molecular weight <strong>of</strong> <strong>the</strong> upper 

continental crust, based on experimental results ra<strong>the</strong>r than assumptions, can be 

easily obtained. The new calculated value is MW cr= 142,1 g/mole, which is very 

close to <strong>the</strong> estimation done by Ranz. Our model threw up a mean molecular weight 

<strong>of</strong> <strong>the</strong> upper crust <strong>of</strong> MW cr=155,2 g/mole. 

5.2.3.4 Update <strong>of</strong> <strong>the</strong> liquid reference substances 

Rivero and Garfias [281] have found <strong>the</strong> influence <strong>of</strong> salinity <strong>of</strong> seawater on <strong>the</strong> 

calculated values <strong>of</strong> standard chemical exergy <strong>of</strong> elements calculated by means <strong>of</strong> 

reference substances dissolved in seawater. However, an increased salinity (greater 

than 35 per thousand) appears seldom (Red Sea), and <strong>the</strong> deviations are not large 

(usually less than 1,6%). Every introduction <strong>of</strong> solid reference substances can decrease 

<strong>the</strong> accuracy <strong>of</strong> calculations. Therefore we are assuming <strong>the</strong> solid reference 

substances only for <strong>the</strong> elements from <strong>the</strong> second column <strong>of</strong> <strong>the</strong> periodic system. 

Following ionic and molecular reference substances dissolved in seawater have been 

accepted in <strong>the</strong> recent publication <strong>of</strong> Szargut [338] and will be used for this proposal: 

Cl − , AgCl − 

H gCl −2 

4 , IO− 

Zn +2 . 

2 , B(OH) 3 (aq), BiO + , Br − , CdCl 2 (aq), Cs + , Cu +2 , H PO −2 

4 

3 , K+ , Li + , M oO −2 

4 , N a+ , N i +2 , P bCl 2 (aq), Rb + , SO −2 

4 4 

, HAsO−2 

, SeO−2, 

W O−2 

Major ions in seawater are ions with fractions greater than 1 ppm. The seawater 

reference environment taken into account in this proposal comprises <strong>the</strong> following 

major ions: N a + , K + , HAsO −2 

4 , BiO+ , Cl − , SO −2 

4 , Br− , B(OH) 3. Values <strong>of</strong> <strong>the</strong> 

activity coefficients and molarity <strong>of</strong> <strong>the</strong>se species basing on information presented 

in Millero [224], [225], Pilson [264] and Mottl [231] were reviewed and compared 

with those which Ranz and Rivero took into account. 

4 , 

4 ,


5.2.3.5 The updated reference environment. Results 

Table 5.4 shows <strong>the</strong> results obtained in this study for <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> 

elements with <strong>the</strong> geochemical information <strong>of</strong> <strong>the</strong> crust (MW cr and z 0i) obtained 

in this PhD (This study 1) and <strong>the</strong> one provided by Grigor’ev [127] (This study 2). 

The solid R.S. assumed are those taken by Szargut [336], basing on <strong>the</strong> Szargut’s 

criterion mentioned before. Additionally, <strong>the</strong> values are compared to those given by 

Szargut [336], Valero, Ranz and Botero [371] and Rivero and Garfias [281]. The 

different reference substances divided into liquid, gaseous and solid R.S. and <strong>the</strong> 

values required for <strong>the</strong> calculations are shown in tables A.13, A.14 and A.15 in <strong>the</strong> 

appendix, page 384. 

The average difference between our study (1) and Szargut’s values is around 0,66% 

on average, while between study (2) with Grigor’ev’s model and Szarguts’, about 

0,93%. Hence, in both cases, <strong>the</strong> average differences are very small. Never<strong>the</strong>less, 

small differences multiplied by huge numbers, such as <strong>the</strong> quantity <strong>of</strong> all <strong>mineral</strong>s 

on earth, make <strong>the</strong>se discrepancies to be not so insignificant. Next, each <strong>of</strong> <strong>the</strong> 

three subsystems (gaseous, liquid and solid R.S.) is analyzed, stressing <strong>the</strong> biggest 

differences found in <strong>the</strong> different models. 

The obtained values for gaseous R.S. are <strong>the</strong> same <strong>of</strong> those obtained by Szargut 

[336] and Valero, Ranz and Botero [371], since <strong>the</strong> methodology and <strong>the</strong> values 

used for this R.E. have been <strong>the</strong> same. The differences between this study (1) and 

(2) and that <strong>of</strong> Rivero and Garfias [281] are due to <strong>the</strong> different partial pressures in 

<strong>the</strong> atmosphere assumed. 

The new chemical exergies obtained differ in 0,5% in average for study (1) and 

1% for study (2) with respect to <strong>the</strong> values obtained by Szargut in [336] for solid 

reference substances. Taking <strong>the</strong> empirical standard molar concentration <strong>of</strong> solid 

R.S. from our model instead <strong>of</strong> obtaining it with Eq. 5.3, implies a difference in <strong>the</strong> 

element chemical exergy <strong>of</strong> about 0,2% except for Au (9,5%) and F (6,7%). For 

<strong>the</strong> latter elements, <strong>the</strong> greater difference is due to <strong>the</strong> greater sensitivity <strong>of</strong> Au to 

x i (since its ∆G f is equal to zero) and <strong>the</strong> great proportion <strong>of</strong> atoms <strong>of</strong> Ca in <strong>the</strong> 

reference substance <strong>of</strong> F (CaF 2), respectively. It must be stressed that choosing a 

certain c j or ano<strong>the</strong>r a 100 times greater, throws less differences in <strong>the</strong> chemical 

exergy <strong>of</strong> <strong>the</strong> elements than choosing ano<strong>the</strong>r R.S., as can be seen in <strong>the</strong> models <strong>of</strong> 

Valero et al. [371] and Rivero et al. [281], when o<strong>the</strong>r R.S. are considered. The 

same thing happens with <strong>the</strong> molecular weight <strong>of</strong> <strong>the</strong> earth’s crust. An MW cr <strong>of</strong> 

142,1 or 155,2 only modifies <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> elements in 0,03%, and 

hence that parameter is not crucial at all. 

For <strong>the</strong> liquid R.S., with <strong>the</strong> exception <strong>of</strong> SO −2 

4 <strong>the</strong> differences are negligible from 

<strong>the</strong> point <strong>of</strong> view <strong>of</strong> <strong>the</strong> influence on <strong>the</strong> final exergy <strong>of</strong> <strong>the</strong> considered element. In 

<strong>the</strong> case <strong>of</strong> SO − 

4 , Szargut and Valero et al. assumed a value <strong>of</strong> mSO −2 = 1,17E-2, and 

4 

Rivero m −2 

SO = 1,24E-2. The molarity calculated basing on <strong>the</strong> three independent 

4 

sources [225], [264] and [231] is estimated as m −2 

SO = 2,93E-2 and is almost 2,5 

4


times greater. This difference decreases <strong>the</strong> chemical exergy <strong>of</strong> sulfur only about 2 

kJ/mole. The rest <strong>of</strong> <strong>the</strong> obtained results are very similar to previous investigations 

and <strong>the</strong> differences are negligible. 

Table 5.4: Standard chemical exergies <strong>of</strong> <strong>the</strong> elements 

Standard chemical exergy <strong>of</strong> <strong>the</strong> elements, bch j (kJ/mole) 

Element This study This study Szargut Valero et al. Rivero et al. 

1 

2 

[336] [371] [281] 

Ag 69,7 69,7 70,2 70,3 R.S.=AgCl 

99,3 

Al 794,3 795,8 888,2 R.S. =Al2O3 796,7 

795,7 

Ar 11,7 11,7 11,7 11,7 11,6 

As 494,1 494,1 494,6 R.S.=As2O5 411,5 

492,6 

Au 51,5 56,4 50,5 53,4 50,6 

B 628,6 628,6 628,5 628,5 628,1 

Ba 765,5 777,2 775,1 774,3 775,4 

Be 602,6 606,4 604,4 R.S.=BeO 

615,6 

604,3 

Bi 274,8 274,8 274,5 274,6 274,8 

Br2 101,1 101,1 101,2 101,3 101,0 

C 410,3 410,3 410,3 410,3 410,3 

Ca 723,8 719,9 729,1 R.S.=Ca 2+ 

712,4 

729,1 

Cd 293,2 293,2 293,8 293,8 R.S.=CdCO 3 

298,4 

Ce 1054,2 1054,5 1054,6 1054,4 1054,7 

Cl 2 124,2 124,2 123,6 123,7 123,7 

Co 308,9 308,6 312,0 R.S.=Co3O4 270,4 

313,4 

C r 584,4 584,5 584,3 R.S.=C r2O3 559,1 

584,4 

Cs 404,5 404,5 404,4 404,6 404,6 

Cu 134,0 134,0 134,2 134,2 R.S.=CuCO 3 

132,6 

D y 974,9 975,1 975,9 975,3 976,0 

Er 973,0 973,2 972,8 973,1 972,8 

Eu 1003,9 1004,1 1003,8 1004,4 1003,8 

F2 556,1 595,5 504,9 R.S.=CaF 2 

482,7 

505,8 

Fe 376,8 377,1 374,8 374,8 374,3 

Ga 514,6 514,7 514,9 514,7 515,0 

Gd 969,9 970,1 969,0 969,6 969,0 

Ge 556,5 556,7 557,6 556,3 557,7 

H2 236,1 236,1 236,1 236,1 236,1 

He 30,4 30,4 30,4 30,4 31,3 

H f 1061,3 1061,5 1062,9 1061,3 1063,1 

H g 114,8 114,8 115,9 115,9 R.S.=H gCl 2 

107,9 

Ho 979,3 979,5 978,6 979,5 978,7 



Table 5.4: Standard chemical exergies <strong>of</strong> <strong>the</strong> elements – continued from previous 

page 



1 

2 

[336] [371] [281] 

I2 175,0 175,0 174,7 174,8 175,7 

In 437,4 437,5 436,8 437,6 436,9 

I r 256,1 256,4 246,8 256,5 247,0 

K 366,5 366,5 366,6 366,7 366,7 

K r 34,4 34,4 34,4 34,4 34,3 

La 994,3 994,5 994,6 994,5 994,7 

Li 392,9 392,9 393,0 393,0 392,7 

Lu 946,6 946,9 945,7 946,7 945,8 

M g 629,6 629,4 626,1 R.S.=M g +2 

611,0 

626,9 

M n 484,6 490,1 482,0 482,9 487,7 

M o 730,5 730,5 730,3 730,3 731,3 

N2 0,7 0,7 0,7 0,7 0,7 

N a 336,6 336,6 336,6 336,7 336,7 

N b 900,2 900,3 899,7 899,4 899,7 

N d 969,8 970,0 970,1 970,1 970,1 

N e 27,2 27,2 27,2 27,2 27,1 

N i 232,5 232,5 232,7 232,7 R.S.=N iO 

242,6 

O2 4,0 4,0 4,0 4,0 3,9 

Os 370,8 371,0 368,1 369,8 368,4 

P 861,6 861,6 861,4 861,4 861,3 

P b 232,2 232,2 232,8 232,8 R.S.=P bCO3 249,2 

Pd 145,7 145,9 138,6 146,0 138,7 

P r 963,8 964,1 963,8 964,0 963,9 

P t 146,5 146,7 141,0 140,9 141,2 

Pu 1099,7 1099,9 1100,0 1099,8 1100,1 

Ra 825,8 826,1 823,9 823,7 824,2 

Rb 388,8 388,8 388,6 388,9 388,7 

Re 561,3 561,4 559,5 560,3 559,6 

Rh 183,0 183,1 179,7 176,6 179,7 

Ru 315,2 315,5 318,6 318,4 318,6 

S 607,3 607,3 609,6 609,6 609,3 

Sb 437,1 437,2 438,0 438,0 438,2 

Sc 923,8 923,9 925,2 924,1 925,3 

Se 346,7 346,7 346,5 346,5 347,5 

Si 854,2 854,1 854,9 854,2 855,0 

Sm 993,9 994,1 993,6 994,2 993,7 

Sn 547,6 536,8 551,9 549,2 551,8 

Sr 758,8 773,6 749,8 748,6 749,8 

Ta 974,8 975,0 974,0 973,8 974,1 

T b 999,0 999,2 998,4 999,4 998,5 

Te 326,4 326,6 329,2 329,1 329,3 

Th 1214,5 1220,7 1202,6 1202,1 1202,7 

T i 904,4 902,0 907,2 902,9 907,2 

T l 193,8 194,0 194,9 194,2 194,9 



Table 5.4: Standard chemical exergies <strong>of</strong> <strong>the</strong> elements – continued from previous 

page 



1 

2 

[336] [371] [281] 

T m 952,5 952,7 951,7 952,5 951,8 

U 1196,1 1196,3 1196,6 1196,2 1196,6 

V 721,5 721,6 720,4 722,2 721,3 

W 827,7 827,7 827,5 827,5 828,5 

X e 40,3 40,3 40,3 40,3 40,3 

Y 966,3 966,5 965,5 966,4 965,6 

Y b 944,9 945,2 944,3 944,8 944,3 

Zn 339,0 339,0 339,2 339,2 R.S.=ZnCO 3 

344,7 

Z r 1077,4 1080,9 1083,4 R.S.=Z rO2 1060,7 

1083,0 


5.2.4 Drawbacks <strong>of</strong> Szargut’s R.E. methodology 

As stated in section 5.2, <strong>the</strong> R.E. can be considered as one, in which all <strong>the</strong> substances 

contained in it have reacted, dispersed and mixed. Such an environment, would 

have probably a hydrosphere with a composition <strong>of</strong> groundwaters, rivers, lakes, etc. 

similar to that <strong>of</strong> <strong>the</strong> sea. The atmosphere would have a much greater CO 2 and o<strong>the</strong>r 

pollutant’s content than it does now, due to <strong>the</strong> complete burning <strong>of</strong> fossil fuels. And 

<strong>the</strong> continental crust would have likely a very similar composition to <strong>the</strong> current one 

(except for <strong>the</strong> absence <strong>of</strong> fossil fuels), but completely dispersed with no enriched 

<strong>mineral</strong> deposits. 

Szargut’s and subsequent reference environments are composed <strong>of</strong> only one reference 

substance per element, i.e. 85 R.S. Obviously a degraded earth would contain 

many more substances. Additionally, <strong>the</strong> variables used in Szargut’s and subsequent 

models are based on current and not eventual values 1 . Fur<strong>the</strong>rmore, many <strong>mineral</strong>s 

that are more stable than <strong>the</strong> R.S. have negative exergies. This fact occurs not that 

<strong>of</strong>ten than with Ranz’s abundance criterion, but it still happens, as we will see later 

in chapter 6. A chemically inactive R.E. would be <strong>the</strong> one created by Ahrendts [4] 

and fur<strong>the</strong>r developed by Diederichsen [74]. In both models <strong>the</strong> positiveness <strong>of</strong> any 

substance is assured. But as stated before, <strong>the</strong>se reference environment’s compositions 

are far removed from <strong>the</strong> currently known and from an eventually degraded 


1 For instance partial pressures <strong>of</strong> gaseous R.S., temperatures or molalities are taken as those ap- 

pearing currently in <strong>the</strong> atmosphere and <strong>the</strong> sea.

The exergy <strong>of</strong> <strong>mineral</strong> resources 157 

Hence, <strong>the</strong> reference environment based on Szargut’s criterion should not be considered 

as a dead R.E., but ra<strong>the</strong>r as a ma<strong>the</strong>matical tool for obtaining standard 

chemical exergies <strong>of</strong> <strong>the</strong> elements. Fur<strong>the</strong>rmore, it is always subject to updates, as 

new geochemical information is more available. 

5.3 The exergy <strong>of</strong> <strong>mineral</strong> resources 

5.3.1 The energy involved in <strong>the</strong> process <strong>of</strong> formation <strong>of</strong> a <strong>mineral</strong> 

deposit 

As stated in Ranz’s PhD [276], a <strong>mineral</strong> deposit can be seen as a very unfrequent 

aggregates <strong>of</strong> rocks, which in turn rocks are aggregate <strong>of</strong> <strong>mineral</strong>s, and <strong>the</strong>se are 

aggregates <strong>of</strong> certain molecular substances, which are composed by aggregates <strong>of</strong> 

atoms. This definition can be summarized as in Eq. 5.7: 

Deposit = rocks = <strong>mineral</strong>s = 

molecules = atoms 

(5.7) 

Each aggregate is characterized by two different properties: a cohesion energy or 

binding energy, represented by its enthalpy <strong>of</strong> formation, and <strong>the</strong> entropy <strong>of</strong> <strong>the</strong> 

mixture or <strong>of</strong> formation, which indicates <strong>the</strong> probability degree <strong>of</strong> forming <strong>the</strong> substance 

under consideration. The four steps implicated in <strong>the</strong> formation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> 

deposit are outlined as follows [276]: 

Step I: Formation <strong>of</strong> <strong>the</strong> molecule: Σ Atoms (g) → Molecule (g)+ ∆ H, ∆ S 

Step II: Solidification: Molecule (g) → Molecule (s)+ ∆ H, ∆ S 

Step III: Solid 1 + Solid 2 → Mineral+ ∆ H, ∆ S 

Step IV: Formation <strong>of</strong> <strong>the</strong> deposit: % Mineral + Rocks → Mine + ∆ H, ∆ S 

The first two steps are basically chemical processes, in which <strong>the</strong> energies involved 

are determined by <strong>the</strong> change <strong>of</strong> enthalpy and entropy that accompanies <strong>the</strong> formation 

<strong>of</strong> 1 mole <strong>of</strong> a substance from its constituent elements. The solidification 

energy is much smaller than <strong>the</strong> <strong>the</strong>rmodynamic process <strong>of</strong> formation <strong>of</strong> <strong>the</strong> <strong>mineral</strong>. 

Usually, <strong>the</strong> process <strong>of</strong> formation <strong>of</strong> a <strong>mineral</strong> proceeds directly to its solid 

phase. 

The third step is subdivided into two processes: <strong>mineral</strong>ization and formation <strong>of</strong> 

<strong>the</strong> rock. The <strong>mineral</strong>ization stage is a chemical process, in which <strong>the</strong> molecules 

combine to form <strong>the</strong> <strong>mineral</strong>. The formation <strong>of</strong> <strong>the</strong> rock is a physical process, where 

<strong>the</strong> solids (or <strong>mineral</strong>s) are mixed to form a conglomeration. The general expression 

for <strong>the</strong> entropy generated in a mixture process <strong>of</strong> two ideal gases, solids or liquids is 

expressed as in Eq. 5.8. 

∆S = ∆S 1 + ∆S 2 = −n 1 ¯R 

x1P 

P 

d P 

P − n2 ¯R 

x2P 

d P 

P P 

= −¯R 

n1lnx 1 + n2lnx 2 (5.8)


Generally, <strong>the</strong> generation <strong>of</strong> entropy in mixtures, and especially in solid solutions, 

is much smaller than that for <strong>the</strong>rmal exchanges associated to <strong>the</strong> formation <strong>of</strong> <strong>the</strong> 

compound, temperature increases or phase changes. 

Finally, <strong>the</strong> fourth step deals with <strong>the</strong> formation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> deposit. Mineral 

deposits have <strong>the</strong> special feature that contain certain <strong>mineral</strong>s at much greater concentrations 

than in <strong>the</strong> earth’s crust. 

According to Faber [90], if <strong>the</strong> resource <strong>of</strong> a <strong>mineral</strong> deposit at a concentration 

x i is extracted, <strong>the</strong> entropy will decrease, and <strong>the</strong> entropy change per mole <strong>of</strong> <strong>the</strong> 

resource is given by Eq. 5.9. 

 

∆S = ¯R lnx i + (1 − x 

i) 

ln(1 − xi) < 0 (5.9) 

xi According to <strong>the</strong> second law <strong>of</strong> <strong>the</strong>rmodynamics, this negative entropy flux is only 

possible if <strong>the</strong>re is ano<strong>the</strong>r system to which it flows. Hence, an external energy 

supply is needed. The standard energy involved in separating <strong>the</strong> resource from <strong>the</strong> 

<strong>mineral</strong> deposit is <strong>the</strong>n <strong>the</strong> concentration exergy b c, in kJ/mole: 

bc i = −¯RT 0 

 

lnx i + (1 − x 

i) 

ln(1 − xi) xi (5.10) 

where ¯R is <strong>the</strong> universal gas constant (8,314 kJ/kmole K), T 0 is <strong>the</strong> standard ambient 

temperature (298,15 K) and x is <strong>the</strong> molar concentration <strong>of</strong> <strong>the</strong> substance. 

Additionally to <strong>the</strong> concentration exergy, which accounts for a minimum, <strong>the</strong> binding 

forces in <strong>the</strong> formation <strong>of</strong> <strong>the</strong> crystal should be accounted for [276]. The bonds 

generated are <strong>of</strong> different nature. 1) Covalent or ionic bonds, forming a threedimensional 

crystalline structure. In <strong>the</strong> absence <strong>of</strong> crystalline defects, <strong>the</strong> energy 

needed to separate <strong>the</strong>m is equal to <strong>the</strong> interatomic bonding energy. 2) Cohesion <strong>of</strong> 

interphase forces and capillarity suction, which is commonly found in <strong>the</strong> agglomeration 

<strong>of</strong> a solid by a liquid, acting as an adhesive cement. 3) Intermolecular and 

electrostatic forces, binding very thin particles. 4) Mechanical interpenetration <strong>of</strong> 

particles, typically formed by compression. 

The energy needed to separate a solid particle from o<strong>the</strong>rs <strong>of</strong> smaller size depend on 

different physical aspects such as size, hardness or surface area. Some expressions 

have been developed for relating <strong>the</strong> particle size with <strong>the</strong> grinding energy. Kicks’s 

law or Bond’s law are two <strong>of</strong> those studies (see for instance, [259] for more details). 

Both laws indicate that <strong>the</strong> grinding energy increases exponentially as <strong>the</strong> particle 

size decreases. 

As we will see in later sections, <strong>the</strong> chemical energies involved in <strong>the</strong> formation <strong>of</strong> 

<strong>the</strong> deposit are considerably higher than <strong>the</strong> physical energies explained in this last 

step.


5.3.2 The exergy <strong>of</strong> non-fuel <strong>mineral</strong> resources 

The <strong>the</strong>rmodynamic value <strong>of</strong> a natural resource can be defined as <strong>the</strong> minimum 

work necessary to produce it with a specific structure and concentration from common 

materials in <strong>the</strong> environment. This minimum amount <strong>of</strong> work is <strong>the</strong>oretical 

by definition and is equal to <strong>the</strong> material’s exergy (Riekert [278]). The exergy <strong>of</strong> 

a system gives an idea <strong>of</strong> its <strong>evolution</strong> potential for not being in <strong>the</strong>rmodynamic 

equilibrium with <strong>the</strong> environment, or what is <strong>the</strong> same, for not being in a dead state 

related to <strong>the</strong> reference environment (R.E.). 

The physical features that make <strong>mineral</strong>s valuable are mainly <strong>the</strong>ir specific composition 

and <strong>the</strong> greater concentration in <strong>the</strong> ores in which <strong>the</strong>y are found [371]. The 

energy involved in <strong>the</strong> process <strong>of</strong> formation <strong>of</strong> a <strong>mineral</strong> comprises <strong>the</strong> formation <strong>of</strong> 

<strong>the</strong> compound from its elements, and <strong>the</strong> cohesion <strong>of</strong> <strong>the</strong> molecules to form <strong>the</strong> <strong>mineral</strong>’s 

crystal structure (step 1 to 3 in section 5.3.1). The minimum <strong>the</strong>oretical work 

that nature should invest to provide <strong>mineral</strong>s at a specific composition and structure 

from a degraded earth is equal to <strong>the</strong> standard chemical exergy [336] and it can be 

calculated by means <strong>of</strong> <strong>the</strong> exergy balance <strong>of</strong> a reversible formation reaction as in 

Eq. 5.1. 

 

bch i = ∆G f i + r j,i bch j 

Once <strong>the</strong> <strong>mineral</strong> has been created, it mixes with o<strong>the</strong>r <strong>mineral</strong>s to form rocks, which 

in turn, are combined with o<strong>the</strong>r rocks forming <strong>the</strong> deposit (step 4 in section 5.3.1). 

The minimum <strong>the</strong>oretical work needed to concentrate a substance from an ideal 

mixture <strong>of</strong> two components is given by <strong>the</strong> concentration exergy (b c), as in Eq. 5.10. 

The binding energy between <strong>mineral</strong>s and rocks is not considered in <strong>the</strong> ideal case. 

Therefore, <strong>the</strong> exergy needed to separate <strong>the</strong> <strong>mineral</strong>s from <strong>the</strong> deposit is <strong>the</strong> same 

as <strong>the</strong> exergy to mix <strong>the</strong>m. Never<strong>the</strong>less this binding exergy is taken into account 

through <strong>the</strong> unit exergy costs explained in section 5.3.4. 

The difference between <strong>the</strong> concentration exergies obtained with <strong>the</strong> <strong>mineral</strong> concentration 

in a mine (x m) 2 and with <strong>the</strong> average concentration in <strong>the</strong> earth’s crust 

(x c) 3 is <strong>the</strong> minimum energy that nature had to spend to bring <strong>the</strong> <strong>mineral</strong>s from <strong>the</strong> 

concentration in <strong>the</strong> reference state to <strong>the</strong> concentration in <strong>the</strong> mine. The concentration 

exergy <strong>of</strong> a <strong>mineral</strong> in a completely degraded planet is zero, and it increases, 

as its concentration increases. The work needed to separate a substance from a 

mixture does not follow a linear behavior with its concentration. On <strong>the</strong> contrary, 

<strong>the</strong> second law <strong>of</strong> <strong>the</strong>rmodynamics, reflected in Eq. 5.10 and represented in Fig. 

5.1 dictates that <strong>the</strong> effort required to separate <strong>the</strong> <strong>mineral</strong> from <strong>the</strong> mine follows 

a negative logarithmic pattern with its ore grade. This means that as <strong>the</strong> ore grade 

2 xm replaces x in Eq. 5.3.4 for obtaining <strong>the</strong> concentration exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> in <strong>the</strong> mine 

3 xc replaces x in Eq. 5.3.4 for obtaining <strong>the</strong> concentration exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> in <strong>the</strong> R.E. 

j


35 

30 

25 

20 

15 

10 

5 

b c, MJ/kmole 

0 

0,00001 0,15 0,4 0,65 0,9 

xi 

Figure 5.1. <strong>Exergy</strong> required for separating a substance from a mixture, according to 

Eq. 5.10. 

tends to zero, <strong>the</strong> energy needed to extract <strong>the</strong> <strong>mineral</strong> tends to infinity. Right that 

component <strong>of</strong> <strong>the</strong> <strong>mineral</strong>’s exergy is what makes exergy a more realistic measure <strong>of</strong> 

magnitude than mass, for instance [392]. Fur<strong>the</strong>rmore, it invalidates <strong>the</strong> statement 

<strong>of</strong> Brooks and Andrews [41] that exhaustion <strong>of</strong> <strong>mineral</strong>s is ridiculous because <strong>the</strong> 

entire planet is composed <strong>of</strong> <strong>mineral</strong>s. The energy that nature saves us when concentrating 

<strong>mineral</strong>s in high grade ores, is too elevated to reproduce it with current 

technology. 

The unit exergies are converted into absolute ones (here denoted by B ch and B c), by 

multiplying b ch and b c with <strong>the</strong> moles <strong>of</strong> <strong>the</strong> resource under consideration (n). The 

sum <strong>of</strong> B ch and B c, indicates <strong>the</strong> total exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> deposit (B t), including 

<strong>the</strong> chemical and concentration components (see Eq. 5.11). 

B t i = n i · b ch i + n i · b c i = B ch i + B c i 

5.3.3 The chemical energy and exergy <strong>of</strong> fossil fuels 

(5.11) 

Fossil fuels are a type <strong>of</strong> <strong>mineral</strong>s and <strong>the</strong>refore, <strong>the</strong>ir chemical and concentration 

exergies can be calculated with Eqs. 5.1 and 5.10. Liquid and gaseous fuels have 

<strong>the</strong> particularity, that <strong>the</strong>ir quality (grade) keeps nearly constant with extraction,


whereas solid <strong>mineral</strong>s don’t (<strong>mineral</strong>’s concentration decreases as <strong>the</strong> deposit is 

being exploited). Hence, for those cases, <strong>the</strong> concentration exergy is not so relevant 

than with o<strong>the</strong>r types <strong>of</strong> <strong>mineral</strong> resources and it will not be taken into account for 

our calculations. Fur<strong>the</strong>rmore, <strong>the</strong> value <strong>of</strong> fuels is tightly related to its chemical 

exergy content. 

The heterogeneity and complexity <strong>of</strong> <strong>the</strong> chemistry <strong>of</strong> fuels make <strong>the</strong> chemical exergy 

to be very difficult to predict with Eq. 5.1. But different <strong>the</strong>rmodynamic models 

have been proposed to calculate <strong>the</strong> exergy <strong>of</strong> fossil fuels. Stepanov [330], compiles 

some <strong>of</strong> <strong>the</strong> different methodologies proposed. Rant [275], for instance, calculated 

<strong>the</strong> ratios <strong>of</strong> exergies to heating values and <strong>the</strong>n estimated average values <strong>of</strong> <strong>the</strong>se 

ratios for liquid and gaseous fuels 4 . Szargut and Styrylska [342] corrected Rant’s 

formulas by taking into consideration <strong>the</strong> chemical composition <strong>of</strong> fuels. Shieh and 

Fan [310] obtained expressions for <strong>the</strong> exergy calculation <strong>of</strong> materials with complex 

structures. We will focus on <strong>the</strong> models developed by Valero and Lozano [369] 

for obtaining <strong>the</strong> chemical exergy <strong>of</strong> fossil fuels, but it must be pointed out, that 

more complex calculation procedures, do not mean more reliable results. Both, <strong>the</strong> 

experimental error associated to <strong>the</strong> determination <strong>of</strong> <strong>the</strong> heating values and <strong>the</strong> 

error associated to <strong>the</strong> correlations are comprised reasonably in an interval close to 

±2 %. Additionally, it has been largely demonstrated, that <strong>the</strong> chemical exergy <strong>of</strong> 

fuels can, in many cases, be satisfactorily approximated to <strong>the</strong> HHV. 

For <strong>the</strong> case <strong>of</strong> gaseous fuels, Valero and Lozano [369], showed that <strong>the</strong> chemical 

exergy can be estimated as <strong>the</strong> exergy <strong>of</strong> a mixture <strong>of</strong> ideal gases (Eq. 5.12). 

 

bch gas = xi(b 0 

ch i + ¯RT 0lnx i) (5.12) 

Where xi is <strong>the</strong> molar fraction <strong>of</strong> <strong>the</strong> chemical substance i and b0 chemical exergy <strong>of</strong> substance i. 

ch i 

is <strong>the</strong> standard 

The exergy for gaseous fuels can thus be calculated with Eq. 5.12, or with <strong>the</strong> general 

methodology applied to liquid and solid fuels, explained next. 

The procedure is based on <strong>the</strong> general molecular formula <strong>of</strong> Eq. 5.13. 

CH hO oN nS s + W w + Z z 

(5.13) 

Where W represents <strong>the</strong> moles <strong>of</strong> liquid water (moisture) and Z <strong>of</strong> <strong>the</strong> ashes. Coefficients 

h, o, n, s, w and z are <strong>the</strong> moles <strong>of</strong> elements H, O, N, S, water and ashes 

contained in <strong>the</strong> molecular structure <strong>of</strong> <strong>the</strong> fuel, per mole <strong>of</strong> C content, respectively: 

h = H 12,011 

C 1,008 

s = S 12,011 

C 32,064 

o = O 12,011 

C 15,999 

W 12,011 

w = 

C 18,015 

n = N 12,011 

C 14,007 

z = Z 12,011 

C 1,000 

4 The ratios determined by Rant were 0,975 for liquid fuels and 0,95 for gaseous fuels. This 

indicates that <strong>the</strong> chemical exergy is very close to <strong>the</strong> high heating value <strong>of</strong> <strong>the</strong> substance.


Note that W and Z apply only to solid fossil fuels and s = 0 in gaseous fuels. The 

standard average energy and exergy <strong>of</strong> <strong>the</strong> fuel on a molar basis is <strong>the</strong>n: 

And e 0 

i 

and b0 

i 

Where ∆H 0 

f ,i 

e 0 

f uel = e0 

CH + we 

hOoNnS s 0 

W + ze0 Z 

b 0 

f uel = b0 

CH + w b 

hOoNnS s 0 

W + z b0 

Z 

are calculated as follows: 

b 0 

i 

e 0 

i 

= ∆H0 f ,i − 

 

f jH j,00 

= ∆H0 f ,i − T 0 s 0 

i − 

 

f jµ j,00 

(5.14) 

(5.15) 

(5.16) 

(5.17) 

and s0 

i are <strong>the</strong> standard enthalpy and entropy <strong>of</strong> <strong>the</strong> fuel, T 0 <strong>the</strong> stan- 

dard ambient temperature, f j <strong>the</strong> elements <strong>of</strong> <strong>the</strong> atomic composition vector <strong>of</strong> <strong>the</strong> 

fuel f = [1, h, o, n, s] ′ , and H j,00 and µ j,00 <strong>the</strong> enthalpy and <strong>the</strong> chemical potential 

<strong>of</strong> <strong>the</strong> elements in <strong>the</strong> dead state. 

The atomic composition vector <strong>of</strong> a gaseous fuel f j,gas, can be obtained with Eq. 

5.18: 

f j,gas = 

n 

i=1 r j,i · ξ i 

d 1 

(5.18) 

Being r j,i <strong>the</strong> number <strong>of</strong> atoms j contained in component i <strong>of</strong> <strong>the</strong> mixture <strong>of</strong> gases 

and ξ i <strong>the</strong> molar composition <strong>of</strong> substance i in <strong>the</strong> fuel 5 . The moles <strong>of</strong> C contained 

in <strong>the</strong> fuel is expressed as d 1 and is calculated as n 

i=1 r C,i · ξ i. 

The formation enthalpy can be calculated with <strong>the</strong> high or low heating values (HHV, 

LHV), using <strong>the</strong> following expressions: 

∆H 0 

f ,f uel = HHV + ∆H f ,CO 2 + h 

2 ∆H0 

f ,(H 2O) l + s∆H 0 

f ,SO 2 

 

h 

HHV = LHV + 

2 

 

+ w ∆H 0 

− ∆H f ,(H2O) g 0 

 

f ,(H2O) l 

(5.19) 

(5.20) 

In case <strong>the</strong> experimental heating values are not available, <strong>the</strong>y can be approximated 

through <strong>the</strong> following expressions: 

5 Gaseous fuels are assumed to contain <strong>the</strong> following 7 gases: CH4, C 2H 6, C 3H 8, C 4H 10, C 5H 12, N 2 

and CO 2.


Liquid fossil fuels. Lloyd’s correlation [198] in cal/mole C: 

HHV = 102720 + 27360 · h − 32320 · o + 19890 · n + 85740 · s (5.21) 

Solid fossil fuels. Boie correlation [279] in cal/ mole C: 

HHV = 100890 + 27990 · h − 42400 · o + 21010 · n + 80160 · s (5.22) 

For gaseous fuels, ∆H 0 

f 

can be calculated with <strong>the</strong> following equation: 

∆H 0 

f ,f uel = 

ξi · ∆H 0 

f ,i 

d 1 

(5.23) 

The standard entropy is calculated with <strong>the</strong> correlations proposed by Ikumi [158] 

for liquid fossil fuels and those <strong>of</strong> Eisermann, Johnson and Conger [83] for solid 

fuels. 

Liquid fossil fuels, in cal/(mole C· K): 

s 0 

f uel = 1, 12 + 4, 40 · h + 10, 66 · o + 20, 56 · n + 20, 70 · s (5.24) 

Solid fossil fuels, in cal/(mole C· K): 

s 0 

 

 

h 

o 

 

 

n 

 

 

s 

 

= 8, 88272 − 7, 5231e−0,56482 1+n + 4, 80748 + 12, 9807 + 10, 6767 

f uel 1 + n 

1 + n 

1 + n 

(5.25) 

Gaseous fossil fuels, in cal/(mole C· K): 

s 0 

f uel = 

 

0 

ξi si − ¯Rln( Pi P0 ) 

d 1 

(5.26) 

The calculation <strong>of</strong> <strong>the</strong> enthalpy and chemical potential for each element (H j,00 and 

µ j,00) are calculated with Eqs. 5.27 and 5.28 and depends on <strong>the</strong> species composing 

<strong>the</strong> reference environment. 

H j,00 = ∆H f , j + ∆C p, j 

T0 − T 0 

 

µ j,00 = ∆H f , j − T0∆s j + ∆Cp, j T0 − T 0 − T0ln T0 T 0 

 

x j,00 · P0 + ¯RT 0ln 

P0 

(5.27) 

(5.28)


Where x j,00 is a vector, including <strong>the</strong> molar concentration <strong>of</strong> <strong>the</strong> gases in <strong>the</strong> reference 

environment, ∆H f ,j, ∆s j and ∆C p,j are <strong>the</strong> enthalpy and entropy <strong>of</strong> formation 

and <strong>the</strong> specific heat change <strong>of</strong> <strong>the</strong> species in <strong>the</strong> reference environment required to 

form <strong>the</strong> element as in equations 5.29 and 5.30. Subscript 0 denotes <strong>the</strong> environment, 

while superscript 0, <strong>the</strong> standard reference environment. 

Lozano [201] proposed <strong>the</strong> three R.E. (I, II and III) shown in table 5.5, for calculating 

<strong>the</strong> chemical energy and exergy <strong>of</strong> <strong>the</strong> substances: 

Table 5.5. Composition <strong>of</strong> <strong>the</strong> three R.E. proposed 

I II III 

(j=1) C ↔(jj=1) CO 2 (g) CO 2 (g) CO 2 (g) 

(j=2) H ↔(jj=2) H 2O (g) H 2O (l) H 2O (l) 

(j=3) O ↔(jj=3) O 2 (g) O 2 (g) O 2 (g) 

(j=4) N ↔(jj=4) N 2 (g) N 2 (g) N 2 (g) 

(j=5) S ↔(jj=5) SO 2 (g) SO 2 (g) CaSO 4 · 2H 2O (s) 

(j=6) Ca ↔(jj=6) CaCO 3 (s) 

For R.E. I and II, ∆H f ,j is calculated as in Eqs. 5.29. The expression for <strong>the</strong> calculation 

<strong>of</strong> ∆s j and ∆C p, j are analogous to that <strong>of</strong> ∆H f , j. Note that for element H, <strong>the</strong> 

enthalpy and specific heat taken for H 2O must be in <strong>the</strong> gaseous and liquid state for 

R.E. I and II, respectively. 

(j = 1) C : ∆H f ,C = ∆H f ,CO2 − ∆H f ,O2 

(j = 2) H : ∆H f ,H = ∆H f ,H 2O 

2 

(j = 3) O : ∆H f ,O = ∆H f ,O 2 

2 

− ∆H f ,O 2 

4 

(j = 4) N : ∆H f ,N = ∆H f ,N 2 

2 

(j = 5) S : ∆H f ,S = −∆H f ,O2 + ∆H f ,SO2 

For R.E. III, <strong>the</strong> following expressions are valid: 

(5.29)


(j = 1) C : ∆H f ,C = ∆H f ,CO2 − ∆H f ,O2 

(j = 2) H : ∆H f ,H = ∆H f ,H 2O 

2 

(j = 3) O : ∆H f ,O = ∆H f ,O 2 

2 

(j = 4) N : ∆H f ,N = ∆H f ,N 2 

2 

− ∆H f ,O 2 

4 

(j = 5) S : ∆H f ,S = ∆H f ,CO2 − 2∆H f ,H2O − 3∆H f ,O 2 

2 

(j = 6) Ca : ∆H f ,Ca = −∆H f ,CO2 − ∆H f ,O 2 

2 

The resolution <strong>of</strong> Eq. 5.28 is given in table 5.6. 

+ ∆H f ,CaCO3 

(5.30) 

+ ∆H f ,CaSO4·2H2O − ∆H f ,CaCO3


Table 5.6. Calculation <strong>of</strong> <strong>the</strong> chemical potential <strong>of</strong> <strong>the</strong> elements according to three different R.E. 

Element j C H O N S Ca C H O N S Ca C H O N S Ca 

∆H f ,j, cal/mole ∆Cp, j, cal/(mole K) ∆s j, (cal/ mole K) 

R.E. I -94052 -28898 0 0 -70960 0 1,855 2,259 3,508 3,481 2,515 0 2,065 10,302 24,502 22,885 10,285 0 

R.E. II -94052 -34158 0 0 -70960 0 1,855 7,245 3,508 3,481 2,515 0 2,065 -3,876 24,502 22,885 10,285 0 

R.E. III -94052 -34158 0 0 -152032 -194398 1,855 7,245 3,508 3,481 -12,717 1,702 2,065 -3,876 24,502 22,885 -31,77 -53,373 

e1 e2 e3 

R.E. I 1 0 0 0 0 0 0 0,5 0 0 0 0 -1 -0,25 0,5 0 -1 0 

R.E. II 1 0 0 0 0 0 0 0 0 0 0 0 -1 -0,25 0,5 0 -1 0 

R.E. III 1 0 0 0 1 -1 0 0 0 0 0 0 -1 -0,25 0,5 0 -1,5 -0,5 

e4 e5 µ j,00, cal/mole 

R.E. I 0 0 0 0,5 0 0 0 0 0 0 1 0 -98546 -32760 -7777 -6902 -85372 0 

R.E. II 0 0 0 0,5 0 0 0 0 0 0 1 0 -98546 -32767 -7777 -6902 -85372 0 

R.E. III 0 0 0 0,5 0 0 0 0 0 0 0 0 -98546 -32767 -7777 -6902 -145967 -173192 

 

(5.31) 

+ ¯RT 0ln (x CO2,00 · P 0) e1 · (x H2O,00 · P 0) e2 · (x O2,00 · P 0) e3 · (x N2,00 · P 0) e4 · (x SO2,00 · P 0) e5 

 

T0 − T 0 − T0ln T0 T 0 

µ j,00 = ∆H f , j − T 0∆s j + ∆C p, j 

Where: e1, e2, e3, e4 and e5 are <strong>the</strong> exponentials used to calculate <strong>the</strong> contribution <strong>of</strong> <strong>the</strong> entropy change for gaseous reference substances. x j,00 is calculated 

with <strong>the</strong> following equations for each gaseous component [11]: xCO2,00 = 0, 0003(1 − xH2O,00); xO2,00 = 0, 2099(1 − xH2O,00); xN2,00 = 0, 7898(1 − xH2O,00); xSO2,00 = 10−9 

0,01 

(1 − xH2O,00); xH2O,00 = Pv,H2O(T 0) = 217, 99ex p (374, 16 − t0) 8 i=1 Fi(0, 65 − 0, 01τ0) 1−1 

 

T 0 

τ 0 = T 0 − 273, 15; F 1 = −741, 9242; F 2 = −29, 7210; F 3 = −11, 55286; F 4 = −0, 868535; F 5 = 0, 1094098; F 6 = 0, 439993; F 7 = 0, 2520658


If <strong>the</strong> ambient temperature is different to that <strong>of</strong> <strong>the</strong> standard, <strong>the</strong>n b 0 

i is replaced 

by b i in Eq. 5.15 (see Eq. 5.32). And b i is calculated with Eq. 5.33. Similarly, e 0 

i is 

replaced by e i in Eq. 5.14 and e i is calculated with Eq. 5.34. 

b f uel = b CHhO oN nS s + w · b W + z · b Z 

 

bi = ∆H f ,i − T0si − f jµ j,00 

 

ei = ∆H f ,i − f jµ j,00 

(5.32) 

(5.33) 

(5.34) 

The enthalpy and entropy <strong>of</strong> <strong>the</strong> clean fuel and <strong>the</strong> moisture for liquid and solid fuels 

is obtained with Eqs. 5.35 and 5.36. 

∆H f ,i = ∆H 0 

f ,i + 

s i = s 0 

i + 

T 

T 0 

T 

T 0 

C p(T)d T (5.35) 

Cp(T) d T (5.36) 

T 

The specific heat for liquid fuels at a density <strong>of</strong> 15 ◦ C (ρ 15) comprised in an interval 

between 0,75 and 0,96 kg/dm 3 , can be obtained through Eq. 5.37 in cal/(kgK) 

[258]. 

Cp,L(T) = 1 

(181 − 0, 81T) (5.37) 

ρ15 

The specific heats in cal/(kgK) for <strong>the</strong> clean solid fuel, <strong>the</strong> moisture W and <strong>the</strong> ashes 

Z are calculated with <strong>the</strong> correlations <strong>of</strong> Kirov 6 [258]: 

C p,F(T) = −52 + 0, 909T − 0, 420 · 1 −3 T 2 

C p,W (T) = 703 + 0, 632T + 9, 610 · 10 6 /T 2 

(5.38) 

(5.39) 

C p,Z(T) = 142 + 0, 140T (5.40) 

The exergy <strong>of</strong> <strong>the</strong> ashes Z is obtained directly through Eq. 5.41: 

6 Note that Cp,L, C p,F and C p,W must be converted into cal/mole K for <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> enthalpy 

and entropy.


b Z = 

T 

CZ T0 The enthalpy <strong>of</strong> gaseous fuels can be calculated with Eq. 5.42: 

∆H f ,i = ∆H 0 

f ,i + 

 

1 − T 

0 

d T (5.41) 

T 

n 

i=1 x i 

 

∗ hi (T) − h∗ 

i (T 0 ) 

d1 (5.42) 

Where h∗ i (T) is obtained with <strong>the</strong> help <strong>of</strong> <strong>the</strong> method <strong>of</strong> Zelenik and Gordon [413]: 

h ∗ 

 

T 

i (T) = RT a1 + a2 2 + a T 

3 

2 

3 + a T 

4 

3 

4 + a5 T 4 

5 + a6 T 

The entropy <strong>of</strong> <strong>the</strong> gaseous fuel can be calculated with Eq. 5.44: 

s = 

n i=1 x 

∗ 

i si (T) − Rln Pi P0 

d1 Where s∗ i (T) is obtained through [413] with Eq. 5.45 

s ∗ 

i (T) = R 

 

a 1lnT + a 2T + a 3 

T 2 

2 + a 4 

T 3 

3 + a 5 

T 4 

4 + a 7 

 

 

(5.43) 

(5.44) 

(5.45) 

Coefficients a1 through a7 for <strong>the</strong> calculation <strong>of</strong> h∗ (T) and s∗ i (T) are provided in 

table A.16 in <strong>the</strong> appendix for <strong>the</strong> different gases composing <strong>the</strong> gaseous fuel. 

From Eqs. 5.17 through 5.32, one can conclude that <strong>the</strong> exergy <strong>of</strong> fuels is a function 

<strong>of</strong> <strong>the</strong> conditions <strong>of</strong> <strong>the</strong> ambient. This means, that if <strong>the</strong> temperature, pressure or <strong>the</strong> 

concentration <strong>of</strong> for instance CO 2 change, <strong>the</strong> exergy <strong>of</strong> fuels will do so accordingly. 

5.3.4 The exergy costs 

The sum <strong>of</strong> <strong>the</strong> chemical and concentration components defined previously in section 

5.3.2 represents <strong>the</strong> total exergy that can be understood as <strong>the</strong> minimum energy 

required for restoring <strong>the</strong> resource from <strong>the</strong> reference environment. 

As stated before, fuel <strong>mineral</strong>s are useful for <strong>the</strong>ir inherent chemical exergy. Consequently, 

<strong>the</strong> value associated to fossil fuels is tightly related to its exergy. However, 

non-fuel <strong>mineral</strong>s are not necessarily useful for <strong>the</strong>ir chemical exergy content. The 

value <strong>of</strong> a non-fuel <strong>mineral</strong> resource is ra<strong>the</strong>r associated to <strong>the</strong> extraction costs. A 

very abundant and concentrated <strong>mineral</strong> in <strong>the</strong> crust, such as iron, will have a high 

exergy value and a low exergy cost <strong>of</strong> extraction. On <strong>the</strong> contrary, a very dispersed


and scarce <strong>mineral</strong> such as gold, has a low exergy value, but a very high exergy cost 

<strong>of</strong> extraction. Obviously, <strong>the</strong> cost is a very important ingredient <strong>of</strong> <strong>the</strong> final price in 

<strong>the</strong> market and that is why scarce <strong>mineral</strong>s tend to be <strong>the</strong> most expensive ones. 

The exergy replacement cost (B ∗ ) <strong>of</strong> <strong>mineral</strong>s measures something similar to <strong>the</strong>ir 

natural cost. It was defined by Valero et al. [370] as <strong>the</strong> exergy required by <strong>the</strong> given 

available technology to return a resource from <strong>the</strong> dispersed state <strong>of</strong> <strong>the</strong> reference 

environment, into <strong>the</strong> physical and chemical conditions in which it was delivered by 

<strong>the</strong> ecosystems. Actual energy requirements to obtain a resource are always greater 

than those dictated by <strong>the</strong> second law. 

For instance, <strong>the</strong> <strong>the</strong>rmodynamic energy required to separate two substances such 

as sugar and salt, is equal to <strong>the</strong> energy to mix <strong>the</strong>m, which is in fact very low. 

This is <strong>the</strong> reason why concentration exergies <strong>of</strong> <strong>mineral</strong>s are usually one order <strong>of</strong> 

magnitude greater than chemical ones. However, current processes are far from ideal 

conditions because <strong>of</strong> inefficiencies <strong>of</strong> our technology resulting in irreversibilities. 

In order to overcome that problem, we must include <strong>the</strong> actual physical unit costs, 

here named as unit exergy replacement costs, in <strong>the</strong> <strong>the</strong>rmodynamic evaluation <strong>of</strong> 

resources. Valero et al. [370] defined <strong>the</strong>m as <strong>the</strong> relationship between <strong>the</strong> energy 

invested in <strong>the</strong> actual process for obtaining <strong>the</strong> resource and <strong>the</strong> minimum energy 

required if <strong>the</strong> process were reversible. Unit exergy replacement costs are dimensionless 

and measure <strong>the</strong> number <strong>of</strong> exergy units needed to obtain one unit <strong>of</strong> exergy <strong>of</strong> 

<strong>the</strong> product. 

The actual exergy value <strong>of</strong> a resource (total exergy replacement cost) B ∗ is determined 

<strong>the</strong>n by <strong>the</strong> sum <strong>of</strong> B c and B ch multiplied respectively by <strong>the</strong> unit exergy 

replacement costs <strong>of</strong> <strong>the</strong> processes to obtain it (k ch and k c) as in Eq. 5.46. 

B ∗ 

t = k ch · B ch + k c · B c 

(5.46) 

Where k c is <strong>the</strong> physical unit exergy replacement cost <strong>of</strong> concentration, calculated as 

<strong>the</strong> ratio between <strong>the</strong> real energy invested in <strong>the</strong> process and <strong>the</strong> minimum concentration 

exergy (B c). It has to be determined for each type <strong>of</strong> <strong>mineral</strong>. It is assumed 

that <strong>the</strong> same technology is applied in all concentration ranges, including <strong>the</strong> range 

between <strong>the</strong> concentration <strong>of</strong> <strong>the</strong> reference environment and <strong>the</strong> average concentration 

in <strong>the</strong> <strong>mineral</strong> deposits. 

And k ch is <strong>the</strong> physical unit exergy replacement cost <strong>of</strong> <strong>the</strong> refining process, calculated 

as <strong>the</strong> ratio between <strong>the</strong> real energy invested in <strong>the</strong> process, and <strong>the</strong> minimum 

chemical exergy (B ch). As opposed to k c, <strong>the</strong> chemical unit cost <strong>of</strong> refining a <strong>mineral</strong> 

from <strong>the</strong> mine to <strong>the</strong> metallic state cannot be applied to <strong>the</strong> process <strong>of</strong> refining <strong>the</strong> 

<strong>mineral</strong> from <strong>the</strong> R.E. to <strong>the</strong> mine, due to <strong>the</strong> differences <strong>of</strong> both processes. However, 

once <strong>the</strong> refining costs <strong>of</strong> <strong>mineral</strong> oxides and sulfides were analyzed, Valero and 

Botero [371] realized that on average, <strong>the</strong> energy expenditure for obtaining a ton <strong>of</strong> 

<strong>the</strong> pure element from <strong>the</strong> oxide was about 80 GJ greater than from <strong>the</strong> sulfide. This


is as if sulfides would have a natural bonus <strong>of</strong> 80 GJ/ton and a chemical unit exergy 

replacement cost k ch <strong>of</strong> 10 on average. On <strong>the</strong> o<strong>the</strong>r side, oxides and monatomic 

<strong>mineral</strong>s are assumed to have a k ch at least equal to one. 

The contribution <strong>of</strong> <strong>the</strong> chemical and concentration components to <strong>the</strong> actual exergy 

value <strong>of</strong> a resource is usually well balanced, since unit chemical exergy costs are one 

or two orders <strong>of</strong> magnitude smaller than unit concentration exergy costs. 

Note that it has no sense to apply exergy replacement costs to fossil fuels, due to <strong>the</strong> 

impossibility <strong>of</strong> current technology to replace <strong>the</strong> photosyn<strong>the</strong>tic process that once 

created <strong>the</strong> resource. 

Table 5.7 shows <strong>the</strong> unit exergy replacement costs <strong>of</strong> some <strong>mineral</strong>s, according to 

Valero and Botero [371], which in turn were improved from <strong>the</strong> initial ones given 

by Botero [34]. Martínez et al. [207] studied additionally <strong>the</strong> unit exergy costs for 

some <strong>mineral</strong>s <strong>of</strong> industrial importance and updated Botero’s values <strong>of</strong> aluminium, 

gold, iron, zinc, lead, copper, nickel and silver. 

Table 5.7: <strong>Exergy</strong> costs <strong>of</strong> selected substances [371] & [207] 

Substance k c k ch Substance k c k ch 

Ag 7042 10 M n 284 1 

Al 2250 8,0 M o 947 1 

As 80 10 N a 38 1 

Au 422879 1 N b N.A. 1 

Ba N.A. 1 N i 432 58,2 

Be 112 1 P 44 1 

Bi 90 10 P b 219 25,4 

Cd 804 10 P t N.A. 1 

Co 1261 10 Re 1939 10 

C r 37 1 S b 28 10 

Cs N.A. 1 Se N.A. 1 

Cu 343 80,2 Si 2 1 

F 2 1 Sn 1493 1 

Fe 97 5,3 Ta 12509 1 

Ga N.A. 1 Te N.A. 1 

Ge N.A. 1 T i 348 1 

H f N.A. 1 U 7723 188,3 

H g 1707 10 V 572 1 

In N.A. 10 W 3105 1 

K 39 1 Zn 126 13,2 

Li 158 1 Z r 7744 1 

M g 1 1 

<strong>Exergy</strong> replacement costs represent a suitable indicator for assessing <strong>the</strong> value <strong>of</strong> 

non-fuel <strong>mineral</strong> resources, as <strong>the</strong>y integrate in one parameter, concentration, composition 

and also <strong>the</strong> state <strong>of</strong> technology. Never<strong>the</strong>less, as opposed to exergy, <strong>the</strong>y


cannot be considered as a property <strong>of</strong> <strong>the</strong> resource, since unit exergy costs introduce 

to some extent an uncertain factor to <strong>the</strong> calculation. Something similar happens to 

<strong>the</strong> emergy analysis, explained in section 1.3, through <strong>the</strong> introduction <strong>of</strong> <strong>the</strong> transformities. 

It should be noted that as stated by Naredo and Valero [239], unit exergy 

replacement costs are a function <strong>of</strong> <strong>the</strong> state <strong>of</strong> technology and hence vary with time. 

A way to assess <strong>the</strong> <strong>evolution</strong> <strong>of</strong> technological development, is through <strong>the</strong> <strong>the</strong>ory <strong>of</strong> 

learning curves. With learning-by-doing, increases in material and energy efficiency 

increase with cumulative production. Alchian [5] was <strong>the</strong> first to estimate <strong>the</strong> effects 

<strong>of</strong> cumulative production on changes in efficiency. He found a linear relationship 

between <strong>the</strong> logarithm <strong>of</strong> direct labor inputs per unit output and <strong>the</strong> logarithm <strong>of</strong> 

cumulative production, as in Eqs. 5.47. 

ln j(t) = a j1 − a j2lnΓ(t) 

lne(t) = a e1 − a e2lnΓ(t) (5.47) 

With j(t) and e(t), <strong>the</strong> flows <strong>of</strong> materials and energy used to perform a certain 

process; a j1 and a e1 <strong>the</strong> intercepts <strong>of</strong> <strong>the</strong> learning curve with <strong>the</strong> vertical axes and 

a j2 and a e2 parameters relating material and energy inputs per unit output at time 

period t to cumulative production in period t, Γ(t). 

Ruth [294] argued that such a specification <strong>of</strong> <strong>the</strong> learning curves, allows materials 

and energy input per unit output to approach zero as cumulative production approaches 

infinity, thus violating <strong>the</strong>rmodynamic lower limits on j(t) and e(t). The 

expressions <strong>of</strong> Eqs. 5.48 are according to Ruth more realistic in <strong>the</strong> sense that material 

and energy efficiencies decrease asymptotically towards zero in double-log space 

as Γ(t) approaches infinity. Thus as cumulative production increases, material and 

energy use per unit output can at best assume <strong>the</strong> value one, indicating perfect efficiency. 

ln j(t) = a j1ex p(−a j2lnΓ(t)) 

lne(t) = a e1ex p(−a e2lnΓ(t)) (5.48) 

In this PhD, we have considered unit exergy replacement costs constant, i.e. we have 

assumed that <strong>the</strong> state <strong>of</strong> technology has been <strong>the</strong> same throughout <strong>the</strong> 20 th century. 

A more exact determination <strong>of</strong> <strong>the</strong> exergy costs <strong>of</strong> <strong>mineral</strong>s throughout history would 

imply changing unit exergy replacement costs. These could be calculated through 

<strong>the</strong> help <strong>of</strong> <strong>the</strong> learning curves explained above. But this task remains outside <strong>the</strong> 

scope <strong>of</strong> this PhD and is open for fur<strong>the</strong>r refinements.


5.4 Prediction <strong>of</strong> Enthalpy and Gibbs free energy <strong>of</strong> 

formation <strong>of</strong> <strong>mineral</strong>s 

The determination <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> substances requires <strong>the</strong> 

knowledge <strong>of</strong> <strong>the</strong>ir corresponding enthalpies and Gibbs free energies <strong>of</strong> formation. 

Many <strong>of</strong> <strong>the</strong>se have been already estimated through empirical and semi-empirical 

processes 7 and are tabulated. Comprehensive compilations <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic 

properties <strong>of</strong> inorganic substances can be found in Faure [94], Wagman [391], Robie 

et al. [284], [285] or Weast et al. [400]. 

Unfortunately, not all <strong>the</strong> enthalpies and Gibbs free energies <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s that 

we have taken into account in our model are recorded in <strong>the</strong> literature. Never<strong>the</strong>less, 

many <strong>of</strong> <strong>the</strong>m can be predicted satisfactorily through different semi-empirical 

methods. In <strong>the</strong> next sections, <strong>the</strong> estimation methods <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties 

used to obtain <strong>the</strong> standard enthalpy and Gibbs free energy <strong>of</strong> formation <strong>of</strong> 

<strong>the</strong> <strong>mineral</strong>s in <strong>the</strong> model <strong>of</strong> <strong>the</strong> upper crust developed in chapter 3 will be provided. 

5.4.1 Calculation <strong>of</strong> ∆H 0 

f 

or ∆G0 

f 

from s0 

If ei<strong>the</strong>r ∆H 0 or ∆G0 

f f and <strong>the</strong> entropy (s0 ) <strong>of</strong> <strong>the</strong> <strong>mineral</strong> under consideration are 

available, <strong>the</strong> unknown property can be easily calculated applying Eq. 5.49. 

∆G 0 

f 

= ∆H0 

f − T 0 · ∆S (5.49) 

Where <strong>the</strong> entropy change ∆S is calculated from <strong>the</strong> standard entropy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> 

and its constituent elements in <strong>the</strong> standard state (T 0 = 298, 15 K and 1 bar), as in 

Eq. 5.50: 

∆S = s 0 

<strong>mineral</strong> − 

 

s 0 

elements 

(5.50) 

Note that this procedure does not have associated any error, since it is based on <strong>the</strong> 

definition <strong>of</strong> ∆G f . 

Example: for <strong>mineral</strong> bronzite FeM gSi2O 6, <strong>the</strong> enthalpy and entropy <strong>of</strong> formation 

is known from [309]: ∆H 0 

f = −2753, 38 kJ/mole and s0 = 149, 13 J/(mole K). The 

entropy change <strong>of</strong> bronzite is calculated as: 

∆sFeM gSi2O 6 = s 0 

FeM gSi − (s 

2O6 0 

M g + s0 

Fe + 2 · s0 

Si + 3 · s0 

O ) 

2 

= 149, 13 − (27, 09 + 32, 67 + 2 · 18, 81 + 3 · 205, 15) 

= −563, 70 J/(mole.K) 

7 Such as calorimetric or solubility measurements.

Prediction <strong>of</strong> Enthalpy and Gibbs free energy <strong>of</strong> formation <strong>of</strong> <strong>mineral</strong>s 173 

Where s0 are obtained from [284]. The Gibbs free energy <strong>of</strong> formation <strong>of</strong> 

elements 

bronzite can be finally calculated with Eq 5.49: 

∆G 0 

563, 70 

f ,FeM gSi = −2753, 38 − 298, 15 · = −2585, 31 kJ/mole 

2O6 1000 

5.4.2 The ideal mixing model 

An ideal solid solution <strong>of</strong> i components with x i molar fractions obeys <strong>the</strong> equations: 

and 

∆G m = +RT 

∆H m = 0 (5.51) 

 

x ilnx i 

(5.52) 

Where ∆H m and ∆G m, are <strong>the</strong> enthalpy and Gibbs free energy <strong>of</strong> mixing. This 

means that <strong>the</strong> ideal mixing will take place without any heat loss or heat production. 

Moreover, <strong>the</strong> different cations will be fully interchangeable [254]. The enthalpy 

and Gibbs free energy <strong>of</strong> formation <strong>of</strong> <strong>the</strong> solid solution is calculated <strong>the</strong>n with Eqs. 

5.53: 

∆G 0 

f ,solution = 

∆H 0 

f ,solution = 

 

i 

xi∆G 0 

f ,i + RT 

 

i 

x i∆H 0 

f ,i 

 

x ilnx i 

(5.53) 

The error associated to <strong>the</strong> assumption <strong>of</strong> <strong>the</strong> <strong>mineral</strong> as an ideal solid solution varies 

greatly with <strong>the</strong> <strong>mineral</strong> under consideration and decreases with <strong>the</strong> disorder among 

components. We will assume a maximum error <strong>of</strong> ±1%. 

Example: <strong>mineral</strong> tetradymite Bi2Te 2S can be considered as a solid solution <strong>of</strong> 

Bi2Te 3, and Bi2S3, for which ∆H 0 and ∆G0 are well known from [226] and [94]: 

f f 

Bi 2Te 2S ⇔ 2 

3 Bi 2Te 3 + 1 

3 Bi 2S 3 

Hence, ∆H 0 and ∆G0 are calculated as follows with Eqs: 5.53: 

f ,tet rad ymite f ,tet rad ymite


∆G 0 

f ,tet rad ymite 

∆H 0 

f ,tet rad ymite 

2 

= 

3 · ∆H f ,Bi + 2Te3 1 

3 ∆H f ,Bi2S3 = 2 

1 

· (−78, 7) + (−143, 2) 

3 3 

= −100, 2 kJ/mole 

2 

= 

3 · ∆G f ,Bi + 2Te3 1 

3 ∆G 

2 

f ,Bi + RT 

2S3 3 ln 

 

2 

+ 

3 

1 

3 ln 

 

1 

3 

= 2 

1 

8, 314 

· (−78, 3) + (−140, 7) + · 298, 15(−0, 63) 

3 3 1000 

= −100, 6 kJ/mole 

5.4.3 Assuming ∆G r and ∆H r constant 

5.4.3.1 Thermochemical approximations for sulfosalts and complex oxides 

Craig and Barton [67] developed an approximation method for estimating <strong>the</strong> <strong>the</strong>rmodynamic 

properties <strong>of</strong> sulfosalts in terms <strong>of</strong> mixtures <strong>of</strong> <strong>the</strong> simple sulfides. The 

ideal mixing model does not apply correctly to most sulfosalts, because <strong>the</strong> mixtures 

<strong>of</strong> layers are ra<strong>the</strong>r ordered. The modified ideal mixing model <strong>of</strong> Craig and Barton 

involves a mixing term (∆G m) in <strong>the</strong> estimation <strong>of</strong> <strong>the</strong> Gibbs free energy <strong>of</strong> formation 

<strong>of</strong> <strong>the</strong> sulfosalt per gram atom <strong>of</strong> S that is added to <strong>the</strong> weighted sum <strong>of</strong> free 

energies <strong>of</strong> <strong>the</strong> simple sulfides: 

∆G m = (1, 2 ± 0, 8)(+RT 

 

x ilnx i) (5.54) 

The mixing term can be divided into two parts, one estimated from <strong>the</strong> crystal structure 

as an entropy change, and <strong>the</strong> reminder as a non-ideal term. The non-ideal 

term <strong>of</strong> this model was assumed to be constant for all sulfosalts. However, Vieillard 

[387] showed that <strong>the</strong> properties <strong>of</strong> complex sulfides with respect to <strong>the</strong>ir simple 

sulfides are a function <strong>of</strong> <strong>the</strong> electronegativity difference between <strong>the</strong> cations <strong>of</strong> <strong>the</strong> 

sulfosalt. 

The <strong>the</strong>rmodynamic properties <strong>of</strong> sulfosalts may <strong>the</strong>n be calculated by adding a term 

(∆H r or ∆G r) to <strong>the</strong> appropriately weighted sum <strong>of</strong> <strong>the</strong> enthalpies or free energies 

<strong>of</strong> <strong>the</strong> simple component sulfides i (Eq. 5.55). 

 

∆H f sul f osal t = xi∆H f i + nS sul f osal t∆H r 

 

∆G f sul f osal t = xi∆G f i + nS sul f osal t∆G r 

(5.55)


The reaction term, which is analogous to <strong>the</strong> mixing term <strong>of</strong> Craig and Barton is 

associated to one atom <strong>of</strong> sulfur in <strong>the</strong> <strong>mineral</strong> (n S,sul f osal t) and is obtained from a 

sulfosalt for which its <strong>the</strong>rmodynamic properties and those <strong>of</strong> its simple sulfides are 

known. The calculated reaction terms can be applied to a family <strong>of</strong> sulfosalts formed 

by <strong>the</strong> same cations and with partial element substitutions. 

Example: <strong>mineral</strong> cubanite CuFe 2S 3 can be decomposed into <strong>the</strong> sulfides CuFeS 2 

and FeS, for which <strong>the</strong> <strong>the</strong>rmodynamic properties are provided [226]. The properties 

<strong>of</strong> cubanite can be calculated with Eq. 5.55, once ∆H r and ∆G r are known. The 

reaction terms are obtained from <strong>mineral</strong> bornite Cu 5FeS 4 as follows: 

∆H r,Cu5FeS 4 = ∆H f ,Cu 5FeS 4 − ( 5 

2 ∆H f ,Cu 2S + 1 

2 ∆H f ,Fe 2S 3 ) 

= (−371, 6) − [ 5 

2 

= −5, 48 kJ/mole S 

4 

(−83, 9) + 1 

2 

4 

(−279, 91)] 

∆Gr,Cu5FeS 4 = 

5 

1 

(−394, 7) − [ (−89, 2) + (−280, 75)] 

2 2 

4 

= −7, 83 kJ/mole S 

Where <strong>the</strong> properties <strong>of</strong> bornite and its constituents are provided in [284] and [241]. 

Hence, ∆H f and ∆G f <strong>of</strong> cubanite are calculated as: 

∆H f ,CuFe2S 3 = ∆H f ,CuFeS2 + ∆H f ,FeS + 3 · ∆H r 

= (−176, 8) + (−99, 98) + 3 · (−5, 48) 

= −293, 22 kJ/mole 

∆G f ,CuFe2S 3 = (−178, 49) + (−100, 40) + 3 · (−7, 83) 

= −302, 38 kJ/mole 

Vieillard et al. [387] demonstrated <strong>the</strong> analogy between <strong>the</strong> electronegativity scale 

<strong>of</strong> cations with respect to sulfur and to oxygen. They showed that <strong>the</strong> methodology 

<strong>of</strong> estimation <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> sulfosalts from simple sulfides can 

be equally applied to complex oxides able to be decomposed into simple oxides. As 

for sulfosalts, <strong>the</strong> reaction terms ∆H r and ∆G r (for this case denoted as ∆H ox and 

∆G ox) should be obtained for an oxide <strong>of</strong> <strong>the</strong> same family <strong>of</strong> <strong>the</strong> <strong>mineral</strong> under 

analysis. The maximum error associated to this methodology is assumed to be ±1%.


5.4.3.2 The method <strong>of</strong> corresponding states 

Similarly, <strong>the</strong> ∆H r and ∆G r can be assumed to be constant in <strong>the</strong> substitution reaction 

<strong>of</strong> <strong>mineral</strong>s A-x and B-x into A-y and B-y, if A-x and B-y are isomorphous (Eq. 

5.56). The associated error is assumed to be equal to <strong>the</strong> previous method, hence 

±1%. 

A − x + y → A − y + x (∆H r, ∆G r) 

B − x + y → B − y + x (∆H r, ∆G r) (5.56) 

Consider <strong>mineral</strong> fluor-annite K Fe 3(Si 3Al)O 10(F) 2 as an example, for which no 

empirical <strong>the</strong>rmodynamic values are available. Fluor-annite can be formed from 

hydroxy-annite K Fe 3(Si 3Al)O 10(OH) 2 as in <strong>the</strong> following reaction: 

K Fe 3(Si 3Al)O 10(OH) 2 + 2H F → K Fe 3(Si 3Al)O 10(F) 2 + 2H 2O 

Similarly, fluor-phlogopite can be formed from hydroxy-phlogopite. Since <strong>the</strong> <strong>the</strong>rmodynamic 

properties <strong>of</strong> both substances are known, <strong>the</strong> reaction energy <strong>of</strong> substitution 

can be calculated: 

K M g 3(Si 3Al)O 10(OH) 2 + 2H F → K M g 3(Si 3Al)O 10(F) 2 + 2H 2O 

∆Hr = ∆H 0 

+ 2∆H f ,K M g3(Si3Al)O 10(F) 2 0 

f ,H − ∆H0 

− 2∆H 

2O f ,K M g3(Si3Al)O 10(OH) 2 0 

f ,H F 

= (−6375, 5) + 2 · (−285, 8) − (−6246, 0) − 2 · (−332, 6) 

= −17, 9 kJ/mole H F 

∆Gr = ∆G 0 

+ 2∆G f ,K M g3(Si3Al)O 10(F) 2 0 

f ,H − ∆G0 

− 2∆G 

2O f ,K M g3(Si3Al)O 10(OH) 2 0 

f ,H F 

= (−6030, 1) + 2 · (−237, 1) − (−5860, 5) − 2 · (−278, 8) 

= −43, 11 kJ/mole H F 

Where <strong>the</strong> <strong>the</strong>rmodynamic properties are obtained from [391]. Fluor-annite can 

now be calculated, assuming <strong>the</strong> same reaction energy calculated with phlogopite:


∆H 0 

f ,K Fe3(Si 3Al)O10(F) 2 

= ∆H 0 

+ 2∆H f ,K Fe3(Si 3Al)O10(OH) 2 0 

f ,H F − 2∆H0 f ,H2O + 2∆Hr = (−5149, 3) + 2 · (−332, 6) − 2 · (−285, 8) + 2 · (−17, 9) 

= −5278, 8 kJ/mole 

∆G 0 

f ,K Fe3(Si 3Al)O10(F) 2 

= ∆G 0 

+ 2∆G f ,K Fe3(Si 3Al)O10(OH) 2 0 

f ,H F − 2∆G0 f ,H2O + 2∆Gr = (−4798, 3) + 2 · (−278, 8) − 2 · (−237, 1) + 2 · (−43, 11) 

= −4967, 9 kJ/mole 

The <strong>the</strong>rmodynamic properties <strong>of</strong> hydroxy-annite are obtained from [383]. 

5.4.4 The method <strong>of</strong> Chermak and Rimstidt for silicate <strong>mineral</strong>s 

The method proposed by Chermak and Rimstidt [55] predicts <strong>the</strong> <strong>the</strong>rmodynamic 

properties (∆G0 and ∆H0) 

<strong>of</strong> silicate <strong>mineral</strong>s from <strong>the</strong> sum <strong>of</strong> polyhedral oxide and 

f 

f 

hydroxide contributions. The technique is based on <strong>the</strong> observation that silicate <strong>mineral</strong>s 

have been shown to act as a combination <strong>of</strong> basic polyhedral units. Chermak 

and Rimstidt determined by multiple linear regression, <strong>the</strong> contribution <strong>of</strong> Al 2O [4] 

3 , 

, Al(OH)[6] 3 , SiO[4] 

2 , M gO[6] , M g(OH) [6] 

2 , CaO[6] , CaO [8−z] , N a2O [6−8] , 

K2O [8−12] , H2O, FeO [6] , Fe(OH) [6] 

2 and Fe2O [6] 

3 to <strong>the</strong> total ∆G0 and ∆H0 <strong>of</strong> a 

f f 

Al 2O [6] 

3 

selected group <strong>of</strong> silicate <strong>mineral</strong>s 8 . The <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s 

are calculated with Eqs. 5.57 and 5.58: 

∆H 0 

f = 

 

xi · hi ∆G 0 

f = 

 

xi · gi (5.57) 

(5.58) 

Where x i is <strong>the</strong> number <strong>of</strong> moles <strong>of</strong> <strong>the</strong> oxide or hydroxide per formula unit and h i 

and g i are <strong>the</strong> respective molar enthalpy and free energy contribution <strong>of</strong> 1 mole <strong>of</strong> 

each oxide or hydroxide component. Table A.17 in <strong>the</strong> appendix shows <strong>the</strong> values 

<strong>of</strong> h i and g i for <strong>the</strong> different polyhedral components described in <strong>the</strong> methodology 

[55]. 

The errors associated to <strong>the</strong> estimated vs. experimentally measured values can reach 

±1% for ∆G0 and ∆H0, 

depending on <strong>the</strong> nature <strong>of</strong> <strong>the</strong> compounds. Note that this 

f f 

methodology can only be applied to those <strong>mineral</strong>s able to be decomposed by <strong>the</strong> 

oxides and hydroxides mentioned before. 

8 The brackets next to <strong>the</strong> chemical formulas <strong>of</strong> oxides and hydroxides indicate <strong>the</strong> coordination 

number <strong>of</strong> <strong>the</strong> polyhedral structure.


Example: <strong>the</strong> properties <strong>of</strong> <strong>mineral</strong> thomsonite N aCa2Al 5Si5O20 · 6H2O are calculated 

as <strong>the</strong> sum <strong>of</strong> <strong>the</strong> gi and hi from its constituent oxides (N a2O [6−8] , CaO [8−z] , 

Al2O [4] 

3 , SiO[4] 

2 and H2O): ∆H 0 

f ,N aCa 2Al 5Si 5O 20·6H 2O 

∆G 0 

f ,N aCa 2Al 5Si 5O 20·6H 2O 

5.4.5 The ∆O −2 method 

1 

= 

2 hN a2O [6−8] + 2h 5 

CaO [8−z] + 

2 h Al2O [4] + 5h [4] + 6h 

3 SiO H2O 

2 

= 1 

5 

(−683, 00) + 2(−736, 04) + (−1716, 4) 

2 2 

+5(−910, 97) + 6(−239, 91) 

= −11543, 92 kJ/mole 

1 

5 

= (−672, 50) + 2(−710, 08) + (−1631, 32) 

2 2 

5 + (−853, 95) + 6(−292, 37) 

= −12413, 65 kJ/mole 

The linear additivity procedures based on <strong>the</strong> ∆O −2 parameter were developed by 

Yves Tardy and colleagues [348], [349], [350], [351], [352], [347], [108], [380], 

[383]. The parameter ∆O −2 , corresponds to <strong>the</strong> enthalpy ∆ HO −2 or Gibbs free 

energy ∆ GO −2 <strong>of</strong> formation <strong>of</strong> a generic oxide MO x(c) from its aqueous ion, where 

z + is <strong>the</strong> charge <strong>of</strong> <strong>the</strong> ion and x <strong>the</strong> number <strong>of</strong> oxygen atoms combined with one 

atom M in <strong>the</strong> oxide (x = z + /2): 

∆ HO −2 M z+ = 1 

x [∆H0 

∆ GO −2 M z+ = 1 

x [∆G0 

f MOx(c) − ∆H 0 

f 

f MOx(c) − ∆G 0 

f 

z+ 

M ] (5.59) 

(aq) 

z+ 

M ] (5.60) 

(aq) 

For hydroxides, silicates, phosphates, nitrates and carbonates involving two cations, 

it was found that <strong>the</strong> enthalpy and Gibbs free energy <strong>of</strong> formation <strong>of</strong> a given compound 

from its constituent oxides vary linearly with ∆O −2 and have <strong>the</strong> general 

expressions [347]: 

and 

∆H 0 

ox = α H 

∆G 0 

 

ni · nj ∆HO ni + nj 2− M z+ 

i 

i (aq) − ∆HO 2− M z+ 

j 

ox = α 

ni · n j 

G ∆GO ni + nj 2− M z+ 

i 

i (aq) − ∆GO 2− M z+ 

j 

j (aq) 

j (aq) 

 

 

(5.61) 

(5.62)


Being ∆H 0 

ox and ∆G0 ox : 

∆H 0 

ox [(M i) ni (M j) nj O N ] = ∆H 0 

f [(M i) ni (M j) nj O N ](c) − n i∆H 0 

f M iO xi (c) 

−n j∆H 0 

f M jO x j (c) (5.63) 

∆G 0 

ox [(M i) ni (M j) nj O N ] = ∆G 0 

f [(M i) ni (M j) n j O N ](c) − n 1∆G 0 

f M iO xi (c) 

−n 2∆G 0 

f M jO x j (c) (5.64) 

Where ni and nj are <strong>the</strong> numbers <strong>of</strong> oxygen ions linked, respectively, to <strong>the</strong> M z+ 

i 

i and 

M z+ 

j 

j cations; and N is <strong>the</strong> number <strong>of</strong> oxygens linked to <strong>the</strong> molecular structure <strong>of</strong> 

<strong>the</strong> double oxide (N = xi + x j). Parameters αH and αG are empirical coefficients 

variable from one family <strong>of</strong> compounds to ano<strong>the</strong>r one (αG is 0,84 for hydroxides, 

1,01 for silicates, 1,15 for carbonates, 1,30 for nitrates, etc.). 

Equation 5.62, yields a statistical deviation <strong>of</strong> 35 kJ/mole for <strong>the</strong> Gibbs free energy 

<strong>of</strong> formation and depends on <strong>the</strong> family <strong>of</strong> compounds. We will assume a maximum 

error associated to <strong>the</strong> ∆O 2− general method <strong>of</strong> ±1% 9 . 

Example: for <strong>the</strong> silicate Ca3Si 2O7, <strong>the</strong> α parameter was determined at -1,01 and 

∆GO−2 Ca2+ = −50, 31 and ∆GO−2Si 4+ = −188, 08 kJ/mole [350]; so that ∆G0 ox 

can be calculated with Eq. 5.64 as: 

And 

∆G 0 

ox (Ca3Si 2O7) = 

3 · 4 

(−1, 01) 

3 + 4 · [∆GO −2 Ca 2+ (aq) − ∆GO −2 Si 4+ (aq)] 

= −238, 5 kJ/mole 

∆G 0 

f (Ca3Si 2O7)(c) = 3∆G 0 

f CaO(c) + 2∆G0 f SiO2(c) +∆G 0 

ox (Ca3Si 2O7)(c) = −3748, 1 kJ/mole 

The value is close to ∆G 0 

f (Ca 3Si 2O 7) = −3760, 4 kJ/mole from Robie and Hemingway 

[284]. 

9 This methodology was later on improved by Vieillard ([380], [390], [381]) and Vieillard and 

Tardy [389], by introducing a new empirical parameter representing <strong>the</strong> electronegativity <strong>of</strong> <strong>the</strong> cation 

M z+ (comp).


5.4.5.1 The ∆O −2 method for hydrated clay <strong>mineral</strong>s and for phyllosilicates 

Vieillard extended <strong>the</strong> methodology described above for <strong>the</strong> prediction <strong>of</strong> hydrated 

clay <strong>mineral</strong>s [382] and for phyllosilicates [383]. 

Hydrated clay <strong>mineral</strong>s, have formulas expressed as: 

(Ml1 , Ml2 , Ml3 ) (M go1 , Fe2+ o , Alo3 , Fe 

2 3+ 

o ) (Si (4−t)Al t)O10(OH) 2. Layer silicates can be 

4 

<strong>of</strong> two types: (a) 2:1 layer type, (Mli , Moj )(Si (4−t)Al t)O10(OH) 2, with li <strong>the</strong> number 

<strong>of</strong> interlayer atom which varies from 0 (pyrophyllite, talc) to 1 (micas, if 

M = K + or N a + , brittle micas, if M = Ca2+ , or Ba2+ ) and (b) 2:1:1 layer type 

(Mo )Si j (4−t)Al t)O10(OH) 2 · (Mbk (OH) 6), where bk is <strong>the</strong> number <strong>of</strong> brucitic cations. 

Subscripts l, o, and t denote, respectively, <strong>the</strong> interlayer, octahedral, and tetrahedral 

sites. The possible cations occupying each site <strong>of</strong> <strong>the</strong> <strong>mineral</strong> can be seen in table 

A.18 for clays and phyllosilicates. 

The Gibbs free energy <strong>of</strong> formation <strong>of</strong> a hydrated clay <strong>mineral</strong> or a phyllosilicate 

composed by n s cations located in different sites and with n s(n s − 1)/2 interaction 

terms is calculated as: 

∆G 0 

f = 

i=n s 

(ni)∆G 0 

f (MiOxi ) + ∆G 0 

ox 

The Gibbs free energy <strong>of</strong> formation from <strong>the</strong> oxides ∆G0 which is analogous to Eq. 5.64: 

∆G 0 

ox = −N 

⎧ 

⎨ 

⎩ 

 

i=n s−1 

i=i 

j=n s 

j=i+1 

i=1 

ox 

(5.65) 

is calculated with Eq. 5.66, 

 

X iX j ∆GO 2− M zi+ i (cla y) − ∆GO 2− M z ⎬ 

j+ 

j (cla y) 

⎭ 

where N is <strong>the</strong> total number <strong>of</strong> O atoms <strong>of</strong> all oxides; X i and X j are <strong>the</strong> molar 

fraction <strong>of</strong> oxygen related to <strong>the</strong> cations M zi+ i and M z j+ 

j in <strong>the</strong> individual oxides 

MiOxi and MjO x , respectively (X j i = (1/N)(ni xi) and X j = (1/N)(n j x j)). Parameters 

M zi+ i (clay) and M z j+ 

j (clay) characterize <strong>the</strong> electronegativity <strong>of</strong> cations M zi+ i 

and M z j+ 

j in a specific site and are calculated by minimizing <strong>the</strong> difference between 

experimental Gibbs free energies and calculated ones from constituent oxides. Table 

A.18 in <strong>the</strong> appendix shows M zi+ i (clay) values for some <strong>of</strong> <strong>the</strong> main ions for hydrated 

clays and phyllosilicates. 

The predicted Gibbs free energy values showed an error between 0,0 and 0,6 %. 

⎫


5.4.5.2 The ∆O −2 method for different compounds with <strong>the</strong> same cations 

Tardy [347] showed that <strong>the</strong> Gibbs free energy <strong>of</strong> formation <strong>of</strong> a compound from 

its two constituent oxides calculated per one oxygen in <strong>the</strong> formula was a parabolic 

function <strong>of</strong> mean ∆O −2 compound. Subsequently, an expression for calculating <strong>the</strong> 

Gibbs free energy <strong>of</strong> formation <strong>of</strong> a compound C intermediate in composition to two 

compounds A and B, A + B → C was developed: 

 

∆Gox,A+B→C = +αG ∆GO 2− M z+ 

i 

i − ∆GO 2− M z+ 

 

j 

j nC(X C 

i 

A C 

− X i )(X i 

B 

− X i ) (5.66) 

where nc designates <strong>the</strong> total number <strong>of</strong> oxygens <strong>of</strong> <strong>the</strong> compound C and X A B 

i , X i , 

X C 

i <strong>the</strong> mole fractions <strong>of</strong> oxygen that balance cation M z+ 

i 

i in compounds A, B, and C 

and α <strong>the</strong> correlation parameter for a given class <strong>of</strong> compounds, as in Eq. 5.62. 

5.4.6 Assuming ∆S r zero 

Helgeson et al. [134] showed that <strong>the</strong> entropy <strong>of</strong> formation <strong>of</strong> <strong>mineral</strong> B can be 

determined, assuming that <strong>the</strong> entropy <strong>of</strong> <strong>the</strong> reaction involved in <strong>the</strong> formation <strong>of</strong> 

<strong>the</strong> <strong>mineral</strong> is zero (Helgeson’s algorithm). Helgeson algorithm is useful when ei<strong>the</strong>r 

∆G 0 

f 

or ∆H0 

f 

are known. Once <strong>the</strong> entropy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> is known, ∆G0 f 

(or ∆G0 

f f 

can be calculated with ∆H 0 

approximation is up to 5%. 

Example: 

(or ∆H0 

f ) 

) through Eq. 5.49. The error associated to this 

ThSiO 4 + UO 2 → USiO 4 + ThO 2 

s 0 ThSiO 4 = s 0 

USiO 4 + s 0 

ThO 2 − s 0 

UO 2 

= 118, 0 + 62, 2 − 77, 0 

= 106, 2 

5.4.7 Assuming ∆G r and ∆H r zero 

5.4.7.1 The element substitution method 

In some cases, <strong>the</strong>rmodynamic properties are available for a certain <strong>mineral</strong> (A), 

belonging to <strong>the</strong> same family <strong>of</strong> <strong>the</strong> substance under consideration (B), but with 

partial element substitutions. In such a case, <strong>the</strong> ∆H 0 and ∆G0 <strong>of</strong> <strong>mineral</strong> B can 

f f 

be calculated from <strong>mineral</strong> A, assuming that <strong>the</strong> reaction enthalpy or free energy


<strong>of</strong> formation <strong>of</strong> <strong>mineral</strong> B from A is zero. This approximation increases with <strong>the</strong> 

magnitude <strong>of</strong> substitution and may yield to associated errors <strong>of</strong> up to 5%, although 

it rarely exceeds ±2%. We will outline this method with an example. 

Consider <strong>the</strong> <strong>mineral</strong> hydrosodalite N a 8Al 6Si 6O 24(OH) 2, for which no empirical 

<strong>the</strong>rmodynamic values are available. Hydrosodalite can be formed from sodalite 

N a 8Al 6Si 6O 24(Cl) 2 as in <strong>the</strong> following reaction: 

N a 8Al 6Si 6O 24(OH) 2 + 2HCl → N a 8Al 6Si 6O 24(Cl) 2 + 2H 2O 

Assuming that <strong>the</strong> energy <strong>of</strong> reaction is zero, ∆H 0 

f 

calculated as: 

and ∆G0 

f 

<strong>of</strong> hydrosodalite are 

∆H 0 

f ,N a8Al6Si 6O24(OH) 2 

= ∆H 0 

+ 2 · ∆H f ,N a8Al6Si 6O24(Cl) 2 0 

f ,2H − 2∆H0 

2O f ,HCl 

= (−13457) + 2 · (−285, 8) − 2 · (−167, 2) 

= −13408, 5 kJ/mole 

∆G 0 

f ,N a8Al6Si 6O24(OH) 2 

= ∆G 0 

+ 2 · ∆G f ,N a8Al6Si 6O24(Cl) 2 0 

f ,2H − 2∆G0 

2O f ,HCl 

= (−12703, 6) + 2 · (−237, 1) − 2 · (−131, 1) 

= −12678, 2 kJ/mole 

Where <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> sodalite, H 2O and H F are obtained from 

[187] and [391], respectively. 

5.4.7.2 The addition method for hydrated <strong>mineral</strong>s 

Hydrated <strong>mineral</strong>s have <strong>the</strong> ability to absorb n w water molecules, forming part <strong>of</strong> 

<strong>the</strong>ir crystal structure: 

A + n w · H 2O → A · n wH 2O 

Usually, <strong>the</strong>rmodynamic properties are available for <strong>the</strong> non-hydrated <strong>mineral</strong>. But 

<strong>the</strong> enthalpy and Gibbs free energy <strong>of</strong> formation <strong>of</strong> <strong>the</strong> hydrated substance can be 

estimated by addition <strong>of</strong> <strong>the</strong> hydration enthalpy and Gibbs free energy ∆G0 hyd r or 

∆H 0 to those <strong>of</strong> <strong>the</strong> dehydrated substance, as in Eqs. 5.67. 

hydr 

∆H 0 

f ,A·nw H = ∆H0 

2O f ,A + nw · ∆H 0 

hyd r,A 

∆G 0 

f ,A·nw H = ∆G0 

2O f ,A + nw · ∆G 0 

hyd r,A 

(5.67)


If ∆G0 and ∆H0 are not available, one can assume that <strong>the</strong> enthalpy and 

hydr hydr 

Gibbs free energy <strong>of</strong> <strong>the</strong> hydration reaction are zero (as in section 5.4.7.1). And 

hence, <strong>the</strong> properties <strong>of</strong> <strong>the</strong> liquid water molecules contained in <strong>the</strong> hydrated substance 

must be added in place <strong>of</strong> ∆G0 and ∆H0 . This is not rigourously exact, 

hyd r hyd r 

as demonstrated by Vieillard and Jenkins ([386], [384], [385]) and <strong>the</strong> error associated 

depends on <strong>the</strong> nature <strong>of</strong> <strong>the</strong> dehydrated component10 . We will assume an 

associated error <strong>of</strong> ±5%, although it rarely exceeds ±2%. 

Example: <strong>the</strong> contribution <strong>of</strong> tetrahedral silica Si4+ to <strong>the</strong> hydration energy is 

not known, so <strong>the</strong> enthalpy <strong>of</strong> opal SiO2 · 0, 5H2O is calculated assuming that 

<strong>the</strong> reaction energy <strong>of</strong> <strong>the</strong> hydration process is zero. Hence, ∆H 0 

f ,SiO2·0,5H2O = 

∆H 0 +0, 5∆H f ,SiO2 0 = −901, 6 + 0, 5 · (−285, 8) = −1044, 5 kJ/mole. The en- 

f ,H2O(l) thalpy <strong>of</strong> formation <strong>of</strong> SiO2 (amorph.) and H2O (l) are obtained from [284]. 

5.4.7.3 The decomposition method 

If non <strong>of</strong> <strong>the</strong> previously described methods can be applied, <strong>the</strong> <strong>the</strong>rmodynamic properties 

<strong>of</strong> a certain <strong>mineral</strong> can be estimated as <strong>the</strong> last resort by decomposing it into 

its major constituents for which <strong>the</strong> enthalpy and Gibbs free energy <strong>of</strong> formation are 

known. It will be assumed that <strong>the</strong> energy <strong>of</strong> reaction <strong>of</strong> <strong>the</strong> constituents to form 

<strong>the</strong> <strong>mineral</strong> under consideration is zero. The error associated to this methodology is 

significantly greater than with <strong>the</strong> substitution and addition methods, since in this 

case we are not dealing with partial substitutions or additions <strong>of</strong> a known <strong>mineral</strong>, 

but with <strong>the</strong> formation <strong>of</strong> a completely new <strong>mineral</strong> from its building blocks. The <strong>mineral</strong> 

under analysis will be decomposed into its most complex compounds (usually 

double silicates). If this is not possible, most <strong>mineral</strong>s can be decomposed into its 

simple oxides, sulfides, carbonates, etc. We will assume that <strong>the</strong> decomposition 

method throws an error <strong>of</strong> up to 10%. 

Example: <strong>mineral</strong> pyroxene CaAl 2SiO 6 can be decomposed into 1: CaO and 

Al 2Si 2O5. Alternatively, into 2: CaO, SiO 2 and Al 2O 3. 

CaAl 2SiO 6 → CaO + Al 2Si 2O5 

→ CaO + Al 2O 5 + SiO 2 

10 This methodology is not applied for hydrated clay <strong>mineral</strong>s and phyllosilicates. In those cases, 

<strong>the</strong> ∆O 2− method is applied.


Hence, <strong>the</strong> Gibbs free energy <strong>of</strong> pyroxene is estimated as follows, with <strong>the</strong> help <strong>of</strong> 

<strong>the</strong> <strong>the</strong>rmodynamic properties tabulated in [94]: 

∆G 0 

f ,CaAl 2SiO 6 

= ∆G 0 

f ,CaO + ∆G0 f ,Al2Si 2O5 

= (−603, 1) + (−2440, 1) 

or 

= −3043, 2 kJ/mole 

∆G 0 

f ,CaAl 2SiO 6 

= ∆G 0 

f ,CaO + ∆G0 f ,Al + ∆G 

2O3 0 

f ,SiO2 = (−603, 1) + (−1583, 4) − (−856, 3) 

= −3042, 8 kJ/mole 

The measured Gibbs free energy <strong>of</strong> pyroxene reported in [94] is ∆G0 = −3119, 7, 

f 

what gives an error <strong>of</strong> 2,4 and 2,5% <strong>of</strong> <strong>the</strong> estimated values with decompositions 1 

and 2, respectively. 

5.4.8 Summary <strong>of</strong> <strong>the</strong> methodologies 

The described methodologies in <strong>the</strong> previous sections, will be used for calculating 

<strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> most abundant <strong>mineral</strong>s in <strong>the</strong> earth’s upper 

crust. Each methodology is given a number so as to specify in <strong>the</strong> next chapter, 

which methodology has been used for determining <strong>the</strong> enthalpy or free energy <strong>of</strong> 

formation <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s (see table 5.8). Additionally, <strong>the</strong> assumed maximum errors 

associated to <strong>the</strong> estimation methods (± Error %) are given. 

Table 5.8. Summary <strong>of</strong> <strong>the</strong> methodologies used to predict <strong>the</strong> <strong>the</strong>rmodynamic properties 

<strong>of</strong> <strong>mineral</strong>s 

Method Nr. ±Error, % 

Calculation <strong>of</strong> ∆H 0 

f 

or ∆G0 

f from s0 1 0 

The ideal mixing model 2 1 

Thermochemical approximations for sulfosalts and complex oxides 3 1 

The method <strong>of</strong> corresponding states 4 1 

The method <strong>of</strong> Chermak and Rimstidt for silicate <strong>mineral</strong>s 5 1 

The ∆O −2 method 6 1 

The ∆O −2 method for hydrated clay <strong>mineral</strong>s and for phyllosilicates 7 0,6 

The ∆O −2 method for different compounds with <strong>the</strong> same cations 8 1 

Assuming ∆S r zero 9 5 

The element substitution method 10 5 

The addition method for hydrated <strong>mineral</strong>s 11 5 

The decomposition method 12 10



This chapter has provided <strong>the</strong> <strong>the</strong>rmodynamic tools required for <strong>the</strong> calculation <strong>of</strong> 

natural resources, especially for <strong>mineral</strong>s. We have seen, that <strong>the</strong> exergy <strong>of</strong> any 

substance is always associated to a reference environment. The conditions <strong>of</strong> <strong>the</strong> 

reference environment determine <strong>the</strong> final exergy value, <strong>the</strong>refore, <strong>the</strong> R.E. had to 

be carefully selected. For that purpose, <strong>the</strong> different R.E. proposed so far have been 

reviewed. It has been stated, that <strong>the</strong> best suitable R.E. for determining <strong>the</strong> exergy 

<strong>of</strong> natural resources is <strong>the</strong> one based on Szargut’s criterion. The model developed 

by Szargut has been adapted to our requirements with <strong>the</strong> help <strong>of</strong> new geochemical 

information and <strong>the</strong> updates carried out by o<strong>the</strong>r authors. As a result, two different 

R.E. have been proposed, <strong>the</strong> first one, taking into account <strong>the</strong> model <strong>of</strong> <strong>the</strong> continental 

crust developed in chapter 3, and <strong>the</strong> o<strong>the</strong>r one, considering <strong>the</strong> parameters 

included in Grigor’ev’s model [127]. It has been stated, that <strong>the</strong> difference between 

<strong>the</strong>se R.E. and Szargut’s original environment, differ for both cases in less than 1%. 

Never<strong>the</strong>less, when <strong>the</strong> whole continental crust is considered, <strong>the</strong>se small numbers 

become not so insignificant. 

Next, <strong>the</strong> energy involved in <strong>the</strong> formation processes <strong>of</strong> a <strong>mineral</strong> deposit has been 

shown. The most energy intensive processes are those related to <strong>the</strong> chemical formation 

<strong>of</strong> <strong>the</strong> <strong>mineral</strong>. The physical processes associated to <strong>the</strong> mixing and binding 

<strong>of</strong> <strong>the</strong> crystal structure <strong>of</strong> <strong>the</strong> <strong>mineral</strong> are not so energy-intensive. 

We have seen that <strong>the</strong> minimum exergy embedded in a <strong>mineral</strong> has two components: 

<strong>the</strong> chemical and concentration components. The first parameter accounts for <strong>the</strong> 

formation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> from <strong>the</strong> R.E. The concentration exergy expresses <strong>the</strong> minimum 

energy that nature had to spend to bring <strong>the</strong> <strong>mineral</strong>s from <strong>the</strong> concentration 

in <strong>the</strong> reference state to <strong>the</strong> concentration in <strong>the</strong> mine. We have seen, that <strong>the</strong> latter 

shows a negative logarithmic pattern with <strong>the</strong> grade. This means that as <strong>the</strong> ore 

grade <strong>of</strong> <strong>the</strong> mine tends to zero, <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> deposit approaches also zero and 

<strong>the</strong> exergy required for replacing <strong>the</strong> mine tends to infinity. 

Fossil fuels are a type <strong>of</strong> <strong>mineral</strong>s, in which <strong>the</strong> concentration exergy is not so relevant. 

The chemical exergy <strong>of</strong> fuels is difficult to obtain with <strong>the</strong> formulas provided 

for <strong>the</strong> rest <strong>of</strong> <strong>mineral</strong>s, because <strong>of</strong> <strong>the</strong> complexity <strong>of</strong> <strong>the</strong>ir chemical structure. Hence, 

special calculation procedures are applied. It has been seen, that <strong>the</strong> chemical exergy 

<strong>of</strong> fossil fuels can be in many cases approximated to its HHV. Never<strong>the</strong>less, <strong>the</strong> different 

formulas developed by Valero and Lozano [369] have been provided, because 

through <strong>the</strong>m, we can calculate <strong>the</strong> effect <strong>of</strong> variations in <strong>the</strong> conditions <strong>of</strong> <strong>the</strong> ambient 

on <strong>the</strong> exergy <strong>of</strong> fuels. 

The exergy values are very small, if compared to <strong>the</strong> real energy required for <strong>the</strong> 

replacement <strong>of</strong> natural resources to <strong>the</strong>ir original state. In order to account for 

<strong>the</strong> inefficiencies <strong>of</strong> man-made processes, <strong>the</strong> exergy values are multiplied by <strong>the</strong> 

unit exergy replacement costs. These are dimensionless and measure <strong>the</strong> number 

<strong>of</strong> exergy units needed to obtain one unit <strong>of</strong> exergy <strong>of</strong> <strong>the</strong> product. The resulting


exergy costs represent <strong>the</strong> exergy required by <strong>the</strong> given available technology to return 

a resource into <strong>the</strong> physical and chemical conditions in which it was delivered 

by <strong>the</strong> ecosystem. As opposed to exergy, exergy costs cannot be considered as a property 

<strong>of</strong> <strong>the</strong> resource, since unit exergy costs introduce to some extent an uncertain 

factor to <strong>the</strong> calculation. Never<strong>the</strong>less, <strong>the</strong>y can be used as a suitable indicator for 

assessing <strong>the</strong> value <strong>of</strong> non-fuel <strong>mineral</strong> resources, as <strong>the</strong>y integrate in one parameter, 

concentration, composition and also <strong>the</strong> state <strong>of</strong> technology. Although unit exergy 

replacement costs are considered in this PhD to be constant, in reality <strong>the</strong>y vary with 

time, as technology is being developed. The assessment <strong>of</strong> unit exergy replacement 

costs as a function <strong>of</strong> time with <strong>the</strong> help <strong>of</strong> learning curves is a task that remains 

open for fur<strong>the</strong>r studies. 

The chapter ends with <strong>the</strong> description <strong>of</strong> <strong>the</strong> twelve semi-<strong>the</strong>oretical models for <strong>the</strong> 

calculation <strong>of</strong> enthalpies and Gibbs free energies <strong>of</strong> formation, required for <strong>the</strong> calculation 

<strong>of</strong> <strong>the</strong> chemical exergy <strong>of</strong> <strong>mineral</strong>s. 

All <strong>the</strong>se tools, will allow us to assess in subsequent chapters, <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> 

substances that compose <strong>the</strong> earth, previously described in chapters 2, 3 and 4.

Chapter 6 

The <strong>the</strong>rmodynamic properties <strong>of</strong> 

<strong>the</strong> earth and its <strong>mineral</strong> 

resources 


This chapter is devoted to <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> standard <strong>the</strong>rmodynamic properties 

<strong>of</strong> <strong>the</strong> earth (enthalpy, Gibbs free energy and exergy) focusing on each <strong>of</strong> its outer 

layers: <strong>the</strong> atmosphere, hydrosphere and upper continental crust. For that purpose, 

<strong>the</strong> geochemistry <strong>of</strong> our planet described in Part I is required, toge<strong>the</strong>r with <strong>the</strong> 

<strong>the</strong>rmodynamic tools provided in chapter 5. 

Additionally, a first approach to <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> entropic earth is 

provided. 

Finally, <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources <strong>of</strong> <strong>the</strong> earth (<strong>of</strong> fuel and non-fuel origin) 

will be calculated and added to <strong>the</strong> energy sources described in chapter 4. The 

exergy <strong>of</strong> <strong>the</strong> natural resources will be analyzed and compared to <strong>the</strong> global chemical 

exergy <strong>of</strong> <strong>the</strong> earth calculated before. 

6.2 The properties <strong>of</strong> <strong>the</strong> earth 

As we anticipated in previous chapters, <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> earth 

are related to <strong>the</strong> species contained in it and not to <strong>the</strong>ir elements. In <strong>the</strong> model 

developed in section 3.4.1, this implies that <strong>the</strong> average Enthalpy (∆H f ), Gibbs free 

energy (∆G f ) or Chemical <strong>Exergy</strong> (b ch) <strong>of</strong> <strong>the</strong> earth expressed as kJ/g <strong>of</strong> earth, are 

calculated as: 

187

188 THE THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES 

∆H f = 

∆G f = 

b ch = 

m 

(ξi · ∆H f i) (6.1) 

i=1 

m 

(ξi · ∆G f i) (6.2) 

i=1 

m 

(ξi · bch i) (6.3) 

i=1 

Being ξ i, <strong>the</strong> specific quantity <strong>of</strong> <strong>the</strong> species composing <strong>the</strong> earth, expressed in 

mole/g, and ∆H f i, ∆G f i and b ch i, <strong>the</strong>ir enthalpy, Gibbs free energy and chemical 

exergy in kJ/mole, respectively. 

The enthalpy and Gibbs free energy <strong>of</strong> <strong>the</strong> substances are obtained ei<strong>the</strong>r through 

<strong>the</strong> literature or through <strong>the</strong> estimation methods described in section 5.4. 

Remember also that <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> substance (bch i) in kJ/mole is calculated 

with Eq. 5.1: 

 

bch i = ∆G f + rj,i bch j 

where b ch j is <strong>the</strong> standard chemical exergy <strong>of</strong> <strong>the</strong> elements that compose substance 

i. In our case we will use <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> elements obtained with <strong>the</strong> R.E. 

developed in this study and shown in table 5.4. 

Since we have divided <strong>the</strong> earth into three subsystems, its average properties will 

be first calculated separately for <strong>the</strong> atmosphere, hydrosphere and continental crust. 

The average enthalpy, Gibbs free energy and exergy <strong>of</strong> <strong>the</strong> earth’s layers, can be 

expressed in molar units by substituting ξ i with <strong>the</strong> molar fraction x i for <strong>the</strong> i constituents 

<strong>of</strong> each sphere. Equation 6.4 relates both properties through <strong>the</strong> molecular 

weight <strong>of</strong> <strong>the</strong> sphere considered (MW sphere): 

x i = ξ i · MW sphere 

j 

(6.4) 

Next, <strong>the</strong> specific and global standard properties <strong>of</strong> <strong>the</strong> substances composing <strong>the</strong> 

atmosphere, hydrosphere and upper continental crust are shown. 

6.2.1 The <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> atmosphere 

Table 6.1 shows <strong>the</strong> standard <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> substances contained 

in <strong>the</strong> atmosphere (on a dry basis), according to <strong>the</strong> composition provided in section 

are taken from Weast et al. [400]. 

2.3.1. Values for ∆H 0 

f ,i 

and ∆G0 

f ,i

The properties <strong>of</strong> <strong>the</strong> earth 189 

Table 6.1: Thermodynamic properties <strong>of</strong> <strong>the</strong> atmosphere. Values 

<strong>of</strong> ∆H 0 , ∆G0 , b0 in kJ/mole 

f i f i ch i 

Substance Formula x i [-] ∆H 0 

f i 

∆G0 

f i 

Nitrogen N 2 7,81E-01 0,0 0,0 0,72 

Oxygen O 2 2,09E-01 0,0 0,0 3,97 

Argon Ar 9,34E-03 0,0 0,0 11,7 

Carbon dioxide CO 2 3,60E-04 -393,7 -394,4 19,9 

Neon N e 1,82E-05 0,0 0,0 27,2 

Helium He 5,24E-06 0,0 0,0 30,4 

Methane CH 4 1,70E-06 -74,8 -50,8 831,7 

Hydrogen H 2 5,50E-07 0,0 0,0 236,1 

Nitrogen oxides NO 2 5,05E-07 33,2 51,3 55,7 

Nitrous oxide N 2O 3,10E-07 82,1 104,2 106,9 

Ozone (troposphere) O 3 2,55E-07 142,7 163,3 169,2 

Carbon monoxide CO 1,25E-07 -137,2 -110,6 301,7 

NMHC (assuming ethylene) C 2H 4 1,25E-08 52,3 70,3 1363,0 

Ozone (stratosphere) O 3 5,25E-09 142,7 163,3 169,2 

Hydrogen peroxide H 2O 2 5,05E-09 -191,3 -131,9 108,2 

Formaldehyde CH 2O 5,50E-10 -117,2 -113,0 535,3 

Chlor<strong>of</strong>luorocarbon 12 C F2Cl 2 5,40E-10 -477,2 -439,5 651,1 

Ammonia N H 3 5,05E-10 -46,1 -16,5 338,0 

Sulfur dioxide SO 2 5,05E-10 -297,0 -300,3 310,9 

Carbonyl sulfide OCS 5,00E-10 -142,2 -169,4 850,1 

Chlor<strong>of</strong>luorocarbon 11 C F Cl 3 2,65E-10 -276,3 -238,6 636,1 

Hydrogen sulfide H 2S 2,53E-10 -20,6 -27,9 815,5 

Carbon disulfide CS 2 1,51E-10 117,4 67,2 1692,0 

Carbon tetrachloride CCl 4 9,80E-11 -103,0 -60,7 598,1 

Methylchlor<strong>of</strong>orm CH 3CCl 3 6,50E-11 35,6 51,9 1412,9 

Dimethyl sulfide CH 3SCH 3 5,50E-11 -45,8 -4,4 2131,7 

Hydroperoxyl radical HO 2 2,00E-12 20,9 22,6 144,6 

Hydroxyl radical OH 5,00E-14 39,0 34,2 154,3 

Sum 1,00 

According to table 6.1, <strong>the</strong> average standard enthalpy, Gibbs free energy and chemical 

exergy <strong>of</strong> <strong>the</strong> atmosphere can be obtained as: 

b 0 

ch i


(∆H 0 

f ) atm = 

(∆G 0 

f ) atm = 

(b 0 

ch ) atm = 

m 

i=1 

m 

i=1 

m 

i=1 

(x i · ∆H 0 

f ,i ) = −1, 42E − 01 kJ/mole 

(x i · ∆G 0 

f ,i ) = −1, 42E − 01 kJ/mole 

(x i · b 0 

ch i ) = 1, 51 kJ/mole 

Obviously, <strong>the</strong> average properties are very close to those <strong>of</strong> N 2 and O 2, for being both 

<strong>the</strong> major constituents <strong>of</strong> <strong>the</strong> atmosphere. 

6.2.2 The <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> hydrosphere 

In this section, <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> main constituents <strong>of</strong> oceans, 

rivers, groundwaters and glacial run<strong>of</strong>f are provided. For all subsystems, values for 

∆H 0 and ∆G0 are taken from Weast et al. [400]. 

f i f i 

Table 6.2 shows <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> major substances that compose 

seawater. The composition <strong>of</strong> <strong>the</strong> oceans is <strong>the</strong> one listed in table 2.5. The more 

comprehensive composition given in table 2.6 could not be used, since although <strong>the</strong> 

concentration <strong>of</strong> minor elements found in seawater are listed, <strong>the</strong>ir specific molecular 

formulas are not specified 1 . It should be noted however, that <strong>the</strong> first composition 

comprises more than 99% <strong>of</strong> <strong>the</strong> total substances included in seawater and hence, 

its uncertainty cannot be compared to that <strong>of</strong> <strong>the</strong> continental crust, which had to be 

estimated in this PhD. 

Table 6.2: Thermodynamic properties <strong>of</strong> seawater. Values in 

kJ/mole 

Substance x i [-] ∆H 0 

f i 

∆G 0 

f i 

b 0 

ch i 

H 2O 9,80E-01 -286,0 -237,3 0,79 

Cl − 9,98E-03 -167,2 -131,3 -69,2 

N a + 8,57E-03 -240,2 -262,0 74,6 

M g 2+ 9,65E-04 -467,1 -455,0 174,6 

SO4 −2 5,16E-04 -909,7 -745,0 -129,8 

Ca 2+ 1,88E-04 -543,1 -553,8 170,0 

K + 1,87E-04 -252,5 -283,4 83,2 

HCO − 

3 3,20E-05 -692,3 -587,1 -52,9 

1 For instance, <strong>the</strong> concentration <strong>of</strong> vanadium is given, but this element could be in <strong>the</strong> form <strong>of</strong> 

VO + 

2 , V + , V 3+ , etc. Obviously, <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> different forms <strong>of</strong> vanadium are 

different.


Table 6.2: Thermodynamic properties <strong>of</strong> seawater. Values in 

kJ/mole. – continued from previous page. 


f i 

∆G 0 

f i 

b ch i 0 

Br − 1,54E-05 -121,6 -104,0 -53,5 

F − 1,24E-05 -332,8 -279,0 -0,9 

B(OH) 3 5,67E-06 -1072,8 -969,3 19,4 

CO 2− 

3 4,93E-06 -677,5 -528,1 -111,9 

B(OH) − 

4 1,83E-06 -1344,7 -1153,9 -45,1 

Sr 2+ 1,64E-06 -547,2 -560,0 198,8 

SUM 1,00 

The average standard enthalpy, Gibbs free energy and chemical exergy <strong>of</strong> seawater 

(sw) can now be obtained as: 

(∆H 0 

f ) sw = −284, 9 kJ/mole 

(∆G 0 

f ) sw = −237, 0 kJ/mole 

(b 0 

ch ) sw 

= 0, 87 kJ/mole 

The average standard <strong>the</strong>rmodynamic properties <strong>of</strong> rivers, according to <strong>the</strong> composition 

given by Livingstone [197] are shown in table 6.3. 

Table 6.3: Thermodynamic properties <strong>of</strong> average rivers. Values 

in kJ/mole 


f i 

∆G0 

f i 

b 0 

ch i 

H 2O 1,00E+00 -286,0 -237,2 0,79 

HCO3 − 1,72E-05 -692,3 -586,9 -52,9 

Ca 2+ 6,74E-06 -543,1 -553,5 170,0 

N a + 4,93E-06 -240,2 -261,9 74,6 

Cl − 3,96E-06 -167,2 -131,0 -69,2 

SiO 2 3,92E-06 -911,4 -856,7 174,6 

M g +2 3,04E-06 -467,1 -454,8 174,6 

SO4 −2 2,10E-06 -909,7 -774,5 -129,8 

K + 1,06E-06 -252,5 -283,3 83,2 

NO3 − 2,90E-07 -207,5 -111,3 -105,1 

Fe 2+ 2,16E-07 -89,2 -78,9 297,9 

SUM 1,00


The average standard enthalpy, Gibbs free energy and chemical exergy <strong>of</strong> rivers (rw) 

is <strong>the</strong>n: 

(∆H 0 

f ) rw = −286, 0 kJ/mole 

(∆G 0 

f ) rw = −237, 2 kJ/mole 

(b 0 

ch ) rw 

= 0, 79 kJ/mole 

The average standard properties <strong>of</strong> glacial run<strong>of</strong>f, obtained from <strong>the</strong> composition 

provided in section 2.4.3.1, are given in table 6.4. 

Table 6.4: Thermodynamic properties <strong>of</strong> glacial run<strong>of</strong>f. Values 

in kJ/mole 


f i 

∆G0 

f i 

b 0 

ch i 

H 2O 1,00E+00 -286,0 -237,2 0,79 

N a + 1,44E-05 -240,2 -261,9 74,6 

HCO3 − 1,42E-05 -692,3 -586,9 -52,9 

Ca +2 5,71E-06 -543,1 -553,5 170,0 

SO4 −2 5,13E-06 -909,7 -774,5 -129,8 

Cl − 3,92E-06 -167,2 -131,0 -69,2 

M g +2 1,92E-06 -467,1 -454,8 174,6 

K + 9,13E-07 -252,5 -283,3 83,2 

SUM 1,00 

The average standard enthalpy, Gibbs free energy and chemical exergy <strong>of</strong> glacial 

run<strong>of</strong>f (gl) is: 

(∆H 0 

f ) gl = −286, 0 kJ/mole 

(∆G 0 

f ) gl = −237, 2 kJ/mole 

(b 0 

ch ) gl 

= 0, 79 kJ/mole 

Since <strong>the</strong> composition <strong>of</strong> river waters and glacial run<strong>of</strong>f is very close, similar <strong>the</strong>rmodynamic 

properties <strong>of</strong> both types <strong>of</strong> waters were expected, as corroborated by <strong>the</strong> 

figures provided above.


Table 6.5. Thermodynamic properties <strong>of</strong> groundwaters. Values in kJ/mole 


f i 

∆G0 

f i 

b 0 

ch i 

H 2O 1,00E+00 -286,0 -237,3 0,79 

HCO3 − 6,46E-05 -692,3 -587,1 -52,9 

Ca 2+ 3,95E-05 -543,1 -553,8 170,0 

SO4 −2 2,96E-05 -909,7 -745,0 -129,8 

M g +2 2,13E-05 -467,1 -455,0 174,6 

SiO 2 7,54E-06 -911,4 -857,1 1,1 

Cl − 6,98E-06 -167,2 -131,3 -69,2 

N a + 6,66E-06 -240,2 -262,0 74,6 

Al +3 2,05E-06 -531,6 -485,6 308,7 

NO3 − 1,47E-06 -207,5 -111,4 -105,1 

K + 9,67E-07 -252,5 -283,4 83,2 

Fe 2+ 5,55E-07 -89,2 -78,9 297,9 

SUM 1,00 

Table 6.5 shows <strong>the</strong> estimated average standard <strong>the</strong>rmodynamic properties <strong>of</strong> 

groundwaters on earth. The mean composition <strong>of</strong> groundwaters has been assumed 

to be equivalent to <strong>the</strong> average <strong>of</strong> <strong>the</strong> compositions for granite, shale and serpentinite 

groundwaters given in table 2.10. 

According to table 6.5, <strong>the</strong> average standard enthalpy, Gibbs free energy and chemical 

exergy <strong>of</strong> groundwater (gw) is <strong>the</strong>n: 

(∆H 0 

f ) gw = −286, 0 kJ/mole 

(∆G 0 

f ) gw = −237, 4 kJ/mole 

(b 0 

ch ) gw 

= 0, 80 kJ/mole 

Summarizing, table 6.6 shows <strong>the</strong> standard <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> hydrosphere. 

Since <strong>the</strong> ocean accounts for 97% <strong>of</strong> all earth’s waters, <strong>the</strong> global enthalpy, 

Gibbs free energy and exergy <strong>of</strong> <strong>the</strong> hydrosphere can be approximated to that <strong>of</strong> seawater. 

It has been assumed, that <strong>the</strong> composition <strong>of</strong> lakes is equal to that <strong>of</strong> average 

rivers. 

It is remarkable in <strong>the</strong> hydrosphere’s tables presented above, that <strong>the</strong> specific exergy 

<strong>of</strong> all negative ions is also negative. As explained in <strong>the</strong> previous chapter, <strong>the</strong> chemical 

exergy expresses <strong>the</strong> minimum work required for combining chemically <strong>the</strong> 

reference substances dispersed in <strong>the</strong> reference environment to obtain <strong>the</strong> resource. 

If <strong>the</strong> reference species are more stable than <strong>the</strong> considered substance, <strong>the</strong>n its chemical 

exergy will be negative. In Ranz’s R.E. [276], this situation came up very


Table 6.6. Summary <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> hydrosphere. Values in 

kJ/mole 

Reservoir Volume (M km3 ) xi ∆H 0 

f i 

xi.b ch i 

Oceans 1370 9,73E-01 -284,9 -237,0 0,87 -2,77E+02 -2,30E+02 8,47E-01 

Ice Caps and 

Glaciers 

29 2,05E-02 -286,0 -237,2 0,79 -5,86E+00 -4,86E+00 1,63E-02 

Groundwater 9,5 6,80E-03 -286,0 -237,4 0,80 -1,94E+00 -1,61E+00 5,41E-03 

Lakes 0,125 1,00E-04 -286,0 -237,2 0,79 -2,86E-02 -2,37E-02 7,93E-05 

Streams 

Rivers 

and 0,0017 1,00E-06 -286,0 -237,2 0,79 -2,86E-04 -2,37E-04 7,93E-07 

SUM 1408,63 1,00 -284,9 -237,0 0,87 

∆G 0 

f i b ch i x i.∆H 0 

f i 

x i. ∆G 0 

f i 

frequently, as she chose reference substances according to <strong>the</strong> abundance criterion. 

In <strong>the</strong> R.E. developed in this PhD, which is based on partial stability, we have selected 

reference substances trying to avoid negative chemical exergies. However, in 

<strong>the</strong> light <strong>of</strong> <strong>the</strong> hydrosphere’s results, we have not succeeded in that task. 

A deeper analysis <strong>of</strong> <strong>the</strong> equilibrium substances found in seawater should be carried 

out. A good starting point would be <strong>the</strong> work <strong>of</strong> Pinaev [266], [265]. Pinaev calculated 

<strong>the</strong> chemical exergy <strong>of</strong> elements, assuming that all reference substances are in 

<strong>the</strong> ocean medium, with <strong>the</strong> exception <strong>of</strong> gas reference substances, which were <strong>the</strong> 

same as in this PhD. As opposed to o<strong>the</strong>r methodologies, for Pinaev, <strong>the</strong> exergy <strong>of</strong> an 

element is not obtained from a single reference substance. He takes into account not 

only <strong>the</strong> dominant, but also <strong>the</strong> main secondary species found in <strong>the</strong> ocean medium 

<strong>of</strong> each element, at <strong>the</strong> concentration ruled by <strong>the</strong>ir equilibrium constants. This 

way, <strong>the</strong> exergy <strong>of</strong> an element is calculated as <strong>the</strong> sum <strong>of</strong> <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> element 

previously obtained with <strong>the</strong> dominant reference substance and <strong>the</strong> exergy <strong>of</strong> <strong>the</strong>ir 

secondary species, obtained through <strong>the</strong>ir equilibrium concentrations. 

Never<strong>the</strong>less, Pinaev’s element exergies generate also negative chemical exergies <strong>of</strong> 

negative ions, as corroborated by <strong>the</strong> next example. 

Example: standard chemical exergy <strong>of</strong> Cl − , calculated from <strong>the</strong> standard chemical 

= 60, 8 kJ/mole). 

exergy <strong>of</strong> <strong>the</strong> elements proposed by Pinaev [265]: (b 0 

ch Cl 

b 0 

ch Cl − = ∆G 0 

f ,Cl − + b 0 

ch Cl 

= −131, 3 + 60, 8 = −70, 5 kJ/mole 

It is not <strong>the</strong> point <strong>of</strong> this PhD to show <strong>the</strong> exergy <strong>of</strong> all substances on earth calculated 

with Pinaev’s R.E. But it has been stated, that <strong>the</strong> results are very close to ours. In 

<strong>the</strong> example, Pinaev’s exergy <strong>of</strong> Cl − is -70,5 kJ/mole, versus -69,2 kJ/mole obtained 

here. That is because his methodology is based in outline on <strong>the</strong> conventional calculation 

procedures, also used in this PhD. This makes us to question <strong>the</strong> validity 

<strong>of</strong> <strong>the</strong> conventional methodology, when <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> natural <strong>capital</strong> is 

assessed.


6.2.3 The <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> upper continental crust 

Table 6.7 shows <strong>the</strong> standard <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> major <strong>mineral</strong>s that 

compose <strong>the</strong> upper continental crust, according to <strong>the</strong> model developed in chapter 3. 

Only <strong>the</strong> references (Re f .) <strong>of</strong> <strong>the</strong> experimental values <strong>of</strong> ∆H 0 and ∆G0 are pro- 

f i f i 

vided in <strong>the</strong> table. For those <strong>mineral</strong>s where <strong>the</strong> latter values have been estimated 

in this PhD, <strong>the</strong> method used for its estimation (M eth.) 2 , as well as its associated 

error (±ɛ %) is given. The detailed calculations for <strong>the</strong> estimation <strong>of</strong> <strong>the</strong> <strong>mineral</strong>’s 

properties is shown in <strong>the</strong> appendix (section A.5.3). 

2 See table 5.8 for details about <strong>the</strong> different estimation methods.


Table 6.7: Thermodynamic properties <strong>of</strong> <strong>the</strong> upper continental crust 

Mineral Formula ξi, ∆H 

mole/g 

0 

f i , ∆G 

kJ/mole 

0 

f i , Reference Method ±ε, % bch i, 

kJ/mole 

kJ/mole 

Quartz SiO2 3,81E-03 -911,6 -857,2 [94] 1,0 

Albite N aAlSi 3O8 5,14E-04 -3927,6 -3704,5 [94] 4,8 

Oligoclase N a0.8Ca 0.2Al1.2Si2.8O8 4,49E-04 -796,0 -750,9 [94] 3023,9 

Orthoclase/ K- KAlSi 3O8 4,22E-04 -3977,5 -3752,1 1 0 -12,8 

feldspar 

Andesine N a0.6Ca 0.4Al1.4Si2.6O8 2,03E-04 -808,9 -763,7 [94] 3076,6 

Opal SiO2· 0, 5H2O 1,42E-04 -1044,5 -967,9 11 5 9,3 

Augite Ca0.9N a0.1M g0.9Fe 2+ 

0.2Al0.4Ti 0.1Si1.9O6 1,27E-04 -3201,5 -3026,8 [284] -446,9 

Labradorite N a0.5Ca 0.5Al1.5Si2.5O8 9,25E-05 -815,0 -769,8 [94] 3103,2 

Biotite K(M g2,5Fe 0,5)(Si3Al)O 10 (OH) 1,75F0,25 8,80E-05 -6079,4 -5706,7 2; 4 1 78,6 

Calcite CaCO 3 8,00E-05 -1207,7 -1129,0 [94] 11,0 

Hydromusco- K0,6(H3O) 0,4Al2 M g0,4Fe vite/ Illite 

2+ 

0,1 Si3,5O10(OH) 2 7,73E-05 -5886,2 -5499,1 5 1 325,2 

Sillimanite Al2SiO 5 6,15E-05 -2587,4 -2441,0 [94] 11,7 

Paragonite N aAl3Si 3O10(OH) 2 4,95E-05 -5932,5 -5557,6 [94] -15,7 

Nontronite N a0.3Fe 3+ 

2 (Si3,7 Al0,3)O10(OH) 2 · 4(H2O) 3,88E-05 -6841,0 -5447,7 1; 7 0,6 738,2 

Magnetite Fe 3+ 

2 Fe2+ O4 3,43E-05 -1118,3 -1015,9 [94] 122,6 

Kaolinite Al2Si 2O5(OH) 4 3,24E-05 -4117,7 -3796,0 [94] -9,0 

Ilmenite Fe2+ T iO3 3,10E-05 -1237,2 -1163,5 [94] 123,7 

Diaspore AlO(OH) 2,95E-05 -998,1 -917,6 [94] -1,3 

Hornblende- Ca2Fe Fe 

2+ 

4 Al0,75Fe 3+ 

0,25 (Si7AlO 22)(OH) 2 2,78E-05 -10976,4 -10303,7 3 398,5 

Muscovite KAl3Si 3O10(OH) 1,8F0,2 2,54E-05 -5991,3 -5616,6 4 1 -13,1 

Titanite CaT iSiO5 2,28E-05 -2597,1 -2455,1 1 0 37,2 

Almandine Fe 2+ 

3 Al2(SiO 4) 3 2,09E-05 -5305,5 -4969,8 [94] 335,7 

Graphite C 2,01E-05 0,0 0,0 [94] 410,3 

Ripidolite (M g3,75Fe 1,25Al) (Si3Al)O 10(OH) 2(OH) 6 2,01E-05 -8429,2 -7788,2 7 0,6 175,2 

Epidote Ca2Fe 3+ Al2(SiO 4) 3(OH) 1,87E-05 -6466,1 -6076,3 [94] 43,1 

C org C 1,84E-05 N.A. N.A. N.A. 

Hydragillite/ Al(OH) 3 1,77E-05 -1282,2 -1155,8 [94] -1,4 

Gibbsite 

Diopside CaM gSi2O 6 1,40E-05 -3031,2 -3026,3 [94] 47,4 

Beidellite N a0,33Al2,33Si3,67 O10(OH) 2 1,39E-05 -5691,6 -5317,2 3 1 39,4 

Ankerite CaFe 2+ 

0,6M g0,3Mn 2+ 

0,1 (CO3) 2 1,36E-05 -2076,8 -1923,1 12 10 96,6 

Aegirine N aFe 3+ Si2O6 1,32E-05 -2585,5 -2417,2 [284] 16,5 

Andalusite Al2SiO 5 1,25E-05 -2590,4 -24443,0 [94] 9,7 

Hyperstene M gFe 2+ Si2O6 1,17E-05 -2757,4 -2594,6 [94] 132,2 

Goethite Fe3+ O(OH) 1,17E-05 -559,4 -489,2 [94] 9,7 

Halite N aCl 1,01E-05 -386,3 -384,4 [94] 14,3 

Boehmite AlO(OH) 9,65E-06 -988,1 -914,1 [94] 2,2 

Bytownite N a0.2Ca 0.8Al1.8Si2.2O8 9,08E-06 -4186,8 -3960,7 [94] 10,5 



Table 6.7: Thermodynamic properties <strong>of</strong> <strong>the</strong> upper continental crust. – continued from previous 

page. 


mole/g 

0 

f i , ∆G 

kJ/mole 

0 


kJ/mole 

kJ/mole 

Phosphate Ca3(PO 4) 2 8,99E-06 -3886,6 -3878,2 [94] 32,4 

rock 

Natrolite N a2Al2Si 3O10 · 2(H2O) 7,82E-06 -5722,1 -5316,6 [94] 3,8 

Dolomite CaM g(CO 3) 2 7,63E-06 -2327,9 -2167,9 [94] 18,0 

Clinochlore M g3,75Fe 1,25Al2 Si3O10(OH) 8 7,33E-06 -8435,5 -7796,6 3 1 166,8 

Montmori- N a0,165Ca 0,084Al2,33 Si3,67O10(OH) 2 6,52E-06 -5523,8 -5354,5 2 1 39,6 

llonite 

Lawsenite CaAl 2Si2O 7(OH) 2 · H2O 6,36E-06 -4812,8 -4510,6 3; 11 5 2,2 

Riebeckite N a2Fe 2+ 

3 Fe3+ 

2 (Si8O22)(OH) 2 6,14E-06 -10087,1 -9399,5 1 0 318,9 

Hematite Fe2O3 6,05E-06 -826,1 -742,2 [94] 17,4 

Sepiolite M g4Si6O 15(OH) 2 · 6(H2O) 5,67E-06 -10123,7 -9257,8 [94] 1284,5 

Hydrobiotite (K0,3Ca 0,1)(M g2,3Fe 3+ 

0,6 Al0,1)(Si2,8Al1,2) O10((OH) 1,8F0,2) · 5,26E-06 -7362,2 -6238,9 1; 7; 10 5 46,2 

3(H2O) Ulvöspinel T iFe 2+ 

2 O4 5,21E-06 -1489,4 -1392,9 12 10 273,1 

Distene/Kyanite Al2SiO 5 4,37E-06 -2593,7 -2442,0 [94] 10,7 

Cummingtonite/ M g7(Si8O 22)(OH) 2 3,73E-06 -12070,0 -11343,0 [284] 181,6 

Anthopyllite 

Glaucophane N a2(M g3Al2)Si 8O22(OH) 2 3,65E-06 -12080,6 -11346,7 [94] -78,8 

Celestine SrSO 4 3,65E-06 -1454,1 -1341,6 [94] 32,4 

Prehnite Ca2Al 2Si3O 10(OH) 2 3,58E-06 -6197,3 -5823,0 [94] 35,7 

Rutile T iO2 3,41E-06 -945,4 -890,1 [94] 18,3 

Barite BaSO4 3,04E-06 -1470,4 -1361,9 [94] 18,8 

Niter KNO 3 2,96E-06 -495,0 -395,2 [94] -22,3 

Nitratine N aNO3 2,96E-06 -468,2 -367,1 [94] -24,2 

Pennine (M g3,75Fe 1,25Al) (Si3Al)O 10(OH) 2(OH) 6 2,87E-06 -8429,2 -7788,2 7 0,6 175,2 

Actinolite Ca2M g3Fe 2Si8O 22(OH) 2 2,82E-06 -11519,4 -10801,5 3 1 405,9 

Pyrite FeS2 2,75E-06 -175,0 -163,3 [94] 1428,1 

Sanidine K0,75N a0,25AlSi 3O8 2,67E-06 -3860,7 -3715,9 3 1 15,9 

Hastingsite N aCa2Fe 2+ 

4 Fe3+ (Si6Al 2O22)(OH) 2 2,60E-06 -11926,3 -11343,4 [178] 289,2 

Ferrosilite Fe2+ M gSi2O 6 2,32E-06 -2757,4 -2594,6 [94] 132,2 

Zircon Z rSiO 4 2,11E-06 -2034,8 -1919,5 [94] 20,0 

Siderite Fe2+ CO3 2,08E-06 -742,3 -671,1 [94] 122,0 

Spodumene LiAlSi 2O6 2,06E-06 -3056,8 -2882,9 [94] 24,6 

Pigeonite M g1,35Fe 0,55Ca 0,1(Si2O 6) 1,99E-06 -1535,4 -1448,8 2 1 1401,1 

Leucoxene CaT iSiO5 1,90E-06 -2591,6 -2454,8 [94] 37,5 

Pyrrhotite Fe2+ S 1,79E-06 -105,5 -100,5 [94] 883,6 

Lepidomelane/ K Fe 

Annite 

2+ 

2,5M g0,5Fe 3+ 

0,75 Al0,25Si3O 10(OH) 2 1,78E-06 -4995,0 -4642,3 3 1 284,8 

Bronzite M gFeSi 2O6 1,77E-06 -2753,4 -2585,3 1 0 141,5 

Anhydrite CaSO 4 1,73E-06 -1435,1 -1322,7 [94] 16,3 




page. 


mole/g 

0 

f i , ∆G 

kJ/mole 

0 


kJ/mole 

kJ/mole 

Serpentine/ M g3Si2O 5(OH) 4 1,64E-06 -4363,4 -4035,4 1 0 51,9 

Clinochrysotile 

Olivine M g1,6Fe 2+ 

0.4 (SiO4) 1,53E-06 -2083,3 -1925,0 ∆G0 : [94] ∆H0 : 5 1 95,3 

f f 

Enstatite M g2Si2O 6 1,39E-06 -3055,5 -2919,9 [94] 59,6 

Corundum Al2O3 1,20E-06 -1668,9 -1563,0 [94] 31,5 

Thuringite- (Fe3M g2Fe Chamosite 

3+ 

0,5Al3+ 0,5 ) (Si3Al)O 10(OH) 2 1,14E-06 -7596,0 -6981,9 7 0,6 -389,8 

Neptunite KN a2 LiFe 2+ 

1,5M n2+ 

0,5 T i2Si8O 24 1,10E-06 -10724,6 -10061,3 12 10 868,9 

Sphalerite ZnS 1,02E-06 -206,1 -201,4 [94] 744,9 

Analcime N aAlSi2O 6∆(H2O) 1,01E-06 -3310,2 -3088,5 [94] 0,8 

Anorthite CaAl 2Si2O 8 9,90E-07 -4274,4 -4021,0 [94] ∆H 0: 

5 1 15,6 

f 

Rhodochrosite M nCO3 9,48E-07 -894,7 -817,1 [94] 83,8 

Chromite Fe2+ C r2O4 8,83E-07 -1445,7 -1358,4 [94] 195,1 

Gypsum CaSO 4 · 2H2O 7,96E-07 -2024,0 -1798,6 [94] 16,6 

Apatite Ca5(PO 4) 3(OH) 0,33 F0,33Cl 0,33 7,91E-07 -6773,4 -6386,9 3; 10 5 -23,2 

Staurolite Fe2+ Al9Si 4O23(OH) 7,68E-07 -12066,8 -11215,6 [94] 269,1 

Talc M g3Si4O 10(OH) 2 7,67E-07 -5907,2 -5543,0 [94] 22,6 

Aragonite CaCO 3 7,64E-07 -1207,9 -1128,6 [94] 11,4 

Clinozoisite Ca2Al 3(SiO 4) 3(OH) 7,51E-07 -6883,9 -6483,9 [94] 53,0 

Vermiculite M g3Si4O 10(OH) 2 · 2(H2O) 6,78E-07 -7018,8 -5957,2 [94] ∆H 0: 

12 10 1717,4 

f 

Tephroite M n 2+ 

2 (SiO4) 6,30E-07 -1733,3 -1632,1 [94] 199,3 

Thomsonite N aCa2Al5Si 5O20 · 6H2O 6,19E-07 -12413,7 -11543,9 5 1 -49,1 

Zoisite Ca2Al 3Si3O 12(OH) 5,68E-07 -6883,9 -5416,5 [94] 1120,4 

Pyrolusite M nO2 5,64E-07 -520,4 -465,2 [94] 23,4 

Anatase T iO2 5,59E-07 -940,4 -883,7 [94] 24,7 

Psilomelane Ba2Mn 2+ 

2 M n4+ 

3 O10 · 2H2O 5,10E-07 -2569,1 -2347,2 3 1 2103,1 

Nepheline N a0,75K0,25Al(SiO 4) 5,09E-07 -2087,6 -1972,4 3 1 28,1 

Forsterite M g2SiO 4 4,95E-07 -2175,5 -2057,8 [94] 63,6 

Jadeite N aAl0,9Fe 3+ 

0,1 (Si2O6) 4,78E-07 -2990,4 -2812,1 3 1 -2,7 

Spessartine M n2 + 3Al2(SiO4)3 4,77E-07 -5646,3 -5326,3 [144] 302,6 

Monazite (Ce) Ce0,5 La0,25N d0,2 Th0,05(PO 4) 4,29E-07 -2074,0 -1943,3 12 10 -43,3 

Tremolite Ca2M g5Si8O 22(OH) 2 4,28E-07 -12367,8 -11639,3 [94] 73,7 

Crossite N a2M g2Fe 2+ Al2 (Si8O22)(OH) 2 4,06E-07 -11600,3 -10925,8 1; 2 1 133,0 

Braunite M n2+ M n 3+ 

6 SiO12 4,06E-07 -4260,0 -3944,7 [284] 325,8 

Chalcopyrite CuFeS 2 3,62E-07 -194,6 -195,1 [284] 1530,3 

Sassolite H3BO 3 3,60E-07 -1095,1 -969,0 [94] 19,7 

Magnesite M gCO 3 3,58E-07 -1114,1 -1030,2 [94] 15,6 

Ilmenorutile T i0,7N b0,15Fe 2+ 

0,225O2 3,22E-07 -864,6 -813,2 1; 2 1 45,5 

Wi<strong>the</strong>rite BaCO 3 3,04E-07 -1217,1 -1137,6 [94] 44,1 

Stilplomelane K0,8Fe 8Al0,85Si11,1 O21(OH)8 · 6H2O 2,77E-07 -16655,5 -15197,0 1 0 5459,7 




page. 

Reference Method ±ε, % bch i, 

kJ/mole 


mole/g 

0 

f i , ∆G 

kJ/mole 

0 

f i , 

kJ/mole 

Hedenbergite CaFe 2+ Si2O6 2,75E-07 -2842,4 -2676,1 [94] 8651,4 

Hollandite Ba0,8P b0,2N a0,125 Fe1,3Al0,2Si0,1 M n 2+ 

0,5M n4+ 

6 O16 2,63E-07 -4733,3 -4330,4 3 1 288,3 

Fayalite Fe 2+ 

2 SiO4 2,34E-07 -1480,9 -1369,2 [94] 246,6 

Rhodonite M n2+ SiO3 2,32E-07 -1321,6 -1243,1 [94] 101,7 

Cristobalite SiO2 2,06E-07 -910,1 -855,5 [94] 2,7 

Pumpellyte Ca2M gAl2(SiO 4) (Si2O7)(OH) 2 · H2O 1,89E-07 -7148,6 -6672,5 3 1 57,9 

Phlogopite K M g3AlSi 3O10F(OH) 1,58E-07 -6292,8 -5902,2 4 1 128,1 

Manganite M nO(OH) 1,55E-07 -622,4 -557,3 ∆H 0: 

12 10 49,4 

f 

Fluorite CaF 2 1,44E-07 -1220,5 -1168,1 [94] 111,9 

Amblygonite Li0,75N a0,25Al(PO 4) F0,75(OH) 0,25 1,29E-07 -307,1 -282,7 10; 12 10 1992,6 

Vesuvianite Ca10M g2Al4(SiO 4) 5(Si2O 7) 2(OH) 4 1,20E-07 -21175,8 -19948,7 [144] 219,0 


0,6Fe2+ 0,3M g2+ Fe 3+ 

1,5M n3+ 

0,5O4 1,20E-07 -1237,4 -1137,5 1; 2; 9 5 711,5 

Bastnaesite La(CO 3)F 1,16E-07 -1660,9 -1527,8 1; 8; 10 5 160,8 

Arfvedsonite N a3Fe 2+ 

4 Fe3+ (Si8O22)(OH) 2 1,09E-07 -11926,3 -11201,5 [178] -1146,5 

Spinel M gAl2O 4 1,07E-07 -2281,0 -2172,5 [94] 53,6 

Lepidolite K Li2AlSi 4O10F(OH) 1,03E-07 -6003,2 -5654,7 7; 4 1 126,7 

Cordierite M g2Al4Si 5O18 9,52E-08 -9114,7 -8603,9 [94] 139,2 

Kernite N a2O · 2B2O3 · 4H2O 8,99E-08 -4104,9 -3713,1 10 5 440,8 

Pyrophyllite Al2Si 4O10(OH) 2 8,93E-08 -5632,5 -5257,6 [94] 7,6 

Francolite Ca5(PO4) 2,63 (CO3) 0,5F1,11 8,68E-08 -5984,4 -5698,1 1; 3; 9 1 714,3 

Ca(Ce 0,4Ca 0,2Y0,133) (Al2Fe 3+ )Si3O12(OH) 7,81E-08 -6481,6 -6055,4 3 1 32,3 

Orthite- Allanite 

Pentlandite Fe 2+ 

4,5N i4,5S8 7,44E-08 -778,3 -766,2 12 10 6833,9 

Ulexite N aCa(B 5O6(OH) 6)· 5H2O 7,19E-08 -6762,2 -6151,5 1 0 2855,3 

Scapolite- N a4Al3Si 9O24Cl 6,34E-08 -12197,4 -11504,2 1 0 22,5 

Marialite 

Chloritoid Fe 2+ 

1,2M g0,6Mn 2+ 

0,2 Al4Si 2O10(OH) 4 6,18E-08 -6606,9 -6152,6 3 1 159,8 

Pollucite Cs0,6N a0,2Rb0,1Al0,9 Si2,1O6 · (H2O) 6,14E-08 -3297,1 -3074,2 12 10 10,0 

Colemanite Ca2B 6O11· 5H2O 5,99E-08 -6949,7 -6277,0 1; 6; 11 5 -796,8 

Beryl Be3Al 2Si6O 18 5,99E-08 -9006,5 -8500,4 1 0 56,9 

Marcasite FeS2 5,24E-08 -154,9 -156,6 [400] 1434,8 

Grossular Ca3Al 2(SiO 4) 3 4,62E-08 -6631,1 -6281,0 [94] 65,4 

Vaesite N iS2 4,23E-08 -134,2 -126,4 [409] 1320,6 

Gedrite M g5Al2(Si 6Al2O 22)(OH) 2 4,12E-08 -12319,7 -11584,2 1 0 149,9 

Tourmaline- N aFe 

Schorl 

2+ 

3 Al6(BO 3) 3Si6 O18(OH) 4 4,09E-08 -14401,4 -13453,5 1 0 377,6 

Wollastonite CaSiO 3 4,08E-08 -1631,6 -1550,9 [94] 33,1 

Clementite Fe 2+ 

3 M g1,5Al Fe3+ Si3AlO 12(OH) 6 3,81E-08 -7657,8 -7043,1 5 1 504,6 

Cryptomelane K8(M n 4+ 

7,5M n2+ 

0,5 ) O16 3,09E-08 -3743,6 -3432,2 3 1 3409,1 

Kieserite M gSO4 · (H2O) 3,06E-08 -1602,1 -1428,7 [391] 54,2 




page. 


mole/g 

0 

f i , ∆G 

kJ/mole 

0 


kJ/mole 

kJ/mole 

Arsenopyrite FeAsS 2,89E-08 -41,9 -50,2 [94] 1428,0 

Galena P bS 2,79E-08 -100,5 -95,9 [94] 743,6 

Murmanite N a4Ti 3,6N b0,4(Si2O 7) 2O4 · 4(H2O) 2,78E-08 -9804,0 -9096,6 12 10 354,0 

Sylvite KCl 2,74E-08 -437,0 -410,2 [94] 18,5 

Brucite M g(OH) 2 2,71E-08 -925,9 -834,8 [94] 34,9 

Anthophyllite M g7Si8O 22(OH) 2 2,67E-08 -12094,6 -11396,0 [94] 128,6 

Ferrocolum- Fe 

bite 

2+ N b2O6 2,40E-08 -2172,8 -2018,6 12 10 170,5 

Covellite CuS 2,27E-08 -53,2 -53,6 [94] 687,7 

Vernadite M n 4+ 

0,6Fe3+ 0,2Ca 0,2 N a0,1O1,5(OH) 0,5 · 1, 4(H2O) 2,18E-08 -637,8 -571,4 3 1 393,5 

Thorite ThSiO 4 2,13E-08 -2160,5 -2048,8 1; 9 5 27,8 

Nickeline N iAs 2,04E-08 N.A. N.A. N.A. 

Sapphirine M g4Al6.5Si1.5O20 2,04E-08 -10563,3 -9962,9 [94] 2366,3 

Andradite Ca3Fe 2+ 

2 (SiO4) 3 1,96E-08 -5764,4 -5419,4 [94] 92,1 

Chrysoberyl BeAl2O 4 1,80E-08 -2302,3 -2178,2 [94] 20,9 

Cassiterite SnO2 1,73E-08 -581,1 -519,6 [94] 32,0 

Violarite Fe2+ N i2S4 1,72E-08 -378,0 -368,9 1; 9 1 2902,0 

Todorokite N a2Mn 4+ 

4 M n3+ 

2 O12· 3H2O 1,34E-08 -4037,4 -3576,5 3 1 742,6 

Cubanite CuFe 2S3 1,33E-08 -293,7 -302,8 3 1 2406,7 

Topaz Al2(SiO 4)F1,1(OH) 0,9 1,29E-08 -3044,4 -2875,2 10 5 -11,4 

Glauconite (K0,6N a0,05)(Fe 3+ 

1,3 M g0,4Fe 2+ 

0,2Al3+ 0,15 ) (Si3,8Al0,2)O10(OH) 2 1,21E-08 -5150,3 -4785,6 7 0,6 52,1 

Garnierite (N i2M g)Si2O 5(OH) 4 1,18E-08 -3494,6 -3267,1 1; 7; 9 1 25,9 

Molybdenite M oS2 1,14E-08 -271,8 -262,8 [284] 1682,2 

Clinohumite M g6,75Fe 2,25Si4O 16 (OH) 0,5F1,5 1,10E-08 -8966,4 -8410,0 10 1 613,5 

Tridymite SiO2 1,05E-08 -909,7 -855,9 [94] 2,3 

Euxenite Y0,7Ca 0,2Ce 0,1(Ta0,2) 2 (N b0,7) 2(T i0,025)O6 1,02E-08 -2671,5 -2506,3 12 10 136,7 

Gersdorffite N iAsS 9,70E-09 N.A. -144,3 [205] 1189,5 

Jarosite K Fe 3+ 

3 (SO4) 2(OH) 6 9,57E-09 -3521,7 -3318,7 ∆G0 : [94] ∆H0 : 12 10 208,5 

f f 

Humite M g5,25Fe 2+ 

1,75 (SiO4) 3 F1,5(OH) 0,5 9,46E-09 -6953,7 -6512,3 3; 10 5 504,3 

Scheelite CaW O4 9,28E-09 -1646,2 -1419,6 [94] 139,8 

Kornerupine M g1,1Fe 0,2Al5,7 (Si3,7B0,3)O17,2(OH) 9,24E-09 -9172,9 -8624,8 3 1 173,8 

Omphacite Ca0,6N a0,4M g0,6Al0,3 Fe0,1Si2O 6 7,48E-09 -3075,5 -2904,3 2 1 38,7 

Phenakite Be2SiO 4 7,31E-09 -2146,2 -2033,3 [94] 34,1 

Hisingerite Fe 3+ 

2 Si2O5(OH) 4 · 2(H2O) 6,25E-09 -3229,6 -2895,6 [383] 1012,8 

Uraninite UO2 5,60E-09 -1085,6 -1032,5 [94] 167,6 

Malachite Cu2(CO 3)(OH) 2 5,46E-09 -1052,1 -906,0 [94] 24,3 

Strontianite SrCO 3 5,34E-09 -1220,9 -1140,1 [94] 34,9 

Brookite T iO2 5,27E-09 -942,4 -821,9 [94] 86,5 

Perovskite CaT iO3 5,10E-09 -1662,2 -1575,7 [94] 58,5 

Yttrialite Y1.5Th 0.5Si2O 7 4,64E-09 N.A. N.A. N.A. 




page. 


mole/g 

0 

f i , ∆G 

kJ/mole 

0 


kJ/mole 

kJ/mole 

Azurite Cu3(CO 3) 2(OH) 2 4,38E-09 -1633,3 -1447,5 [94] 39,0 

Copper Cu 3,90E-09 0,0 0,0 [94] 134,0 

Pyrochlore N aCaN b2O6(OH) 0,75F0,25 3,47E-09 -2897,9 -2687,3 10; 12 10 345,0 

Bertrandite Be4Si 2O7(OH) 2 3,38E-09 -4586,1 -4300,6 1 0 72,3 


5 T iSi6O20 3,16E-09 -8184,4 -7660,9 12 10 -164,8 

Carnotite K2(UO 2) 2(VO 4) 2 · 3H2O 2,80E-09 -4907,3 -4585,5 [191] 792,4 

Palygorskite M gAlSi 4O10(OH) · 4(H2O) 2,77E-09 -6477,8 -5939,9 5 1 440,4 

Dietzeite Ca2(IO 3) 2(C rO4) 2,76E-09 -2425,4 -2148,1 12 10 78,7 

Lautarite Ca(IO 3) 2 2,76E-09 -1002,5 -839,3 [391] 71,4 

Bornite Cu5FeS 4 2,65E-09 -334,5 -393,1 [94] 3083,0 

Dawsonite N aAl(CO 3)(OH) 2 2,51E-09 -1965,3 -1787,3 [94] -0,1 

Cryolite N a3AlF 6 2,36E-09 -3311,3 -3144,7 [94] 327,9 

Orpiment As2S3 1,85E-09 -169,1 -168,7 [94] 2641,2 

Sulphur S8 1,84E-09 0,0 0,0 [94] 4858,2 

Zinc Zn 1,55E-09 0,0 0,0 [94] 339,0 

Helvine/ M n4Be3(SiO 4) 3S 1,45E-09 -5843,9 -5532,4 12 10 1407,7 

Helvite 

Carnallite K M gCl 3 · 6(H2O) 1,45E-09 -2946,7 N.A. [132] N.A. 

Gadolinite Y2Fe 2+ Be2(Si 2O10) 1,41E-09 -5220,0 -4943,3 12 10 299,7 

Xenotime Y bPO4 1,38E-09 -1868,6 -1790,3 [388] 24,2 

Nosean N a8Al6Si 6O24 SO4 1,29E-09 -13936,7 -13131,5 10 5 115,0 


0,5M n0,5W O4 1,06E-09 -1246,2 -1146,4 2 1 120,0 

Hydrosodalite N a8Al6Si 6O24 (OH) 2 9,06E-10 -13408,5 -12678,2 3, 10 5 193,1 

Cerussite P bCO3 8,27E-10 -700,0 -627,5 [94] 20,9 

Stibnite Sb2S 3 8,10E-10 -175,0 -173,7 [94] 2522,3 

Greenockite CdS 8,01E-10 -162,0 -156,5 [94] 743,9 

Chalcocite Cu2S 6,83E-10 -79,5 -86,2 [94] 789,1 

Smithsonite ZnCO 3 6,36E-10 -813,3 -731,9 [94] 23,3 

Blomstran- U0,3Ca 0,2N b0,9Ti 0,8Al0,1 Fe 

dite/ Betafite 

3+ 

0,1Ta0,5O6(OH) 4,96E-10 -2884,5 -2683,8 12 10 90,0 

Loparite - (Ce) N a0,6Ce 0,22 La0,11 Ca0,1Ti 0,8N b0,2O3 4,81E-10 -1430,8 -1343,6 12 10 181,6 

Pleonaste/ M gFe 

Magnesi<strong>of</strong>errite 

3+ 

2 O4 4,40E-10 -1429,4 -1351,0 [94] 40,2 

Eudyalite N a4Ca 2Fe 2+ 

0,7M n0,3Z r Si8O22(OH) 1,5Cl 1,5 4,30E-10 -11859,9 -11062,9 1; 3; 10 1 335,0 

Sirtolite Z rSiO 4 4,02E-10 -2034,8 -1919,2 [94] 20,3 

Bisch<strong>of</strong>ite M gCl 2 · 6(H2O) 3,96E-10 -2500,7 -2116,4 [94] 66,0 

Tin Sn 3,87E-10 0,0 0,0 [94] 547,6 

Anglesite P bSO4 3,82E-10 -920,0 -784,5 [94] 62,9 

Ramsayite/ N a2Ti 2Si2O 9 3,62E-10 -4360,1 -4103,9 12 10 104,3 

Lorenzenite 




page. 


mole/g 

0 

f i , ∆G 

kJ/mole 

0 


kJ/mole 

kJ/mole 

Ferrotantalite Fe2+ Ta2O6 3,07E-10 -2319,3 -2163,9 12 10 174,5 

Lead P b 3,05E-10 0,0 0,0 [94] 232,2 

Chondrodite M g3,75Fe 2+ 

1,25 (SiO4) 2 F1,5(OH) 0,5 2,93E-10 -5023,0 -4701,4 10; 5 5 564,2 

Arsenolite As2O3 2,80E-10 -659,8 -579,1 [94] 415,0 

Cinnabar H gS 2,46E-10 -58,2 -50,7 [94] 671,3 

Iotsite FeO 2,38E-10 -272,1 -251,5 [94] 127,3 

Britholite Ca2,9Ce 0,9Th 0,6 La0,4N d0,2 Si2,7P0,5O12(OH) 0,8F0,2 2,18E-10 -7057,3 -6666,9 10; 12 10 734,0 

Sodalite N a8Al6Si 6O24Cl 2 2,05E-10 -13457,0 -12703,6 [187] 51,9 

Native silver Ag 1,94E-10 0,0 0,0 [94] 69,7 

Axinite- Fe Ca2Fe 2+ Al2BO 3 Si4O12(OH) 1,93E-10 -7640,4 -7180,9 12 10 427,3 

Realgar As4S4 1,40E-10 -140,3 -132,7 1 0 4272,6 

Bismuth Bi 1,30E-10 0,0 0,0 [94] 274,8 

Bismutite Bi2(CO 3)O2 1,19E-10 -968,0 -888,7 12 10 81,1 

Rhabdophane Ce0,75 La0,25(PO 4) · H2O 1,03E-10 -1964,9 -1821,9 2 1 325,0 

Bismite Bi2O3 9,91E-11 -574,3 -493,7 [94] 61,9 

Bismuthinite Bi2S3 9,91E-11 -143,2 -140,6 [94] 2230,8 

Baddeleyite Z rO2 9,75E-11 -1101,3 -1043,3 [94] 38,1 

Fergusonite N d0,4Ce 0,4Sm0,1Y0,1N bO4 8,08E-11 -2808,3 -2631,2 12 10 -717,4 

Cobaltite CoAsS 5,06E-11 -163,1 N.A. 3 1 N.A. 

Smaltite CoAs 2 5,06E-11 -61,5 N.A. [391] N.A. 

Argentite Ag2S 4,99E-11 -29,4 -39,4 [94] 707,3 

Cancrinite N a6Ca 2Al6Si 6O24(CO 3) 2 4,20E-11 -14980,9 -14136,3 12 10 101,8 

Moissanite SiC 3,51E-11 -62,8 -60,3 [94] 1204,1 

Uranium- ThSiO 4 3,18E-11 -2160,5 -2048,8 1; 9 5 27,8 

Thorite 

Powellite CaM oO4 3,05E-11 -1542,4 -1434,7 [94] 27,6 

Chevkinite Ce1,7 La1,4Ca 0,8Th 0,1 Fe 2+ 

1,8M g0,5 T i2,5Fe 3+ 

0,5Si4O 22 2,76E-11 -10499,8 -9894,5 12 10 1006,2 

Acanthite Ag2S 2,74E-11 -32,4 -40,3 [94] 706,4 

Lavenite N a1,1Ca 0,9Mn 2+ 

0,5Fe2+ 0,5Z r0,8Ti 0,1N b0,1(Si2O 7) 

2,59E-11 -4191,1 -3925,1 10; 12 10 604,8 

O0,6(OH) 0,3F0,1 Pyrargirite Ag3S bS3 2,38E-11 -131,5 -142,2 9 5 2325,9 

Linnaeite Co3S 4 1,69E-11 -307,3 -323,6 [94] 3032,2 

Thorianite ThO2 1,56E-11 -1227,2 -1169,6 [94] 48,8 

Troilite FeS 1,19E-11 -100,5 -99,9 [94] 884,2 

Microlite N a0,4Ca 1,6Ta2O 6,6 (OH) 0,3F0,1 8,71E-12 -3208,3 -3004,3 10; 12 10 315,1 

Delorenzite/ Y0,7Ca 0,2Ce 0,12(Ta0,7) 2 (N b0,2) 2(T i0,1)O5,5(OH) 0,5 8,33E-12 -2721,2 -2549,9 12 10 54,6 

Tanteuxenite 

Stephanite Ag5S bS4 7,72E-12 -166,1 -184,5 3 5 3030,3 

Naegite Z rSiO 4 6,98E-12 -2034,8 -1919,2 [94] 20,3 

Gold Au 6,47E-12 0,0 0,0 [94] 51,5 




page. 


mole/g 

0 

f i , ∆G 

kJ/mole 

0 


kJ/mole 

kJ/mole 

Lampro- phyl- N a2SrBaT i3Si4O 16(OH)F 5,61E-12 -8401,2 -7865,3 10; 12 10 892,0 

lite 

Chlorargirite AgCl 5,47E-12 -127,2 -109,9 [94] 22,0 

Periclase M gO 3,77E-12 -602,2 -569,5 [94] 62,1 

Chrysocolla Cu2Si 2O6(H 2O) 4 3,54E-12 -3279,4 -2964,6 ∆G0 : [94] ∆H0 :12 10 -23,9 

f f 

Freibergite Ag7,2Cu 3,6Fe 2+ 

1,2 Sb3AsS 13 3,52E-12 -703,2 -727,5 3 5 10786,0 

Metacinnabar H gS 3,17E-12 -53,6 -47,7 [94] 674,3 

Vivianite Fe3(PO 4) 2(H2O) 8 2,59E-12 -4608,4 -4428,2 ∆H 0: 

12 10 457,4 

f 

Cooperite P t0,6Pd 0,3N i0,1S 2,11E-12 -79,8 -73,8 3 1 688,3 

Miserite KCa 2Ce 3Si8O 22 (OH) 1,5F0,5 2,00E-12 -11738,2 -11035,1 10; 12 10 1138,1 

Tortbernite Cu(UO 2)2(PO 4)2 · 8(H2O) 1,81E-12 -4455,9 -4129,8 [191] 151,6 

Weinschenkite Y PO4 1,68E-12 -1987,7 -1871,1 1 0 -35,2 

Wulfenite P bM oO4 1,66E-12 -1112,9 -952,8 [94] 17,8 

Loellingite FeAs2 1,30E-12 -85,7 -80,2 1 0 1284,7 

Tennantite Cu10Fe 2As4S 13 1,24E-12 -1968,6 -1999,6 1 0 9965,1 

Tellurite TeO2 1,14E-12 -322,8 -270,3 [94] 60,0 

Sylvanite Au0,75Ag0,25Te2 7,62E-13 N.A. N.A. N.A. 

Nordite N a2,8Mn 2+ 

0,2Sr0,5Ca 0,5 La0,33Ce 0,6Zn 0,6 M g0,4Si6O 17 7,20E-13 -8020,8 -7532,2 12 10 958,5 

Calaverite AuTe2 5,71E-13 -19,0 -17,4 1 0 686,8 

Samsonite Ag4MnSb2S 6 5,29E-13 -444,9 -463,5 3 5 4817,9 

Tetrahedrite Cu10Fe 2S b4S13 3,47E-13 -1909,5 -1939,7 1 0 9797,1 

Thortveitite Sc1,5Y0,5Si2O 7 2,71E-13 -3740,2 -3540,6 2; 9 5 50,5 

Tetradymite Bi2Te 2S 2,27E-13 -100,2 -100,6 2 1 1709,0 

Rinkolite/ N a2Ca 3Ce 1,5Y0,5 T i0,4N b0,5Z r0,1(Si2O 7) 2 O1,5F3,5 2,25E-13 -9415,1 -8808,5 10; 12 10 1441,1 

Mosandrite 

Alunite KAl3(SO 4)2(OH) 6 2,20E-13 -5173,2 -4652,2 [94] 127,3 

Osmium Os0.75I r0.25 1,57E-13 N.A. N.A. 342,1 

Iridium I r0.5Os0.3Ru0.2 1,50E-13 N.A. N.A. N.A. 

Dumortierite Al6.9(BO3)(SiO4) 3O2.5(OH) 0.5 1,33E-13 -9109,0 -8568,0 [135] 108,9 

Polycrase (Y) Y0,5Ca 0,1Ce 0,1U0,1 Th0,1Ti 1,2N b0,6Ta0,2O6 2,46E-14 -2847,7 -2681,3 12 10 125,4 

I-Platinum P t 1,54E-14 0,0 0,0 [94] 146,5 

Polixene/ P t Fe 1,20E-14 N.A. N.A. N.A. 

Tetraferroplatinum 

Boulangerite P b5S b4S11 2,12E-15 -1034,5 -1023,7 1; 9 5 8565,5 

Wohlerite N aCa2Z r0,6N b0,4 Si2O8,4(OH) 0,3F0,3 1,27E-15 -4439,7 -4170,0 10; 12 10 466,6 



According to table 6.7, <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> 291 main <strong>mineral</strong>s included 

in <strong>the</strong> crust have been obtained. About a half <strong>of</strong> <strong>the</strong> properties (159) were 

compiled directly from <strong>the</strong> literature. The remaining were obtained with <strong>the</strong> 12 

different estimation methods described in section 5.4. From <strong>the</strong> latter, 18 <strong>mineral</strong>s 

were calculated with method 1, and hence without committing any associated error. 

Five <strong>mineral</strong>s were estimated with <strong>the</strong> method for hydrated clay <strong>mineral</strong>s and for 

phyllosilicates (M.7), committing a maximum error <strong>of</strong> ε < 0, 6%. Thirty-eight <strong>mineral</strong>s 

were estimated with an error smaller than 1%, 20 substances with ε < 5%, 

and 44 <strong>mineral</strong>s with ε < 10%. Only <strong>the</strong> properties <strong>of</strong> 6 <strong>mineral</strong>s 3 : iridium, osmium 

4 , nickeline, polixene, sylvanite and yttrialite were not able to be estimated. 

Additionally, <strong>the</strong> enthalpy <strong>of</strong> formation <strong>of</strong> gersdorffite and <strong>the</strong> Gibbs free energy <strong>of</strong> 

smaltite are missing. Never<strong>the</strong>less, all toge<strong>the</strong>r account for only 3, 5 × 10 −6 % <strong>of</strong> <strong>the</strong> 

continental crust. 

The average standard enthalpy, Gibbs free energy and chemical exergy <strong>of</strong> <strong>the</strong> upper 

continental crust, for an average molecular weight <strong>of</strong> <strong>the</strong> crust 5 equal to MW cr = 

157, 7 g/mole is: 

(∆H 0 

f ) cr = 

(∆G 0 

f ) cr = 

(b 0 

ch ) cr = 

m 

(ξi · ∆H 0 

f ,i ) · MWcr = −1958, 92 kJ/mole 

i=1 

m 

(ξi · ∆G 0 

f ,i ) · MWcr = −1835, 82 kJ/mole 

i=1 

m 

(ξi · b 0 

ch i ) · MWcr = 372, 60 kJ/mole 

i=1 

As it happened to <strong>the</strong> hydrosphere, our R.E. generates some negative exergies <strong>of</strong> <strong>the</strong> 

<strong>mineral</strong>s, but far less than with Ranz’s R.E [276]. This is because, as stated above, 

we chose our R.E. based on Szargut’s criterion <strong>of</strong> partial stability. According to this, 

among a group <strong>of</strong> reasonable abundant substances, <strong>the</strong> most stable will be chosen 

if <strong>the</strong>y also complain with <strong>the</strong> “earth similarity criterion”. This criterium is different 

from that <strong>of</strong> Ahrendt’s [4] or Diederichsen [74], where complete stability was 

assumed. As a consequence, <strong>the</strong> latter R.E. do not generate any negative exergies, 

but <strong>the</strong> resulting environment is completely different from that <strong>of</strong> <strong>the</strong> current earth. 

3 Excluding Cor g, since no exact composition can be applied. 

4 The standard enthalpy and Gibbs free energy <strong>of</strong> iridium and osmium (Os0,5I r 0,3Ru 0,2 and 

Os 0,75I r 0,25) could be estimated considering <strong>the</strong> compunds as solid solutions <strong>of</strong> elements Os, I r, and 

Re. Since for all three substances ∆G f =0 and ∆H f =0, <strong>the</strong> standard enthalpy <strong>of</strong> formation <strong>of</strong> iridium 

and osmium would be also ∆H f =0, applying <strong>the</strong> solid solution method. Similarly, <strong>the</strong> standard Gibbs 

free energy <strong>of</strong> formation would correspond to <strong>the</strong> entropy <strong>of</strong> <strong>the</strong> mixture. Hence, ∆G f =2,5 kJ/mole 

for iridium and ∆G f =5,1 kJ/mole for osmium. We do not include <strong>the</strong>se values in <strong>the</strong> table, since <strong>the</strong> 

errors associated might be very significant. 

5 As calculated in this study (section 3.6).

An approach to <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> crepuscular earth 205 

Our chosen R.E. obeys in principle <strong>the</strong> “earth similarity criterion”, but does generate 

some negative exergies. Hence, this leads us to question again <strong>the</strong> methodology 

used and <strong>the</strong> proposed R.E. 

6.2.4 The chemical exergy <strong>of</strong> <strong>the</strong> earth 

In chapter 2, we described some physical properties <strong>of</strong> <strong>the</strong> bulk earth that are now 

required for our calculations. According to Beichner [23], <strong>the</strong> earth has a mass <strong>of</strong> 

around 5, 98 × 10 24 kg. The earth’s relative mass proportions <strong>of</strong> each <strong>of</strong> <strong>the</strong> earth’s 

spheres are according to Javoy [169]: core (35,5%), mantle (67%), oceanic crust 

(0,072%), continental crust (0,36%), hydrosphere (0,023%) and atmosphere (0,842 

ppm). The upper layer <strong>of</strong> <strong>the</strong> crust constitutes a mass <strong>of</strong> around 50% <strong>of</strong> <strong>the</strong> whole 

continental crust [411]. With <strong>the</strong> information provided in <strong>the</strong> previous sections, 

we are now able to calculate <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> outer layers <strong>of</strong> <strong>the</strong> earth, 

namely <strong>the</strong> atmosphere, hydrosphere and upper continental crust. Table 6.8 shows 

<strong>the</strong> standard chemical exergy <strong>of</strong> <strong>the</strong> aforementioned layers and <strong>the</strong>ir sum. 

Table 6.8. The standard chemical exergy <strong>of</strong> <strong>the</strong> earth’s outer layers 

, kJ/mole B0 

ch , Gtoe 

Atmosphere 5,04E+18 28,96 1,51 6,27E+03 

Hydrosphere 1,38E+21 18,29 0,87 7,80E+05 

Upper continental crust 1,08E+22 157,7 372,60 1,21E+09 

SUM 1,22E+09 

Layer Mass, kg MW, g/mole b 0 

ch 

The results <strong>of</strong> table 6.8 indicate that <strong>the</strong> standard chemical exergy <strong>of</strong> <strong>the</strong> earth’s 

outer spheres is 1, 22 × 10 9 Gtoe. This can be considered as a rough number, and is 

subject to updates, especially when a more appropriate R.E. is found. But <strong>the</strong> order 

<strong>of</strong> magnitude is good enough for realizing <strong>the</strong> huge chemical exergy content <strong>of</strong> <strong>the</strong> 

earth. From all layers, <strong>the</strong> upper continental crust is responsible for most <strong>of</strong> <strong>the</strong> 

exergy (99,9%), due to its greater mass portion and specific exergy. Although <strong>the</strong> 

relative proportion <strong>of</strong> <strong>the</strong> atmosphere and hydrosphere is small when compared to 

<strong>the</strong> whole, <strong>the</strong>ir chemical exergies are also huge: 6, 27 × 10 3 Gtoe and 7, 80 × 10 5 

Gtoe, respectively. Since <strong>the</strong> earth can be considered as a closed system, its chemical 

exergy is considered as a non-renewable reservoir. 

6.3 An approach to <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> 

crepuscular earth 

As stated before, <strong>the</strong> crepuscular or entropic planet, is a completely degraded earth, 

where all materials have reacted, dispersed and mixed. And this degraded earth is


not necessarily equivalent to <strong>the</strong> reference environments used so far. The crepuscular 

earth represents a planet towards we are inexorably approaching, as <strong>mineral</strong> 

resources are extracted and dispersed, fossil fuels are burned, and waters are polluted 

by humankind. The model <strong>of</strong> crepuscular earth is composed by an atmosphere, 

hydrosphere and continental crust, but differs from <strong>the</strong> current one in <strong>the</strong> absence 

<strong>of</strong> concentrated <strong>mineral</strong>s and freshwater. Fur<strong>the</strong>rmore, <strong>the</strong> atmosphere contains a 

higher CO 2 concentration due to <strong>the</strong> complete burning <strong>of</strong> fossil fuels. 

According to table 4.10, <strong>the</strong> amount <strong>of</strong> <strong>the</strong> considered non-fuel <strong>mineral</strong> world resources 

by <strong>the</strong> USGS is in <strong>the</strong> order <strong>of</strong> 10 15 kg. When <strong>the</strong> rest <strong>of</strong> <strong>mineral</strong>s are 

considered, <strong>the</strong> total quantity <strong>of</strong> concentrated <strong>mineral</strong>s might increase in one or two 

orders <strong>of</strong> magnitude, hence to around 10 17 kg. The amount <strong>of</strong> possible available 

fuels, according to table 6.19 is around 10 16 kg 6 . This means that all concentrated 

<strong>mineral</strong> resources <strong>of</strong> fuel and non fuel origin only represent 0,001% <strong>of</strong> <strong>the</strong> total 

mass <strong>of</strong> <strong>the</strong> earth’s upper crust. Therefore, we can state with no significant error, 

that <strong>the</strong> upper continental crust <strong>of</strong> <strong>the</strong> entropic planet can be approximated to <strong>the</strong> 

average <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> earth’s crust. And this in turn can be approximated 

to <strong>the</strong> composition estimated in this PhD (table 3.5), at least until it is 

fur<strong>the</strong>r improved with better geochemical information. 

Concerning <strong>the</strong> hydrosphere, we saw that <strong>the</strong> amount <strong>of</strong> freshwater on earth stored 

in <strong>the</strong> form <strong>of</strong> rivers, lakes, glaciers and groundwater represents only 3%. Therefore, 

<strong>the</strong> final composition <strong>of</strong> <strong>the</strong> hydrosphere <strong>of</strong> <strong>the</strong> crepuscular planet when all waters 

are mixed, can be very well approximated to that <strong>of</strong> seawater, which is well known 

(tables 2.5 and 2.6). 

Finally <strong>the</strong> atmosphere <strong>of</strong> <strong>the</strong> entropic planet will be composed <strong>of</strong> <strong>the</strong> same substances 

appearing in <strong>the</strong> current atmosphere (table 2.2), but presumably with a 

higher concentration <strong>of</strong> CO 2 and o<strong>the</strong>r anthropogenic gases. According to <strong>the</strong> IPCC 

SRES report [160], in <strong>the</strong> worst scenario <strong>of</strong> emissions, where practically all available 

conventional fossil fuels are burned, <strong>the</strong> CO 2 concentration in <strong>the</strong> atmosphere will 

increase to 710 ppm. Assuming that <strong>the</strong> ratio 7 , <strong>of</strong> burned fuel to increase <strong>of</strong> CO 2 concentration 

is 4 Gtoe/CO 2 ppm, <strong>the</strong> burning <strong>of</strong> available unconventional fossil fuels 

(around 2600 Gtoe), would imply an additional increase <strong>of</strong> 650 ppm in <strong>the</strong> atmosphere. 

Consequently, <strong>the</strong> final carbon dioxide concentration in <strong>the</strong> atmosphere <strong>of</strong> <strong>the</strong> 

crepuscular planet would be around 1400 ppm. This value is only approximative, 

since it has been assumed a linear relationship between <strong>the</strong> burning <strong>of</strong> fossil fuels, 

and <strong>the</strong> increase <strong>of</strong> CO 2 in <strong>the</strong> atmosphere. In fact, <strong>the</strong> processes that rule <strong>the</strong> carbon 

cycle and <strong>the</strong> earth’s climate are very complex and in many cases unpredictable. 

It should be noted, that an increase <strong>of</strong> CO 2 concentration would imply an equivalent 

reduction <strong>of</strong> <strong>the</strong> O 2 content in <strong>the</strong> atmosphere. Hence, instead <strong>of</strong> being 20,94% 

<strong>the</strong> volume fraction <strong>of</strong> oxygen in <strong>the</strong> atmosphere, this would be 20,83%, since 1100 

6This corresponds to around 300 Gtons <strong>of</strong> oil, 3000 Gtons <strong>of</strong> coal, 500 Gtons <strong>of</strong> natural gas and 

7000 Gtons <strong>of</strong> unconventional fossil fuels. 

7According to <strong>the</strong> trends observed in <strong>the</strong> SRES report [160] for all six different scenarios analyzed.

The exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources 207 

ppm would be included in <strong>the</strong> molecules <strong>of</strong> <strong>the</strong> extra CO 2 appearing in <strong>the</strong> entropic 

earth. In addition to <strong>the</strong> latter, increases in <strong>the</strong> concentration <strong>of</strong> methane, nitrous 

oxide, carbon monoxide, nitrogen oxides, chlorides, sulphides, etc. are expected in 

<strong>the</strong> crepuscular planet, due to <strong>the</strong> anthropogenic action. But <strong>the</strong> latter figures cannot 

be easily estimated and remain open for fur<strong>the</strong>r studies. 

With this preliminary model <strong>of</strong> crepuscular planet, toge<strong>the</strong>r with <strong>the</strong> <strong>the</strong>rmodynamic 

properties <strong>of</strong> all its constituents estimated in this PhD, a new reference environment 

could be proposed, for <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> chemical exergies <strong>of</strong> <strong>the</strong> elements. A 

model <strong>of</strong> degraded earth would not contain only a reference substance per element, 

as it happens to <strong>the</strong> R.E. in which we have based our calculations. The new model 

should calculate <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> elements, taking into account all <strong>the</strong> substances 

appearing in <strong>the</strong> planet that contain that element. Hence, we think that <strong>the</strong> 

calculation procedures and even <strong>the</strong> philosophy for obtaining <strong>the</strong> chemical exergies 

<strong>of</strong> <strong>the</strong> elements should be reviewed, since <strong>the</strong> selection <strong>of</strong> an appropriate R.E. is a 

required but not a sufficient condition, as seen with Pinaev’s environment. But this 

activity remains open for fur<strong>the</strong>r studies in <strong>the</strong> future. 

6.4 The exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources 

In <strong>the</strong> last sections, we have obtained <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> main substances 

that compose <strong>the</strong> earth. We will now focus on a very small part <strong>of</strong> <strong>the</strong> earth’s constituents: 

<strong>the</strong> <strong>mineral</strong> resources. 

For that purpose, <strong>the</strong> average exergy <strong>of</strong> <strong>the</strong> main fuel <strong>mineral</strong>s (coal, oil and natural 

gas) is obtained, so as to calculate <strong>the</strong> world’s proven fuel reserves. Additionally, <strong>the</strong> 

exergy <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong> reserves, reserve base and world resources is 

obtained. 

This information, toge<strong>the</strong>r with <strong>the</strong> data provided in chapter 4 about o<strong>the</strong>r energy 

sources, will allow us to analyze <strong>the</strong> current state <strong>of</strong> <strong>the</strong> main natural resources on 


6.4.1 The exergy contained in fossil fuels 

We saw in chapter 5, that <strong>the</strong> physical value <strong>of</strong> fuels is tightly related to its chemical 

exergy content. Hence, <strong>the</strong> physical value <strong>of</strong> <strong>the</strong> world’s proven fuel reserves can 

be approximated to <strong>the</strong>ir chemical exergy 8 , which is obtained with <strong>the</strong> equations 

provided in section 5.3.3. It must be remembered, that <strong>the</strong> exergy calculation <strong>of</strong> 

fuels is undertaken with <strong>the</strong> models developed by Valero and Lozano [369] and not 

with Eq. 5.1, due to <strong>the</strong> complexity and heterogeneity <strong>of</strong> <strong>the</strong> fuel’s composition. 

8 It must be remembered that in chapter 4, an approximative exergy value in terms <strong>of</strong> Gtoe was 

given for <strong>the</strong> proven reserves <strong>of</strong> coal, oil and natural gas.


Table 6.9. High heating value and elementary analysis (% by weight) considered in 

<strong>the</strong> study <strong>of</strong> Valero and Arauzo [366] to define different types <strong>of</strong> coal. 

RANK HHV, 

kJ/kg 

O H C N S Z W 

Anthracite 30675 2,4 3,0 80,9 1,0 0,5 10,1 2,1 

Bituminous 28241 7,6 4,5 68,7 1,6 1,2 8,4 8,0 

Subbitum. 23590 12,2 3,8 58,8 1,3 0,3 4,0 19,6 

Lignite 16400 8,9 2,7 38,9 0,6 5,3 19,8 23,8 

Table 6.10. Thermodynamic properties <strong>of</strong> <strong>the</strong> different types <strong>of</strong> coal. Values in 

kJ/kg, except for s 0 (kJ/kgK) 

Type HHV ∆H 0 

f s 0 e I e I I e I I I b I b I I b I I I 

Anthrac. 30675 -136,2 0,9 29980,2 30687,1 30739,9 31583,8 31584,7 31624,2 

Bitum. 28241 -757,7 1,1 27083,4 28262,1 28389,3 28950,6 28952,1 29047,1 

Subitum. 23590 -1125,0 1,0 22264,5 23574,2 23606,0 24251,0 24252,7 24276,5 

Lignite 16400 -662,7 0,8 15241,9 16413,9 16975,0 16930,2 16931,6 17351,1 

The calculations will be carried out, assuming an average composition <strong>of</strong> <strong>the</strong> different 

types <strong>of</strong> coal, oil and natural gas. A mean composition <strong>of</strong> <strong>the</strong> fuels, was already 

studied by Valero and Arauzo [366], taking into account <strong>the</strong> conversion factors reported 

by <strong>the</strong> IEA assigned to <strong>the</strong> fuels in each country. Their analysis will be used in 

this study. It must be pointed out, that although <strong>the</strong> latter analysis was carried out 

with quite old data (statistics from 1989), and that <strong>the</strong> reserves figures have changed 

since <strong>the</strong>n, <strong>the</strong> average composition <strong>of</strong> <strong>the</strong> fuels should not have varied significantly. 

6.4.1.1 Coal 

The elementary analysis <strong>of</strong> each rank <strong>of</strong> coal chosen by Valero and Arauzo [366] is 

shown in table 6.9. 

The composition <strong>of</strong> <strong>the</strong> fuels listed in table 6.9, throw up <strong>the</strong> properties shown in 

table 6.10, where ∆H 0 

f and s0 are <strong>the</strong> standard enthalpy and entropy <strong>of</strong> formation, 

eI, eI I and eI I I, <strong>the</strong> chemical energy <strong>of</strong> <strong>the</strong> fuel corresponding to <strong>the</strong> R.E. I, II and III 

from table 5.5, and bI, bI I and bI I I <strong>the</strong> chemical exergy for <strong>the</strong> three R.E., respectively. 

As can be seen from <strong>the</strong> table, R.E. III produces <strong>the</strong> greatest exergy values, although 

<strong>the</strong> difference between <strong>the</strong> three is very small (around 0,3% and a maximum <strong>of</strong> 2,5% 

for lignite between I and III). Assuming an exergy content <strong>of</strong> coal equal to <strong>the</strong> HHV, 

implies an associated error <strong>of</strong> about 3%, although for lignite, this could be up to 6%. 

Next, <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> proven reserves <strong>of</strong> coal is calculated. The main sources <strong>of</strong> 

data for coal reserves come from BP and WEC. The WEC study complements <strong>the</strong>


BP Statistical Review and <strong>the</strong> World Energy Outlook. It collects <strong>the</strong>se data from 96 

WEC Member Committees worldwide. The difference <strong>of</strong> <strong>the</strong> proven reserve figures 

between both entities (WEC and BP) is 7,3%. According to <strong>the</strong> Energy Watch Group 

[89], <strong>the</strong> BP report just reproduces <strong>the</strong> data which are collected by <strong>the</strong> World Energy 

Council. Therefore, we will take into account <strong>the</strong> figures <strong>of</strong> <strong>the</strong> WEC’s Survey <strong>of</strong> 

Energy Resources 2007 [401]. 

The proven reserves data are provided for <strong>the</strong> different countries, reported as three 

different types <strong>of</strong> coal: 1) anthracite and bituminous, 2) subbituminous and 3) lignite. 

Since we need to know <strong>the</strong> separate quantities <strong>of</strong> anthracite and bituminous in 

order to calculate <strong>the</strong> exergy, we will assume that only hard coal 9 coming from <strong>the</strong> 

USA is anthracite 10 . 

The exergy values shown in table 6.11, are generated from R.E. III, which is <strong>the</strong> most 

commonly used for fuel calculations (Lozano and Valero [202]). 

Table 6.11: The exergy <strong>of</strong> <strong>the</strong> world’s coal proven reserves reported 

in [401]. Values in million tonnes if not specified 

Country Anthracite Bitumin. Subbitum. Lignite Exegy, Mtoe 

Algeria 59 40,8 

Botswana 40 27,7 

Central 

3 1,2 

African 

publicRe- 

Congo 

(Democratic 

Rep.) 

88 60,9 

Egypt 

Rep.) 

(Arab 

21 14,5 

Malawi 2 1,2 

Morocco N.A. N.A. 

Mozambique 212 146,6 

Niger 70 48,4 

Nigeria 21 169 112,2 

South Africa 48000 33196,7 

Swaziland 208 143,9 

Tanzania 200 138,3 

Zambia 10 6,9 


9Hard coal is ano<strong>the</strong>r name given to anthracite and bituminous, as opposed to brown coal, which 

is given to subbituminous and lignite. 

10The conversion factors reported by <strong>the</strong> IEA [153] for coal in <strong>the</strong> different countries indicates that 

US coal is <strong>the</strong> one with <strong>the</strong> highest heating capacity.



in [401]. Values in million tonnes if not specified. – 



Zimbabwe 502 347,2 

Total Africa 49431 171 3 34286,5 

Canada 3471 871 2236 3827,7 

Greenland 183 105,8 

Mexico 860 300 51 789,2 

USA 112261 100086 30374 154926,6 

Total 

America 

N. 112261 4331 101440 32661 159649,3 

Argentina 424 245,1 

Bolivia 1 0,7 

Brazil 7068 4085,4 

Chile 31 1150 686,2 

Colombia 6578 381 4769,6 

Ecuador 24 9,9 

Peru 140 96,8 

Venezuela 479 331,3 

Total 

America 

S. 

7229 9023 24 10224,9 

Afghanistan 66 45,6 

China 62200 33700 18600 70180,4 

India 52240 4258 37888,2 

Indonesia 1721 1809 798 2565,5 

Japan 355 245,5 

Kazakhstan 28170 3130 20775,4 

Korea 

(Democratic 

People’s 

Rep.) 

300 300 380,9 

Korea 

public)(Re- 

135 78,0 

Kyrgyzstan 812 335,5 

Malaysia 

Mongolia 

4 2,8 

Myanmar 

(Burma) 

2 1,4 

Nepal 1 0,6 

Pakistan 1 167 1814 846,6 







Philippines 41 170 105 170,0 

Taiwan, 

China 

1 0,7 

Thailand 1354 559,4 

Turkey 1814 749,4 

Uzbekistan 1000 2000 1517,8 

Vietnam 150 103,7 

Total Asia 146251 36282 34685 136447,4 

Albania 794 328,0 

Bulgaria 5 63 1928 836,4 

Czech Republic 

1673 2617 211 2756,9 

Germany 152 6556 2813,5 

Greece 3900 1611,2 

Hungary 199 170 2933 1447,6 

Ireland 14 9,7 

Italy 10 5,8 

Montenegro 0,0 

Norway 5 2,9 

Poland 6012 1490 4773,4 

Portugal 3 33 15,7 

Romania 12 2 408 178,0 

Russian 

erationFed- 

49088 97472 10450 94606,2 

Serbia 6 379 13500 5800,4 

Slovakia 2 260 108,8 

Slovenia 21 211 99,3 

Spain 200 300 30 324,1 

Ukraine 15351 16577 1945 21001,9 

United Kingdom 

155 107,2 

Total Europe 72872 117616 44649 136826,9 

Iran (Islamic 

Rep.) 

1386 958,6 

Total Middle 

East 

1386 0 0 958,6 

Australia 37100 2100 37400 42322,9 







New Caledonia 

2 1,4 

New Zealand 33 205 333 278,9 

Total 

niaOcea- 

37135 2305 37733 42603,1 

TOTAL 

WORLD 

112261 318635 266837 149755 520996,7 


According to table 6.11, <strong>the</strong> exergy <strong>of</strong> coal proven reserves is 521 Gtoe, which is very 

similar to <strong>the</strong> previous calculated value in chapter 4 (523 Gtoe). The 2006 production 

data in exergy terms is equal 3,3 Gtoe 11 . Similarly, <strong>the</strong> WEC [401] estimated 

additional resources amount in place and <strong>the</strong> estimated additional recoverable reserves 

are 1025,7 and 108,6 Gtoe, respectively. 

It must be stressed, that different assumptions had to be made, such as considering 

only four different classes <strong>of</strong> coal, with <strong>the</strong> same composition and high heating values. 

Never<strong>the</strong>less, <strong>the</strong> error introduced with <strong>the</strong> previous assumption is most likely 

much smaller than <strong>the</strong> one made estimating <strong>the</strong> proven reserves. The Energy Watch 

Group [89], after analyzing present and historical trends, stated that data quality <strong>of</strong> 

coal reserves is poor, both on global and national levels. But <strong>the</strong>re is no objective 

way to determine how reliable <strong>the</strong> available data actually are. 

6.4.1.2 Oil 

The composition <strong>of</strong> <strong>the</strong> main types <strong>of</strong> fuel, according to <strong>the</strong> British standard 

BS2869:1998 (see section 4.6.6.2), is listed in table 6.12. Only Fuels 1, 2 and 4 

are considered, since <strong>the</strong>y are <strong>the</strong> most commonly used. 

The chemical composition <strong>of</strong> <strong>the</strong> fuels described above, throw up <strong>the</strong> <strong>the</strong>rmodynamic 

properties <strong>of</strong> table 6.13. 

As it happened to coal, <strong>the</strong> energy and exergy <strong>of</strong> <strong>the</strong> fuels increase from R.E. I to III. 

For <strong>the</strong> case <strong>of</strong> oil, <strong>the</strong> exergy can be approximated with no significant error to <strong>the</strong> 

HHV <strong>of</strong> <strong>the</strong> fuel, since <strong>the</strong> maximum error introduced is 0,26%. 

kJ/kg. 

11 An average coal is considered to have an exergy content <strong>of</strong> 22692 kJ/kg and a HHV <strong>of</strong> 21876


Table 6.12. High heating value and elementary analysis (% by weight) <strong>of</strong> <strong>the</strong> different 

types <strong>of</strong> oil, according to <strong>the</strong> British standard BS2869:1998 

RANK HHV, kJ/kg O H C N S 

Fuel-Oil 1 46.365 0,2 13,2 86,5 0 0,1 

Fuel-Oil 2 45.509 0,2 12,7 86,4 0,1 0,6 

Fuel-Oil 4 43.920 0,4 11,9 86,1 0,2 1,4 

Table 6.13. Thermodynamic properties <strong>of</strong> <strong>the</strong> different types <strong>of</strong> oil. Values in kJ/kg, 

except for s 0 (kJ/kgK) 

Type HHV ∆H 0 


Fuel-Oil 1 46365 -622,1 2,8 43591,5 46475,6 46486,2 46247,4 46251,3 46259,1 

Fuel-Oil 2 45509 -763,7 2,7 42859,4 45633,9 45697,2 45466,2 45469,8 45517,4 

Fuel-Oil 4 43920 -1279,1 2,6 41359,3 43958,9 44107,1 43888,4 43891,7 44002,4 

Next, <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> world’s proven reserves <strong>of</strong> oil will be calculated (table 6.14). 

For that purpose, <strong>the</strong> figures provided by BP in <strong>the</strong> Statistical Review 2007 will be 

used [35]. The estimates <strong>of</strong> BP are compiled using a combination <strong>of</strong> primary <strong>of</strong>ficial 

sources, third-party data from <strong>the</strong> OPEC Secretariat, World Oil, Oil & Gas Journal 

and an independent estimate <strong>of</strong> Russian reserves based on information in <strong>the</strong> public 

domain. The WEC publishes regularly also reserve figures for oil in <strong>the</strong> Survey <strong>of</strong> 

Energy Resources. Never<strong>the</strong>less, <strong>the</strong> latest WEC publication [401] includes reserve 

values for <strong>the</strong> end <strong>of</strong> 2005 and not for 2006, as opposed to <strong>the</strong> BP report. The 

classification <strong>of</strong> <strong>the</strong> world’s oil proven reserves into <strong>the</strong> different types <strong>of</strong> fuel (1, 2 

and 4) is taken from <strong>the</strong> study <strong>of</strong> Valero and Arauzo [366]. 

Table 6.14: The exergy <strong>of</strong> <strong>the</strong> world’s oil proven reserves reported in [35]. 

Values in thousand million tonnes if not specified 

Country Fuel-Oil 1 Fuel-Oil 2 Fuel-Oil 3 Exegy, Mtoe 

USA 3,7 3999,9 

Canada 2,4 2586,0 

Mexico 1,7 1884,0 

Total 

America 

North - 7,8 - 8469,9 

Argentina 0,3 294,7 

Brazil 1,7 1813,5 

Colombia 0,2 224,2 

Ecuador 0,7 709,9 

Peru 0,1 157,9 

Trinidad 

bago 

& To- 

0,1 125,4 

Venezuela 11,5 


12494,6



Values in thousand million tonnes if not specified. – continued from previous 

page. 


O<strong>the</strong>r S. & Cent. 

America 

0,2 195,6 

Total S. & Cent. 

America 

- 14,8 - 16015,9 

Azerbaijan 1,0 1039,2 

Denmark 0,2 167,5 

Italy 0,1 113,9 

Kazakhstan 5,5 5912,8 

Norway 1,1 1231,4 

Romania 0,1 64,6 

Russian Federation 

10,9 11415,4 

Turkmenistan 0,1 81,1 

United Kingdom 0,5 559,2 

Uzbekistan 0,1 88,2 

O<strong>the</strong>r Europe & 

Eurasia 

0,3 332,1 

Total Europe & 

Eurasia 

- 8,8 10,9 21005,3 

0,0 

Iran 18,9 20467,6 

Iraq 15,5 16819,3 

Kuwait 14,0 15151,6 

Oman 0,8 819,4 

Qatar 2,0 2162,8 

Saudi Arabia 36,3 39338,1 

Syria 0,4 443,6 

United 

Emirates 

Arab 

13,0 14038,5 

Yemen 0,4 404,8 

O<strong>the</strong>r 

East 

Middle 

0,1 54,2 

Total 

East 

Middle - 101,2 - 109699,8 

Algeria 1,5 1702,0 

Angola 1,2 1321,4 

Chad 0,1 140,3 

Rep. <strong>of</strong> Congo 

0,3 291,6 

(Brazzaville) 

Egypt 0,5 567,8 

Equatorial 

Guinea 

0,2 266,5 

Gabon 0,3 318,2 

Libya 5,4 5851,1 

Nigeria 4,9 5297,3 

Sudan 0,9 936,3 

Tunisia 0,1 


99,0



Values in thousand million tonnes if not specified. – continued from previous 

page. 


O<strong>the</strong>r Africa 0,1 85,2 

Total Africa 1,6 13,9 - 16876,8 

Australia 0,5 592,3 

Brunei 0,2 163,2 

China 2,2 2409,0 

India 0,8 851,8 

Indonesia 0,6 644,7 

Malaysia 0,5 595,8 

Thailand 0,1 63,8 

Vietnam 0,4 456,8 

O<strong>the</strong>r 

cific 

Asia Pa- 

0,1 116,5 

Total 

cific 

Asia Pa- 0,5 4,9 - 5893,9 

TOTAL WORLD 2,2 151,5 10,9 177961,6 


According to table 6.14, <strong>the</strong> world’s proven oil exergy reserves generated from R.E. 

III are 177,9 Gtoe. This means, that <strong>the</strong> reserves <strong>of</strong> oil have around one third <strong>of</strong> <strong>the</strong> 

coal’s exergy reserves. The 2006 production data in exergy terms <strong>of</strong> fuel-oil is equal 

3,9 Gtoe 12 

It should be remembered, that in addition to <strong>the</strong> conventional oil reserves, a corresponding 

range <strong>of</strong> additionally recoverable resources in exergy terms between 40 and 

150 Gtoe should be taken into account [211]. 

6.4.1.3 Natural gas 

In <strong>the</strong> case <strong>of</strong> natural gas, Valero and Arauzo [366] took into account <strong>the</strong> average 

standard composition <strong>of</strong> table 6.15. 

Table 6.15. Standard volumetric composition <strong>of</strong> natural gas considered in [366] 

HHV, kJ/N m 3 CH 4 C 2H 6 C 3H 8 C 4H 10 C 5H 12 CO 2 N 2 

42110 0,9225 0,0653 0,0055 0,0007 0,0001 0,0001 0,0058 

The chemical composition <strong>of</strong> <strong>the</strong> average natural gas described above, throw up <strong>the</strong> 

<strong>the</strong>rmodynamic properties <strong>of</strong> table 6.16. 

kJ/kg. 

12 An average fuel-oil is considered to have an exergy content <strong>of</strong> 45664 kJ/kg and a HHV <strong>of</strong> 45455


Table 6.16. Thermodynamic properties <strong>of</strong> natural gas. Values in kJ/N m 3 , except for 

∆H f (kJ/kg) and s 0 (kJ/kgK) 

HHV ∆H 0 


N. Gas 42110 -3117,4 8,6 38047,1 42108,7 42108,7 39388,6 39393,8 39393,8 

R.E. II and III generate for <strong>the</strong> case <strong>of</strong> natural gas, <strong>the</strong> same values <strong>of</strong> energy and 

exergy, since no sulphur is contained in <strong>the</strong> fuel. The difference between <strong>the</strong> exergy 

generated with I and III is very small, only 0,01%. For <strong>the</strong> case <strong>of</strong> natural gas, 

assuming <strong>the</strong> exergy as <strong>the</strong> HHV, introduces an error <strong>of</strong> around 6,5%, and hence this 

approximation should be taken with more precaution than for fuel-oil or coal. 

The calculated proven exergy reserves <strong>of</strong> natural gas are given in table 6.17. The 

values for <strong>the</strong> reserves are obtained from BP [35], because it presents more comprehensive 

and up-to-date data than <strong>the</strong> figures provided by <strong>the</strong> WEC. 

Table 6.17: The exergy <strong>of</strong> <strong>the</strong> world’s natural gas proven reserves reported in 

[35] 

Country Trillion N m 3 Exegy, Mtoe 

USA 5,93 5557,3 

Canada 1,67 1561,7 

Mexico 0,39 363,9 

Total North America 7,98 7482,9 

Argentina 0,42 389,2 

Bolivia 0,74 694,1 

Brazil 0,35 326,3 

Colombia 0,12 115,4 

Peru 0,34 318,9 

Trinidad & Tobago 0,53 497,1 

Venezuela 4,32 4047,2 

O<strong>the</strong>r S. & Cent. America 0,07 63,8 

Total S. & Cent. America 6,88 6452,0 

Azerbaijan 1,35 1266,2 

Denmark 0,08 72,2 

Germany 0,16 145,4 

Italy 0,16 149,6 

Kazakhstan 3,00 2813,8 

Ne<strong>the</strong>rlands 1,35 1263,4 

Norway 2,89 2712,5 

Poland 0,10 97,5 

Romania 0,63 589,0 

Russian Federation 47,65 44693,9 

Turkmenistan 2,86 2682,5 

Ukraine 1,10 1031,7 

United Kingdom 0,48 451,2 

Uzbekistan 1,87 1754,0 

O<strong>the</strong>r Europe & Eurasia 0,45 424,8 



Table 6.17: The exergy <strong>of</strong> <strong>the</strong> world’s natural gas proven reserves reported in 

[35]. – continued from previous page. 

Country Trillion N m 3 Exegy, Mtoe 

Total Europe & Eurasia 64,13 60148,0 

Bahrain 0,09 84,4 

Iran 28,13 26384,4 

Iraq 3,17 2973,3 

Kuwait 1,78 1669,5 

Oman 0,98 919,2 

Qatar 25,36 23787,3 

Saudi Arabia 7,07 6634,1 

Syria 0,29 272,0 

United Arab Emirates 6,06 5684,9 

Yemen 0,49 454,9 

O<strong>the</strong>r Middle East 0,05 47,8 

Total Middle East 73,47 68911,9 

Algeria 4,50 4224,7 

Egypt 1,94 1819,6 

Libya 1,32 1234,3 

Nigeria 5,21 4886,7 

O<strong>the</strong>r Africa 1,21 1137,7 

Total Africa 14,18 13303,1 

Australia 2,61 2443,4 

Bangladesh 0,44 408,0 

Brunei 0,34 314,2 

China 2,45 2297,0 

India 1,08 1008,3 

Indonesia 2,63 2468,7 

Malaysia 2,48 2326,1 

Myanmar 0,54 504,6 

Pakistan 0,80 748,5 

Papua New Guinea 0,44 408,0 

Thailand 0,30 282,3 

Vietnam 0,40 375,2 

O<strong>the</strong>r Asia Pacific 0,34 316,1 

Total Asia Pacific 14,82 13900,4 

TOTAL WORLD 181,46 170198,3 


According to table 6.17, <strong>the</strong> exergy reserves <strong>of</strong> natural gas are around 170 Gtoe, as 

opposed to <strong>the</strong> 163,4 estimated in chapter 4 with <strong>the</strong> conversion data provided by 

BP. This indicates, that <strong>the</strong> natural gas exergy reserves are very close to those <strong>of</strong> fueloil. 

The 2006 production data in exergy terms <strong>of</strong> natural gas is equal 2,4 Gtoe 13 . It 

should be remembered, that additional available natural gas resources are estimated 

13 An average natural gas is considered to have an exergy content <strong>of</strong> 51276 kJ/kg and a HHV <strong>of</strong> 

54811 kJ/kg.


in exergy terms as between 210 and 520 Gtoe, according to <strong>the</strong> International Gas 

Union [156] and to Gregory and Rogner [123]. 

6.4.2 The exergy <strong>of</strong> non-fuel <strong>mineral</strong> resources 

As opposed to fossil fuels, non-fuel <strong>mineral</strong>s are physically valued not only by <strong>the</strong>ir 

chemical exergy content, but also by <strong>the</strong>ir concentration exergy. From <strong>the</strong> point <strong>of</strong> 

view <strong>of</strong> man, <strong>the</strong> value <strong>of</strong> non-fuel <strong>mineral</strong>s is also associated to <strong>the</strong> extraction costs. 

A very abundant and concentrated <strong>mineral</strong> in <strong>the</strong> crust, such as iron, has a high 

exergy value and a low exergy cost <strong>of</strong> extraction. On <strong>the</strong> contrary, a very dispersed 

and scarce <strong>mineral</strong> such as gold, has a low exergy value, but a very high exergy cost 

<strong>of</strong> extraction. 

This is why <strong>the</strong> exergy replacement costs <strong>of</strong> <strong>mineral</strong>s, explained in section 5.3.4 

provide additional and interesting information for assigning a physical value to nonfuel 

<strong>mineral</strong>s. <strong>Exergy</strong> costs are obviously closer to price than <strong>the</strong> minimum exergies. 

In fact, <strong>the</strong> exergy cost could be considered as a fundamental ingredient <strong>of</strong> <strong>the</strong> final 

price <strong>of</strong> non-fuel <strong>mineral</strong>s. 

In this section, <strong>the</strong> total minimum exergy Bt and total exergy cost B∗ t <strong>of</strong> <strong>the</strong> <strong>mineral</strong>’s 

reserve, base reserve and world resources compiled by <strong>the</strong> USGS and described in 

chapter 4 are calculated (Table 6.18). The total minimum exergy Bt is <strong>the</strong> sum <strong>of</strong> 

<strong>the</strong> chemical Bch and concentration exergy Bc, which are calculated with Eqs. 5.1 

and 5.10, from <strong>the</strong> R.E. developed in this PhD (section 5.2). The total exergy cost14 , 

which represents <strong>the</strong> exergy required for restoring <strong>the</strong> resource with <strong>the</strong> best available 

technology from <strong>the</strong> R.E. to <strong>the</strong> current conditions found in nature, is obtained 

with Eq. 5.46. The unit exergy costs are <strong>the</strong> ones shown in table 5.7. The detailed 

calculations for <strong>the</strong> chemical and concentration exergies <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources are 

shown in table A.20 and A.21 in <strong>the</strong> appendix. 

14 Remember that <strong>the</strong> application <strong>of</strong> exergy costs to fossil fuels has no sense, since it is impossible 

with current technology to reproduce <strong>the</strong> photosyn<strong>the</strong>tic process that once created <strong>the</strong> fuel resource.


Table 6.18: The exergy and exergy cost <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves, base reserve 

and world resources. Values are expressed in ktoe 

Production Reserves Reserve base Resources 

Bt B∗ B t t B∗ B t t B∗ B t t B∗ t 

Aluminium 2,39E+04 5,19E+05 3,22E+06 6,99E+07 4,13E+06 8,95E+07 9,67E+06 2,10E+08 

Antimony 1,22E+01 1,36E+02 1,92E+02 2,13E+03 3,93E+02 4,37E+03 N.A. N.A. 

Arsenic 9,78E+00 1,23E+02 1,96E+02 2,46E+03 2,93E+02 3,69E+03 1,80E+03 2,26E+04 

Barite 4,09E+01 N.A. 9,77E+02 N.A. 4,53E+03 N.A. 1,03E+04 N.A. 

Beryllium 7,75E-03 4,05E-01 N.A. N.A. N.A. N.A. N.A. N.A. 

Bismuth 1,94E-01 3,16E+00 1,09E+01 1,77E+02 2,32E+01 3,77E+02 N.A. N.A. 

Boron oxide 1,57E+02 N.A. 6,28E+03 N.A. 1,51E+04 N.A. N.A. N.A. 

Bromine 8,24E+00 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 

Cadmium 1,27E+00 6,93E+01 3,23E+01 1,76E+03 7,92E+01 4,31E+03 3,96E+02 2,16E+04 

Cesium 0,00E+00 N.A. 5,43E+00 5,09E+00 8,53E+00 8,00E+00 N.A. N.A. 

Chromium 1,63E+03 3,70E+03 N.A. N.A. N.A. N.A. 1,06E+06 2,40E+06 

Cobalt 8,73E+00 4,38E+02 9,06E+02 4,55E+04 1,68E+03 8,44E+04 1,94E+03 9,74E+04 

Copper 9,01E+02 9,35E+04 2,92E+04 3,04E+06 5,61E+04 5,82E+06 1,79E+05 1,86E+07 

Feldspar 5,06E+01 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 

Fluorspar 2,33E+02 N.A. 1,05E+04 N.A. 2,10E+04 N.A. 2,19E+04 N.A. 

Gallium 1,29E-02 1,29E-02 N.A. N.A. N.A. N.A. 1,77E+02 1,76E+02 

Germanium 1,67E-02 1,65E-02 N.A. N.A. N.A. N.A. N.A. N.A. 

Gold 1,91E-02 1,56E+03 3,25E-01 2,66E+04 6,97E-01 5,71E+04 N.A. N.A. 

Graphite 8,70E+02 N.A. 7,26E+04 N.A. 1,77E+05 N.A. 6,76E+05 N.A. 

Gypsum 4,02E+02 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 

Hafnium N.A. N.A. 8,68E+01 N.A. 1,57E+02 N.A. N.A. N.A. 

Helium 5,09E+00 5,09E+00 N.A. N.A. 1,17E+03 1,17E+03 N.A. N.A. 

Indium 5,52E-02 5,29E-01 1,05E+00 1,00E+01 1,52E+00 1,46E+01 N.A. N.A. 

Iodine 4,67E-01 N.A. 2,80E+02 N.A. 5,04E+02 N.A. 6,35E+02 N.A. 

Iron 1,42E+05 9,97E+05 1,20E+07 8,40E+07 2,63E+07 1,84E+08 3,78E+07 2,65E+08 

Lead 9,99E+01 3,90E+03 2,28E+03 8,88E+04 4,90E+03 1,91E+05 4,32E+04 1,69E+06 

Lithium N.A. N.A. 5,64E+03 2,11E+04 1,51E+04 5,66E+04 1,79E+04 6,69E+04 

Magnesium 4,33E+02 4,33E+02 N.A. N.A. N.A. N.A. N.A. N.A. 



Table 6.18: The exergy and exergy cost <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves, base reserve 

and world resources. Values are expressed in ktoe.– continued from previous 

page. 

Production Reserves Reserve base Resources 

Bt B∗ B t t B∗ B t t B∗ B t t B∗ t 

Manganese 2,59E+03 2,50E+04 1,00E+05 9,68E+05 1,13E+06 1,09E+07 N.A. N.A. 

Mercury 2,51E-02 8,59E+00 7,82E-01 2,67E+02 4,08E+00 1,39E+03 1,02E+01 3,48E+03 

Molybdenum 3,41E+01 6,40E+02 1,59E+03 2,99E+04 3,52E+03 6,61E+04 2,41E+03 4,52E+04 

Nickel 1,58E+02 1,26E+04 6,72E+03 5,33E+05 1,50E+04 1,19E+06 N.A. N.A. 

Niobium 1,05E+01 1,03E+01 6,36E+02 6,25E+02 7,06E+02 6,94E+02 N.A. N.A. 

Phosphate rock (as fosforite) 1,22E+03 1,58E+03 1,55E+05 2,00E+05 4,30E+05 5,56E+05 N.A. N.A. 

PGM 1,05E-02 N.A. 1,43E+00 N.A. 1,61E+00 N.A. 2,02E+00 N.A. 

Potash (K2O) 3,12E+03 4,84E+03 8,89E+05 1,38E+06 1,93E+06 2,99E+06 2,68E+07 4,16E+07 

REE (as Ce2O 3) 3,72E+00 N.A. 2,66E+03 N.A. 4,53E+03 N.A. N.A. N.A. 

Rhenium 3,61E-03 4,40E-01 1,91E-01 2,33E+01 7,65E-01 9,31E+01 8,41E-01 1,02E+02 

Selenium 1,76E-01 1,62E-01 9,37E+00 8,60E+00 1,94E+01 1,78E+01 N.A. N.A. 

Silver 3,61E-01 3,46E+02 4,82E+00 4,63E+03 1,02E+01 9,78E+03 N.A. N.A. 

Strontium 1,24E+02 N.A. 1,44E+03 N.A. 2,54E+03 N.A. 2,12E+05 N.A. 

Tantalum 3,03E-01 8,42E+01 2,84E+01 7,88E+03 3,93E+01 1,09E+04 N.A. N.A. 

Tellurium 8,39E-03 8,07E-03 1,33E+00 1,28E+00 2,99E+00 2,87E+00 N.A. N.A. 

Thorium N.A. N.A. 1,34E+02 N.A. 1,56E+02 N.A. N.A. N.A. 

Tin 3,45E+01 1,77E+03 6,96E+02 3,58E+04 1,25E+03 6,46E+04 N.A. N.A. 

Titanium (T iO2) 3,52E+01 9,13E+02 4,43E+03 1,15E+05 9,10E+03 2,36E+05 1,21E+04 3,15E+05 

Vanadium 1,94E+01 2,19E+02 4,48E+03 5,05E+04 1,31E+04 1,48E+05 2,17E+04 2,45E+05 

Wolfram 1,00E+01 7,58E+02 3,20E+02 2,42E+04 6,94E+02 5,26E+04 N.A. N.A. 

Zinc 1,30E+03 2,37E+04 2,33E+04 4,26E+05 6,23E+04 1,14E+06 2,46E+05 4,50E+06 

Zircon (Z rO2) 1,21E+01 1,16E+04 3,89E+02 3,73E+05 7,36E+02 7,07E+05 N.A. N.A. 

Sum 1,80E+05 1,70E+06 1,65E+07 1,61E+08 3,43E+07 2,98E+08 7,67E+07 5,44E+08 



According to table 6.18, <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong>’s reserves, reserve base and world 

resources studied is at least 16,5, 34,3 and 76,7 Gtoe, respectively. Their associated 

exergy costs increase to 161, 298 and 544 Gtoe, respectively, what highlights how far 

is our technology from reversibility. The exergy cost <strong>of</strong> <strong>the</strong> reserve base and world 

resources are comparable to <strong>the</strong> exergy reserves <strong>of</strong> fossil fuels: 19%, 34% and 63% 

<strong>of</strong> <strong>the</strong> total available fossil fuels in 2006 (869 Gtoe), while <strong>the</strong>ir exergy represent 

only 2, 4 and 9%, respectively. 

The latest consumption rate <strong>of</strong> non-fuel <strong>mineral</strong>s recorded in terms <strong>of</strong> exergy cost 

is 1,7 Gtoe/yr or around 0,6% (0,2 Gtoe/yr <strong>of</strong> exergy) <strong>of</strong> <strong>the</strong> total reserve base. 

Only four <strong>mineral</strong>s account for near 96% <strong>of</strong> <strong>the</strong> total exergy cost consumption: iron 

(58,5%), aluminium (30,4%), copper (5,5%) and zinc (1,4%). However, <strong>the</strong> <strong>mineral</strong>s 

which are consumed at <strong>the</strong> highest rates compared to <strong>the</strong> available reserves are 

in decreasing order indium, silver, arsenic, antimony, tin and gold, with a rate <strong>of</strong> 

between 3,5 and 2,5% <strong>of</strong> <strong>the</strong> reserves consumed yearly. 

As opposed to fossil fuels, <strong>mineral</strong>s do not lose <strong>the</strong>ir exergy when <strong>the</strong>y are consumed. 

In fact, through <strong>the</strong> process <strong>of</strong> refining and concentrating <strong>of</strong> ores, <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> 

final product increases. The problem arises when <strong>the</strong> already refined <strong>mineral</strong> is 

dumped in landfills or becomes dispersed when <strong>the</strong> life cycle <strong>of</strong> <strong>the</strong> product has 

finished. In that case, <strong>the</strong> demand for <strong>the</strong> <strong>mineral</strong> must be satisfied by extracting 

new ore from <strong>the</strong> mine, <strong>the</strong>reby exhausting <strong>the</strong> resource and reducing <strong>the</strong> grade <strong>of</strong> 

<strong>the</strong> <strong>mineral</strong> deposit. As stated before, <strong>the</strong> second law <strong>of</strong> <strong>the</strong>rmodynamics, reflected 

in Eq. 5.10 dictates that <strong>the</strong> effort required to separate <strong>the</strong> <strong>mineral</strong> from <strong>the</strong> mine 

follows a negative logarithmic pattern with its ore grade. This means that as <strong>the</strong> ore 

grade tends to zero, <strong>the</strong> energy needed to extract <strong>the</strong> <strong>mineral</strong> tends to infinity. This 

is why recycling is essential to our society. 

It must be stressed that nei<strong>the</strong>r reserves, nor reserve base are good indicators for 

assessing <strong>the</strong> earth’s <strong>mineral</strong> <strong>capital</strong>. As stated by Highley [141], total world reserve 

base <strong>of</strong> most <strong>mineral</strong> commodities are larger now than at any time in <strong>the</strong> past due 

to wider geological information, more efficient technologies and price changes. The 

world resources data would be <strong>the</strong> best approximation <strong>of</strong> numbers compiling <strong>the</strong> 

<strong>mineral</strong> <strong>capital</strong> on earth. However, for being indeed <strong>the</strong> most comprehensive classification, 

<strong>the</strong> information is <strong>of</strong>ten scarce, inaccurate and incomplete, as can be seen 

in table 6.18. The fact is that too little is still known about <strong>the</strong> earth’s crust, since 

exploration costs are extremely high. 

6.4.3 The exergy <strong>of</strong> <strong>the</strong> natural resources on earth 

In <strong>the</strong> previous sections we have expressed all <strong>mineral</strong> resources <strong>of</strong> fuel and non-fuel 

origin with <strong>the</strong> same units, using <strong>the</strong> property exergy. We are now in a position <strong>of</strong>


analyzing and comparing <strong>the</strong> global exergy resources <strong>of</strong> <strong>the</strong> earth, with <strong>the</strong> information 

<strong>of</strong> <strong>the</strong> rest energy resources 15 provided in chapter 4. 

Table 6.19 summarizes <strong>the</strong> results, showing <strong>the</strong> available exergy, potential exergy use 

and current exergy consumption <strong>of</strong> natural resources on earth. As stated in chapter 

4, with potential exergy, we mean probable exergy capacity using advanced technology, 

not necessarily developed nowadays. Consumption values are referred to <strong>the</strong> 

end <strong>of</strong> 2006, except for geo<strong>the</strong>rmal, PV, wind, biomass and tidal energy, which are 

2005 values. The information is divided into renewable (RW) and non-renewable 

resources (Non-RW). For <strong>the</strong> group <strong>of</strong> renewables, <strong>the</strong> ratio between <strong>the</strong> current 

exergy consumption and <strong>the</strong> potential exergy use (RW use %) is provided. For nonrenewables, 

<strong>the</strong> base reserve to production ratio (R/P, yrs) is given, as a measure <strong>of</strong> 

<strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> considered <strong>mineral</strong>. 

According to table 6.19, <strong>the</strong> available renewable resources on earth, which are <strong>the</strong> 

sum <strong>of</strong> solar, tidal and geo<strong>the</strong>rmal energy is huge: around 32.537 Gtoe/year 16 . Of 

course this value is only <strong>the</strong>oretical, since currently and in <strong>the</strong> near future, <strong>the</strong>re is 

no way to technologically recover so much energy. 

Never<strong>the</strong>less, <strong>the</strong> potential exergy use is not insignificant ei<strong>the</strong>r: 62 Gtoe/year. This 

means, that with a feasible improve <strong>of</strong> our technology, we could supply with renewable 

energy more than 6 times <strong>the</strong> energy consumption <strong>of</strong> <strong>the</strong> entire world nowadays 

(10,9 Gtoe in 2006). The RW use indicator, shows that with <strong>the</strong> exception <strong>of</strong> water 

power, which is being used at 54% <strong>of</strong> its potential, <strong>the</strong> rest energy sources are 

barely exploited. Geo<strong>the</strong>rmal electricity is using 7,5% <strong>of</strong> its potential 17 , biomass 3%, 

wind power 0,4%, tidal energy 0,2% and solar and ocean waves current energy use 

is practically imperceptible with respect to <strong>the</strong>ir capacities. Therefore, <strong>the</strong>re is an 

enormous improving potential in <strong>the</strong> use <strong>of</strong> renewables. 

For <strong>the</strong> case <strong>of</strong> non renewable resources, including nuclear energy, fossil fuels and 

non-fuel <strong>mineral</strong>s, <strong>the</strong> available exergy is at least around 114.000 Gtoe, from which 

65% come from <strong>the</strong> not yet technologically developed fusion <strong>of</strong> deuterium and tritium. 

The potential exergy use <strong>of</strong> non-renewable resources is around 6.103 Gtoe. 

In fact, with <strong>the</strong> exception <strong>of</strong> <strong>the</strong> different types <strong>of</strong> nuclear energies and unconventional 

fossil fuels, our technology is developed enough to extract <strong>the</strong> majority <strong>of</strong> <strong>the</strong> 

available non-renewable resources on earth. And that is exactly what humankind 

has been doing since especially <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> industrialization period. 

The R/P ratios show that <strong>the</strong>re is enough uranium for at least 8667 years, coal for 

156, natural gas for 63, oil for 42 and non-fuel <strong>mineral</strong>s for 191, if <strong>the</strong> consump- 

15Note that <strong>the</strong> exergy <strong>of</strong> electrical energy is equivalent to its energy content. Hence, <strong>the</strong> figures 

<strong>of</strong> geo<strong>the</strong>rmal, solar, wind, water and oceans power are <strong>the</strong> same expressed in energy or exergy 

terms. The rest energy sources: nuclear and unconventional fuels were already expressed in table 6.19 

through its exergy content. 

16Note that wind, water, ocean and biomass power are sun-driven. Obviously, solar energy is only 

accounted once. 

17The potential <strong>the</strong>rmal use <strong>of</strong> geo<strong>the</strong>rmal energy is not quantified, but is presumably much higher 

than its potential for electricity generation. Hence, global geo<strong>the</strong>rmal RW use indicator is even smaller.


tion rates <strong>of</strong> <strong>the</strong> commodities remain as in 2006. The total non-renewable energy 

resources, would last for at least 595 years. 

Taking up again <strong>the</strong> global chemical exergy <strong>of</strong> <strong>the</strong> earth obtained in section 6.2.4, we 

can now compare <strong>the</strong> order <strong>of</strong> magnitude <strong>of</strong> <strong>the</strong> resources, with <strong>the</strong> whole chemical 

exergy <strong>of</strong> our planet. 

The chemical exergy <strong>of</strong> <strong>the</strong> atmosphere, hydrosphere and continental crust, is equivalent 

to <strong>the</strong> renewables potential during more than 38.000 years. This value allows 

us to put into perspective <strong>the</strong> huge physical value <strong>of</strong> our planet. 

In fact, non-renewable available resources contribute to a very small fraction <strong>of</strong> <strong>the</strong> 

total chemical exergy <strong>of</strong> <strong>the</strong> earth: less than 0,01%. The exergy <strong>of</strong> conventional 

fossil fuels and non energy <strong>mineral</strong> resources, constitute only 0,0001% <strong>of</strong> <strong>the</strong> upper 

continental crust’s chemical exergy. And <strong>the</strong>ir exergy is equivalent to that <strong>of</strong> <strong>the</strong> 

atmosphere, which is <strong>the</strong> layer with <strong>the</strong> least chemical exergy content. 

The wealth <strong>of</strong> our planet is enormous, but man can only take advantage <strong>of</strong> a very 

small part <strong>of</strong> it: <strong>the</strong> resources. With current technology, it is impossible to use <strong>the</strong> 

chemical exergy <strong>of</strong> dispersed substances. Non-renewable resources are considered as 

such, because <strong>the</strong>y represent a stock <strong>of</strong> concentrated chemical exergy. Therefore, <strong>the</strong> 

earth’s 1, 22 × 10 9 Gtoe <strong>of</strong> chemical exergy constitutes nowadays a useless reservoir 

<strong>of</strong> exergy. Consequently, we should resign ourselves with only 0,01% <strong>of</strong> that amount. 

The results obtained lead us to conclude that <strong>the</strong>re is no energy scarcity, but <strong>mineral</strong>’s 

scarcity. Vast amounts <strong>of</strong> energy are available on earth, much more than we could 

ever use. The depletion <strong>of</strong> fossil fuels should not be a problem at least in <strong>the</strong> medium 

term, as <strong>the</strong>re are many energy alternatives. Obviously, <strong>the</strong> way <strong>of</strong> recovering <strong>the</strong>m 

needs to be developed, so as to be economically competitive. Hence we cannot speak 

about energy crisis, but ra<strong>the</strong>r material’s and environmental crisis. 

Unfortunately non-fuel <strong>mineral</strong>s cannot be replaced by renewable resources. In <strong>the</strong> 

short term, substitution among <strong>mineral</strong>s will be possible with technological development, 

but this can only last whenever o<strong>the</strong>r <strong>mineral</strong> resources are available. Fur<strong>the</strong>rmore, 

<strong>the</strong> extraction <strong>of</strong> <strong>mineral</strong>s produce a considerable quantity <strong>of</strong> waste rock, pollutant 

emissions and consume considerable amounts <strong>of</strong> water, energy and in many 

cases toxic chemicals for refining processes. The consumption <strong>of</strong> <strong>the</strong>se resources implies 

an even greater additional loss <strong>of</strong> natural resource wealth. Therefore, recycling 

and especially, <strong>the</strong> search <strong>of</strong> a dematerialized society becomes essential. 

Surprisingly, this fact that seems to be unquestionable has not really started <strong>the</strong> 

alarms bells ringing regarding resources scarcity, at least for non-fuel <strong>mineral</strong>s. Many 

institutions, such as <strong>the</strong> European Commission, do not regard it as a prioritized issue 

in <strong>the</strong>ir environmental action plan [88], and claim that <strong>the</strong> environmental impacts 

<strong>of</strong> using non-renewable resources like metals, <strong>mineral</strong>s or fossil fuels are <strong>of</strong> greater 

concern than <strong>the</strong>ir possible scarcity. Probably <strong>the</strong> lack <strong>of</strong> information about resource 

scarcity avoids assigning this problem <strong>the</strong> priority that deserves.


Table 6.19. Available exergy, potential exergy use and current exergy consumption <strong>of</strong> natural resources on earth. Letter e denotes 

electrical consumption, while th <strong>the</strong>rmal consumption. 

RESOURCE AVAILABLE POTENTIAL CURRENT 

Renewable resources TW Gtoe/yr TW Gtoe/yr TW Gtoe/yr RW use % 

Geo<strong>the</strong>rmal 17,9 13,5 0,06 - 0,04 - 9,3E-03 e / 0,007 e / 7,5 e 

0,12 e 0,09 e 0,03 th 0,02 th 

Tidal power 2,7 2 0,166 0,13 3,00E-04 2,00E-04 0,2 

Solar PV 43200 32521 51,4 38,7 0,003 0,002 5,8E-03 

Solar <strong>the</strong>rmal power 43200 32521 0,63 - 4,7 0,47 - 3,5 0,00035 e 0,00026 e 7,4E-06 

Water power 11 8,2 1,8 1,3 0,92 0,7 53,8 

Wind power 1000 753 14,5 10,9 0,06 0,045 0,4 

Ocean <strong>the</strong>rmal gradient 1,4E+08 Gtoe - - - - - 

Ocean conveyor belt 2.000 1506 - - - - - 

Ocean waves 3 2,3 0,5 0,4 7,50E-07 5,60E-06 1,5E-04 

Biomass 92 70 19 - 56 14 - 42 1,7 1,3 3,0 

Non renewable resources Gtoe Gtoe Gtoe R/P, yrs 

Uranium - fission 27.100 5.200 0,6 8667 

Thorium - fission 7.500 - - 

Deutorium + Tritium (fusion) 74000 - - 

Coal 1549 521 3,3 156 

Natural gas 380-690 170,2 2,4 63 

Oil 220-330 177,9 3,9 42 

Unconventional fuels ∼ 2600 - 0,07 - 

Non-fuel <strong>mineral</strong>s 76,7 34,3 0,18 191 

RW w/o ocean th. grad. 32537 Gtoe/yr 62Gtoe/yr 1,33 Gtoe/yr RW use: 1,9% 

Non RW >114000 Gtoe 6103 Gtoe 10,3 Gtoe R/P: 595 yrs 

Conv. fuels + Min. ∼2800 Gtoe 903 Gtoe 9,6 Gtoe R/P: 94 yrs



In <strong>the</strong> first part <strong>of</strong> this chapter, <strong>the</strong> standard <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> main 

constituents <strong>of</strong> <strong>the</strong> outer earth’s spheres have been provided for <strong>the</strong> first time. That 

is <strong>the</strong> standard enthalpy, Gibbs free energy and chemical exergy <strong>of</strong> more than 330 

natural substances. 

The enthalpies and Gibbs free energies, have been obtained ei<strong>the</strong>r from <strong>the</strong> literature, 

or have been calculated with <strong>the</strong> 12 estimation methods described in section 

5.4. The exergy <strong>of</strong> <strong>the</strong> substances has been calculated with <strong>the</strong> chemical exergies <strong>of</strong> 

<strong>the</strong> elements, generated with <strong>the</strong> R.E. developed in this PhD. 

The average <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> atmosphere, hydrosphere (divided 

into seawater, rivers, glacial run<strong>of</strong>f and groundwater) and upper continental crust 

have been calculated with <strong>the</strong> molar fractions <strong>of</strong> <strong>the</strong> substances in each layer. 

It has been stated, that all negative ions in <strong>the</strong> hydrosphere throw up negative chemical 

exergies. Additionally, some substances <strong>of</strong> <strong>the</strong> continental crust show also 

negative exergy values. This is because <strong>the</strong> reference species <strong>of</strong> our R.E. are more 

stable than <strong>the</strong> considered substance. This leads us to question <strong>the</strong> suitability <strong>of</strong> 

<strong>the</strong> R.E. developed in this PhD, for natural resource accounting. Fur<strong>the</strong>rmore, this 

R.E. differs substantially from <strong>the</strong> model <strong>of</strong> degraded earth (or entropic planet) that 

should become. 

A first approximation <strong>of</strong> <strong>the</strong> crepuscular planet has been provided. It has been stated, 

that this degraded earth contains an atmosphere similar to <strong>the</strong> current one, but with 

a higher CO 2 concentration due to <strong>the</strong> burning <strong>of</strong> fossil fuels, a hydrosphere were 

all fresh waters are mixed with salt water, and a continental crust without fossil fuels 

or concentrated <strong>mineral</strong> deposits. Since <strong>the</strong> relative quantity <strong>of</strong> freshwater with 

respect to saltwater on earth is irrelevant, <strong>the</strong> hydrosphere <strong>of</strong> this hypo<strong>the</strong>tical earth 

has <strong>the</strong> same composition <strong>of</strong> <strong>the</strong> oceans. Something similar occurs with <strong>the</strong> continental 

crust, <strong>the</strong> abundance <strong>of</strong> <strong>mineral</strong> deposits and fossil fuels is negligible when 

compared to <strong>the</strong> whole continental crust. Hence, <strong>the</strong> composition <strong>of</strong> <strong>the</strong> degraded 

crust can be approximated to <strong>the</strong> model developed in this PhD. This preliminary 

model <strong>of</strong> entropic planet, and <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> constituents <strong>of</strong> 

each sphere, are <strong>the</strong> starting point <strong>of</strong> a new conception <strong>of</strong> reference environment for 

<strong>the</strong> calculation <strong>of</strong> chemical exergies <strong>of</strong> <strong>the</strong> elements. But this task remains open for 

fur<strong>the</strong>r studies. 

Despite <strong>of</strong> <strong>the</strong> limitations <strong>of</strong> <strong>the</strong> R.E. developed in this study, it still constitutes a tool 

for obtaining chemical exergies. Since <strong>the</strong> mass <strong>of</strong> <strong>the</strong> earth and <strong>of</strong> its spheres is 

known, we were able to calculate <strong>the</strong> absolute chemical exergy <strong>of</strong> <strong>the</strong> atmosphere, 

hydrosphere and upper continental crust: 6, 27 × 10 3 , 7, 80 × 10 5 and 1, 21 × 10 9 

Gtoe, respectively. Of course <strong>the</strong>se are very rough numbers, and are subject to ulterior 

updates, especially when a more appropriate R.E. is found. But <strong>the</strong>y are good 

enough, for providing an order <strong>of</strong> magnitude <strong>of</strong> <strong>the</strong> huge chemical wealth <strong>of</strong> our 

planet.


The second part <strong>of</strong> this chapter has provided an inventory <strong>of</strong> <strong>the</strong> most important 

resources on earth, expressed through a single unit <strong>of</strong> measure: exergy. The main 

novelty introduced in <strong>the</strong> inventory is <strong>the</strong> combined assessment <strong>of</strong> energy resources 

with non-fuel <strong>mineral</strong>s, thanks to <strong>the</strong> use <strong>of</strong> <strong>the</strong> exergy indicator. 

We have stated that <strong>the</strong>re is a huge amount <strong>of</strong> energy sources on earth, <strong>of</strong> both 

renewable and non-renewable nature. There are many energy alternatives that could 

replace fossil fuels when <strong>the</strong>y become depleted. But obviously <strong>the</strong> technology for 

recovering <strong>the</strong>se alternatives needs to be fur<strong>the</strong>r developed. 

Despite <strong>of</strong> <strong>the</strong> enormous chemical exergy <strong>of</strong> our planet, only 0,01% <strong>of</strong> that amount 

can be considered as available for human use. With current technology, it is impossible 

to use <strong>the</strong> chemical exergy <strong>of</strong> dispersed substances. And only those <strong>mineral</strong>s 

that are concentrated, can be considered as resources. 

In <strong>the</strong> short run, technological development will allow substitution among <strong>mineral</strong>s, 

but this can only last whenever o<strong>the</strong>r concentrated <strong>mineral</strong> stocks are available. 

Hence, <strong>the</strong> scarcity problems that man could be facing are based on <strong>the</strong> use <strong>of</strong> materials, 

ra<strong>the</strong>r than on <strong>the</strong> use <strong>of</strong> energy sources. This is why recycling and especially, 

<strong>the</strong> search <strong>of</strong> a dematerialized society becomes essential, in order to be consistent 

with <strong>the</strong> sustainability doctrine.

Chapter 7 

The time factor in <strong>the</strong> exergy 

assessment <strong>of</strong> <strong>mineral</strong> resources 


The aim <strong>of</strong> this chapter is to include a new dimension in <strong>the</strong> exergy evaluation <strong>of</strong> 

natural <strong>capital</strong>: time. A new concept called “<strong>Exergy</strong> distance” is presented. By means 

<strong>of</strong> <strong>the</strong> <strong>Exergy</strong> distance, we will be able to measure <strong>the</strong> level <strong>of</strong> degradation <strong>of</strong> <strong>mineral</strong> 

resources on earth and to evaluate <strong>the</strong> velocity <strong>of</strong> degradation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> <strong>capital</strong>. 

The degradation might be assessed for <strong>the</strong> entire earth, as well as for local areas in 

<strong>the</strong> past, present and in <strong>the</strong> future with <strong>evolution</strong> models. This way, for example, we 

will be able to see how climate change or <strong>the</strong> extraction <strong>of</strong> <strong>mineral</strong> resources affect 

<strong>the</strong> degradation <strong>of</strong> <strong>the</strong> natural <strong>capital</strong> by <strong>the</strong> decrease <strong>of</strong> its exergy. 

Additionally, <strong>the</strong> Hubbert peak model is proposed for evaluating <strong>the</strong> peaking production 

<strong>of</strong> <strong>mineral</strong> commodities. The model is applied to <strong>the</strong> exergy production and 

not to <strong>the</strong> tonnage, <strong>the</strong>reby introducing <strong>the</strong> concentration factor not included in <strong>the</strong> 

conventional estimations. 

The <strong>the</strong>ory behind <strong>the</strong> exergy distance and <strong>the</strong> Hubbert peak model applied to exergy 

is described, and two case studies are presented: 1) <strong>the</strong> exergy loss <strong>of</strong> copper in <strong>the</strong> 

US, and 2) <strong>the</strong> exergy loss <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s in Australia. 

7.2 The exergy distance 

As explained in chapter 2, <strong>the</strong> earth can be considered as a closed system with a finite 

number <strong>of</strong> substances in it, regardless <strong>the</strong> occasional input <strong>of</strong> meteorites. There 

is a constant mass and energy transfer among <strong>the</strong> different layers <strong>of</strong> <strong>the</strong> earth. These 

kinds <strong>of</strong> transfers can be <strong>of</strong> natural or anthropogenic nature. Usually, mass transfers 

227

228 THE TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES 

<strong>of</strong> natural origin between <strong>the</strong> earth’s layers follow cycles that are stabilized by negative 

feedbacks. These are at a stationary state, from a planetary perspective. This 

means that materials and energy flow from one system to ano<strong>the</strong>r, but <strong>the</strong> systems 

<strong>the</strong>mselves do not change much because <strong>the</strong> different parts <strong>of</strong> <strong>the</strong> flow paths balance 

each o<strong>the</strong>r. Most natural processes such as <strong>the</strong> hydrological cycle or photosyn<strong>the</strong>sis 

are essential for life and do not alter <strong>the</strong> ecological equilibrium on earth. 

However human interactions with <strong>the</strong> environment may be changing <strong>the</strong> natural 

fluxes. Industrial processes consume natural resources and return <strong>the</strong>m to nature as 

non-useful wastes mostly harmful for <strong>the</strong> ecosystem. A very clear case <strong>of</strong> this fact is 

for instance <strong>the</strong> burning <strong>of</strong> fossil fuels and <strong>the</strong> emission <strong>of</strong> CO 2 to <strong>the</strong> atmosphere. 

The clearing <strong>of</strong> forests, intensive agriculture with massive additions <strong>of</strong> fertilizers to 

<strong>the</strong> soil and <strong>the</strong> mining <strong>of</strong> ever-larger amounts <strong>of</strong> <strong>mineral</strong> resources are o<strong>the</strong>r cases 

<strong>of</strong> human alterations <strong>of</strong> <strong>the</strong> planet. Fur<strong>the</strong>rmore, according to Skinner, [318] if 

changes are made in one part <strong>of</strong> a closed system, <strong>the</strong> results <strong>of</strong> those changes will 

eventually affect o<strong>the</strong>r parts <strong>of</strong> <strong>the</strong> system. 

Following <strong>the</strong> conservation mass principle, it will be true that <strong>the</strong> total mass <strong>of</strong> <strong>the</strong> 

elements (ε j) in <strong>the</strong> atmosphere plus hydrosphere plus continental crust will remain 

constant, at any situation <strong>of</strong> <strong>the</strong> planet. Considering two different situations <strong>of</strong> <strong>the</strong> 

planet, (1) and (2), where (2) represents a more degraded earth due to <strong>the</strong> human 

action, and taking into account that r j,i · ξ i = ε j (Eq. 3.1) 1 , <strong>the</strong>n: 

⎡ 

⎤ 

⎢ 

 

 

 

⎥ 

⎣( r j,i · ξi) atm + ( r j,i · ξi) hyd r + ( r j,i · ξi) cr ⎦ 

j 

j 

⎡ 

⎤ 

⎢ 

 

 

 

⎥ 

⎣( r j,i · ξi) atm + ( r j,i · ξi) hyd r + ( rj,i · ξi) cr ⎦ 

j 

j 

This means that regardless <strong>the</strong> human action, <strong>the</strong> total budget <strong>of</strong> elements in <strong>the</strong> 

earth will be constant. 

In <strong>the</strong> same way, <strong>the</strong> sum <strong>of</strong> <strong>the</strong> energy (e i) contained in <strong>the</strong> three spheres <strong>of</strong> <strong>the</strong> 

earth will be also conserved in both situations: 

⎡ 

⎣ 

⎤ 

 

 

(ξi · ei) atm + (ξi · ei) hyd r + (ξi · ei) cr) ⎦ 

i 

i 

⎡ 

⎣ 

⎤ 

 

 

(ξi · ei) atm + (ξi · ei) hyd r + (ξi · ei) ⎦ 

cr 

i 

i 

1 Remember that rj,i represents <strong>the</strong> stoichiometric coefficient matrix between species ξ i and 

elements ε j. 

i 

j 

i 

j 

1 

1 

= 

2 

= 

2

The exergy distance 229 

However, and regardless <strong>the</strong> small amount <strong>of</strong> solar energy that <strong>the</strong> earth converts 

into biomass through photosyn<strong>the</strong>sis (only a 0,023%), this is not true if <strong>the</strong> parameter 

measured is exergy (b i): 

⎡ 

⎣ 

⎤ 

 

 

(ξi · bi) atm + (ξi · bi) hyd r + (ξi · bi) cr) ⎦ 

i 

i 

⎡ 

⎣ 

⎤ 

 

 

(ξi · bi) atm + (ξi · bi) hyd r + (ξi · bi) ⎦ 

cr 

i 

i 

In o<strong>the</strong>r words, even if mass and energy are conserved in all processes according 

to <strong>the</strong> first law <strong>of</strong> <strong>the</strong>rmodynamics, <strong>the</strong> second law states that as resources are consumed, 

<strong>the</strong> useful energy or exergy <strong>of</strong> <strong>the</strong> earth will decrease. 

The degradation <strong>of</strong> a natural resource can come from three effects: 

• an alteration <strong>of</strong> its composition, 

• a change <strong>of</strong> its concentration 2 , 

• a variation <strong>of</strong> <strong>the</strong> reference environment. 

And all three effects can be detected by a decrease <strong>of</strong> its exergy. Hence, for instance, 

when a fossil fuel is burned with oxygen, its chemical composition is transformed 

into water, carbon dioxide and o<strong>the</strong>r gases, <strong>the</strong>reby, losing chemical exergy. In <strong>the</strong> 

same way, when <strong>mineral</strong>s are extracted from a deposit, <strong>the</strong> mine decreases its ore 

grade, <strong>the</strong>reby losing concentration exergy. Therefore, <strong>the</strong> current exergy <strong>of</strong> <strong>the</strong> 

earth and its exergy <strong>evolution</strong> over time can be an objective measure for <strong>the</strong> depletion 

degree <strong>of</strong> <strong>the</strong> planet. 

We define <strong>the</strong> exergy distance (D) between two situations <strong>of</strong> <strong>the</strong> planet as <strong>the</strong> exergy 

difference between both states, as in Eq. 7.1: 

 

 

 

D = ξi · bi i=1 

1 

i 

 

 

− ξi · bi i=1 

i 

2 

1 

> 

2 

(7.1) 

The exergy distance can be applied on a global scale to <strong>the</strong> total quantity <strong>of</strong> substances 

on earth, or to a certain natural resource, if <strong>the</strong> aim is to assess its specific 

degradation. In fact, due to <strong>the</strong> very small relative weight <strong>of</strong> what we consider resources 

with respect to <strong>the</strong> o<strong>the</strong>r substances on earth, it makes more sense to apply 

2 Note that a decrease <strong>of</strong> its quantity is not considered as a degradation, since <strong>the</strong> conservation <strong>of</strong> 

mass statement must be obeyed. The matter is not lost, it is ei<strong>the</strong>r chemically transformed or dispersed.


<strong>the</strong> exergy distance concept to <strong>the</strong> resources only, separating <strong>the</strong>m from <strong>the</strong> rest 

components on earth. 

Additionally, we define <strong>the</strong> exergy degradation velocity (˙D) between two states as 

<strong>the</strong> exergy distance between <strong>the</strong> states (D) divided by <strong>the</strong> period <strong>of</strong> time separating 

<strong>the</strong>m (∆t), as in Eq. 7.2: 

˙D = ∆B 

∆t = 

 

i=1 ξ 

i · bi − 

1 i=1 ξ 

i · bi ∆t 

2 

(7.2) 

In <strong>the</strong> same way, <strong>the</strong> exergy distance and exergy degradation velocity can be applied 

to <strong>the</strong> exergy replacement costs 3 , obtaining <strong>the</strong> irreversible exergy distance (D ∗ ) and 

<strong>the</strong> irreversible exergy degradation velocity (˙D ∗ ). Through <strong>the</strong> exergy replacement 

costs, we introduce <strong>the</strong> irreversibility factor not included in <strong>the</strong> exergy parameter, 

since <strong>the</strong> latter only considers minimum energies. 

D ∗ = 

 

i=1 

ξ i · b ∗ 

i 

 

1 

− 

 

i=1 

˙D ∗ = ∆B∗ 

∆t = 

 

i=1 ξi · b∗ 

i 1 

∆t 

− 

ξ i · b ∗ 

i 

 

2 

i=1 ξ i · b ∗ 

i 

 

2 

(7.3) 

(7.4) 

Figure 7.1 shows a conceptual diagram <strong>of</strong> <strong>the</strong> exergy distance and exergy degradation 

velocity terms <strong>of</strong> <strong>mineral</strong> reserves. 

7.3 The tons <strong>of</strong> <strong>mineral</strong> equivalent 

One <strong>of</strong> <strong>the</strong> drawbacks that could be attributed to exergy is that most people and 

policy makers are not familiar with energy units for natural resource accounting. 

So anybody can understand how much is a kg or a ton <strong>of</strong> a certain material, but 

<strong>the</strong> equivalent amount in kJ or kcal does not give any practical information to <strong>the</strong> 

majority <strong>of</strong> <strong>the</strong> population. 

Fortunately exergy can be measured in different kinds <strong>of</strong> units, not only kJ or kcal, 

but also in tons <strong>of</strong> oil equivalent -toe- (<strong>the</strong> exergy contained in one ton <strong>of</strong> oil). 

Therefore, <strong>the</strong> same principle can be applied to non-fuel <strong>mineral</strong>s as with oil. Since 

<strong>the</strong> exergy <strong>of</strong> a resource, and particularly <strong>of</strong> a <strong>mineral</strong> deposit changes with <strong>the</strong> ore 

grade and <strong>the</strong> reference environment, <strong>the</strong> unit <strong>of</strong> measure ton <strong>of</strong> <strong>mineral</strong> equivalent 

has to be fixed to a specific year and a specific place. Hence, we define <strong>the</strong> parameter 

ton <strong>of</strong> Mineral equivalent t M e as <strong>the</strong> exergy content <strong>of</strong> one ton <strong>of</strong> <strong>mineral</strong> in a certain 

time and place, as in Eq. 7.5. 

3 Explained in section 5.3.4

The tons <strong>of</strong> <strong>mineral</strong> equivalent 231 

Degradation <strong>Exergy</strong> 

Resources 

. 

D D=dD/dt 

Figure 7.1. Conceptual diagram for <strong>the</strong> terms exergy distance and exergy degradation 

velocity 

t M e = 

Δt 

BM 

m M 

 

t 

Time 

(7.5) 

Being B M <strong>the</strong> absolute exergy <strong>of</strong> <strong>mineral</strong> M, and m M <strong>the</strong> tonnage <strong>of</strong> <strong>mineral</strong> M 

considered. Once <strong>the</strong> time and place has been specified and taken as reference 

(situation 1), one can calculate <strong>the</strong> tons <strong>of</strong> Mineral equivalent <strong>of</strong> <strong>the</strong> <strong>mineral</strong> deposit 

at ano<strong>the</strong>r situation (2). Then <strong>the</strong> t M e <strong>of</strong> situation 2 will be: 

(t M e) 2 = (B M) 2 

(t M e) 1 

(7.6) 

Again, this concept can be applied ei<strong>the</strong>r to exergy or to exergy replacement costs. 

For <strong>the</strong> latter, <strong>the</strong> tons <strong>of</strong> Mineral equivalent will be calculated as: 

t M e ∗ = 

 

∗ BM mM t 

(7.7) 

The t M e can be also used for comparing <strong>the</strong> quality <strong>of</strong> different <strong>mineral</strong> deposits, 

containing <strong>the</strong> same resource. This is clarified next through a simple example. 

Mine A contains in year 2007 m A tons <strong>of</strong> gold and B A toe <strong>of</strong> exergy. If mine A is taken 

as reference in that year, <strong>the</strong>n one ton <strong>of</strong> gold equivalent has an exergy content <strong>of</strong>:


t Aue = B A/m A. Mine B has <strong>the</strong> same amount <strong>of</strong> gold than mine A (m A = m B) but with 

a worse quality (lower ore grade) than that <strong>of</strong> A (B B 

would be as good as mine A. But if we use <strong>the</strong> exergy indicator, mine B has less tons 

<strong>of</strong> gold equivalent than <strong>the</strong> reference: (tAue) B = B B/(tAue) = m A · (B B/B A). 

In <strong>the</strong> same way, <strong>the</strong> reserves <strong>of</strong> a certain <strong>mineral</strong> in a country could be expressed 

in a practical and elegant way as tons <strong>of</strong> Mineral equivalent. This combines <strong>the</strong> 

advantages <strong>of</strong> both indicators: on one hand <strong>the</strong> more comprehensive unit <strong>of</strong> measure 

exergy and on <strong>the</strong> o<strong>the</strong>r hand <strong>the</strong> more understandable unit <strong>of</strong> measure mass. 

Never<strong>the</strong>less, as <strong>the</strong> property mass is involved in <strong>the</strong> calculation, <strong>the</strong> t M e loses <strong>the</strong> 

additive capacity that characterizes <strong>the</strong> exergy indicator. 

7.4 The R/P ratio applied to exergy 

The resources to production ratio (R/P) is an estimative measure for assessing <strong>the</strong> 

years until depletion <strong>of</strong> a certain resource. For that purpose, <strong>the</strong> tonnage <strong>of</strong> <strong>the</strong> 

estimated reserves is divided into <strong>the</strong> production <strong>of</strong> <strong>the</strong> year under consideration. 

Since both, production and reserves fluctuate throughout <strong>the</strong> years, R/P ratios may 

increase or decrease accordingly. Remember that <strong>the</strong> reserves might increase if new 

deposits are discovered or if technological development or <strong>mineral</strong> prices allow to 

extract lower grade deposits not considered as pr<strong>of</strong>itable before. Therefore, <strong>the</strong> R/P 

ratio should always be accompanied by <strong>the</strong> calculation year. 

In this PhD, we calculate <strong>the</strong> resources to production ratio in exergy terms. This 

allows to include additional information about <strong>the</strong> concentration <strong>of</strong> <strong>the</strong> deposit, not 

taken into account with <strong>the</strong> conventional calculation in mass terms. 

7.5 The Hubbert peak applied to exergy 

M. King Hubbert ([146], [147]) found in <strong>the</strong> mid-fifties that <strong>the</strong> production <strong>of</strong> fossil 

fuel trends had a strong family resemblance. The curves started slowly and <strong>the</strong>n 

rose more steeply tending to increase exponentially with time, until finally an inflection 

point was reached after it became concave downward. The observed trends 

are based on <strong>the</strong> fact that no finite resource can sustain for longer than a brief period 

such a rate <strong>of</strong> growth <strong>of</strong> production; <strong>the</strong>refore, although production rates tend 

initially to increase exponentially, physical limits prevent <strong>the</strong>ir continuing to do so. 

So for any production curve <strong>of</strong> a finite resource <strong>of</strong> fixed amount, two points on <strong>the</strong> 

curve are known at <strong>the</strong> outset, namely that at t = 0 and again at t = ∞. The production 

rate will be zero when <strong>the</strong> reference time is zero, and <strong>the</strong> rate will again be 

zero when <strong>the</strong> resource is exhausted, after passing through one or several maxima. 

The second consideration is that <strong>the</strong> area under <strong>the</strong> production curve must equal <strong>the</strong> 

quantity <strong>of</strong> <strong>the</strong> resource available (R). In this way, <strong>the</strong> production curve <strong>of</strong> a certain

The Hubbert peak applied to exergy 233 

Production (P) 

∞ 

Q= Pdt 

0 

Time (t) 

Figure 7.2. The Hubbert’s bell shape curve <strong>of</strong> <strong>the</strong> production cycle <strong>of</strong> any exhaustible 

resource [146]. 

resource throughout history takes <strong>the</strong> ideal form <strong>of</strong> <strong>the</strong> bell-shape curve shown in 

Fig. 7.2. 

The model was successful in predicting <strong>the</strong> peak <strong>of</strong> oil extraction in <strong>the</strong> US lower 

48 states and <strong>the</strong> subsequent decline in production. Recently, several authors used 

Hubbert’s model to predict <strong>the</strong> <strong>evolution</strong> <strong>of</strong> crude oil extraction at <strong>the</strong> planetary 

level (Deffeyes [72], Bentley [24], Campbell and Laherre [47], [46]). According to 

<strong>the</strong>se estimates, <strong>the</strong> corresponding production peak could take place within <strong>the</strong> first 

decade <strong>of</strong> <strong>the</strong> 21st century or not much later. And as Campbell and Laherre [47] 

argue, from an economic perspective, when <strong>the</strong> world runs completely out <strong>of</strong> fuels is 

not directly relevant: what matters is when production begins to taper <strong>of</strong>f. Beyond 

that point, prices will rise unless demand declines commensurately. 

It must be pointed out that <strong>the</strong> successful prediction <strong>of</strong> <strong>the</strong> model depends on many 

factors, being <strong>the</strong> most important one, <strong>the</strong> reliability <strong>of</strong> <strong>the</strong> estimated reserves. Forrester/Meadows 

models [96], [218] are almost always asymmetric with <strong>the</strong> decline 

much sharper than <strong>the</strong> growth. Bardi [18] showed that <strong>the</strong> bell-shaped curve may 

turn out to be strongly asymmetric depending on extraction strategies. As Bartlett 

argues [22], actual production curves will be probably modified by economic, geological, 

political, technological, and o<strong>the</strong>r factors, which may result in a deterioration 

<strong>of</strong> <strong>the</strong> quality <strong>of</strong> <strong>the</strong> fit between <strong>the</strong> data and <strong>the</strong> Gaussian, but <strong>the</strong> role <strong>of</strong> <strong>the</strong>se 

important factors is limited to changing <strong>the</strong> quality <strong>of</strong> this fit. 

Basically, <strong>the</strong> Hubbert model can be applied to those <strong>mineral</strong>s, where <strong>the</strong> concentration 

factor is not important, i.e. to liquid and gaseous fossil fuels. Roberts and 

Torrens [283] applied also <strong>the</strong> Hubbert model in 1974 to examine <strong>the</strong> production 

cycle <strong>of</strong> copper. At that time, <strong>the</strong>re was not so much information as today regarding 

consumption rates or future reserve estimates, which are essential ingredients for 

<strong>the</strong> methodology. Therefore, <strong>the</strong> model had to be applied making quite lot assump-


tions. Nowadays, <strong>the</strong> curve can be defined through more points and <strong>the</strong>re are more 

reliable estimations for <strong>mineral</strong> reserves (as for instance <strong>the</strong> data provided by <strong>the</strong> US 

Bureau <strong>of</strong> Mines). 

Fur<strong>the</strong>rmore, we think that <strong>the</strong> bell-shape curve is better suited to <strong>mineral</strong>s, if it 

is fitted with exergy over time instead <strong>of</strong> mass over time. Oil quality keeps nearly 

constant with extraction, whereas o<strong>the</strong>r non-fuel <strong>mineral</strong>s don’t (<strong>mineral</strong>’s concentration 

decreases as <strong>the</strong> mine is being exploited). Therefore exergy is a much better 

unit <strong>of</strong> measure than mass, since it accounts not only for quantity, but also for ore 

grades and composition. The well known bell-shaped curve can be fitted to <strong>the</strong> 

exergy consumption data provided, in order to estimate when <strong>mineral</strong> production 

will start declining. Next, <strong>the</strong> ma<strong>the</strong>matical procedure for <strong>the</strong> application <strong>of</strong> <strong>the</strong> 

model is explained. 

Hubbert’s bell-shape curve can be described through <strong>the</strong> generic gaussian curve described 

in Eq. 7.8. 

f (t) = y 0e − 

 

t−t0 

The integral <strong>of</strong> <strong>the</strong> gaussian curve is equal to <strong>the</strong> reserves (R) <strong>of</strong> <strong>the</strong> commodity: 

+∞ 

−∞ 

And <strong>the</strong> integral <strong>of</strong> Eq. 7.8 is given by Eq. 7.10. 

∞ 

e − 

 

t−t0 

b0 0 

b 0 

(7.8) 

f (t)d t = R (7.9) 

d t = b 

0 π 

2 

(7.10) 

Combining Eqs. 7.9 and 7.10, and taking into account that <strong>the</strong> curve is symmetric, 

<strong>the</strong> reserves can be expressed as: 

 

y0b0 π = R (7.11) 

Hence, <strong>the</strong> model <strong>of</strong> <strong>the</strong> curve to be adjusted is given by Eq. 7.12: 

f (t) = R 

e 

b0 π − 

Where parameters b 0 and t 0 are <strong>the</strong> unknowns. 

 

t−t0 

b 0 

(7.12) 

In our case, we will represent <strong>the</strong> yearly exergy loss <strong>of</strong> <strong>the</strong> commodity vs. time. 

With a least squares procedure, <strong>the</strong> points will be adjusted to <strong>the</strong> curve given by Eq. 

7.12. The maximum <strong>of</strong> <strong>the</strong> function is given by parameter t 0, and it verifies that 

f (t0) = R 

. 

b0 π

The exergy loss <strong>of</strong> <strong>mineral</strong> deposits due to <strong>mineral</strong> extraction. The case <strong>of</strong> copper in 

<strong>the</strong> US 235 

7.6 The exergy loss <strong>of</strong> <strong>mineral</strong> deposits due to <strong>mineral</strong> 

extraction. The case <strong>of</strong> copper in <strong>the</strong> US 

Before explaining <strong>the</strong> exergy decrease <strong>of</strong> <strong>mineral</strong> deposits, it must be pointed out 

that extraction does not necessarily mean that <strong>the</strong> inherent exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> 

is being lost. On <strong>the</strong> contrary, through <strong>the</strong> process <strong>of</strong> mining and concentrating 

<strong>of</strong> ores, we are increasing <strong>the</strong> exergy per unit <strong>of</strong> resource and in fact, that exergy 

will remain in wires, buildings, industrial machinery and o<strong>the</strong>r products were <strong>the</strong> 

<strong>mineral</strong>s are used. The problem arises when <strong>the</strong> objects made <strong>of</strong> <strong>the</strong> refined <strong>mineral</strong> 

are disposed <strong>of</strong> in landfills at <strong>the</strong> end <strong>of</strong> <strong>the</strong>ir useful life. In that case, <strong>the</strong> demand 

for <strong>the</strong> <strong>mineral</strong> must be satisfied by extracting new one from <strong>the</strong> mine, <strong>the</strong>reby 

exhausting <strong>the</strong> resource and reducing <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> mine (<strong>the</strong> mine contains a 

lower quantity <strong>of</strong> <strong>mineral</strong> at a lower grade). Fortunately, recycling reduces <strong>the</strong> need 

for so much new <strong>mineral</strong> to be extracted. Therefore, recycling is very important to 

our society, by preventing dispersion once a material has been concentrated. 

Hence, when we refer to <strong>the</strong> exergy loss <strong>of</strong> <strong>mineral</strong> deposits, we are indicating <strong>the</strong> 

exergy that <strong>the</strong> mines are losing through <strong>mineral</strong> extraction. In practice, this exergy 

is only lost when <strong>the</strong> refined <strong>mineral</strong> is dumped in landfills or becomes dispersed. 

The calculation <strong>of</strong> <strong>the</strong> exergy loss <strong>of</strong> non-fuel <strong>mineral</strong>s requires a great amount <strong>of</strong> 

information: world trends <strong>of</strong> natural resources production and consumption, trends 

<strong>of</strong> ore grades and <strong>mineral</strong> reserve projections. Unfortunately, <strong>the</strong>se data is not always 

available and requires a lot <strong>of</strong> effort to ga<strong>the</strong>r it. The US Geological Survey, 

British Geological Survey, British Petroleum and o<strong>the</strong>r entities publish periodically 

new information about world <strong>mineral</strong> commodities. Never<strong>the</strong>less, <strong>the</strong> data is usually 

insufficient, since for most commodities, ore grade trends are not studied. 

In <strong>the</strong> next sections, we will present <strong>the</strong> application <strong>of</strong> <strong>the</strong> exergy analysis to <strong>the</strong> 

assessment <strong>of</strong> <strong>the</strong> exergy loss <strong>of</strong> US copper mines. The calculations will be explained 

in detail, so as to serve as an example for <strong>the</strong> Australian case, presented in section 

7.7. 

7.6.1 Copper mining features 

Copper has been mined in <strong>the</strong> United States at an industrial scale, at least from 

1709, in Simbsbury, Connecticut. The industrial r<strong>evolution</strong> intensified <strong>the</strong> use <strong>of</strong> 

copper in <strong>the</strong> mid <strong>of</strong> <strong>the</strong> nineteenth century, and consequently its production. The 

USGS provides historical production and grades data since year 1900. The published 

reserves and reserve base <strong>of</strong> US copper, as well as ore grade trends throughout <strong>the</strong> 

20th century by <strong>the</strong> US Geological Survey [361], allow us to calculate <strong>the</strong> exergy 

decrease <strong>of</strong> US copper mines in <strong>the</strong> last century. 

Copper in <strong>mineral</strong> deposits is usually found in nature in association with sulfur, as 

chalcopyrite (CuFeS 2), but it can be also found as an oxide. The most important


(0) 

Dispersed 

earth with 

R.S. 

[xc] 

Cu +2 + 2SO4 -2 +1/2 Fe2O3 

(0) 

Cu is dispersed on 

Earth in form <strong>of</strong> Cu +2 

(aq) 

Naturally occurring 

chemical process 

(1) 

Dispersed 

earth with 

<strong>mineral</strong>s 

A chemical reaction takes 

place, forming CuFeS2 from 

<strong>the</strong>ir corresponding reference 

substances 

[xc] 

CuFeS2 + 19/2O2 

(1) 

Naturally 

occurring 

concentration 

process 

(2) 

Actual 

Earth 

[xm] 

CuFeS2 

(2) 

Minerals 

concentrated in 

mines 

The dispersed CuFeS2 at 

xc is concentrated into <strong>the</strong> 

mines at xm. 

Figure 7.3. Hypo<strong>the</strong>tical processes involved in obtaining <strong>the</strong> <strong>mineral</strong> <strong>of</strong> copper from 

<strong>the</strong> reference environment 

copper ore deposits (<strong>the</strong> “porphyry coppers”) normally have quite low concentrations 

<strong>of</strong> copper (0,3 to 0,6% Cu) but this is compensated by <strong>the</strong>ir size (hundreds to 

thousands <strong>of</strong> million tons <strong>of</strong> ore). 

The production <strong>of</strong> pure copper from <strong>the</strong> ore can be summarized in two processes. 

The first one is concerned with <strong>the</strong> mining and concentrating <strong>of</strong> low grade ores 

containing copper <strong>mineral</strong>. The second one is fundamentally a chemical process 

in which <strong>the</strong> concentrated ore is smelted and <strong>the</strong>n refined through an electrolytic 

process. 

The hypo<strong>the</strong>tical processes needed for replacing <strong>the</strong> <strong>mineral</strong> from <strong>the</strong> reference earth 

to <strong>the</strong> conditions in <strong>the</strong> mine are outlined in Fig. 7.3. As a first approximation, it 

has been assumed, that all <strong>the</strong> copper occurs in <strong>the</strong> mines as chalcopyrite. These 

processes are needed to replace <strong>the</strong> <strong>mineral</strong> from <strong>the</strong> R.E. 

At state 0, <strong>the</strong> earth is composed <strong>of</strong> only reference substances (R.S.) dispersed in 

<strong>the</strong> three subsystems <strong>of</strong> <strong>the</strong> R.E.: continental crust, atmosphere and hydrosphere. 

At state 1, <strong>the</strong> reference substances <strong>of</strong> <strong>the</strong> reference environment defined in this 

PhD (section 5.2) composing <strong>the</strong> <strong>mineral</strong> (Cu +2 and SO −2 

4 from <strong>the</strong> hydrosphere 

and Fe 2O 3 from <strong>the</strong> continental crust), react to form CuFeS 2. Finally, at state 2, 

<strong>the</strong> dispersed chalcopyrite is concentrated from x c to <strong>the</strong> ore grade <strong>of</strong> <strong>the</strong> mine x m.



The concentration <strong>of</strong> copper in <strong>the</strong> reference environment x c is assumed to be equal 

to 2,8E-5 g/g, which is <strong>the</strong> average concentration <strong>of</strong> copper in <strong>the</strong> earth’s crust, 

according to Rudnick and Gao [292]. 

The unit concentration cost <strong>of</strong> copper i.e. <strong>the</strong> energy required to concentrate copper 

from x c to x m with today’s technology was estimated by Valero and Botero [371] as 

k c = 385, 61. This value 4 was obtained considering that <strong>the</strong> unit concentration cost 

for <strong>the</strong> real process <strong>of</strong> mining and concentrating is <strong>the</strong> same as in <strong>the</strong> hypo<strong>the</strong>tical 

process <strong>of</strong> concentration between <strong>the</strong> R.E. and <strong>the</strong> mine conditions. The energy 

requirement for mining and concentrating considered (e c) was <strong>the</strong> one obtained 

by Chapman and Roberts [53]: 66,7 GJ/ton for an ore grade <strong>of</strong> 0,5% Cu. The 

ratio between <strong>the</strong> real energy required and <strong>the</strong> minimum exergy to concentrate <strong>the</strong> 

<strong>mineral</strong> from <strong>the</strong> earth’s crust to <strong>the</strong> ore grade <strong>of</strong> <strong>the</strong> mine gives <strong>the</strong> unit exergy cost 

mentioned before. The result obtained means that with current technology, we have 

to invest 385,61 times more energy for concentrating copper from <strong>the</strong> R.E. to <strong>the</strong> 

mine than in <strong>the</strong> reversible process. Martínez et al. [207] updated <strong>the</strong> value <strong>of</strong> k c 

for copper with more recent information. The value obtained, which is <strong>the</strong> one used 

for our calculations was: k c,Cu = 343, 1. 

The real quantity <strong>of</strong> energy required for “refining” <strong>the</strong> <strong>mineral</strong> between <strong>the</strong> earth’s 

crust (as in <strong>the</strong> Reference Environment) and <strong>the</strong> conditions in <strong>the</strong> mine is also usually 

greater than <strong>the</strong> standard chemical exergy given by Eq. 5.1. As explained in section 

5.3.4, Valero and Botero estimated <strong>the</strong> unit chemical exergy costs <strong>of</strong> sulfides as being 

at least k ch = 10. Martínez et al. [207] updated that value for copper, obtaining 

k ch,Cu = 80, 2. Remember that in chapter 5, table 5.7 shows <strong>the</strong> unit exergy costs <strong>of</strong> 

selected <strong>mineral</strong>s, according to Valero and Botero [371] and Martínez et al. [207]. 

7.6.2 Chemical exergy 

The reserves and reserve base <strong>of</strong> copper in <strong>the</strong> US in year 2000 were 45.000 kt and 

90.000 kt respectively [362]. 

The chemical exergy <strong>of</strong> copper mines will be calculated assuming that Cu is found in 

<strong>the</strong> deposit as <strong>the</strong> metal. This approximation is used as <strong>the</strong>re is a lack <strong>of</strong> information 

about <strong>the</strong> amount <strong>of</strong> copper extracted from chalcopyrite and <strong>the</strong> o<strong>the</strong>r copper ores 

such as oxides and o<strong>the</strong>r sulfides. Hence, our first goal is to obtain <strong>the</strong> exergy <strong>of</strong> 

state 1 in Fig. 7.3. The chemical exergy <strong>of</strong> Cu, calculated with Eq. 5.1 (b ch i = 

∆G f i + r j,i b ch j), being ∆G f Cu = −190, 9 kJ/mole and obtaining <strong>the</strong> chemical 

exergy <strong>of</strong> <strong>the</strong> elements from <strong>the</strong> R.E. developed in this study and described in section 

5.2.3.5 is: b ch Cu = 134, 0 MJ/kmole. 

Surprisingly, <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> is higher than that <strong>of</strong> <strong>the</strong> pure element: 

b ch CuFeS2 = 1534, 5 MJ/kmole (11,45 times greater). This is due to <strong>the</strong> fact 

racy. 

4 Although 5 significant figures are given for kc, <strong>the</strong> number cannot be considered with that accu


that since stability (criterion taken partially by Szargut et al. [343] and in this study 

for choosing <strong>the</strong> reference substances) does not coincide with abundance in a number 

<strong>of</strong> cases, some <strong>mineral</strong>s that are quite abundant in nature, such as sulfides, have 

a fairly high chemical exergy that can be considered as an exergy reservoir that <strong>the</strong> 

earth provides us for free. This helps our technology to avoid <strong>the</strong> expenditure huge 

amounts <strong>of</strong> commercial energy during <strong>the</strong> process <strong>of</strong> obtaining <strong>the</strong> corresponding 

pure element. 

The component <strong>of</strong> <strong>the</strong> minimum chemical exergy <strong>of</strong> a substance remains constant 

over time, since it only depends on its chemical composition. Hence, in absolute 

terms, <strong>the</strong> chemical exergy consumption <strong>of</strong> any substance is proportional to its production 

rate. 

The chemical exergy decrease <strong>of</strong> copper mines in <strong>the</strong> United States in <strong>the</strong> 20th century 

(B), can be calculated by multiplying <strong>the</strong> molar copper primary production ( ˙m) 

with <strong>the</strong> exergy <strong>of</strong> copper obtained before: B = ˙m · b. The production <strong>of</strong> copper 

in <strong>the</strong> US during <strong>the</strong> past century (see Fig. 7.4), was obtained from <strong>the</strong> Historical 

Statistics for Mineral and Material Commodities in <strong>the</strong> United States [361], which is a 

compilation <strong>of</strong> data from publications primarily <strong>of</strong> <strong>the</strong> USGS and USBM, such as <strong>the</strong> 

Minerals Yearbook [363]. 

Figure 7.5 shows <strong>the</strong> cumulative chemical exergy decrease <strong>of</strong> copper mines in <strong>the</strong> 

US ( B ch). At <strong>the</strong> end <strong>of</strong> year 2000, <strong>the</strong> total chemical exergy distance <strong>of</strong> copper 

mines from <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> century, was D ch = 5, 66 Mtoe. This exergy was 

consumed at an average degradation velocity ˙D ch = 56, 04 ktoe/year, although <strong>the</strong> 

trend since <strong>the</strong> seventies shows an average degradation velocity <strong>of</strong> around 77,39 

ktoe/year. The maximum velocity was attained in year 1998 (107,81 ktoe/year), 

while <strong>the</strong> minimum was in 1900 (14,66 ktoe/year). Copper production has shown a 

continuous growth, since it is strongly linked to <strong>the</strong> electrical and telecommunication 

industries. The chemical exergy <strong>of</strong> copper reserves, calculated as pure copper at 

<strong>the</strong> end <strong>of</strong> year 2000, was 2,27 Mtoe. If we add <strong>the</strong> cumulative chemical exergy 

consumption to <strong>the</strong> exergy reserves at <strong>the</strong> end <strong>of</strong> year 2000, we obtain <strong>the</strong> exergy 

reserves at year 1900: 7,93 Mtoe. Similarly, <strong>the</strong> chemical exergy <strong>of</strong> copper reserve 

base at <strong>the</strong> beginning and end <strong>of</strong> <strong>the</strong> century were 10,19 and 4,53 Mtoe, respectively. 

7.6.3 Concentration exergy 

Next, <strong>the</strong> concentration exergy <strong>of</strong> <strong>the</strong> mine (step 3 in Fig. 7.3) will be obtained as <strong>the</strong> 

difference between <strong>the</strong> concentration exergies obtained with <strong>the</strong> <strong>mineral</strong> concentration 

in a mine (x m) and with <strong>the</strong> average concentration in <strong>the</strong> earth’s crust (x c). The 

latter are calculated with Eq. 5.10 (bc i = −¯RT 0 lnx i + (1−x 

i) 

ln(1 − x 

x i) ). Since no 

i 

ore grades are provided between years 1901 and 1905, it has been assumed that <strong>the</strong> 

concentration <strong>of</strong> those years is <strong>the</strong> same as in 1900. The concentration exergy <strong>of</strong> <strong>the</strong> 

mine, i.e. <strong>the</strong> minimum energy that nature had to spend to bring <strong>mineral</strong>s from xc to xm, is not constant over time, because it changes with <strong>the</strong> ore grade <strong>of</strong> <strong>the</strong> mine



B ch, ktoe 

120 

100 

80 

60 

40 

20 

0 

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 

Year 

Bch (ktoe) bch (MJ/kmol) 

Figure 7.4. Yearly chemical exergy consumption in <strong>the</strong> US <strong>of</strong> pure copper due to 

copper production throughout <strong>the</strong> 20th century 

ΣB ch, ktoe 

6000 

5000 

4000 

3000 

2000 

1000 

0 

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 

Figure 7.5. Cumulative chemical exergy decrease <strong>of</strong> copper mines in <strong>the</strong> US throughout 

<strong>the</strong> 20th century 

(see Fig. 7.6). The mine has <strong>the</strong> greatest exergy concentration, when <strong>the</strong> ore grade 

is at <strong>the</strong> maximum and becomes lower as <strong>the</strong> ore grade decreases. At <strong>the</strong> beginning 

<strong>of</strong> <strong>the</strong> century, when <strong>the</strong> ore grades were at above 2% Cu, <strong>the</strong> concentration exergy 

was <strong>the</strong> highest, namely b c Cu > 18 MJ/kmole. In <strong>the</strong> last years, <strong>the</strong> ore grades have 

declined to values less than 0,45% Cu and hence <strong>the</strong> concentration exergy <strong>of</strong> <strong>the</strong> 

mine has decreased accordingly: b c Cu < 15 MJ/kmole. Copper ore grade trends in 

Year 

140 

120 

100 

80 

60 

40 

20 

0 

bch,MJ/kmol


B c, ktoe 

12,0 

10,0 

8,0 

6,0 

4,0 

2,0 

0,0 

13 

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 

Year 

Bc (ktoe) bc (MJ/kmol) 

Figure 7.6. Yearly concentration exergy consumption in <strong>the</strong> US <strong>of</strong> pure copper due 

to copper production throughout <strong>the</strong> 20th century 

<strong>the</strong> US are obtained from <strong>the</strong> work done by Ruth [295] and completed and updated 

with information from <strong>the</strong> Minerals Yearbook [363]. 

Figure 7.7 shows <strong>the</strong> cumulative concentration exergy decrease <strong>of</strong> copper mines in 

<strong>the</strong> US ( B c). The total concentration exergy distance <strong>of</strong> copper mines between 

<strong>the</strong> beginning and end <strong>of</strong> <strong>the</strong> century was D c = 628, 98 ktoe. This exergy was consumed 

at an average degradation velocity <strong>of</strong> ˙D c = 6, 22 ktoe/year. The maximum 

degradation velocity was attained in year 2000 (10,56 ktoe/year), while <strong>the</strong> minimum 

in year 1906 (1,89 ktoe/year). The concentration exergy <strong>of</strong> copper reserves 

and reserve base in year 1900 were 875,3 and 1121,71 ktoe respectively, while in 

year 2000, 246,36 and 492,73 ktoe. 

Figure 7.7 shows <strong>the</strong> cumulative concentration exergy decrease <strong>of</strong> copper mines in 

<strong>the</strong> US. 

7.6.4 Total exergy 

We can now calculate <strong>the</strong> total exergy distance <strong>of</strong> US copper mines between <strong>the</strong> 

beginning and end <strong>of</strong> <strong>the</strong> century: 

D = (B t,1900 − B t,2000) = (D ch + D c) = (5660, 37 + 628, 98) = 6289, 35 ktoe. 

Dividing this quantity into <strong>the</strong> years considered, we obtain <strong>the</strong> average exergy degradation 

velocity <strong>of</strong> US copper: ˙D = 62, 2 ktoe/year. 

As can be seen, <strong>the</strong> exergy concentration component is much lower than <strong>the</strong> chemical 

one. For more abundant <strong>mineral</strong>s than copper, such as aluminium or iron, 

20 

19 

18 

17 

16 

15 

14 

b c , MJ/kmol



ΣB c, ktoe 

700 

600 

500 

400 

300 

200 

100 

0 

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 

Figure 7.7. Cumulative concentration exergy decrease <strong>of</strong> copper mines in <strong>the</strong> US 

throughout <strong>the</strong> 20th century 

Year 

this fact is even more enhanced. The minimum <strong>the</strong>rmodynamic energy required to 

separate two substances such as sugar and salt for example, is equal to <strong>the</strong> energy 

to mix <strong>the</strong>m, which is in fact very low. This is <strong>of</strong> course not true and <strong>the</strong> exergy 

required to separate substances is much greater than in <strong>the</strong> reversible case. In order 

to overcome that problem, we need to resort to <strong>the</strong> exergy costs <strong>of</strong> <strong>the</strong> mine. 

7.6.5 <strong>Exergy</strong> costs 

Through unit exergy costs, reversible exergies are converted into real exergies with 

Eq. 5.46 (B∗ t = kch · Bch + kc · Bc). That equation assumes that exergy costs are constant 

over time. In fact this is not completely correct, because <strong>the</strong>re are two factors 

that must be taken into account. The first one is that technological development 

improves <strong>the</strong> efficiency <strong>of</strong> mining and refining processes and thus costs tend to decrease 

(<strong>the</strong>ory <strong>of</strong> learning curves). The second factor is that as extraction continues 

and technology is being improved, lower quality resources can be extracted. However, 

<strong>the</strong> use <strong>of</strong> lower quality resources requires an increase in energy input, which 

increases costs. 

If we convert <strong>the</strong> total minimum exergy consumption into real exergy, making <strong>the</strong> assumption 

that <strong>the</strong> costs are constant, we obtain that <strong>the</strong> irreversible exergy distance 

D ∗ is: 

D∗ = (B∗ t,1900 − B∗ 

t,2000 ) = Dch · kch + Dc · kc = 5660, 37 ∗ 80, 2 + 628, 98 ∗ 343, 1 = 

669.764, 7 ktoe 

And <strong>the</strong> average irreversible exergy degradation velocity ˙D ∗ = 6631, 3 ktoe/year.


Around 68% <strong>of</strong> <strong>the</strong> exergy costs are due to <strong>the</strong> chemical exergy <strong>of</strong> copper and 32% 

to its concentration exergy. The cost represents <strong>the</strong> exergy consumed <strong>of</strong> US copper 

mines during <strong>the</strong> 20th century and is equivalent to 71,3% <strong>of</strong> 2006 oil consumption 

in <strong>the</strong> US (938,8 Mtoe [35]). This figure gives an idea <strong>of</strong> <strong>the</strong> huge amount <strong>of</strong> energy 

that we are degrading by extracting <strong>mineral</strong>s. It must be remembered, that this 

study only applies to copper mines in <strong>the</strong> US. 

Additionally, we can calculate <strong>the</strong> tons <strong>of</strong> copper equivalent (tCue ∗ ) associated to 

<strong>the</strong> exergy costs <strong>of</strong> <strong>the</strong> reserves and reserve base. For that purpose, we take as 

reference, <strong>the</strong> exergy cost B∗ t <strong>of</strong> <strong>the</strong> reserves in 1900 (5,95 toe/t <strong>of</strong> Cu extracted). 

The M tCue ∗ is slightly lower than <strong>the</strong> tonnage due to <strong>the</strong> loss <strong>of</strong> concentration 

exergy (44,7 M tCue ∗ vs 45 Mt for <strong>the</strong> reserves and 89,5 M tCue ∗ vs 90 Mt for <strong>the</strong> 

reserve base). 

7.6.6 The R/P ratio and <strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> deposits 

The resources to production ratio for US copper, is calculated by dividing <strong>the</strong> reserve 

base’s exergy in year 2000 (5027 ktoe), with <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> metal produced in 

that year (90,16 ktoe). The resulting R/P ratio indicates that if production <strong>of</strong> US Cu 

remains as in year 2000, and <strong>the</strong> reserve base does not increase after that year, <strong>the</strong> 

reserves would be completely depleted in 56 years. 

The depletion degree <strong>of</strong> US copper deposits (%R loss and %R.B. loss) is calculated 

as <strong>the</strong> ratio between <strong>the</strong> exergy distance D, and <strong>the</strong> total reserves <strong>of</strong> <strong>the</strong> commodity. 

The latter are obtained as <strong>the</strong> published reserves or reserve base <strong>of</strong> <strong>the</strong> commodity in 

2000, plus <strong>the</strong> exergy distance D from 1900 to 2000. Accordingly, copper production 

in <strong>the</strong> US throughout <strong>the</strong> 20th century has leaded to <strong>the</strong> depletion <strong>of</strong> 71% and 56% 

<strong>of</strong> its national copper reserves and reserve base, respectively. 

7.6.7 The Hubbert peak model 

We are now going to apply <strong>the</strong> Hubbert peak model to US copper mining, in order 

to estimate its peak <strong>of</strong> production. For that purpose, <strong>the</strong> exergy production has to be 

plotted against <strong>the</strong> corresponding years. At a first stage, we are going to adjust <strong>the</strong> 

points to <strong>the</strong> gaussian curve, given by Eq. 7.8, i.e. without applying <strong>the</strong> constraint 

about a fixed amount <strong>of</strong> reserves. The resulting curve represented in Fig. 7.8 is 

described by Eq. 7.13: 

f (t) = 107, 1e 

 

1 t−2041 

− 

2 87,08 

(7.13) 

The maximum is reached at t = t0 in year 2041. The integral <strong>of</strong> Eq. 7.13 represents 

<strong>the</strong> reserves: +∞ 

f (t) = 24.053, 4 ktoe. The regression <strong>of</strong> <strong>the</strong> curve is quite low: 

−∞ 

RF = 0, 7532.



Therefore, <strong>the</strong> production behavior <strong>of</strong> US copper is associated to available reserves 

equal to around 24 Mtoe, assuming that it follows <strong>the</strong> bell-shaped curve defined by 

Hubbert. 

Bt 

Integral Bt 

120 

100 

80 

60 

40 

20 

0 

x 104 

2.5 

2 

1.5 

1 

0.5 

2041 

0 

1700 1800 1900 2000 2100 2200 2300 2400 

Figure 7.8. The Hubbert peak applied to US copper production. Best fitting curve. 

Values in ktoe. 

Never<strong>the</strong>less, according to <strong>the</strong> USGS, <strong>the</strong> reserve base in year 2000 is equal to 5,02 

Mtoe. Adding <strong>the</strong> already exergy extracted from 1900 to 2000, <strong>the</strong> base reserves increase 

to 11,3 Mtoe. Since no data is provided before 1900 and <strong>the</strong>re were certainly 

important amounts <strong>of</strong> copper extracted at least in <strong>the</strong> second half <strong>of</strong> <strong>the</strong> nineteenth 

century, we will make <strong>the</strong> assumption, that Cu extraction from 1700 to 1900 followed 

<strong>the</strong> curve <strong>of</strong> Eq. 7.13. Hence, <strong>the</strong> 1700 reserve base are approximated to: 

2000 

R1700 = R2000 + Bt + 

1900 

1900 

1700 

107, 1e 

 

1 t−2041 

− 

2 87,08 = 5026, 7 + 6289, 4 + 1233, 8 

= 12549, 9ktoe (7.14)


Therefore, instead <strong>of</strong> <strong>the</strong> 24 Mtoe <strong>of</strong> reserves obtained from <strong>the</strong> model without constraints, 

<strong>the</strong> US total base reserves amount to around one half <strong>of</strong> that: 12,55 Mtoe. 

With <strong>the</strong> constraint <strong>of</strong> <strong>the</strong> reserves, we can now apply <strong>the</strong> Hubbert peak model, 

adjusting <strong>the</strong> production points to Eq. 7.12. 

Figure 7.9 shows <strong>the</strong> final curve, with again a low regression factor RF = 0, 7305. 

According to <strong>the</strong> model, <strong>the</strong> production would have reached <strong>the</strong> peak in year 1994. 

In fact, recent data about copper production in <strong>the</strong> US reveals that <strong>the</strong> peak was 

reached in year 1998 with 2,1 Mt extracted. Since <strong>the</strong>n production has decreased 

more rapidly than it increased before reaching <strong>the</strong> peak. This indicates that <strong>the</strong> observations 

<strong>of</strong> Meadows [218], where production follows asymmetric curves with <strong>the</strong> 

decline much sharper than <strong>the</strong> growth, apply better at least for US copper production. 

Ano<strong>the</strong>r conclusion that can be extracted from <strong>the</strong> application <strong>of</strong> <strong>the</strong> model is that if 

<strong>the</strong> production curves are generally asymmetrical, <strong>the</strong> peak will be reached after <strong>the</strong> 

year predicted by <strong>the</strong> Hubbert model. During a short period <strong>of</strong> time, <strong>the</strong> commodities 

will be probably over-exploited and <strong>the</strong> production points will appear over <strong>the</strong> bellshaped 

curve. The compensation <strong>of</strong> <strong>the</strong> overproduction is <strong>the</strong> much sharper decrease 

<strong>of</strong> production after <strong>the</strong> peak, instead <strong>of</strong> a gradual and steady reduction. 

Applying <strong>the</strong> Hubbert peak model to production in mass terms, instead <strong>of</strong> exergy 

terms gives 1993 as <strong>the</strong> peaking year for US copper. As can be seen, <strong>the</strong> difference 

between both approaches is very small, since as stated before, in minimum exergy 

terms, <strong>the</strong> concentration component is considerably less important than <strong>the</strong> chemical 

one. And it should be remembered, that as opposed to <strong>the</strong> concentration exergy, 

<strong>the</strong> chemical exergy is proportional to <strong>the</strong> quantity <strong>of</strong> <strong>mineral</strong> extracted. The effect 

<strong>of</strong> decreasing ore grades with production would be better observed if exergy costs, 

ra<strong>the</strong>r than minimum exergies are used for <strong>the</strong> plotting. In such a case, <strong>the</strong> concentration 

and <strong>the</strong> chemical exergy terms are well balanced. However, in this study 

we have assumed that unit exergy costs remain constant over time. For a correct 

representation <strong>of</strong> exergy costs vs. time, we would require that <strong>the</strong> exergy costs are 

calculated with <strong>the</strong> corresponding unit exergy costs <strong>of</strong> <strong>the</strong> period <strong>of</strong> time considered, 

incorporating <strong>the</strong> learning curves <strong>of</strong> <strong>the</strong> technologies. But this task remains open for 

fur<strong>the</strong>r studies. 

7.6.8 Summary <strong>of</strong> <strong>the</strong> results 

Table 7.1 summarizes <strong>the</strong> results obtained, showing <strong>the</strong> exergy and exergy costs, 

<strong>the</strong> exergy distance, average degradation velocity, <strong>the</strong> tons <strong>of</strong> <strong>mineral</strong> equivalent, 

<strong>the</strong> R/P ratio, depletion degree <strong>of</strong> <strong>the</strong> reserves and reserve base (% R. loss and % 

R.B. loss) and <strong>the</strong> estimated and real peak <strong>of</strong> production <strong>of</strong> US copper reserves and 

reserve base during <strong>the</strong> 20th century.

The exergy loss <strong>of</strong> a country due to <strong>mineral</strong> extraction. The case <strong>of</strong> Australia 245 

Integral Bt 

Bt 

120 

100 

80 

60 

40 

20 

0 

14000 

12000 

10000 

8000 

6000 

4000 

2000 

1994 

0 

1800 1900 2000 2100 2200 

Figure 7.9. The Hubbert peak applied to US copper base reserves. Values in ktoe. 

7.7 The exergy loss <strong>of</strong> a country due to <strong>mineral</strong> extraction. 

The case <strong>of</strong> Australia 

In <strong>the</strong> example above, we have applied <strong>the</strong> exergoecological method to a single 

commodity <strong>of</strong> a country. Since exergy is an additive property, we can analyze <strong>the</strong> 

exergy loss due to <strong>mineral</strong> extraction <strong>of</strong> all commodities in a region, country or even 

in <strong>the</strong> entire world. 

The objective now it to assess from <strong>the</strong> exergoecological point <strong>of</strong> view, <strong>the</strong> degradation 

<strong>of</strong> <strong>the</strong> main <strong>mineral</strong> resources <strong>of</strong> fuel and non-fuel origin <strong>of</strong> a country throughout 

its mining history. 

Australia is <strong>the</strong> country chosen for our purpose for two reasons: 1) a comprehensive 

analysis <strong>of</strong> Australian mining data was provided by Mudd [234], [232], [233] and 

2) Australia is a major <strong>mineral</strong> producer and exports numerous commodities around


Table 7.1. Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> US copper mines during 

<strong>the</strong> 20th century. 

RESERVES BASE RESERVE 

Year 1900 2000 1900 2000 

Minimum exergy, Mtoe 

B ch 7,93 2,27 10,19 4,53 

B c 0,86 0,25 1,11 0,49 

B t 8,79 2,51 11,30 5,03 

D 6,28 

˙D, ktoe/yr 62,25 

Non-reversible exergy, Mtoe 

B ∗ 

ch 635,77 181,81 817,58 363,62 

B ∗ 

c 300,33 84,53 384,86 169,05 

B ∗ 

t 936,10 266,34 1202,44 532,68 

D ∗ 669,76 

˙D ∗ , ktoe/yr 6631,33 

m Cu, Mtons 157,36 45,00 202,36 90,00 

M tCue ∗ 157,36 44,77 202,13 89,54 

R/P, yrs 56 

% R. loss 71 56 

Hubbert’s peak 1994 

Real peak 1998 

<strong>the</strong> world. Fur<strong>the</strong>rmore, its resources are periodically updated and published in 

Geoscience Australia [112]. 

The study <strong>of</strong> Mudd aims to shed light on <strong>the</strong> current debate on sustainable mining in 

Australia, establishing <strong>the</strong> extent <strong>of</strong> <strong>the</strong> changes in ore grades for various <strong>mineral</strong>s 

and metals as well as quantifying <strong>the</strong> production <strong>of</strong> wastes. Mudd provides valuable 

information among o<strong>the</strong>rs, about historical production data, ore grades and 

economic demonstrated reserves. For some commodities such as copper, <strong>the</strong> information 

dates back to 1844. 

Assimilating such a great amount <strong>of</strong> information for each commodity is not always 

easy and not very useful for decision makers. However, all <strong>the</strong>se data can be easily 

processed and summarized in one indicator, namely <strong>the</strong> exergy indicator. 

7.7.1 Non-fuel <strong>mineral</strong>s 

The aim <strong>of</strong> this section is to obtain <strong>the</strong> exergy and exergy cost <strong>of</strong> <strong>the</strong> main Australian 

metals throughout <strong>the</strong>ir mining history: Au, Cu, N i, Ag, P b, Zn and Fe. 

The reversible and irreversible exergy distances D and D∗ , <strong>the</strong> exergy degradation 

velocities ˙D and ˙D ∗ , and <strong>the</strong> tons <strong>of</strong> <strong>mineral</strong> equivalent t M e∗ lost <strong>of</strong> <strong>the</strong> economic 

demonstrated reserves are provided. The tons <strong>of</strong> <strong>mineral</strong> equivalent are calculated 

as <strong>the</strong> average exergy cost B∗ t <strong>of</strong> one ton <strong>of</strong> <strong>mineral</strong> in <strong>the</strong> Australian <strong>mineral</strong> deposits


in year 1900 (whenever data is available for that year). The reserves <strong>of</strong> <strong>the</strong> mine 

at <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> mining period are considered to be equal to <strong>the</strong> cumulated 

production throughout <strong>the</strong> mining history until 2004, plus <strong>the</strong> published reserves in 

2004 (<strong>the</strong> same principle is applied to <strong>the</strong> reserves in terms <strong>of</strong> exergy costs). 

The peaking <strong>of</strong> <strong>mineral</strong> production is estimated with <strong>the</strong> application <strong>of</strong> <strong>the</strong> Hubbert 

peak model described in section 7.5. Additionally, <strong>the</strong> R/P ratio assessed in exergy 

terms is given as a measure <strong>of</strong> <strong>the</strong> estimated years until depletion <strong>of</strong> <strong>the</strong> different 

commodities. 

The same equations, data sources and ideas used for US copper mines are here applied. 

For calculating b ch, Eq. 5.1 is used, taking as input <strong>the</strong> chemical exergies <strong>of</strong> 

<strong>the</strong> elements generated from <strong>the</strong> R.E. defined in this study (Table 5.4). The concentration 

exergy b c is calculated with Eq. 5.10. The value <strong>of</strong> x c is taken from <strong>the</strong> latest 

geochemical study <strong>of</strong> <strong>the</strong> earth’s continental crust from Rudnick and Gao [292]. Finally, 

<strong>the</strong> unit exergy costs applied are those obtained by Valero and Botero [371] 

and updated by Martínez et al. [207]. 

Figures 7.10 through 7.22 show <strong>the</strong> cumulated minimum concentration and chemical 

exergy consumption over time on <strong>the</strong> left axis and <strong>the</strong> ore grade trend on <strong>the</strong> 

right axis <strong>of</strong> <strong>the</strong> main base-precious metals extracted in Australia. As can be seen 

from <strong>the</strong> figures, and as it happened to <strong>the</strong> case <strong>of</strong> copper in <strong>the</strong> US, <strong>the</strong> concentration 

exergy Bc is usually much smaller than <strong>the</strong> chemical one Bch. But this fact 

changes when <strong>the</strong> values are converted into exergy costs B∗ c and B∗ , as shown in 

ch 

tables 7.2 to 7.8. The graphs reveal as well that consumption <strong>of</strong> all commodities has 

increased continuously, following a general exponential trend. The quality <strong>of</strong> Australian 

mines, or in o<strong>the</strong>r words, <strong>the</strong>ir ore grade trends, have been notably reduced 

throughout <strong>the</strong> last century. This implies an even greater loss <strong>of</strong> <strong>the</strong> mine’s exergy 

and an important production <strong>of</strong> waste rock. 

For <strong>the</strong> sake <strong>of</strong> simplicity, <strong>the</strong> direct results are provided. 

7.7.1.1 Gold 

Gold has played an important role in Australia’s history, influencing <strong>the</strong> economic, 

social, environmental and political life <strong>of</strong> <strong>the</strong> country. The decade <strong>of</strong> 1850’s is <strong>of</strong>ten 

denoted as <strong>the</strong> gold rush decade and since <strong>the</strong>n, great amounts <strong>of</strong> gold have been 

extracted from all states. Australian gold industry is characterized as having continuous 

cycles <strong>of</strong> boom and bust. The most representative inflection points occurred 

in <strong>the</strong> late 1800’s and around 1980. In both cases, <strong>the</strong> discovery <strong>of</strong> new fields caused 

that production, which had gradually declined before those dates, rose to new highs 

(see Fig. 7.10). 

Gold’s ore grade has followed a general declining trend, even though <strong>the</strong>re have 

been various intermediate peaks coinciding with new discoveries. Ore grades have 

descended from 37,27 g/t in 1859, to <strong>the</strong> current 2,02 g/t. The concentration exergy 

) decreased respectively from 1,28 to 0,91 toe/kg. 

costs <strong>of</strong> gold mines (b ∗ 

c


Cumulative total exergy Bt, toe 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

0 

1859 1869 1879 1889 1899 1909 1919 1929 1939 1949 1959 1969 1979 1989 1999 

Year 

Bc Bch Xm 

Figure 7.10. Ore grade and cumulated exergy consumption <strong>of</strong> Australian gold mines 

The exergy distance (D) between Australian gold mines in 2004 and 1859 is equal 

to 88,97 toe, while <strong>the</strong> irreversible exergy distance D ∗ : 10.683 ktoe. The great 

difference between <strong>the</strong> reversible and irreversible exergy distances are due to <strong>the</strong> 

extremely high unit concentration costs for gold: 422.879 [207]. The average exergy 

degradation velocity (˙D) <strong>of</strong> Australian gold mines is 0,61 toe/year, ranging from 

0,12 toe/year reached in 1929, to <strong>the</strong> last high <strong>of</strong> 2,64 toe/year in 1997. This figure 

has fluctuated frequently due to changing gold prices, available resources, policy, 

technology and socioeconomic factors. The average irreversible degradation velocity 

˙D ∗ is equal to 73,17 ktoe/year. 

The ktons <strong>of</strong> gold equivalent in terms <strong>of</strong> exergy costs extracted in <strong>the</strong> mining period 

from 1859 to 2004 was 11,06 ktAue ∗ , being <strong>the</strong> reference actual exergy <strong>of</strong> one ton <strong>of</strong> 

gold in year 1900 equal to 0,97 ktoe. The economic demonstrated reserves <strong>of</strong> gold 

in year 2004 are estimated as 5,59 kt, or 5,30 ktAue ∗ (B∗ t = 5118,61 ktoe), although 

<strong>the</strong>y might probably increase in <strong>the</strong> future, since exploration continues to take place 

and technological development will probably allow to mine low grade deposits. 

Note that since year 1900 was taken as reference for estimating <strong>the</strong> ktons <strong>of</strong> gold 

equivalent, <strong>the</strong> ktAue ∗ before that year will be greater than <strong>the</strong> tonnage, since <strong>the</strong> 

ores were more concentrated. The contrary happens after <strong>the</strong> reference year. 

The R/P ratio for Australian gold deposits is estimated as 22 years, being 2004 <strong>the</strong> 

reference year for <strong>the</strong> calculations. Additionally, gold production in Australia has 

depleted around 65% <strong>of</strong> its economic demonstrated reserves. 

The Hubbert peak is applied for Australian gold deposits since year 1943. Previous 

years are discarded in <strong>the</strong> analysis due to <strong>the</strong> fluctuation <strong>of</strong> <strong>the</strong> production rates, 

as new gold fields were found. Since 1943, it is assumed that most <strong>of</strong> <strong>the</strong> reserves 

40 

35 

30 

25 

20 

15 

10 

5 

Ore grade Xm, g/t


have been found. The value for R in that year is calculated as <strong>the</strong> sum <strong>of</strong> <strong>the</strong> exergy 

reserves in 2004, plus <strong>the</strong> cumulated exergy between 1943 and 2004 (R 1943 = 96, 02 

toe). Accordingly, <strong>the</strong> production peak is reached in year 2006 (see Fig. 7.11), with 

a regression factor <strong>of</strong> <strong>the</strong> fitting curve <strong>of</strong> RF = 0, 9014. This implies, that although 

production in <strong>the</strong> last years has decreased, it was not caused by <strong>the</strong> resource limitation 

and ra<strong>the</strong>r by external factors such as company’s strategies. 

Bt 

Integral Bt 1943 

3 

2.5 

2 

1.5 

1 

0.5 

0 

100 

80 

60 

40 

20 

2006 

0 

1940 1960 1980 2000 2020 2040 2060 2080 

Figure 7.11. The Hubbert peak applied to Australian gold reserves. Values in toe. 

The results for Australian Gold deposits is summarized in table 7.2. 

7.7.1.2 Copper 

Copper has been also a relevant contributor to <strong>the</strong> country’s richness, since Australia 

is a major copper producer in <strong>the</strong> world. Their metal deposits were discovered and 

worked on a significant and pr<strong>of</strong>itable scale from 1842. The production <strong>of</strong> copper 

has been continuous ever since.


Table 7.2. Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian gold mines. 

Reserves 

Year 1859 2004 

Minimum exergy, toe 

B ch 98,62 34,91 

B c 37,37 12,10 

B t 135,99 47,02 

D 88,97 

˙D, toe/yr 0,61 

Non-reversible exergy, ktoe 

B ∗ 

ch 0,10 0,03 

B ∗ 

c 15801,82 5118,57 

B ∗ 

t 15801,92 5118,61 

D ∗ 10.683,31 

˙D ∗ , ktoe/yr 73,17 

t Au 15.789 5.589 

tAue ∗ 

1900 16.358 5.299 

R/P, yrs 22 

% R. loss 65 

Year <strong>of</strong> <strong>the</strong> peak 2006 

Australian copper ore grades have declined from over 26% to 1,33%, accordingly, its 

concentration exergy costs decreased from a maximum <strong>of</strong> 2,97E-3 toe/kg reached 

in year 1849 to 1,97E-3 toe/kg in 2004. Despite <strong>the</strong> 33% <strong>of</strong> b∗ c decrease, Australian 

copper ore grades are still greater than in o<strong>the</strong>r countries (according to <strong>the</strong> USGS 

[363] in <strong>the</strong> US, <strong>the</strong> current ore grade is around 0,5%). Additionally, a significant 

amount <strong>of</strong> copper mines have been discovered throughout <strong>the</strong> past century and 

prospects for <strong>the</strong> current scale <strong>of</strong> <strong>the</strong> Australian copper industry to continue remain 

promising. 

The exergy distance D from 1844 to 2004 is 956,12 ktoe, and <strong>the</strong> irreversible one 

D ∗ : 103,93 Mtoe. The exergy degradation velocity (˙D) increased from less than 1 

ktoe/year before year 1898, to 50,5 ktoe/year in 2001. On average <strong>the</strong> minimum 

and irreversible exergy degradation velocities were ˙D = 5, 94 and ˙ D ∗ = 645, 5, respectively. 

In <strong>the</strong> period <strong>of</strong> 1844 to 2004, Australian copper mines lost 17,2 M tCue ∗ (1900 reference 

exergy cost <strong>of</strong> 1 tCue ∗ is equal to 6,04 toe). The economic demonstrated reserves 

<strong>of</strong> copper in year 2004 are estimated as 42,1 Mt, or 41,88 MtCue (B∗ t = 253, 1 

Mtoe). The resources to production ratio (R/P) is 48 years, and <strong>the</strong> percentage <strong>of</strong> 

<strong>the</strong> economic reserves loss is about 29%. 

The Hubbert peak model applied to Australian copper reserves is shown in Fig. 7.11. 

Considering that <strong>the</strong> reserves <strong>of</strong> copper since 1884 are R = 3.319 ktoe, <strong>the</strong> peak is 

reached in year 2021. The regression factor is RF = 0, 9336. 

Table 7.3 shows a summary <strong>of</strong> <strong>the</strong> results.


Cumulative total exergy Bt, ktoe 

1000 

900 

800 

700 

600 

500 

400 

300 

200 

100 

0 

1844 

1854 

1864 

1874 

1884 

1894 

1904 

1914 

1924 

1934 

Bc 

Year 

Bch Xm 

1944 

1954 

1964 

1974 

1984 

1994 

2004 

Figure 7.12. Ore grade and cumulated exergy consumption <strong>of</strong> Australian copper 

mines 

Integral Bt 

Bt 

60 

50 

40 

30 

20 

10 

0 

4000 

3000 

2000 

1000 

0 

1850 1900 1950 2000 2050 2100 2150 

Figure 7.13. The Hubbert peak applied to Australian copper reserves. Values in ktoe. 

2021 

30 

25 

20 

15 

10 

5 

0 

Ore grade Xm, %


Table 7.3. Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian copper mines. 

7.7.1.3 Nickel 

Reserves 

Year 1844 2004 

Minimum exergy, ktoe 

B ch 2973,36 2120,87 

B c 345,65 242,02 

B t 3319,01 2362,89 

D 956,12 

˙D, ktoe/yr 5,94 


B ∗ 

ch 238,46 170,09 

B ∗ 

c 118,59 83,04 

B ∗ 

t 357,06 253,13 

D ∗ 103,93 

˙D ∗ , Mtoe/yr 0,645 

M t Cu 58,98 42,10 

M tCue ∗ 

1900 59,08 41,88 

R/P, yrs 48 

% R. loss 29 


The large-scale production <strong>of</strong> nickel is one <strong>of</strong> Australia’s most recent additions to 

its mining industry. Although <strong>the</strong> earliest nickel production started in year 1913, 

it was not until 1966, with <strong>the</strong> discovering <strong>of</strong> a large high grade deposit, when 

N i production and exploration boomed. Since <strong>the</strong>n, extraction has continued to 

increase, even though in <strong>the</strong> period from 1977 to 1994, N i production suffered a 

slight stagnation (see Fig. 7.14). 

The ore grade has decreased from 4,57 to 1,16%. Accordingly, <strong>the</strong> concentration 

exergy costs <strong>of</strong> N i mines (b∗ c ) decreased from 3,01 to 2,44 tep/t. 

The exergy distance D between 1963 and 2004 is equal to 323,68 ktoe, while D ∗ = 

9, 46 Mtoe. The exergy degradation velocity ˙D increased from 0,26 ktoe/year to 

around <strong>the</strong> current 19 ktoe/year. On average, <strong>the</strong> minimum and irreversible exergy 

degradation velocities <strong>of</strong> nickel mines are ˙D = 8, 52 and ˙D ∗ = 683, 13 ktoe/year, 

respectively. 

The megatons <strong>of</strong> N i equivalent lost in <strong>the</strong> period 1967 to 2004 are equal to 3,27 

M tN ie∗ (<strong>the</strong> reference year is in this case 1967, since <strong>the</strong>re is no information for former 

years; M tN ie∗ 1967 = 7, 93 toe). The economic demonstrated reserves <strong>of</strong> nickel 

in year 2004 are estimated as 22,6 Mt, or 22,55 M tN ie∗ (B∗ t =178,8 Mtoe). The R/P 

ratio <strong>of</strong> Australian nickel deposits, indicate that <strong>the</strong>re is enough metal for at least 

121 years. Additionally, <strong>the</strong> percentage <strong>of</strong> <strong>the</strong> economic reserves loss is around 13%.


Cumulative total exergy, ktoe 

350 

300 

250 

200 

150 

100 

50 

0 

1967 1972 1977 1982 1987 

Year 

1992 1997 2002 

Bc Bch Xm 

Figure 7.14. Ore grade and cumulated exergy consumption <strong>of</strong> Australian nickel 

mines 

Integral Bt 

Bt 

40 

30 

20 

10 

0 

3000 

2500 

2000 

1500 

1000 

500 

2040 

0 

1960 1980 2000 2020 2040 2060 2080 2100 2120 2140 

Figure 7.15. The Hubbert peak applied to Australian nickel reserves. Values in ktoe. 

Figure 7.15 shows <strong>the</strong> Hubbert peak model applied to Australian nickel reserves. 

Considering that <strong>the</strong> reserves <strong>of</strong> nickel in 1967 are R 1967 = 2.587, 6 ktoe, <strong>the</strong> peak is 

reached in year 2040. The regression factor <strong>of</strong> <strong>the</strong> curve is RF = 0, 7549. 

Table 7.4 shows a summary <strong>of</strong> <strong>the</strong> results. 

5,0 

4,5 

4,0 

3,5 

3,0 

2,5 

2,0 

1,5 

1,0 

0,5 

0,0 

Ore grade Xm, %


Table 7.4. Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian nickel mines. 

7.7.1.4 Silver 

Reserves 

Year 1967 2004 


B ch 2442,76 2138,14 

B c 144,80 125,75 

B t 2587,57 2263,89 

D 323,68 



B ∗ 

ch 142198,16 124465,18 

B ∗ 

c 62524,61 54298,66 

B ∗ 

t 204722,77 178763,84 

D ∗ 25968,93 

˙D ∗ , ktoe/yr 683,13 

M t N i 25,82 22,60 

M tN ie ∗ 

1967 25,82 22,55 

R/P, yrs 121 

% R. loss 13 


Silver is usually found in mines containing also lead and zinc and hence <strong>the</strong>ir production 

rates are tightly connected. The establishment <strong>of</strong> major mining companies 

in Australia was in <strong>the</strong> decade <strong>of</strong> <strong>the</strong> 1880’s. 

The ore grades <strong>of</strong> silver have suffered a drastic reduction, passing from over 3000 

g/t at <strong>the</strong> initial years, to less than 800 g/t in just one decade. Since 1931, <strong>the</strong> 

ore grades have declined to less than 200 g/t, being <strong>the</strong> current ore grade equal to 

133,5 g/t (see Fig. 7.16). This quality loss <strong>of</strong> silver mines is reflected in <strong>the</strong> actual 

concentration exergy component: in year 1884, b∗ c was equal to 42,9 tep/t, while in 

2004, 30,3 tep/t (30% <strong>of</strong> concentration exergy loss). 

The exergy distance between <strong>the</strong> reserves in 1884 and 2004 are D = 1416, 91 toe 

and D ∗ = 2227, 4 ktoe. This minimum exergy was consumed at an average rate <strong>of</strong> 

˙D = 11, 71 toe/year (˙D ∗ = 18.407 toe/yr), but since year 2000, <strong>the</strong> silver degradation 

velocity has increased to about ˙D = 40 (˙D ∗ = 61.129) toe/year. 

Silver mines in Australia lost throughout <strong>the</strong>ir mining history a total <strong>of</strong> 72,81 ktAge ∗ 

(being <strong>the</strong> 1900 reference exergy equal to 30,6 toe/t). The economic demonstrated 

reserves <strong>of</strong> silver in year 2004 are estimated as 41,0 kt, or 40,8 ktAge (B∗ t = 1247, 4 

ktoe). The R/P ratio indicates that <strong>the</strong> depletion <strong>of</strong> silver mines could occur in 19 

years, if production remains as in 2004 and no fur<strong>the</strong>r reserves are found. The 

majority <strong>of</strong> <strong>the</strong> economic reserves <strong>of</strong> silver in Australia have been already extracted, 

as indicated by <strong>the</strong> %R loss ratio: 97%.


Cumulative total exergy, toe 

1500 

1400 

1300 

1200 

1100 

1000 

900 

800 

700 

600 

500 

400 

300 

200 

100 

0 

1884 

1889 

1894 

1899 

1904 

1909 

1914 

1919 

1924 

1929 

1934 

1939 

1944 

1949 

Year 

Bc Bch Xm 

1954 

1959 

1964 

1969 

1974 

1979 

1984 

1989 

1994 

1999 

2004 

Figure 7.16. Ore grade and cumulated exergy consumption <strong>of</strong> Australian silver 

mines 

The Hubbert peak model applied to Australian silver reserves does not throw out 

good results. The regression factor is very low (RF = 0, 577), considering <strong>the</strong> reserves 

in year 1884: R = 2226 toe. The maximum <strong>of</strong> <strong>the</strong> peak would have been 

reached in year 2005 (see Fig. 7.17). It must be pointed out that silver is a special 

<strong>mineral</strong> commodity in Australia, since it is extracted only as a by-product <strong>of</strong> o<strong>the</strong>r 

<strong>mineral</strong>s such as copper, lead zinc and to a lesser extent, gold [112]. Hence, <strong>the</strong> production 

patterns may not follow <strong>the</strong> general rules expected for o<strong>the</strong>r commodities. 

Table 7.5 summarizes <strong>the</strong> results obtained. 

7.7.1.5 Lead 

Lead production has followed a general increasing trend since <strong>the</strong> beginning <strong>of</strong> its 

mining industry. In deposits mined today, lead (in <strong>the</strong> form <strong>of</strong> galena, P bS) is usually 

associated with zinc, silver and commonly copper, and is extracted as a co-product 

<strong>of</strong> <strong>the</strong>se metals [112]. 

As in <strong>the</strong> case <strong>of</strong> silver, lead ore grades decreased dramatically in a short period 

<strong>of</strong> time. During <strong>the</strong> first 20 years <strong>of</strong> <strong>the</strong> lead industry, ore grades kept at around 

60%. From that point, <strong>the</strong> quality <strong>of</strong> P b in <strong>the</strong> mines dropped to levels below 20%, 

reaching <strong>the</strong> current level <strong>of</strong> 4,32%. The concentration exergy cost <strong>of</strong> P b in <strong>the</strong> 

mines (b∗ c ) decreased from 0,63 toe/t at <strong>the</strong> highest point reached in 1877, to 0,49 

toe/t in 2004 (see Fig. 7.18). 

The exergy distance <strong>of</strong> lead between 1859 and 2004 is equal to D = 982, 10 ktoe, 

and D ∗ = 40, 74 Mtoe. The exergy degradation velocity <strong>of</strong> lead increased from 

3500 

3000 

2500 

2000 

1500 

1000 

500 

0 

Ore grade Xm, g/t


Integral Bt 

Bt 

50 

40 

30 

20 

10 

0 

2500 

2000 

1500 

1000 

500 

0 

2005 

1900 1950 2000 2050 2100 2150 

Figure 7.17. The Hubbert peak applied to Australian silver reserves. Values in toe. 

Table 7.5. Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian silver mines. 

Reserves 

Year 1880 2004 

Minimum exergy, toe 

B ch 1735,08 632,91 

B c 490,99 176,24 

B t 2226,07 809,15 

D 1416,91 

˙D, toe/yr 11,71 


B ∗ 

ch 17,35 6,33 

B ∗ 

c 3459,49 1241,07 

B ∗ 

t 3476,84 1247,40 

D ∗ 2227,36 

˙D, ktoe/yr 18,42 

t Ag 112399 41000 

tAge ∗ 

1900 113588 40777 

R/P, years 19 

% R. loss 97 

Year <strong>of</strong> <strong>the</strong> peak 2005



1000 

900 

800 

700 

600 

500 

400 

300 

200 

100 

0 

0 

1859 1869 1879 1889 1899 1909 1919 1929 1939 1949 1959 1969 1979 1989 1999 

Year 

Bc Bch Xm 

Figure 7.18. Ore grade and cumulated exergy consumption <strong>of</strong> Australian lead mines 

˙D = 0, 20 toe/year (˙D ∗ = 9 toe/year) to around 20 ktoe/year (˙D ∗ = 780 ktoe/year) 

registered since year 2000. On average, ˙D and ˙D ∗ are 6,73 and 279,04 ktoe/year, 

respectively. 

The megatons <strong>of</strong> lead equivalent lost in Australia’s mining history are equal to 34,12 

M t P be∗ (being <strong>the</strong> 1900 reference actual exergy <strong>of</strong> one ton <strong>of</strong> lead equal to 0,766 

toe). The economic demonstrated reserves <strong>of</strong> lead in year 2004 are estimated as 22,9 

Mt, or 22,45 M t P be (B∗ t = 26, 81 Mtoe). According to <strong>the</strong> R/P ratio, <strong>the</strong> complete 

degradation <strong>of</strong> Australian lead deposits would occur in 34 years, if <strong>the</strong> reference year 

is 2004. Additionally, <strong>the</strong> percentage <strong>of</strong> <strong>the</strong> economic demonstrated reserves loss is 

around 60%. 

Figure 7.19 shows <strong>the</strong> Hubbert peak model applied to lead. The peaking year is 

reached in 1997, considering that <strong>the</strong> economic demonstrated reserves are R 1859 = 

1646, 6 ktoe. The regression factor <strong>of</strong> <strong>the</strong> curve is RF = 0, 8691. And <strong>the</strong> production 

points for <strong>the</strong> latest years (1998 - 2004) are not included under <strong>the</strong> curve. According 

to <strong>the</strong> production data, <strong>the</strong> real peak might have been reached in year 2002. This 

might indicate that, in <strong>the</strong> period between 1997 to 2002, <strong>the</strong>re has been an overproduction 

<strong>of</strong> <strong>the</strong> reserves. Consequently an abrupt decrease <strong>of</strong> production rates is now 

expected, as it happens with US copper. Never<strong>the</strong>less, <strong>the</strong> production pattern for 

lead might not follow <strong>the</strong> general behavior <strong>of</strong> o<strong>the</strong>r commodities, as it is extracted 

as a by-product, and <strong>the</strong> model cannot be applied satisfactorily. 

Table 7.6 summarizes <strong>the</strong> results obtained for Australian lead <strong>mineral</strong> deposits. 

90 

80 

70 

60 

50 

40 

30 

20 

10 

Ore grade Xm, %


Integral Bt 

Bt 

25 

20 

15 

10 

5 

0 

2000 

1500 

1000 

500 

1997 

0 

1850 1900 1950 2000 2050 2100 2150 

Figure 7.19. The Hubbert peak applied to Australian lead reserves. Values in ktoe. 

Table 7.6. Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian lead mines. 

Reserves 

Year 1859 2004 


B ch 1513,39 613,09 

B c 133,24 51,44 

B t 1646,63 664,53 

D 982,10 



B ∗ 

ch 38394,47 15554,01 

B ∗ 

c 29156,24 11256,51 

B ∗ 

t 67550,71 26810,52 

D ∗ 40740,19 

˙D, ktoe/yr 279,04 

M t P b 56,53 22,90 

M t ∗ 

P be,1900 56,57 22,45 

R/P 34 

% R. loss 60 

Year <strong>of</strong> <strong>the</strong> peak 1997



6000 

5000 

4000 

3000 

2000 

1000 

0 

1898 

1903 

1908 

1913 

1918 

1923 

1928 

1933 

1938 

1943 

1948 

1953 

1958 

1963 

1968 

1973 

1978 

1983 

1988 

1993 

1998 

2003 

Year 

Bc Bch Xm 

Figure 7.20. Ore grade and cumulated exergy consumption <strong>of</strong> Australian zinc mines 

7.7.1.6 Zinc 

Very little interest was shown in zinc until <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> 20th century because 

no known method for efficient Zn separation and recovery was found. At that time, 

Zn was seen as a problem appearing in silver and lead mining. However, with <strong>the</strong> 

new method <strong>of</strong> flotation, firstly applied in 1905, <strong>the</strong> Zn industry started to emerge. 

The Zn grade <strong>of</strong> Australian mines has fluctuated strongly between 3 and 17%, especially 

until <strong>the</strong> late 1940’s. Since <strong>the</strong>n, Zn grades tend to stabilize to around 8,5% 

= 0, 82 toe/t). 

(b ∗ 

c 

The exergy distance since 1905 has been D = 5381 ktoe, and D ∗ = 102 Mtoe. 

The exergy has been extracted at an average rate <strong>of</strong> ˙D=50 ktoe/year (˙D ∗ =950 

ktoe/year). In <strong>the</strong> last 5 years, <strong>the</strong> yearly minimum and irreversible exergy degradation 

velocity <strong>of</strong> zinc (˙D and ˙D ∗ ) has increased to about 178 and 3367 ktoe/year, 

respectively. 

The megatons <strong>of</strong> zinc equivalent lost in <strong>the</strong> mining period from 1898 to 2004 was 

44,56 M t Zne (M t Zne1900 = 2, 28 toe). The economic demonstrated reserves <strong>of</strong> zinc 

in year 2004 are estimated as 41 Mt, or 37,69 M t Zne (B∗ t = 85, 95 Mtoe). The R/P 

ratio <strong>of</strong> Zn economic reserves is estimated at around 30 years. The depletion degree 

<strong>of</strong> <strong>the</strong> economic reserves is around 51%. 

The Hubbert peak model applied to <strong>the</strong> Australian Zn reserves is shown in Fig. 7.21. 

As zinc mining is closely related to <strong>the</strong> mining <strong>of</strong> lead and silver, a similar behavior 

<strong>of</strong> <strong>the</strong> model to <strong>the</strong> latter <strong>mineral</strong>s is expected. The latest production points are 

not included under <strong>the</strong> curve (from 2000 to 2004). However, <strong>the</strong> adjusted curve 

has a better regression factor than that <strong>of</strong> lead and silver, namely RF = 0, 8806. 

20 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

Ore grade Xm, %


Integral Bt 

Bt 

200 

150 

100 

50 

0 

12000 

10000 

8000 

6000 

4000 

2000 

2010 

0 

1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 

Figure 7.21. The Hubbert peak applied to Australian zinc reserves. Values in ktoe. 

Table 7.7. Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian zinc mines. 

Reserves 

Year 1898 2004 


B ch 10188,07 5078,73 

B c 421,86 150,24 

B t 10609,94 5228,96 

D 5380,97 



B ∗ 

ch 134494,54 67045,15 

B ∗ 

c 53108,63 18913,37 

B ∗ 

t 187603,17 85958,52 

D ∗ 68205,94 

˙D, ktoe/yr 637,53 

M t Zn 82,25 41,00 

M t ∗ 

Zne,1900 82,25 37,69 

R/P, yrs 30 

% R. loss 51 


The expected peaking year, assuming <strong>the</strong> economic demonstrated reservers R 1898 = 

10.610, 7 ktoe is 2010. 

Table 7.7 summarizes <strong>the</strong> results obtained for Australian zinc <strong>mineral</strong> deposits.


Cumulative total exergy Bt, ktoe 

700000 

600000 

500000 

400000 

300000 

200000 

100000 

0 

1907 1917 1927 1937 1947 1957 

Year 

1967 1977 1987 1997 

Bc Bch Xm 

Figure 7.22. Ore grade and cumulated exergy consumption <strong>of</strong> Australian iron mines 

7.7.1.7 Iron 

Australia is <strong>the</strong> third iron ore production country in <strong>the</strong> world, after China and Brazil. 

The economic demonstrated iron ore reserves have fluctuated throughout last century 

and accordingly, its associated ore grade. In addition to <strong>the</strong> discoveries <strong>of</strong> new 

iron deposits, o<strong>the</strong>rs have been reclassified as economic due to <strong>the</strong> increase <strong>of</strong> iron 

prices. The available reliable data about grades and production trends for iron dates 

back to 1907, although <strong>the</strong>re are single figures for some years since 1850. There are 

ore grades missing for <strong>the</strong> following year periods: 1930 - 1934; 1936 - 1940; 1946 - 

1951; 1966 and 1994. For <strong>the</strong> latter, <strong>the</strong> same ore grade <strong>of</strong> <strong>the</strong> previous year, where 

grade data was available, was assumed. The missing grades are represented hence 

as a horizontal straight line in figure 7.22. 

The abundance <strong>of</strong> iron rich deposits has allowed <strong>the</strong> ore grades to stabilize and even 

increase throughout its mining history. Iron concentration in Australia rarely goes 

down to 62%, equivalent to around b∗ c =0,29 toe/t (see Fig. 7.22). 

The exergy distance between 1907 and 2004 has been D = 704 Mtoe, and D ∗ = 

4.901 Mtoe. The average exergy degradation velocity since 1907 was ˙D = 7183 

ktoe/year (˙D ∗ = 50.012 ktoe/year), although it increased sharply since <strong>the</strong> seventies 

to near ˙D = 40.000 ktoe/year (˙D ∗ = 265.000 ktoe/year). 

The megatons <strong>of</strong> iron equivalent lost in <strong>the</strong> mining period from 1907 to 2004 

was 3318 M t Fee ∗ (The first available year was taken as <strong>the</strong> reference, 1907: 

1t Fee ∗ =1,47 toe). The economic demonstrated reserves <strong>of</strong> iron in year 2004 are 

estimated as 10.310 Mt, or 11.282 M t Fee (B∗ t = 16665 Mtoe). The Mtons <strong>of</strong> iron 

equivalent are greater than <strong>the</strong> tonnage, because in <strong>the</strong> reference year 1907, <strong>the</strong> 

70 

60 

50 

40 

30 

20 

10 

0 

Ore grade Xm, %


Bt 

Integral Bt 

x 105 

2.5 

2 

1.5 

1 

0.5 

0 

x 107 

4 

3 

2 

1 

2068 

0 

1850 1900 1950 2000 2050 2100 2150 2200 2250 2300 

Figure 7.23. The Hubbert peak applied to Australian iron reserves. Values in ktoe. 

concentration was smaller than in 2004 (54% vs. 62%). The R/P ratio indicates 

that Australian iron reserves will become depleted in 63 years, after <strong>the</strong> reference 

year 2004. Additionally, <strong>the</strong> percentage <strong>of</strong> <strong>the</strong> economic demonstrated reserves loss 

is around 23%. 

The Hubbert peak model is satisfactorily applied to Australian iron reserves, as can 

be seen in Fig. 7.23. The peaking year will be reached in 2026, considering that <strong>the</strong> 

economic demonstrated reserves R 1907 = 3100 Mtoe. The regression factor is very 

acceptable: RF = 0, 9515. 

Table 7.8 shows a summary <strong>of</strong> <strong>the</strong> results obtained for Australian iron <strong>mineral</strong> deposits. 

7.7.2 Fuel <strong>mineral</strong>s 

In this section we are going to calculate <strong>the</strong> exergy degradation <strong>of</strong> Australian fuel 

reserves, which are composed <strong>of</strong> vast amounts <strong>of</strong> coal and some oil and natural gas. 

The exergy is calculated with <strong>the</strong> equations provided in section 5.3.3, with <strong>the</strong> 

methodology developed by Valero and Lozano [369]. As stated in previous chapters, 

<strong>the</strong> exergy <strong>of</strong> fuels is tightly related to its chemical exergy content (<strong>the</strong> concentration 

exergy component is insignificant). Note also that it has no sense <strong>of</strong> calculating 

exergy costs <strong>of</strong> fossil fuels, as it is impossible to replace <strong>the</strong> photosyn<strong>the</strong>sis process 

with current technology.


Table 7.8. Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian iron mines. 

Reserves 

Year 1907 2004 

Minimum exergy, Mtoe 

B ch 3044,65 2353,31 

B c 55,50 42,86 

B t 3100,15 2396,17 

D 703,98 

˙D, ktoe/yr 7.183,45 


B ∗ 

ch 16163,18 12493,08 

B ∗ 

c 5403,71 4172,74 

B ∗ 

t 21566,89 16665,82 

D ∗ 4901,07 

˙D, Mtoe/yr 50,01 

M t Fe 14599,83 10310,77 

M t ∗ 

Fee,1907 14599,83 11282,02 

R/P, yrs 63 

% R. loss 23 


As for <strong>the</strong> case <strong>of</strong> non-fuel <strong>mineral</strong>s, R/P ratios, <strong>the</strong> depletion degree, and <strong>the</strong> year 

estimation <strong>of</strong> maximum peaks <strong>of</strong> production are provided for Australian coal, oil and 

natural gas. 

7.7.2.1 Coal 

Coal was first discovered in Australia in 1791 in New South Wales and <strong>the</strong> first coal 

mining settlement was established <strong>the</strong>re in 1801 [12]. 

Since <strong>the</strong>n, coal production has increased dramatically. It is mined in every state 

<strong>of</strong> Australia. Around 75% <strong>of</strong> <strong>the</strong> coal mined in Australia is exported, mostly to 

eastern Asia. Consequently, Australia has become <strong>the</strong> fourth largest coal producer 

in <strong>the</strong> world. Coal also provides about 85% <strong>of</strong> Australia’s electricity production The 

relative abundance, reliability and low cost <strong>of</strong> coal have ensured that it remains <strong>the</strong> 

most commonly used fuel source for electricity generation in Australia [164]. 

The main type <strong>of</strong> coal extracted in Australia is bituminous and to a lesser extent 

lignite. Small amounts <strong>of</strong> subbituminous and traces <strong>of</strong> semi-anthracite are also produced. 

Table A.22 in <strong>the</strong> appendix, shows <strong>the</strong> production <strong>of</strong> <strong>the</strong> different types <strong>of</strong> 

Australian coal in <strong>the</strong> period between 1913 and 2006. The data has been extracted 

from <strong>the</strong> historical statistics compiled by <strong>the</strong> British Geological Survey and its preceding 

organizations. The exergies <strong>of</strong> <strong>the</strong> coal extracted in <strong>the</strong> mentioned period 

are shown in figure 7.24. The specific exergies <strong>of</strong> anthracite, bituminous, subbituminous 

and lignite used are <strong>the</strong> ones listed in table 6.10 (b I I I). According to BP [35],


Bt, ktoe 

250000 

200000 

150000 

100000 

50000 

0 

1913 

1917 

1921 

1925 

1929 

1933 

1937 

Coal production in Australia 

Semi-anthracite Bituminous Subbituminous Lignite 

Subbituminous 

1941 

1945 

1949 

1953 

1957 

1961 

1965 

1969 

1973 

1977 

1981 

1985 

1989 

Lignite 

Bituminous 

1993 

1997 

2001 

2005 

Figure 7.24. The exergy loss <strong>of</strong> Australian coal reserves. Values in ktoe. 

Australian coal’s reserves are in 2006, around 38,6 Mtons <strong>of</strong> anthracite and bituminous, 

and 39,9 Mtons <strong>of</strong> subbituminous and lignite. The latter reserves expressed in 

exergy terms, are equivalent to a total <strong>of</strong> 37,7 Gtoe. 

The exergy loss <strong>of</strong> Australian coal reserves, i.e. <strong>the</strong> exergy distance D, between 1913 

and 2006 has been around 5,6 Gtoe. This exergy was consumed at an average exergy 

degradation velocity ˙D <strong>of</strong> near 60 Mtoe/year, but since year 2000, <strong>the</strong> velocity has 

increased to more than 200 Mtoe/year. 

Assuming that <strong>the</strong> exergy reserves in 1913 were those <strong>of</strong> year 2006 plus <strong>the</strong> exergy 

distance between 1913 and 2006, i.e. R 1913 = 43, 4 Gtoe, <strong>the</strong> Hubbert’s bell-shaped 

curve applied to Australian coal production reveals that <strong>the</strong> peak <strong>of</strong> production will 

be reached in year 2048. As can be seen in fig. 7.25, <strong>the</strong> model has been very well 

fitted, with a regression factor <strong>of</strong> 0,9883. 

The resources to production ratio R/P in 2006, calculated as <strong>the</strong> ratio between <strong>the</strong> 

exergy reserves in 2006 and <strong>the</strong> exergy production in <strong>the</strong> same year, indicates that it 

will be enough coal for at least 153 years. The percentage <strong>of</strong> <strong>the</strong> economic reserves 

loss is around 13%, what indicates that <strong>the</strong>re are still large amounts <strong>of</strong> coal in <strong>the</strong> 

country. 

7.7.2.2 Oil 

According to BP [35], Australia has around 0,54 Gtons <strong>of</strong> oil reserves. The majority 

<strong>of</strong> <strong>the</strong>se reserves are located <strong>of</strong>f Western Australia in <strong>the</strong> Carnarvon basin and in <strong>the</strong> 

Year


Bt 

Integral Bt 

5 

4 

3 

2 

1 

x 10 5 

0 

x 107 

5 

4 

3 

2 

1 

2048 

0 

1900 1950 2000 2050 2100 2150 2200 

Figure 7.25. The Hubbert peak applied to Australian coal reserves. Values in ktoe. 

Bass Strait <strong>of</strong>f Sou<strong>the</strong>rn Australia. Australian oil production does not cover internal 

consumption and around 39% <strong>of</strong> total consumption needs to be imported. Oil production 

in Australia has increased gradually since 1980, peaking in 2000. Thereafter, 

Australia has experienced decreasing oil production due to oil producing basins such 

as Cooper-Eromanga and Gippsland experiencing natural declines, coupled with a 

lack <strong>of</strong> new fields coming online [82]. However, new exploration efforts, especially 

<strong>of</strong>fshore could help stabilize <strong>the</strong> country’s oil production over <strong>the</strong> next few years. 

Historical data about Australian oil production is very fragmented. Reliable and 

continuous information can only be found since <strong>the</strong> sixties. In fact, it was not until 

those years, when <strong>the</strong> country started to produce considerable amounts <strong>of</strong> oil. It is 

worth to mention that in addition to crude petroleum, oil shale 5 has been extracted 

in <strong>the</strong> past and might be taken up again in <strong>the</strong> future. 

Table A.23 shows Australian oil production data from 1913 until 2006, published by 

<strong>the</strong> British Geological Survey and its former organizations. With <strong>the</strong> specific exergy 

<strong>of</strong> Fuel-oil Nr.1 (46259,1 kJ/kg - table 6.13), we obtain that <strong>the</strong> exergy distance D <strong>of</strong> 

Australian oil production from 1964 to 2006 is equal to around 1 Gtoe. This exergy 

was consumed at an average degradation velocity ˙D <strong>of</strong> 21,7 Mtoe/year, reaching a 

peak in 2000 <strong>of</strong> more than 40 Mtoe/year (see table 7.26). 

The Hubbert peak model has been applied also for Australian oil production (see fig. 

7.27). It has been assumed, that <strong>the</strong> total amount <strong>of</strong> exergy reserves are equal to 

5 Oil Shales are sedimentary rocks containing a high proportion <strong>of</strong> organic matter (kerogen) which 

can be converted to syn<strong>the</strong>tic oil or gas by processing.


Bt, ktoe 

45000 

40000 

35000 

30000 

25000 

20000 

15000 

10000 

5000 

0 

1960 

1962 

Oil production in Australia 

1964 

1966 

1968 

1970 

1972 

1974 

1976 

1978 

1980 

1982 

1984 

1986 

1988 

1990 

1992 

1994 

1996 

1998 

2000 

2002 

2004 

2006 

Figure 7.26. The exergy loss <strong>of</strong> Australian oil reserves. Values in ktoe. 

<strong>the</strong> current ones (0,59 Gtoe), plus <strong>the</strong> exergy degradation due to extraction in past 

years (1,02 Gtoe), i.e. R = 1, 61 Gtoe. Our results throw up that <strong>the</strong> peak 6 should 

have been reached in 1997. The real peak was however reached in year 2000, and 

was followed by a sharp production decrease afterwards. This behavior is <strong>the</strong> same 

found in US copper mines and in <strong>the</strong> models <strong>of</strong> Meadows et al. [218], indicating 

that <strong>the</strong> symmetrical exponential curve <strong>of</strong> Hubbert might not be <strong>the</strong> best fit. 

The resources to production ratio for Australian oil production indicates that in less 

than 26 years, oil reserves will be completely depleted, if no more deposits are found. 

Additionally, around 60% <strong>of</strong> <strong>the</strong> economic reserves have been also exploited. As 

stated before, this situation might change, since Australia is investing in oil exploration. 

7.7.2.3 Natural gas 

Australia has sizable natural gas reserves located in <strong>of</strong>fshore basins, and in most <strong>of</strong> 

all Australia’s states. The country is <strong>the</strong> fifth largest exporter <strong>of</strong> liquefied natural 

gas (LNG) in <strong>the</strong> world. Natural gas production in Australia has increased steadily 

over <strong>the</strong> last decade. In <strong>the</strong> same time period, consumption has grown as well. Australia 

is expected to maintain natural gas self-sufficiency for <strong>the</strong> ensuing decade at 

a minimum. Additionally, recent natural gas exploration in Australia has resulted in 

several important discoveries, mainly <strong>of</strong>fshore. Fur<strong>the</strong>r natural gas discoveries will 

6 The fit has a regression factor <strong>of</strong> RF=0,853. 

Year


Bt 

Integral Bt 

x 104 

4 

3 

2 

1 

0 

x 106 

2 

1.5 

1 

0.5 

1997 

0 

1940 1960 1980 2000 2020 2040 2060 

Figure 7.27. The Hubbert peak applied to Australian oil reserves. Values in ktoe. 

likely be made inadvertently as a byproduct <strong>of</strong> Australia’s recent surge in petroleum 

exploration [82]. 

Historical data on Australian natural gas production dates back to 1961. Table A.24 

shows production data compiled by <strong>the</strong> British Geological Survey. The 2006 Australian 

natural gas reserves are around 2,61 trillion <strong>of</strong> cubic meters, according to BP 

[35]. The exergy loss <strong>of</strong> Australian natural gas reserves due to extraction is shown 

in fig. 7.28. The specific exergy <strong>of</strong> natural gas assumed is 39393,8 kJ/N m 3 (table 

6.16). Accordingly, Australia has lost in <strong>the</strong> period between 1961 to 2006, 649 Mtoe. 

This exergy was consumed at an average degradation velocity ˙D <strong>of</strong> 13,8 Mtoe/year, 

although it has increased to more than 30 Mtoe/year since <strong>the</strong> last decade (see fig. 

7.28). 

The application <strong>of</strong> <strong>the</strong> Hubbert bell shape-curve to Australian natural gas production, 

throws up a peak <strong>of</strong> production in year 2025. It has been assumed, that <strong>the</strong> 

total reserves are equal to 3,1 Gtoe 7 . The regression factor <strong>of</strong> <strong>the</strong> curve RF was 

0,98. Assuming that production will stabilize to 2007 rates and that reserves will 

not increase in <strong>the</strong> future, <strong>the</strong> R/P ratio <strong>of</strong> Australian natural gas reserves would be 

equal to 67 years. Fur<strong>the</strong>rmore, about 21% <strong>of</strong> <strong>the</strong> natural gas reserves have been already 

extracted. Of course <strong>the</strong>se numbers are only hypo<strong>the</strong>tical and will presumably 

increase, as new deposits are found. 

7 The total reserves are obtained as <strong>the</strong> exergy reserves in 2006, plus <strong>the</strong> exergy distance between 

1961 and 2006.


Bt, ktoe 

40000 

35000 

30000 

25000 

20000 

15000 

10000 

5000 

0 

Natural gas production in Australia 

1960 

1962 

1964 

1966 

1968 

1970 

1972 

1974 

1976 

1978 

1980 

1982 

1984 

1986 

1988 

1990 

1992 

1994 

1996 

1998 

2000 

2002 

2004 

2006 

Figure 7.28. The exergy loss <strong>of</strong> Australian natural gas reserves. Values in ktoe. 

Bt 

Integral Bt 

x 104 

6 

5 

4 

3 

2 

1 

0 

x 106 

4 

3 

2 

1 

2025 

0 

1940 1960 1980 2000 2020 2040 2060 2080 2100 2120 

Figure 7.29. The Hubbert peak applied to Australian natural gas reserves. Values in 

ktoe. 

Year


Table 7.9. Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy assessment <strong>of</strong> <strong>the</strong> main Australian 

<strong>mineral</strong>s. 

Mineral ∆t Peak R/P, % R ∆M t M e D, ktoe D 

yrs Loss 

∗ , Mtoe ˙D, ktoe, yr ˙D ∗ , ktoe, yr 

Au 1859 - 2004 2006 22 65 1,11E-02 0,1 10,7 6,1E-04 73,2 

Cu 1844 - 2004 2021 48 29 17,2 956,1 103,9 5,9 645,5 

N i 1967 - 2004 2040 121 13 3,3 323,7 26,0 8,5 683,1 

Ag 1884 - 2004 2005 19 97 7,28E-02 1,4 2,2 0,0 18,4 

P b 1859 - 2004 1997 34 60 34,1 982,1 40,7 6,7 279,0 

Zn 1897 - 2004 2010 30 51 44,6 5381,0 101,6 50,3 950,1 

Fe 1907 - 2004 2026 63 23 3317,8 703978,4 4901,1 7183,5 50012,4 

Coal 1913 - 2006 2048 153 13 - 5637923,1 - 59977,9 - 

Oil 1964 - 2006 1997 26 63 - 1019500,0 - 21691,5 - 

N.Gas 1961 - 2006 2025 67 21 - 649045,8 - 13809,5 - 

TOTAL 8018091,5 5186,3 102733,8 52661,8 

7.7.3 Summary and discussion <strong>of</strong> <strong>the</strong> results 

Table 7.9, summarizes <strong>the</strong> results obtained from this study, showing <strong>the</strong> year were 

<strong>the</strong> peak <strong>of</strong> production is reached (Peak), <strong>the</strong> R/P ratio <strong>of</strong> <strong>the</strong> last recorded year, 

<strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> commodities (% R. loss), <strong>the</strong> quantity <strong>of</strong> Metal extracted 

(∆M t M e) in Mtons, <strong>the</strong> minimum and irreversible exergy distance (D and D ∗ ) and 

degradation velocities (˙D and ˙D ∗ ) <strong>of</strong> <strong>the</strong> fuel and non-fuel <strong>mineral</strong> Australian reserves 

throughout <strong>the</strong> period <strong>of</strong> time considered (∆t). Thanks to <strong>the</strong> additive property 

<strong>of</strong> exergy, <strong>the</strong> total minimum and irreversible exergy distance <strong>of</strong> <strong>the</strong> mines in 

Australia considered can be calculated. 

The Hubbert peak model to <strong>the</strong> exergy reserves <strong>of</strong> <strong>the</strong> Australian <strong>mineral</strong>s considered 

was satisfactorily applied to gold, copper, nickel, iron, coal, oil 8 and natural gas. 

That was not <strong>the</strong> case for commodities silver, lead and zinc were <strong>the</strong> regression factors 

<strong>of</strong> <strong>the</strong> curves were quite low and <strong>the</strong> latest production points were not included 

under <strong>the</strong> bell-shaped curve. Probably <strong>the</strong> fact that <strong>the</strong> production <strong>of</strong> all three metals 

are tightly connected, makes that <strong>the</strong>ir production patterns do not follow <strong>the</strong> general 

behavior <strong>of</strong> o<strong>the</strong>r commodities. According to <strong>the</strong> economic demonstrated reserves 

<strong>of</strong> <strong>the</strong> listed <strong>mineral</strong>s, <strong>the</strong> Hubbert peak model applied in this study predicts that <strong>the</strong> 

maximum production has been already reached for gold (2006), silver (2005), lead 

(1997) and oil (1997). Zinc will reach <strong>the</strong> peak in 2010, copper in 2021, natural 

gas in 2025, iron in 2026, nickel in 2040, and finally coal in 2048. The resources to 

production data, informs us about <strong>the</strong> estimated years until depletion. Accordingly, 

<strong>the</strong> most depleted commodities are in decreasing order: silver, gold, oil, zinc and 

lead, with R/P ratios below 35 years. They are followed by <strong>the</strong> commodities <strong>of</strong> copper, 

iron, natural gas, nickel and finally coal, with R/P ratios <strong>of</strong> 48, 63, 67, 121 and 

153 years, respectively. Of course <strong>the</strong>se figures are only approximative, since <strong>the</strong>y 

depend strongly on production rates and reserves. The latter might increase as new 

8 Despite <strong>of</strong> <strong>the</strong> irregular oil production in Australia, <strong>the</strong> Hubbert peak model here applied has 

predicted with only three years <strong>of</strong> difference <strong>the</strong> peaking <strong>of</strong> production.


discoveries are found, or as technology or <strong>the</strong> increase <strong>of</strong> prices allows to extract 

lower-grade deposits. 

Although <strong>the</strong> quantity extracted <strong>of</strong> all commodities in terms <strong>of</strong> mass cannot be 

summed up (gold and silver are extracted at rates <strong>of</strong> some tons per year, whereas <strong>the</strong> 

o<strong>the</strong>r metals at rates <strong>of</strong> kilotons/year), <strong>the</strong> order <strong>of</strong> magnitude in terms <strong>of</strong> exergy 

costs (B ∗ ) is similar for all commodities and its sum gives valuable information. The 

irreversible exergy distance D ∗ obtained for all metals in Australia listed in Table 7.9 

is equal to 5186 Mtoe. The irreversible degradation velocity <strong>of</strong> <strong>the</strong> same metals is 

on average 52,6 Mtoe/yr. This means that if we would like to replace <strong>the</strong> metals 

extracted throughout Australia’s mining history, with current available technology, 

we would require 154 times <strong>the</strong> 2006 primary energy consumption <strong>of</strong> that country 

(33,7 Mtoe [35]). Moreover, each year Australia is degrading on average by <strong>the</strong> 

extraction <strong>of</strong> metals <strong>the</strong> equivalent <strong>of</strong> 1,56 times its primary oil consumption. From 

all metals, iron is responsible for 95% <strong>of</strong> <strong>the</strong> exergy consumption, due to <strong>the</strong> great 

quantity <strong>of</strong> iron ore produced in Australia. 

Figures 7.30 to 7.32 show <strong>the</strong> total consumption in exergy replacement costs terms 

(B∗ t ) <strong>of</strong> all metals considered, from 1844 to 2004. In <strong>the</strong> first period illustrated in Fig. 

7.30, <strong>the</strong> extraction <strong>of</strong> copper and gold contribute to most <strong>of</strong> <strong>the</strong> exergy consumed, 

although lead acquires a relevant role from <strong>the</strong> last years <strong>of</strong> <strong>the</strong> 19th century. In <strong>the</strong> 

second period, from 1907 to 1963 (Fig. 7.31), <strong>the</strong> extraction <strong>of</strong> zinc, lead and iron 

represents <strong>the</strong> major exergy consumption. From 1950 to our days, iron dominates 

clearly <strong>the</strong> non-fuel <strong>mineral</strong> exergy consumption in Australia. 

700 

B* t, ktoe 

600 

500 

400 

300 

200 

100 

0 

1844 

1846 

1848 

1850 

1852 

1854 

1856 

1858 

Silver 

1860 

1862 

1864 

1866 

1868 

1870 

1872 

1874 

1876 

1878 

1880 

1882 

1884 

1886 

1888 

1890 

1892 

1894 

Silver Gold Copper Iron Nickel Lead Zinc 

Zinc 

Lead 

Copper 

Gold 

1896 

1898 

1900 

1902 

1904 

1906 

Figure 7.30. Irreversible exergy consumption <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong>s in Australia 

in <strong>the</strong> period from 1884 to 1906


10000 

B* t, ktoe 

9000 

8000 

7000 

6000 

5000 

4000 

3000 

2000 

1000 

0 

1907 

1909 

1911 

1913 

1915 

1917 

1919 

1921 

Zinc 

Lead 

1923 

1925 

1927 

1929 

1931 

1933 

1935 

1937 

1939 

1941 

1943 

1945 

1947 

1949 

1951 

1953 

1955 

1957 



in <strong>the</strong> period from 1907 to 1964 

300000 

250000 

200000 

150000 

100000 

50000 

0 

B* t, ktoe 

Zinc 

Iron 

Copper 


Copper 

1959 

1961 

1963 

1965 

1967 

1969 

1971 

1973 

1975 

1977 

1979 

1981 

1983 

1985 

1987 

1989 

1991 

1993 

1995 

1997 

1999 

2001 

2003 



in <strong>the</strong> period from 1965 to 2004


80000 

70000 

60000 

50000 

40000 

30000 

20000 

10000 

0 

B* t, ktoe 

1914 

1916 

1918 

1920 

1922 

1924 

1926 

1928 

1930 

1932 

O<strong>the</strong>r metals Iron Oil N.G. Coal 

1934 

1936 

1938 

1940 

1942 

1944 

1946 

1948 

1950 

1952 

1954 

1956 

1958 

1960 

Figure 7.33. Irreversible exergy consumption <strong>of</strong> <strong>the</strong> main fuel and non-fuel <strong>mineral</strong>s 

in Australia in <strong>the</strong> period <strong>of</strong> 1914 to 1968 

We have stated before, that calculating exergy costs <strong>of</strong> fuel <strong>mineral</strong>s has no sense, 

as it is impossible to replace <strong>the</strong>m, at least with current technology. Never<strong>the</strong>less, its 

chemical exergy is so large, that can be compared to <strong>the</strong> exergy costs <strong>of</strong> <strong>the</strong> metals 

studied. This way, we can estimate <strong>the</strong> exergy destruction <strong>of</strong> <strong>the</strong> global <strong>mineral</strong> 

resources <strong>of</strong> a country. 

We have divided <strong>the</strong> information into <strong>the</strong> commodities coal, oil, natural gas, iron 

and o<strong>the</strong>r non-fuel metals. This is because <strong>the</strong> exergy cost <strong>of</strong> iron is significantly 

greater than <strong>the</strong> rest <strong>of</strong> <strong>the</strong> metals and is comparable to that <strong>of</strong> <strong>the</strong> fuel <strong>mineral</strong>s. 

Fur<strong>the</strong>rmore, we have considered two periods <strong>of</strong> time: from 1914 to 1968 and from 

1969 to 2004 (before and after <strong>the</strong> significant production <strong>of</strong> oil and natural gas). 

As can be seen in figure 7.33, in <strong>the</strong> first period <strong>of</strong> time considered, <strong>the</strong> exergy consumption 

was clearly dominated by <strong>the</strong> extraction <strong>of</strong> coal and to a lesser extent <strong>of</strong> 

iron, especially towards <strong>the</strong> end <strong>of</strong> <strong>the</strong> period. The global extraction trend increased 

very rapidly, following an exponential-like behavior. This way, <strong>the</strong> exergy degradation 

velocity increased from around 10 Mtoe/year at <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> period, 

until <strong>the</strong> 70 Mtoe/year reached in 1968. 

The coming out <strong>of</strong> significant reserves <strong>of</strong> oil and natural gas (cleaner and more handy 

fuels than coal), lead to an important drop <strong>of</strong> coal’s production in <strong>the</strong> beginning <strong>of</strong> 

<strong>the</strong> second period considered (see fig. 7.34). This resulted in a 25-year hegemony 

<strong>of</strong> iron production in Australia. Never<strong>the</strong>less, <strong>the</strong> abundance <strong>of</strong> coal in <strong>the</strong> country, 

toge<strong>the</strong>r with <strong>the</strong> foreseeable depletion <strong>of</strong> oil, provoked a new increase <strong>of</strong> coal extraction. 

Since <strong>the</strong>n, both coal and iron dominate <strong>the</strong> exergy destruction each year 

<strong>of</strong> <strong>the</strong> <strong>mineral</strong> <strong>capital</strong> in Australia (see fig. 7.35). 

Coal 


O<strong>the</strong>r metals 

1962 

1964 

1966 

1968 

Oil


600000 

500000 

400000 

300000 

200000 

100000 

0 

B* t, ktoe 

Coal 

Oil 

N.G. 


1969 

1971 

1973 

1975 

1977 

1979 

1981 

1983 

1985 

1987 

1989 

1991 

1993 

1995 

1997 

1999 

2001 

2003 


Figure 7.34. Irreversible exergy consumption <strong>of</strong> <strong>the</strong> main fuel and non-fuel <strong>mineral</strong>s 

in Australia in <strong>the</strong> period <strong>of</strong> 1969 to 2004 

%, B* T 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 

Coal 


O<strong>the</strong>r metals 

Oil 

N.G. 

0 

1914 1924 1934 1944 1954 1964 1974 1984 1994 2004 

Year 


Figure 7.35. Relative contribution <strong>of</strong> <strong>the</strong> extraction <strong>of</strong> fuel and non-fuel <strong>mineral</strong>s to 

<strong>the</strong> global exergy degradation <strong>of</strong> Australia in <strong>the</strong> period <strong>of</strong> 1914 to 2004


Despite <strong>of</strong> <strong>the</strong> shifts in extraction trends among <strong>the</strong> different commodities, it is remarkable 

that <strong>the</strong> global behavior has continued to be exponential-like. In 2004, 

<strong>the</strong> exergy degradation velocity exceeded 550 Mtoe/year (around 15% <strong>of</strong> current 

world’s oil consumption). And presumably, it will continue to increase exponentially 

at least for 20 to 40 years, until <strong>the</strong> peaks <strong>of</strong> iron and coal are reached. 

In figures 7.36 and 7.37, we have represented <strong>the</strong> Hubbert’s bell-shaped curves <strong>of</strong> 

all <strong>mineral</strong> commodities considered in terms <strong>of</strong> <strong>the</strong>ir exergy replacement costs. This 

type <strong>of</strong> representation will be named here as “<strong>Exergy</strong> countdown”, since it shows 

in a very schematic way <strong>the</strong> amount <strong>of</strong> exergy resources available and <strong>the</strong> possible 

exhaustion behavior that <strong>the</strong>y will follow. It should be noted that representing B 

vs t or B ∗ vs t brings up in our case similar results for <strong>the</strong> peaking year, as unit 

replacement costs have been considered constant throughout <strong>the</strong> time considered. 

The use <strong>of</strong> exergy replacement costs allows us to compare <strong>the</strong> exergy content <strong>of</strong> 

fuels and non-fuel <strong>mineral</strong>s. However, as stated before, a better fit should take into 

account <strong>the</strong> change <strong>of</strong> technology, <strong>the</strong>reby using <strong>the</strong> appropriate unit exergy costs at 

each period <strong>of</strong> time. 

In figure 7.36, <strong>the</strong> bell shaped curves <strong>of</strong> all fuels plus those <strong>of</strong> iron and copper 

are represented. As can be seen, in exergy cost terms, coal is <strong>the</strong> most abundant resource, 

followed by iron. Until <strong>the</strong> first decade <strong>of</strong> <strong>the</strong> 21st century, both commodities 

will be extracted at similar rates. However, <strong>the</strong> coming <strong>of</strong> <strong>the</strong> peak <strong>of</strong> iron production 

in <strong>the</strong> second decade <strong>of</strong> <strong>the</strong> 21st century, will slow down <strong>the</strong> extraction <strong>of</strong> <strong>the</strong> 

metal, while coal will clearly dominate <strong>the</strong> <strong>mineral</strong> extraction in Australia. Fig. 7.36 

shows additionally <strong>the</strong> significant lower amount <strong>of</strong> <strong>the</strong> reserves <strong>of</strong> natural gas and 

oil, with respect to iron and coal. 

The same thing occurs with <strong>the</strong> rest <strong>of</strong> <strong>the</strong> metals considered, which are shown 

in a separate figure (fig. 7.37). It is interesting to notice that although copper is 

<strong>the</strong> most abundant commodity in exergy terms, <strong>the</strong> greater extraction rate <strong>of</strong> that 

<strong>mineral</strong> will provoke a faster depletion <strong>of</strong> copper than <strong>of</strong> nickel. Similarly, although 

<strong>the</strong> irreversible exergy reserves <strong>of</strong> zinc and nickel are similar, <strong>the</strong> greater extraction 

rate <strong>of</strong> zinc, implies that <strong>the</strong> peaking year <strong>of</strong> that metal will be reached before that 

<strong>of</strong> nickel. The graph also shows <strong>the</strong> smaller relative amount <strong>of</strong> <strong>the</strong> commodities <strong>of</strong> 

lead, gold and silver, being <strong>the</strong> reserves <strong>of</strong> <strong>the</strong> latter commodity barely perceptible 

in <strong>the</strong> figure. 

The exergy countdown diagram <strong>of</strong> a country allows us to predict future <strong>mineral</strong> 

productions and <strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> commodities. This way, for instance, 

we can forecast according to our results, that in year 2050, about 64% <strong>of</strong> <strong>the</strong> total 

considered <strong>mineral</strong> reserves in Australia will be depleted. Particularly, gold will be 

depleted at 99,9%, copper at 90,3%, lead at 87%, zinc at 97,3%, nickel at 60,4%, 

iron at 80%, coal at 52,4%, oil at 95,9% and natural gas at 85,2%. 

It must be pointed out, that <strong>the</strong> latter <strong>mineral</strong>s are not <strong>the</strong> only ones extracted in 

Australia. O<strong>the</strong>r non-fuel <strong>mineral</strong>s such as uranium, alumina, manganese, tin, diamonds 

and industrial sands are also produced. The lack <strong>of</strong> information <strong>of</strong> especially

Conversion <strong>of</strong> exergy costs into monetary costs 275 

500000 

400000 

300000 

200000 

100000 

Bt*, ktoe 

Oil 


Natural gas 

Copper 

0 

1890 1940 1990 2040 2090 2140 2190 

Figure 7.36. <strong>Exergy</strong> countdown <strong>of</strong> <strong>the</strong> main consumed <strong>mineral</strong>s in Australia 

ore grade trends for <strong>the</strong> latter materials avoids us to complete <strong>the</strong> analysis. Never<strong>the</strong>less, 

<strong>the</strong> figures provided are good enough for giving an order <strong>of</strong> magnitude <strong>of</strong> 

<strong>the</strong> depletion <strong>of</strong> Australian <strong>mineral</strong> reserves due to <strong>mineral</strong> extraction. 

7.8 Conversion <strong>of</strong> exergy costs into monetary costs 

The conversion <strong>of</strong> exergy costs into monetary costs is a ra<strong>the</strong>r simple task through 

conventional energy prices. It must be stated though, that this should not be necessarily 

<strong>the</strong> final objective, as <strong>the</strong> physical information is valuable by itself. 

As an example, we will estimate <strong>the</strong> monetary cost <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> reserve’s 

depletion suffered in Australia in year 2004, due to <strong>mineral</strong> extraction. 

The monetary value <strong>of</strong> fuel <strong>mineral</strong>s, can be directly calculated by <strong>the</strong>ir corresponding 

prices in <strong>the</strong> year under consideration. For non-fuel <strong>mineral</strong>s, we will consider 

an average price <strong>of</strong> <strong>the</strong> energy mix consumed in <strong>the</strong> country. This is because <strong>the</strong> 

exergy cost <strong>of</strong> non-fuel <strong>mineral</strong>s represents <strong>the</strong> amount <strong>of</strong> energy required to restore 

<strong>the</strong>m with current technology. 

According to <strong>the</strong> 2007 BP statistical report [35], <strong>the</strong> average price <strong>of</strong> coal 9 in 

2004 was 64,33 $US/t or 118,91 US$/toe, considering <strong>the</strong> specific exergy <strong>of</strong> coal. 

9 This price corresponds to <strong>the</strong> US Central Appalachian coal spot price. 

Coal 

Year


7000 

Bt*, ktoe 

6000 

5000 

4000 

3000 

2000 

1000 

Zinc 

Lead 

Gold 

Copper 

0 

Silver 

1890 1940 1990 2040 2090 2140 

Figure 7.37. <strong>Exergy</strong> countdown <strong>of</strong> metals copper, zinc, nickel, lead and silver in 

Australia 

The same report includes oil and natural gas prices 10 : 40,83 $US/barrel (274,62 

$US/toe), and 5,85 $US/million Btu (232,14 $US/toe), respectively. 

According to ABARE [1], <strong>the</strong> 2004 primary consumption energy mix in Australia 

was: 41% <strong>of</strong> coal, 35% <strong>of</strong> oil, 19% <strong>of</strong> natural gas and 5% <strong>of</strong> renewables. Assuming 

zero <strong>the</strong> renewables cost, we obtain an average energy price in Australia <strong>of</strong> 189,0 

$US/toe. 

Table 7.10 shows an estimation <strong>of</strong> <strong>the</strong> monetary costs associated to <strong>the</strong> depletion <strong>of</strong> 

<strong>the</strong> main Australian <strong>mineral</strong> reserves due to <strong>mineral</strong> extraction in year 2004. 

Table 7.10. Monetary costs <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> reserves depletion suffered in Australia 

due to <strong>mineral</strong> production in year 2004 

Mineral <strong>Exergy</strong> extracted, Mineral’s price, Monetary cost, Bil- 

Mtoe 

US$/toe 

lion US$ 

Coal 231,3 118,9 27,5 

Oil 22,6 274,6 6,2 

N. Gas 33 232,1 7,7 

Non-fuels 274,7 189,0 51,9 

TOTAL 561,6 93,3 

10 The natural gas price corresponds to USA Henry Hub &. 

Nickel 

Year


According to <strong>the</strong> results obtained, Australia would have lost in 2004 an equivalent 

<strong>of</strong> 93,3 billions <strong>of</strong> $US <strong>of</strong> its <strong>mineral</strong> <strong>capital</strong>, due to resource extraction. This corresponds 

to 15,2% <strong>of</strong> <strong>the</strong> 2004 Australian GDP (611,7 billions <strong>of</strong> $US [56], adjusted 

for <strong>the</strong> countrie’s purchasing capacity 11 ). 

The same amount <strong>of</strong> physical <strong>capital</strong> lost, calculated with 2006 and 2008 energy 

prices, would be equivalent to around 115 and 178 billions <strong>of</strong> $US, respectively 

(19 and 29% <strong>of</strong> <strong>the</strong> 2004 Australian GDP 12 ). This clearly indicates, that assessing 

<strong>the</strong> loss <strong>of</strong> <strong>mineral</strong> <strong>capital</strong> in monetary costs is not very suitable, as <strong>the</strong> volatility 

and arbitrariness <strong>of</strong> prices distorts <strong>the</strong> real physical value, which is absolute and 

understandable worldwide. 

However, monetary values provides us with an order <strong>of</strong> magnitude <strong>of</strong> <strong>the</strong> importance 

<strong>of</strong> <strong>mineral</strong> extraction. The considerable amount <strong>of</strong> money just calculated as an example, 

is what Australia should pay <strong>the</strong> earth, for <strong>the</strong> amount <strong>of</strong> <strong>mineral</strong> extracted 

only in year 2004. It should be stated, that less developed countries, whose economy 

is mainly based on <strong>the</strong> extraction <strong>of</strong> <strong>the</strong>ir <strong>mineral</strong> <strong>capital</strong> could even obtain negative 

GDP values. That maybe <strong>the</strong> case for countries like South Africa or Chile, but this 

should be studied more carefully with detailed production data <strong>of</strong> those countries. 

What is clear is that economy treats our planet as a reservoir <strong>of</strong> free goods. As 

<strong>the</strong> earth becomes depleted, man slowly realizes <strong>the</strong> importance <strong>of</strong> conserving its 

resources. And maybe in a not very distant future, we will have to take “Nature into 

account”, as stated by Dieren’s book <strong>of</strong> <strong>the</strong> same name [75], and correct accordingly 

<strong>the</strong> economic indices. As King argues in <strong>the</strong> book, if production is creating scarcity 

ra<strong>the</strong>r than reducing it, economic growth is negative. 


We have seen in this chapter that nei<strong>the</strong>r mass, nor energy are appropriate indicators 

for assessing <strong>the</strong> loss <strong>of</strong> <strong>mineral</strong> wealth on earth, as <strong>the</strong>y are conservative properties. 

In all physical transformations <strong>of</strong> matter or energy, it is always exergy that is lost. 

Therefore, any degradation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> <strong>capital</strong> which can come ei<strong>the</strong>r from an 

alteration in its composition, a decrease <strong>of</strong> its concentration, or a change in <strong>the</strong> 

reference environment, can be accounted for with exergy. 

Starting from <strong>the</strong> property exergy, we have built a series <strong>of</strong> indicators which should 

measure <strong>the</strong> scarcity degree <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves on earth. The exergy difference 

between two situations <strong>of</strong> <strong>the</strong> planet has been named as exergy distance D. The 

exergy degradation velocity ˙D, calculated as <strong>the</strong> exergy distance divided by <strong>the</strong> period 

<strong>of</strong> time considered, should account for <strong>the</strong> rate <strong>of</strong> exergy destruction <strong>of</strong> a certain 

resource. 

11 The Purchasing Power Parity takes into account how much an individual can buy within a country 

along with <strong>the</strong> currency exchange rate between <strong>the</strong> individual country’s currency and <strong>the</strong> U.S. dollar. 

12 For <strong>the</strong> following energy prices in 2006 and 2008, respectively: 116,4 and 167,7 $US/toe <strong>of</strong> coal; 

438,2 and 807,1$US/toe <strong>of</strong> oil; 268,3 and 287,0 $US/toe <strong>of</strong> natural gas.


We have also defined <strong>the</strong> ton <strong>of</strong> <strong>mineral</strong> equivalent (t M e), as <strong>the</strong> exergy content <strong>of</strong> 

one ton <strong>of</strong> <strong>mineral</strong> in a certain time and place. The reference value <strong>of</strong> <strong>the</strong> ton <strong>of</strong> 

<strong>mineral</strong> equivalent has to be established for each resource. The t M e is analogous 

to <strong>the</strong> ton <strong>of</strong> oil equivalent, but it accounts for <strong>the</strong> tonnage, grade and chemical 

composition <strong>of</strong> <strong>the</strong> substance. This new indicator allows us to assess <strong>the</strong> exergy 

content <strong>of</strong> a certain deposit before and after extraction, and to compare <strong>the</strong> quality 

<strong>of</strong> different deposits containing <strong>the</strong> same <strong>mineral</strong>, but with a more understandable 

unit <strong>of</strong> measure. 

The estimated years until depletion <strong>of</strong> a resource are usually calculated with <strong>the</strong> R/P 

ratio, which is obtained as <strong>the</strong> quotient between its reserves and its production in a 

certain year in mass terms. We have proposed to calculate <strong>the</strong> R/P ratio in exergy 

terms, <strong>the</strong>reby accounting for <strong>the</strong> concentration factor as well. 

All indicators described above can be assessed ei<strong>the</strong>r with minimum exergies, or 

with exergy replacement costs. With <strong>the</strong> latter, <strong>the</strong> irreversibility factor present in all 

real processes is taken into account. 

Finally, we have proposed <strong>the</strong> application <strong>of</strong> <strong>the</strong> Hubbert peak model for <strong>the</strong> assessment 

<strong>of</strong> <strong>the</strong> production peak <strong>of</strong> non-fuel <strong>mineral</strong>s. It has been stated that <strong>the</strong> 

bell-shape curve is better suited to non-fuel <strong>mineral</strong>s if it is fitted with exergy over 

time, instead <strong>of</strong> mass over time. This way, we would not ignore <strong>the</strong> concentration 

factor, which is very important for <strong>the</strong> case <strong>of</strong> solid <strong>mineral</strong>s. 

As a first case study, we have obtained <strong>the</strong> exergy decrease <strong>of</strong> US copper deposits 

throughout <strong>the</strong> 20th century, and have applied all indicators described above. For 

that purpose, <strong>the</strong> chemical and concentration exergy components <strong>of</strong> <strong>the</strong> mines, as 

well as <strong>the</strong>ir associated exergy replacement costs have been obtained for <strong>the</strong> period 

between years 1900 and 2000. It has been estimated, that <strong>the</strong> global exergy cost 

associated to <strong>the</strong> degradation <strong>of</strong> US copper deposits in <strong>the</strong> 20th century was around 

700 Mtoe, consumed at an average exergy degradation velocity <strong>of</strong> 6,6 Mtoe/year. 

The R/P ratio <strong>of</strong> US copper deposits reveals for year 2000, that reserves would be 

completely depleted after 56 years. Moreover, <strong>the</strong> application <strong>of</strong> <strong>the</strong> Hubbert peak 

in exergy terms, gives as a result, that <strong>the</strong> peak was already reached in year 1994. 

In fact <strong>the</strong> real peak was attained in year 1998. Although <strong>the</strong> exergy production 

pattern did not perfectly fit in <strong>the</strong> bell-shaped curve, interesting conclusions have 

been extracted. Generally, production follows asymmetric curves with <strong>the</strong> decline 

much sharper than <strong>the</strong> growth. Hence, <strong>the</strong> real production peak is most probably 

attained after <strong>the</strong> year predicted by <strong>the</strong> Hubbert model. During a short period <strong>of</strong> 

time, <strong>the</strong> commodities will be probably over-exploited and <strong>the</strong> production points 

will appear over <strong>the</strong> bell-shaped curve. The compensation <strong>of</strong> <strong>the</strong> overproduction is 

<strong>the</strong> much sharper decrease <strong>of</strong> production after <strong>the</strong> peak, instead <strong>of</strong> a gradual and 

steady reduction. 

The second case study was aimed at assessing <strong>the</strong> exergy loss <strong>of</strong> a country due to 

<strong>mineral</strong> extraction. Australia has been chosen for <strong>the</strong> analysis, because it is one <strong>of</strong>


<strong>the</strong> most important <strong>mineral</strong> exporting countries in <strong>the</strong> world and is <strong>the</strong> only one 

with registered ore grade trends <strong>of</strong> its main <strong>mineral</strong>s. The commodities analyzed 

throughout <strong>the</strong>ir mining history until 2004 were gold, copper, nickel, silver, lead, 

zinc, iron, coal, oil and natural gas. It has been stated, that generally, production 

<strong>of</strong> all commodities has followed an exponential-like behavior. The most depleted 

commodities are in decreasing order: silver, gold, oil, zinc and lead, with R/P ratios 

below 35 years. On <strong>the</strong> contrary, <strong>the</strong> reserves <strong>of</strong> copper, iron, natural gas, nickel and 

finally coal will last at least for 48, 63, 67, 121 and 153 years, respectively. 

The Hubbert peak model was satisfactorily applied for all commodities, with <strong>the</strong> 

exception <strong>of</strong> <strong>the</strong> group lead-zinc-silver, whose production patterns differ from <strong>the</strong> 

rest, as <strong>the</strong>y are extracted toge<strong>the</strong>r. The study predicts that <strong>the</strong> maximum production 

has been already reached for gold (2006), silver (2005), lead (1997) and oil (1997). 

Zinc will reach <strong>the</strong> peak in 2010, copper in 2021, natural gas in 2025, iron in 2026, 

nickel in 2040, and finally coal in 2048. 

By <strong>the</strong> extraction <strong>of</strong> metals, Australia has degraded <strong>the</strong> equivalent <strong>of</strong> 5,2 Gtoe (in 

exergy replacement cost terms). This corresponds to 154 times <strong>the</strong> 2006 primary 

energy consumption <strong>of</strong> that country. Moreover, each year Australia is degrading on 

average by <strong>the</strong> extraction <strong>of</strong> metals <strong>the</strong> equivalent <strong>of</strong> 1,6 times its primary oil consumption. 

Adding <strong>the</strong> exergy loss <strong>of</strong> fossil fuels, <strong>the</strong> global degradation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> 

reserves in Australia increase to 12,5 Gtoe. And this degradation is dominated 

by <strong>the</strong> extraction <strong>of</strong> two commodities, coal and iron. In 2004, <strong>the</strong> global exergy 

degradation velocity exceeded 550 Mtoe/year (around 15% <strong>of</strong> current world’s oil 

consumption). And it will probably continue to increase exponentially at least for 

20 to 40 years, until <strong>the</strong> peaks <strong>of</strong> iron and coal are reached. 

A very practical representation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves available and <strong>the</strong> possible 

extraction behavior <strong>of</strong> <strong>the</strong> commodities is through <strong>the</strong> “<strong>Exergy</strong> countdown” graphs. 

In <strong>the</strong> latter, <strong>the</strong> different Hubbert peak models in terms <strong>of</strong> irreversible exergy are 

shown in a single diagram. This has allowed us to compare <strong>the</strong> past, present and 

possible future extraction rates and available reserves <strong>of</strong> fuel and non-fuel <strong>mineral</strong>s 

in Australia. With <strong>the</strong> exergy countdown, we have predicted that in year 2050, 

about 64% <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> commodities produced in Australia will be depleted. 

Moreover, except for coal, iron and nickel, more than 85% <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves 

will be exhausted by <strong>the</strong>n. 

The exergy analysis toge<strong>the</strong>r with <strong>the</strong> exergy countdown <strong>of</strong> <strong>mineral</strong>s could constitute 

a universal and transparent prediction tool for assessing <strong>the</strong> degradation degree <strong>of</strong> 

non-renewable resources, with dramatic consequences for <strong>the</strong> future management 

<strong>of</strong> <strong>the</strong> earth’s physical stock. 

We additionally estimated <strong>the</strong> monetary cost <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> reserve’s depletion 

suffered in Australia in year 2004. This was carried out, by <strong>the</strong> conversion <strong>of</strong> exergy 

costs into monetary costs through conventional energy prices. According to <strong>the</strong> results 

obtained, Australia would have lost an equivalent <strong>of</strong> 93,3 billions <strong>of</strong> $US <strong>of</strong> its 

<strong>mineral</strong> <strong>capital</strong>, due to resource extraction in 2004. This corresponds to 15,2% <strong>of</strong>


<strong>the</strong> 2004 Australian GDP. However, if 2006 and 2008 energy prices are considered, 

<strong>the</strong> same amount <strong>of</strong> physical stock extracted would correspond to 19 and 29% <strong>of</strong> 

2004 Australian GDP. This indicates that monetary costs might not be a very suitable 

indicator for assessing <strong>the</strong> <strong>mineral</strong> <strong>capital</strong>, as <strong>the</strong> volatility and arbitrariness <strong>of</strong> prices 

distorts <strong>the</strong> real physical value. Never<strong>the</strong>less, it provides an order <strong>of</strong> magnitude <strong>of</strong> 

<strong>the</strong> importance <strong>of</strong> <strong>the</strong> extraction <strong>of</strong> <strong>mineral</strong>s to <strong>the</strong> economy. 

It should be noted, that <strong>the</strong> results obtained are estimations and hence <strong>the</strong> numbers 

cannot be taken as final. More reserves could be found in <strong>the</strong> future, <strong>the</strong>reby 

increasing <strong>the</strong> years until depletion and <strong>the</strong> peak <strong>of</strong> production <strong>of</strong> <strong>the</strong> commodities. 

However, <strong>the</strong> huge amount <strong>of</strong> energy and its equivalent in money terms involved in 

<strong>the</strong> degradation <strong>of</strong> <strong>mineral</strong>s on earth, alerts us about <strong>the</strong> importance <strong>of</strong> conserving 

our resources.

Chapter 8 

The exergy <strong>evolution</strong> <strong>of</strong> planet 

earth 


The aim <strong>of</strong> this chapter is to analyze <strong>the</strong> depletion <strong>of</strong> <strong>the</strong> exergy reservoir <strong>of</strong> <strong>mineral</strong>s 

on earth, due to <strong>the</strong> human action. For that purpose, <strong>the</strong> <strong>mineral</strong> exergy degradation 

throughout <strong>the</strong> 20th century, will be studied. Fur<strong>the</strong>rmore, we will analyze <strong>the</strong> effect 

<strong>of</strong> <strong>the</strong> emission <strong>of</strong> greenhouse gases in <strong>the</strong> exergy loss <strong>of</strong> fossil fuels. Finally, with 

<strong>the</strong> help <strong>of</strong> scenarios, we will estimate <strong>the</strong> exergy depletion <strong>of</strong> <strong>mineral</strong> resources in 

<strong>the</strong> next century. 

8.2 The exergy loss <strong>of</strong> world’s <strong>mineral</strong> reserves in <strong>the</strong> 20th 

century 

As stated before, exergy is an accounting tool that allows us to assess resources <strong>of</strong> 

single or aggregated commodities <strong>of</strong> a region, country or even <strong>of</strong> <strong>the</strong> whole world. 

In chapter 7 we evaluated <strong>the</strong> exergy degradation <strong>of</strong> <strong>mineral</strong> <strong>capital</strong> <strong>of</strong> a country 

and our aim now is to extrapolate <strong>the</strong> assessment to <strong>the</strong> entire planet. 

This ambitious task is not free <strong>of</strong> difficulties. The first and most important problem 

that we have to face is <strong>the</strong> lack <strong>of</strong> current and historical data <strong>of</strong> many commodities. 

A few geological institutions, such as <strong>the</strong> USGS or BGS, compile world production 

data <strong>of</strong> <strong>the</strong> most important <strong>mineral</strong>s. But only <strong>the</strong> USGS provides estimations <strong>of</strong> 

non-fuel <strong>mineral</strong> reserves. Fur<strong>the</strong>rmore, with <strong>the</strong> exception <strong>of</strong> copper in <strong>the</strong> US, 

no ore grade trends <strong>of</strong> <strong>the</strong> commodities are compiled. The case <strong>of</strong> Australia is an 

exceptional example <strong>of</strong> a country with available historical ore grades <strong>of</strong> <strong>the</strong> main 

metals produced. And this was thanks to <strong>the</strong> own initiative <strong>of</strong> Mudd [232], [234]. 

281

282 THE EXERGY EVOLUTION OF PLANET EARTH 

To <strong>the</strong>se limitations, we have to add that unit exergy replacement costs are available 

for many important non-fuel <strong>mineral</strong> commodities, but not for all <strong>of</strong> <strong>the</strong>m. 

In order to overcome <strong>the</strong> difficulties mentioned before, we are obliged to make different 

assumptions at <strong>the</strong> expense <strong>of</strong> an important accuracy loss in <strong>the</strong> results. Firstly, 

we will assume that <strong>the</strong> ore grade <strong>of</strong> non-fuel <strong>mineral</strong> commodities remains constant 

and equal to <strong>the</strong> average ore grades estimated in this PhD (table 4.10). This implies 

that <strong>the</strong> specific concentration exergy will not change over time. Consequently, <strong>the</strong> 

calculation <strong>of</strong> tons <strong>of</strong> <strong>mineral</strong> equivalent has no practical sense anymore. Moreover, 

<strong>the</strong> application <strong>of</strong> <strong>the</strong> Hubbert peak model in terms <strong>of</strong> exergy will ignore <strong>the</strong> concentration 

factor, which is quite significant in many non-fuel <strong>mineral</strong>s. As it happened to 

<strong>the</strong> previous case studies, unit exergy replacement costs are assumed to be constant. 

In reality, unit costs are a function <strong>of</strong> <strong>the</strong> state <strong>of</strong> technology and hence vary with 

time. 

With <strong>the</strong> latter assumptions, we can make a rough estimate <strong>of</strong> <strong>the</strong> following variables 

for fuel and non fuel <strong>mineral</strong>s: 

• The <strong>mineral</strong> exergy degradation on earth since <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> 20th century 

(D), 

• <strong>the</strong> earth’s exergy degradation velocity due to <strong>mineral</strong> extraction (˙D), 

• <strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> reserves and reserve base (% R. loss and % R.B. 

loss), 

• <strong>the</strong> years until depletion <strong>of</strong> <strong>the</strong> commodities (R/P), and 

• <strong>the</strong> year where <strong>the</strong> peak <strong>of</strong> production is reached (Year <strong>of</strong> <strong>the</strong> peak) 

8.2.1 Non-fuel <strong>mineral</strong>s 

With <strong>the</strong> help <strong>of</strong> <strong>the</strong> historical data compiled by <strong>the</strong> USGS [361], and <strong>the</strong> same 

calculation procedures applied for US copper and <strong>the</strong> main metals in Australia, we 

have calculated <strong>the</strong> exergy distances D and D ∗ and <strong>the</strong> average exergy degradation 

velocities ˙D and ˙D ∗ <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong> commodities throughout <strong>the</strong> 20th 

century 1 . Since production rates usually increase exponentially, it is interesting to 

analyze <strong>the</strong> latest exergy degradation velocities registered. Therefore, we have additionally 

calculated <strong>the</strong> average degradation velocities <strong>of</strong> <strong>the</strong> last decade (from 2000 

to 2006). The depletion degree <strong>of</strong> <strong>the</strong> commodities (% R and % R.B.) has been 

obtained as <strong>the</strong> ratio between <strong>the</strong> exergy distance D, and <strong>the</strong> total reserves <strong>of</strong> <strong>the</strong> 

commodity. The latter are obtained as <strong>the</strong> published reserves or reserve base <strong>of</strong> <strong>the</strong> 

commodity in 2006, plus <strong>the</strong> exergy distance D from 1900 to 2006. Finally, <strong>the</strong> R/P 

ratio applied to exergy is provided, as a measure <strong>of</strong> <strong>the</strong> years until depletion. It has 

1 Some commodities have started to be extracted after <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> century.

The exergy loss <strong>of</strong> world’s <strong>mineral</strong> reserves in <strong>the</strong> 20th century 283 

been assumed that production remains as in year 2006, and that reserves do not 

increase after that year. 

The <strong>mineral</strong> <strong>of</strong> uranium has been included in <strong>the</strong> non-fuel <strong>mineral</strong> classification 2 . 

For that purpose, <strong>the</strong> world uranium statistics published by <strong>the</strong> World Nuclear Association 

[408] have been used (see table A.25). Current uranium assured reserves 

were estimated by <strong>the</strong> OECD [248] as 3,804 Mtons, while <strong>the</strong> inferred reserves, as 

4,742 Mtons. The average ore grade <strong>of</strong> U 3O 8 is 0,33%, as calculated in this study 

(table 4.9), or 0,28% <strong>of</strong> U). 

Table 8.1 shows a summary <strong>of</strong> <strong>the</strong> results obtained for <strong>the</strong> 51 <strong>mineral</strong> commodities 

taken into account. 

As can be seen from <strong>the</strong> table and in figure 8.1, in reversible exergy terms, <strong>the</strong> 

exergy degradation <strong>of</strong> <strong>the</strong> non-fuel <strong>mineral</strong> <strong>capital</strong> on earth is clearly dominated by 

<strong>the</strong> extraction <strong>of</strong> two commodities: iron and aluminium, representing around 81 and 

10% <strong>of</strong> <strong>the</strong> total exergy consumption. The exergy distance due to non-fuel <strong>mineral</strong> 

extraction between 1900 and 2006 is at least 3 5,68 Gtoe. As expected, <strong>the</strong> general 

consumption pattern has followed an exponential-like behavior 4 . This is reflected 

in <strong>the</strong> drastic change <strong>of</strong> <strong>the</strong> exergy degradation velocity ˙D, passing from around 10 

Mtoe/year in 1910, to 180 Mtoe/year in 2006. 

In irreversible terms, i.e. analyzing <strong>the</strong> exergy replacement costs (actual exergy) <strong>of</strong> 

<strong>the</strong> commodities, we observe in fig. 8.2, that copper acquires a more important role. 

Copper is responsible for 6% <strong>of</strong> <strong>the</strong> total exergy degradation costs on earth, while 

iron and aluminium, 63 and 24%, respectively. The irreversible exergy distance D ∗ 

<strong>of</strong> all analyzed commodities is at least 51 Gtoe. This means that with current technology, 

we would require a minimum <strong>of</strong> a third <strong>of</strong> all current fuel oil reserves on earth 

(178 Gtoe [35]) for <strong>the</strong> replacement <strong>of</strong> all depleted non-fuel <strong>mineral</strong> commodities. 

Excluding iron and aluminium, which eclipse <strong>the</strong> rest commodities, we observe in 

fig. 8.3 that in decreasing order, <strong>the</strong> production <strong>of</strong> manganese, zinc, nickel, zirconium, 

lead, chromium, uranium, tin and gold contribute also significantly to <strong>the</strong> 

planet’s non-fuel <strong>mineral</strong> <strong>capital</strong> degradation. Again, an exponential behavior <strong>of</strong> <strong>the</strong> 

exergy costs <strong>of</strong> all commodities is observed. The average exergy cost degradation 

velocity D ∗ in <strong>the</strong> 20th century is at least 0,5 Gtoe/year. However in <strong>the</strong> last decade, 

this velocity increased to 1,3 Gtoe/year. 

2The nuclear exergy <strong>of</strong> uranium, which is huge compared to its chemical exergy (see chapter 4), 

has not been taken into account. 

3This value corresponds only to <strong>the</strong> 51 <strong>mineral</strong> commodities taken into account. 

4With <strong>the</strong> exception <strong>of</strong> uranium, whose production depends on o<strong>the</strong>r external factors, such as 

political decisions.


Table 8.1: The exergy loss <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> commodities in <strong>the</strong> world. 

Values are expressed in ktoe 

1900-2006 1996-2006 2006 

Mineral D D∗ ˙D ˙D ∗ ˙D ˙D ∗ % R loss % R. B. R/P, yrs R.B./P, 

loss 

yrs 

Aluminium 5,64E+05 1,22E+07 5,27E+03 1,14E+05 1,85E+04 4,01E+05 14,9 12,0 135 173 

Antimony 5,13E+02 5,71E+03 4,80E+00 5,34E+01 1,18E+01 1,31E+02 72,8 56,6 16 32 

Arsenic 5,75E+02 7,23E+03 5,37E+00 6,76E+01 6,91E+00 8,70E+01 74,6 66,2 20 30 

Barite 1,53E+03 N.A. 1,43E+01 N.A. 3,47E+01 N.A. 61,0 25,2 24 111 

Beryllium 6,88E-01 3,60E+01 6,43E-03 3,37E-01 7,97E-03 4,17E-01 N.A. N.A. N.A. N.A. 

Bismuth 7,61E+00 1,24E+02 7,12E-02 1,16E+00 1,54E-01 2,50E+00 41,1 24,7 56 119 

Boron oxide 4,04E+03 N.A. 3,78E+01 N.A. 1,69E+02 N.A. 39,2 21,1 40 96 

Bromine 2,41E+02 N.A. 2,26E+00 N.A. 7,96E+00 N.A. N.A. N.A. N.A. N.A. 

Cadmium 6,51E+01 3,54E+03 6,08E-01 3,31E+01 1,28E+00 6,98E+01 66,8 45,1 25 62 

Cesium 6,62E-02 N.A. 6,18E-04 N.A. N.A. N.A. 1,2 0,8 N.A. N.A. 

Chromium 4,53E+04 1,03E+05 4,23E+02 9,62E+02 1,32E+03 3,00E+03 N.A. N.A. N.A. N.A. 

Cobalt 2,20E+02 1,10E+04 2,05E+00 1,03E+02 5,70E+00 2,86E+02 19,5 11,5 104 193 

Copper 2,96E+04 3,07E+06 2,76E+02 2,87E+04 7,94E+02 8,24E+04 50,3 34,5 32 62 

Feldspar 8,77E+02 N.A. 8,20E+00 N.A. 3,51E+01 N.A. N.A. N.A. N.A. N.A. 

Fluorspar 9,95E+03 N.A. 9,30E+01 N.A. 2,03E+02 N.A. 48,6 32,1 45 90 

Gallium 2,75E-01 N.A. 2,57E-03 N.A. 1,31E-02 N.A. N.A. N.A. N.A. N.A. 

Germanium 6,52E-01 N.A. 6,09E-03 N.A. 1,24E-02 N.A. N.A. N.A. N.A. N.A. 

Gold 9,98E-01 8,17E+04 9,33E-03 7,64E+02 1,93E-02 1,58E+03 75,4 58,9 17 37 

Graphite 3,26E+04 N.A. 3,05E+02 N.A. 7,13E+02 N.A. 31,0 15,5 83 204 

Gypsum 1,40E+04 N.A. 1,30E+02 N.A. 3,51E+02 N.A. N.A. N.A. N.A. N.A. 

Helium 1,32E+02 N.A. 1,23E+00 N.A. 4,11E+00 N.A. N.A. N.A. N.A. N.A. 

Indium 5,45E-01 N.A. 5,10E-03 N.A. 3,35E-02 N.A. 34,3 26,4 19 28 

Iodine 1,12E+01 N.A. 1,05E-01 N.A. 3,86E-01 N.A. 3,8 2,2 600 1080 

Iron 4,60E+06 3,22E+07 4,30E+04 3,01E+05 1,04E+05 7,26E+05 27,7 14,9 84 185 

Lead 6,01E+03 2,35E+05 5,62E+01 2,19E+03 8,99E+01 3,51E+03 72,5 55,1 23 49 

Lithium 9,32E+03 3,49E+04 8,71E+01 3,26E+02 3,26E+02 1,22E+03 62,3 38,1 12 33 

Magnesium 1,01E+04 1,01E+04 9,45E+01 9,45E+01 2,96E+02 2,96E+02 N.A. N.A. N.A. N.A. 



Table 8.1: The exergy loss <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> commodities in <strong>the</strong> world. 

Values are expressed in ktoe.– continued from previous page. 

1900-2006 1996-2006 2006 

Mineral D D∗ ˙D ˙D ∗ ˙D ˙D ∗ % R loss % R. B. R/P, yrs R.B./P, 

loss 

yrs 

Manganese 1,08E+05 1,04E+06 1,01E+03 9,75E+03 1,82E+03 1,76E+04 51,9 8,7 39 437 

Mercury 9,24E+00 3,16E+03 8,63E-02 2,95E+01 2,75E-02 9,40E+00 92,2 69,4 31 162 

Molybdenum 9,58E+02 1,80E+04 8,95E+00 1,68E+02 2,62E+01 4,92E+02 37,5 21,4 47 103 

Nickel 4,48E+03 3,55E+05 4,18E+01 3,32E+03 1,31E+02 1,04E+04 40,0 22,9 42 95 

Niobium 1,57E+02 N.A. 1,46E+00 N.A. 6,90E+00 N.A. 19,8 18,1 61 67 

Phosphate rock 5,47E+04 7,08E+04 5,12E+02 6,62E+02 1,19E+03 1,54E+03 26,1 11,3 127 352 

PGM 2,41E-01 N.A. 2,25E-03 N.A. 8,35E-03 N.A. 14,4 13,0 137 154 

Potash 1,30E+05 2,02E+05 1,22E+03 1,89E+03 2,94E+03 4,56E+03 12,8 6,3 285 619 

REE 6,65E+01 N.A. 6,22E-01 N.A. 2,85E+00 N.A. 2,4 1,4 715 1220 

Rhenium 6,10E-02 7,43E+00 5,70E-04 6,95E-02 2,71E-03 3,30E-01 24,2 7,4 53 212 

Selenium 8,72E+00 N.A. 8,15E-02 N.A. 1,77E-01 N.A. 48,2 31,0 53 110 

Silver 1,76E+01 1,69E+04 1,65E-01 1,58E+02 3,24E-01 3,11E+02 78,5 63,4 13 28 

Strontium 1,83E+03 N.A. 1,71E+01 N.A. 8,52E+01 N.A. 56,0 41,9 12 21 

Tantalum 4,71E+00 1,31E+03 4,41E-02 1,22E+01 2,30E-01 6,38E+01 14,2 10,7 94 130 

Tellurium 4,65E-01 N.A. 4,35E-03 N.A. 7,03E-03 N.A. 25,8 13,5 159 356 

Thorium 1,58E+00 N.A. 1,47E-02 N.A. N.A. N.A. 1,2 1,0 N.A. N.A. 

Tin 2,11E+03 1,08E+05 1,97E+01 1,01E+03 2,92E+01 1,51E+03 75,2 62,7 20 36 

Uranium 2,47E+02 7,29E+04 2,31E+00 6,81E+02 4,68E+00 1,38E+03 34,8 29,9 96 120 

Vanadium 4,40E+02 4,96E+03 4,11E+00 4,64E+01 1,56E+01 1,76E+02 8,9 3,2 231 675 

Wolfram 3,01E+02 2,28E+04 2,81E+00 2,13E+02 6,02E+00 4,56E+02 48,5 30,2 32 69 

Zinc 4,98E+04 9,09E+05 4,65E+02 8,49E+03 1,13E+03 2,06E+04 68,1 44,4 18 48 

Zirconium 3,03E+02 2,91E+05 2,83E+00 2,72E+03 8,52E+00 8,18E+03 43,8 29,2 32 61 

SUM 5,68E+06 5,11E+07 5,31E+04 4,78E+05 1,34E+05 1,29E+06 25,6 14,2 92 191 



200000 

180000 

160000 

140000 

120000 

100000 

80000 

60000 

40000 

20000 

0 

1900 

1904 

B T, ktoe 

1908 

1912 

1916 

1920 

1924 

1928 

1932 

1936 

1940 

1944 

1948 

1952 

1956 

1960 

1964 

1968 

1972 

1976 

1980 

1984 

1988 


Aluminium 

1992 

1996 

2000 

2004 

Uranium 


Zinc 

Wolfram 

Vanadium 

Tin 

Thorium 

Tellurium 

Tantalum 

Strontium 

Silver 

Selenium 

Rhenium 

REE 

Potash 

PGM 

Phosphate rock 

Niobium 

Nickel 

Molybdenum 

Mercury 

Manganese 

Magnesium 

Lithium 

Lead 


Iodine 

Indium 

Helium 

Gypsum 

Graphite 

Gold 

Germanium 

Gallium 

Fluorspar 

Feldspar 

Copper 

Cobalt 

Chromium 

Cesium 

Cadmium 

Bromine 

Boron oxide 

Bismuth 

Beryllium 

Barite 

Arsenic 

Antimony 

Aluminium 

Figure 8.1. The exergy loss <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong> commodities on earth in 

<strong>the</strong> twentieth century 

According to <strong>the</strong> depletion ratios (% R loss and % R.B. loss) in table 8.1, man has 

depleted in just one century around 26% <strong>of</strong> its world non-fuel <strong>mineral</strong> reserves, and 

around 14% <strong>of</strong> its reserve base. The estimated years until depletion <strong>of</strong> <strong>the</strong> total 

reserves and reserve base are around 92 and 191 years, respectively. It must be 

pointed out that <strong>the</strong>se are only minimum numbers, as it has been assumed that no 

more deposits are going to be found. However, as we observed before, extraction 

follows an exponential behavior, what may lead that <strong>the</strong> finding <strong>of</strong> new deposits 

does not compensate <strong>the</strong> increasing production rates. 

According to fig. 8.4, <strong>the</strong> most depleted commodities are in decreasing order: mercury, 

with 92% <strong>of</strong> <strong>the</strong> reserves extracted, silver (79%), gold (75%), tin (75%), arsenic 

(75%), antimony (72%) and lead (72%). On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> <strong>mineral</strong>s 

<strong>of</strong> cesium, thorium, REE, iodine vanadium, PGM’s, tantalum, aluminium cobalt and 

niobium are <strong>the</strong> least depleted commodities, having extracted less than 20% <strong>of</strong> <strong>the</strong>ir 

respective world resources. The depletion degree <strong>of</strong> <strong>mineral</strong>s depend on two factors: 

<strong>the</strong> abundance <strong>of</strong> <strong>the</strong> considered <strong>mineral</strong> reserve, and its production rates. Usually, 

<strong>the</strong> least depleted <strong>mineral</strong>s coincide with those substances, for which no important 

usefulness has been found until to date. Never<strong>the</strong>less, it can also be due to <strong>the</strong> 

important abundance <strong>of</strong> <strong>the</strong> resource. That is <strong>the</strong> case for iodine, aluminium or iron.


1800000 

1600000 

1400000 

1200000 

1000000 

800000 

600000 

400000 

200000 

0 

B* T , ktoe 

1900 

1904 

Manganese 

1908 

1912 

1916 

1920 

1924 

1928 

1932 

1936 

1940 

1944 

1948 

1952 

1956 

1960 

1964 

1968 

1972 

1976 

1980 


Copper 

Aluminium 

1984 

1988 

1992 

1996 

2000 

2004 

Uranium 


Zinc 

Wolfram 

Vanadium 

Tin 

Thorium 

Tellurium 

Tantalum 


Silver 

Selenium 

Rhenium 

REE 

Potash 

PGM 


Niobium 

Nickel 

Molybdenum 

Mercury 

Manganese 

Magnesium 

Lithium 

Lead 


Iodine 

Indium 

Helium 

Gypsum 

Graphite 

Gold 

Germanium 

Gallium 

Fluorspar 

Feldspar 

Copper 

Cobalt 

Chromium 

Cesium 

Cadmium 

Bromine 


Bismuth 

Beryllium 

Barite 

Arsenic 


Aluminium 

Figure 8.2. The actual exergy loss <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong> commodities on 

earth in <strong>the</strong> twentieth century 

Despite <strong>of</strong> <strong>the</strong> intensive extraction <strong>of</strong> iron and aluminium throughout <strong>the</strong> 20th century, 

<strong>the</strong>ir respective abundances have avoided scarcity problems. Their reserve’s 

depletion rates are around 28 and 15%, respectively. Unfortunately that is not <strong>the</strong> 

case for copper, which has been and is still being massively extracted. More than 

50% <strong>of</strong> <strong>the</strong> world’s copper reserves have been already depleted. 

For <strong>the</strong> latter three <strong>mineral</strong>s we have applied <strong>the</strong> Hubbert peak model, considering 

<strong>the</strong>ir respective reserve base in year 19005 . Since unit exergy replacement costs 

are assumed to be constant over time, plotting production versus time in minimum 

exergy or in exergy replacement cost terms will not affect <strong>the</strong> final result. In this 

case, <strong>the</strong> exergy replacement costs (B∗ t ) versus time and not <strong>the</strong> minimum exergies 

(Bt) versus time have been plotted, because <strong>the</strong> production patterns obtained will 

be later used for estimating exergy degradation costs <strong>of</strong> <strong>the</strong> reserves in <strong>the</strong> future. 

Accordingly, it has been obtained that <strong>the</strong> peak <strong>of</strong> production <strong>of</strong> iron will be reached 

in year 2068, <strong>of</strong> aluminium in 2057 and <strong>of</strong> copper in 2024 (see figs. 8.5, 8.6, and 

8.7). It must be remembered, that <strong>the</strong> concentration factor has not been accounted 

for. 

5 The reserve base in year 1900 is calculated as <strong>the</strong> reserve base in year 2006 plus <strong>the</strong> exergy 

distance in <strong>the</strong> period between 1900 and 2006.


200000 

180000 

160000 

140000 

120000 

100000 

80000 

60000 

40000 

20000 

0 

1900 

1904 

B* T, ktoe 

Uranium 

Nickel 

1908 

1912 

1916 

1920 

1924 

1928 

1932 

1936 

1940 

1944 

1948 

1952 

1956 

1960 

1964 

1968 

1972 

1976 

Zinc 

Manganese 


Tin 

Lead 

Copper 

Gold 

Chromium 

1980 

1984 

1988 

1992 

1996 

2000 

2004 

Uranium 


Zinc 

Tin 

Silver 

Nickel 

Mercury 

Manganese 

Magnesium 

Figure 8.3. The actual exergy loss <strong>of</strong> <strong>the</strong> main 15 non-fuel <strong>mineral</strong> commodities on 

earth in <strong>the</strong> twentieth century, excluding iron and aluminium 

100 

90 

80 

70 

60 

50 

40 

30 

Arsenic 


20 

Aluminium 

10 

0 

% 

Barite 

Cadmium 

Bismuth 


Cobalt 

Cesium 

Gold 

Copper 

Fluorspar 

Indium 

Graphite 

Iodine 


Lead 

Lithium 

Mercury 

Manganese 

Nickel 

Molybdenum 


Rhenium 

Niobium 

PGM 

Potash 

REE 

Silver 

Selenium 


Tellurium 

Tantalum 

Tin 

Thorium 

Uranium 

Lead 

Gypsum 

Graphite 

Gold 

Vanadium 

Gallium 

Copper 

Chromium 

Zinc 

Wolfram 


Figure 8.4. Depletion degree in % <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong> commodity reserves


The results obtained should not be taken as definitive. They should be ra<strong>the</strong>r considered 

as an approximation <strong>of</strong> <strong>the</strong> state <strong>of</strong> non-fuel <strong>mineral</strong> reserves on earth. In 

addition to <strong>the</strong> assumptions made, we should not forget that <strong>the</strong>re are still many 

places in <strong>the</strong> world that remain unexplored. Never<strong>the</strong>less, and despite that <strong>the</strong> numbers 

are only approximations, <strong>the</strong> results are pointing out that <strong>the</strong> rate <strong>of</strong> <strong>mineral</strong> 

extraction in just one century has been excessive, when compared to past periods 

<strong>of</strong> time. Moreover, many commodities are already suffering scarcity problems. In a 

not very distant future, man will have to search for material alternatives <strong>of</strong> <strong>the</strong> most 

depleted commodities. This has already occurred for some applications, for example 

<strong>the</strong> shift away from copper to aluminium for conductors in wires and cables. But 

substitution will be only possible, whenever o<strong>the</strong>r <strong>mineral</strong> resources are available. 

Bt* 

Integral Bt* 

x 10 

15 

5 

10 

5 

0 

x 108 

2.5 

2 

1.5 

1 

0.5 

2068 

0 

1900 1950 2000 2050 2100 2150 2200 2250 

Figure 8.5. The Hubbert peak applied to world iron production. Data in ktoe


Bt 

Integral Bt 

x 105 

10 

8 

6 

4 

2 

0 

x 107 

12 

10 

8 

6 

4 

2 

2057 

0 

1900 1950 2000 2050 2100 2150 2200 

Figure 8.6. The Hubbert peak applied to world aluminium production. Data in ktoe 

Bt 

Integral Bt 

x 104 

10 

8 

6 

4 

2 

0 

x 106 

10 

8 

6 

4 

2 

2024 

0 

1900 1950 2000 2050 2100 2150 

Figure 8.7. The Hubbert peak applied to world copper production. Data in ktoe


8.2.2 Fuel <strong>mineral</strong>s 

The degradation <strong>of</strong> fuel <strong>mineral</strong>s throughout history, requires historical production 

data <strong>of</strong> coal, oil and natural gas. Historical statistics <strong>of</strong> world fuel <strong>mineral</strong>s had to 

be reconstructed from different information sources, being <strong>the</strong> most important ones 

those from <strong>the</strong> British Geological Survey and its preceding organizations. Tables 

A.26, A.27 and A.28 in <strong>the</strong> appendix show world production data <strong>of</strong> coal, oil and 

natural gas, between years 1900 and 2006. 

The exergy <strong>of</strong> <strong>the</strong> three types <strong>of</strong> fuel <strong>mineral</strong>s has been obtained in <strong>the</strong> same way as 

for <strong>the</strong> case <strong>of</strong> Australia, and assuming a single type <strong>of</strong> coal and oil 6 , with <strong>the</strong> average 

properties calculated by Valero and Arauzo [366]. This way, <strong>the</strong> exergy <strong>of</strong> average 

coal and oil on earth are assumed to be 22.692 and 45.664 kJ/kg, respectively. 

Table 8.2 summarizes <strong>the</strong> results obtained for world fuels throughout <strong>the</strong> 20th century. 

Table 8.2. The exergy loss <strong>of</strong> coal, oil and natural gas in <strong>the</strong> 20th century. 

1900-2006 1996-2006 2006 

Mineral D, Mtoe ˙D, Mtoe/yr ˙D, M toe/yr % R. loss R/P, yrs Year <strong>of</strong> <strong>the</strong> 

Peak 

Coal 1,45E+05 1,37E+03 2,73E+03 27,9 156 2060 

Oil 1,61E+05 1,50E+03 3,96E+03 47,5 42 2008 

Natural gas 7,60E+04 1,74E+03 2,34E+03 30,9 63 2023 

SUM 3,82E+05 4,61E+03 9,03E+03 30,5 114 2029 

Figure 8.8 shows <strong>the</strong> exergy loss <strong>of</strong> coal, oil and natural gas deposits in <strong>the</strong> last 

century. Although <strong>the</strong> most extracted fuel in <strong>the</strong> world is coal, as revealed by <strong>the</strong> 

historical statistics included in tables A.26, A.27 and A.28, in exergy terms, <strong>the</strong> most 

consumed fuel has been oil. Oil has accounted for 42% <strong>of</strong> <strong>the</strong> total fuel exergy degradation 

in <strong>the</strong> 20th century, while coal and natural gas for 38 and 20%, respectively. 

The exergy distance between 1900 and 2006 (D), i.e. <strong>the</strong> total fuel’s exergy depleted 

has been 382 Gtoe, corresponding to 30,5% <strong>of</strong> total world’s proven fuel reserves in 

2006. 

The exergy <strong>of</strong> fuels was consumed at an average exergy degradation velocity (˙D) 

<strong>of</strong> 4,6 Gtoe/year. However in <strong>the</strong> last decade, this velocity increased to around 9 

Gtoe/year. From <strong>the</strong> latter figure, coal contributes to 2,7, oil to 4,0 and natural gas 

to 2,3 Gtoe/year. 

If we add <strong>the</strong> exergy loss <strong>of</strong> fossil fuels, to <strong>the</strong> exergy replacement costs <strong>of</strong> non-fuel 

<strong>mineral</strong>s, we obtain that man has depleted in <strong>the</strong> 20th century a total <strong>of</strong> 433 Gtoe, 

which were consumed at an average velocity <strong>of</strong> around 4 Gtoe/year. However, <strong>the</strong> 

6 Natural gas was already assumed to have a single composition, with a standard exergy <strong>of</strong> 39.394 

kJ/N m 3 (see section 6.4.1.3).


12000000 12000 

10000000 10000 

8000000 8000 

6000000 6000 

4000000 4000 

2000000 2000 

0 

B* t , Mtoe 

1900 

1904 

Copper 

1908 

1912 

1916 

1920 

1924 

1928 

1932 

1936 

1940 

1944 

1948 

1952 

1956 

1960 

1964 

1968 

1972 

1976 

1980 

1984 

N. Gas 

Oil 

Coal 

1988 

1992 

1996 

2000 

Figure 8.8. Actual exergy consumption <strong>of</strong> <strong>the</strong> world’s fuel and non-fuel <strong>mineral</strong>s 

throughout <strong>the</strong> 20th century 

2006 <strong>mineral</strong>’s exergy degradation velocity increased to around 12 Gtoe. Most part 

<strong>of</strong> this exergy degradation (82%) was due to <strong>the</strong> combustion <strong>of</strong> fossil fuels. The extraction 

<strong>of</strong> iron was responsible for 7,4% <strong>of</strong> <strong>the</strong> total exergy destruction, aluminium 

for 2,8%, copper for 0,7% and <strong>the</strong> remaining <strong>mineral</strong>s for 0,8% (see fig. 8.8). 

Without exception, production <strong>of</strong> all fossil fuels have followed an exponential-like 

behavior, what allows a satisfactorily application <strong>of</strong> <strong>the</strong> Hubbert’s bell-shaped curve. 

Among all conventional fossil fuels, coal is <strong>the</strong> least depleted commodity (27,9%), 

because <strong>of</strong> its large reserves worldwide. Assuming that no more coal reserves will 

be found, and that <strong>the</strong> production rate remains as in 2006, <strong>the</strong> R/P ratio indicates 

that <strong>the</strong>re will be enough resource for 156 years. The Hubbert peak model applied 

to <strong>the</strong> exergy consumption <strong>of</strong> coal (fig. 8.9), reveals that <strong>the</strong> peak will be reached in 

year 2060 7 . Our study contradicts <strong>the</strong> recent estimate by <strong>the</strong> Energy Watch Group 

(EWG), which reports that global coal production could peak in 2025 [89]. 

The reserves <strong>of</strong> natural gas are significantly more depleted than coal. In <strong>the</strong> period 

between 1900 and 2006, natural gas consumption has leaded to <strong>the</strong> depletion <strong>of</strong> 

30,9% <strong>of</strong> its exergy reserves. Its R/P ratio for 2006, reveals that <strong>the</strong>re is enough 

natural gas for 63 years. The peak <strong>of</strong> world’s natural gas production will be reached 

in year 2023, according to <strong>the</strong> Hubbert peak model applied and represented in fig. 

7 It has been assumed that <strong>the</strong> quantity <strong>of</strong> coal extracted in <strong>the</strong> period between 1800 and 1900 

followed <strong>the</strong> same exponential behavior detected by <strong>the</strong> rest <strong>of</strong> <strong>the</strong> points. Hence, it has been assumed 

that <strong>the</strong> total reserves in 1800 were 675 Gtoe. 


Aluminium 

2004


Bt 

4000 

3000 

2000 

1000 

Integral Bt 

0 

x 105 

8 

6 

4 

2 

2060 

0 

1800 1850 1900 1950 2000 2050 2100 2150 2200 2250 2300 

Figure 8.9. The Hubbert peak applied to world coal production. Data in Mtoe 

Bt 

Integral Bt 

3000 

2500 

2000 

1500 

1000 

500 

0 

x 105 

2.5 

2 

1.5 

1 

0.5 

2023 

0 

1900 1950 2000 2050 2100 2150 

Figure 8.10. The Hubbert peak applied to world natural gas production. Data in 

Mtoe 

8.10. Bentley estimated in year 2002 [24] that <strong>the</strong> global peak in conventional gas 

production was already in sight, in perhaps 20 years. Hence, Bentley’s estimation 

fits very well with <strong>the</strong> calculation carried out in this study. 

Beyond doubt, oil is <strong>the</strong> most depleted commodity, having extracted almost half <strong>of</strong> 

its resources (47,5%). The R/P ratio <strong>of</strong> oil indicates that <strong>the</strong>re is enough fuel for only


Bt 

Integral Bt 

5000 

4000 

3000 

2000 

1000 

0 

x 105 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

2008 

0 

1900 1950 2000 2050 2100 

Figure 8.11. The Hubbert peak applied to world oil production. Data in Mtoe 

42 years, before complete depletion occurs. Hubbert’s bell-shaped curve applied to 

world oil’s exergy (fig. 8.11) alerts that <strong>the</strong> peak is reached in year 2008. The latter 

value fits very well with <strong>the</strong> predictions <strong>of</strong> o<strong>the</strong>r authors, such as Hatfield [133], Kerr 

[183] or Campbell and Laherre [47], who estimated that <strong>the</strong> peak year <strong>of</strong> world oil 

will be between 2004 and 2008. In fact, Campbell and Laherre’s prediction in 1998 

that <strong>the</strong> world could see radical increases in oil prices ten years later, has turned out 

to be completely right. The price <strong>of</strong> a barrel <strong>of</strong> crude oil increased by a 100% in just 

one year, surpassing in January 2008, <strong>the</strong> psychological barrier <strong>of</strong> 100 $US. And <strong>the</strong> 

observed tendency is that it will probably reach 200 $US by <strong>the</strong> end <strong>of</strong> year 2008 or 

not much later. 

Since exergy is an additive property, we can apply Hubbert’s bell-shape curve to <strong>the</strong> 

sum <strong>of</strong> all three fuels. In fact, <strong>the</strong> depletion <strong>of</strong> one fossil fuel may lead to a greater 

consumption <strong>of</strong> <strong>the</strong> o<strong>the</strong>rs. This way, <strong>the</strong> fact that <strong>the</strong> peak <strong>of</strong> oil has been already 

reached, will probably lead in <strong>the</strong> short and mid-run, to <strong>the</strong> consumption <strong>of</strong> more 

natural gas and coal. Therefore, it is interesting to analyze all three fuels as a single 

entity, making <strong>the</strong> assumption that <strong>the</strong>y are mutually replaceable. If no more fuel 

resources are found, and if <strong>the</strong> production rate remains as in 2006, <strong>the</strong> R/P ratio 

indicates that in 114 years, all conventional fossil fuels will be completely depleted. 

Moreover, as revealed by fig. 8.12, <strong>the</strong> peak <strong>of</strong> production <strong>of</strong> all conventional fossil 

fuels would be reached in 2029. If this prediction is true, fuel prices will increase 

sharply 8 , putting at risk world economies. Hopefully o<strong>the</strong>r energy alternatives will 

be ready by <strong>the</strong>n and are able to supply <strong>the</strong> increasing world energy demand. 

8 As it is happening already with oil and natural gas.

The exergy loss <strong>of</strong> world’s fossil fuel reserves due to <strong>the</strong> greenhouse effect 295 

Bt 

12000 

10000 

Integral Bt 

8000 

6000 

4000 

2000 

0 

x 105 

15 

10 

5 

2029 

0 

1900 1950 2000 2050 2100 2150 

Figure 8.12. The Hubbert peak applied to <strong>the</strong> world’s conventional fossil fuel production. 

Data in Mtoe 

Similarly, <strong>the</strong> Hubbert peak model can be applied to <strong>the</strong> exergy cost <strong>of</strong> non-fuel 

<strong>mineral</strong>s plus <strong>the</strong> exergy <strong>of</strong> fossil fuels. Taking into account <strong>the</strong> global extraction 

<strong>of</strong> iron, aluminium, copper, coal, oil and natural gas, <strong>the</strong> peak <strong>of</strong> production would 

be reached in year 2034, as shown in fig. 8.13. The same figure presents also <strong>the</strong> 

derivative <strong>of</strong> <strong>the</strong> bell shape curve, i.e. <strong>the</strong> acceleration experienced in <strong>the</strong> production 

processes throughout history. Accordingly, we observe that <strong>mineral</strong> production has 

undergone acceleration until 1989. From that moment on, <strong>the</strong> velocity <strong>of</strong> extraction 

rises until 2034, but at increasingly slower rates. 

Figure 8.14 summarizes <strong>the</strong> results obtained in <strong>the</strong> previous sections, showing <strong>the</strong> 

exergy countdown <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s extracted on earth, <strong>of</strong> fuel and non-fuel 

nature. As it can be seen, coal, iron and aluminium are <strong>the</strong> commodities having <strong>the</strong> 

least scarcity problems. On <strong>the</strong> o<strong>the</strong>r end we find in decreasing order <strong>of</strong> scarcity 

degree, oil, natural gas and copper. These values assume that no more resources 

than <strong>the</strong> reserve base for non-fuel <strong>mineral</strong>s, and <strong>the</strong> proven reserves for fuels will 

be available in <strong>the</strong> future. Obviously <strong>the</strong> figures may change, as new discoveries are 

made. 

8.3 The exergy loss <strong>of</strong> world’s fossil fuel reserves due to 

<strong>the</strong> greenhouse effect 

The exergy <strong>of</strong> fossil fuel reserves may decrease ei<strong>the</strong>r through extraction and subsequent 

burning, or through an alteration <strong>of</strong> <strong>the</strong> reference environment. This section


Bt 

Derivative Bt 

15 

10 

5 

0 

0.2 

0.1 

0 

-0.1 

1989 

2034 

-0.2 

1900 1950 2000 2050 2100 2150 2200 

Figure 8.13. The Hubbert peak applied to <strong>the</strong> world’s main <strong>mineral</strong>s production. 

Data in Mtoe 

4500 

4000 

3500 

3000 

2500 

2000 

1500 

1000 

500 

Bt*, Mtoe 

Oil 

Natural gas 

Copper 

Coal 


Aluminium 

0 

1890 1940 1990 2040 2090 2140 2190 2240 2290 

Figure 8.14. The exergy countdown <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s extracted on earth


is devoted to analyze <strong>the</strong> exergy loss <strong>of</strong> fossil fuel reserves due to <strong>the</strong> increase <strong>of</strong> 

greenhouse gases in <strong>the</strong> atmosphere (mainly CO 2) and <strong>the</strong> subsequent temperature 

rise. 

A similar study was carried out for <strong>the</strong> first time in 1991 by Valero and Arauzo [366]. 

In <strong>the</strong>ir analysis, <strong>the</strong> exergy decrease <strong>of</strong> an “average fossil fuel” was determined, 

assuming that CO 2 concentration would double over <strong>the</strong> next hundred years. 

In this section, <strong>the</strong> information provided by <strong>the</strong> latter authors will be updated with 

recent GHG emission scenarios and <strong>the</strong> exergy loss <strong>of</strong> <strong>the</strong> reserves <strong>of</strong> coal, natural 

gas and oil will be studied separately. 

8.3.1 The carbon cycle and <strong>the</strong> greenhouse effect 

The carbon cycle is a well-known natural flux occurring on earth. The mass transfer 

<strong>of</strong> carbon takes place between <strong>the</strong> three spheres <strong>of</strong> our planet: hydrosphere, continental 

crust and atmosphere. According to Post [270], <strong>the</strong> annual natural flux <strong>of</strong> 

carbon in <strong>the</strong> form <strong>of</strong> CO 2 between terrestrial plus oceanic reservoirs and <strong>the</strong> atmosphere 

is about 200 Gt per year, from which 100-115 are exchanged between <strong>the</strong> 

ocean and atmosphere, and 100-120 between earth biomasses and <strong>the</strong> atmosphere 

(see Fig. 8.15). 

On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> anthropic annual flux <strong>of</strong> CO 2 from fossil fuel combustion 

and modification <strong>of</strong> terrestrial ecosystems is estimated at 7-8 Gt C/year [296], or 

only 3,5 to 4% <strong>of</strong> <strong>the</strong> natural flux. Never<strong>the</strong>less, <strong>the</strong> combined climate and biogeochemical 

systems that regulate <strong>the</strong> CO 2 content <strong>of</strong> <strong>the</strong> atmosphere cannot handle 

<strong>the</strong> anthropogenic perturbation without accumulating in <strong>the</strong> atmosphere in <strong>the</strong> near 

term about half <strong>of</strong> <strong>the</strong> CO 2 being released. 

According to <strong>the</strong> IPCC’s forth assessment report [162], annual fossil carbon dioxide 

emissions increased from an average <strong>of</strong> 6,4 GtC (23,5 GtCO 2) per year in <strong>the</strong> 

1990s to 7,2 GtC (26,4 GtCO 2) per year in 2000-2005. Accordingly, <strong>the</strong> annual 

carbon dioxide concentration growth rate in <strong>the</strong> atmosphere was larger during <strong>the</strong> 

years 1995-2005 (average: 1,9 ppm per year), than it has been since <strong>the</strong> beginning 

<strong>of</strong> continuous direct atmospheric measurements (1960-2005 average: 1,4 ppm per 

year). The record at Mauna Loa observatory shows that concentrations have increased 

from about 310 to <strong>the</strong> current 379 ppm since 1958. And preindustrial CO 2 

concentrations did not exceed 280 ppm. 

Eleven <strong>of</strong> <strong>the</strong> twelve years between 1995 and 2006 rank among <strong>the</strong> 12 warmest years 

in <strong>the</strong> instrumental record <strong>of</strong> global surface temperature (since 1850). The linear 

warming trend over <strong>the</strong> last 50 years (0,13 ◦ C per decade) is nearly twice <strong>of</strong> that for 

<strong>the</strong> last 100 years. The total temperature increase from 1850-1899 to 2001-2005 is 

0,76 ◦ C [162]. 

There is considerable scientific consensus that <strong>the</strong> rapid buildup <strong>of</strong> CO 2 is tightly related 

to <strong>the</strong> increase <strong>of</strong> atmospheric temperature, due to <strong>the</strong> well known greenhouse


Figure 8.15. Schematic presentation <strong>of</strong> <strong>the</strong> global carbon cycle as estimated by Post 

et al. [270] 

effect. O<strong>the</strong>r gases cause <strong>the</strong> same or even a more enhanced greenhouse effect on 

<strong>the</strong> atmosphere. The most important ones are methane CH 4 (released from agriculture, 

waste and energy) and nitrous oxides N 2O (from agriculture and industry), 

accounting for about 14 and 8% <strong>of</strong> <strong>the</strong> total greenhouse gas (GHG) emissions, respectively. 

The global warming impact <strong>of</strong> GHG gases is related to that <strong>of</strong> CO 2 and is 

measured in CO 2 − eq units. The global warming impact <strong>of</strong> CH 4 is 21 times <strong>of</strong> that 

<strong>of</strong> CO 2, while that <strong>of</strong> N 2O is 310 greater. 

According to <strong>the</strong> IPCC [162], atmospheric concentrations <strong>of</strong> CO 2 (379 ppm) and 

CH 4 (1774 ppb) in 2005 exceeded by far <strong>the</strong> natural range over <strong>the</strong> last 650.000 

years. Greenhouse gases are already having a major impact on <strong>the</strong> world climate 

and sea level; and within 40 to 80 years atmospheric greenhouse gases will more 

than double with alarming implications for world climate, agriculture, sea levels, 

national economics, etc. 

8.3.2 Scenarios 

There is a great variety <strong>of</strong> scenarios published about national and world energy 

consumptions. Two <strong>of</strong> <strong>the</strong> latest world scenarios are <strong>the</strong> ones carried out by <strong>the</strong>


World Energy Council in 2007 [44] and <strong>the</strong> International Energy Agency in 2006 

[152]. 

The WEC report, more focused on political actions, takes into account four scenarios, 

based on economic, population and policy aspects. The main conclusion <strong>of</strong> <strong>the</strong> study 

is that to meet <strong>the</strong> energy demand <strong>of</strong> all households worldwide, energy supplies must 

double by 2050. 

The IEA considers two different scenarios: <strong>the</strong> reference and <strong>the</strong> alternative policy 

scenario. In <strong>the</strong> latter one, governments take stronger action to steer <strong>the</strong> energy 

system onto a more sustainable path. Globally, fossil fuels will remain <strong>the</strong> dominant 

source <strong>of</strong> energy to 2030 in both scenarios. Primary energy demand in <strong>the</strong> reference 

scenario is projected to increase by just over one-half between now and 2030 and 

<strong>the</strong> associated carbon dioxide emissions increase by 55%. World primary energy 

demand in 2030 is about 10% lower in <strong>the</strong> alternative policy scenario than in <strong>the</strong> 

reference scenario, coming <strong>the</strong> biggest energy savings from coal. The carbon dioxide 

emissions are cut by 16% in 2030 relative to <strong>the</strong> reference scenario. 

The scenarios for GHG emissions most widely used are those <strong>of</strong> <strong>the</strong> IPCC published in 

2000 for use in <strong>the</strong> Third Assessment Report (Special Report on Emissions Scenarios 

- SRES - [160]). We will focus on <strong>the</strong> SRES scenarios, as <strong>the</strong>y were constructed to 

explore future developments in <strong>the</strong> global environment with special reference to <strong>the</strong> 

production <strong>of</strong> greenhouse gases and aerosol 9 precursor emissions. 

The SRES defined four scenarios A1, A2, B1 and B2, describing <strong>the</strong> relationships 

between <strong>the</strong> forces driving greenhouse gas and aerosol emissions and <strong>the</strong>ir <strong>evolution</strong> 

during <strong>the</strong> 21st century for large world regions and globally. Each scenario 

represents different demographic, social, economic, technological, and environmental 

developments that diverge in increasingly irreversible ways. The scenarios are 

summarized as follows: 

• A1 scenario family: a future world <strong>of</strong> very rapid economic growth, global 

population that peaks in mid-century and declines <strong>the</strong>reafter, and rapid introduction 

<strong>of</strong> new and more efficient technologies. 

• A2 scenario family: a very heterogeneous world with continuously increasing 

global population and regionally oriented economic growth that is more 

fragmented and slower than in o<strong>the</strong>r storylines. 

• B1 scenario family: a convergent world with <strong>the</strong> same global population as 

in <strong>the</strong> A1 storyline but with rapid changes in economic structures toward a 

service and information economy, with reductions in material intensity, and 

<strong>the</strong> introduction <strong>of</strong> clean and resource-efficient technologies. 

• B2 scenario family: a world in which <strong>the</strong> emphasis is on local solutions to economic, 

social, and environmental sustainability, with continuously increasing 

population (lower than A2) and intermediate economic development. 

9 Aerosol emissions cause <strong>the</strong> opposite effect <strong>of</strong> greenhouse gases.


Figure 8.16. Scenarios for GHG emissions from 2000 to 2100 and projections <strong>of</strong> 

surface temperatures [160] 

Table 8.3. Projected global averaged temperature change ( ◦ C at 2090-2099 relative 

to 1980-1999) at <strong>the</strong> end <strong>of</strong> <strong>the</strong> 21st century. After [160] 

Scenario Temperature change 

Constant year 2000 concentrations 

0,6 

B1 1,8 

A1T 2,4 

B2 2,4 

A1B 2,8 

A2 3,4 

A1FI 4,0 

Six groups <strong>of</strong> scenarios were drawn from <strong>the</strong> four families: one group each in <strong>the</strong> 

A2, B1 and B2 families, and three groups in <strong>the</strong> A1 family, characterizing alternative 

developments <strong>of</strong> energy technologies: A1FI (fossil intensive), A1T (predominantly 

non-fossil) and A1B (balanced across energy sources). 

The SRES scenarios project an increase <strong>of</strong> global GHG emissions by 25-90% (CO 2eq) 

between 2000 and 2030 (Fig. 8.16), with fossil fuels maintaining <strong>the</strong>ir dominant 

position in <strong>the</strong> global energy mix to 2030 and beyond. 

According to those scenarios, <strong>the</strong> projected global averaged surface warming is <strong>the</strong> 

one shown in table 8.3. 

In order to stabilize <strong>the</strong> concentration <strong>of</strong> GHGs in <strong>the</strong> atmosphere, emissions would 

need to peak and decline <strong>the</strong>reafter. Table 8.4 and figure 8.17 summarize <strong>the</strong> re-


Table 8.4. Characteristics <strong>of</strong> stabilization scenarios and resulting long-term equilibrium 

global average temperature rise above pre-industrial at equilibrium from 

<strong>the</strong>rmal expansion only. After [162] 

Category CO2 conc. CO2-eq conc. Peaking year Global aver. temp. 

for CO2 sionsemis- 

ppm ppm year ◦C I 350-400 445-490 2000-2015 2,0-4,0 

II 400-440 490-535 2000-2020 2,4-2,8 

III 440-485 535-590 2010-2030 2,8-3,2 

IV 485-570 590-710 2020-2060 3,2-4,0 

V 570-660 710-855 2050-2080 4,0-4,9 

VI 660-790 855-1130 2060-2090 4,9-6,1 

Figure 8.17. CO 2 emissions and equilibrium temperature increases for a range <strong>of</strong> 

stabilization levels [162] 

quired emission levels for different group <strong>of</strong> stabilization concentrations and <strong>the</strong> 

resulting equilibrium global warming, according to <strong>the</strong> IPCC [162]. 

Combining <strong>the</strong> scenarios <strong>of</strong> table 8.3 and <strong>the</strong> stabilization temperatures <strong>of</strong> table 8.4, 

we obtain <strong>the</strong> required variables to be introduced in <strong>the</strong> model <strong>of</strong> fossil fuels (table 

8.5). The more energy intensive scenario, with an intensive use <strong>of</strong> fossil fuels (A1FI) 

leads to <strong>the</strong> greatest CO 2 concentrations and temperature increase. On <strong>the</strong> contrary, 

scenario B1 is <strong>the</strong> most sustainable one in terms <strong>of</strong> CO 2 emissions. Scenarios B2 

and A1T throw out <strong>the</strong> same CO 2 concentrations and temperature increase, since 

<strong>the</strong> rapid economic growth assumed in A1T is mainly achieved through non-fossil 

fuel technologies. Scenario A1B, which assumes a balanced use <strong>of</strong> fossil and nonfossil 

fuel energies, comes right after <strong>the</strong> latter scenarios in terms <strong>of</strong> CO 2 emissions, 

followed by scenario A2.


Table 8.5. Temperature rise and CO 2 concentration in <strong>the</strong> SRES scenarios 

Scenario B1 A1T B2 A1B A2 A1FI 

∆T, ◦ C 1,8 2,4 2,4 2,8 3,4 4 

CO 2, ppm 350 400 400 440 620 710 

Table 8.6. Specific exergy (b in kJ/kg) and <strong>Exergy</strong> loss (%) <strong>of</strong> anthracite, bituminous, 

subbituminous, and lignite coal according to <strong>the</strong> different SRES scenarios 

Anthracite Bituminous Subbituminous Lignite 

Scenario b loss, b loss, b loss, b loss, 

% 

% 

% 

% 

0 31624,2 0,00 29047,1 0,00 24276,5 0,00 17351,1 0,00 

B1 31603,6 0,07 29028,7 0,06 24261,7 0,06 17340,2 0,06 

A1T 31582,7 0,13 29010,7 0,13 24246,5 0,12 17329,5 0,12 

B2 31582,7 0,13 29010,7 0,13 24246,5 0,12 17329,5 0,12 

A1B 31567,8 0,18 28997,8 0,17 24235,7 0,17 17321,9 0,17 

A2 31511,4 0,36 28949,7 0,34 24194,9 0,34 17293,3 0,33 

A1FI 31489,9 0,42 28931,0 0,40 24179,3 0,40 17282,3 0,40 

8.3.3 The fossil fuel exergy decrease 

With <strong>the</strong> help <strong>of</strong> <strong>the</strong> equations explained in section 5.3.3 and <strong>the</strong> fossil fuel’s reserves 

data provided in section 6.4.1, we are able to calculate <strong>the</strong> fossil fuel exergy decrease 

<strong>of</strong> <strong>the</strong> different scenarios <strong>of</strong> table 8.5, with respect to <strong>the</strong> current situation. For 

that purpose, <strong>the</strong> exergy difference will be calculated for <strong>the</strong> four types <strong>of</strong> average 

coal: anthracite, bituminous, sub-bituminous and lignite; for <strong>the</strong> three most common 

types <strong>of</strong> average oil: fuel-oil 1, fuel-oil 2 and fuel-oil 4; and for natural gas 10 . The 

composition <strong>of</strong> <strong>the</strong> R.E. chosen for <strong>the</strong> calculations is number III, which contains <strong>the</strong> 

following substances 11 : O 2, N 2, CO 2, H 2O, CaSO 4 · 2H 2O and CaCO 3. 

Tables 8.6 through 8.8 and Figs. 8.18 to 8.20 show <strong>the</strong> exergy loss <strong>of</strong> <strong>the</strong> different 

fuels, according to <strong>the</strong> SRES scenarios. Scenario “0” is <strong>the</strong> starting point, where <strong>the</strong> 

R.E.’s temperature is assumed to be 298,15 K and <strong>the</strong> CO 2 concentration, 300 ppm. 

As can be seen from <strong>the</strong> figures and tables, <strong>the</strong> exergy loss increases with temperature 

and CO 2 concentration. Therefore, <strong>the</strong> maximum exergy loss is achieved in 

<strong>the</strong> scenario A1FI (rapid economic and population growth, intensive in fossil fuels), 

with an exergy decrease <strong>of</strong> around 0,4%. This figure is very close to <strong>the</strong> one found 

by Valero and Arauzo [366], where <strong>the</strong> exergy loss fell by approximately 0,31 to 

0,38% if <strong>the</strong> CO 2 concentration would double. 

10 See section 6.4.1 for <strong>the</strong> properties <strong>of</strong> <strong>the</strong> different types <strong>of</strong> fuels. 

11 See section 5.3.3 for more details about <strong>the</strong> different R.E. proposed for fossil fuels.


<strong>Exergy</strong> loss, % 

0,45 

0,40 

0,35 

0,30 

0,25 

0,20 

0,15 

0,10 

0,05 

0,00 

300 360 420 480 540 600 660 720 

CO2, ppm 

Anthracite Bituminous Subbituminous Lignite 

Figure 8.18. <strong>Exergy</strong> loss <strong>of</strong> <strong>the</strong> different types <strong>of</strong> coal as a function <strong>of</strong> <strong>the</strong> CO 2 

concentration in <strong>the</strong> atmosphere 

Table 8.7. Specific exergy (b) and <strong>Exergy</strong> loss (%) <strong>of</strong> fuel-oil 1, fuel-oil 2 and fuel-oil 

4, according to <strong>the</strong> different SRES scenarios. 

Fuel-oil1 Fuel-oil 2 Fuel-oil 4 

Scenario T0 CO2, b, kJ/kg loss, b, kJ/kg loss, b, kJ/kg loss, 

ppm 

% 

% 

% 

0 298,15 300 46259,1 0,00 45517,4 0,00 44002,4 0,00 

B1 299,95 350 46229,9 0,06 45488,2 0,06 43973,9 0,06 

A1T 300,55 400 46205,2 0,12 45463,5 0,12 43949,6 0,12 

B2 300,55 400 46205,2 0,12 45463,5 0,12 43949,6 0,12 

A1B 300,95 440 46187,4 0,16 45446,0 0,16 43931,9 0,16 

A2 301,55 620 46124,6 0,29 45383,4 0,29 43869,5 0,30 

A1F1 302,15 710 46099,3 0,35 45358,1 0,35 43844,5 0,36



0,40 

0,35 

0,30 

0,25 

0,20 

0,15 

0,10 

0,05 

0,00 

300 360 420 480 540 600 660 720 

CO2, ppm 

Fuel-oil1 Fuel-oil 2 Fuel-oil 4 

Figure 8.19. <strong>Exergy</strong> loss <strong>of</strong> <strong>the</strong> different types <strong>of</strong> fuel-oils as a function <strong>of</strong> <strong>the</strong> CO 2 

concentration in <strong>the</strong> atmosphere 

Table 8.8. Specific exergy (b) and <strong>Exergy</strong> loss (%) <strong>of</strong> natural gas according to <strong>the</strong> 

different SRES scenarios. 

Natural gas 

Scenario T0 CO2, b, kJ/N m 

ppm 

3 loss, 

% 

0 298,15 300 39393,8 0,00 

B1 299,95 350 39355,7 0,10 

A1T 300,55 400 39333,0 0,15 

B2 300,55 400 39333,0 0,15 

A1B 300,95 440 39317,2 0,19 

A2 301,55 620 39269,3 0,32 

A1F1 302,15 710 39246,3 0,37



0,40 

0,35 

0,30 

0,25 

0,20 

0,15 

0,10 

0,05 

0,00 

300 360 420 480 540 600 660 720 

CO2, ppm 

Figure 8.20. <strong>Exergy</strong> loss <strong>of</strong> natural gas as a function <strong>of</strong> <strong>the</strong> CO 2 concentration in <strong>the</strong> 

atmosphere 

Among all fuels, <strong>the</strong> different types <strong>of</strong> coal are <strong>the</strong> most sensible to CO 2 concentrations, 

leaded by anthracite. Natural gas follows coal, while fuel-oils are <strong>the</strong> least 

affected fossil fuels by <strong>the</strong> greenhouse effect. 

Tables 8.9 through 8.11 show <strong>the</strong> exergy loss <strong>of</strong> <strong>the</strong> world’s 2006 coal, fuel-oil and 

natural gas reserves, considering only <strong>the</strong> change <strong>of</strong> <strong>the</strong> conditions <strong>of</strong> <strong>the</strong> R.E. The 

reserves for coal are <strong>the</strong> ones provided by <strong>the</strong> World Energy Council, while those 

for fuel-oil and natural gas come from <strong>the</strong> statistics <strong>of</strong> BP 12 . As can be seen from 

<strong>the</strong> tables, <strong>the</strong> worst scenario A1F I would lead to an exergy loss <strong>of</strong> 2102,4 Mtoe <strong>of</strong> 

coal, 623,7 Mtoe for fuel-oil and 637,3 Mtoe for natural gas. The global fossil fuel 

exergy loss would amount to 3363,4 Mtoe, 84% <strong>of</strong> <strong>the</strong> 2006 USA oil reserves (4000 

Mtoe). Obviously <strong>the</strong> real exergy loss would be much greater, since <strong>the</strong> consumption 

<strong>of</strong> <strong>the</strong> resource in <strong>the</strong> different scenarios has not been taken into account. The latter 

analysis is accomplished in <strong>the</strong> next section. 

12 See <strong>the</strong> detailed reserves in tables 6.11, 6.14 and 6.17.


Table 8.9. <strong>Exergy</strong> loss <strong>of</strong> <strong>the</strong> 2006 coal reserves due to <strong>the</strong> increase <strong>of</strong> GHG emissions, 

according to <strong>the</strong> different SRES scenarios. Values in Mtoe 

Scen. Africa N. Amer- S. Amer- Asia Europe Middle Oceania WORLD 

icaica East 

0 B 34286,5 159649,3 10224,9 136447,4 136826,9 958,6 42603,1 520996,7 

A1 B 34264,7 159548,3 10218,5 136361,5 136742,1 957,9 42576,3 520669,4 

∆B 21,8 101,0 6,4 85,9 84,9 0,6 26,9 327,4 

A1T&B2 B 34243,5 159445,7 10212,2 136277,0 136657,0 957,4 42549,9 520342,8 

∆B 43,0 203,6 12,7 170,4 169,9 1,2 53,2 654,0 

A1B B 34228,2 159372,3 10207,6 136216,3 136596,1 956,9 42531,1 520108,6 

∆B 58,2 277,0 17,3 231,1 230,8 1,6 72,1 888,1 

A2 B 34171,4 159095,8 10190,5 135989,9 136367,9 955,3 42460,6 519231,5 

∆B 115,05 553,50 34,34 457,59 459,00 3,22 142,56 1765,26 

A1F1 B 34149,4 158990,4 10184,0 135902,3 136280,2 954,7 42433,3 518894,3 

∆B 137,1 658,9 40,9 545,2 546,7 3,8 169,8 2102,4 

Table 8.10. <strong>Exergy</strong> loss <strong>of</strong> <strong>the</strong> 2006 fuel-oil reserves due to <strong>the</strong> increase <strong>of</strong> GHG 

emissions, according to <strong>the</strong> different SRES scenarios 

Scen. N. America 

S. & C. 

America 

Europe 

& Eurasia 

Middle 

East 

Africa Asia Pacific 

WORLD 

A1 B, Mtoe 8464,5 16005,6 20991,7 109629,4 16866,0 5890,1 177847,3 

∆B 5,44 10,28 13,55 70,40 10,81 3,78 114,26 

A1T&B2 B, Mtoe 8459,9 15997,0 20980,2 109569,9 16856,8 5886,9 177750,7 

∆B 10,03 18,97 25,06 129,92 19,96 6,97 210,90 

A1B B, Mtoe 8456,6 15990,8 20972,0 109527,8 16850,4 5884,7 177682,2 

∆B 13,28 25,11 33,33 172,02 26,43 9,23 279,41 

A2 B, Mtoe 8445,0 15968,8 20942,6 109376,8 16827,2 5876,6 177436,8 

∆B 24,94 47,15 62,73 322,98 49,62 17,33 524,76 

A1FI B, Mtoe 8440,2 15959,9 20930,8 109315,8 16817,8 5873,3 177337,8 

∆B 29,64 56,06 74,52 383,95 58,99 20,60 623,76 

Table 8.11. <strong>Exergy</strong> loss <strong>of</strong> <strong>the</strong> 2006 natural gas reserves due to <strong>the</strong> increase <strong>of</strong> GHG 

emissions, according to <strong>the</strong> different SRES scenarios 

Scen. N. America 

S. & C. 

America 

Europe 

& Eurasia 

Middle 

East 

Africa Asia Pacific 

WORLD 

A1 B, Mtoe 7475,7 6445,8 60089,8 68845,3 13290,2 13886,9 170033,8 

∆B 7,23 6,24 58,14 66,61 12,86 13,44 164,52 

A1T&B2 B, Mtoe 7471,4 6442,1 60055,2 68805,7 13282,6 13878,9 169935,9 

∆B 11,54 9,95 92,72 106,23 20,51 21,43 262,37 

A1B B, Mtoe 7468,4 6439,5 60031,1 68778,0 13277,2 13873,4 169867,5 

∆B 14,54 12,54 116,90 133,93 25,85 27,02 330,78 

A2 B, Mtoe 7459,3 6431,7 59957,9 68694,2 13261,1 13856,5 169660,6 

∆B 23,64 20,38 190,03 217,72 42,03 43,92 537,73 

A1FI B, Mtoe 7454,9 6427,9 59922,7 68653,9 13253,3 13848,3 169561,0 

∆B 28,02 24,16 225,23 258,04 49,81 52,05 637,31

A prediction <strong>of</strong> <strong>the</strong> exergy loss <strong>of</strong> world’s <strong>mineral</strong> reserves in <strong>the</strong> 21st century 307 

8.4 A prediction <strong>of</strong> <strong>the</strong> exergy loss <strong>of</strong> world’s <strong>mineral</strong> 

reserves in <strong>the</strong> 21st century 

Future consumption <strong>of</strong> <strong>mineral</strong>s will be affected by many different factors, such as 

economic, population, policy, or environmental aspects. In addition to <strong>the</strong> latter, <strong>mineral</strong> 

extraction will be obviously constrained by <strong>the</strong> amount <strong>of</strong> available resources. 

We will explore seven different scenarios, for which <strong>the</strong> future <strong>mineral</strong> degradation 

will be calculated: a scenario based on <strong>the</strong> Hubbert models developed in <strong>the</strong> last 

sections, and <strong>the</strong> six scenarios included in <strong>the</strong> IPCC SRES report [160]. 

8.4.1 Hubbert scenario 

At a first stage, we will suppose that <strong>the</strong> amount <strong>of</strong> available resources are those <strong>of</strong> 

<strong>the</strong> reserve base for non-fuel <strong>mineral</strong>s published by <strong>the</strong> USGS for year 2006 [362], 

and <strong>the</strong> proven reserves <strong>of</strong> fuel commodities, published by BP [35] and WEC [401] 

for <strong>the</strong> same year. It is assumed that no more resources are going to be found, 

and that production <strong>of</strong> <strong>the</strong> commodities will follow <strong>the</strong> bell-shaped curves obtained 

before. As we saw in section 8.2.1, iron, aluminium and copper dominate <strong>the</strong> world’s 

non fossil fuel extraction, representing 93% <strong>of</strong> <strong>the</strong> total actual exergy degradation 

in <strong>the</strong> 20th century. We will consider that <strong>the</strong> same behavior will be found in this 

new century and hence only <strong>the</strong> latter three metals will be analyzed inside <strong>the</strong> nonfuels 

category. Moreover, <strong>the</strong> only fossil fuel <strong>mineral</strong>s considered will be coal, oil 

and natural gas, although <strong>the</strong> extraction <strong>of</strong> o<strong>the</strong>r types such as tar sands, oil shales, 

natural bitumen or heavy crude oil might be economically competitive by <strong>the</strong>n. In 

order to be compared, <strong>the</strong> exergy <strong>of</strong> fuels (B) is added to <strong>the</strong> exergy costs (B ∗ ) <strong>of</strong> 

non-fuel <strong>mineral</strong>s 13 . 

Figure 8.21 shows <strong>the</strong> possible <strong>mineral</strong> reserve’s degradation in <strong>the</strong> 21st century 

based on <strong>the</strong> latter assumptions. 

According to fig. 8.21, if <strong>the</strong> reserves <strong>of</strong> <strong>the</strong> different commodities do not increase, 

<strong>the</strong> peak <strong>of</strong> maximum <strong>mineral</strong> extraction will be reached in <strong>the</strong> decade <strong>of</strong> <strong>the</strong> 2020s, 

exceeding 12 Gtoe/year. By <strong>the</strong>n, production <strong>of</strong> all <strong>mineral</strong>s would increase with 

respect to 2010, with <strong>the</strong> exception <strong>of</strong> oil, which had reached <strong>the</strong> peak in 2008. 

In <strong>the</strong> 2030s, <strong>the</strong> exergy consumption <strong>of</strong> conventional fossil fuels will come at approximately 

equal rates from all three fuels. From that moment on, oil will lose <strong>the</strong> 

hegemony <strong>of</strong> exergy production in favor <strong>of</strong> coal. 

In <strong>the</strong> middle <strong>of</strong> <strong>the</strong> 21st century, oil extraction will be reduced to more than a half 

<strong>of</strong> <strong>the</strong> amount produced in 2010. Natural gas and copper production, which should 

reach <strong>the</strong> peak in years 2023 and 2024, respectively, will be reduced to 23 and 13% 

13 Remember that calculating exergy costs <strong>of</strong> fuel <strong>mineral</strong>s has no sense, as it is impossible to replace 

<strong>the</strong>m at least with current technology. Never<strong>the</strong>less, its chemical exergy is so large, that can be 

compared to <strong>the</strong> exergy costs <strong>of</strong> <strong>the</strong> metals studied.


14 

12 

10 

8 

6 

4 

2 

0 

Bt* 

Copper 

Aluminium 


N. Gas 

Oil 

Coal 

1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Year 

Coal Oil N. Gas Iron Aluminium Copper 

Figure 8.21. Actual exergy consumption <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s in <strong>the</strong> 21st century 

based on <strong>the</strong> Hubbert peak model. Values in Gtoe 

<strong>of</strong> <strong>the</strong>ir respective extractions in 2010. On <strong>the</strong> contrary, iron, aluminium and coal 

production will continue to increase exponentially. By <strong>the</strong> decade <strong>of</strong> 2070s, all considered 

<strong>mineral</strong>s would have reached <strong>the</strong> peak, leading to production decelerations 

also <strong>of</strong> <strong>the</strong> most abundant ones, i.e. <strong>of</strong> iron, aluminium and coal. 

At <strong>the</strong> end <strong>of</strong> <strong>the</strong> 21st century, <strong>the</strong> exergy degradation velocity due to <strong>mineral</strong> extraction 

will be reduced to 5,3 Gtoe/year (a reduction <strong>of</strong> more than 50% with respect 

to <strong>the</strong> peaking year). By <strong>the</strong>n, 82% <strong>of</strong> <strong>the</strong> <strong>mineral</strong>’s exergy reserves available in 

year 1900 will be depleted. Among all, <strong>the</strong> reserves <strong>of</strong> oil, natural gas and copper 

will be almost completely exhausted (more than 99%). Aluminium, coal and iron 

commodities will be depleted at 83%, 72% and 69% respectively. Table 8.12 shows 

<strong>the</strong> exergy distance and <strong>the</strong> degradation degree <strong>of</strong> <strong>the</strong> reserves for <strong>the</strong> periods from 

1900 to 2000 and from 1900 to 2100. 

It should be noted however that future exploration efforts will result in <strong>the</strong> discovery 

<strong>of</strong> new deposits. Moreover, technological development will likely allow to extract 

mines that are economically unaffordable nowadays. 

In <strong>the</strong> next scenarios, we will assume that <strong>the</strong> registered world resources by <strong>the</strong> 

USGS [361] <strong>of</strong> <strong>the</strong> non-fossil fuel commodities, ra<strong>the</strong>r than <strong>the</strong> reserve base will 

be available for extraction. This supposes that technology is enough developed and 

<strong>mineral</strong> prices are high enough to extract resources that are currently not prifitable. 

Accordingly, <strong>the</strong> peak <strong>of</strong> production <strong>of</strong> iron, aluminium and copper will be reached 

in years 2087, 2089 and 2066, respectively (see figures A.1, A.2, and A.3 in <strong>the</strong> ap-


Table 8.12. Actual exergy degradation <strong>of</strong> <strong>the</strong> main extracted <strong>mineral</strong>s in <strong>the</strong> 21st 

century based on <strong>the</strong> Hubbert peak model 

1900 1900 - 2000 1900 - 2100 

Mineral R.B., Gtoe D ∗ , Gtoe % R.B. Loss D ∗ , Gtoe % R.B. Loss 

Coal 666,4 127,8 19,2 480,2 72,1 

Oil 338,8 136,3 40,2 333,9 98,6 

Natural gas 246,2 61,0 24,8 243,9 99,1 

Iron 216,4 26,5 12,3 145,1 67,0 

Aluminium 101,8 9,6 9,4 84,7 83,2 

Copper 8,9 2,6 29,5 8,9 99,7 

SUM 1578,4 363,9 23,1 1296,6 82,1 

pendix). The extraction <strong>of</strong> coal, oil and natural gas is defined by <strong>the</strong> assumptions <strong>of</strong> 

<strong>the</strong> IPCC SRES scenarios, which indirectly assume an increase <strong>of</strong> all proven reserves. 

Tables A.29 through A.34 show <strong>the</strong> primary energy consumption and cumulative resources 

production assumed in each SRES scenario. Additionally, <strong>the</strong> exergy loss <strong>of</strong> 

fossil fuels due to <strong>the</strong> greenhouse effect will be taken into account. We will assume 

that this decrease will affect <strong>the</strong> fuels consumed from year 2050 on, letting CO 2 

emissions and temperatures stabilize in <strong>the</strong> atmosphere. 

8.4.2 The IPCC’s B1 scenario 

As stated before, IPCC’s B1 [160] scenario is characterized by a world toward a 

service and information economy, with reductions in material intensity, and <strong>the</strong> introduction 

<strong>of</strong> clean and resource-efficient technologies. Among all SRES scenarios, 

it is <strong>the</strong> most respectful with <strong>the</strong> extraction <strong>of</strong> fuel resources. 

In addition to <strong>the</strong> exergy loss <strong>of</strong> <strong>the</strong> reserves due to <strong>mineral</strong> extraction, <strong>the</strong> exergy 

degradation <strong>of</strong> fuels due to <strong>the</strong> greenhouse effect is taken into account. In scenario 

B1, we obtained that <strong>the</strong> exergy loss <strong>of</strong> fuels was 0,06% for average coal and oil and 

0,10% for natural gas. 

Figure 8.22 shows <strong>the</strong> actual exergy consumption <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s extracted in 

<strong>the</strong> 21st century, based on <strong>the</strong> hypo<strong>the</strong>sis <strong>of</strong> <strong>the</strong> B1 scenario for fuels. For non fuel 

<strong>mineral</strong>s it has been assumed that <strong>the</strong> extraction behavior follows Hubbert’s bellshaped 

curve, considering that <strong>the</strong> world resources published by <strong>the</strong> USGS [361] 

are available for extraction. 

According to B1 scenario, <strong>the</strong> peak <strong>of</strong> production <strong>of</strong> all considered fuels will be 

reached in <strong>the</strong> decade <strong>of</strong> <strong>the</strong> 2040s with 13,2 Gtoe extracted each year, and declining 

<strong>the</strong>reafter. Current relative consumptions <strong>of</strong> each fuel will be kept until <strong>the</strong> peak, i.e. 

oil will dominate world’s extraction, followed by coal and finally natural gas. After 

<strong>the</strong> peaking year, <strong>the</strong> relative consumption <strong>of</strong> coal will gradually decrease in favor <strong>of</strong> 

<strong>the</strong> cleaner fuel natural gas. But oil will still dominate world’s fuel consumption.


18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

Bt* 

Copper 

Aluminium 


N. Gas 

Oil 

Coal 

1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Year 



based on <strong>the</strong> IPCC’s B1 scenario. Values in Gtoe 

The dynamic <strong>of</strong> <strong>the</strong> B1 scenario would imply an exergy degradation cost <strong>of</strong> <strong>mineral</strong>s 

in <strong>the</strong> 21st century <strong>of</strong> over 1300 Gtoe, from <strong>the</strong>se, around 1050 come only from 

<strong>the</strong> consumption <strong>of</strong> fossil fuels. With <strong>the</strong> exception <strong>of</strong> coal, <strong>the</strong> total exergy cost 

degraded <strong>of</strong> all considered commodities is greater than in <strong>the</strong> previous Hubbert scenario. 

In order to meet <strong>the</strong> fuel consumption expectations <strong>of</strong> B1 scenario, <strong>the</strong> oil 

proven reserves should increase by 69% and <strong>of</strong> natural gas by 52%. On <strong>the</strong> contrary, 

current proven reserves <strong>of</strong> coal would suffice for meeting future world’s consumption. 

In fact, in year 2100, 64% <strong>of</strong> <strong>the</strong> current proven coal reserves will be depleted. 

Obviously, <strong>the</strong> degradation <strong>of</strong> non-fuel <strong>mineral</strong>s here is greater than in Hubbert’s 

scenario, as <strong>the</strong> peaks are reached 20 to 40 years later, due to <strong>the</strong> greater available 

resources considered. Moreover <strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> commodities would be 

also smaller: 57% for iron, 58% for aluminium and 74% for copper. 

Table 8.13 shows <strong>the</strong> irreversible exergy distance D ∗ <strong>of</strong> <strong>the</strong> considered <strong>mineral</strong> resources 

in <strong>the</strong> period from 1900 to 2100, and <strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> commodities, 

according to <strong>the</strong> B1 scenario. 

8.4.3 The IPCC’s A1T scenario 

In <strong>the</strong> IPCC’s AIT scenario, <strong>the</strong> very rapid economic growth, and <strong>the</strong> rapid introduction 

<strong>of</strong> new and more efficient technologies is achieved with predominantly non-fuel 

technologies.



century based on <strong>the</strong> B1 scenario 

1900 1900 - 2000 1900 - 2100 

Mineral W.R., Gtoe D ∗ , Gtoe % W.R. Loss D ∗ , Gtoe %W.R. Loss 

Coal 666,4 127,8 19,2 427,0 64,1 

Oil 338,8 136,3 40,2 573,1 169,2 

Natural gas 246,2 61,0 24,8 373,9 151,9 


Aluminium 222,0 9,6 4,3 129,4 58,3 

Copper 21,6 2,6 12,1 16,0 74,3 

SUM 1792,0 363,9 20,3 1688,5 94,2 

According to <strong>the</strong> calculations carried out before, <strong>the</strong> exergy loss <strong>of</strong> fossil fuels due to 

<strong>the</strong> greenhouse effect in <strong>the</strong> A1T scenario are: 0,12% for average coal and oil, and 

0,15% for natural gas. 

Taking into account <strong>the</strong> extraction <strong>of</strong> <strong>mineral</strong>s, and <strong>the</strong> exergy decrease <strong>of</strong> fuels 

due to <strong>the</strong> GHG emissions in <strong>the</strong> A1T scenario, we obtain that <strong>the</strong> peak <strong>of</strong> <strong>mineral</strong> 

extraction is reached in <strong>the</strong> middle <strong>of</strong> <strong>the</strong> 21st century, with 19 Gtoe/year, coinciding 

with <strong>the</strong> peak <strong>of</strong> population. 

At <strong>the</strong> end <strong>of</strong> <strong>the</strong> century, <strong>the</strong> global irreversible exergy degradation velocity ˙D ∗ 

decreases to 10,4 Gtoe/year. Oil dominates world fuel consumption until <strong>the</strong> 2040s. 

Thereafter, natural gas is <strong>the</strong> most extracted fuel, followed by oil and finally by coal 

(see fig. 8.23). 

The exergy cost degradation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves considered in <strong>the</strong> 21st century 

amounts to more than 1500 Gtoe. And <strong>the</strong> extraction <strong>of</strong> fossil fuels is responsible 

for around 80% <strong>of</strong> <strong>the</strong> global <strong>mineral</strong> depletion. Coal is <strong>the</strong> least depleted fuel 

commodity, with a degradation degree <strong>of</strong> its proven reserves since 1900, <strong>of</strong> 59%. 

On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> reserves <strong>of</strong> natural gas and oil should increase by 77% and 

144%, in order to meet <strong>the</strong> world fuel requirements specified in scenario A1T. The 

depletion degrees <strong>of</strong> <strong>the</strong> non-fuel <strong>mineral</strong> commodities are <strong>the</strong> same as for <strong>the</strong> latter 

scenario, since <strong>the</strong> same assumptions have been taken into account (see table 8.14). 

8.4.4 The IPCC’s B2 scenario 

In <strong>the</strong> IPCC’s B2 scenario, a world with continuously increasing population and 

intermediate economic development, <strong>mineral</strong> consumption increases continuously 

throughout <strong>the</strong> century, although <strong>the</strong> rate <strong>of</strong> increase slows down in <strong>the</strong> decade <strong>of</strong> 

<strong>the</strong> 2050s. 

The exergy loss <strong>of</strong> fuels due to <strong>the</strong> greenhouse effect in <strong>the</strong> B2 scenario is identical 

to <strong>the</strong> previous case, namely 0,12% for coal and oil, and 0,15% for natural gas.


20 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

Bt* 

Copper 

Aluminium 


N. Gas 

Oil 

Coal 

1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Year 



based on <strong>the</strong> IPCC’s A1T scenario. Values in Gtoe 


century based on <strong>the</strong> A1T scenario 

1900 1900 - 2000 1900 - 2100 


Coal 666,4 127,8 19,2 393,3 59,0 

Oil 338,8 136,3 40,2 598,9 176,7 

Natural gas 246,2 61,0 24,8 600,6 244,0 


Aluminium 222,0 9,6 4,3 129,4 58,3 

Copper 21,6 2,6 12,1 16,0 74,3 

SUM 1792,0 363,9 20,3 1907,2 106,4 

According to figure 8.24, in year 2100, <strong>the</strong> global <strong>mineral</strong> degradation velocity will 

reach near 20 Gtoe/year. By <strong>the</strong>n, fuel demand will be satisfied at approxamtely 

equal rates with natural gas and coal. Oil will reach <strong>the</strong> peak <strong>of</strong> production in 

<strong>the</strong> 2040s. From that moment on, coal and natural gas production will increase, 

compensating <strong>the</strong> lack <strong>of</strong> oil, although <strong>the</strong> peak <strong>of</strong> natural gas will be reached in <strong>the</strong> 

2080s. 

At <strong>the</strong> end <strong>of</strong> <strong>the</strong> century, <strong>the</strong> global exergy degradation cost <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves 

will be around 1580 Gtoe, slightly greater than in <strong>the</strong> A1T scenario. From <strong>the</strong>se, 83% 

correspond to <strong>the</strong> consumption <strong>of</strong> fossil fuels. Since 1900, coal extraction would


20 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

Bt* 

Copper 

Aluminium 


N. Gas 

Oil 

Coal 

1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Year 



based on <strong>the</strong> IPCC’s B2 scenario. Values in Gtoe 


century based on <strong>the</strong> B2 scenario 

1900 1900 - 2000 1900 - 2100 


Coal 666,4 127,8 19,2 417,6 62,7 

Oil 338,8 136,3 40,2 567,4 167,5 

Natural gas 246,2 61,0 24,8 644,8 261,9 


Aluminium 222,0 9,6 4,3 129,4 58,3 

Copper 21,6 2,6 12,1 16,0 74,3 

SUM 1792,0 363,9 20,3 1944,2 108,5 

lead to <strong>the</strong> degradation <strong>of</strong> 63% <strong>of</strong> <strong>the</strong> total reserves. However, <strong>the</strong> proven reserves <strong>of</strong> 

natural gas and oil should increase by 63% and 167%, in order to meet <strong>the</strong> world fuel 

requirements specified in scenario B2. Again, <strong>the</strong> same figures than in <strong>the</strong> previous 

scenarios are obtained for non-fuel <strong>mineral</strong>s, as <strong>the</strong> same assumptions have been 

taken into account (see table 8.15).


8.4.5 The IPCC’s A1B scenario 

In <strong>the</strong> A1B scenario, <strong>the</strong> rapid economic growth and rapid increase <strong>of</strong> new and more 

efficient technologies is achieved with a balance between fuel and non-fuel energy 

sources. It is assumed that since <strong>the</strong> decade <strong>of</strong> <strong>the</strong> 2030s, <strong>the</strong> consumption <strong>of</strong> fossil 

fuels is dominated by natural gas. 

The exergy loss <strong>of</strong> fossil fuels due to <strong>the</strong> greenhouse effect was calculated for A1B 

scenario as 0,17% for average coal, 0,16% for average fuel, and 0,19% for natural 

gas. 

According to <strong>the</strong> hypo<strong>the</strong>sis <strong>of</strong> <strong>the</strong> A1B scenario, <strong>the</strong> peaks <strong>of</strong> oil and coal production 

are reached in <strong>the</strong> decades <strong>of</strong> 2030s and 2050s, respectively with around 5,7 Gtoe 

<strong>of</strong> oil extracted per year and 4,6 Gtoe/year <strong>of</strong> coal. The global <strong>mineral</strong> production 

peak is reached in <strong>the</strong> decade <strong>of</strong> 2070s, with around 24 Gtoe/year extracted (see fig 

8.25). 

25 

20 

15 

10 

5 

0 

Bt* 

Copper 

Aluminium 


N. Gas 

Oil 

Coal 

1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Year 



based on <strong>the</strong> IPCC’s A1B scenario. Values in Gtoe 

The global exergy degradation cost <strong>of</strong> all considered <strong>mineral</strong> reserves in <strong>the</strong> 21st 

century exceeds 2000 Gtoe, from which 86% correspond to <strong>the</strong> extraction <strong>of</strong> fuels. 

At <strong>the</strong> end <strong>of</strong> <strong>the</strong> 21st century, 74% <strong>of</strong> <strong>the</strong> total coal reserves would be depleted. The 

A1B scenario assumes that oil and natural gas proven reserves should increase by 

76% and 200%, respectively, in order to meet future fuel demands. The depletion 

degree <strong>of</strong> non-fuel <strong>mineral</strong> reserves are identical to <strong>the</strong> previous cases, since <strong>the</strong> 

same assumptions have been considered. Table 8.16 shows a summary <strong>of</strong> <strong>the</strong> results 

for <strong>the</strong> A1B scenario.



century based on <strong>the</strong> A1B scenario 

1900 1900 - 2000 1900 - 2100 


Coal 666,4 127,8 19,2 495,4 74,3 

Oil 338,8 136,3 40,2 595,1 175,6 

Natural gas 246,2 61,0 24,8 982,1 399,0 


Aluminium 222,0 9,6 4,3 129,4 58,3 

Copper 21,6 2,6 12,1 16,0 74,3 

SUM 1792,0 363,9 20,3 2387,1 133,2 

8.4.6 The IPCC’s A2 scenario 

The energy demand <strong>of</strong> <strong>the</strong> continuously increasing global population <strong>of</strong> IPCC’s A2 

scenario is mainly satisfied by <strong>the</strong> increasing consumption <strong>of</strong> fossil fuels. World oil 

consumption reaches <strong>the</strong> maximum <strong>of</strong> production in <strong>the</strong> 2020s, decreasing <strong>the</strong>reafter 

until its complete substitution towards <strong>the</strong> end <strong>of</strong> <strong>the</strong> century. Since <strong>the</strong> peaking 

<strong>of</strong> oil production, coal is <strong>the</strong> dominant fuel consumed in this scenario. It passed 

from representing 25% <strong>of</strong> all fossil fuels consumed in <strong>the</strong> 2020s, to over 75% in year 

2100. 

To <strong>the</strong> exergy decrease <strong>of</strong> <strong>mineral</strong>s due to extraction, we add <strong>the</strong> fuel’s exergy degradation 

due to <strong>the</strong> greenhouse effect, which is in <strong>the</strong> A2 scenario: 0,34% for average 

coal, 0,29% for average fuel, and 0,32% for natural gas. 

Accordingly <strong>the</strong> global peak <strong>of</strong> world <strong>mineral</strong> extraction in <strong>the</strong> 21st century is 

reached in year 2100, with over 33 Gtoe/year extracted. In order to satisfy this 

energy demand, <strong>the</strong> proven reserves <strong>of</strong> coal, oil, and natural gas should increase by 

89%, 50%, and 140%, respectively (see fig. 8.26). 

In table 8.17, <strong>the</strong> irreversible exergy distance between 1900 and 2100 is shown. 

According to it, A2 scenario would imply a global exergy degradation in <strong>the</strong> 21st 

century <strong>of</strong> over 2300 Gtoe (6,3 times more <strong>the</strong> exergy degraded in <strong>the</strong> previous 

century). This implies <strong>the</strong> degradation <strong>of</strong> almost 150% <strong>of</strong> <strong>the</strong> global <strong>mineral</strong> resources 

available in 1900. Again, <strong>the</strong> same figures than in <strong>the</strong> previous scenarios 

are obtained for non-fuel <strong>mineral</strong>s, as <strong>the</strong> same assumptions have been taken into 

account. 

8.4.7 The IPCC’s A1FI scenario 

In <strong>the</strong> IPCC’s A1FI scenario, <strong>the</strong> world’s rapid economic growth and rapid introduction 

<strong>of</strong> new and more efficient technologies is achieved through <strong>the</strong> intensive


35 

30 

25 

20 

15 

10 

5 

0 

Bt* 

Copper 

Aluminium 


N. Gas 

Oil 

Coal 

1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Year 



based on <strong>the</strong> IPCC’s A2 scenario. Values in Gtoe 


century based on <strong>the</strong> A2 scenario 

1900 1900 - 2000 1900 - 2100 


Coal 666,4 127,8 19,2 1261,8 189,3 

Oil 338,8 136,3 40,2 510,0 150,5 

Natural gas 246,2 61,0 24,8 592,0 240,5 


Aluminium 222,0 9,6 4,3 129,4 58,3 

Copper 21,6 2,6 12,1 16,0 74,3 

SUM 1792,0 363,9 20,3 2678,2 149,5 

consumption <strong>of</strong> fossil fuels. Consequently, it is <strong>the</strong> most <strong>mineral</strong> predatory scenario 

taken into account. 

The decrease <strong>of</strong> fuel’s exergy due to <strong>the</strong> greenhouse effect in <strong>the</strong> scenario A1FI obtained 

was: 0,4% for average coal, 0,35% for average fuel, and 0,37% for natural 

gas. 

According to figure 8.27, <strong>the</strong> peak <strong>of</strong> <strong>mineral</strong> production is reached in <strong>the</strong> decade <strong>of</strong> 

<strong>the</strong> 2080s, coinciding with <strong>the</strong> peaks <strong>of</strong> oil and natural gas consumption. Thereafter, 

<strong>the</strong> decrease <strong>of</strong> oil and natural gas production is compensated by an increase in <strong>the</strong> 

world extraction. The global <strong>mineral</strong> degradation velocity in <strong>the</strong> eighties reaches


39,8 Gtoe/year, from which over 90% are due to <strong>the</strong> extraction <strong>of</strong> fossil fuels. It 

should be remembered, that <strong>the</strong> consumption <strong>of</strong> non-fuel <strong>mineral</strong>s has been assumed 

to be identical to <strong>the</strong> previous cases. 

45 

40 

35 

30 

25 

20 

15 

10 

5 

0 

Bt* 

Copper 

Aluminium 


N. Gas 

1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Year 



based on <strong>the</strong> IPCC’s A1FI scenario. Values in Gtoe 

The global <strong>mineral</strong> exergy degradation cost in <strong>the</strong> 21st century is in <strong>the</strong> A1FI scenario 

over 2750 Gtoe. This implies that man would have depleted 7,6 times more 

<strong>mineral</strong> reserves than in <strong>the</strong> 20th century, and <strong>the</strong> degradation <strong>of</strong> around 174% <strong>of</strong> 

<strong>the</strong> global <strong>mineral</strong> resources available in 1900 (see table 8.18). Fur<strong>the</strong>rmore, <strong>the</strong> 

proven reserves <strong>of</strong> coal, oil and natural gas should increase at least by 56%, 140% 

and 289%, in order to meet <strong>the</strong> fuel requirements <strong>of</strong> scenario A1FI. 

8.4.8 Summary <strong>of</strong> <strong>the</strong> scenarios 

Table 8.19 and figure 8.28 show a summary <strong>of</strong> <strong>the</strong> possible exergy degradation costs 

<strong>of</strong> <strong>the</strong> main <strong>mineral</strong> reserves extracted in <strong>the</strong> period between 1900 and 2100, according 

to <strong>the</strong> different scenarios considered before. It should be noted that to <strong>the</strong> 

obtained values, we should add <strong>the</strong> exergy loss <strong>of</strong> o<strong>the</strong>r <strong>mineral</strong>s not accounted for 

in this study. Additional non-fuel <strong>mineral</strong>s could increase <strong>the</strong> global <strong>mineral</strong> exergy 

consumption in 20% or more. 

As can be seen from <strong>the</strong> table and <strong>the</strong> figure, <strong>the</strong> scenario that leads to <strong>the</strong> least 

degradation degree <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves, is <strong>the</strong> one based on <strong>the</strong> Hubbert model. 

It should be remembered, that for this scenario it has been assumed that <strong>the</strong> only 

available <strong>mineral</strong> resources for extraction are those <strong>of</strong> <strong>the</strong> reserve base, and that 

Oil 

Coal



century based on <strong>the</strong> A1FI scenario 

1900 1900 - 2000 1900 - 2100 


Coal 666,4 127,8 19,2 1036,9 155,6 

Oil 338,8 136,3 40,2 811,3 239,4 

Natural gas 246,2 61,0 24,8 955,6 388,2 


Aluminium 222,0 9,6 4,3 129,4 58,3 

Copper 21,6 2,6 12,1 16,0 74,3 

SUM 1792,0 363,9 20,3 3118,1 174,0 

Table 8.19. Summary <strong>of</strong> <strong>the</strong> actual exergy degradation <strong>of</strong> <strong>the</strong> main extracted <strong>mineral</strong>s 

in <strong>the</strong> period between years 1900 and 2100 based on <strong>the</strong> Hubbert and <strong>the</strong> 

IPCC’s SRES scenarios 

Scenario Hubbert B1 A1T B2 AIB A2 A1FI 

D ∗ 1900 - 2100 1297 1689 1907 1944 2387 2678 3118 

% Reserves lost 82 94 106 108 133 149 174 

no more resources will be found in <strong>the</strong> future. Accordingly, at <strong>the</strong> end <strong>of</strong> <strong>the</strong> 21st 

century, man would have depleted around 82% <strong>of</strong> <strong>the</strong> reserve base available in 1900. 

For <strong>the</strong> rest scenarios, it has been assumed that <strong>the</strong> non-fuel <strong>mineral</strong> reserves available 

for extraction, are those <strong>of</strong> <strong>the</strong> world resources published by <strong>the</strong> USGS [361]. 

Accordingly, <strong>the</strong> rate <strong>of</strong> extraction <strong>of</strong> non-fuel <strong>mineral</strong>s is greater than in <strong>the</strong> previous 

case, as more resources can be extracted. 

In addition to <strong>the</strong> consumption <strong>of</strong> fossil fuels assumed in <strong>the</strong> different SRES scenarios, 

we have taken into account <strong>the</strong> exergy loss <strong>of</strong> fuels due to <strong>the</strong> emission 

<strong>of</strong> greenhouse gases to <strong>the</strong> atmosphere. Depending on <strong>the</strong> scenario considered, 

<strong>the</strong> greenhouse effect increases <strong>the</strong> global <strong>mineral</strong> exergy loss between 0,04% and 

0,31%. 

Among all SRES scenarios, A1FI implies <strong>the</strong> greatest degradation <strong>of</strong> <strong>mineral</strong> reserves, 

leading to <strong>the</strong> depletion <strong>of</strong> more than 3100 Gtoe. On <strong>the</strong> o<strong>the</strong>r end, scenario B1 leads 

to <strong>the</strong> least <strong>mineral</strong> degradation, with near 1700 Gtoe depleted. Never<strong>the</strong>less, all 

IPCC’s scenarios involve greater degradation degrees <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves than in 

<strong>the</strong> case where <strong>the</strong> Hubbert behavior has been assumed. This indicates that for satisfying 

<strong>the</strong> energy consumption assumed in <strong>the</strong> SRES scenarios, <strong>the</strong> proven reserves 

<strong>of</strong> coal, oil and natural gas should increase considerably. 

New discoveries are indeed increasing <strong>the</strong> reserves <strong>of</strong> many <strong>mineral</strong> resources. A 

recent case has been <strong>the</strong> discovery <strong>of</strong> <strong>the</strong> Carioca oil well in <strong>the</strong> Santos Basin <strong>of</strong>f-


3500 

3000 

2500 

2000 

1500 

1000 

500 

0 

Bt*, Gtoe 

Copper 

Aluminium 


Natural gas 

Oil 

Coal 

Hubbert B1 A1T B2 A1B A2 A1FI 

Coal Oil Natural gas Iron Aluminium Copper 

Figure 8.28. Summary <strong>of</strong> <strong>the</strong> actual exergy degradation <strong>of</strong> <strong>the</strong> main extracted <strong>mineral</strong>s 

in <strong>the</strong> period between years 1900 and 2100 based on <strong>the</strong> Hubbert and <strong>the</strong> 

IPCC’s SRES scenarios 

shore Brazil, which registered a test production <strong>of</strong> 2900 barrels/day <strong>of</strong> oil and 57000 

m 3 /day <strong>of</strong> gas. 

But in <strong>the</strong> relatively mature oil industry, <strong>the</strong> quantity <strong>of</strong> additional reserves that remain 

to be discovered is unclear [160]. Ivanhoe and Leckie [165], Laherrere [190], 

Campbell [45] or Hatfield [133] argue that few new oil fields are being discovered 

and that most <strong>of</strong> <strong>the</strong> increases in reserves results from revisions <strong>of</strong> underestimating 

existing reserves. However, optimistic views such as <strong>the</strong> one <strong>of</strong> Smith and Robinson 

[324], appeal to improvements in technology, which will increase recovery rates 

from existing reservoirs and make pr<strong>of</strong>itable <strong>the</strong> development <strong>of</strong> fields previously 

regarded as uneconomic. 

In <strong>the</strong> case <strong>of</strong> natural gas, estimates <strong>of</strong> reserves and resources are being revised 

continuously. Optimistic additional gas reserves are estimated as between 200, according 

to <strong>the</strong> International Gas Union [156] and 500 Gtoe, according to Gregory 

and Rogner [123]. 

Coal proven reserves are larger than those <strong>of</strong> oil and natural gas. Fur<strong>the</strong>rmore, 

according to <strong>the</strong> WEC [401] estimates <strong>of</strong> additional resources in place, <strong>the</strong> global 

coal reserves could be multiplied by more than two. But as <strong>the</strong> EWG [89] argues, 

<strong>the</strong> historical assessment <strong>of</strong> global resources has revealed substantial downgradings 

over <strong>the</strong> last decades. Estimated coal resources have declined from 10 billion tons 

coal equivalent ( 8300 Mtoe) to about 4,5 billion tons coal equivalent ( 3750 Mtoe), 

a decline <strong>of</strong> 55% within <strong>the</strong> last 25 years. Moreover, this downgrading <strong>of</strong> estimated


coal resources shows a trend supported by each new assessment. Therefore it is 

possible that resource estimates will be fur<strong>the</strong>r reduced in <strong>the</strong> future. 

Hence, it remains to be seen whe<strong>the</strong>r <strong>the</strong> rate <strong>of</strong> discoveries and <strong>the</strong> reclassification 

<strong>of</strong> <strong>mineral</strong> reserves as recoverable are sufficient to meet <strong>the</strong> demands <strong>of</strong> a rapidly 

industrializing world. 

8.5 Final reflections 

8.5.1 The Limits to Growth to be reconsidered? 

In <strong>the</strong> early seventies, Meadows et al. [218] raised <strong>the</strong> concern about <strong>the</strong> limits to 

growth. Their conclusion was that if no immediate action is undertaken, <strong>the</strong> current 

standard <strong>of</strong> living will not be sustained and world economies will eventually collapse. 

Pollution will increase and food and <strong>mineral</strong> commodities will suffer important 

shortages, leading to a reduction in population. The book constituted a world 

shock and incited reflection about <strong>the</strong> urgent need for a sustainable development. 

The Limits to Growth predicted oil running out in 1992 among o<strong>the</strong>r natural resources 

14 . Instead <strong>of</strong> shortages, <strong>the</strong> last two decades <strong>of</strong> <strong>the</strong> 20th century were 

marked by a generalized excess. The world ended up enjoying significant declines 

in almost all commodity prices. Consequently, <strong>the</strong> message <strong>of</strong> <strong>the</strong> Club <strong>of</strong> Rome was 

soon discredited. But <strong>the</strong> lack <strong>of</strong> precise data and hence inexact and early predictions 

about future shortages does not excuse <strong>the</strong> reality <strong>of</strong> <strong>the</strong> message provided in 

<strong>the</strong> Meadow’s book. It was also in <strong>the</strong> late eighties and early nineties when more 

voices were raised on a global scale in favor <strong>of</strong> putting limits to growth, in view 

<strong>of</strong> <strong>the</strong> systematic destruction <strong>of</strong> <strong>the</strong> environment. Clear examples <strong>of</strong> that were <strong>the</strong> 

Brundtland report [398] in 1987 or <strong>the</strong> Earth Summit celebrated in Rio de Janeiro 

in 1992. The beginning <strong>of</strong> <strong>the</strong> 21st century has been marked by a drastic increase <strong>of</strong> 

<strong>mineral</strong> and food prices. In <strong>the</strong> period between may 2007 and may 2008 <strong>the</strong> prices 

<strong>of</strong> wheat, soy or rice have increased by 62, 79 and 95%, respectively. Similarly, <strong>the</strong> 

prices <strong>of</strong> aluminium, gold, natural gas or brent increased in <strong>the</strong> same period by 25, 

36, 238 and 57%, respectively. These few examples can be extrapolated to o<strong>the</strong>r 

commodities. The sharp increase <strong>of</strong> prices that we are currently facing, toge<strong>the</strong>r 

with <strong>the</strong> results <strong>of</strong>fered in this PhD more than justify to reconsider <strong>the</strong> reflections 

incited by <strong>the</strong> Club <strong>of</strong> Rome. 

Obviously <strong>the</strong> aim <strong>of</strong> this PhD was not to reanalyze <strong>the</strong> truth or falseness <strong>of</strong> <strong>the</strong>ir 

predictions, but to shed light on a more precise methodology that could improve 

<strong>the</strong> capacity <strong>of</strong> <strong>the</strong> analysis, almost forty years later. The exergoecological analysis 

<strong>of</strong> fuel and non-fuel <strong>mineral</strong>s could be extended to <strong>the</strong> loss <strong>of</strong> fertile soils and 

14 The authors <strong>of</strong> <strong>the</strong> report <strong>of</strong>fered also an upper value for <strong>the</strong> expiry time, as <strong>the</strong>y accepted that 

<strong>the</strong> known resources <strong>of</strong> <strong>mineral</strong>s and energy could, and would, grow in <strong>the</strong> future, and consumption 

growth rates could also decline. Assuming that <strong>the</strong> resources are multiplied by two, virtually all major 

<strong>mineral</strong>s and energy resources would expire within <strong>the</strong> following 100 years.

Final reflections 321 

consequently to <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> increasing world food demand and <strong>the</strong> carrying 

capacity <strong>of</strong> <strong>the</strong> planet. If <strong>the</strong> demand <strong>of</strong> bi<strong>of</strong>uels as an alternative to conventional oil 

should compete with food production, one could question which will be <strong>the</strong> availability 

<strong>of</strong> food, bi<strong>of</strong>uels and biodiversity in a world with increasing demands and 

accelerated degradations. The analysis could be also extended to <strong>the</strong> growing freshwater 

requirements in a world with unpredictable climate changes. 

On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> production <strong>of</strong> materials is still cheap, so even if <strong>the</strong>y are partially 

recycled, extraction continues to increase. This indicates that mankind has put 

nei<strong>the</strong>r energy nor mass limits to <strong>the</strong> extraction <strong>of</strong> <strong>mineral</strong>s. Maybe <strong>the</strong> solution is 

to establish some kind <strong>of</strong> global law stating that extraction should be limited to <strong>the</strong> 

quantity <strong>of</strong> <strong>mineral</strong>s that are naturally degraded through oxidation. This is, humanbeings 

should live with a certain amount <strong>of</strong> recyclable metals and materials and 

should exploit only limited resources. Ulterior extractions should not be permitted, 

except for extraordinary cases. This is, it should be stated that <strong>the</strong>re has been extracted 

enough iron, aluminium, copper and o<strong>the</strong>r <strong>mineral</strong> commodities throughout 

history, and mankind should learn to recycle and save materials, instead <strong>of</strong> promoting 

wasting. This new economy would be more focused toward use than toward 

<strong>the</strong> consumption <strong>of</strong> raw materials. The dematerialization <strong>of</strong> a society could only be 

achieved by limiting drastically <strong>the</strong> extraction <strong>of</strong> <strong>the</strong> earth’s resources. It should be 

noted that this limitation would not avoid an increasing energy consumption. The 

energy demand should be supplied through renewable resources for compensating 

<strong>the</strong> exergy destruction associated to recycling. 

It is not enough to establish conventional measures <strong>of</strong> energy efficiency, renewable 

energies or more advanced energy technologies such as CO 2 sequestration, fission or 

fusion. We should propose a drastic limitation in <strong>the</strong> extraction <strong>of</strong> raw materials from 

<strong>the</strong> earth. We should live from and with <strong>the</strong> already extracted materials, converting 

<strong>the</strong>ir use and <strong>the</strong>ir recycling into an art that comes from <strong>the</strong> necessity. As long as 

<strong>the</strong> “Great Mine Earth” continues providing cheap materials in which <strong>the</strong>ir value is 

associated to extraction costs, ra<strong>the</strong>r than replacement costs, it will be always less 

expensive to continue exhausting <strong>the</strong> planet, than to live with <strong>the</strong> available and 

already extracted <strong>mineral</strong>s. Society requires development, not growth. 

However, as <strong>the</strong> former UK prime minister Tony Blair stated [84], “we cannot forget 

that more than three and a half billion people live in countries rich in oil, gas or 

<strong>mineral</strong>s. These natural resources provide great opportunities to improve <strong>the</strong> lives 

<strong>of</strong> poor people. But <strong>the</strong>re are risks. Bad management and lack <strong>of</strong> transparency <strong>of</strong> 

<strong>the</strong>se resources can lead to poverty, conflict and corruption. However this is not 

inevitably”. 

If economic development <strong>of</strong> so many people in <strong>the</strong> world depends on <strong>the</strong> extraction 

<strong>of</strong> <strong>the</strong>ir raw materials, limiting such activity is at <strong>the</strong> present time unfeasible and not 

very practical. If this drastic limitation will surely come eventually, today <strong>the</strong> immediate 

and realistic requirement is to promote conservation measures <strong>of</strong> <strong>the</strong> resources 

for <strong>the</strong> future use <strong>of</strong> coming generations and a more rational management <strong>of</strong> <strong>the</strong>


extraction and use <strong>of</strong> <strong>mineral</strong>s. The conservation <strong>of</strong> natural resources has worried 

a number <strong>of</strong> renowned economists throughout <strong>the</strong> middle <strong>of</strong> <strong>the</strong> 20th century. Although 

this topic exceeds <strong>the</strong> objectives <strong>of</strong> this PhD, we want to shortly address this 

problem. 

As stated by Ciriacy-Wantrup [57], <strong>the</strong> economy is <strong>the</strong> study <strong>of</strong> <strong>the</strong> election between 

alternative ways <strong>of</strong> action for solving scarcity. Conservation is interested in when 

resources should be used. Conservation and its anti<strong>the</strong>sis depletion are defined in 

terms <strong>of</strong> <strong>the</strong> change in <strong>the</strong> intertemporal distribution <strong>of</strong> <strong>the</strong> use <strong>of</strong> resources. Such 

changes lead to <strong>the</strong> comparison <strong>of</strong> two or more alternative temporal distributions 

<strong>of</strong> resources extraction. According to Ciriacy-Wantrup, <strong>the</strong> optimum conservation 

state is <strong>the</strong> temporal distribution <strong>of</strong> <strong>the</strong> use that maximizes <strong>the</strong> current value and 

<strong>the</strong> income flux. An economic study <strong>of</strong> conservation should explain how a conservation 

state is produced and how it changes. In many practical situations, keeping a 

minimum standard <strong>of</strong> living does not imply any abstention in <strong>the</strong> use <strong>of</strong> resources, 

it ra<strong>the</strong>r implies a change in <strong>the</strong> technical ways (not in <strong>the</strong> quantity) <strong>of</strong> use. 

8.5.2 The need for global agreements on <strong>the</strong> extraction and use <strong>of</strong> 

natural resources 

In <strong>the</strong> previous chapters, we have stated that <strong>the</strong>re are two different types <strong>of</strong> accelerations 

appearing in <strong>the</strong> use <strong>of</strong> natural resources. One is <strong>the</strong> increasing demand <strong>of</strong> 

<strong>mineral</strong>s, and <strong>the</strong> o<strong>the</strong>r more subtle one is associated to <strong>the</strong> decline <strong>of</strong> ore grades. 

This last phenomenon, corroborated throughout <strong>the</strong> 20th century for almost all <strong>mineral</strong>s 

lead to increasing energy requirements per unit <strong>of</strong> <strong>mineral</strong> extracted. 

The result is that not only <strong>the</strong> absolute quantity <strong>of</strong> energy increases for <strong>the</strong> extraction 

<strong>of</strong> <strong>mineral</strong>s in <strong>the</strong> planet, but also <strong>the</strong> energy per unit <strong>of</strong> <strong>mineral</strong>, as <strong>the</strong> ore grade 

decreases. Currently, between 5 and 6% <strong>of</strong> <strong>the</strong> yearly world’s fossil fuel consumption 

is used for <strong>the</strong> extraction and processing <strong>of</strong> iron, aluminium, copper and cement 15 . 

If <strong>the</strong> demand <strong>of</strong> <strong>mineral</strong>s increase and at <strong>the</strong> same time ore grades decline, <strong>the</strong> 

energy demand for extraction will likely suffer a doubly exponential increase in <strong>the</strong> 

next decades. Although <strong>the</strong> recycling <strong>of</strong> materials, especially <strong>of</strong> metals has grown 

in <strong>the</strong> last decades, <strong>the</strong>se are far from reaching <strong>the</strong> accelerated extraction rate <strong>of</strong> 

<strong>the</strong>ir precursors. It is still cheaper to continue extracting than to save materials. And 

probably this trend will not change in <strong>the</strong> short run. 

Therefore, global agreements are urgently required. Paraphrasing <strong>the</strong> words <strong>of</strong> <strong>the</strong> 

e-Parliament 16 [86], “We are burning oil, coal and gas and extracting <strong>mineral</strong>s and 

rocks at an ever increasing rate, while at <strong>the</strong> same time destroying our forests, our 

biodiversity, our land and our mines. As a result, <strong>the</strong> earth is heating up fast. These 

15 According to energy requirements data from <strong>the</strong> SimaPro 7.1 LCA s<strong>of</strong>tware. 

16 The e-Parliament is <strong>the</strong> first world institution whose members are elected by <strong>the</strong> people. It links 

democratic members <strong>of</strong> parliament and congress into a global forum, combining meetings and electronic 

communication.


problems are global, but we are trying to solve <strong>the</strong>m with an international system 

<strong>of</strong> some 200 national interests. Each national <strong>capital</strong> makes policy decisions within 

its own borders, with no easy way to learn from <strong>the</strong> experience <strong>of</strong> <strong>the</strong> o<strong>the</strong>rs. The 

governments have been trying for years to agree on what to do to protect <strong>the</strong> planet. 

It isn’t working. To act in time, we need to create quickly a critical mass <strong>of</strong> lawmakers 

from all parties who understand <strong>the</strong> dangers, share a vision for a sustainable 

world, and are ready to take <strong>the</strong> lead in <strong>the</strong>ir national parliaments. We need to invest 

not only in renewable energy, but in information for planet management and 

political leadership. The only shortage we face is a lack <strong>of</strong> political will and political 

leadership to make <strong>the</strong> transition to a sustainable world.” 

It is surprising that <strong>the</strong> international worries are still very far removed from this 

topic. Pancala and Socolow [256] have laid out a menu <strong>of</strong> 15 currently available 

options for meeting <strong>the</strong> world’s energy needs over <strong>the</strong> next 50 years while stabilizing 

CO 2 emissions near <strong>the</strong> current level <strong>of</strong> 7 billion tons <strong>of</strong> carbon per year. These 

options include energy efficiency, renewable energies, CO 2 capture and storage, new 

generations <strong>of</strong> nuclear power plants, <strong>the</strong> massive use <strong>of</strong> hybrid and hydrogen vehicles 

and even a change in <strong>the</strong> energy model. Never<strong>the</strong>less, it has not been proposed 

in a quantitative way what it may suppose a drastic world reduction and an appropriate 

management <strong>of</strong> <strong>the</strong> massive use <strong>of</strong> <strong>the</strong> extractive mining industry. 

It seems though, that early birds in <strong>the</strong> sector are determined to improve public 

transparency in <strong>the</strong>ir activities at least in economic terms. This way, <strong>the</strong> Extractive 

Industries Transparency Initiative (EITI) [84] came into being in 2002 at <strong>the</strong> 

World Summit on Sustainable Development in Johannesburg. It brought toge<strong>the</strong>r a 

global coalition <strong>of</strong> governments, companies, civil society organizations and investors 

to promote greater transparency in <strong>the</strong> payment and receipts <strong>of</strong> natural resource revenues. 

As a consequence, EITI is becoming <strong>the</strong> internationally accepted standard 

for transparency in <strong>the</strong> oil, gas and mining sectors. 

If EITI is an initiative that should be applauded, it is still not ambitious enough in 

<strong>the</strong> physical frame. Indeed, we share with <strong>the</strong> EITI <strong>the</strong> following principles and most 

relevant criteria [84]: 

• We share <strong>the</strong> belief that <strong>the</strong> prudent use <strong>of</strong> natural resource wealth should 

be an important engine for sustainable economic growth that contributes to 

sustainable development and poverty reduction, but if not managed property, 

can create negative economic and social impacts. 

• We affirm that management <strong>of</strong> natural resource wealth for <strong>the</strong> benefit <strong>of</strong> a 

country’s citizens is in <strong>the</strong> domain <strong>of</strong> sovereign governments to be exercised in 

<strong>the</strong> interests <strong>of</strong> <strong>the</strong>ir national development. 

• We recognize that <strong>the</strong> benefits <strong>of</strong> resource extraction occur as revenue streams 

over many years and can be highly price dependent.


• We recognize that public understanding <strong>of</strong> government revenues and expenditure 

over time could help public debate and inform choice <strong>of</strong> appropriate and 

realistic options for sustainable development. 

• We underline <strong>the</strong> importance <strong>of</strong> transparency by governments and companies 

in <strong>the</strong> extractive industries and <strong>the</strong> need to enhance public financial management 

and accountability. 

• In seeking solutions we believe that all stakeholders have important and relevant 

contributions to make, including governments and <strong>the</strong>ir agencies, extractive 

industry companies, service companies, multilateral organizations, financial 

organizations, investors and non-governmental organizations. 

• Regular publication should be accomplished <strong>of</strong> all material oil, gas and mining 

payments by companies to governments and all material revenues received 

by governments from oil, gas and mining companies should be forwarded to 

a wide audience in a publicly accessible, comprehensive and comprehensible 

manner. 

• Civil society is actively engaged as a participant in <strong>the</strong> design, monitoring and 

evaluation <strong>of</strong> this process and contributes towards public debate. 

Obviously, <strong>the</strong> global benefits obtained through a global EITI implementation would 

be impressive. Underlying this work is <strong>the</strong> belief that more public accountability and 

more transparency can raise <strong>the</strong> quality <strong>of</strong> public expenditure, cut corruption, reduce 

poverty and raise <strong>the</strong> credibility and prestige <strong>of</strong> extractive companies. Moreover, it 

provides <strong>the</strong> information that allows to decide on a global scale whe<strong>the</strong>r or not to 

change extraction rates from an economic perspective. 

Never<strong>the</strong>less, <strong>the</strong> EITI lays stress only on economic transparency, forgetting physical 

parameters that are extraordinarily relevant for understanding <strong>the</strong> decline <strong>of</strong> benefits 

or <strong>the</strong> extractive velocity in relation to its reserves. So EITI proposes transparency in 

extraction, but after all it enhances extraction. 

Physical and objective information about <strong>the</strong> amount <strong>of</strong> available resources, <strong>the</strong>ir 

composition and quality, <strong>the</strong> ore grades, <strong>the</strong> quantity <strong>of</strong> energy and water required 

for extraction, <strong>the</strong> amount <strong>of</strong> waste rock and o<strong>the</strong>r physical parameters that would 

allow an objective analysis <strong>of</strong> <strong>the</strong> state <strong>of</strong> our <strong>mineral</strong> <strong>capital</strong> is rarely published. In 

fact, in many cases this information is hidden or distorted by companies, institutions 

or even governments for <strong>the</strong>ir own economic benefits. The EITI simply ignores this 

issue. What really matters is <strong>the</strong> amount <strong>of</strong> money produced by a country through 

<strong>the</strong> extraction <strong>of</strong> its <strong>mineral</strong> resources, for carrying out a more transparent and credible 

management in <strong>the</strong> international markets. In short, it is about where do <strong>the</strong> 

pr<strong>of</strong>its from extraction go to and in any case, maximize <strong>the</strong>m for a more universal 

and fair benefit. But <strong>the</strong> possibility <strong>of</strong> reducing or stopping extraction is not even 

questioned.


8.5.3 The need for an accountability <strong>the</strong>ory <strong>of</strong> <strong>mineral</strong> resources. The 

Physical Geonomics 

On <strong>the</strong> o<strong>the</strong>r hand, it is surprising how <strong>the</strong> <strong>mineral</strong>’s wealth classification has been 

carried out traditionally through purely qualitative criteria: <strong>the</strong> terms reserves or 

resources are accompanied by adjectives like economically or technically feasible to 

extract, hypo<strong>the</strong>tical, identified, indicated, probable, etc. The definition is usually 

imprecise and depends generally on those owning <strong>the</strong> data, who diminish or increase 

<strong>the</strong> resources for <strong>the</strong>ir own interest. 

The countries account economically for <strong>the</strong>ir increase <strong>of</strong> wealth through <strong>the</strong> GDP 

indicator. However, <strong>the</strong> physical wealth, its decline and its eventual replacement 

does not appear in any national account. The depletion <strong>of</strong> natural resources <strong>of</strong> a 

country are seen as an asset that generates immediate wealth. Nei<strong>the</strong>r <strong>the</strong> associated 

pollution, nor <strong>the</strong> loss <strong>of</strong> wealth are considered in <strong>the</strong> national accounts <strong>of</strong> <strong>the</strong> 

countries. It is as if we would sell <strong>the</strong> bricks <strong>of</strong> ca<strong>the</strong>drals to tourists, <strong>the</strong>reby increasing 

<strong>the</strong> wealth <strong>of</strong> local people. As stated by Seymour and Zadek [305], we need to 

examine <strong>the</strong> underlying assumptions about energy and <strong>the</strong> environment on which 

today’s governance and accountability systems have been built. Such an assessment 

challenges us to develop a new generation <strong>of</strong> institutions with system <strong>of</strong> rules for 

our economy and politics which incorporates energy, materials and water scarcity 

and environmental fragility into its design. This will require dramatic innovations 

moving forward in our understanding and practice <strong>of</strong> governance and accountability. 

As long as <strong>the</strong>re is not a unifying <strong>the</strong>ory that allows to convert quantities, compositions 

and ore grades into non monetary units and thus not subject to variabilities 

beyond mining extraction such as currency value, this physical and parallel accountability 

will probably remain in <strong>the</strong> level <strong>of</strong> dialectic speeches. 

But this PhD, and in general, <strong>the</strong> development <strong>of</strong> <strong>the</strong> Exergoecology approach, could 

break this <strong>the</strong>oretical barrier and provoke a global stream in favor <strong>of</strong> <strong>the</strong> physical accountability 

<strong>of</strong> <strong>the</strong> <strong>mineral</strong> wealth on a global and local scale and disaggregated by 

<strong>mineral</strong> type, companies involved, etc. Hence, we propose a physical accountability 

<strong>of</strong> <strong>mineral</strong> resources taking into account at least three physical properties: quantity, 

composition and ore grade. Additionally, an estimation <strong>of</strong> <strong>the</strong> environmental impact 

for <strong>the</strong> opening, exploitation and shutdown <strong>of</strong> mining activities in terms <strong>of</strong> energy, 

water and material costs (not only in economic cost-effective terms) should be required. 

This is, mining resources should be evaluated in <strong>the</strong> same way as industrial 

products, which can be assessed through <strong>the</strong> Life Cycle Assessment methodology. On 

<strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> relationship between physical and monetary cost will be always 

possible through energy prices. This could at <strong>the</strong> same time keep <strong>the</strong> objectivity <strong>of</strong> 

physical data and <strong>the</strong> more intelligible meaning <strong>of</strong> monetary units. 

In any case, more high quality data collection processes and better indicators are 

required. Despite <strong>of</strong> <strong>the</strong> enormous currently available IT means, governmental agencies 

do not have <strong>the</strong> <strong>mineral</strong>ogical information level attained until <strong>the</strong> seventies <strong>of</strong>


last century. Those series and <strong>the</strong> critical mass built around <strong>the</strong> knowledge about 

<strong>the</strong> <strong>mineral</strong>ogical wealth <strong>of</strong> <strong>the</strong> countries and <strong>the</strong>ir yearly physical exploitation and 

associated impacts, were progressively disappearing throughout <strong>the</strong> 20th century. 

This was due to <strong>the</strong> neoliberal streams that transferred to <strong>the</strong> private initiative and 

<strong>the</strong> markets, <strong>the</strong> responsibility <strong>of</strong> <strong>mineral</strong> extraction. The government agencies that 

carried out <strong>the</strong> surveys through a network <strong>of</strong> experts were converted into research 

institutes, leaving <strong>the</strong> systematic and controlled knowledge <strong>of</strong> <strong>the</strong> <strong>mineral</strong> and natural 

environment. Under this information and databases gap, it is impossible to 

develop laws for improving <strong>the</strong> governance <strong>of</strong> national and global resources. Because 

in practical terms, current economy considers that we live in a planet full <strong>of</strong> 

resources and it is only a matter <strong>of</strong> prices, i.e. <strong>of</strong> supply and demand, <strong>the</strong> solution <strong>of</strong> 

<strong>the</strong> scarcity problem. 

The <strong>the</strong>oretical principles <strong>of</strong> Exergoecology, stated in this <strong>the</strong>sis and in preceding 

studies show <strong>the</strong> way. Never<strong>the</strong>less, it is necessary to work in <strong>the</strong> field and put 

into practice <strong>the</strong>se principles. This is already happening with <strong>the</strong> recent developed 

methodology for water cost assessment called “Physical Hydronomics” developed 

by Valero et al. [412], [372], which is based on <strong>the</strong> principles <strong>of</strong> Exergoecology. 

Physical Hydronomics assesses <strong>the</strong> physical cost <strong>of</strong> a water body along its course 

with a single unit <strong>of</strong> measure, exergy, which accounts for chemical quality, height, 

temperature, velocity and flow. This way, any natural or human alteration <strong>of</strong> <strong>the</strong> 

water body can be physically accounted for. Through <strong>the</strong> exergy replacement costs, 

we have an objective tool for environmental cost assessment, allowing an alternative 

management <strong>of</strong> water bodies for a certain region. The rules or accounting principles 

are being developed thanks to specific experiences were problems are detected and 

solved by <strong>the</strong> simple method <strong>of</strong> learning by doing. 

In <strong>the</strong> same way, this <strong>the</strong>sis proposes as final corollary a new accounting tool for 

<strong>the</strong> management <strong>of</strong> <strong>the</strong> <strong>mineral</strong> wealth on earth, including not only fossil fuels, but 

also <strong>the</strong> much more complex and apparently less relevant information <strong>of</strong> non-fuel 

<strong>mineral</strong>s. We propose to call this tool “Physical Geonomics”. Obviously, <strong>the</strong> accounting 

principles on which it is based will be created through <strong>the</strong> learning by doing 

technique. If Exergoecology considers that a <strong>mineral</strong> deposit is a <strong>the</strong>rmodynamic 

system that contains exergy because it is differentiated from its environment, <strong>the</strong> 

accounting principles that allow to convert <strong>the</strong> <strong>the</strong>ory into numbers should be fur<strong>the</strong>r 

developed. And this should be carried out not only for exergy, but also for <strong>the</strong> 

exergy replacement costs. The latter provide more significant numbers, but are more 

arbitrary, since <strong>the</strong>y depend on technologies and hence on international agreements. 

Physical Geonomics should not only account for <strong>the</strong> <strong>mineral</strong>s extracted from <strong>the</strong> 

planet, but also for those that are being recycled. Consequently, we could obtain 

a global accountancy <strong>of</strong> <strong>the</strong> planetary stocks <strong>of</strong> chemical elements available for 

mankind in a certain period <strong>of</strong> time. This would allow to detect <strong>the</strong> quantity <strong>of</strong> 

<strong>mineral</strong>s that have been returned to <strong>the</strong> planet in a complete dispersed way. That 

quantity is always positive, what tells us that <strong>the</strong> planet inexorably approaches <strong>the</strong> 

degraded state. The assessment <strong>of</strong> that entropic planet will have to be fur<strong>the</strong>r de-


veloped in o<strong>the</strong>r studies for thinking over <strong>the</strong> degradation velocity <strong>of</strong> our planetary 

resources. 

Can we move to more efficient, equitable and cleaner use <strong>of</strong> <strong>the</strong> earth’s resources by 

shifting conventional accountability practices into physical accounting systems? The 

answer is not simply a clear “yes”, but we think that Physical Geonomics proposed 

in this <strong>the</strong>sis can positively help in this task. 


This chapter has extrapolated at planetary level, <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> exergy degradation 

<strong>of</strong> <strong>mineral</strong> reserves carried out before for Australia. For that purpose, many 

assumptions had to be made at <strong>the</strong> expense <strong>of</strong> accuracy loss in <strong>the</strong> results. This 

is because <strong>the</strong>re is an important information gap about current and historical data 

<strong>of</strong> many commodities. Bearing in mind <strong>the</strong>se considerations, we have been able to 

give a rough estimate <strong>of</strong> <strong>the</strong> <strong>mineral</strong> loss on earth since <strong>the</strong> beginning <strong>of</strong> <strong>the</strong> 20th 

century, <strong>the</strong> earth’s degradation velocity, <strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> reserves and 

reserve base, <strong>the</strong> years until depletion <strong>of</strong> <strong>the</strong> commodities, and <strong>the</strong> year where <strong>the</strong> 

peak <strong>of</strong> production is reached for <strong>the</strong> main <strong>mineral</strong>s extracted on earth. 

According to our calculations, <strong>the</strong> irreversible exergy distance D ∗ <strong>of</strong> <strong>the</strong> 51 non-fuel 

<strong>mineral</strong> commodities analyzed is at least 51 Gtoe, consumed at an average exergy 

degradation velocity ˙D ∗ <strong>of</strong> 1,3 Gtoe/year in <strong>the</strong> last decade. This means that with 

current technology, <strong>the</strong> replacement <strong>of</strong> all depleted non-fuel commodities would 

require a third <strong>of</strong> current world fuel oil reserves (178 Gtoe). 

The exergy degradation <strong>of</strong> <strong>the</strong> non-fuel <strong>mineral</strong> reserves on earth is clearly dominated 

by <strong>the</strong> extraction <strong>of</strong> iron, aluminium and to a lesser extent <strong>of</strong> copper. Never<strong>the</strong>less, 

<strong>the</strong> latter three <strong>mineral</strong>s are not <strong>the</strong> most depleted commodities. We have 

stated that <strong>the</strong> reserves <strong>of</strong> mercury, silver, gold, tin, arsenic, antimony and lead are 

suffering <strong>the</strong> greatest scarcity problems. On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> <strong>mineral</strong>s <strong>of</strong> cesium, 

thorium, REE, iodine, vanadium, PGM’s, tantalum, aluminium, cobalt and niobium 

are <strong>the</strong> least depleted commodities. 

For <strong>the</strong> most extracted non-fuel <strong>mineral</strong>s on earth, we have applied <strong>the</strong> Hubbert 

bell-shaped curve, assuming that only <strong>the</strong> reserve base published by <strong>the</strong> USGS [362] 

are available for extraction. Accordingly, we have obtained that <strong>the</strong> peak <strong>of</strong> production 

for iron, aluminium and copper is reached in years 2068, 2057 and 2024, 

respectively. 

With respect to fossil fuels, we have stated that in exergy terms, oil has been <strong>the</strong> most 

consumed fuel, accounting for 42% <strong>of</strong> <strong>the</strong> total fuel exergy degradation in <strong>the</strong> 20th 

century (coal and natural gas accounted for 38 and 20%, respectively). The total 

fuel’s exergy depleted between 1900 and 2006 is estimated at 382 Gtoe, consumed 

at an average exergy degradation velocity <strong>of</strong> 9 Gtoe/year in <strong>the</strong> last decade. The 

degradation corresponds to 30,5% <strong>of</strong> total world’s proven fuel reserves in 2006.


Hubbert’s bell shaped curves applied to <strong>the</strong> exergy production <strong>of</strong> fossil fuels revealed 

that <strong>the</strong> peak <strong>of</strong> coal will be reached in year 2060, <strong>of</strong> natural gas in 2023, and <strong>of</strong> oil 

in 2008. The latter value fits very well with <strong>the</strong> predictions <strong>of</strong> o<strong>the</strong>r authors, who 

estimated that <strong>the</strong> peak year <strong>of</strong> world oil will be between 2004 and 2008. Fur<strong>the</strong>rmore, 

it gives sense to <strong>the</strong> radical increase <strong>of</strong> oil prices registered recently. The price 

<strong>of</strong> a barrel <strong>of</strong> crude has been doubled in just one year, surpassing in January 2008, 

<strong>the</strong> psychological barrier <strong>of</strong> 100 $US. 

If we add <strong>the</strong> exergy loss <strong>of</strong> fossil fuels to <strong>the</strong> exergy replacement costs <strong>of</strong> non-fuel 

<strong>mineral</strong>s, we obtain that man has depleted in <strong>the</strong> 20th century a total <strong>of</strong> 433 Gtoe. 

In 2006, <strong>the</strong> exergy <strong>of</strong> <strong>mineral</strong> deposits was depleted at a degradation velocity <strong>of</strong> 

around 12 Gtoe. Fur<strong>the</strong>rmore, considering all main <strong>mineral</strong> resources on earth, we 

have estimated that <strong>the</strong> peak <strong>of</strong> production will be reached in year 2034. 

The exergy <strong>of</strong> <strong>mineral</strong> reserves can be also affected by <strong>the</strong> conditions <strong>of</strong> <strong>the</strong> environment. 

With <strong>the</strong> help <strong>of</strong> <strong>the</strong> IPPC’s reference scenarios, we were able to estimate 

<strong>the</strong> exergy loss <strong>of</strong> fuels due to <strong>the</strong> increase <strong>of</strong> GHG emissions in <strong>the</strong> atmosphere 

and <strong>the</strong> temperature rise. According to our calculations, <strong>the</strong> exergy <strong>of</strong> fossil fuels 

could decrease to up to 0,40%, if <strong>the</strong> current CO 2 concentration in <strong>the</strong> atmosphere 

doubles. 

Finally, we have made an estimation <strong>of</strong> <strong>the</strong> possible depletion degree that <strong>mineral</strong> 

reserves might suffer in <strong>the</strong> 21st century. For that purpose, we took into account 

seven different scenarios. 

In <strong>the</strong> first scenario, we assumed that production <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> commodities 

extracted, namely coal, oil, natural gas, iron, aluminium and copper, would follow 

<strong>the</strong> bell-shaped curves calculated before. Accordingly, <strong>the</strong> global <strong>mineral</strong> exergy 

decrease in <strong>the</strong> period between 1900 and 2100 would be near 1300 Gtoe. Fur<strong>the</strong>rmore, 

at <strong>the</strong> end <strong>of</strong> <strong>the</strong> 21st century, man would have depleted around 82% <strong>of</strong> <strong>the</strong> 

reserve base available in 1900. 

The o<strong>the</strong>r six case studies correspond to <strong>the</strong> IPPC’s SRES scenarios concerning fossil 

fuel consumption. For non-fuel <strong>mineral</strong>s, we assumed that world resources, ra<strong>the</strong>r 

than <strong>the</strong> reserve base are available for extraction. Additionally, we have taken into 

account <strong>the</strong> exergy loss <strong>of</strong> fuels due to <strong>the</strong> emission <strong>of</strong> greenhouse gases to <strong>the</strong> 

atmosphere. 

All IPCC’s scenarios involve greater degradation degrees <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves than 

in <strong>the</strong> case where <strong>the</strong> Hubbert behavior has been assumed. In <strong>the</strong> worst case, <strong>the</strong> 

exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources degraded exceeds 3100 Gtoe. This indicates that 

for satisfying <strong>the</strong> energy consumption assumed in <strong>the</strong> SRES scenarios, <strong>the</strong> proven 

reserves <strong>of</strong> coal, oil and natural gas should increase considerably. Although new 

discoveries are indeed increasing <strong>the</strong> reserves <strong>of</strong> many <strong>mineral</strong> resources, it remains 

to be seen whe<strong>the</strong>r <strong>the</strong> rate <strong>of</strong> discoveries and <strong>the</strong> reclassification <strong>of</strong> <strong>mineral</strong> reserves 

as recoverable are sufficient enough to supply <strong>the</strong> huge future <strong>mineral</strong> demand.


In <strong>the</strong> final reflections <strong>of</strong> this PhD, we have taken up again <strong>the</strong> ideas provided by 

Meadows et al. [218] in <strong>the</strong>ir book “The Limits to Growth”. In view <strong>of</strong> <strong>the</strong> results 

obtained in this study, we have stated that <strong>the</strong> message <strong>of</strong> <strong>the</strong> Club <strong>of</strong> Rome was 

not as false as many claimed, even if <strong>the</strong> last decades <strong>of</strong> <strong>the</strong> 20th century indicated 

<strong>the</strong> contrary. In fact, we have reached a point in which we might think about limiting 

radically extraction and living only with <strong>the</strong> already extracted materials. This 

is recycling, ra<strong>the</strong>r than wasting should be promoted. But nowadays, this practice 

would be impossible to undertake, as many economies are sustained by <strong>the</strong> extraction 

<strong>of</strong> resources. Hence, <strong>the</strong> realistic requirement now is to promote conservation 

measures for assuring enough resources for coming generations and a more rational 

management <strong>of</strong> <strong>the</strong> extraction and use <strong>of</strong> <strong>mineral</strong>s. 

We have stated that conventional measures <strong>of</strong> energy efficiency, renewable energies, 

CO 2 sequestration, etc., are not enough for achieving sustainability. We believe that 

a drastic world reduction and an appropriate management <strong>of</strong> <strong>the</strong> massive use <strong>of</strong> 

<strong>the</strong> extractive mining industry should be also required. For that purpose, global 

agreements are a must. 

An appropriate management should be based on a solid, transparent and objective 

physical accountability system <strong>of</strong> resources. As final corollary <strong>of</strong> this PhD, we have 

proposed a new accountability tool for <strong>the</strong> management <strong>of</strong> <strong>the</strong> <strong>mineral</strong> wealth on 

earth, based on <strong>the</strong> Exergoecological principles stated in this study. We have proposed 

to call this tool “Physical Geonomics”. Obviously, <strong>the</strong> accounting principles on 

which it is based will have to be fur<strong>the</strong>r developed through <strong>the</strong> learning by doing 

technique.


Chapter 9 

Conclusions 

In this chapter, a syn<strong>the</strong>sis <strong>of</strong> this PhD is accomplished and <strong>the</strong> main scientific contributions 

<strong>of</strong> <strong>the</strong> work are outlined. Finally, <strong>the</strong> perspectives <strong>of</strong> future interesting 

studies that have arisen from this PhD are presented. 

9.2 Syn<strong>the</strong>sis <strong>of</strong> <strong>the</strong> PhD 

The aim <strong>of</strong> this PhD has been <strong>the</strong> assessment <strong>of</strong> <strong>the</strong> resources available on earth and 

<strong>the</strong>ir degradation velocity, due to human action. This has been accomplished under 

<strong>the</strong> framework <strong>of</strong> <strong>the</strong> exergoecological analysis. The latter allows to value <strong>mineral</strong> 

resources, according to <strong>the</strong> physical cost that would require to obtain <strong>the</strong>m from 

<strong>the</strong> materials contained in a hypo<strong>the</strong>tical earth that has reached <strong>the</strong> maximum level 

<strong>of</strong> deterioration. In o<strong>the</strong>r words, it quantifies <strong>the</strong> physical cost <strong>of</strong> restoring natural 

resources from a degraded state in <strong>the</strong> so called reference environment to <strong>the</strong> conditions 

in which <strong>the</strong>y are currently presented in nature. The exergoecology approach 

uses <strong>the</strong> property exergy as <strong>the</strong> universal unit <strong>of</strong> measure. The main advantage <strong>of</strong> its 

use with respect to o<strong>the</strong>r physical indicators is that in a single property, all <strong>the</strong> physical 

features <strong>of</strong> a resource are accounted for. Fur<strong>the</strong>rmore, exergy has <strong>the</strong> capability 

<strong>of</strong> aggregating heterogeneous energy and material assets. This is not <strong>the</strong> case, if <strong>the</strong> 

assessment is carried out in terms <strong>of</strong> mass, because we cannot add tons <strong>of</strong> oil with 

tons <strong>of</strong> gold, for instance. Unlike standard economic valuations, <strong>the</strong> exergy analysis 

gives objective information since it is not subject to monetary policy, or currency 

speculation. 

This PhD has been structured into two different parts. The first one, <strong>of</strong> an eminently 

geological and geochemical character, has described and modeled <strong>the</strong> geochemistry 

331

332 CONCLUSIONS 

<strong>of</strong> <strong>the</strong> earth and its resources. The second part has developed and used <strong>the</strong> <strong>the</strong>rmodynamic 

tools required for analyzing <strong>the</strong> state <strong>of</strong> our planet. 

In chapter 2, a comprehensive analysis <strong>of</strong> <strong>the</strong> physical and geochemical features <strong>of</strong> 

<strong>the</strong> earth has been undertaken as a starting point for determining its properties. 

First, a coarse composition <strong>of</strong> <strong>the</strong> bulk earth with <strong>the</strong> relative mass proportions <strong>of</strong> 

each sphere has been presented. This overview has given way to <strong>the</strong> more detailed 

explanation <strong>of</strong> <strong>the</strong> geochemistry <strong>of</strong> <strong>the</strong> atmosphere, hydrosphere and upper continental 

crust, which are <strong>the</strong> layers <strong>of</strong> <strong>the</strong> earth with which man interacts. 

It has been stated that <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> atmosphere is ra<strong>the</strong>r uniform 

to heights up to 100 km. Apart from <strong>the</strong> natural occurring gases, <strong>the</strong>re are traces <strong>of</strong> 

anthropogenic substances in <strong>the</strong> atmosphere that may alter <strong>the</strong> conditions on earth. 

The hydrosphere is composed by <strong>the</strong> oceans (representing over 97% <strong>of</strong> <strong>the</strong> hydrosphere’s 

volume), renewable water resources (rivers, lakes and underground water), 

ice, and atmospheric water. As it happens to <strong>the</strong> atmosphere, <strong>the</strong> composition <strong>of</strong> seawater 

is quite uniform. On <strong>the</strong> contrary, <strong>the</strong> composition <strong>of</strong> <strong>the</strong> rest hydrosphere’s 

components may vary from place to place. Never<strong>the</strong>less, some examples and averages 

have been provided for all water reservoirs. 

The continental crust is <strong>the</strong> outer layer <strong>of</strong> <strong>the</strong> solid earth, and is composed by <strong>the</strong> 

core, mantle and crust. The crust is fur<strong>the</strong>r divided into <strong>the</strong> lower, middle and 

upper crust. We have focused our attention only in <strong>the</strong> upper part <strong>of</strong> it, as it is 

<strong>the</strong> reservoir <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s and o<strong>the</strong>r natural resources for mankind. The 

chemical composition <strong>of</strong> <strong>the</strong> upper continental crust in terms <strong>of</strong> <strong>mineral</strong>s is well 

known, although it is still subject <strong>of</strong> numerous updates. However, its composition in 

terms <strong>of</strong> <strong>mineral</strong>s has been barely studied. 

Since <strong>the</strong> determination <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> upper continental 

crust requires <strong>the</strong> knowledge <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s included in it, <strong>the</strong> aim <strong>of</strong> chapter 3 was 

to obtain a model <strong>of</strong> its <strong>mineral</strong>ogical composition. 

For that purpose, a revision <strong>of</strong> <strong>the</strong> studies concerning <strong>the</strong> <strong>mineral</strong>ogical composition 

<strong>of</strong> <strong>the</strong> earth’s crust was carried out. It was stated, that <strong>the</strong> heterogeneity and complexity 

<strong>of</strong> <strong>the</strong> crust have hindered deep and accurate studies <strong>of</strong> its composition in 

terms <strong>of</strong> <strong>mineral</strong>s. In fact a single author N.A. Grigor’ev has been very recently <strong>the</strong> 

first one in giving a comprehensive <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> upper crust. 

We checked <strong>the</strong> satisfaction <strong>of</strong> <strong>the</strong> mass balance between <strong>the</strong> <strong>mineral</strong>s proposed by 

Grigor’ev and <strong>the</strong> better known chemical composition in terms <strong>of</strong> elements <strong>of</strong> <strong>the</strong> 

upper crust. The no satisfaction <strong>of</strong> <strong>the</strong> mass balance, lead us to update Grigor’ev’s 

composition. The methodology used minimizes <strong>the</strong> difference between Grigor’ev’s 

and our target composition, under <strong>the</strong> constraint <strong>of</strong> assuring chemical coherence 

with <strong>the</strong> average chemical composition <strong>of</strong> <strong>the</strong> earth’s crust in terms <strong>of</strong> elements. 

Fur<strong>the</strong>rmore, <strong>the</strong> final composition includes important <strong>mineral</strong>s not taken into account 

in Grigor’ev’s analysis. As a result, we obtained an estimate <strong>of</strong> <strong>the</strong> average

Syn<strong>the</strong>sis <strong>of</strong> <strong>the</strong> PhD 333 

<strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> upper crust, consisting <strong>of</strong> <strong>the</strong> 307 most abundant 

<strong>mineral</strong>s. 

The composition obtained should not be considered as final and closed, since many 

assumptions had to be made. Never<strong>the</strong>less, it is <strong>the</strong> first step for obtaining a coherent 

<strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> crust. 

Chapter 4 closes <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> earth’s components (Part I <strong>of</strong> this report), by 

undertaking a review <strong>of</strong> <strong>the</strong> different natural resources useful to man. 

Generally, information is available for most <strong>of</strong> <strong>the</strong> energy resources. This is not <strong>the</strong> 

case for non-fuel <strong>mineral</strong>s, where <strong>the</strong> data is <strong>of</strong>ten scarce and inaccurate. 

Hence at a first step, <strong>the</strong> revision was focused on <strong>the</strong> energy sources <strong>of</strong> renewable 

and non renewable nature. With <strong>the</strong> most updated information sources, <strong>the</strong> available 

energy, potential energy use and current world energy consumption has been 

provided. The energy resources studied were: geo<strong>the</strong>rmal, nuclear, tidal, solar, wind 

and ocean power, as well as biomass, coal, natural gas, oil and unconventional fuels. 

For <strong>the</strong> most important non-fuel <strong>mineral</strong>s, <strong>the</strong> current production, and <strong>the</strong> available 

reserves, reserve base and world resources has been obtained from <strong>the</strong> US Geological 

Survey. But as opposed to fossil fuels, <strong>the</strong> abundance <strong>of</strong> <strong>mineral</strong>s is not important 

if <strong>the</strong>se are dispersed throughout <strong>the</strong> crust. Therefore, <strong>the</strong> grade <strong>of</strong> <strong>the</strong> <strong>mineral</strong> 

deposits is also required for assessing <strong>the</strong> state <strong>of</strong> <strong>mineral</strong> resources. From different 

information sources, we were able to estimate world <strong>mineral</strong> average ore grades. 

Part II <strong>of</strong> this PhD begins in chapter 5 with <strong>the</strong> description <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic 

models required for assessing <strong>the</strong> properties <strong>of</strong> <strong>the</strong> earth and its resources. 

In order to obtain <strong>the</strong> exergy <strong>of</strong> any substance, a reference environment (R.E.) 

should be defined. Therefore, <strong>the</strong> first aim <strong>of</strong> chapter 5 was to select an appropriate 

R.E. for <strong>the</strong> exergy assessment <strong>of</strong> <strong>the</strong> <strong>mineral</strong> <strong>capital</strong> on earth. 

For that purpose, <strong>the</strong> different R.E. proposed so far were reviewed. It was stated, 

that <strong>the</strong> best suitable available R.E. for determining <strong>the</strong> exergy <strong>of</strong> natural resources 

was <strong>the</strong> one based on Szargut’s criterion. Hence, Szargut’s R.E. [336], later modified 

by Ranz [276], was updated and adapted to our requirements with <strong>the</strong> help <strong>of</strong> new 

geochemical information and <strong>the</strong> model <strong>of</strong> continental crust developed in this PhD. 

Next, we analyzed <strong>the</strong> energy involved in <strong>the</strong> formation processes <strong>of</strong> a <strong>mineral</strong> deposit 

from a defined R.E., and provided <strong>the</strong> equations required for <strong>the</strong> exergy calculation 

<strong>of</strong> <strong>mineral</strong>s. We stated that <strong>the</strong> minimum exergy embedded in a <strong>mineral</strong> has 

two components, one based on <strong>the</strong> chemical composition and <strong>the</strong> o<strong>the</strong>r one on its 

concentration or ore grade. The first parameter accounts for <strong>the</strong> formation <strong>of</strong> <strong>the</strong> 

<strong>mineral</strong> from <strong>the</strong> R.E. The concentration exergy expresses <strong>the</strong> minimum energy that 

nature had to spend to bring <strong>the</strong> <strong>mineral</strong>s from <strong>the</strong> concentration in <strong>the</strong> reference 

state to <strong>the</strong> concentration in <strong>the</strong> mine. We saw, that <strong>the</strong> latter shows a negative logarithmic 

pattern with <strong>the</strong> grade. This means that as <strong>the</strong> ore grade <strong>of</strong> <strong>the</strong> mine tends 

to zero, <strong>the</strong> exergy <strong>of</strong> <strong>the</strong> deposit approaches also zero and <strong>the</strong> exergy required for 

replacing <strong>the</strong> mine tends to infinity.


In <strong>the</strong>ory, <strong>the</strong> exergy <strong>of</strong> fossil fuels can be calculated with <strong>the</strong> general formulas provided 

for <strong>mineral</strong>s. However, <strong>the</strong> complexity <strong>of</strong> <strong>the</strong>ir chemical structure, makes this 

task very difficult and special calculation procedures are applied. It was stated that 

<strong>the</strong> chemical exergy <strong>of</strong> fossil fuels can be in many cases approximated to its HHV. Never<strong>the</strong>less, 

we used <strong>the</strong> different formulas developed by Valero and Lozano [369], 

since <strong>the</strong>y take into account <strong>the</strong> conditions <strong>of</strong> <strong>the</strong> environment. 

Generally, <strong>the</strong> minimum exergy values are very small, if compared to <strong>the</strong> real energy 

required for <strong>the</strong> replacement <strong>of</strong> natural resources to <strong>the</strong>ir original state. In order to 

account for <strong>the</strong> inefficiencies <strong>of</strong> man-made processes, <strong>the</strong> exergy values are multiplied 

by <strong>the</strong> unit exergy replacement costs. These are dimensionless and measure 

<strong>the</strong> number <strong>of</strong> exergy units needed to obtain one unit <strong>of</strong> exergy <strong>of</strong> <strong>the</strong> product. The 

resulting exergy costs represent <strong>the</strong> exergy required by <strong>the</strong> given available technology 

to return a resource into <strong>the</strong> physical and chemical conditions in which it was 

delivered by <strong>the</strong> ecosystem. As opposed to exergy, exergy costs cannot be considered 

as a property <strong>of</strong> <strong>the</strong> resource, since unit exergy costs introduce an arbitrary factor 

to <strong>the</strong> calculation. Never<strong>the</strong>less, <strong>the</strong>y can be used as a suitable indicator for assessing 

<strong>the</strong> value <strong>of</strong> non-fuel <strong>mineral</strong> resources, as <strong>the</strong>y integrate in one parameter, 

concentration, composition and also <strong>the</strong> state <strong>of</strong> technology. 

The chapter ends with <strong>the</strong> description <strong>of</strong> <strong>the</strong> twelve semi-<strong>the</strong>oretical models for <strong>the</strong> 

estimation <strong>of</strong> enthalpies and Gibbs free energies <strong>of</strong> formation, required for <strong>the</strong> calculation 

<strong>of</strong> <strong>the</strong> chemical exergy <strong>of</strong> <strong>mineral</strong>s. 

In chapter 6, <strong>the</strong> standard <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> main constituents <strong>of</strong> 

<strong>the</strong> outer earth’s spheres have been provided for <strong>the</strong> first time. That is <strong>the</strong> standard 

enthalpy, Gibbs free energy and chemical exergy <strong>of</strong> more than 330 natural 

substances. The enthalpies and Gibbs free energies, have been obtained ei<strong>the</strong>r from 

<strong>the</strong> literature, or have been calculated with <strong>the</strong> 12 estimation methods described 

in <strong>the</strong> previous chapter. The exergy <strong>of</strong> <strong>the</strong> substances has been calculated with <strong>the</strong> 

chemical exergies <strong>of</strong> <strong>the</strong> elements, generated with <strong>the</strong> R.E. developed in this PhD. 

Through <strong>the</strong> molar fractions <strong>of</strong> <strong>the</strong> substances in each layer, determined in part I 

<strong>of</strong> this report, we were able to determine <strong>the</strong> average <strong>the</strong>rmodynamic properties 

<strong>of</strong> <strong>the</strong> atmosphere, hydrosphere (divided into seawater, rivers, glacial run<strong>of</strong>f and 

groundwater) and upper continental crust. 

It has been stated, that all negative ions in <strong>the</strong> hydrosphere throw up negative chemical 

exergies. Additionally, some substances <strong>of</strong> <strong>the</strong> continental crust show also 

negative exergy values. This is because <strong>the</strong> reference species <strong>of</strong> our R.E. are more 

stable than <strong>the</strong> considered substance. This lead us to question <strong>the</strong> suitability <strong>of</strong> <strong>the</strong> 

R.E. developed in this PhD, for natural resource accounting. Fur<strong>the</strong>rmore, this R.E. 

differs substantially from <strong>the</strong> model <strong>of</strong> degraded earth that should become. 

The degraded earth could be assimilated to a dead planet, with an atmosphere similar 

to <strong>the</strong> current one, but with a higher CO 2 concentration due to <strong>the</strong> burning 

<strong>of</strong> fossil fuels, a hydrosphere were all fresh waters are mixed with salt water, and


a continental crust without fossil fuels or concentrated <strong>mineral</strong> deposits. Since <strong>the</strong> 

relative quantity <strong>of</strong> freshwater with respect to saltwater on earth is irrelevant, <strong>the</strong> hydrosphere 

<strong>of</strong> this hypo<strong>the</strong>tical earth has <strong>the</strong> same composition <strong>of</strong> <strong>the</strong> oceans. Something 

similar occurs with <strong>the</strong> continental crust, <strong>the</strong> abundance <strong>of</strong> <strong>mineral</strong> deposits 

and fossil fuels is negligible when compared to <strong>the</strong> whole continental crust. Hence, 

<strong>the</strong> composition <strong>of</strong> <strong>the</strong> degraded crust can be approximated to <strong>the</strong> model developed 

in this PhD. 

From this model <strong>of</strong> degraded earth firstly defined in this PhD, we could recalculate 

<strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> elements. We think that <strong>the</strong> calculation procedures and 

even <strong>the</strong> philosophy for obtaining <strong>the</strong> chemical exergies <strong>of</strong> <strong>the</strong> elements should be 

reviewed, since <strong>the</strong> selection <strong>of</strong> an appropriate R.E. is a required but not a sufficient 

condition. However, this activity remains open for fur<strong>the</strong>r studies in <strong>the</strong> future. 

Despite <strong>of</strong> <strong>the</strong> limitations <strong>of</strong> <strong>the</strong> R.E. developed here with Szargut’s methodology, it 

still constitutes a tool for obtaining chemical exergies. Since <strong>the</strong> mass <strong>of</strong> <strong>the</strong> earth 

and <strong>of</strong> its spheres is known, we were able to calculate <strong>the</strong> absolute chemical exergy 

<strong>of</strong> <strong>the</strong> atmosphere, hydrosphere and upper continental crust: 6, 27×10 3 , 7, 80×10 5 

and 1, 21 × 10 9 Gtoe, respectively. Of course <strong>the</strong>se are very rough numbers, and are 

subject to ulterior updates, especially when a more appropriate R.E. is found. But 

<strong>the</strong>y are good enough, for providing an order <strong>of</strong> magnitude <strong>of</strong> <strong>the</strong> huge chemical 

wealth <strong>of</strong> our planet. 

The second part <strong>of</strong> chapter 6 has provided an inventory <strong>of</strong> <strong>the</strong> most important energy 

resources and non-fuel <strong>mineral</strong>s on earth, expressed through a single unit <strong>of</strong> measure: 

exergy. We have stated that <strong>the</strong>re is a huge amount <strong>of</strong> energy sources on 

earth, <strong>of</strong> both renewable and non-renewable nature. There are many energy alternatives 

that could replace fossil fuels when <strong>the</strong>y become depleted. But obviously <strong>the</strong> 

technology for recovering <strong>the</strong>se alternatives needs to be fur<strong>the</strong>r developed. 

Despite <strong>of</strong> <strong>the</strong> enormous chemical exergy <strong>of</strong> our planet, only 0,01% <strong>of</strong> that amount 

can be considered as available for human use. With current technology, it is impossible 

to use <strong>the</strong> chemical exergy <strong>of</strong> dispersed substances. And only those <strong>mineral</strong>s that 

are concentrated, can be considered as resources. In <strong>the</strong> short run, technological development 

will allow substitution among <strong>mineral</strong>s, but this can only last whenever 

o<strong>the</strong>r concentrated <strong>mineral</strong> stocks are available. 

Hence, we have stated that <strong>the</strong> scarcity problems that man could be facing are based 

on <strong>the</strong> use <strong>of</strong> materials, ra<strong>the</strong>r than on <strong>the</strong> use energy sources. This is why recycling 

and especially, <strong>the</strong> search <strong>of</strong> a dematerialized society becomes essential, in order to 

be consistent with <strong>the</strong> sustainability doctrine. 

In chapter 7, we have included <strong>the</strong> time dimension in <strong>the</strong> exergy evaluation <strong>of</strong> <strong>mineral</strong> 

<strong>capital</strong> on earth. 

We stated that nei<strong>the</strong>r mass, nor energy are appropriate indicators for assessing <strong>the</strong> 

degradation <strong>of</strong> <strong>mineral</strong> wealth on earth, as <strong>the</strong>y are conservative properties. On <strong>the</strong> 

contrary, in all physical transformations <strong>of</strong> matter or energy, it is always exergy that


is lost. Therefore, any degradation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> <strong>capital</strong> which can come ei<strong>the</strong>r 

from an alteration in its composition, a decrease <strong>of</strong> its concentration, or a change in 

<strong>the</strong> reference environment, can be accounted for with exergy. 

Starting from <strong>the</strong> property exergy, we have built a series <strong>of</strong> indicators which should 

measure <strong>the</strong> scarcity degree <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves on earth. The exergy difference 

between two situations <strong>of</strong> <strong>the</strong> planet has been named as exergy distance D. The 

exergy degradation velocity ˙D, calculated as <strong>the</strong> exergy distance divided by <strong>the</strong> period 

<strong>of</strong> time considered, should account for <strong>the</strong> rate <strong>of</strong> exergy destruction <strong>of</strong> a certain 

resource. 

We have also defined <strong>the</strong> ton <strong>of</strong> <strong>mineral</strong> equivalent (t M e), which allows us to assess 

<strong>the</strong> exergy content <strong>of</strong> a certain deposit before and after extraction, and to compare 

<strong>the</strong> quality <strong>of</strong> different deposits containing <strong>the</strong> same <strong>mineral</strong>, but with a more understandable 

unit <strong>of</strong> measure. 

Fur<strong>the</strong>rmore, we have proposed to calculate <strong>the</strong> resources to production ratio <strong>of</strong> 

<strong>mineral</strong> deposits in exergy terms, <strong>the</strong>reby accounting for <strong>the</strong> concentration factor as 

well. 

All indicators described above can be assessed ei<strong>the</strong>r with minimum exergies, or 

with exergy replacement costs. With <strong>the</strong> latter, <strong>the</strong> irreversibility factor present in all 

real processes is taken into account. 

Finally, we have proposed <strong>the</strong> application <strong>of</strong> <strong>the</strong> Hubbert peak model for <strong>the</strong> assessment 

<strong>of</strong> <strong>the</strong> production peak <strong>of</strong> non-fuel <strong>mineral</strong>s. It has been stated that <strong>the</strong> 

bell-shape curve is better suited to non-fuel <strong>mineral</strong>s if it is fitted with exergy over 

time, instead <strong>of</strong> mass over time. This way, we would not ignore <strong>the</strong> concentration 

factor, which is very important for <strong>the</strong> case <strong>of</strong> solid <strong>mineral</strong>s. 

As a first case study, we have obtained <strong>the</strong> exergy decrease <strong>of</strong> US copper deposits 

throughout <strong>the</strong> 20th century, and have applied all indicators described above. It 

has been estimated, that <strong>the</strong> global exergy cost associated to <strong>the</strong> degradation <strong>of</strong> US 

copper deposits in <strong>the</strong> 20th century was around 700 Mtoe, consumed at an average 

exergy degradation velocity <strong>of</strong> 6,6 Mtoe/year. The R/P ratio <strong>of</strong> US copper deposits 

reveals for year 2000, that reserves would be completely depleted after 56 years. 

Moreover, <strong>the</strong> application <strong>of</strong> <strong>the</strong> Hubbert peak in exergy terms, gave as a result, that 

<strong>the</strong> peak was already reached in year 1994. In fact <strong>the</strong> real peak was attained in 

year 1998. 

Although <strong>the</strong> exergy production pattern did not perfectly fit in <strong>the</strong> bell-shaped curve, 

interesting conclusions could be extracted. Generally, production follows asymmetric 

curves with <strong>the</strong> decline much sharper than <strong>the</strong> growth. Hence, <strong>the</strong> real production 

peak is most probably attained after <strong>the</strong> year predicted by <strong>the</strong> Hubbert model. During 

a short period <strong>of</strong> time, <strong>the</strong> commodities will be probably over-exploited and <strong>the</strong> 

production points will appear over <strong>the</strong> bell-shaped curve. The compensation <strong>of</strong> <strong>the</strong> 

overproduction is <strong>the</strong> much sharper decrease <strong>of</strong> production after <strong>the</strong> peak, instead 

<strong>of</strong> a gradual and steady reduction.


The second case study was aimed at assessing <strong>the</strong> exergy loss <strong>of</strong> a country due to 

<strong>mineral</strong> extraction. Australia has been chosen for <strong>the</strong> analysis, because it is one <strong>of</strong> 

<strong>the</strong> most important <strong>mineral</strong> exporting countries in <strong>the</strong> world and is <strong>the</strong> only one 

with registered ore grade trends <strong>of</strong> its main <strong>mineral</strong>s. It has been stated that <strong>the</strong> 

most depleted commodities are in decreasing order: silver, gold, oil, zinc and lead, 

with R/P ratios below 35 years. On <strong>the</strong> contrary, <strong>the</strong> reserves <strong>of</strong> copper, iron, natural 

gas, nickel and finally coal will last at least for 48, 63, 67, 121 and 153 years, 

respectively. 

The Hubbert peak model was satisfactorily applied for all commodities, with <strong>the</strong> 

exception <strong>of</strong> <strong>the</strong> group lead-zinc-silver, whose production patterns differ from <strong>the</strong> 

rest, as <strong>the</strong>y are extracted toge<strong>the</strong>r. The study predicts that <strong>the</strong> maximum production 

has been already reached for gold (2006), silver (2005), lead (1997) and oil (1997). 

Zinc will reach <strong>the</strong> peak in 2010, copper in 2021, natural gas in 2025, iron in 2026, 

nickel in 2040, and finally coal in 2048. 

By <strong>the</strong> extraction <strong>of</strong> <strong>mineral</strong>s, Australia has degraded <strong>the</strong> equivalent <strong>of</strong> 12,5 Gtoe. 

And this degradation is dominated by <strong>the</strong> extraction <strong>of</strong> two commodities, coal and 

iron. In 2004, <strong>the</strong> global exergy degradation velocity exceeded 550 Mtoe/year 

(around 15% <strong>of</strong> current world’s oil consumption). And it will probably continue 

to increase exponentially at least for 20 to 40 years, until <strong>the</strong> peaks <strong>of</strong> iron and coal 

are reached. 

We additionally estimated <strong>the</strong> monetary cost <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> reserve’s depletion 

suffered in Australia in year 2004. This was carried out, by <strong>the</strong> conversion <strong>of</strong> exergy 

costs into monetary costs through conventional energy prices. According to <strong>the</strong> results 

obtained, Australia would have lost an equivalent <strong>of</strong> 93,3 billions <strong>of</strong> $US <strong>of</strong> its 

<strong>mineral</strong> <strong>capital</strong>, due to resource extraction only in year 2004. This corresponds to 

15,2% <strong>of</strong> <strong>the</strong> 2004 Australian GDP. 

It should be noted, that <strong>the</strong> results obtained are estimations and hence <strong>the</strong> numbers 

cannot be taken as final. More reserves could be found in <strong>the</strong> future, <strong>the</strong>reby increasing 

<strong>the</strong> years until depletion and <strong>the</strong> peak <strong>of</strong> production <strong>of</strong> <strong>the</strong> commodities. 

However, <strong>the</strong> huge amount <strong>of</strong> energy and its equivalent in money terms involved in 

<strong>the</strong> degradation <strong>of</strong> <strong>mineral</strong>s on earth, alerts us about <strong>the</strong> importance <strong>of</strong> conserving 

our resources. 

The last chapter <strong>of</strong> this PhD, chapter 8, has extrapolated at planetary level, <strong>the</strong> 

analysis <strong>of</strong> <strong>the</strong> exergy degradation <strong>of</strong> <strong>mineral</strong> reserves carried out for Australia. For 

that purpose, many assumptions had to be made at <strong>the</strong> expense <strong>of</strong> accuracy loss in 

<strong>the</strong> results. This is because <strong>the</strong>re is an important information gap about current and 

historical data <strong>of</strong> many commodities. Bearing in mind <strong>the</strong>se considerations, we have 

been able to give a rough estimate <strong>of</strong> <strong>the</strong> <strong>mineral</strong> loss on earth since <strong>the</strong> beginning 

<strong>of</strong> <strong>the</strong> 20th century, <strong>the</strong> earth’s degradation velocity, <strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> 

reserves and reserve base, <strong>the</strong> years until depletion <strong>of</strong> <strong>the</strong> commodities, and <strong>the</strong> year 

where <strong>the</strong> peak <strong>of</strong> production is reached for <strong>the</strong> main <strong>mineral</strong>s extracted on earth.


According to our calculations, <strong>the</strong> irreversible exergy distance D ∗ <strong>of</strong> <strong>the</strong> 51 nonfuel 

<strong>mineral</strong> commodities analyzed is at least 51 Gtoe, consumed at an average 

exergy degradation velocity <strong>of</strong> 1,3 Gtoe/year in <strong>the</strong> last decade. This means that with 

current technology, <strong>the</strong> replacement <strong>of</strong> all depleted non-fuel commodities would 

require a third <strong>of</strong> current world fuel oil reserves (178 Gtoe). 

The exergy degradation <strong>of</strong> <strong>the</strong> non-fuel <strong>mineral</strong> reserves on earth is clearly dominated 

by <strong>the</strong> extraction <strong>of</strong> iron, aluminium and to a lesser extent <strong>of</strong> copper. Never<strong>the</strong>less, 

<strong>the</strong> latter three <strong>mineral</strong>s are not <strong>the</strong> most depleted commodities. We have 

stated that <strong>the</strong> reserves <strong>of</strong> mercury, silver, gold, tin, arsenic, antimony and lead are 

suffering <strong>the</strong> greatest scarcity problems. On <strong>the</strong> o<strong>the</strong>r hand, <strong>the</strong> <strong>mineral</strong>s <strong>of</strong> cesium, 

thorium, REE, iodine vanadium, PGM’s, tantalum, aluminium cobalt and niobium 

are <strong>the</strong> least depleted commodities. 

For <strong>the</strong> most extracted non-fuel <strong>mineral</strong>s on earth, we have applied <strong>the</strong> Hubbert 

bell-shaped curve, assuming that only <strong>the</strong> reserve base published by <strong>the</strong> USGS [362] 

are available for extraction. Accordingly, we have obtained that <strong>the</strong> peak <strong>of</strong> production 

for iron, aluminium and copper is reached in years 2068, 2057 and 2024, 

respectively. 

With respect to fossil fuels, we have stated that in exergy terms, oil has been <strong>the</strong> most 

consumed fuel, accounting for 42% <strong>of</strong> <strong>the</strong> total fuel exergy degradation in <strong>the</strong> 20th 

century (coal and natural gas accounted for 38 and 20%, respectively). The total 

fuel’s exergy depleted between 1900 and 2006 is estimated at 382 Gtoe, consumed 

at an average exergy degradation velocity <strong>of</strong> 9 Gtoe/year in <strong>the</strong> last decade. The 

degradation corresponds to 30,5% <strong>of</strong> total world’s proven fuel reserves in 2006. 

Hubbert’s bell shaped curves applied to <strong>the</strong> exergy production <strong>of</strong> fossil fuels revealed 

that <strong>the</strong> peak <strong>of</strong> coal will be reached in year 2060, <strong>of</strong> natural gas in 2023, and <strong>of</strong> oil 

in 2008. The latter value fits very well with <strong>the</strong> predictions <strong>of</strong> o<strong>the</strong>r authors, who 

estimated that <strong>the</strong> peak year <strong>of</strong> world oil will be between 2004 and 2008. Fur<strong>the</strong>rmore, 

it gives sense to <strong>the</strong> radical increase <strong>of</strong> oil prices registered recently. The price 

<strong>of</strong> a barrel <strong>of</strong> crude has been doubled in just one year, surpassing in January 2008, 

<strong>the</strong> psychological barrier <strong>of</strong> 100 $US. 

If we add <strong>the</strong> exergy loss <strong>of</strong> fossil fuels to <strong>the</strong> exergy replacement costs <strong>of</strong> non-fuel 

<strong>mineral</strong>s, we obtain that man has depleted in <strong>the</strong> 20th century a total <strong>of</strong> 433 Gtoe. 

In 2006, <strong>the</strong> exergy <strong>of</strong> <strong>mineral</strong> deposits was depleted at a degradation velocity <strong>of</strong> 

around 12 Gtoe. 

The exergy <strong>of</strong> <strong>mineral</strong> reserves can be also affected by <strong>the</strong> conditions <strong>of</strong> <strong>the</strong> environment. 

With <strong>the</strong> help <strong>of</strong> <strong>the</strong> IPPC’s reference scenarios, we were able to estimate 

<strong>the</strong> exergy loss <strong>of</strong> fuels due to <strong>the</strong> increase <strong>of</strong> GHG emissions in <strong>the</strong> atmosphere 

and <strong>the</strong> temperature rise. According to our calculations, <strong>the</strong> exergy <strong>of</strong> fossil fuels 

could decrease to up to 0,40%, if <strong>the</strong> current CO 2 concentration in <strong>the</strong> atmosphere 

doubles.


Finally, we have made an estimation <strong>of</strong> <strong>the</strong> possible depletion degree that <strong>mineral</strong> 

reserves might suffer in <strong>the</strong> 21st century. For that purpose, we took into account 

seven different scenarios. 

In <strong>the</strong> first scenario, we assumed that production <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> commodities 

extracted, namely coal, oil, natural gas, iron, aluminium and copper, would follow 

<strong>the</strong> bell-shaped curves calculated before. Accordingly, <strong>the</strong> global <strong>mineral</strong> exergy 

decrease in <strong>the</strong> period between 1900 and 2100 would be near 1300 Gtoe. Fur<strong>the</strong>rmore, 

at <strong>the</strong> end <strong>of</strong> <strong>the</strong> 21st century, man would have depleted around 82% <strong>of</strong> <strong>the</strong> 

reserve base available in 1900. 

The o<strong>the</strong>r six case studies correspond to <strong>the</strong> IPPC’s SRES scenarios concerning fossil 

fuel consumption. For non-fuel <strong>mineral</strong>s, we assumed that world resources, ra<strong>the</strong>r 

than <strong>the</strong> reserve base are available for extraction. Additionally, we took into account 

<strong>the</strong> exergy loss <strong>of</strong> fuels due to <strong>the</strong> emission <strong>of</strong> greenhouse gases to <strong>the</strong> atmosphere. 

All IPCC’s scenarios involve greater degradation degrees <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves than 

in <strong>the</strong> case where <strong>the</strong> Hubbert behavior has been assumed. In <strong>the</strong> worst case, <strong>the</strong> 

exergy <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources degraded exceeds 3100 Gtoe. This indicates that 

for satisfying <strong>the</strong> energy consumption assumed in <strong>the</strong> SRES scenarios, <strong>the</strong> proven 

reserves <strong>of</strong> coal, oil and natural gas should increase considerably. Although new 

discoveries are indeed increasing <strong>the</strong> reserves <strong>of</strong> many <strong>mineral</strong> resources, it remains 

to be seen whe<strong>the</strong>r <strong>the</strong> rate <strong>of</strong> discoveries and <strong>the</strong> reclassification <strong>of</strong> <strong>mineral</strong> reserves 

as recoverable are sufficient enough to supply <strong>the</strong> huge future <strong>mineral</strong> demand. 

In <strong>the</strong> final reflections <strong>of</strong> this PhD, we have taken up again <strong>the</strong> ideas provided by 

Meadows et al. [218] in <strong>the</strong>ir book “The Limits to Growth”. In view <strong>of</strong> <strong>the</strong> results 

obtained in this study, we have stated that <strong>the</strong> message <strong>of</strong> <strong>the</strong> Club <strong>of</strong> Rome was not 

as false as many claimed, even if <strong>the</strong> last decades <strong>of</strong> <strong>the</strong> 20th century indicated <strong>the</strong> 

contrary. In fact, we have reached a point in which we might think about stopping 

extraction and living only with <strong>the</strong> already extracted materials. This is recycling, 

ra<strong>the</strong>r than wasting should be promoted. But nowadays, this practice would be 

impossible to undertake, as many economies are sustained by <strong>the</strong> extraction <strong>of</strong> resources. 

Hence, <strong>the</strong> realistic requirement now is to promote conservation measures 

for assuring enough resources for coming generations and a more rational management 

<strong>of</strong> <strong>the</strong> extraction and use <strong>of</strong> <strong>mineral</strong>s. 

We have stated that conventional measures <strong>of</strong> energy efficiency, renewable energies, 

CO 2 sequestration, etc. are not enough for achieving sustainability. We believe that 

a drastic world reduction and an appropriate management <strong>of</strong> <strong>the</strong> massive use <strong>of</strong> <strong>the</strong> 

extractive mining industry should be also required. 

An appropriate management should be based on a solid, transparent and objective 

physical accountability system <strong>of</strong> resources. As final corollary <strong>of</strong> this PhD, we have 

proposed a new accountability tool for <strong>the</strong> management <strong>of</strong> <strong>the</strong> <strong>mineral</strong> wealth on 

earth, based on <strong>the</strong> Exergoecological principles stated in this study. We have proposed 

to call this tool “Physical Geonomics”. Obviously, <strong>the</strong> accounting principles on


which it is based will have to be fur<strong>the</strong>r developed through <strong>the</strong> learning by doing 

technique. 

9.3 Scientific contributions <strong>of</strong> <strong>the</strong> PhD 

The main scientific contributions generated in this PhD are outlined next. 

1. This PhD has provided average chemical compositions <strong>of</strong> <strong>the</strong> atmosphere, seawater, 

rivers, lakes, groundwater and glacial-run<strong>of</strong>f. Fur<strong>the</strong>rmore, <strong>the</strong> main studies 

about <strong>the</strong> chemical composition in terms <strong>of</strong> elements <strong>of</strong> <strong>the</strong> upper continental crust, 

have been compiled. Although this information is available in <strong>the</strong> literature, it is 

ra<strong>the</strong>r dispersed in a significant number <strong>of</strong> different publications. The integration <strong>of</strong> 

all <strong>the</strong>se data accomplished in this work, provides a global overview <strong>of</strong> <strong>the</strong> geochemistry 

<strong>of</strong> our planet with special attention to <strong>the</strong> substances that compose <strong>the</strong> earth’s 

outer spheres. 

2. We have estimated for <strong>the</strong> first time <strong>the</strong> composition <strong>of</strong> <strong>the</strong> upper continental crust 

in terms <strong>of</strong> <strong>mineral</strong>s, through a procedure that assures chemical coherence between 

species and elements. 

The model <strong>of</strong> upper crust developed in this PhD is based on <strong>the</strong> recent and single 

published study concerning <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> upper crust, by <strong>the</strong> 

Russian geochemist Grigor’ev [127]. He calculated <strong>the</strong> average contents <strong>of</strong> 265 rock 

forming and accessory <strong>mineral</strong>s in <strong>the</strong> upper part <strong>of</strong> <strong>the</strong> continental crust. Grigor’ev’s 

model accounts for 56 elements, as opposed to <strong>the</strong> 78 included in <strong>the</strong> chemical 

composition <strong>of</strong> <strong>the</strong> continental crust <strong>of</strong> Rudnick and Gao [292]. 

Since <strong>the</strong> earth and in particular <strong>the</strong> upper continental crust can be considered as a 

closed system, <strong>the</strong> mass conservation principle dictates that <strong>the</strong> elements contained 

in <strong>the</strong> <strong>mineral</strong>s <strong>of</strong> <strong>the</strong> crust, must be equal to <strong>the</strong> chemical composition <strong>of</strong> <strong>the</strong> crust, 

which is reasonably known. We stated that Grigor’ev’s <strong>mineral</strong>ogical composition, 

although comprehensive, does not fulfill <strong>the</strong> mass balance <strong>of</strong> <strong>the</strong> earth. Therefore, 

we optimized Grigor’ev model, assuring <strong>the</strong> mass balance between species and elements. 

A rigorous analysis <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s <strong>of</strong> each element was carried out, 

and some important substances not included in Grigor’ev’s composition were considered 

in this model. As a result, we obtained a model <strong>of</strong> upper continental crust, 

consisting <strong>of</strong> <strong>the</strong> 307 most abundant <strong>mineral</strong>s. Fur<strong>the</strong>rmore, <strong>the</strong> new model takes 

into account all 78 elements included in <strong>the</strong> chemical composition <strong>of</strong> Rudnick and 

Gao [292]. 

Although <strong>the</strong> composition obtained should not be considered as definitive, since 

different assumptions had to be made, it constitutes <strong>the</strong> first step for obtaining a 

coherent and comprehensive <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> upper earth’s crust. 

3. The full physical characterization <strong>of</strong> non-fuel <strong>mineral</strong> resources should be based 

on at least two physical features: <strong>the</strong> tonnage and <strong>the</strong> grade <strong>of</strong> <strong>the</strong> deposits. Only <strong>the</strong>

Scientific contributions <strong>of</strong> <strong>the</strong> PhD 341 

US Geological Survey provides world figures <strong>of</strong> <strong>the</strong> reserves for <strong>the</strong> most important 

<strong>mineral</strong> commodities. However, average ore grades <strong>of</strong> <strong>the</strong> reserves are unknown. 

This study has estimated <strong>the</strong> weighted average grades <strong>of</strong> <strong>the</strong> most important nonfuel 

<strong>mineral</strong> reserves. This was mainly accomplished basing on <strong>the</strong> <strong>the</strong> compendium 

<strong>of</strong> <strong>the</strong> descriptive geologic models <strong>of</strong> Cox and Singer [66], who estimated pre-mining 

tonnage’s grades from over 3900 well-characterized deposits all over <strong>the</strong> world. 

With <strong>the</strong> published information about <strong>the</strong> reserves by <strong>the</strong> USGS, and <strong>the</strong> average ore 

grade <strong>of</strong> <strong>the</strong> <strong>mineral</strong> commodities estimated here, we have been able to illustrate for 

<strong>the</strong> first time in global terms, <strong>the</strong> quantity and quality <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> deposits 

on earth. 

4. We have stated in this PhD, that <strong>the</strong> most appropriate <strong>of</strong> <strong>the</strong> reference environments 

published so far for assessing <strong>the</strong> chemical exergy <strong>of</strong> natural resources, is <strong>the</strong> 

one based on Szargut’s methodology [336]. 

Ranz [276] and Rivero [281] made important contributions to <strong>the</strong> update <strong>of</strong> 

Szargut’s R.E, proposing new reference substances. Never<strong>the</strong>less, it was stated 

that <strong>the</strong> latter studies could be fur<strong>the</strong>r adapted to our requirements. Consequently, 

we have improved Szargut’s R.E., with <strong>the</strong> help <strong>of</strong> new geochemical information, 

and <strong>the</strong> model <strong>of</strong> continental crust developed in this study. The criterion used for 

choosing <strong>the</strong> reference substances <strong>of</strong> <strong>the</strong> R.E., which differs from Ranz’s and Rivero’s 

models, is based on Szargut’s partial stability. This is, among a group <strong>of</strong> reasonable 

abundant substances, <strong>the</strong> most stable will be chosen if <strong>the</strong>y also fulfill <strong>the</strong> “earth 

similarity criterion”. If <strong>the</strong> stability <strong>of</strong> <strong>the</strong> possible different reference substances for 

a specific element (measured in terms <strong>of</strong> <strong>the</strong> formation Gibbs energy) is within a 

certain threshold, <strong>the</strong>n <strong>the</strong> most abundant R.S. will be chosen. If <strong>the</strong> differences 

exceed this threshold, <strong>the</strong> most stable substance will be taken as R.S. as long as <strong>the</strong> 

“earth similarity criterion” is not contradicted. 

The new R.E. generates chemical exergies <strong>of</strong> <strong>the</strong> elements that differ on average in 

only 1% with respect to <strong>the</strong> original environment. Never<strong>the</strong>less, when <strong>the</strong> whole 

earth is considered, <strong>the</strong>se small numbers become not so insignificant. 

5. In this study a compendium <strong>of</strong> twelve different estimation methods for calculating 

standard enthalpies and Gibbs free energies <strong>of</strong> substances are provided for <strong>the</strong> first 

time. The calculation methodologies come from different <strong>the</strong>rmochemical studies 

published in <strong>the</strong> literature. The novelty introduced in this PhD is <strong>the</strong> compilation 

<strong>of</strong> all procedures, <strong>the</strong> specification <strong>of</strong> <strong>the</strong>ir respective applications within <strong>the</strong> geochemical 

framework, and <strong>the</strong> estimation <strong>of</strong> <strong>the</strong> relative errors introduced with each 

methodology. 

This way, we have provided methodologies with estimation errors comprised between 

0% and 10%. The first method is based on <strong>the</strong> definition <strong>of</strong> <strong>the</strong> Gibbs free 

energy and <strong>the</strong>refore does not introduce any error in <strong>the</strong> calculation. The second 

most accurate estimation procedure is Vieillard’s method for hydrated clay <strong>mineral</strong>s 

and for phyllosilicates, entailing an error <strong>of</strong> around ±0, 6%. Five fur<strong>the</strong>r methods


have associated an estimation error <strong>of</strong> ±1%. These are: <strong>the</strong> ideal mixing model; 

<strong>the</strong> <strong>the</strong>rmochemical approximations for sulfosalts and complex oxides; <strong>the</strong> method 

<strong>of</strong> corresponding states; <strong>the</strong> method <strong>of</strong> Chermak and Rimstidt for silicate <strong>mineral</strong>s; 

<strong>the</strong> ∆O −2 method; and <strong>the</strong> ∆O −2 method for different compounds with <strong>the</strong> same 

cations. The following three methods entail a maximum error <strong>of</strong> ±5%: assuming 

∆S r zero; <strong>the</strong> element substitution method; and <strong>the</strong> addition method for hydrated 

<strong>mineral</strong>s. Finally, <strong>the</strong> estimation procedure proposed with <strong>the</strong> greatest associated 

error (±10%) is <strong>the</strong> decomposition method. 

6. We have developed for <strong>the</strong> first time a complete <strong>the</strong>rmochemical data base <strong>of</strong> <strong>the</strong> 

main substances that compose <strong>the</strong> atmosphere, hydrosphere and upper continental 

crust. For that purpose, <strong>the</strong> standard Gibbs free energy, enthalpy <strong>of</strong> formation and 

specific exergy <strong>of</strong> more than 330 natural substances has been provided. The enthalpy 

and Gibbs free energy <strong>of</strong> <strong>the</strong> compounds have been compiled from <strong>the</strong> literature, or 

have been calculated with <strong>the</strong> 12 estimation methods described previously. Generally, 

published <strong>the</strong>rmochemical data is available for those substances with industrial 

importance. Consequently, many components <strong>of</strong> <strong>the</strong> crust (a total <strong>of</strong> 125), lacked 

<strong>of</strong> experimental <strong>the</strong>rmochemical values and had to be estimated. From <strong>the</strong> Gibbs 

free energy data and <strong>the</strong> chemical exergies <strong>of</strong> <strong>the</strong> elements generated from <strong>the</strong> R.E. 

developed in this PhD, we were able to obtain <strong>the</strong> specific chemical exergy <strong>of</strong> <strong>the</strong> 

considered substances. 

7. With <strong>the</strong> relative abundance <strong>of</strong> <strong>the</strong> substances in each <strong>of</strong> <strong>the</strong> earth’s outer spheres 

obtained in this PhD, and <strong>the</strong> <strong>the</strong>rmochemical information, we were able to calculate 

for <strong>the</strong> first time, <strong>the</strong> average Gibbs free energy, enthalpy <strong>of</strong> formation and chemical 

exergy <strong>of</strong> <strong>the</strong> atmosphere, hydrosphere and upper continental crust. 

Fur<strong>the</strong>rmore, since <strong>the</strong> mass <strong>of</strong> each layer <strong>of</strong> <strong>the</strong> earth is well known, we have obtained 

<strong>the</strong> first estimation <strong>of</strong> <strong>the</strong> earth’s specific chemical exergy: 1, 22 × 10 9 Gtoe. 

We have stated that <strong>the</strong> upper continental crust is responsible for most <strong>of</strong> <strong>the</strong> exergy 

(99,9%), due to its greater mass portion and specific exergy. Although <strong>the</strong> relative 

proportion <strong>of</strong> <strong>the</strong> atmosphere and hydrosphere is small when compared to <strong>the</strong> 

whole, <strong>the</strong>ir chemical exergies are also huge: 6, 27 × 10 3 Gtoe and 7, 80 × 10 5 Gtoe, 

respectively. 

8. This PhD has provided <strong>the</strong> first model <strong>of</strong> degraded earth. It has been stated, that 

this crepuscular planet is composed <strong>of</strong> an atmosphere similar to <strong>the</strong> current one, but 

with a CO 2 concentration <strong>of</strong> around 1400 ppm due to <strong>the</strong> complete burning <strong>of</strong> fossil 

fuel resources. The composition <strong>of</strong> <strong>the</strong> hydrosphere is equivalent to that <strong>of</strong> seawater, 

since in <strong>the</strong> degraded planet all fresh waters are mixed with salt water. We stated 

that <strong>the</strong> freshwater contribution to <strong>the</strong> final composition <strong>of</strong> <strong>the</strong> seas is irrelevant, 

due to <strong>the</strong>ir small relative volume. Finally, <strong>the</strong> continental crust <strong>of</strong> <strong>the</strong> degraded 

planet is one in which no fossil fuels or concentrated <strong>mineral</strong> deposits exist. Since 

<strong>the</strong> abundance <strong>of</strong> <strong>mineral</strong> deposits and fossil fuels is negligible when compared to 

<strong>the</strong> whole continental crust (<strong>the</strong>y account for about 0,001%), <strong>the</strong> composition <strong>of</strong> <strong>the</strong> 

degraded crust can be approximated to <strong>the</strong> model developed in this PhD.


9. This study has obtained an inventory <strong>of</strong> <strong>the</strong> most important renewable and nonrenewable 

resources on earth measured in exergy terms. The main novelty introduced 

in <strong>the</strong> inventory is <strong>the</strong> combined assessment <strong>of</strong> energy resources with nonfuel 

<strong>mineral</strong>s. Since exergy is an additive property, we have been able to obtain <strong>the</strong> 

total exergy <strong>of</strong> <strong>the</strong> non renewable energy resources, including nuclear, fossil fuels 

and non-fuel <strong>mineral</strong> reserves. Fur<strong>the</strong>rmore we could estimate for all renewable resources, 

<strong>the</strong> rate <strong>of</strong> current consumption with respect to <strong>the</strong> available potential use. 

Similarly, for non-renewables, we estimated <strong>the</strong> resource to production ratio. 

We came to <strong>the</strong> important conclusion that vast amounts <strong>of</strong> energy resources are 

available on earth, especially <strong>of</strong> renewable nature. However, we are currently using 

less than 2% <strong>of</strong> its potential. On <strong>the</strong> o<strong>the</strong>r hand, we have estimated that <strong>the</strong> reserves 

<strong>of</strong> concentrated fuel and non fuel <strong>mineral</strong>s, which can be practically used by man, 

represent only 0,01% <strong>of</strong> <strong>the</strong> chemical exergy <strong>of</strong> <strong>the</strong> earth. Fur<strong>the</strong>rmore, <strong>the</strong>ir global 

R/P ratio excluding nuclear materials, is less than 100 years. Hence, humankind is 

not facing an energy crisis, as many claim, but ra<strong>the</strong>r a material’s scarcity. 

10. An important advance entailed in this PhD with respect to <strong>the</strong> works <strong>of</strong> Ranz 

[276] and Botero [34] has been <strong>the</strong> inclusion <strong>of</strong> <strong>the</strong> time factor in <strong>the</strong> exergy assessment 

<strong>of</strong> natural resources. Consequently, we have been able not only to calculate 

what is <strong>the</strong> exergy reservoir <strong>of</strong> <strong>the</strong> earth’s <strong>mineral</strong> <strong>capital</strong>, but also at which rate 

<strong>the</strong>se resources are being degraded by man. For that purpose, we defined several 

indicators, aimed at quantifying <strong>the</strong> degradation degree <strong>of</strong> our planet. The exergy 

distance (D) accounts for <strong>the</strong> total exergy degraded by man in a certain period <strong>of</strong> 

time. Its derivative, <strong>the</strong> exergy degradation velocity (˙D), measures <strong>the</strong> rate at which 

<strong>the</strong> resources are being depleted. The resource to production ratio (R/P), usually 

calculated in mass terms, is proposed to be assessed in exergy terms, <strong>the</strong>reby taking 

also into account <strong>the</strong> concentration factor <strong>of</strong> <strong>the</strong> <strong>mineral</strong> deposits. 

We have additionally defined a new indicator called <strong>the</strong> ton <strong>of</strong> <strong>mineral</strong> equivalent 

(t M e), as <strong>the</strong> exergy content <strong>of</strong> one ton <strong>of</strong> <strong>mineral</strong> in a certain time and place. 

The t M e is analogous to <strong>the</strong> ton <strong>of</strong> oil equivalent, but it accounts at <strong>the</strong> same time, 

for <strong>the</strong> tonnage, grade and chemical composition <strong>of</strong> <strong>the</strong> considered <strong>mineral</strong>. This 

indicator allows us to assess <strong>the</strong> exergy content <strong>of</strong> a certain deposit before and after 

extraction, and to compare <strong>the</strong> quality <strong>of</strong> different deposits containing <strong>the</strong> same 

<strong>mineral</strong>, but with a more understandable unit <strong>of</strong> measure. 

11. This PhD has applied for <strong>the</strong> first time <strong>the</strong> Hubbert model to non-fuel <strong>mineral</strong>s, 

with <strong>the</strong> aim <strong>of</strong> estimating <strong>the</strong> year were <strong>the</strong> peak <strong>of</strong> production is reached. It 

has been stated that <strong>the</strong> bell-shape curve is better suited to non-fuel <strong>mineral</strong>s if 

it is fitted with exergy over time, instead <strong>of</strong> mass over time. This way, we take 

into account <strong>the</strong> concentration factor, which is very important for <strong>the</strong> case <strong>of</strong> solid 

<strong>mineral</strong>s. Consequently, we have developed <strong>the</strong> required equations for estimating 

<strong>the</strong> Hubbert’s peak for all kinds <strong>of</strong> <strong>mineral</strong>s in exergy terms. 

12. With <strong>the</strong> help <strong>of</strong> <strong>the</strong> indicators previously defined, we were able to analyze <strong>the</strong> 

exergy degradation <strong>of</strong> US copper during <strong>the</strong> 20th century, <strong>the</strong> average exergy degra-


dation velocity, <strong>the</strong> R/P ratio, and <strong>the</strong> peak <strong>of</strong> US copper production. Among o<strong>the</strong>rs, 

it has been estimated, that <strong>the</strong> global exergy cost associated to <strong>the</strong> degradation <strong>of</strong> 

US copper deposits in <strong>the</strong> 20th century was around 700 Mtoe, and that <strong>the</strong> peak <strong>of</strong> 

production was reached in 1994. Since <strong>the</strong> real peak <strong>of</strong> production was reached in 

1998, we came to <strong>the</strong> interesting conclusion that in fact production follows ra<strong>the</strong>r 

an asymmetric curve with <strong>the</strong> decline much sharper than <strong>the</strong> growth. 

13. This PhD has analyzed for <strong>the</strong> first time <strong>the</strong> degradation <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> 

deposits in a country, Australia. For that purpose, historical statistics <strong>of</strong> <strong>mineral</strong> 

consumption and average ore grade trends have been taking into account <strong>of</strong> fuel 

and non-fuel origin. We have been able to estimate <strong>the</strong> amount <strong>of</strong> exergy depleted 

through <strong>mineral</strong> extraction, <strong>the</strong> rate at which that exergy is degraded, and <strong>the</strong> depletion 

degree <strong>of</strong> <strong>the</strong> commodities. 

Fur<strong>the</strong>rmore, <strong>the</strong> application <strong>of</strong> <strong>the</strong> Hubbert peak model in exergy terms to all considered 

<strong>mineral</strong>s has allowed us to establish <strong>the</strong> “<strong>Exergy</strong> countdown <strong>of</strong> <strong>the</strong> country”. 

This is, in a single graphic, we have represented <strong>the</strong> bell-shaped curves <strong>of</strong> <strong>the</strong> production 

<strong>of</strong> Australian gold, silver, iron, zinc, lead, nickel, copper, coal, oil and natural 

gas. Such a representation would be impossible if <strong>the</strong> analysis were carried out in 

mass terms, as <strong>the</strong> orders <strong>of</strong> magnitude are radically different. The exergy countdown 

diagram provides in a simple and visual way a comparative <strong>of</strong> <strong>the</strong> available 

reserves <strong>of</strong> <strong>the</strong> country, <strong>the</strong> year were <strong>the</strong> peak <strong>of</strong> production is reached, or <strong>the</strong> depletion 

degree <strong>of</strong> <strong>the</strong> different commodities. Fur<strong>the</strong>rmore it allows to predict future 

<strong>mineral</strong> productions and <strong>the</strong> depletion degree <strong>of</strong> <strong>the</strong> commodities. 

This way, for instance, we could forecast that in year 2050, about 64% <strong>of</strong> <strong>the</strong> total 

considered <strong>mineral</strong> reserves in Australia will be depleted. Particularly, gold will be 

depleted at 99,9%, copper at 90,3%, lead at 87%, zinc at 97,3%, nickel at 60,4%, 

iron at 80%, coal at 52,4%, oil at 95,9% and natural gas at 85,2%. 

The results obtained could lead to spectacular consequences in <strong>the</strong> future <strong>of</strong> Australian 

mining and its economic implications. Fur<strong>the</strong>rmore, <strong>the</strong> exergy countdown 

<strong>of</strong> <strong>mineral</strong>s could constitute a universal and transparent prediction tool for assessing 

<strong>the</strong> degradation degree <strong>of</strong> non-renewable resources, with dramatic consequences for 

<strong>the</strong> future management <strong>of</strong> <strong>the</strong> earth’s physical stock. 

14. The physical analysis <strong>of</strong> <strong>the</strong> <strong>mineral</strong> degradation <strong>of</strong> a country has allowed us to 

assess in monetary terms <strong>the</strong> value associated to <strong>mineral</strong> extraction. The conversion 

<strong>of</strong> exergy into money is accomplished through conventional energy prices. The resulting 

monetary value represents <strong>the</strong> price that a country should pay <strong>the</strong> earth, for 

degrading <strong>the</strong> resources that are being extracted. 

This way, we have provided a first example <strong>of</strong> <strong>the</strong> contribution <strong>of</strong> <strong>mineral</strong> extraction 

in <strong>the</strong> GDP <strong>of</strong> a country. Assuming 2004 energy prices, Australia would have lost 

through <strong>mineral</strong> extraction in <strong>the</strong> same year, <strong>the</strong> equivalent <strong>of</strong> 15% <strong>of</strong> its 2004 GDP. 

However, if 2006 or 2008 energy prices are considered, <strong>the</strong> corresponding monetary 

cost associated to <strong>the</strong> same degradation <strong>of</strong> <strong>mineral</strong> <strong>capital</strong> would increase to 19 and


29% <strong>of</strong> <strong>the</strong> Australian 2004 GDP, respectively. This ratifies that <strong>the</strong> physical cost is a 

more objective and robust unit <strong>of</strong> measure than <strong>the</strong> monetary cost, which is highly 

dependent on external factors. However, <strong>the</strong> monetary value provides us with an 

order <strong>of</strong> magnitude <strong>of</strong> <strong>the</strong> importance <strong>of</strong> <strong>mineral</strong> extraction, which is understandable 

by <strong>the</strong> majority <strong>of</strong> <strong>the</strong> population. This procedure would allow to correct <strong>the</strong> 

economic indices, taking nature into account, as stated by Dieren [75]. 

15. With <strong>the</strong> available information about world <strong>mineral</strong> historic statistics and available 

reserves, we have carried out <strong>the</strong> first diagnosis <strong>of</strong> <strong>the</strong> state <strong>of</strong> non-renewable 

<strong>mineral</strong>s on earth. This PhD has estimated through <strong>the</strong> exergy analysis, <strong>the</strong> degradation 

degree <strong>of</strong> <strong>the</strong> <strong>mineral</strong> commodities, detecting <strong>the</strong> ones being degraded at <strong>the</strong> 

highest rates, and <strong>the</strong> ones facing important scarcity problems. 

We have stated that iron and aluminium are <strong>the</strong> most extracted commodities but not 

<strong>the</strong> most depleted ones, due to <strong>the</strong>ir crustal abundance. On <strong>the</strong> contrary, copper, 

which is also being extracted at very high rates, is already suffering scarcity problems, 

with more than 50% <strong>of</strong> its world reserves depleted. O<strong>the</strong>r commodities such 

as mercury, silver, gold, tin, arsenic, antimony or lead are even more degraded, with 

more than 70% <strong>of</strong> <strong>the</strong>ir reserves depleted. 

Additionally, we have estimated <strong>the</strong> peak <strong>of</strong> production <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> reserves. 

Extensive literature is found on <strong>the</strong> application <strong>of</strong> <strong>the</strong> Hubbert peak model for local 

and world oil production ([147], [133], [183], [47]). To our knowledge, <strong>the</strong>re is 

also at least one study about world coal production [89] and one about natural gas 

[24]. The novelty introduced by our work is <strong>the</strong> application <strong>of</strong> <strong>the</strong> Hubbert peak 

in exergy terms, what allows not only to obtain <strong>the</strong> peaking year <strong>of</strong> <strong>the</strong> separated 

commodities, but also for <strong>the</strong> whole <strong>mineral</strong>s. Our results fit very well with <strong>the</strong> 

already published studies about <strong>the</strong> peaking <strong>of</strong> oil and natural gas, which are reached 

in years 2008 and 2023, respectively. This is not <strong>the</strong> case with our prediction about 

<strong>the</strong> peaking <strong>of</strong> coal, which is achieved according to this study in 2060. The Energy 

Watch Group [89] reported recently that global coal production could peak in 2025. 

If all fossil fuels are considered as a single entity, assuming that <strong>the</strong>y are mutually 

replaceable, <strong>the</strong> peaking <strong>of</strong> production will be reached in year 2029. Moreover <strong>the</strong> 

R/P ratio reveals that <strong>the</strong>re will be enough conventional fossil fuels for 114 years 

more. 

In addition to <strong>the</strong> analysis <strong>of</strong> fossil fuels, we have applied <strong>the</strong> Hubbert peak model to 

world’s iron, copper and aluminium production. This task was never accomplished 

before. According to our results, <strong>the</strong> peak <strong>of</strong> world iron production will be reached 

in year 2068, <strong>of</strong> aluminium in 2057 and <strong>of</strong> copper in 2024. 

Thanks to <strong>the</strong> use <strong>of</strong> <strong>the</strong> unit <strong>of</strong> measure exergy, we have been able to provide for <strong>the</strong> 

first time <strong>the</strong> “<strong>the</strong> exergy countdown <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s on earth”, representing 

in a single graph <strong>the</strong> Hubbert peak curves for coal, oil, natural gas, iron, copper and 

aluminium. 

16. This PhD has assessed <strong>the</strong> loss <strong>of</strong> fossil fuel exergy due to <strong>the</strong> greenhouse effect. 

This estimation was firstly carried out by Valero and Arauzo [366], for an average


fuel composition that should account for <strong>the</strong> coal, oil and natural gas reserves, and 

assuming that CO 2 concentration in <strong>the</strong> atmosphere would double. 

In our case, we have considered separately <strong>the</strong> world resources <strong>of</strong> each type <strong>of</strong> coal, 

oil and natural gas. Fur<strong>the</strong>rmore, we have based our calculations on <strong>the</strong> IPCC’s SRES 

scenarios <strong>of</strong> future CO 2 concentration. According to our results, in <strong>the</strong> worst case, 

<strong>the</strong> reserves <strong>of</strong> fossil fuels would be decreased by 0,4%. 

17. In addition to <strong>the</strong> global overview <strong>of</strong> <strong>the</strong> state <strong>of</strong> our <strong>mineral</strong> resources in <strong>the</strong> 

past and in <strong>the</strong> present provided before, this PhD has estimated <strong>the</strong> possible exergy 

degradation <strong>of</strong> <strong>mineral</strong>s throughout <strong>the</strong> 21st century. This was carried out considering 

7 different scenarios. 

In <strong>the</strong> first scenario, <strong>the</strong> production <strong>of</strong> <strong>mineral</strong>s was constrained by <strong>the</strong> current available 

reserves (i.e. base reserves for non-fuel <strong>mineral</strong>s and proven reserves for fossil 

fuels). Accordingly if <strong>the</strong> 2006 reserves do not increase, at <strong>the</strong> end <strong>of</strong> <strong>the</strong> 21st century 

man would have depleted around 82% <strong>of</strong> <strong>the</strong> reserve base available in 1900. 

The remaining 6 scenarios are based on <strong>the</strong> IPCC’s SRES models, which indirectly 

assume a considerable increase <strong>of</strong> fossil fuel reserves. To <strong>the</strong> fossil fuel consumption 

estimated by <strong>the</strong> IPCC, we have included as a novelty <strong>the</strong> possible consumption 

<strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong>s, namely iron, aluminium and copper, assuming that 

<strong>the</strong> world resources, ra<strong>the</strong>r than <strong>the</strong> reserve base published by <strong>the</strong> USGS [362] are 

available for extraction. This way, we have provided a global perspective <strong>of</strong> future 

<strong>mineral</strong> production. According to our results, for satisfying <strong>the</strong> demand <strong>of</strong> fossil 

fuels in <strong>the</strong> SRES scenarios, <strong>the</strong> reserves <strong>of</strong> fossil fuels should double and in some 

cases, <strong>the</strong>y should be multiplied by a factor <strong>of</strong> four. Consequently, we think that <strong>the</strong> 

fuel consumption estimations <strong>of</strong> <strong>the</strong> SRES scenarios should be reviewed. 

18. This PhD has proposed an accounting tool for <strong>the</strong> management <strong>of</strong> <strong>the</strong> <strong>mineral</strong> 

wealth on earth, including not only fossil fuels, but also <strong>the</strong> much more complex and 

apparently less relevant information <strong>of</strong> non-fuel <strong>mineral</strong>s. This tool has been named 

here as “Physical Geonomics”. It should take into account all physical changes <strong>of</strong> 

<strong>the</strong> <strong>mineral</strong> stock on earth, considering both <strong>the</strong> extracted and recycled materials. 

The concrete accounting procedures <strong>of</strong> Physical Geonomics should be created with 

<strong>the</strong> learning by doing technique. But <strong>the</strong> principles on which it is based have been 

already developed in this PhD and in o<strong>the</strong>r exergoecological studies. Physical Geonomics 

should help to achieve a more rational management <strong>of</strong> <strong>the</strong> extraction and 

use <strong>of</strong> <strong>mineral</strong>s. 

9.4 Perspectives 

This PhD has opened <strong>the</strong> way for assessing <strong>the</strong> exergy resources <strong>of</strong> <strong>the</strong> earth and 

<strong>the</strong>ir degradation rate, providing <strong>the</strong> <strong>the</strong>oretical tools required for filling <strong>the</strong> existing 

knowledge gap on that field. Obviously it is subject to fur<strong>the</strong>r improvements and 

refinements in future studies, with <strong>the</strong> help <strong>of</strong> better statistics, geochemical updates

Perspectives 347 

and especially, <strong>the</strong> conception <strong>of</strong> a new model <strong>of</strong> degraded earth. Next, <strong>the</strong> ideas 

and calculations that have arisen throughout <strong>the</strong> accomplishment <strong>of</strong> this PhD but 

that have remained undone, are discussed. 

The first thing that we realized when we embarked on <strong>the</strong> adventure <strong>of</strong> assessing 

<strong>the</strong> state <strong>of</strong> <strong>the</strong> earth’s resources was that <strong>the</strong>re is a huge information gap about our 

<strong>mineral</strong> <strong>capital</strong>. It is incredible that in this high developed and ironically named 

“knowledge society”, <strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> earth’s continental crust 

is unknown. Similarly, data on <strong>the</strong> available <strong>mineral</strong> resources or <strong>the</strong> average ore 

grade <strong>of</strong> <strong>the</strong> deposits on earth is uncertain. 

An efficient management <strong>of</strong> our resources should be based on global and reliable 

information sources. Hence, more data bases, better global statistics, <strong>the</strong> opening 

<strong>of</strong> global information channels and impartial and serious interpretations <strong>of</strong> <strong>the</strong> information 

are urgently required. But for that purpose, we think that at least <strong>the</strong> 

following data should be compiled worldwide for all <strong>mineral</strong> commodities: 

• Yearly production data. 

• Ore grade trends <strong>of</strong> all <strong>mineral</strong> deposits. 

• Energy, water and raw material consumption. 

• Production <strong>of</strong> waste rock. 

• Tonnage and grade <strong>of</strong> available reserves. 

In many cases, this information is hidden or distorted by companies or even governments 

for <strong>the</strong>ir own economic benefits. We cannot forget that <strong>the</strong> earth and its 

resources are a common good. Consequently <strong>the</strong> state <strong>of</strong> our planet should be <strong>of</strong> 

global knowledge. 

This work has been based on many different and partially fragmented information 

sources. Fur<strong>the</strong>rmore, <strong>the</strong> lack <strong>of</strong> some data needed for <strong>the</strong> calculations, lead us to 

make important assumptions at <strong>the</strong> expense <strong>of</strong> accuracy loss in <strong>the</strong> results. 

This way, for instance, <strong>the</strong> first step for determining <strong>the</strong> <strong>mineral</strong>ogical composition 

<strong>of</strong> <strong>the</strong> earth’s crust has been accomplished. Now is <strong>the</strong> turn <strong>of</strong> world geologists and 

geochemists to update <strong>the</strong> model with better geochemical information. 

Something similar occurs with <strong>the</strong> exergy assessment <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves on 

earth and <strong>the</strong>ir degradation velocity, carried out in this PhD. With <strong>the</strong> help <strong>of</strong> improved 

statistical data, an update <strong>of</strong> <strong>the</strong> results would be expected. 

But <strong>the</strong> results <strong>of</strong> our study cannot only be improved with better data bases. We have 

stated that some calculation procedures could be fur<strong>the</strong>r developed and adapted to 

<strong>the</strong> requirements <strong>of</strong> <strong>the</strong> study.


The main activity that has remain undone and that is crucial for an appropriate natural 

resource assessment, is a deeper analysis <strong>of</strong> <strong>the</strong> entropic earth towards we are 

approaching. Moreover, <strong>the</strong> establishment <strong>of</strong> a methodology able to calculate <strong>the</strong> 

chemical exergies <strong>of</strong> <strong>the</strong> elements from a realistic degraded reference environment 

is still missing. In this PhD, we have stated that <strong>the</strong> R.E. based on Szargut’s criterion 

gives some problems when calculating <strong>the</strong> exergy <strong>of</strong> certain natural substances. 

With <strong>the</strong> help <strong>of</strong> <strong>the</strong> model <strong>of</strong> continental crust developed in this PhD and <strong>the</strong> well 

known average compositions <strong>of</strong> <strong>the</strong> atmosphere and seawater, we have been able 

to develop <strong>the</strong> first model <strong>of</strong> a realistic degraded earth (or entropic planet). However, 

<strong>the</strong> selection <strong>of</strong> an appropriate R.E. is a required but not a sufficient condition. 

Hence, <strong>the</strong> calculation procedures and even <strong>the</strong> philosophy for obtaining <strong>the</strong> chemical 

exergies <strong>of</strong> <strong>the</strong> elements should be reviewed. But this activity remains open for 

fur<strong>the</strong>r studies in <strong>the</strong> future. 

In this PhD, we have stated that exergy replacement costs represent a suitable indicator 

for assessing <strong>the</strong> value <strong>of</strong> non-fuel <strong>mineral</strong> resources, as <strong>the</strong>y integrate in one 

parameter, concentration, composition and also <strong>the</strong> state <strong>of</strong> technology. <strong>Exergy</strong> costs 

are calculated through unit exergy replacement costs, which are a function <strong>of</strong> <strong>the</strong> 

state <strong>of</strong> technology and hence vary with time. 

Never<strong>the</strong>less, in this work, we have considered unit exergy replacement costs to 

be constant. A more exact determination <strong>of</strong> <strong>the</strong> exergy costs <strong>of</strong> <strong>mineral</strong>s throughout 

history would imply changing unit exergy replacement costs, according to <strong>the</strong> corresponding 

energy requirements. Generally, historical information <strong>of</strong> energy <strong>of</strong> extraction 

is usually unavailable for most commodities. But future energy requirements 

could be assessed with <strong>the</strong> help <strong>of</strong> <strong>the</strong> <strong>the</strong>ory <strong>of</strong> learning curves. With learning-bydoing, 

increases in material and energy efficiency increase with cumulative production. 

The assessment <strong>of</strong> unit exergy replacement costs as a function <strong>of</strong> time remains open 

for fur<strong>the</strong>r studies. However, it should be noted that with appropriate historical and 

future unit exergy replacement costs, <strong>the</strong> Hubbert peak model could be applied to 

exergy replacement costs, ra<strong>the</strong>r than to minimum exergies, <strong>the</strong>reby introducing <strong>the</strong> 

technological factor. This would provide a more accurate prediction <strong>of</strong> <strong>the</strong> peaking 

year <strong>of</strong> <strong>mineral</strong> commodities. 

Finally, we have stated that a gaussian model applied to <strong>the</strong> behavior <strong>of</strong> world <strong>mineral</strong> 

production might not be <strong>the</strong> perfect fit. We have seen, that generally production 

follows asymmetric curves with <strong>the</strong> decline much sharper than <strong>the</strong> growth. Hence 

o<strong>the</strong>r types <strong>of</strong> curves should be analyzed for improving <strong>the</strong> accuracy <strong>of</strong> <strong>the</strong> results. 

In summary we have stated that with <strong>the</strong> required information, <strong>the</strong> exergoecological 

approach used here could constitute a universal and transparent tool for assessing 

natural resources. The study could be extended to <strong>the</strong> loss <strong>of</strong> fertile soils and consequently 

to <strong>the</strong> analysis <strong>of</strong> <strong>the</strong> increasing world food demand and <strong>the</strong> carrying 

capacity <strong>of</strong> <strong>the</strong> planet. Similarly, it could be also extended to <strong>the</strong> growing freshwater 

requirements in a world with unpredictable climate changes.

Perspectives 349 

From <strong>the</strong> principles <strong>of</strong> <strong>the</strong> exergoecological approach, a new physical accounting tool 

could be developed. This proposed tool, that we have called “Physical Geonomics”, 

would account for all physical changes in <strong>the</strong> <strong>mineral</strong> stock on earth. Fur<strong>the</strong>rmore, 

<strong>the</strong> conversion <strong>of</strong> physical into monetary costs with <strong>the</strong> procedure shown in this 

PhD, would allow to keep at <strong>the</strong> same time <strong>the</strong> objectivity <strong>of</strong> physical data and <strong>the</strong> 

more intelligible meaning <strong>of</strong> monetary units. But <strong>the</strong> specific accounting principles 

<strong>of</strong> Physical Geonomics need to be developed with <strong>the</strong> help <strong>of</strong> <strong>the</strong> learning by doing 

technique. In fact, <strong>the</strong> materialization <strong>of</strong> <strong>the</strong> proposal would require <strong>the</strong> formation 

<strong>of</strong> international working groups participated by governments, <strong>the</strong> scientific community, 

industry and civil society organizations, allowing international agreements on 

<strong>the</strong> methodological principles. Obviously, that would require a firm political will <strong>of</strong> 

extending <strong>the</strong> current economic criteria. 

In short, <strong>the</strong> Exergoecology method and its corollary, Physical Geonomics, could help 

decision makers for an appropriate management <strong>of</strong> <strong>the</strong> earth’s physical stock.

Appendix A 

Additional calculations 

A.1 Input data. Mineralogical composition <strong>of</strong> <strong>the</strong> earth’s 

crust 

This section shows vectors ˆε i, ξ i and matrix R[ j × i] required for <strong>the</strong> calculation <strong>of</strong> 

<strong>the</strong> <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> earth’s crust, according to Eq. 3.1. Additionally, 

<strong>the</strong> resulting vector ˆ ξ i is presented. 

Table A.1 shows vector ˆε j from Rudnick and Gao [292] and ε j, obtained applying Eq. 

3.1 to Grigorev’s <strong>mineral</strong>ogical composition (ξ i) [127]. Table A.2, shows vectors ξ i 

and <strong>the</strong> resulting ˆ ξ i. Finally, tables A.3 and A.4 show <strong>the</strong> transposed <strong>of</strong> <strong>the</strong> coefficient 

matrix R [ j × i]. R ′ <strong>of</strong> dimensions [307 × 78] is given ra<strong>the</strong>r than R [78 × 307] in 

order to make easier its representation. Additionally, <strong>the</strong> matrix is divided into two 

tables because <strong>of</strong> lack <strong>of</strong> space. 

Table A.1: Vector ˆε j [78×1], according to Rudnick and Gao [292] and vector 

ε j [78 × 1], obtained from Grigor’ev [127]. Values in mole/g 

Element j ˆε j ε j Element j ˆε j ε j 

Au 1 7,62E-12 9,14E-13 Ag 40 4,91E-10 2,82E-11 

Te 2 3,92E-11 4,54E-13 Sb 41 3,29E-09 4,14E-12 

Cs 3 3,69E-08 0 Bi 42 7,66E-10 1,07E-11 

Na 4 1,19E-03 8,65E-04 Os 43 1,63E-13 0 

Rb 5 9,83E-07 0 Ir 44 1,14E-13 0 

Al 6 3,02E-03 2,60E-03 Ru 45 3,36E-12 0 

Si 7 1,10E-02 1,02E-02 Pt 46 2,56E-12 2,51E-14 

O 8 2,97E-02 Pd 47 4,89E-12 4,83E-15 

H 9 2,11E-03 Ni 48 8,01E-07 6,94E-09 

Ge 10 1,93E-08 0 Rh 49 5,83E-13 0 

Y 11 2,36E-07 1,12E-08 Sm 50 3,13E-08 8,08E-12 

Sc 12 3,11E-07 4,07E-13 Pr 51 5,04E-08 0 


351

352 ADDITIONAL CALCULATIONS 

Table A.1: Vector ˆε j [78×1], according to Rudnick and Gao [292] and vector 

ε j [78×1], obtained from Grigor’ev [127]. Values in mole/g – continued from 

previous page. 

Element j ˆε j ε j Element j ˆε j ε j 

Ga 13 2,51E-07 0 Nd 52 1,87E-07 1,09E-08 

Re 14 1,06E-12 0 Ce 53 4,50E-07 5,84E-08 

Tb 15 4,40E-09 0 Nb 54 1,29E-07 1,28E-09 

Dy 16 2,40E-08 0 Pb 55 8,20E-08 2,34E-09 

Ho 17 5,03E-09 0 Sn 56 1,77E-08 1,70E-10 

Er 18 1,38E-08 0 Sr 57 3,65E-06 9,28E-09 

Eu 19 6,58E-09 0 C 58 1,66E-04 6,85E-04 

Tm 20 1,78E-09 0 Ba 59 4,57E-06 4,26E-08 

Gd 21 2,03E-08 0 F 60 2,93E-05 5,73E-05 

Lu 22 1,77E-09 0 Ti 61 8,01E-05 3,13E-05 

Hf 23 2,97E-08 0 B 62 1,57E-06 1,34E-07 

Cd 24 8,01E-10 0 Mg 63 6,15E-04 9,24E-04 

S 25 1,93E-05 1,91E-05 Li 64 3,46E-06 8,15E-11 

Hg 26 2,49E-10 2,57E-12 Mo 65 1,15E-08 7,52E-10 

Ca 27 6,40E-04 9,64E-04 U 66 1,13E-08 2,51E-10 

I 28 1,10E-08 0 Th 67 4,53E-08 4,68E-09 

Cr 29 1,77E-06 1,70E-08 V 68 1,90E-06 0 

In 30 4,88E-10 0 Ta 69 4,97E-09 8,87E-11 

N 31 5,93E-06 0 Cu 70 4,41E-07 7,30E-09 

K 32 5,95E-04 6,22E-04 Be 71 2,33E-07 1,07E-08 

Se 33 1,14E-09 0 Zr 72 2,12E-06 5,46E-07 

Tl 34 4,40E-09 0 Cl 73 1,04E-05 3,37E-05 

W 35 1,03E-08 2,52E-10 La 74 2,23E-07 2,82E-08 

Fe 36 7,02E-04 6,41E-04 Zn 75 1,02E-06 4,75E-09 

Mn 37 1,41E-05 1,10E-06 Co 76 2,94E-07 5,06E-11 

Yb 38 1,13E-08 1,38E-09 As 77 6,41E-08 1,23E-09 

P 39 2,11E-05 8,15E-06 Br 78 2,00E-08 0 


Table A.2: Vector ξ i [324 × 1], according to Grigor’ev [127] and vector ˆ ξ i 

[324 × 1] obtained in this study 

Mineral i ξ i, mole/g ˆ ξi, mole/g 

Gold 1 9,14E-13 6,47E-12 

Calaverite 2 0 5,71E-13 

Sylvanite 3 0 7,62E-13 

Pollucite 4 0 6,14E-08 

Dispersed Ge 5 0 1,93E-08 

Thortveitite 6 2,71E-13 2,71E-13 

Dispersed Sc 7 0 3,11E-07 

Dispersed Ga 8 0 2,51E-07 

Dispersed Re 9 0 1,06E-12 

Dispersed Tb 10 0 4,40E-09 

Dispersed Dy 11 0 2,40E-08 


Input data. Mineralogical composition <strong>of</strong> <strong>the</strong> earth’s crust 353 


[324 × 1] obtained in this study – continued from previous page. 


Dispersed Ho 12 0 5,03E-09 

Dispersed Er 13 0 1,38E-08 

Dispersed Eu 14 0 6,58E-09 

Dispersed Tm 15 0 1,78E-09 

Dispersed Gd 16 0 2,03E-08 

Dispersed Lu 17 0 1,77E-09 

Hf in Zr ores 18 0 2,97E-08 

Greenockite 19 0 8,01E-10 

Metacinnabar 20 3,27E-14 3,17E-12 

Cinnabar 21 2,54E-12 2,46E-10 

Lautarite 22 0 2,76E-09 

Dietzeite 23 0 2,76E-09 

In in ZnS 24 0 4,88E-10 

Nitratine 25 0 2,96E-06 

Niter 26 0 2,96E-06 

Se in copper ores 27 0 1,14E-09 

Dispersed Tl 28 0 4,40E-09 

Scheelite 29 2,26E-10 9,28E-09 

Wolframite 30 2,57E-11 1,06E-09 

Xenotime 31 1,38E-09 1,38E-09 

Yb in monazite 32 0 9,95E-09 

Native silver 33 1,11E-11 1,94E-10 

Samsonite 34 3,04E-14 5,29E-13 

Tetradymite 35 2,27E-13 2,27E-13 

Tellurite 36 0 1,14E-12 

Te in Cu ores 37 0 3,49E-11 

Iridium 38 0 1,50E-13 

Osmium 39 0 1,57E-13 

Polixene/ Tetraferroplatinum 40 1,20E-14 1,20E-14 

I-Platinum 41 1,54E-14 1,54E-14 

Cooperite 42 1,61E-14 2,11E-12 

Pt in Ni-Cu ores 43 0 1,27E-12 

Pd in Ni-Cu ores 44 0 4,25E-12 

Rh in Ni-Cu ores 45 0 5,83E-13 

Ru in Ni-Cu ores 46 0 3,33E-12 

Fergusonite 47 8,08E-11 8,08E-11 

Sm in Monazite and Bastnasite 48 0 3,12E-08 

Pr in Monazite and Bastnasite 49 0 5,04E-08 

Stibnite 50 1,30E-13 8,10E-10 

Boulangerite 51 2,12E-15 2,12E-15 

Sb in galena 52 0 1,62E-09 

Tin 53 3,71E-12 3,87E-10 

Cassiterite 54 1,66E-10 1,73E-08 

Lamprophyllite 55 5,61E-12 5,61E-12 

Celestine 56 9,26E-09 3,65E-06 

Strontianite 57 1,35E-11 5,34E-09 

Tourmaline 58 4,09E-08 4,09E-08 

Kornerupine 59 9,24E-09 9,24E-09 

Axinite -Fe 60 1,93E-10 1,93E-10 






Dumortierite 61 1,33E-13 1,33E-13 

Sassolite (natural boric acid) 62 0 3,60E-07 

Colemanite 63 0 5,99E-08 

Kernite 64 0 8,99E-08 

Ulexite 65 0 7,19E-08 

Psilomelane 66 5,25E-09 5,78E-07 

Barite 67 3,13E-08 3,44E-06 

Wi<strong>the</strong>rite 68 0 3,44E-07 

Bismutite 69 2,16E-12 1,19E-10 

Bismuthinite 70 1,79E-12 9,91E-11 

Bismuth 71 2,34E-12 1,30E-10 

Bismite 72 0 9,91E-11 

Spodumene 73 5,16E-11 2,06E-06 

Neptunite 74 2,75E-11 1,10E-06 

Amblygonite 75 3,24E-12 1,29E-07 

Staurolite 76 6,28E-07 7,70E-07 

Chromite 77 8,49E-09 8,83E-07 

Molybdenite 78 7,50E-10 1,14E-08 

Powellite 79 2,00E-12 3,05E-11 

Wulfenite 80 1,09E-13 1,66E-12 

Uraninite 81 2,44E-10 5,60E-09 

Blomstrandite/ Betafite 82 2,17E-11 4,96E-10 

Metatorbenite 83 7,89E-14 1,81E-12 

Polycrase (Y) 84 1,07E-15 2,46E-14 

Carnotite 85 0 2,80E-09 

Beryl 86 2,98E-09 5,99E-08 

Phenakite 87 3,63E-10 7,31E-09 

Bertrandite 88 1,68E-10 3,38E-09 

Helvine/ Helvite 89 7,21E-11 1,45E-09 

Chrysoberyl 90 0 1,80E-08 

Gadolinite 91 7,03E-11 1,41E-09 

Zircon 92 5,46E-07 2,11E-06 

Naegite 93 1,80E-12 6,98E-12 

Sirtolite 94 1,04E-10 4,02E-10 

Eudialyte 95 1,11E-10 4,30E-10 

Baddeleyite 96 2,52E-11 9,75E-11 

Lavenite 97 6,68E-12 2,59E-11 

Rinkolite/ Mosandrite 98 5,80E-14 2,25E-13 

Wohlerite 99 3,29E-16 1,27E-15 

Ferrotantalite 100 5,06E-12 3,07E-10 

Microlite 101 1,44E-13 8,71E-12 

Delorenzite/ Tanteuxenite 102 1,37E-13 8,33E-12 

Bastnasite 103 1,46E-08 1,16E-07 

Loparite - (Ce) 104 6,08E-11 4,81E-10 

Rhabdophane-Ce 105 1,31E-11 1,03E-10 

Chevkinite 106 3,48E-12 2,76E-11 

Monazite (Ce) 107 5,41E-08 4,29E-07 

Britholite 108 2,75E-11 2,18E-10 

Thorite 109 1,76E-09 2,13E-08 






Uranium- Thorite 110 2,63E-12 3,18E-11 

Yttrialite 111 3,83E-10 4,64E-09 

Thorianite 112 1,29E-12 1,56E-11 

Dispersed V 113 0 1,90E-06 

Halite 114 3,25E-05 1,01E-05 

Apatite 115 2,55E-06 7,91E-07 

Scapolite 116 2,05E-07 6,34E-08 

Sylvite 117 8,85E-08 2,74E-08 

Carnallite 118 4,68E-09 1,45E-09 

Sodalite 119 6,60E-10 2,05E-10 

Bisch<strong>of</strong>ite 120 1,28E-09 3,96E-10 

Diadochic Nd 121 0 1,01E-07 

Sphalerite 122 4,74E-09 1,02E-06 

Zinc 123 7,19E-12 1,55E-09 

Smithsonite 124 2,95E-12 6,36E-10 

Cobaltite 125 5,06E-11 5,06E-11 

Smaltite 126 0 5,06E-11 

Linnaeite 127 0 1,69E-11 

Dispersed Co 128 0 2,93E-07 

Arsenopyrite 129 5,40E-10 2,89E-08 

Orpiment 130 3,45E-11 1,85E-09 

Realgar 131 2,62E-12 1,40E-10 

Fahlerz Group: Tennantite 132 2,31E-14 1,24E-12 

Lollingite 133 2,43E-14 1,30E-12 

Nickeline 134 3,82E-10 2,04E-08 

Gersdorffite 135 1,81E-10 9,70E-09 

Arsenolite 136 0 2,80E-10 

Pentlandite 137 1,09E-09 7,44E-08 

Garnierite 138 1,73E-10 1,18E-08 

Violarite 139 2,52E-10 1,72E-08 

Vaesite 140 6,19E-10 4,23E-08 

Diadochic Ni 141 0 3,35E-07 

Galena 142 7,94E-10 2,79E-08 

Lead 143 8,69E-12 3,05E-10 

Cerussite 144 2,36E-11 8,27E-10 

Anglesite 145 1,09E-11 3,82E-10 

Murmanite 146 2,26E-10 2,78E-08 

Ferrocolumbite 147 1,95E-10 2,40E-08 

Pyrochlore 148 2,83E-11 3,47E-09 

Ilmenorutile 149 2,62E-09 3,22E-07 

Euxenite 150 1,68E-10 1,02E-08 

Miserite 151 2,00E-12 2,00E-12 

Diadochic Ce 152 0 2,02E-07 

Weinschenkite 153 1,68E-12 1,68E-12 

Francolite 154 1,70E-07 8,68E-08 

Vivianite 155 2,59E-12 2,59E-12 

Biotite 156 1,73E-04 8,80E-05 

Muscovite 157 4,99E-05 2,54E-05 

Hydrobiotite 158 1,03E-05 5,26E-06 






Phlogopite 159 3,10E-07 1,58E-07 

Clinohumite 160 2,16E-08 1,10E-08 

Fluorite 161 2,82E-07 1,44E-07 

Humite 162 1,86E-08 9,46E-09 

Topaz 163 2,52E-08 1,29E-08 

Chondrodite 164 5,76E-10 2,93E-10 

Cryolite 165 0 2,36E-09 

Orthite-Ce/ Allanite 166 7,81E-08 7,81E-08 

Diadochic Y 167 0 2,09E-07 

Phosphate rock 168 0 8,99E-06 

Chalcopyrite 169 5,99E-09 3,62E-07 

Cubanite 170 2,21E-10 1,33E-08 

Covellite 171 3,77E-10 2,27E-08 

Azurite 172 7,25E-11 4,38E-09 

Bornite 173 4,38E-11 2,65E-09 

Malachite 174 9,04E-11 5,46E-09 

Copper 175 6,45E-11 3,90E-09 

Chalcocite 176 1,13E-11 6,83E-10 

Chrysocolla 177 5,87E-14 3,54E-12 

Diodochic Rb 178 0 9,77E-07 

Lepidolite 179 0 1,03E-07 

Ankerite 180 1,50E-06 1,31E-05 

Rhodochrosite 181 1,04E-07 9,14E-07 

Chloritoid 182 6,81E-09 5,96E-08 

Pyrolusite 183 6,21E-08 5,44E-07 

Todorokite 184 1,48E-09 1,29E-08 

Vernadite 185 2,40E-09 2,10E-08 

Spessartine 186 5,25E-08 4,60E-07 

Orthoclase 187 3,52E-04 4,22E-04 

Hydromuscovite/ Illite 188 6,45E-05 7,73E-05 

Glaukonite 189 3,04E-06 3,65E-06 

Lepidomelane/ Annite 190 1,48E-06 1,78E-06 

Sanidine 191 2,22E-06 2,67E-06 

Stilpnomelane 192 2,31E-07 2,77E-07 

Nepheline 193 4,24E-07 5,09E-07 

Jarosite 194 7,99E-09 9,57E-09 

Alunite 195 1,83E-13 2,20E-13 

Calcite 196 3,98E-04 8,05E-05 

Dolomite 197 3,80E-05 7,69E-06 

Graphite 198 9,99E-05 2,02E-05 

Siderite 199 1,04E-05 2,10E-06 

C org 200 9,16E-05 1,86E-05 

Aragonite 201 3,80E-06 7,69E-07 

Magnesite 202 1,78E-06 3,60E-07 

Dawsonite 203 1,25E-08 2,53E-09 

Cancrinite 204 2,09E-10 4,23E-11 

Moissanite 205 1,75E-10 3,54E-11 

Augite 206 5,12E-05 1,27E-04 

Ilmenite 207 1,25E-05 3,10E-05 






Titanite 208 9,18E-06 2,28E-05 

Ulvöspinel 209 2,10E-06 5,21E-06 

Leucoxene 210 7,65E-07 1,90E-06 

Rutile 211 1,38E-06 3,41E-06 

Anatase 212 2,25E-07 5,59E-07 

Aenigmatite 213 1,28E-09 3,16E-09 

Perovskite 214 2,06E-09 5,10E-09 

Brookite 215 2,13E-09 5,27E-09 

Ramsayite/ Lorenzenite 216 1,46E-10 3,62E-10 

Kieserite 217 4,84E-08 3,06E-08 

Crossite 218 6,41E-07 4,06E-07 

Glaucophane 219 1,91E-08 1,21E-08 

Omphacite 220 1,18E-08 7,49E-09 

Clinochlore 221 1,16E-05 7,34E-06 

Cordierite 222 1,50E-07 9,52E-08 

Gedrite 223 6,51E-08 4,12E-08 

Palygorskite 224 4,38E-09 2,77E-09 

Pumpellyite 225 2,99E-07 1,89E-07 

Ripidolite 226 3,18E-05 2,01E-05 

Sapphirine 227 3,22E-08 2,04E-08 

Spinel 228 1,69E-07 1,07E-07 

Thuringite/ Chamosite 229 1,81E-06 1,14E-06 

Vermiculite 230 1,07E-06 6,78E-07 

Vesubianite/ Idocrase 231 1,90E-07 1,20E-07 

Actinolite 232 4,45E-06 2,82E-06 

Diopside 233 2,22E-05 1,40E-05 

Pigeonite 234 3,14E-06 1,99E-06 

Tremolite 235 6,77E-07 4,29E-07 

Anthophyllite 236 4,23E-08 2,68E-08 

Bronzite 237 2,80E-06 1,77E-06 

Brucite 238 4,29E-08 2,71E-08 

Cummingtonite 239 5,89E-06 3,73E-06 

Enstatite 240 2,19E-06 1,39E-06 

Forsterite 241 7,82E-07 4,95E-07 

Hypers<strong>the</strong>ne 242 1,85E-05 1,17E-05 

Olivine 243 2,41E-06 1,53E-06 

Periclase 244 5,96E-12 3,77E-12 

Pleonaste/ Magnesi<strong>of</strong>errite 245 6,96E-10 4,41E-10 

Sepiolite 246 8,96E-06 5,67E-06 

Serpentine/ Clinochrysotile 247 2,60E-06 1,64E-06 

Talc 248 1,21E-06 7,68E-07 

Clementite 249 6,02E-08 3,81E-08 

Pyrite 250 5,25E-06 2,64E-06 

Anhydrite 251 3,31E-06 1,66E-06 

Pyrrhotite 252 3,41E-06 1,71E-06 

Gypsum 253 1,52E-06 7,64E-07 

Marcasite 254 1,00E-07 5,03E-08 

Sulphur 255 3,51E-09 1,77E-09 

Nosean 256 2,47E-09 1,24E-09 






Troilite 257 2,28E-11 1,14E-11 

Oligoclase 258 5,39E-04 4,49E-04 

Andesine 259 2,44E-04 2,03E-04 

Labradorite 260 1,11E-04 9,24E-05 

Montmorillonite 261 7,83E-06 6,52E-06 

Hastingsite 262 3,13E-06 2,60E-06 

Bytownite 263 1,09E-05 9,08E-06 

Thomsonite 264 7,44E-07 6,19E-07 

Anorthite 265 1,19E-06 9,90E-07 

Clinozoisite 266 9,02E-07 7,51E-07 

Epidote 267 2,25E-05 1,87E-05 

Grossular 268 5,55E-08 4,62E-08 

Hornblende (Fe) 269 3,34E-05 2,78E-05 

Prehnite 270 4,30E-06 3,58E-06 

Zoisite 271 6,82E-07 5,68E-07 

Andradite 272 2,36E-08 1,96E-08 

Hedenbergite 273 3,31E-07 2,75E-07 

Wollastonite 274 4,91E-08 4,08E-08 

Albite 275 1,52E-04 5,14E-04 

Nontronite 276 1,15E-05 3,88E-05 

Riebeckite 277 1,82E-06 6,14E-06 

Beidellite 278 4,11E-06 1,39E-05 

Aegirine 279 3,90E-06 1,32E-05 

Natrolite 280 2,31E-06 7,82E-06 

Analcime 281 3,00E-07 1,01E-06 

Arfvedsonite 282 3,23E-08 1,09E-07 

Jadeite 283 1,41E-07 4,78E-07 

Hydrosodalite 284 2,68E-10 9,06E-10 

Fayalite 285 1,91E-07 2,35E-07 

Ferrosilite 286 1,89E-06 2,32E-06 

Goethite 287 9,57E-06 1,17E-05 

Hematite 288 4,95E-06 6,06E-06 

Hisingerite 289 5,11E-09 6,27E-09 

Magnetite 290 2,81E-05 3,44E-05 

Iotsite 291 1,95E-10 2,39E-10 

Almandine 292 1,71E-05 2,09E-05 

Andalusite 293 3,89E-06 1,25E-05 

Boehmite 294 3,00E-06 9,65E-06 

Corundum 295 3,73E-07 1,20E-06 

Diaspore 296 9,17E-06 2,95E-05 

Distene/ Kyanite 297 1,36E-06 4,37E-06 

Hydragillite/ Gibbsite 298 5,51E-06 1,77E-05 

Kaolinite 299 1,01E-05 3,24E-05 

Pyrophyllite 300 2,78E-08 8,93E-08 

Sillimanite 301 1,91E-05 6,15E-05 

Cristobalite 302 2,16E-07 2,06E-07 

Opal 303 1,49E-04 1,42E-04 

Quarz 304 3,99E-03 3,81E-03 

Tridymite 305 1,10E-08 1,05E-08 






Dispersed Br 306 0 2,00E-08 

Acanthite 307 1,57E-12 2,74E-11 

Argentite 308 2,87E-12 4,99E-11 

Stephanite 309 4,43E-13 7,72E-12 

Pyrargirite 310 1,37E-12 2,38E-11 

Chlorargirite 311 3,14E-13 5,47E-12 

Freibergite 312 2,02E-13 3,52E-12 

Tetrahedrite 313 3,47E-13 3,47E-13 

Nordite 314 7,20E-13 7,20E-13 

Hollandite 315 7,50E-09 2,63E-07 

Jacobsite 316 1,32E-08 1,15E-07 

Cryptomelane 317 3,40E-09 2,98E-08 

Manganite 318 1,71E-08 1,49E-07 

Tephroite 319 6,93E-08 6,07E-07 

Braunite 320 4,47E-08 3,91E-07 

Rhodonite 321 2,56E-08 2,24E-07 

Pennine 322 4,54E-06 2,87E-06 

Lawsenite 323 7,64E-06 6,35E-06 

Paragonite 324 1,47E-05 4,95E-05 



Table A.3: Matrix R ′ [324 × 78] (Part 1) 

i \ j 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 

1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

3 0,75 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,25 

4 0 0 0,6 0,2 0,1 0,9 2,1 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

5 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

6 0 0 0 0 0 0 2 7 0 0 0,5 1,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

7 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

8 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

22 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 

23 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 

24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 

25 0 0 0 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 

26 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 

27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 

28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 

29 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 

30 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0,5 0,5 0 0 0 

31 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 

32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 

33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 

35 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

36 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

37 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 

41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 



Table A.3: Matrix R ′ [324 × 78] (Part 1). – continued from previous page. 

i \ j 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 

44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

46 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

47 0 0 0 0 0 0 0 4 0 0 0,1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

48 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

49 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

51 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

52 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

53 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

54 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

55 0 0 0 2 0 0 4 17 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

56 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

57 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

58 0 0 0 1 0 6 6 31 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 

59 0 0 0 0 0 5,7 3,7 18,2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,2 0 0 0 0 

60 0 0 0 0 0 2 4 16 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 

61 0 0 0 0 0 6,9 3 18 0,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

62 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

63 0 0 0 0 0 0 0 16 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 

64 0 0 0 2 0 0 0 11 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

65 0 0 0 1 0 0 0 17 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 

66 0 0 0 0 0 0 0 12 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 

67 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

68 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

69 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

70 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

71 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

72 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

73 0 0 0 0 0 1 2 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

74 0 0 0 2 0 0 8 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1,5 0,5 0 0 0 

75 0 0 0 0,25 0 1 0 4,25 0,25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 

76 0 0 0 0 0 9 4 24 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 

77 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 

78 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

79 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 

80 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

81 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

82 0 0 0 0 0 0,1 0 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,2 0 0 0 0 0 0 0 0 0,1 0 0 0 0 

83 0 0 0 0 0 0 0 20 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 

84 0 0 0 0 0 0 0 6 0 0 0,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,1 0 0 0 0 0 0 0 0 0 0 0 0 0 

85 0 0 0 0 0 0 0 15 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 

86 0 0 0 0 0 2 6 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 




i \ j 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 

87 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

88 0 0 0 0 0 0 2 9 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

89 0 0 0 0 0 0 3 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 

90 0 0 0 0 0 2 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

91 0 0 0 0 0 0 2 10 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 

92 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

93 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

94 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

95 0 0 0 4 0 0 8 23,5 1,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0,7 0,3 0 0 0 

96 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

97 0 0 0 1,1 0 0 2 7,9 0,3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,9 0 0 0 0 0 0 0 0 0,5 0,5 0 0 0 

98 0 0 0 2 0 0 4 15,5 0 0 0,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 

99 0 0 0 1 0 0 2 8,7 0,3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 

100 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

101 0 0 0 0,4 0 0 0 6,9 0,3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1,6 0 0 0 0 0 0 0 0 0 0 0 0 0 

102 0 0 0 0 0 0 0 6 0,5 0 0,7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,2 0 0 0 0 0 0 0 0 0 0 0 0 0 

103 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,1 0 0 0 0 0 0 0 0 0 0 0 0 0 

104 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

105 0 0 0 0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 

106 0 0 0 0 0 0 4 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,8 0 0 0 0 0 0 0 0 2,3 0 0 0 0 

107 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 

108 0 0 0 0 0 0 2,7 13,8 1,8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2,9 0 0 0 0 0 0 0 0 0 0 0 0,5 0 

109 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

110 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

111 0 0 0 0 0 0 2 7 0 0 1,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

112 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

113 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

114 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

115 0 0 0 0 0 0 0 12,3 0,33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 3 0 

116 0 0 0 2 0 3 9 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 

117 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 

118 0 0 0 0 0 0 0 6 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 

119 0 0 0 8 0 6 6 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

120 0 0 0 0 0 0 0 6 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

121 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

122 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

123 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

124 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

125 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

126 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

127 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

128 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

129 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 




i \ j 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 

130 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

131 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 

133 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 

134 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

135 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

136 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

137 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 4,5 0 0 0 0 

138 0 0 0 0 0 0 2 9 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

139 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 

140 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

141 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

142 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

143 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

144 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

145 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

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324 0 0 0 1 0 3 3 12 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 


Table A.4: Matrix R ′ [324 × 78] (Part 2) 

i \ j 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 




i \ j 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 

14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

34 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

35 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

36 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

38 0 0 0,3 0,5 0,2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

39 0 0 0,75 0,25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

41 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

42 0 0 0 0 0 0,6 0,3 0,1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

43 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

44 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

45 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

46 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

47 0 0 0 0 0 0 0 0 0 0,1 0 0,4 0,4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

48 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

49 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

50 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

51 4 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

52 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

53 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

56 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 




i \ j 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 

57 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

58 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

59 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1,2 3,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

61 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

62 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

64 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

68 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

69 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

70 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

71 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

72 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

73 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

74 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,75 0 0 0 0,75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

76 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

78 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 

79 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 

80 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 

81 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 

82 0 0 0 0 0 0 0 0 0 0 0 0 0 0,9 0 0 0 0 0 0 0,8 0 0 0 0 0,3 0 0 0,5 0 0 0 0 0 0 0 0 0 

83 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 

84 0 0 0 0 0 0 0 0 0 0 0 0 0,1 0,6 0 0 0 0 0 0 1,2 0 0 0 0 0,1 0,1 0 0,2 0 0 0 0 0 0 0 0 0 

85 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 

86 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 

87 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 

88 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 

89 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 

90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 

91 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 

92 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 

93 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 

94 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 

95 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0,5 0 0 0 0 0 

96 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 

97 0 0 0 0 0 0 0 0 0 0 0 0 0 0,1 0 0 0 0 0 0,1 0,1 0 0 0 0 0 0 0 0 0 0 0,8 0 0 0 0 0 0 

98 0 0 0 0 0 0 0 0 0 0 0 0 1,5 0,5 0 0 0 0 0 3,5 0,4 0 0 0 0 0 0 0 0 0 0 0,1 0 0 0 0 0 0 

99 0 0 0 0 0 0 0 0 0 0 0 0 0 0,4 0 0 0 0 0 0,3 0 0 0 0 0 0 0 0 0 0 0 0,6 0 0 0 0 0 0 




i \ j 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 

100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 

101 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 

102 0 0 0 0 0 0 0 0 0 0 0 0 0,1 0,3 0 0 0 0 0 0 0,05 0 0 0 0 0 0 0 1,4 0 0 0 0 0 0 0 0 0 

103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 

104 0 0 0 0 0 0 0 0 0 0 0 0 0,22 0,2 0 0 0 0 0 0 0,8 0 0 0 0 0 0 0 0 0 0 0 0 0,11 0 0 0 0 

105 0 0 0 0 0 0 0 0 0 0 0 0 0,75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,25 0 0 0 0 

106 0 0 0 0 0 0 0 0 0 0 0 0 1,7 0 0 0 0 0 0 0 2,5 0 0,5 0 0 0 0,1 0 0 0 0 0 0 1,4 0 0 0 0 

107 0 0 0 0 0 0 0 0 0 0 0 0,2 0,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0,05 0 0 0 0 0 0 0,25 0 0 0 0 

108 0 0 0 0 0 0 0 0 0 0 0 0,2 0,9 0 0 0 0 0 0 0,2 0 0 0 0 0 0 0,6 0 0 0 0 0 0 0,4 0 0 0 0 

109 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 

110 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 

111 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,5 0 0 0 0 0 0 0 0 0 0 0 

112 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 

113 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 

114 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 

115 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,33 0 0 0 0 0 0 0 0 0 0 0 0 0,33 0 0 0 0 0 

116 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 

117 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 

118 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 

119 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 

120 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 

121 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

122 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 

123 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 

124 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 

125 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 

126 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 

127 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 

128 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 

129 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 

130 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 

131 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 

132 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 4 0 

133 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 

134 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 

135 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 

136 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 

137 0 0 0 0 0 0 0 4,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

138 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

139 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

140 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

141 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

142 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 




i \ j 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 

143 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

144 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

145 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

146 0 0 0 0 0 0 0 0 0 0 0 0 0 0,4 0 0 0 0 0 0 3,6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

147 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

148 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0,25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

149 0 0 0 0 0 0 0 0 0 0 0 0 0 0,15 0 0 0 0 0 0 0,7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

150 0 0 0 0 0 0 0 0 0 0 0 0 0,1 1,4 0 0 0 0 0 0 0,05 0 0 0 0 0 0 0 0,4 0 0 0 0 0 0 0 0 0 

151 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

152 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

153 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

154 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,5 0 1,11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

155 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

156 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,25 0 0 2,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

157 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

158 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,2 0 0 2,3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

159 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

160 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1,5 0 0 6,75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

161 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

162 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1,5 0 0 5,25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

163 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1,1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

164 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1,5 0 0 3,75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

165 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

166 0 0 0 0 0 0 0 0 0 0 0 0 0,4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

167 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

168 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

169 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 

170 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 

171 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 

172 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 

173 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 

174 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 

175 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 

176 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 

177 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 

178 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

179 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

180 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0,3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

181 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

182 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

183 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

184 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

185 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 




i \ j 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 

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188 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

189 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

190 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

191 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

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193 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

194 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

195 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

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203 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

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206 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,1 0 0,9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

207 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

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210 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

211 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

212 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

213 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

214 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

215 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

216 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

217 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

218 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

219 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

220 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

221 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3,75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

222 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

223 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

224 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

225 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

226 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3,75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

227 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

228 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 




i \ j 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 

229 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

230 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

231 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

232 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

233 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

234 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1,35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

235 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

236 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

237 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

238 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

239 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

240 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

241 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

242 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

243 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1,6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

244 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

245 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

246 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

247 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

248 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

249 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

250 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

251 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

252 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

253 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

254 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

255 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

256 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

257 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

258 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

259 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

260 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

261 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

262 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

263 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

264 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

265 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

266 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

267 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

268 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

269 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

270 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

271 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 




i \ j 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 

272 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

273 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

274 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

275 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

276 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

277 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

278 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

279 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

280 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

281 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

282 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

283 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

284 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

285 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

286 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

287 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

288 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

289 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

290 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

291 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

292 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

293 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

294 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

295 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

296 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

297 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

298 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

299 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

300 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

301 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

302 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

303 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

304 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

305 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

306 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

307 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

308 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

309 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

310 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

311 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 

312 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3,6 0 0 0 0 0 0 1 0 

313 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 

314 0 0 0 0 0 0 0 0 0 0 0 0 0,6 0 0 0 0,5 0 0 0 0 0 0,4 0 0 0 0 0 0 0 0 0 0 0,33 0,6 0 0 0 




i \ j 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 

315 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,2 0 0 0 0,8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

316 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0,1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

317 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

318 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

319 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

320 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

321 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

322 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3,75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

323 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 

324 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 



A.2 Calculation <strong>of</strong> average <strong>mineral</strong> ore grades 

The average grade <strong>of</strong> <strong>the</strong> different <strong>mineral</strong> deposits analyzed by Cox and Singer [66] 

is calculated with Eq. 4.4, taking into account <strong>the</strong> tonnage <strong>of</strong> each model and <strong>the</strong> 

number <strong>of</strong> deposits (No. dep.) containing <strong>the</strong> <strong>mineral</strong> under consideration. Tables 

A.5 through A.12 show <strong>the</strong> mean average grade and tonnage <strong>of</strong> each deposit type. 

Table 4.9 in chapter 4 shows <strong>the</strong> final average grade obtained. 

Table A.5. Summary statistics <strong>of</strong> grade-tonnage models-1. After [66] 

Mean No.dep. Mean No.dep. Mean No.dep. 

Deposit type Placer Au-PGE Placer PGE-Au Shoreline Placer 

Tonnage (Mton) 1,07 65 0,13 83 87,50 61 

RE2O5 (%) 

Monazite (%) 0,03 29 

U3O8 (%) 

Zircon (% ZrO2) 0,27 52 

Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 

P2O5 (%) 

Ilmenite (% TiO2) 1,27 61 

Rutile (% TiO2) 0,21 50 

Leucocite (% TiO2) 0,23 24 

Cr2O3 (%) 

Mn (%) 

Fe (%) 

Co (%) 

Ni (%) 

Cu (%) 

Mo (%) 

WO3 (%) 

Pd (ppb) 1,50 13 

Pt (ppb) 1588,55 83 

Rh (ppb) 

Ir (ppb) 8,38 10 

Ru (ppb) 

Os (ppb) 82,22 21 

Ag (g/t) 0,03 16 

Au (g/t) 0,20 65 0,03 23 

Zn (%) 

Hg (%) 

Sn (%) 

Pb (%) 

Sb (%)

Calculation <strong>of</strong> average <strong>mineral</strong> ore grades 377 


Deposit type Mean No.dep. Mean No.dep. Mean No.dep. Mean No.dep. 

Komatiite Ni-Cu Dunitic Ni-Cu Synorg-synvolc. Ni-Cu Minor podiform Cr 

Tonnage (Mton) 1,72 31 28,25 22 2,00 32 0,00 435 

RE2O5 (%) 

Monazite (%) 

U3O8 (%) 

Zircon (% ZrO2) 

Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 

P2O5 (%) 

Ilmenite (% TiO2) 

Rutile (% TiO2) 

Leucocite (% TiO2) 

Cr2O3 (%) 42,13 435 

Mn (%) 

Fe (%) 

Co (%) 0,06 8 0,03 3 0,05 3 

Ni (%) 1,51 31 0,99 22 0,76 32 

Cu (%) 0,14 21 0,04 12 0,48 29 

Mo (%) 

WO3 (%) 

Pd (ppb) 338,61 11 139,19 5 98,86 3 4,70 31 

Pt (ppb) 201,05 5 31,05 2 30,83 33 

Rh (ppb) 8,11 69 

Ir (ppb) 71,61 9 15,07 5 65,31 38 

Ru (ppb) 189,67 29 

Os (ppb) 

Ag (g/t) 

Au (g/t) 0,04 10 0,02 5 0,11 3 

Zn (%) 

Hg (%) 

Sn (%) 

Pb (%) 

Sb (%) 

Major podiform Cu Carbonatite W Skarn Sn Scarn 


RE2O5 (%) 0,10 5 


U3O8 (%) 


Nb2O5 (%) 0,64 20 

Barite (%) 

Al2O3(%) 

P (%) 

P2O5 (%) 




Cr2O3 (%) 44,03 7,291 

Mn (%) 

Fe (%) 

Co (%) 

Ni (%) 

Cu (%) 

Mo (%) 

WO3 (%) 0,66 28 

Pd (ppb) 3,48 16 

Pt (ppb) 14,32 12 

Rh (ppb) 13,06 14 

Ir (ppb) 78,34 9 

Ru (ppb) 220,80 7 

Os (ppb) 

Ag (g/t) 

Au (g/t) 

Zn (%) 

Hg (%) 

Sn (%) 0,31 4 

Pb (%) 

Sb (%)




Replacement Sn W veins Sn Veins Sn Greisen 


RE2O5 (%) 


U3O8 (%) 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 

Fe (%) 

Co (%) 

Ni (%) 

Cu (%) 

Mo (%) 

WO3 (%) 0,91 16 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 

Au (g/t) 

Zn (%) 

Hg (%) 

Sn (%) 0,80 6 1,27 43 0,28 10 

Pb (%) 

Sb (%) 

Climax Mo Porphyry Cu Porphyry Cu skarn-related Cu skarn 


RE2O5 (%) 


U3O8 (%) 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 

Fe (%) 

Co (%) 

Ni (%) 

Cu (%) 0,54 208 0,98 18 1,69 64 

Mo (%) 0,19 9 0,01 103 0,02 4 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 1,65 76 4,78 9 21,43 15 

Au (g/t) 0,12 81 0,33 6 1,78 16 

Zn (%) 

Hg (%) 

Sn (%) 

Pb (%) 

Sb (%)




Zn-Pb skarn Fe skarn deposits Polymet. replacement Replacement Mn 


RE2O5 (%) 


U3O8 (%) 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 0,03 3 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 32,54 37 

Fe (%) 49,61 168 

Co (%) 

Ni (%) 

Cu (%) 0,46 17 0,23 35 0,88 4 

Mo (%) 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 114,55 22 193,20 45 

Au (g/t) 0,45 7 0,71 35 

Zn (%) 5,91 0,2709 3,92 51 

Hg (%) 

Sn (%) 

Pb (%) 3,22 30 5,06 52 

Sb (%) 

Porphyry Cu-Au Porphyry Cu-Mo Porphyry Mo, Low -F Polymetallic vein 


RE2O5 (%) 


U3O8 (%) 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 

Fe (%) 

Co (%) 

Ni (%) 

Cu (%) 0,50 40 0,42 16 0,19 33 

Mo (%) 0,00 20 0,02 16 0,09 33 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 1,59 27 1,22 16 866,96 74 

Au (g/t) 0,38 40 0,01 16 0,62 54 

Zn (%) 2,78 60 

Hg (%) 

Sn (%) 

Pb (%) 8,97 75 

Sb (%)




Cyprus massive sulfide Besshi massive sulfide Volcanogenic Mn Creede epith. vein 


RE2O5 (%) 


U3O8 (%) 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 0,09 8 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 38,80 93 

Fe (%) 

Co (%) 

Ni (%) 

Cu (%) 1,60 49 1,46 44 0,30 19 

Mo (%) 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 12,85 15 7,86 14 125,60 27 

Au (g/t) 0,91 15 0,34 14 2,12 23 

Zn (%) 0,79 16 0,56 6 1,88 26 

Hg (%) 

Sn (%) 

Pb (%) 0,05 3 2,55 24 

Sb (%) 

Comstock epith. vein Sado epith. vein Epith. quartz-alunite Au Volcanogenic U 


RE2O5 (%) 


U3O8 (%) 0,12 21 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 

Fe (%) 

Co (%) 

Ni (%) 

Cu (%) 0,02 18 0,19 9 0,24 5 

Mo (%) 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 114,82 41 37,93 20 17,82 8 

Au (g/t) 7,46 41 6,86 18 7,81 8 

Zn (%) 0,03 3 0,25 1 

Hg (%) 

Sn (%) 

Pb (%) 0,01 19 0,00 2 

Sb (%)




Epi<strong>the</strong>rmal Mn Rhyolite-hosted Sn Volcan.-hosted magnetite Carbonate-hosted Au-Ag 


RE2O5 (%) 


U3O8 (%) 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 0,40 36 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 30,59 59 

Fe (%) 53,72 39 

Co (%) 

Ni (%) 

Cu (%) 

Mo (%) 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 21,88 5 

Au (g/t) 2,57 34 

Zn (%) 

Hg (%) 

Sn (%) 0,39 132 

Pb (%) 

Sb (%) 

Hot-spring Hg Silica-carbonate Hg Sb veins Disseminated Sb 


RE2O5 (%) 


U3O8 (%) 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 

Fe (%) 

Co (%) 

Ni (%) 

Cu (%) 

Mo (%) 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 36,39 8 1,20 1 

Au (g/t) 5,14 9 0,30 2 

Zn (%) 

Hg (%) 0,34 20 0,39 28 

Sn (%) 

Pb (%) 

Sb (%) 34,67 81 3,55 23




Kuroko mass. sulfide Algoma and Sup. Fe Sandstone-hosted Pb-Zn Sedim.-hosted Cu 


RE2O5 (%) 


U3O8 (%) 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 0,06 47 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 

Fe (%) 50,83 66 

Co (%) 0,24 10 

Ni (%) 

Cu (%) 1,26 432 2,15 57 

Mo (%) 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 28,77 284 11,22 9 

Au (g/t) 0,78 238 

Zn (%) 2,81 330 0,59 14 

Hg (%) 

Sn (%) 

Pb (%) 0,75 184 2,15 20 

Sb (%) 

Sedim. Exhal. Zn-Pb Bedded barite Missouri / Appalach. Pb-Zn Sedimentary Mn 


RE2O5 (%) 


U3O8 (%) 


Nb2O5 (%) 

Barite (%) 83,02 25 

Al2O3(%) 

P (%) 0,12 13 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 31,38 39 

Fe (%) 

Co (%) 

Ni (%) 

Cu (%) 0,19 11 

Mo (%) 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 43,32 37 4,67 10 

Au (g/t) 

Zn (%) 5,65 45 4,05 20 

Hg (%) 

Sn (%) 

Pb (%) 2,78 45 1,23 16 

Sb (%)




Phosphate, upwell. Phosphate, warm current Low-sulfide Au-quartz veins Homestake Au 


RE2O5 (%) 


U3O8 (%) 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 

P (%) 

P2O5 (%) 23,96 60 24,16 18 




Cr2O3 (%) 

Mn (%) 

Fe (%) 

Co (%) 

Ni (%) 

Cu (%) 

Mo (%) 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 4,97 39 1,62 52 

Au (g/t) 15,96 313 9,22 116 

Zn (%) 

Hg (%) 

Sn (%) 

Pb (%) 

Sb (%) 

Unconformity U-Au Lateritic Ni Laterite type bauxite Karst type bauxite 


RE2O5 (%) 


U3O8 (%) 0,52 36 


Nb2O5 (%) 

Barite (%) 

Al2O3(%) 44,97 122 49,18 41 

P (%) 

P2O5 (%) 




Cr2O3 (%) 

Mn (%) 

Fe (%) 

Co (%) 0,07 12 

Ni (%) 1,36 71 

Cu (%) 

Mo (%) 

WO3 (%) 

Pd (ppb) 

Pt (ppb) 

Rh (ppb) 

Ir (ppb) 

Ru (ppb) 

Os (ppb) 

Ag (g/t) 

Au (g/t) 

Zn (%) 

Hg (%) 

Sn (%) 

Pb (%) 

Sb (%)


A.3 Calculation <strong>of</strong> <strong>the</strong> R.E. 

Tables A.13, A.14 and A.15, show <strong>the</strong> variables required for <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> 

chemical exergy <strong>of</strong> <strong>the</strong> elements and <strong>the</strong> results, according to <strong>the</strong> assumptions described 

in section 5.2.3 and <strong>the</strong> model <strong>of</strong> <strong>the</strong> earth’s crust developed in this PhD 

(chapter 3) for gaseous, liquid and solid reference substances, respectively. 

Table A.13. Chemical exergies <strong>of</strong> <strong>the</strong> elements for gaseous reference substances 

Element R.S. State P0 i (kPa) bch,R.S. (kJ/mole) 

∆G f i 

(kJ/mole) 

b ch j 

(kJ/mole) 

Ar Ar g 9,06E-03 11,7 0,0 11,7 

C CO 2 g 3,35E-04 19,9 -394,4 410,3 

H 2 H 2O g 2,20E-02 9,5 -228,6 236,1 

He He g 4,85E-06 30,4 0,0 30,4 

K r K r g 9,70E-07 34,4 0,0 34,4 

N 2 N 2 g 7,58E-01 0,7 0,0 0,7 

N e N e g 1,77E-05 27,2 0,0 27,2 

O 2 O 2 g 2,04E-01 4,0 0,0 4,0 

X e X e g 8,70E-08 40,3 0,0 40,3 

Table A.14: Chemical exergies <strong>of</strong> <strong>the</strong> elements for aqueous reference substances 

Element R.S. State z + γi mi (mole/kg) 

∆G f i 

Ag AgCl − 

2 l -1 0,6 2,70E-09 -215,5 69,7 

b ch j 

(kJ/mole) 

As HAsO −2 

4 l -2 0,138 2,10E-08 -714,7 494,1 

B B(OH) 3 l 0 1 3,25E-04 -968,8 628,6 

Bi BiO + l 1 0,52 1,00E-10 -146,4 274,8 

Br 2 Br − l -1 0,73 8,70E-04 -104,0 101,1 

Cd CdCl 2 l 0 1 6,90E-11 -359,4 293,2 

Cl 2 Cl − l -1 0,63 5,66E-01 -131,3 124,2 

Cs Cs + l 1 0,6 2,30E-09 -282,2 404,5 

Cu Cu +2 l 2 0,2 7,30E-10 65,5 134,0 

H g H gCl −2 

I2 4 

IO3 

l -2 0,1 3,40E-10 -446,9 114,8 

− K K 

l -1 0,6 5,20E-07 -128,0 175,0 

+ l 1 0,62 1,06E-02 -282,4 366,5 

Li Li + l 1 0,68 2,50E-05 -294,0 392,9 

M o M oO−2 N a 

4 

N a 

l -2 0,1 1,10E-07 -836,4 730,5 

+ l 1 0,65 4,86E-01 -262,1 336,6 

N i N i +2 l 2 0,2 1,20E-07 -45,6 232,5 

P H PO−2 P b 

Rb 

4 

P bCl 2 

Rb 

l 

l 

-2 

0 

0,1 

1 

4,90E-07 

4,20E-11 

-1089,3 

-297,2 

861,6 

232,2 

+ l 1 0,6 1,40E-06 -282,4 388,8 

S SO −2 

4 l -2 0,12 2,93E-02 -744,6 607,3 

Se SeO −2 

4 l -2 0,1 1,20E-09 -441,4 346,7 

W W O −2 

4 l -2 0,1 5,60E-10 -920,5 827,7 

Zn Zn +2 l 2 0,2 1,70E-08 -147,3 339,0 


Calculation <strong>of</strong> <strong>the</strong> R.E. 385 

Table A.15: Chemical exergies <strong>of</strong> <strong>the</strong> elements for solid reference substances 

Element εj R.S. State c j xi bch,R.S. ∆G f i bch j 

(mole/g) 

(kJ/mole) (kJ/mole) (kJ/mole) 

Al 3,02E-03 Al2SiO 5 s 6,75E-03 1,60E-03 16,0 -2441,0 794,3 

Au 7,62E-12 Au s 8,05E-01 9,63E-10 51,5 0,0 51,5 

Ba 4,57E-06 BaSO4 s 6,49E-01 4,66E-04 19,0 -1361,9 765,5 

Be 2,33E-07 Be2SiO 4 s 5,95E-02 1,09E-06 34,0 -2033,3 602,6 

Ca 6,40E-04 CaCO 3 s 1,26E-01 1,27E-02 10,8 -1129,0 723,8 

Ce 4,50E-07 CeO2 s 0,02 1,41E-06 33,4 -1024,8 1054,2 

Co 2,94E-07 CoFe 2O4 s 0,005 2,31E-07 37,9 -1032,6 308,9 

C r 1,77E-06 K2C r2O7 s 0,01 1,39E-06 33,4 -1882,3 584,4 

D y 2,40E-08 D y(OH) 3 s 0,02 7,54E-08 40,7 -1294,3 974,9 

Er 1,38E-08 Er(OH) 3 s 0,02 4,33E-08 42,0 -1291,0 973,0 

Eu 6,58E-09 Eu(OH) 3 s 0,02 2,07E-08 43,9 -1320,1 1003,9 

F2 2,93E-05 CaF 2Ca 9 

(PO4) 6 

s 0,01 2,30E-05 26,5 -12985,3 556,1 

Fe 7,02E-04 Fe2O3 s 1,08E-02 5,95E-04 18,4 -742,2 376,8 

Ga 2,51E-07 Ga2O3 s 0,02 3,94E-07 36,6 -998,6 514,6 

Gd 2,03E-08 Gd(OH) 3 s 0,02 6,37E-08 41,1 -1288,9 969,9 

Ge 1,93E-08 GeO2 s 0,05 1,52E-07 38,9 -521,5 556,5 

H f 2,97E-08 H f O2 s 0,05 2,33E-07 37,9 -1027,4 1061,3 

Ho 5,03E-09 Ho(OH) 3 s 0,02 1,58E-08 44,5 -1294,8 979,3 

In 4,88E-10 In2O 3 s 0,05 1,92E-09 49,8 -830,9 437,4 

I r 1,14E-13 I rO2 s 0,005 8,95E-14 74,5 -185,6 256,1 

La 2,23E-07 La(OH) 3 s 0,02 7,00E-07 35,1 -1319,2 994,3 

Lu 1,77E-09 Lu(OH) 3 s 0,02 5,56E-09 47,1 -1259,6 946,6 

M g 6,15E-04 M g3Si4O 10 s 3,56E-03 1,15E-04 22,5 -5543,0 629,6 

(OH) 2 

M n 1,41E-05 M nO 2 s 2,66E-02 5,89E-05 24,1 -465,2 484,6 

N b 1,29E-07 N b 2O 3 s 0,01 1,01E-07 39,9 -1766,4 900,2 

N d 1,87E-07 N d(OH) 3 s 0,02 5,87E-07 35,6 -1294,3 969,8 

Os 1,63E-13 OsO 4 s 0,005 1,28E-13 73,6 -305,1 370,8 

Pd 4,89E-12 PdO s 0,005 3,84E-12 65,2 -82,5 145,7 

P r 5,04E-08 P r(OH) 3 s 0,02 1,58E-07 38,8 -1285,1 963,8 

P t 2,56E-12 P tO 2 s 0,005 2,01E-12 66,8 -83,7 146,5 

Pu 6,20E-20 PuO 2 s 0,01 9,73E-20 108,5 -995,1 1099,7 

Ra 4,40E-15 RaSO 4 s 0,05 3,45E-14 76,8 -1364,2 825,8 

Re 1,06E-12 Re 2O 7 s 0,01 8,32E-13 69,0 -1067,6 561,3 

Rh 5,83E-13 Rh 2O 3 s 0,005 2,29E-13 72,2 -299,8 183,0 

Ru 3,36E-12 RuO 2 s 0,005 2,64E-12 66,1 -253,1 315,2 

Sb 3,29E-09 Sb 2O 5 s 0,001 2,58E-10 54,7 -829,3 437,1 

Sc 3,11E-07 Sc 2O 3 s 0,05 1,22E-06 33,8 -1819,7 923,8 

Si 1,10E-02 SiO 2 s 3,33E-01 5,75E-01 1,4 -856,7 854,2 

Sm 3,13E-08 Sm(OH) 3 s 0,02 9,83E-08 40,0 -1314,0 993,9 

Sn 1,77E-08 SnO 2 s 9,27E-01 2,58E-06 31,9 -519,6 547,6 

Sr 3,65E-06 SrCO 3 s 1,39E-03 7,97E-07 34,8 -1140,1 758,8 

Ta 4,97E-09 Ta 2O 5 s 0,01 3,90E-09 48,0 -1911,6 974,8 

T b 4,40E-09 T b(OH) 3 s 0,02 1,38E-08 44,9 -1314,2 999,0 

Te 3,92E-11 TeO 2 s 0,005 3,08E-11 60,0 -270,3 326,4 



Table A.15: Chemical exergies <strong>of</strong> <strong>the</strong> elements for solid reference substances 


Element ε j 

R.S. State cj xi bch,R.S. ∆G f i bch j 

(mole/g) 

(kJ/mole) (kJ/mole) (kJ/mole) 

Th 4,53E-08 ThO2 s 3,27E-04 2,33E-09 49,3 -1169,1 1214,5 

T i 8,01E-05 T iO2 s 4,15E-02 5,22E-04 18,7 -889,5 904,4 

T l 4,40E-09 T l2O4 s 0,01 3,45E-09 48,3 -347,3 193,8 

T m 1,78E-09 T m(OH) 3 s 0,02 5,59E-09 47,1 -1265,5 952,5 

U 1,13E-08 UO3 · H2O s 0,01 1,77E-08 44,2 -1395,9 1196,1 

V 1,90E-06 V2O5 s 0,01 1,49E-06 33,3 -1419,6 721,5 

Y 2,36E-07 Y (OH) 3 s 0,02 7,41E-07 35,0 -1291,4 966,3 

Y b 1,13E-08 Y b(OH) 3 s 0,02 3,55E-08 42,5 -1262,5 944,9 

Z r 2,12E-06 Z rSiO 4 s 9,45E-01 3,15E-04 20,0 -1919,5 1077,4 


A.4 Calculation <strong>of</strong> <strong>the</strong> chemical exergy <strong>of</strong> gaseous fuels 

Table A.16 shows coefficients a 1 through a 7 for ideal gases required for <strong>the</strong> calculation 

<strong>of</strong> h ∗ (T) and s ∗ (T) in Eqs. 5.43 and 5.45, according to Zelenik and Gordon 

[413]. 

Table A.16. Coefficients a 1 through a 7 [413] 

a 1 a 2 a 3 a 4 a 5 a 6 a 7 

CH 4 2,928 0,002569 7,844E-06 -4,91E-09 2,04E-13 -10054 4,634 

C 2H 6 1,463 0,01549 5,781E-06 -1,26E-08 4,59E-12 -11239 14,43 

C 3H 8 0,8969 0,02669 5,431E-06 -2,13E-08 9,24E-12 -13955 19,36 

C 4H 10 1,522 0,03429 8,101E-06 -2,92E-08 1,27E-11 -17126 18,35 

C 5H 12 1,878 0,04122 0,00001253 -3,70E-08 1,53E-11 -20038 18,77 

N 2 3,704 -0,001422 2,867E-06 -1,20E-09 -1,40E-14 -1064 2,234 

CO 2 2,401 0,008735 -6,607E-06 2,00E-09 6,33E-16 -48378 9,695 

A.5 Estimation <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> 


A.5.1 Chermak’s methodology 

Table A.17 shows <strong>the</strong> enthalpy and Gibbs free energy <strong>of</strong> <strong>the</strong> polyhedral units required 

for <strong>the</strong> calculation <strong>of</strong> silicate <strong>mineral</strong>s. The brackets next to <strong>the</strong> chemical formulas 

indicate <strong>the</strong> coordination number.

Estimation <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>mineral</strong>s 387 

Table A.17. The g i and h i <strong>of</strong> each polyhedral type and <strong>the</strong> standard error (%) <strong>of</strong> <strong>the</strong> 

estimate. Values in kJ/mol. [55] 

Polyhedral unit gi Error hi Error 

Al2O [4] 

3 

Al2O -1631,32 13,3 -1716,24 11,0 

[6] 

3 

Al(OH) 

-1594,52 15,3 -1690,18 15,9 

[6] 

3 

SiO 

-1181,62 13,2 -1319,55 12,2 

[4] 

2 

M gO 

-853,95 4,6 -910,97 3,2 

[6] -628,86 10,6 -660,06 7,9 

M g(OH) [6] 

2 

CaO 

-851,86 10,2 -941,62 9,1 

[6] -669,13 5,9 -696,65 5,2 

CaO [8−z] -710,08 7,2 -736,00 7,1 

N a2O [6−8] -672,5 26,0 -683,00 18,4 

K2O [8−12] -722,94 27,4 -735,24 21,1 

H2O -239,91 5,7 292,37 4,6 

FeO [6] -266,29 6,8 -290,55 5,4 

Fe(OH) [6] 

2 

Fe2O -542,04 24,6 -596,07 8,2 

[6] 

3 -776,07 33,0 -939,18 35,6 

A.5.2 Vieillard’s methodology for hydrated clay <strong>mineral</strong>s 

Table A.18 shows <strong>the</strong> values for ∆ GO −2 M z+ (clay) for ions located in <strong>the</strong> interlayer 

(l), octahedral (o), tetrahedral (t) and brucitic (b) sites. These values are required 

for <strong>the</strong> calculation <strong>of</strong> <strong>the</strong> Gibbs free energy <strong>of</strong> formation <strong>of</strong> hydrated clays and phyllosilicates 

with Eqs 5.65 and 5.66. 

A.5.3 Estimated values <strong>of</strong> <strong>the</strong> enthalpy and Gibbs free energy <strong>of</strong> 


Table A.19, shows <strong>the</strong> estimated standard enthalpy and Gibbs free energy <strong>of</strong> formation 

<strong>of</strong> some <strong>of</strong> <strong>the</strong> <strong>mineral</strong>s included in <strong>the</strong> model <strong>of</strong> <strong>the</strong> upper crust developed in 

chapter 3. The number <strong>of</strong> <strong>the</strong> method used to estimate <strong>the</strong> values are outlined in column 

“Meth.” (see table 5.8 for <strong>the</strong> correspondence between methods and numbers). 

The estimation error ±ɛ is taken as <strong>the</strong> greatest associated error to <strong>the</strong> methodologies 

used for <strong>the</strong> determination <strong>of</strong> <strong>the</strong> <strong>mineral</strong>’s properties. This means that if <strong>the</strong>re 

is a substance, for which 2 or more estimation methods were used, only <strong>the</strong> error 

associated to <strong>the</strong> most inaccurate one will be taken into account (<strong>the</strong> maximum is 

<strong>the</strong>n ±ɛ = 10%). 

In <strong>the</strong> determination <strong>of</strong> Gibbs free energies <strong>of</strong> formation from standard entropies 

(method 1), references [284] and [391] were used for <strong>the</strong> required standard en-


Table A.18. Values <strong>of</strong> ∆ GO −2 M z+ (clay) for ions located in different sites [382] for 

hydrated clays and phyllosilicates. Values in kJ/mole 

Ions ∆GO −2 M z+ ∆GO −2 M z+ Ions ∆GO −2 M z+ ∆GO −2 M z+ 

(hydr. Clays) Phyllosil. (hydr. Clays) Phyllosil. 

K + (l) 425,77 476 

N a + (l) 267,19 280 

Li + (l) 77,54 Li + (o) -50,71 -35,2 

M g 2+ (l) -100 -110 M g 2+ (o) -112 -103 

Ca 2+ (l) -32,34 -52 Ca 2+ (o) -74,4 

(N H 4) + (l) -28,4 -76,3 C r +3 (o) -158,6 -160,6 

M n +2 (l) -88 M n +2 (o) -122,9 -119,1 

Cu +2 (l) -136,7 

Co +2 (l) -110 Co 2+ (o) -132,2 

N i +2 (l) -114,8 N i +2 (o) -136,8 -135,3 

Cd +2 (l) -102,6 

Zn +2 (l) -121 Zn +2 (o) -140,3 -139,3 

Al +3 (l) -143,3 Al 3+ (o) -161,23 -157 

La +3 (l) -65,6 

Fe 2+ (l) -148,7 Fe 2+ (o) -134,4 -141 

Cs + (l) 565,9 562,1 Fe 3+ (o) -164,05 -168,5 

Rb + (l) 528,1 545,1 Ga 3+ (o) -167,6 

Ba 2+ (l) 157,6 73,7 T i 4+ (o) -180,5 

Sr 2+ (l) 123,4 18,8 

H + (l) -154,2 H + (o) -220 

Ions ∆GO −2 M z+ ∆GO −2 M z+ Ions ∆GO −2 M z+ ∆GO −2 M z+ 

(hydr. Clays) Phyllosil. (hydr. Clays) Phyllosil. 

M g 2+ (b) -30 

Fe 2+ (b) -115 

Al 3+ (t) -197,31 -196 Al 3+ (b) -171 

Fe 3+ (t) -261,7 Fe 3+ (b) -210 

Ga 3+ (t) -241,9 Li + (b) 70 

Be 2+ (t) -193,9 M n 2+ (b) -87,3 

Zn 2+ (b) -129,1 

N i 2+ (b) -120,8 

Co 2+ (b) -114,5 

C r +3 (b) -173,1 

Ca 2+ (b) 4,7 

H + (b) -228 

Si 4+ (t) -169 Si 4+ (clay) -166,09 

H + (clay) -220 

tropies <strong>of</strong> <strong>the</strong> elements in <strong>the</strong>ir reference state, according to Eq. 5.50. Most <strong>of</strong> <strong>the</strong> 

properties <strong>of</strong> <strong>the</strong> simple oxides used for <strong>the</strong> estimations are also recorded in <strong>the</strong> same 

references. 

In column “M.2: Poles”, <strong>the</strong> poles that compose <strong>the</strong> <strong>mineral</strong> under analysis assuming 

an ideal solid solution (method 2, Eq. 5.53) are given.


Column “M.3; 4; 6; 8: Ref. Minerals” includes <strong>the</strong> reference <strong>mineral</strong> used to determine 

<strong>the</strong> properties <strong>of</strong> <strong>the</strong> substance considered. Remember that in method 3, 

<strong>the</strong> reference <strong>mineral</strong> is decomposed ei<strong>the</strong>r into its sulfides or oxides and <strong>the</strong> obtained 

∆H r and ∆G r is added to <strong>the</strong> weighted sum <strong>of</strong> enthalpies and free energies 

<strong>of</strong> <strong>the</strong> simple sulfides or oxides <strong>of</strong> <strong>the</strong> <strong>mineral</strong> under consideration (see Eq. 5.55). 

In method 4, <strong>the</strong> same reaction energy involved in a substitution reaction is applied 

for <strong>the</strong> <strong>mineral</strong> under analysis and for an isomorphous one. For methods 6 and 8 

(<strong>the</strong> ∆O −2 method for <strong>the</strong> same family <strong>of</strong> compounds, and for different compounds 

with <strong>the</strong> same cations, respectively), <strong>the</strong> reference <strong>mineral</strong>s (at least 2) required for 

<strong>the</strong> determination <strong>of</strong> parameter α in Eqs. 5.62 and 5.66 are given. If not specified, 

<strong>the</strong> reference <strong>mineral</strong> will be used for <strong>the</strong> determination <strong>of</strong> both, ∆H 0 

f 

and ∆G0 

f . 

The properties <strong>of</strong> substances approximated with method 4 (<strong>the</strong> method <strong>of</strong> Chermak 

and Rimstidt for silicate <strong>mineral</strong>s) and 7 (<strong>the</strong> ∆O −2 method for hydrated clay <strong>mineral</strong>s 

and for phyllosilicates), were obtained with <strong>the</strong> information provided in tables 

A.17 and A.18, after decomposing <strong>the</strong> <strong>mineral</strong> into its constituent blocks. 

Column “M.9; 10: Ideal reaction” shows <strong>the</strong> reaction that takes place to form <strong>the</strong> 

<strong>mineral</strong> under analysis. Remember that in method 9 (assuming ∆S f zero), it is 

assumed that <strong>the</strong> entropy <strong>of</strong> reaction is zero. In method 10 (<strong>the</strong> element substitution 

method), <strong>the</strong> enthalpy and Gibbs free energy <strong>of</strong> reaction is approximated to zero. If 

not specified, <strong>the</strong> reference <strong>mineral</strong> will be used for <strong>the</strong> determination <strong>of</strong> both, ∆H 0 

f 

and ∆G 0 

f . 

For those substances whose properties were estimated with method 11 (<strong>the</strong> addition 

method for hydrated <strong>mineral</strong>s), <strong>the</strong> weighted enthalpy or Gibbs free energy <strong>of</strong> liquid 

water contained in <strong>the</strong> <strong>mineral</strong> was added. 

The properties <strong>of</strong> <strong>mineral</strong>s estimated with method 12 are obtained through <strong>the</strong> 

weighted sum <strong>of</strong> <strong>the</strong> simple blocks (ei<strong>the</strong>r oxides or sulfides) that compose <strong>the</strong> substance. 

The properties <strong>of</strong> <strong>the</strong> simple compounds are mainly obtained from Faure 

[94] and Robie [284].


Table A.19: Estimations <strong>of</strong> <strong>the</strong> standard enthalpy and Gibbs free energy <strong>of</strong> <strong>mineral</strong>s. Values in 

kJ/mole 

Mineral Formula ∆H 0 ∆G f 

0 M.2: Poles M.3; 4; 6; 8: Ref. Minerals M.9; 10: Ideal reaction Meth. ±ɛ, References 

f 

% 

Actinolite Ca2M g3Fe 2Si8O 22(OH) 2 -11519,4 -10801,5 Ca2Fe 5Si8O 22(OH) 2 3 1 [94] [284] 


5 T iSi6O20 -8184,4 -7660,9 12 10 [284][94] 

Amblygonite Li0,75N a0,25Al(PO 4) 

-307,1 -282,7 Li0,75N a0,25Al(PO 4) 

10; 10 [284][94] 

F0,75(OH) 0,25 

F0,75(OH) 0,25 + 0, 75H2O 12 

→ Li0,75N a0,25Al(PO 4)(OH) 2 + 

0, 75H F 

Ankerite CaFe 2+ 

0,6M g0,3Mn 2+ 

0,1 (CO3) 2 -2076,8 -1923,1 12 10 [284][94] 

Anorthite CaAl 2Si2O 8 -4274,4 -4021,0 ∆H f : 1 [55] 

5 

Apatite Ca5(PO 4) 3(OH) 0,33 

-6773,4 -6386,9 Ca5(PO 4) 3F; Ca5(PO 4) 3Cl; 

Ca10(PO 4) 6Cl 2 +2H F → 3; 10 5 [94] [284] 

F0,33Cl 0,33 

Ca5(PO 4) 3OH 

Ca10(PO 4) 6F2+2HCl Axinite- Ca2Fe Fe 

2+ Al2BO 3 Si4O12(OH) -7640,4 -7180,9 12 10 [284][94] 

Bastnaesite La(CO 3)F -1660,9 -1527,8 SmOH · CO3 · 0, 5H2O; La(CO 3)F + 1, 5H2O → LaOH · 1; 8; 5 [222][391] 

N dOH · CO3 · 0, 5H2O CO3 · 0, 5H2O + H F 

10 

[223] 

[284] 

Beidellite N a0,33Al2,33Si3,67 O10(OH) 2 -5691,6 -5317,2 ∆H f 

3 1 [94] [284] 

Ca0,167Al2,33Si3,67O10(OH) 2 

Bertrandite Be4Si 2O7(OH) 2 -4586,1 -4300,6 1 0 [136] 

Beryl Be3Al 2Si6O 18 -9006,5 -8500,4 1 0 [136] 

Biotite K(M g2,5Fe 0,5)(Si3Al)O 10 -6079,4 -5706,7 K M g3(Si3Al)O 10(OH) 2; K Fe3(Si 3Al)O10(F) 2 from 

2; 4 1 [284][391] 

(OH) 1,75F0,25 K M g3(Si3Al)O 10(F) 2; K M g3(Si3Al)O 10(OH) 2 and 

K Fe3(Si 3Al)O10(OH) 2; K M g3(Si3Al)O 10(F) 2 

K Fe3(Si 3Al)O10(F) 2 

Bismutite Bi2(CO 3)O2 -968,0 -888,7 12 10 [284][94] 

Blomstran- U0,3Ca 0,2N b0,9Ti 0,8Al0,1 dite/ Fe 

Betafite 

3+ 

0,1Ta -2884,5 -2683,8 12 10 [284][94] 

0,5O6(OH) Boulangerite P b5Sb 4S11 -1034,5 -1023,7 P b5S b4S11 → 5P bS + 2S b2S3 1; 9 5 [67] [284] 

Britholite Ca2,9Ce 0,9Th 0,6 La0,4N d0,2 -7057,3 -6666,9 Ca2,9Ce 0,9Th 0,6 La0,4N d0,2 10; 10 [284][94] 

Si2,7P0,5O12(OH) 1,8F0,2 Si2,7P0,5O12(OH) 0,8F0,2 + 0, 2H2O 12 

→ Ca2,9Ce 0,9Th 0,6 La0,4N d0,2 Si2,7P0,5O12(OH) 2 + 0, 2H F 

Bronzite M gFeSi 2O6 -2753,4 -2585,3 1 0 [309][284] 

Calaverite AuTe2 -19,0 -17,4 1 0 [255] 

Cancrinite N a6Ca 2Al6Si 6O24(CO 3) 2 -14980,9 -14136,3 12 10 [94] 

Chevkinite Ce1,7 La1,4Ca 0,8Th 0,1 

Fe 2+ 

1,8M g0,5 T i2,5Fe 3+ 

0,5Si -10499,8 -9894,5 12 10 [284][94] 

4O22 Chloritoid Fe 2+ 

1,2M g0,6Mn 2+ 

0,2 

-6606,9 -6152,6 FeAl 2SiO 5(OH) 2 3 1 [94] [284] 

Al4Si 2O10(OH) 4 




kJ/mole– continued from previous page. 

References 

∆G0 M.2: Poles M.3; 4; 6; 8: Ref. Minerals M.9; 10: Ideal reaction Meth. ±ɛ, 

f 

% 

Mineral Formula ∆H 0 

f 

Chondrodite M g3,75Fe 2+ 

1,25 (SiO4) 2 

-5023,0 -4701,4 M g3,75Fe F1,5(OH) 0,5 

2+ 

1,25 

(SiO4) 2F1,5(OH) 0,5 + 1, 5H2O → M g3,75Fe 2+ 

1,25 (SiO 5; 10 5 [55] [284] 

[94] 

4) 2(OH) 2 + 

1, 5H F 

Chrysocolla Cu2Si 2O6(H 2O) 4 -3279,4 -2964,6 ∆H 0:12 

10 [94] [400] 

f 

Clementite Fe 2+ 

3 M g1,5Al Fe3+ -7657,8 -7043,1 5 1 [55] 

Si3AlO 12(OH) 6 

Clinochlore M g3,75Fe 1,25Al2 Si3O10(OH) 8 -8435,5 -7796,6 M g5Al2Si 3O10(OH) 8 3 1 [94] [284] 

Clinohumite M g6,75Fe 2,25Si4O 16 

-8966,4 -8410,0 M g6,75Fe 2,25Si4O 16 

10 1 [144][284] 

(OH) 0,5F1,5 (OH) 2 + 2, 25M gO → 

M g9Si4O 16(OH) 2 + 2, 25FeO; 

M g6,75Fe 2,25Si4O 16(OH) 0,5F1,5 +1, 5H F → 

M g6,75Fe 2,25Si4O 16(OH) 2+ 

1, 5H2O Cancrinite N a6Ca 2Al6Si 6O24(CO 3) 2 -14980,9 -14136,3 12 10 [94] 

Cobaltite CoAsS -163,1 N.A. ∆H 0:FeAsS 

3 1 [284][391] 

f 

Colemanite Ca2B 6O11· 5H2O -6949,7 -6277,0 3CaO · B2O3; 2CaO · B2O3; 1; 6; 5 [319][284] 

CaO · 2B2O3 11 

Cooperite P t0,6Pd 0,3N i0,1S -79,8 -73,8 P tS 3 1 [94] [284] 

Crossite N a2M g2Fe 2+ Al2 -11600,3 -10925,8 N a2M g3Al2Si 8O22(OH) 2; 

(Si8O22)(OH) 2 

N a2Fe 2+ 

3 Al 1; 2 1 [120][284] 

2Si8O 22(OH) 2 

CryptomelaneK8(M n 4+ 

7,5M n2+ 

0,5 ) O16 -3743,6 -3432,2 ∆H 0 

f :N a0,033Al0,02K0,12 M n0,94Fe 0,0375Sr0,016 Ba0,012O2; ∆G0 f : M n 3 1 [97] [94] 

[284] 

3O4 Cubanite CuFe 2S3 -293,7 -302,8 Cu5FeS 4 3 1 [241][226] 

[284] 

Delorenzite/ Y0,7Ca 0,2Ce 0,12(Ta0,7) 2 -2721,2 -2549,9 12 10 [284][94] 

Tanteux- (N b0,2) 2(T i0,1)O5,5(OH) 0,5 

enite 

Dietzeite Ca2(IO 3) 2(C rO4) -2425,4 -2148,1 12 10 [391] 

Eudyalite N a4Ca 2Fe 2+ 

0,7M n0,3Z r 

-11859,9 -11062,9 N a12Ca 6Fe 

Si8O22(OH) 1,5Cl 1,5 

2+ 

3 

N a4Ca 2Fe 

Z r3Si24O66(OH) 6 

2+ 

0,7M n0,3Z r 

Si8O22(OH) 2 + 1, 5HCl 

→ N a4Ca 2Fe 2+ 

0,7M n 1; 3; 1 [179][284] 

10 

0,3Z r 

Si8O22(OH) 1,5Cl 1,5 + 1, 5H2O Euxenite Y0,7Ca 0,2Ce 0,1(Ta0,2) 2 

-2671,5 -2506,3 12 10 [284][94] 

(N b0,7) 2(T i0,025)O6 Fergusonite N d0,4Ce 0,4Sm0,1Y0,1N bO4 -2808,3 -2631,2 12 10 [284][94] 

Ferrocolum- Fe 

bite 

2+ N b2O6 -2172,8 -2631,2 12 10 [284][94] 







f 

% 

Ferrotantalite Fe2+ Ta2O6 -2319,3 -2163,9 12 10 [284][94] 

Francolite Ca5(PO4) 2,63 (CO3) 0,5F1,11 -5984,4 -5698,1 Ca10(PO 4) 6F2 1; 3; 1 [167][391] 

9 

Freibergite Ag7,2Cu 3,6Fe 2+ 

1,2 Sb3AsS 13 -703,2 -727,5 Ag3SbS 3 3 5 [284] 

Gadolinite Y2Fe 2+ Be2(Si 2O10) -5220,0 -4943,3 12 10 [284][94] 

Garnierite (N i2M g)Si2O 5(OH) 4 -3494,6 -3267,1 (N i2M g)Si2O 5(OH) 4 + 

1; 7; 1 [383][143] 

2M gO → M g3Si2O 5(OH) 4 + 

9 

[284] 

2N iO 

Gedrite M g5Al2(Si 6Al2O 22)(OH) 2 -12319,7 -11584,2 1 0 [144] 

Glauconite (K0,6N a0,05)(Fe 3+ 

1,3 

-5150,3 -4785,6 7 0,6 [383] 

M g0,4Fe 2+ 

0,2Al3+ 0,15 ) 

(Si3,8Al0,2)O10(OH) 2 

Helvine/ M n4Be3(SiO 4) 3S -5843,9 -5532,4 12 10 [284][94] 

Helvite 

Hollandite Ba0,8P b0,2N a0,125 Fe1,3Al0,2Si0,1 M n 2+ 

0,5M n4+ 

6 O 3 1 [97] [94] 

[284] 

16 

-4733,3 -4330,4 ∆H 0 

f :N a0,0125Al0,029Si0,01 K0,005Mn 0,82Fe 0,165 

Ba0,09P b0,02O2 · 0, 09H2O; ∆G0 f : M n3O4 Hornblende- Ca2Fe Fe 

2+ 

4 Al0,75Fe 3+ 

0,25 

-10976,4 -10303,7 Ca2M g4Al(Si 7AlO22)(OH) 2 3 [320][284] 

(Si7AlO 22)(OH) 2 

Humite M g5,25Fe 2+ 

1,75 (SiO4) 3 

-6953,7 -6512,3 M g9Si4O 16(OH) 2 M g5,25Fe F1,5(OH) 0,5 

2+ 

1,75 (SiO4) 3(OH) 2 

+1, 75M gO → 

M g9Si4O 16(OH) 2 + 1, 75FeO; 

M g5,25Fe 2+ 

1,75 (SiO4) 3F1,5(OH) 0,5 

+1, 5H F → 

M g5,25Fe 2+ 

1,75 (SiO 3; 10 5 [144] 

4) 3(OH) 2 

+1, 5H2O Hydrobiotite (K0,3Ca 0,1)(M g2,3Fe 3+ 

0,6 -7362,2 -6238,9 (K0,3Ca 0,1)(M g2,3Fe Al0,1)(Si2,8Al1,2) O10((OH) 1,8F0,2) · 3(H2O) 3+ 

0,6Al0,1) (Si2,8Al1,2)O10(OH) 1,8F0,2) · 

3(H2O)+ 0, 2H F → 

(K0,3Ca 0,1)(M g2,3Fe 3+ 

0,6Al 1; 7; 5 [382][143] 

10 

[284] 

0,1) 

(Si2,8Al1,2)O10(OH) 2 · 3(H2O) + 

0, 2H2O Hydromusco- K0,6(H3O) 0,4Al2M g0,4Fe vite 

2+ 

0,1 -5886,2 -5499,1 5 1 [55] 

Si3,5O10(OH) 2 

HydrosodaliteN a8Al6Si 6O24 (OH) 2 -13408,5 -12678,2 N a8Al6Si 6O24Cl 2 N a8Al6Si 6O24SO4 + 2H2O → 3, 10 5 [187] 

N a8Al6Si 6O24(OH) 2 + H2SO4 Ilmenorutile T i0,7N b0,15Fe 2+ 

0,225O2 -864,6 -813,2 T iO2; N b2O5; FeO 1; 2 1 [227][94] 

[284] 







f 

% 


0,6Fe2+ 0,3M g2+ 

Fe 3+ 

1,5M n3+ 

0,5O -1237,4 -1137,5 M nFe2O 4; Fe2O4; FeM n2O4; FeM n2O4 + M nO → M nM n2O4 + 1; 2; 5 [227][285] 

M gFe 

4 

2O4; M nM n2O4; FeO 

9 

[284] 

M gMn 2O4 [227] 

[189] 

[118] 

Jadeite N aAl0,9Fe 3+ 

0,1 (Si2O6) -2990,4 -2812,1 N aAlSi 2O6 3 1 [94] [284] 

Jarosite K Fe 3+ 

3 (SO4) 2(OH) 6 -3521,7 -3318,7 ∆H 0 

f : 10 [94] [400] 

12 

Kernite N a2O · 2B2O3 · 4H2O -4104,9 -3713,1 N a2O · 2B2O3 · 4H2O → N a2O + 10 5 [284][94] 

2B2O3 + 4H2O Kornerupine M g1,1Fe 0,2Al5,7 -9172,9 -8624,8 Al6,75BSi 3O17,25(OH) 0,75 3 1 [135][284] 

(Si3,7B0,3)O17,2(OH) Lampro- N a2SrBaT i3Si4O 16(OH)F -8401,2 -7865,3 N a2SrBaT i3Si4O 16(OH)F + H2O 10; 10 [284][94] 

phyllite 

→ N a2SrBaT i3Si4O 16(OH) 2 + 12 

H F 

Lavenite N a1,1Ca 0,9Mn 2+ 

0,5Fe2+ 0,5 

-4191,1 -3925,1 N a1,1Ca 0,9Mn 

Z r0,8Ti 0,1N b0,1(Si2O 7) 

O0,6(OH) 0,3F0,1 2+ 

0,5Fe2+ 0,5 

Z r0,8Ti 0,1N b0,1(Si2O 7) 

O0,6(OH) 0,3F0,1 + 0, 1H2O → N a1,1Ca 0,9Mn 2+ 

0,5Fe2+ 10; 10 [284][94] 

12 

0,5 

Z r0,8Ti 0,1N b0,1(Si2O 7) 

O0,6(OH) 0,4 + 0, 1H F 

Lawsenite CaAl 2Si2O 7(OH) 2 · H2O -4812,8 -4510,6 CaAl 2Si2O 2 3; 11 5 [284][94] 

Lepidolite K Li2AlSi 4O10F(OH) -6003,2 -5654,7 K M g3(Si3Al)O 10(OH) 2; K Li2AlSi 4O10F(OH) + H2O → 7; 4 1 [383][391] 

K M g3(Si3Al)O 10(F) 2 

K Li2AlSi 4O10(OH) 2 + H F 

Lepido- K Fe 

melane/ 

Annite 

2+ 

2,5M g0,5Fe 3+ 

0,75 

-4995,0 -4642,3 K Fe3AlSi 3O10(OH) 2 3 1 [94] [284] 

Al0,25Si3O 10(OH) 2 

Loellingite FeAs2 -85,7 -80,2 1 0 [113] 

Loparite - N a0,6Ce 0,22 La0,11 -1430,8 -1721,8 12 10 [284][94] 

(Ce) Ca0,1Ti 0,8N b0,2O3 Manganite M nO(OH) -622,4 -557,3 ∆H 0 

f : 10 [284] 

12 

Microlite N a0,4Ca 1,6Ta2O 6,6 

-3208,3 -3004,3 N a0,4Ca 1,6Ta2O 6,6(OH) 0,3 F0,1 + 10; 10 [284][94] 

(OH) 0,3F0,1 0, 1H2O → N a0,4Ca 1,6Ta2O 6,6 12 

(OH) 0,4 + 0, 1H F 

Miserite KCa 2Ce 3Si8O 22 (OH) 1,5F0,5 -11738,2 -11035,1 KCa 2Ce 3Si8O 22(OH) 1,5F0,5 + 10; 10 [284][94] 

0, 5H2O → 12 

KCa 2Ce 3Si8O 22(OH) 2 + 0, 5H F 

Monazite Ce0,5 La0,25N d0,2 Th0,05(PO 4) -2074,0 -1943,3 12 10 [284][94] 

(Ce) 







f 

% 

Montmori- N a0,165Ca 0,084Al2,33 -5523,8 -5354,5 Ca0,167Al2,33Si3,67O10(OH) 2; 

2 1 [94] 

llonite Si3,67O10(OH) 2 

N a0,33Al2,33Si3,67O10(OH) 2 

Murmanite N a4Ti 3,6N b0,4(Si2O 7) 2O4 · -9804,0 -9096,6 12 10 [284][94] 

4(H2O) Muscovite KAl3Si 3O10(OH) 1,8F0,2 -5991,3 -5616,6 K M g3(Si3Al)O 10(OH) 2; KAl3Si 3O10(OH) 1,8F0,2 4 1 [391][284] 

K M g3(Si3Al)O 10(F) 2 

+0, 2H2O → KAl3Si 3O10(OH) 2 

+0, 2H F 

Nepheline N a0,75K0,25Al(SiO 4) -2087,6 -1972,4 N aAlSiO 4 3 1 [94] [284] 

Neptunite KN a2 LiFe 2+ 

1,5M n2+ 

0,5 T i2Si8O 24 -10724,6 -10061,3 12 10 [284][94] 

Nontronite N a0.3Fe 3+ 

2 (Si3,7 -6841,0 -5447,7 1; 7 0,6 [382][143] 

Al0,3)O10(OH) 2 · 4(H2O) [284] 

Nordite N a2,8Mn 2+ 

0,2Sr0,5Ca 0,5 

-8020,8 -7532,2 12 10 [284][94] 

La0,33Ce 0,6Zn 0,6 M g0,4Si6O 17 

Nosean N a8Al6Si 6O24 SO4 -13936,7 -13131,5 N a8Al6Si 6O24SO4 + 2HCl → 10 5 [187] 

N a8Al6Si 6O24Cl 2 + H2SO4 Olivine M g1,6Fe 2+ 

0.4 (SiO4) -2083,3 -1925,0 ∆H 0 

f : 1 [55] 

5 

Omphacite Ca0,6N a0,4M g0,6Al0,3 -3075,5 -2904,3 M gSi2O 6; N aFeSi 2O6; 2 1 [284] 

Fe0,1Si2O 6 

CaSi 2O6; N aAlSi 2O6 Opal SiO2· 0, 5H2O -1044,5 -967,9 11 5 [284] 

Orthite- Ca(Ce 0,4Ca 0,2Y0,133) Allanite (Al2Fe 3+ -6481,6 -6055,4 Ca2(Al 2Fe 

)Si3O12(OH) 3+ )Si3O12(OH) 3 1 [144][284] 

[94] 

Orthoclase KAlSi 3O8 -3977,5 -3752,1 1 0 [25] 

Palygorskite M gAlSi 4O10(OH) · 4(H2O) -6477,8 -5939,9 5 1 [55] 

Pentlandite Fe 2+ 

4,5N i4,5S8 -778,3 -766,2 12 10 [284][94] 

Phlogopite K M g3AlSi 3O10F(OH) -6292,8 -5902,2 K M g3(Si3Al)O 10(OH) 2; K M g3AlSi 3O10F(OH)+H 2O → 4 1 [391][284] 

K M g3(Si3Al)O 10(F) 2 

K M g3AlSi 3O10(OH) 2+H F 

Pigeonite M g1,35Fe 0,55Ca 0,1(Si2O 6) -1535,4 -1448,8 M gSi2O 6; CaSi 2O6; 2 1 [284] 

Fe2Si 2O6; Pollucite Cs0,6N a0,2Rb0,1Al0,9 Si2,1O6 · -3297,1 -3074,2 12 10 [284][94] 

(H2O) Polycrase Y0,5Ca 0,1Ce 0,1U0,1 -2847,7 -2681,3 12 10 [284][94] 

(Y) Th0,1Ti 1,2N b0,6Ta0,2O6 Psilomelane Ba2Mn 2+ 

2 M n4+ 

3 O10 · 2H2O -2569,1 -2347,2 ∆H 0 

f :Ba0,4Mn 2+ 

0,4 M n4+ 

0,6O2 · 

0, 4H2O; ∆G0 f : M n 3 1 [97] [94] 

[284] 

3O4 Pumpellyte Ca2M gAl2(SiO 4) 

-7148,6 -6672,5 Ca4M gAl5Si 6O21(OH) 7 3 1 [144][284] 

(Si2O7)(OH) 2 · H2O Pyrargirite Ag3SbS 3 -131,5 -142,2 Ag3S bS3 → 3 

2 Ag2S + 1 

2 S b2S3 9 5 [284] 





References 

∆G0 M.2: Poles M.3; 4; 6; 8: Ref. Minerals M.9; 10: Ideal reaction Meth. ±ɛ, 

f 

% 

Mineral Formula ∆H 0 

f 

10; 10 [284][94] 

12 

0, 25H F 

Ramsayite N a2Ti 2Si2O 9 -4360,1 -4103,9 12 10 [284][94] 

Realgar As4S4 -140,3 -132,7 1 0 [312] 

RhabdophaneCe0,75 La0,25(PO 4) · H2O -1964,9 -1821,9 LaPO 4; CePO4 2 1 [364][388] 

Riebeckite N a2Fe 2+ 

3 Fe3+ 

2 (Si8O22)(OH) 2 -10087,1 -9399,5 1 0 [94] [312] 

Rinkolite/ N a2Ca 3Ce 1,5Y0,5 -9415,1 -8808,5 N a2Ca 3Ce 1,5Y0,5 10; 10 [284][94] 

Mosan- T i0,4N b0,5Z r0,1(Si2O 7) 2 

T i0,4N b0,5Z r0,1(Si2O 7) 2 

12 

drite O1,5F3,5 O1,5F3,5 + 3, 5H2O → 

N a2Ca 3Ce 1,5Y0,5 T i0,4N b0,5Z r0,1(Si2O 7) 2 

O5 + 3, 5H F 

Ripidolite (M g3,75Fe 1,25Al) 

-8429,2 -7788,2 7 0,6 [383] 

(Si3Al)O 10(OH) 2(OH) 6 

Samsonite Ag4MnSb2S 6 -444,9 -463,5 ∆H 0 

f :Ag3SbS 3 3 5 [284] 

Sanidine K0,75N a0,25AlSi 3O8 -3860,7 -3715,9 KAlSi 3O8 3 1 [94] [284] 

Scapolite- N a4Al3Si 9O24Cl -12197,4 -11504,2 1 0 [186][284] 

Marialite 

Serpentine M g3Si2O 5(OH) 4 -4363,4 -4035,4 1 0 [25] 

Stephanite Ag5SbS 4 -166,1 -184,5 ∆H 0 

f :Ag3SbS 3 3 5 [284] 

StilplomelaneK0, 8Fe8Al 0,85Si11,1 -16655,5 -15197,0 1 0 [210][210] 

O21(OH)8 · 6H2O [284] 

Tennantite Cu10Fe 2As4S 13 -1968,6 -1999,6 1 0 [303][284] 

Tetradymite Bi2Te 2S -100,2 -100,6 Bi2Te 3; Bi2S3 2 1 [226][94] 

Tetrahedrite Cu10Fe 2S b4S13 -1909,5 -1939,7 1 0 [303][284] 

Thomsonite N aCa2Al5Si 5O20 · 6H2O -12413,7 -11543,9 5 1 [55] 

Thorite ThSiO 4 -2160,5 -2048,8 ThSiO 4 + UO2 → USiO 4 + ThO2 1; 9 5 [298][192] 

[284] 

Thortveitite Sc1,5Y0,5Si2O 7 -3740,2 -3540,6 Y2Si 2O7; Sc2Si2O 7 Sc2Si2O 7 + Al2O3 → Al2Si 2O7 + 

Sc2O3; s0 f :Y 2; 9 5 [62] [269] 

2Si2O 7 + Al2O3 → 

[213] 

Al2Si 2O7 + Y2O [391] 

3 

[284] 

Thuringite- (Fe3M g2Fe Chamosite 

3+ 

0,5Al3+ 0,5 ) 

-7596,0 -6981,9 7 0,6 [383] 

(Si3Al)O 10(OH) 2 

Titanite CaT iSiO5 -2597,1 -2455,1 1 0 [94] [312] 

Todorokite N a2Mn 4+ 

4 M n3+ 

2 O12· 3H2O -4037,4 -3576,5 ∆H 0 

f :M g0,19Mn 3+ 

0,38 

M n 4+ 

0,62O2 · 0, 75H2O; ∆G0 f : 

3 1 [97] [284] 

[94] 

M n3O4 Continued on next page . . . 

Pyrochlore N aCaN b2O6(OH) 0,75F0,25 -2897,9 -2687,3 N aCaN b2O6(OH) 0.75F0.25 + 

0, 25H2O → N aCaN b2O6(OH) +






f 

% 

Topaz Al2(SiO 4)F1,1(OH) 0,9 -3044,4 -2875,2 Al2(SiO 4)F1,1(OH) 0,9+0,9H F → 10 5 [94] 

Al2SiO 4F2+0,9H2O Tourmaline- N aFe 

Schorl 

2+ 

3 Al6(BO 3) 3Si6 -14401,4 -13453,5 1 0 [107][284] 

O18(OH) 4 

Ulexite N aCa(B 5O6(OH) 6)· 5H2O -6762,2 -6151,5 1 0 [293][284] 

Ulvöspinel T iFe 2+ 

2 O4 -1489,4 -1392,9 12 10 [284][94] 

Vermiculite M g3Si4O 10(OH) 2 · 2(H2O) -7018,8 -5957,2 ∆H 0 

f : 10 [284] 

12 

Vernadite M n 4+ 

0,6Fe3+ 0,2Ca 0,2 

-637,8 -571,4 ∆H 

N a0,1O1,5(OH) 0,5 · 1, 4(H2O) 0 

f :Ba0,13MnO2 · 0, 27H2O M n 4+ 

0,6O2 · 0, 4H2O; ∆G0 f : 

3 1 [284][94] 

M n3O4 Violarite Fe2+ N i2S4 -378,0 -368,9 Fe2+ N i2S4 → 2 

3 N i3S4+ 1 

3 Fe2S3 + 

1 

3 FeS 

1; 9 1 [255][79] 

[241] 

Vivianite Fe3(PO 4) 2(H2O) 8 -4608,4 -4428,2 ∆H 0 

f : 10 [284] 

12 

Weinschen- Y PO4 -1987,7 -1871,1 1 0 [364][345] 

kite 

[284] 

[391] 

Wohlerite N aCa2Z r0,6N b0,4 -4439,7 -4170,0 N aCa2Z r0,6N b0,4 10; 10 [284][94] 

Si2O8,4(OH) 0,3F0,3 Si2O8,4(OH) 0,3F0,3 + 0, 3H2O 12 

→ N aCa2Z r0,6N b0,4 Si2O8,4(OH) 0,6 + 0, 3H F 


0,5M n0,5W O4 -1246,2 -1146,4 FeW O4; M nW O4 2 1 [284] 


<strong>Exergy</strong> calculation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources 397 

A.6 <strong>Exergy</strong> calculation <strong>of</strong> <strong>the</strong> <strong>mineral</strong> resources 

Table A.20 and A.21 show <strong>the</strong> chemical Bch and concentration Bc exergy, as well 

as <strong>the</strong>ir corresponding exergy cost (B∗ and B∗ 

ch c ), <strong>of</strong> <strong>the</strong> world’s <strong>mineral</strong> production 

in 2006, <strong>the</strong> reserve, base reserve and world’s resources, collected from <strong>the</strong> USGS 

[362]. The specific chemical exergies <strong>of</strong> <strong>the</strong> substances bch are calculated with Eq. 

5.1. The concentration exergies bc are calculated as <strong>the</strong> difference between <strong>the</strong> concentration 

exergies obtained with <strong>the</strong> average <strong>mineral</strong> concentration in <strong>the</strong> deposits 

(x m) and with <strong>the</strong> average concentration in <strong>the</strong> earth’s crust (x c), both are calculated 

with Eq. 5.10. The exergy costs are obtained with Eq. 5.46, and <strong>the</strong> unit 

exergy costs kch and kc from table 5.7. The average <strong>mineral</strong> concentration in <strong>the</strong> 

crust and in <strong>the</strong> <strong>mineral</strong> deposits are expressed as xc and xm, respectively.


Table A.20: The chemical exergy and exergy cost <strong>of</strong> <strong>the</strong> 2006 world’s <strong>mineral</strong> production, <strong>mineral</strong> 

reserves, base reserve and world resources. Values are expressed in ktoe if not specified 

Production Reserves Reserve base World resources 

bch [kJ/mol] kch [-] Bch B∗ B ch ch B∗ B ch ch B∗ B ch ch B∗ ch 

Aluminium 794,30 8 2,38E+04 1,91E+05 3,20E+06 2,57E+07 4,10E+06 3,29E+07 9,61E+06 7,72E+07 

Antimony 437,10 10 1,15E+01 1,15E+02 1,80E+02 1,80E+03 3,69E+02 3,69E+03 N.A. N.A. 

Arsenic 494,10 10 9,42E+00 9,42E+01 1,88E+02 1,88E+03 2,83E+02 2,83E+03 1,73E+03 1,73E+04 

Barite 18,40 N.A. 1,50E+01 N.A. 3,58E+02 N.A. 1,66E+03 N.A. 3,77E+03 N.A. 

Beryllium 24,30 1 4,15E-03 4,15E-03 N.A. N.A. N.A. N.A. N.A. N.A. 

Bismuth 274,80 10 1,79E-01 1,79E+00 1,01E+01 1,01E+02 2,14E+01 2,14E+02 N.A. N.A. 

Boron oxide 84,12 N.A. 1,23E+02 N.A. 4,91E+03 N.A. 1,18E+04 N.A. N.A. N.A. 

Bromine 50,56 N.A. 8,24E+00 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 

Cadmium 293,15 10 1,20E+00 1,20E+01 3,05E+01 3,05E+02 7,48E+01 7,48E+02 3,74E+02 3,74E+03 

Cesium 404,46 1 N.A. N.A. 5,09E+00 5,09E+00 8,00E+00 8,00E+00 N.A. N.A. 

Chromium 584,40 1 1,57E+03 1,57E+03 N.A. N.A. N.A. N.A. 1,02E+06 1,02E+06 

Cobalt 308,89 10 8,45E+00 8,45E+01 8,77E+02 8,77E+03 1,63E+03 1,63E+04 1,88E+03 1,88E+04 

Copper 134,03 80 8,20E+02 6,58E+04 2,66E+04 2,13E+06 5,11E+04 4,09E+06 1,63E+05 1,31E+07 

Feldspar 35,02 N.A. 4,63E+01 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 

Fluorspar 112,64 N.A. 1,84E+02 N.A. 8,27E+03 N.A. 1,65E+04 N.A. 1,72E+04 N.A. 

Gallium 514,61 1 1,29E-02 1,29E-02 N.A. N.A. N.A. N.A. 1,76E+02 1,76E+02 

Germanium 556,48 1 1,65E-02 1,65E-02 N.A. N.A. N.A. N.A. N.A. N.A. 

Gold 51,50 1 1,54E-02 1,54E-02 2,62E-01 2,62E-01 5,62E-01 5,62E-01 N.A. N.A. 

Graphite 410,25 N.A. 8,40E+02 N.A. 7,02E+04 N.A. 1,71E+05 N.A. 6,53E+05 N.A. 

Gypsum 17,92 N.A. 1,74E+02 N.A. 0,00E+00 N.A. 0,00E+00 N.A. N.A. N.A. 

Hafnium 1061,31 1 N.A. N.A. 8,64E+01 8,64E+01 1,56E+02 1,56E+02 N.A. N.A. 

Helium 30,37 1 5,09E+00 5,09E+00 N.A. N.A. 1,17E+03 1,17E+03 N.A. N.A. 

Indium 437,36 10 5,29E-02 5,29E-01 1,00E+00 1,00E+01 1,46E+00 1,46E+01 N.A. N.A. 

Iodine 87,48 N.A. 4,12E-01 N.A. 2,47E+02 N.A. 4,45E+02 N.A. 5,60E+02 N.A. 

Iron 376,84 5 1,40E+05 7,41E+05 1,18E+07 6,25E+07 2,58E+07 1,37E+08 3,71E+07 1,97E+08 

Lead 232,18 25 9,29E+01 2,36E+03 2,11E+03 5,37E+04 4,55E+03 1,15E+05 4,02E+04 1,02E+06 

Lithium 392,92 1 4,50E+02 4,50E+02 5,54E+03 5,54E+03 1,49E+04 1,49E+04 1,76E+04 1,76E+04 

Magnesium 629,60 1 4,26E+02 4,26E+02 N.A. N.A. N.A. N.A. N.A. N.A. 

Manganese 484,64 1 2,51E+03 2,51E+03 9,69E+04 9,69E+04 1,10E+06 1,10E+06 N.A. N.A. 

Mercury 114,77 10 2,02E-02 2,02E-01 6,29E-01 6,29E+00 3,28E+00 3,28E+01 8,20E+00 8,20E+01 

Molybdenum 730,50 1 3,35E+01 3,35E+01 1,56E+03 1,56E+03 3,46E+03 3,46E+03 2,36E+03 2,36E+03 

Nickel 232,48 58 1,49E+02 8,70E+03 6,34E+03 3,69E+05 1,42E+04 8,26E+05 N.A. N.A. 

Niobium 900,20 1 1,03E+01 1,03E+01 6,25E+02 6,25E+02 6,94E+02 6,94E+02 N.A. N.A. 

Phosphate rock (as fosforite) 360,45 1 1,21E+03 1,21E+03 1,54E+05 1,54E+05 4,27E+05 4,27E+05 N.A. N.A. 

PGM 146,52 N.A. 9,29E-03 N.A. 1,27E+00 N.A. 1,44E+00 N.A. 1,79E+00 N.A. 

Potash (K2O) 416,26 1 3,07E+03 3,07E+03 8,76E+05 8,76E+05 1,90E+06 1,90E+06 2,64E+07 2,64E+07 

REE (as Ce2O 3) 408,21 N.A. 3,65E+00 N.A. 2,61E+03 N.A. 4,46E+03 N.A. N.A. N.A. 

Rhenium 561,34 10 3,40E-03 3,40E-02 1,80E-01 1,80E+00 7,20E-01 7,20E+00 7,92E-01 7,92E+00 

Selenium 346,70 1 1,62E-01 1,62E-01 8,60E+00 8,60E+00 1,78E+01 1,78E+01 N.A. N.A. 

Silver 69,73 10 3,12E-01 3,12E+00 4,17E+00 4,17E+01 8,80E+00 8,80E+01 N.A. N.A. 

Strontium 758,76 N.A. 1,21E+02 N.A. 1,41E+03 N.A. 2,48E+03 N.A. 2,07E+05 N.A. 



Table A.20: The chemical exergy and exergy cost <strong>of</strong> <strong>the</strong> 2006 world’s <strong>mineral</strong> production, <strong>mineral</strong> 

reserves, base reserve and world resources. Values are expressed in ktoe if not specified.– continued 



bch [kJ/mol] kch [-] Bch B∗ B ch ch B∗ B ch ch B∗ B ch ch B∗ ch 

Tantalum 974,85 1 2,97E-01 2,97E-01 2,78E+01 2,78E+01 3,85E+01 3,85E+01 N.A. N.A. 

Tellurium 326,36 1 8,07E-03 8,07E-03 1,28E+00 1,28E+00 2,87E+00 2,87E+00 N.A. N.A. 

Thorium 1214,50 N.A. 0,00E+00 N.A. 1,32E+02 N.A. 1,54E+02 N.A. N.A. N.A. 

Tin 547,58 1 3,33E+01 3,33E+01 6,72E+02 6,72E+02 1,21E+03 1,21E+03 N.A. N.A. 

Titanium (T iO2) 18,84 1 3,27E+01 3,27E+01 4,11E+03 4,11E+03 8,45E+03 8,45E+03 1,13E+04 1,13E+04 

Vanadium 721,48 1 1,90E+01 1,90E+01 4,40E+03 4,40E+03 1,29E+04 1,29E+04 2,13E+04 2,13E+04 

Wolfram 827,70 1 9,77E+00 9,77E+00 3,12E+02 3,12E+02 6,78E+02 6,78E+02 N.A. N.A. 

Zinc 339,02 13 1,24E+03 1,64E+04 2,23E+04 2,94E+05 5,95E+04 7,85E+05 2,35E+05 3,11E+06 

Zircon (Z rO2) 46,21 1 1,06E+01 1,06E+01 3,40E+02 3,40E+02 6,45E+02 6,45E+02 N.A. N.A. 

Sum 1,77E+05 1,03E+06 1,63E+07 9,22E+07 3,37E+07 1,79E+08 7,55E+07 3,19E+08 



Table A.21: The concentration exergy and exergy cost <strong>of</strong> <strong>the</strong> 2006 world’s <strong>mineral</strong> production, 

<strong>mineral</strong> reserves, base reserve and world resources. Values are expressed in ktoe if not specified 


xm [g/g] xc [g/g] kc [-] Bc B∗ c Bc B∗ c Bc B∗ c Bc B∗ c 

Aluminium 4,60E-01 8,15E-02 2250 1,46E+02 3,28E+05 1,97E+04 4,42E+07 2,52E+04 5,66E+07 5,90E+04 1,33E+08 

Antimony 3,78E-02 4,00E-07 28 7,48E-01 2,12E+01 1,17E+01 3,33E+02 2,40E+01 6,82E+02 N.A. N.A. 

Arsenic 1,00E-02 4,80E-06 80 3,61E-01 2,89E+01 7,23E+00 5,78E+02 1,08E+01 8,67E+02 6,65E+01 5,32E+03 

Barite 8,30E-01 4,13E-06 N.A. 2,60E+01 N.A. 6,19E+02 N.A. 2,87E+03 N.A. 6,52E+03 N.A. 

Beryllium 1,00E-02 2,10E-06 112 3,59E-03 4,01E-01 N.A. N.A. N.A. N.A. N.A. N.A. 

Bismuth 2,00E-03 1,60E-07 90 1,52E-02 1,37E+00 8,56E-01 7,69E+01 1,82E+00 1,63E+02 N.A. N.A. 

Boron oxide 2,00E-01 1,70E-05 N.A. 3,44E+01 N.A. 1,37E+03 N.A. 3,31E+03 N.A. N.A. N.A. 

Bromine 5,00E-03 5,00E-03 N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. 

Cadmium 1,00E-04 9,00E-08 804 7,13E-02 5,73E+01 1,81E+00 1,45E+03 4,43E+00 3,56E+03 2,22E+01 1,78E+04 

Cesium 2,33E-01 4,90E-06 N.A. N.A. N.A. 3,40E-01 N.A. 5,34E-01 N.A. N.A. N.A. 

Chromium 4,35E-01 9,20E-05 37 5,81E+01 2,13E+03 N.A. N.A. N.A. N.A. 3,77E+04 1,38E+06 

Cobalt 1,08E-03 1,73E-05 1262 2,80E-01 3,54E+02 2,91E+01 3,67E+04 5,40E+01 6,81E+04 6,23E+01 7,86E+04 

Copper 5,80E-03 2,80E-05 343 8,10E+01 2,78E+04 2,63E+03 9,01E+05 5,04E+03 1,73E+06 1,61E+04 5,52E+06 

Feldspar 4,50E-01 1,45E-01 N.A. 4,34E+00 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 

Fluorspar 2,50E-01 1,32E-06 N.A. 4,97E+01 N.A. 2,24E+03 N.A. 4,47E+03 N.A. 4,66E+03 N.A. 

Gallium 2,30E-05 1,75E-05 N.A. 1,69E-05 N.A. N.A. N.A. N.A. N.A. 2,32E-01 N.A. 

Germanium 5,00E-05 1,40E-06 N.A. 2,63E-04 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 

Gold 2,20E-07 1,50E-09 422879 3,69E-03 1,56E+03 6,30E-02 2,66E+04 1,35E-01 5,71E+04 N.A. N.A. 

Graphite 5,00E-01 1,99E-03 N.A. 2,96E+01 N.A. 2,47E+03 N.A. 6,04E+03 N.A. 2,30E+04 N.A. 

Gypsum 8,00E-01 1,08E-04 N.A. 2,28E+02 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 

Hafnium 6,00E-05 5,30E-06 N.A. N.A. N.A. 4,89E-01 N.A. 8,83E-01 N.A. N.A. N.A. 

Helium 7,00E-02 7,00E-02 N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. 

Indium 1,40E-04 5,60E-08 N.A. 2,34E-03 N.A. 4,44E-02 N.A. 6,46E-02 N.A. N.A. N.A. 

Iodine 1,60E-04 1,40E-06 N.A. 5,53E-02 N.A. 3,32E+01 N.A. 5,97E+01 N.A. 7,52E+01 N.A. 

Iron 5,11E-01 3,92E-02 97 2,63E+03 2,56E+05 2,22E+05 2,16E+07 4,86E+05 4,73E+07 6,98E+05 6,80E+07 

Lead 2,05E-02 1,70E-05 219 7,05E+00 1,54E+03 1,60E+02 3,51E+04 3,45E+02 7,55E+04 3,05E+03 6,66E+05 

Lithium 4,00E-04 2,40E-05 158 N.A. N.A. 9,84E+01 1,56E+04 2,64E+02 4,18E+04 3,12E+02 4,93E+04 

Magnesium 4,50E-01 1,50E-02 1 6,15E+00 6,15E+00 N.A. N.A. N.A. N.A. N.A. N.A. 

Manganese 3,15E-01 7,74E-04 284 7,93E+01 2,25E+04 3,07E+03 8,71E+05 3,47E+04 9,84E+06 N.A. N.A. 

Mercury 3,83E-03 5,00E-08 1707 4,91E-03 8,39E+00 1,53E-01 2,61E+02 7,97E-01 1,36E+03 1,99E+00 3,40E+03 

Molybdenum 3,10E-04 1,10E-06 947 6,41E-01 6,07E+02 3,00E+01 2,84E+04 6,62E+01 6,26E+04 4,53E+01 4,29E+04 

Nickel 1,30E-02 4,70E-05 432 8,97E+00 3,87E+03 3,80E+02 1,64E+05 8,51E+02 3,68E+05 N.A. N.A. 

Niobium 6,38E-03 1,20E-05 N.A. 1,78E-01 N.A. 1,08E+01 N.A. 1,20E+01 N.A. N.A. N.A. 

Phosphate rock (as fosforite) 1,10E-03 4,03E-04 44 8,34E+00 3,66E+02 1,06E+03 4,64E+04 2,94E+03 1,29E+05 N.A. N.A. 

PGM 8,02E-07 5,00E-10 N.A. 1,16E-03 N.A. 1,59E-01 N.A. 1,79E-01 N.A. 2,24E-01 N.A. 

Potash (K2O) 2,50E-01 2,32E-02 39 4,58E+01 1,77E+03 1,31E+04 5,04E+05 2,83E+04 1,09E+06 3,93E+05 1,52E+07 

REE (as Ce2O 3) 9,70E-04 6,30E-05 N.A. 6,07E-02 N.A. 4,34E+01 N.A. 7,40E+01 N.A. N.A. N.A. 

Rhenium 2,23E-04 1,98E-10 1939 2,09E-04 4,06E-01 1,11E-02 2,15E+01 4,43E-02 8,59E+01 4,87E-02 9,45E+01 

Selenium 2,50E-02 9,00E-08 N.A. 1,45E-02 N.A. 7,72E-01 N.A. 1,60E+00 N.A. N.A. N.A. 

Silver 4,30E-06 5,30E-08 7042 4,88E-02 3,43E+02 6,52E-01 4,59E+03 1,38E+00 9,69E+03 N.A. N.A. 

Strontium 3,40E-01 3,20E-04 0 2,83E+00 0,00E+00 3,29E+01 0,00E+00 5,81E+01 0,00E+00 4,84E+03 N.A. 



Table A.21: The concentration exergy and exergy cost <strong>of</strong> <strong>the</strong> 2006 world’s <strong>mineral</strong> production, 

<strong>mineral</strong> reserves, base reserve and world resources. Values are expressed in ktoe if not specified.– 



xm [g/g] xc [g/g] kc [-] Bc B∗ c Bc B∗ c Bc B∗ c Bc B∗ c 

Tantalum 6,50E-03 9,00E-07 12509 6,71E-03 8,39E+01 6,28E-01 7,86E+03 8,70E-01 1,09E+04 N.A. N.A. 

Tellurium 1,00E-06 5,00E-09 N.A. 3,25E-04 N.A. 5,16E-02 N.A. 1,16E-01 N.A. N.A. N.A. 

Thorium 3,00E-02 1,05E-05 N.A. N.A. N.A. 2,15E+00 N.A. 2,50E+00 N.A. N.A. N.A. 

Tin 4,80E-03 2,10E-06 1493 1,17E+00 1,74E+03 2,35E+01 3,52E+04 4,25E+01 6,34E+04 N.A. N.A. 

Titanium (T iO2) 6,90E-03 3,84E-03 348 2,53E+00 8,80E+02 3,18E+02 1,11E+05 6,53E+02 2,28E+05 8,71E+02 3,03E+05 

Vanadium 2,00E-02 9,70E-05 572 3,49E-01 2,00E+02 8,07E+01 4,61E+04 2,36E+02 1,35E+05 3,91E+02 2,24E+05 

Wolfram 7,17E-03 1,90E-06 3105 2,41E-01 7,48E+02 7,70E+00 2,39E+04 1,67E+01 5,19E+04 N.A. N.A. 

Zinc 4,06E-02 6,70E-05 126 5,82E+01 7,33E+03 1,05E+03 1,32E+05 2,79E+03 3,52E+05 1,11E+04 1,39E+06 

Zircon (Z rO2) 2,69E-03 1,93E-04 7744 1,49E+00 1,16E+04 4,81E+01 3,73E+05 9,12E+01 7,06E+05 N.A. N.A. 

Sum 3,51E+03 6,69E+05 2,70E+05 6,92E+07 6,04E+05 1,19E+08 1,26E+06 2,25E+08 



A.7 Australian fossil fuel production 

A.7.1 Coal 

Table A.22 shows <strong>the</strong> Australian coal production from 1913 to 2006. The data has 

been obtained from <strong>the</strong> British Geological Survey’s historical statistics [159], [157], 

[52], [250], [154], [155], [30], [31] and [29]. 

Table A.22: Evolution <strong>of</strong> <strong>the</strong> Australian coal production. Values in ktons 

Year Anthrac. Bitum. Subbit. Lign. Year Anthrac. Bitum. Subbit. Lign. 

1912 1960 51 20975 1908 15210 

1913 12619 1961 60 22347 1988 16543 

1914 12657 1962 70 22362 2433 17415 

1915 11600 1963 62 22629 2568 18756 

1916 9971 1964 74 24840 2891 19341 

1917 10398 1965 71 28685 3191 20993 

1918 11126 1966 47 30568 3297 22136 

1919 10695 1967 39 31806 3425 23763 

1920 13178 1968 30 37350 3542 23346 

1921 13087 1969 15 42349 3735 23282 

1922 12498 1970 46063 3482 24175 

1923 12720 119 1971 45841 3161 23382 

1924 13980 130 1972 59389 3300 23697 

1925 13850 891 1973 57355 3298 24676 

1926 13465 973 1974 66474 3975 27303 

1927 13742 1479 1975 62417 3300 23697 

1928 12032 1618 1976 69676 5008 28178 

1929 10533 1769 1977 72679 5529 29250 

1930 9686 1861 1978 74094 5733 32860 

1931 8537 2230 1979 72679 5529 29250 

1932 8725 2655 1980 76794 6365 32597 

1933 9239 2622 1981 93405 7190 32990 

1934 9734 2660 1982 99109 7992 37821 

1935 11064 2257 1983 99828 8998 34191 

1936 11555 3094 1984 116018 8288 35166 

1937 12270 3449 1985 158256 36985 

1938 11869 3735 1986 170067 37604 

1939 1987 178399 44877 

1940 1988 176604 43450 

1941 14443 4640 1989 190085 48252 

1942 14612 2 5014 1990 162957 47725 

1943 14423 5174 1991 167472 52124 

1944 13944 35 5098 1992 179144 50228 

1945 13020 42 5533 1993 180045 48458 

1946 14000 138 5799 1994 182553 48582 

1947 14901 196 6240 1995 193534 50751 

1948 15022 6801 1996 198638 53604 

1949 14336 7495 1997 216690 58160 

1950 16816 7446 1998 222040 65600 


Australian fossil fuel production 403 

Table A.22: Evolution <strong>of</strong> <strong>the</strong> Australian coal production. Values in ktons– 


Year Anthrac. Bitum. Subbit. Lign. Year Anthrac. Bitum. Subbit. Lign. 

1951 16373 1521 7963 1999 232860 65820 

1952 18084 1635 8235 2000 244840 67363 

1953 17119 1590 8391 2001 266710 64958 

1954 18212 1871 9482 2002 272560 66661 

1955 17979 1608 10276 2003 280700 66809 

1956 18050 1536 10731 2004 294810 66343 

1957 18596 1645 10915 2005 308000 67152 

1958 58 18917 1798 11832 2006 316000 67737 

1959 55 18877 1695 13246 


A.7.2 Oil 

Table A.23 shows Australian oil production from 1913 to 2006. The data has been 

obtained from <strong>the</strong> British Geological Survey’s historical statistics [159], [157], [52], 

[250], [154], [155], [30], [31] and [29]. For <strong>the</strong> period between 1931 to 1940, 

oil data corresponds only to <strong>the</strong> region <strong>of</strong> Victoria. Until 1964, <strong>the</strong> statistics include 

crude petroleum plus oil shale. 

Table A.23: Evolution <strong>of</strong> <strong>the</strong> Australian oil production. Values in ktons 

Year ktons Year ktons Year ktons Year ktons 

1913 5,52 1937 0,04 1961 1985 30447 

1914 16,26 1938 0,03 1962 1986 27151 

1915 5,03 1939 0,02 1963 1987 29076 

1916 5,66 1940 0,02 1964 278 1988 27493 

1917 10,27 1941 1965 334 1989 25908 

1918 10,52 1942 1966 432 1990 30548 

1919 10,15 1943 1967 993 1991 28835 

1920 8,12 1944 1968 1818 1992 28326 

1921 1945 1969 2065 1993 26300 

1922 1946 1970 8541 1994 28505 

1923 1947 1971 14803 1995 27031 

1924 1948 0,12 1972 15685 1996 28407 

1925 1949 0,14 1973 20635 1997 30000 

1926 1950 0,16 1974 24559 1998 28000 

1927 1951 0,27 1975 21738 1999 27000 

1928 1952 1976 22122 2000 37000 

1929 1953 1977 22793 2001 34000 

1930 1954 1978 22976 2002 33000 

1931 0,08 1955 1979 23141 2003 27000 

1932 0,08 1956 1980 19451 2004 20748 



Table A.23: Evolution <strong>of</strong> <strong>the</strong> Australian oil production. Values in ktons.– 


A.7.3 Natural gas 

Year ktons Year ktons Year ktons Year ktons 

1933 0,08 1957 1981 19799 2005 21439 

1934 0,02 1958 1982 18839 2006 20831 

1935 0,02 1959 1983 21209 

1936 0,02 1960 1984 26377 


Table A.24 shows Australian natural gas production from 1961 to 2006. The data 

has been obtained from <strong>the</strong> British Geological Survey’s historical statistics [154], 

[155], [155], [30], [31] and [29]. 

Table A.24: Evolution <strong>of</strong> <strong>the</strong> Australian natural gas production. Values in 

millions <strong>of</strong> cubic meters 

Year M m 3 Year M m 3 Year M m 3 Year M m 3 

1961 0,34 1973 4099 1985 13470 1997 29876 

1962 1,6 1974 4677 1986 14714 1998 30361 

1963 2,7 1975 5026 1987 15023 1999 30755 

1964 3,0 1976 5929 1988 15383 2000 31165 

1965 4,0 1977 6728 1989 17806 2001 32482 

1966 4,0 1978 7320 1990 20620 2002 32606 

1967 4,3 1979 8381 1991 21694 2003 33180 

1968 6,1 1980 9567 1992 23462 2004 35224 

1969 265 1981 11260 1993 24457 2005 37129 

1970 1502 1982 11565 1994 28147 2006 38883 

1971 2274 1983 11581 1995 29761 

1972 3188 1984 12600 1996 29799 

A.8 World’s fuel production 

A.8.1 Uranium 

Table A.25 shows <strong>the</strong> production <strong>of</strong> uranium in western countries and <strong>the</strong> world 

production from 1945 to 2006. Approximate data about uranium production in 

western countries is extracted from <strong>the</strong> World Nuclear Association [408]. For world 

production data, it has been assumed that western countries contribute to about 69

World’s fuel production 405 

% <strong>of</strong> total world production. From 2002 to 2006, world production information is 

directly provided by <strong>the</strong> WNA [408]. 

Table A.25: Production <strong>of</strong> uranium in western countries and in <strong>the</strong> world. 

Values are expressed in tons 

Year Production 

w. countries 

[408] 

World production 

Year Production 

w. countries 

[408] 

1945 500 725 1976 24000 34783 

1946 500 725 1977 29000 42029 

1947 500 725 1978 35000 50725 

1948 1500 2174 1979 39000 56522 

1949 1500 2174 1980 45000 65217 

1950 3000 4348 1981 45000 65217 

1951 3000 4348 1982 42000 60870 

1952 2000 2899 1983 36000 52174 

1953 4500 6522 1984 38000 55072 

1954 6500 9420 1985 35000 50725 

1955 7500 10870 1986 36500 52899 

1956 10300 14928 1987 34500 50000 

1957 20000 28986 1988 36000 52174 

1958 30000 43478 1989 33000 47826 

1959 34000 49275 1990 27500 39855 

1960 32000 46377 1991 26000 37681 

1961 28000 40580 1992 23000 33333 

1962 25500 36957 1993 22500 32609 

1963 23000 33333 1994 22500 32609 

1964 22500 32609 1995 25000 36232 

1965 15300 22174 1996 27500 39855 

1966 15000 21739 1997 28000 40580 

1967 15400 22319 1998 26500 38406 

1968 17000 24638 1999 22500 32609 

1969 17000 24638 2000 26500 38406 

1970 18300 26522 2001 27500 39855 

1971 19000 27536 2002 26000 36063 

1972 20000 28986 2003 25000 35613 

1973 20000 28986 2004 28000 40251 

1974 19000 27536 2005 41702 

1975 20000 28986 2006 39429 

A.8.2 Coal 

World production 

Table A.26 shows <strong>the</strong> world’s coal production from 1900 to 2006. The data from 

1981 to 2006 has been extracted from BP [35]. From 1900 to 1912 <strong>the</strong> information 

has been obtained from <strong>the</strong> estimations done by Ortiz [253]. From 1913 to 1981,


<strong>the</strong> data was obtained from <strong>the</strong> British Geological Survey’s historical statistics [159], 

[157], [52], [250], [154]. 

A.8.3 Oil 

Table A.26: Evolution <strong>of</strong> <strong>the</strong> world’s coal production 

Year Mt coal Year Mt coal Year Mt coal Year Mt coal 

1900 1927 1450,0 1954 1940,0 1981 3831,1 

1901 800,0 1928 1440,0 1955 2100,0 1982 3980,1 

1902 820,0 1929 1540,0 1956 2220,0 1983 3986,8 

1903 850,0 1930 1390,0 1957 2300,0 1984 4191,5 

1904 900,0 1931 1240,0 1958 2400,0 1985 4420,8 

1905 920,0 1932 1110,0 1959 2480,0 1986 4528,8 

1906 1000,0 1933 1150,0 1960 2590,0 1987 4629,9 

1907 1100,0 1934 1260,0 1961 2440,0 1988 4735,7 

1908 1080,0 1935 1310,0 1962 2510,0 1989 4818,5 

1909 1100,0 1936 1420,0 1963 2610,0 1990 4718,6 

1910 1190,0 1937 1510,0 1964 2710,0 1991 4538,8 

1911 1200,0 1938 1420,0 1965 2760,0 1992 4500,2 

1912 1210,0 1939 1550,0 1966 2790,0 1993 4382,5 

1913 1320,1 1940 1660,0 1967 2677,0 1994 4470,5 

1914 1160,0 1941 1745,0 1968 2702,0 1995 4592,5 

1915 1175,3 1942 1756,0 1969 2826,0 1996 4667,7 

1916 1258,7 1943 1770,0 1970 2944,0 1997 4702,1 

1917 1310,4 1944 1420,0 1971 2950,0 1998 4555,7 

1918 1234,3 1945 1324,0 1972 3041,0 1999 4544,5 

1919 1084,7 1946 1445,0 1973 3065,0 2000 4606,6 

1920 1302,0 1947 1622,0 1974 3107,0 2001 4819,2 

1921 1118,0 1948 1698,0 1975 3253,0 2002 4852,3 

1922 1210,0 1949 1670,0 1976 3349,0 2003 5187,6 

1923 1340,0 1950 1792,0 1977 3510,0 2004 5585,3 

1924 1340,0 1951 1570,0 1978 3558,0 2005 5886,7 

1925 1350,0 1952 1900,0 1979 3719,0 2006 6195,1 

1926 1340,0 1953 1930,0 1980 3806,0 

Table A.27 shows <strong>the</strong> world’s oil production from 1900 to 2006. The data from 1965 

to 2006 has been extracted from BP [35]. Until 1912, <strong>the</strong> information has been 

obtained from <strong>the</strong> estimations done by Ortiz [253]. Between 1913 and 1965, <strong>the</strong> 

data was obtained from <strong>the</strong> British Geological Survey’s historical statistics [159], 

[157], [52], [250], [154].

World’s fuel production 407 

A.8.4 Natural gas 

Table A.27: Evolution <strong>of</strong> <strong>the</strong> world’s oil production 

Year Mt oil Year Mt oil Year Mt oil Year Mt oil 

1900 0,0 1927 181,7 1954 699,0 1981 2910,0 

1901 4,5 1928 183,8 1955 774,5 1982 2795,6 

1902 9,0 1929 207,0 1956 842,7 1983 2759,2 

1903 13,6 1930 197,0 1957 888,4 1984 2814,6 

1904 18,1 1931 190,5 1958 910,8 1985 2792,1 

1905 22,6 1932 180,8 1959 984,0 1986 2935,9 

1906 27,1 1933 199,1 1960 1053,6 1987 2947,1 

1907 31,7 1934 207,3 1961 1131,8 1988 3069,0 

1908 36,2 1935 228,6 1962 1208,0 1989 3102,9 

1909 40,7 1936 249,9 1963 1303,5 1990 3170,6 

1910 45,2 1937 283,5 1964 1403,1 1991 3160,5 

1911 49,8 1938 279,4 1965 1500,6 1992 3190,0 

1912 54,3 1939 289,9 1966 1700,6 1993 3188,6 

1913 56,0 1940 299,0 1967 1824,7 1994 3237,2 

1914 59,0 1941 310,6 1968 1990,9 1995 3281,0 

1915 62,7 1942 290,6 1969 2141,2 1996 3376,5 

1916 67,4 1943 320,6 1970 2355,2 1997 3480,5 

1917 71,8 1944 342,0 1971 2492,6 1998 3548,3 

1918 69,1 1945 361,9 1972 2636,6 1999 3482,9 

1919 79,3 1946 383,4 1973 2866,6 2000 3618,1 

1920 99,8 1947 423,2 1974 2875,2 2001 3602,7 

1921 113,1 1948 477,5 1975 2734,4 2002 3575,6 

1922 124,1 1949 475,1 1976 2969,0 2003 3701,3 

1923 146,9 1950 530,2 1977 3073,2 2004 3862,6 

1924 146,1 1951 600,9 1978 3103,1 2005 3896,8 

1925 154,1 1952 632,6 1979 3233,1 2006 3914,1 

1926 157,4 1953 668,5 1980 3087,9 


Table A.28 shows <strong>the</strong> world’s natural gas production from 1900 to 2006. The data 

from 1970 to 2006 has been extracted from BP [35]. Until 1920, <strong>the</strong> information 

has been estimated from US natural gas production, which is a compilation <strong>of</strong> data 

from <strong>the</strong> “Espasa” encyclopedia [87] between years 1900 -1921. Between 1921 and 

1970, <strong>the</strong> data was obtained from <strong>the</strong> British Geological Survey’s historical statistics 

[159], [157], [52], [250], [154]. For years 1945-1947, a linear increasing rate has 

been assumed, because <strong>of</strong> lack <strong>of</strong> data.


Table A.28: Evolution <strong>of</strong> <strong>the</strong> world’s natural gas production. Data in billion 

<strong>of</strong> cubic meters 

Year World Prod. Year World Prod. Year World Prod. 

1900 3,5 1935 57,5 1970 1009,3 

1901 5,0 1936 65,5 1971 1073,8 

1902 5,9 1937 72,5 1972 1125,3 

1903 6,7 1938 75,2 1973 1180,2 

1904 7,3 1939 80,5 1974 1201,5 

1905 7,5 1940 80,4 1975 1203,3 

1906 10,8 1941 112,2 1976 1252,9 

1907 11,5 1942 91,1 1977 1301,5 

1908 11,2 1943 98,9 1978 1347,3 

1909 13,4 1944 106,6 1979 1438,0 

1910 14,6 1945 121,1 1980 1448,5 

1911 14,7 1946 135,6 1981 1475,8 

1912 15,8 1947 150,1 1982 1478,0 

1913 16,2 1948 164,6 1983 1483,2 

1914 16,5 1949 175,6 1984 1614,9 

1915 17,6 1950 184,1 1985 1666,7 

1916 21,0 1951 239,0 1986 1713,6 

1917 22,1 1952 257,1 1987 1798,7 

1918 20,3 1953 270,1 1988 1882,4 

1919 21,0 1954 295,9 1989 1943,3 

1920 22,4 1955 323,6 1990 1991,8 

1921 19,8 1956 351,8 1991 2023,7 

1922 22,8 1957 386,3 1992 2037,0 

1923 29,8 1958 388,6 1993 2073,1 

1924 33,7 1959 432,4 1994 2093,6 

1925 35,3 1960 472,9 1995 2134,7 

1926 38,9 1961 511,8 1996 2227,9 

1927 42,7 1962 558,5 1997 2231,5 

1928 45,6 1963 609,8 1998 2279,5 

1929 56,4 1964 663,8 1999 2343,7 

1930 57,6 1965 706,9 2000 2425,2 

1931 49,3 1966 759,8 2001 2482,1 

1932 47,0 1967 821,5 2002 2524,6 

1933 47,4 1968 889,1 2003 2614,3 

1934 54,6 1969 955,1 2004 2703,1 

2005 2779,8 

2006 2865,3 

A.9 The Hubbert peak applied to world production <strong>of</strong> <strong>the</strong> 

main non-fuel <strong>mineral</strong>s 

Figures A.1, A.2, and A.3 show <strong>the</strong> Hubbert model applied to <strong>the</strong> exergy costs <strong>of</strong> 

world iron, aluminium and copper production. It is assumed that <strong>the</strong> total world

The Hubbert peak applied to world production <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong>s 409 

Bt* 

Integral Bt* 

x 10 

15 

5 

10 

5 

0 

x 108 

2.5 

2 

1.5 

1 

0.5 

2068 

0 

1900 1950 2000 2050 2100 2150 2200 2250 

Figure A.1. The Hubbert peak applied to <strong>the</strong> exergy cost <strong>of</strong> world’s iron production, 

based on <strong>the</strong> world resources. Data in ktoe 

Bt* 

Integral Bt* 

1.5 

1 

0.5 

x 106 

2 

0 

x 108 

2.5 

2 

1.5 

1 

0.5 

2089 

0 

1900 1950 2000 2050 2100 2150 2200 2250 2300 

Figure A.2. The Hubbert peak applied to <strong>the</strong> exergy cost <strong>of</strong> world’s aluminium production, 


<strong>mineral</strong> reserves are equal to <strong>the</strong> world resources <strong>of</strong> each <strong>mineral</strong> in 2006 published 

by <strong>the</strong> USGS [362] plus <strong>the</strong> irreversible exergy distance D ∗ from 1900 to 2006.


Bt* 

Integral Bt* 

1.5 

1 

0.5 

x 105 

2 

0 

x 107 

2.5 

2 

1.5 

1 

0.5 

2066 

0 

1900 1950 2000 2050 2100 2150 2200 2250 

Figure A.3. The Hubbert peak applied to <strong>the</strong> exergy cost <strong>of</strong> world’s copper production, 


A.10 Fuel consumption in <strong>the</strong> 21st century 

Tables A.29 through A.34 show <strong>the</strong> primary energy consumption and cumulative 

resources production assumed in each <strong>of</strong> <strong>the</strong> SRES scenarios. 

Table A.29. Primary energy consumption and cumulative resources production in 

<strong>the</strong> IPCC’s B1 scenario [160] 

Primary Energy, EJ 

Year 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Coal 105 109 120 134 163 181 167 133 101 76 58 44 

Oil 129 141 176 206 230 236 228 199 167 143 119 99 

Gas 62 71 108 138 153 166 173 168 154 136 121 103 

Cumulative Resources Production, ZJ 

Coal 0,0 1,1 2,2 3,5 4,9 6,7 8,5 10,0 11,1 12,0 12,7 13,2 

Oil 0,0 1,3 2,9 4,8 7,0 9,3 11,6 13,8 15,6 17,2 18,5 19,6 

Gas 0,0 0,6 1,5 2,8 4,2 5,8 7,5 9,2 10,8 12,3 13,6 14,7

Fuel consumption in <strong>the</strong> 21st century 411 


<strong>the</strong> IPCC’s A1T scenario [160] 


Year 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Coal 91 106 125 151 180 153 119 87 60 53 40 25 

Oil 128 155 172 193 223 241 250 236 205 143 113 77 

Gas 71 87 124 166 231 288 324 344 324 291 240 196 


Coal 0,0 0,9 2,0 3,2 4,7 6,5 8,1 9,3 10,1 10,7 11,3 11,7 

Oil 0,0 1,4 3,0 4,7 6,6 8,9 11,3 13,8 16,1 18,2 19,6 20,8 

Gas 0,0 0,8 1,6 2,9 4,5 6,8 9,7 13,0 16,4 19,6 22,6 25,0 


<strong>the</strong> IPCC’s B2 scenario [160] 


Year 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Coal 91 91 98 98 96 93 86 91 119 170 231 300 

Oil 128 168 195 214 240 238 227 201 146 101 72 52 

Gas 71 84 107 150 194 251 297 356 390 402 385 336 


Coal 0,0 0,9 1,8 2,8 3,8 4,7 5,7 6,5 7,4 8,6 10,3 12,6 

Oil 0,0 1,4 3,1 5,1 7,2 9,6 12,0 14,3 16,3 17,7 18,7 19,5 

Gas 0,0 0,7 1,6 2,7 4,2 6,1 8,6 11,6 15,1 19,0 23,1 26,9 


<strong>the</strong> IPCC’s A1B scenario [160] 


Year 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Coal 93 99 134 163 179 182 186 165 148 126 103 84 

Oil 143 167 209 238 239 226 214 188 166 149 136 125 

Gas 73 91 147 196 298 372 465 519 578 604 590 576 


Coal 0,1 1,1 2,2 3,7 5,4 7,0 9,1 10,5 12,2 13,6 14,7 15,9 

Oil 0,1 1,7 3,6 5,8 8,2 10,2 12,7 14,4 16,3 18,0 19,4 20,8 

Gas 0,1 0,9 2,1 3,8 6,3 9,3 13,9 18,2 23,9 29,8 35,5 42,2



<strong>the</strong> IPCC’s A2 scenario [160] 


Year 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Coal 92 90 106 129 184 239 294 415 536 658 781 904 

Oil 134 172 220 291 270 249 228 148 69 23 12 0 

Gas 71 74 89 126 176 225 275 297 319 330 331 331 


Coal 0,0 1,0 2,0 3,2 4,7 6,9 9,5 13,1 17,9 31,1 38,3 46,8 

Oil 0,0 1,7 3,6 6,2 9,0 11,6 13,9 15,7 16,7 17,0 17,2 17,2 

Gas 0,0 0,8 1,6 2,7 4,2 6,2 8,7 11,6 14,7 17,9 21,3 24,6 


<strong>the</strong> IPCC’s A1FI scenario [160] 


Year 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 

Coal 88 115 150 193 299 393 475 448 432 429 518 607 

Oil 131 136 150 173 165 202 283 353 416 471 359 248 

Gas 70 85 129 203 268 333 398 494 573 634 606 578 


Coal 0,1 1,2 2,6 4,2 7,0 10,4 14,6 19,1 23,6 27,9 32,9 37,9 

Oil 0,1 1,5 2,9 4,5 6,2 8,1 10,4 13,8 17,7 22,0 25,8 29,6 

Gas 0,1 0,9 2,1 3,6 6,1 9,2 12,7 17,4 22,8 28,7 34,8 40,9

Nomenclature, Figures, Tables and 

References 

413

Symbols 

a 1 − a 7 : Experimental coefficients for <strong>the</strong> calculation <strong>of</strong> h ∗ (T) and s ∗ (T) [-] 

a i : Effective diameter <strong>of</strong> <strong>the</strong> ion [m] 

a j1 : Intercept <strong>of</strong> <strong>the</strong> learning curve with <strong>the</strong> vertical axes for material’s use [-] 

a e1 : Intercept <strong>of</strong> <strong>the</strong> learning curve with <strong>the</strong> vertical axes for energy’s use [-] 

a j2 : Parameter relating material inputs per unit output at time period t [-] 

a e2 : Parameter relating energy inputs per unit output at time period t [-] 

Nomenclature 

A 1 : Constant in <strong>the</strong> Debye- Huckel equation with <strong>the</strong> value 0,51 kg 1/2 mole −1/2 for water at 25 o C 

A 2 : Constant in <strong>the</strong> Debye- Huckel equation with <strong>the</strong> value 3,287 * 10 9 kg 1/2 m −1 mole −1/2 for water 

at 25 o C 

b : Specific exergy [kJ/mole] 

b 0 : Full width at half maximum <strong>of</strong> <strong>the</strong> Gaussian peak [-] 

b ch : Specific chemical exergy [kJ/mole] 

b c : Specific concentration exergy [kJ/mole] 

B : Absolute exergy [kJ] 

B ∗ : Absolute exergy replacement cost (also named actual exergy) [kJ] 

B c : Absolute concentration exergy [kJ] 

B ch : Absolute chemical exergy [kJ] 

B t : Absolute total exergy [kJ] 

c j : Fraction <strong>of</strong> <strong>the</strong> j-th element appearing in <strong>the</strong> form <strong>of</strong> reference species [-] 

∆C p : Heat capacity [kJ/mole] 

d 1 : Moles <strong>of</strong> C contained in <strong>the</strong> fuel [mole/g] 

D : Minimum exergy distance, equivalent to <strong>the</strong> exergy difference between two situations <strong>of</strong> <strong>the</strong> planet 

[kJ] 

D ∗ : Actual exergy distance, equivalent to <strong>the</strong> difference <strong>of</strong> <strong>the</strong> exergy replacement costs <strong>of</strong> two situations 

<strong>of</strong> <strong>the</strong> planet [kJ] 

415

416 NOMENCLATURE 

˙D : Minimum exergy degradation velocity [kW] 

˙D ∗ : Actual degradation velocity in terms <strong>of</strong> exergy replacement costs [kW] 

e 0 : Standard energy [kJ/mole] 

e1 − e5 : Exponentials used to calculate <strong>the</strong> contribution <strong>of</strong> <strong>the</strong> entropy change for gaseous reference 

substances [-] 

e(t ) : Flow <strong>of</strong> energy used to perform a certain process [kJ] 

f j : Elements <strong>of</strong> <strong>the</strong> atomic composition vector <strong>of</strong> <strong>the</strong> fuel f = [1, h, o, n, s] ′ [-] 

F : Fractal relationship <strong>of</strong> <strong>the</strong> deposit [-] 

F 1 − F 7 : Coefficients for estimating x H2O,00 [-] 

g i : Free energy contribution <strong>of</strong> one mole <strong>of</strong> each oxide or hydroxide component <strong>of</strong> <strong>the</strong> substance, 

according to <strong>the</strong> method <strong>of</strong> Chermak and Rimstid [55] [kJ/mole] 

∆G f : Gibbs free energy <strong>of</strong> formation [kJ/mole] 

∆G m : Gibs free energy <strong>of</strong> mixing [kJ/mole] 

∆G0 : hydration Gibbs free energy [kJ/mole] 

hydr 

∆ GO −2 : Gibbs free energy <strong>of</strong> formation <strong>of</strong> a generic oxide MO x(c) from its aqueous ion [kJ/mole] 

∆G0 : Gibbs free energy <strong>of</strong> formation <strong>of</strong> a given compound as determined from <strong>the</strong> constituent oxides 

ox 

[kJ/mole] 

∆G r : Gibs free energy <strong>of</strong> <strong>the</strong> reaction [kJ/mole] 

h : Moles <strong>of</strong> hydrogen per mole <strong>of</strong> carbon in <strong>the</strong> fuel [mole/mole] 

h i : Enthalpy contribution <strong>of</strong> one mole <strong>of</strong> each oxide or hydroxide <strong>of</strong> <strong>the</strong> substance, according to <strong>the</strong> 

method <strong>of</strong> Chermak and Rimstid [55] [kJ/mole] 

h ∗ (T) : Enthalpy <strong>of</strong> Zelenik and Gordon [413] [kJ/mole] 

H j,00 : Enthalpy <strong>of</strong> <strong>the</strong> elements in <strong>the</strong> dead state [kJ/mole] 

∆H : Enthalpy change [kJ/mole] 

∆H f : Enthalpy <strong>of</strong> formation [kJ/mole] 

∆H m : Enthalpy <strong>of</strong> mixing [kJ/mole] 

∆H 0 : Hydration enthalpy [kJ/mole] 

hydr 

∆ H O −2 : Enthalpy <strong>of</strong> formation <strong>of</strong> a generic oxide MO x(c) from its aqueous ion [kJ/mole] 

∆H 0 : Gibbs free energy <strong>of</strong> formation <strong>of</strong> a given compound as determined from <strong>the</strong> constituent oxides 

ox 

[kJ/mole] 

∆H r : Enthalpy <strong>of</strong> <strong>the</strong> reaction [kJ/mole] 

I : Ionic strength <strong>of</strong> <strong>the</strong> electrolyte [mole/kg] 

j(t ) : Flow <strong>of</strong> material used to perform a certain process [kg] 

k c: Unit concentration exergy replacement cost [-] 

k ch: Unit chemical exergy replacement cost [-] 

l j : Number <strong>of</strong> <strong>the</strong> atoms <strong>of</strong> j-th element in <strong>the</strong> molecule <strong>of</strong> <strong>the</strong> reference species [-] 

m : Mass [kg]

Nomenclature 417 

m i : Conventional standard molarity <strong>of</strong> <strong>the</strong> reference substance i in seawater [mole/kg] 

M : Tonnage <strong>of</strong> <strong>the</strong> deposit [kg] 

M c : Tonnage <strong>of</strong> <strong>the</strong> piece <strong>of</strong> land under consideration [kg] 

M W : Molecular weight [mole/g] 

n : Moles <strong>of</strong> nitrogen per mole <strong>of</strong> carbon in <strong>the</strong> fuel [mole/mole] 

ni : Number <strong>of</strong> moles <strong>of</strong> substance i [mole]. In section 5.4.5, <strong>the</strong> number <strong>of</strong> oxygen ions linked to <strong>the</strong> 

cations [-]. 

M z+ 

i 

n s : Number <strong>of</strong> cations located in different sites <strong>of</strong> <strong>the</strong> hydrated clay <strong>mineral</strong> or phyllosilicate [-]. 

n w : Number <strong>of</strong> molecules <strong>of</strong> water [-] 

N : Number <strong>of</strong> oxygens linked to <strong>the</strong> molecular structure <strong>of</strong> <strong>the</strong> double oxide [-] 

o : Moles <strong>of</strong> oxygen per mole <strong>of</strong> carbon in <strong>the</strong> fuel [mole/mole] 

∆O −2 : Enthalpy ∆ HO −2 or Gibbs free energy ∆ GO −2 <strong>of</strong> formation <strong>of</strong> a generic oxide MO x(c) from its 

aqueous ion [kJ/mole] 

P : Pressure [kPa] and Production <strong>of</strong> a <strong>mineral</strong> commodity [ktoe/year] 

P 0i : Conventional mean ideal gas partial pressure <strong>of</strong> substance i in <strong>the</strong> atmosphere [kPa] 

pH : Exponent <strong>of</strong> <strong>the</strong> concentration <strong>of</strong> hydrogen ion in seawater (pH=8,1) [-] 

Q : Heat loss escaping <strong>the</strong> crust [W /m 3 ] 

Q B : Heat input at <strong>the</strong> base <strong>of</strong> <strong>the</strong> lithosphere due to mantle convection [W /m 3 ] 

Q C : Radiogenic heat production <strong>of</strong> <strong>the</strong> crust [W /m 3 ] 

Q L : Radiogenic heat production in <strong>the</strong> mantle part <strong>of</strong> <strong>the</strong> lithosphere [W /m 3 ] 

Q M : Mantle heat flow [W /m 3 ] 

Q T : Long-term heat production transient due to cooling after a major tectonic or magmatic perturbation 

[W /m 3 ] 

r j,i : Amount <strong>of</strong> moles <strong>of</strong> element j in substance i [mole j/mole i] 

r k,i : Number <strong>of</strong> molecules <strong>of</strong> additional elements k present in <strong>the</strong> molecule <strong>of</strong> reference substance i 

[mole k/mole i] 

R : Available reserves [ktoe] 

R[ j × i] : Stoichiometric coefficient matrix between species i and elements j <strong>of</strong> dimensions [ j × i] 

¯R : Universal gas constant [8,314E-3 kJ/(mole K)] 

RF : Regression factor <strong>of</strong> <strong>the</strong> fit [-] 

R/P : Resources to production ratio [-] 

s : Moles <strong>of</strong> sulphur per mole <strong>of</strong> carbon in <strong>the</strong> fuel [mole/mole] 

s 0 : Standard entropy [kJ/mole] 

s ∗ (T) : Entropy <strong>of</strong> Zelenik and Gordon [413] [kJ/(mole K)] 

∆S : Entropy change [kJ/(mole K)] 

t : time [s, years] 

t 0 : Year where <strong>the</strong> peak <strong>of</strong> production is reached [yr]


T : Temperature [K] 

t Me : <strong>Exergy</strong> content <strong>of</strong> one ton <strong>of</strong> <strong>mineral</strong> in a certain time and place [kJ] 

t Me ∗ : <strong>Exergy</strong> replacement cost <strong>of</strong> one ton <strong>of</strong> <strong>mineral</strong> in a certain time and place [kJ] 

w : Moles <strong>of</strong> water per mole <strong>of</strong> carbon in <strong>the</strong> fuel [mole/mole] 

W : Moles <strong>of</strong> liquid water (moisture) in <strong>the</strong> fuel [mole] 

x : Molar fraction [mole/mole]. In section 5.4.5, <strong>the</strong> number <strong>of</strong> oxygen atoms combined with one 

atom M in <strong>the</strong> oxide [-]. 

x c : Concentration <strong>of</strong> <strong>the</strong> <strong>mineral</strong> in <strong>the</strong> earth’s crust [g/g] 

x m : Concentration <strong>of</strong> <strong>the</strong> <strong>mineral</strong> deposit [g/g] 

X : The molar fraction <strong>of</strong> oxygen related to <strong>the</strong> cations <strong>of</strong> a hydrated clay <strong>mineral</strong> or phyllosilicate [-] 

y 0 : Height <strong>of</strong> <strong>the</strong> Gaussian peak [-] 

z : Moles <strong>of</strong> ashes per mole <strong>of</strong> carbon in <strong>the</strong> fuel [mole/mole] 

z + : Number <strong>of</strong> elementary positive charges [-] 

Z : Moles <strong>of</strong> ashes in <strong>the</strong> fuel [mole] 

Greek letters 

α G : Empirical coefficient variable for estimating ∆G 0 

ox [-] 

α H : Empirical coefficient variable for estimating ∆H 0 

ox [-] 

δ : Thickness <strong>of</strong> <strong>the</strong> crust [m] 

γ : Activity coefficient (molarity scale) <strong>of</strong> <strong>the</strong> reference substance in seawater [-] 

Γ(t ) : Cumulative production in period t [kg] 

ε : Relative error [%] 

ε j : Mean molar concentration <strong>of</strong> element j contained in <strong>the</strong> atmosphere, hydrosphere or continental 

crust [mole/g] 

µ j,00 : Chemical potential <strong>of</strong> <strong>the</strong> elements in <strong>the</strong> dead state [kJ/mole] 

ρ 15 : Density <strong>of</strong> <strong>the</strong> fuel at 15 ◦ C [kg/m 3 ] 

τ : Temperature [ ◦ C] 

ξ i : Mean molar concentration <strong>of</strong> substance i contained in <strong>the</strong> atmosphere, hydrosphere or continental 

crust [mole/g] 

Abbreviations 

BGS : British Geological Survey 

BP : British Petroleum 

EWG : Energy Watch Group 

HHV : High Heating Value

Nomenclature 419 

IGU : International Gas Union 

IPCC : Intergovernmental Panel on Climate Change 

IWP&DC : The International Water Power & Dam Construction 

LHV : Low Heating Value 

PV : Photovoltaic energy 

R.B. : Reserve Base 

R.E. : Reference Environment 

RE 2O 5 : Rare earth’s oxides 

R.S. : Reference Substances in <strong>the</strong> Reference Environment 

RW : Renewable Energies 

SRES : Special Report on Emission Scenarios 

THC : Thermohaline Circulation 

USBM : U.S. Bureau <strong>of</strong> Mines 

USGS : U.S. Geological Survey 

WEC : World Energy Council 

W.R. : World Resources 

Subscripts 

0 : Conditions <strong>of</strong> <strong>the</strong> environment 

00 : Conditions <strong>of</strong> <strong>the</strong> reference environment or dead state 

at m: Atmosphere 

b k : The number <strong>of</strong> brucitic cations 

cr : Upper continental crust 

e: Electrical consumption 

g l: Glaciers 

g w : Groundwater 

hydr: Hydrosphere 

j : Index <strong>of</strong> <strong>the</strong> considered element. In section 5.4.5, also <strong>the</strong> index <strong>of</strong> <strong>the</strong> considered cation 

i : Index <strong>of</strong> <strong>the</strong> considered species. In section 5.4.5, also <strong>the</strong> index <strong>of</strong> <strong>the</strong> considered cation 

k : Index <strong>of</strong> <strong>the</strong> additional element appearing in <strong>the</strong> reference substance <strong>of</strong> element j 

l i : The number <strong>of</strong> interlayer atom 

L : Liquid fuel 

F : Clean solid fuel 

o : The octahedral site 

t : The tetrahedral site


r w : River water 

s pher e: Considered sphere <strong>of</strong> <strong>the</strong> earth, ei<strong>the</strong>r atmosphere, hydrosphere or upper continental crust 

s w : Seawater 

t : Total 

t h: Thermal consumption 

W : Moisture 

Z : Ashes 

Superscripts 

∧ : Property calculated in this study 

− : Average <strong>of</strong> <strong>the</strong> property 

0 : Standard conditions

List <strong>of</strong> Figures 

1.1 Conceptual diagram <strong>of</strong> <strong>the</strong> terms exergoecology and <strong>the</strong>rmo-ecology . 11 

2.1 The atmospheric layers. Source: http://www.atmosphere.mpg.de 

(Max Plank Institute) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 

2.2 Earth’s cutaway. Source: USGS [397] . . . . . . . . . . . . . . . . . . . . . 38 

4.1 Energy flow sheet for <strong>the</strong> surface <strong>of</strong> <strong>the</strong> earth [317] . . . . . . . . . . . . 107 

4.2 The hydrologic cycle. Source: http://www.ec.gc.ca/water (Environment 

Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 

4.3 A simplified summary <strong>of</strong> <strong>the</strong> path <strong>of</strong> <strong>the</strong> Thermohaline Ocean Circulation 

[274] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 

4.4 Primary world energy consumption by fuel type at <strong>the</strong> end <strong>of</strong> 2006. 

Values in Mtoe [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 

4.5 Coal proved reserves at <strong>the</strong> end 2006. Values in thousand millions 

tonnes (share <strong>of</strong> anthracite and bituminous coal in brackets) [35]. . . . 122 

4.6 Coal production and consumption at <strong>the</strong> end <strong>of</strong> 2006. Elaborated from 

data included in [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 

4.7 Oil proved reserves at <strong>the</strong> end 2006. Values in thousand millions <strong>of</strong> 

barrels [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 

4.8 Oil production and consumption at <strong>the</strong> end <strong>of</strong> 2006. Elaborated from 

data included in [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 

4.9 Natural gas proved reserves at <strong>the</strong> end 2006. Values in trillion cubic 

meters [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 

4.10 Natural gas production and consumption at <strong>the</strong> end <strong>of</strong> 2006. Elaborated 

from data included in [35]. . . . . . . . . . . . . . . . . . . . . . . . 126 

4.11 A classification <strong>of</strong> <strong>mineral</strong> resources and reserves [141]. . . . . . . . . . 130 

4.12 Two possible relationships between ore grade and <strong>the</strong> metal, <strong>mineral</strong>, 

or energy content <strong>of</strong> <strong>the</strong> resource base [316]. . . . . . . . . . . . . . . . . 131 

5.1 <strong>Exergy</strong> required for separating a substance from a mixture, according 

to Eq. 5.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 

421

422 LIST OF FIGURES 

7.1 Conceptual diagram for <strong>the</strong> terms exergy distance and exergy degradation 

velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 

7.2 The Hubbert’s bell shape curve <strong>of</strong> <strong>the</strong> production cycle <strong>of</strong> any exhaustible 

resource [146]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 

7.3 Hypo<strong>the</strong>tical processes involved in obtaining <strong>the</strong> <strong>mineral</strong> <strong>of</strong> copper 

from <strong>the</strong> reference environment . . . . . . . . . . . . . . . . . . . . . . . . 236 

7.4 Yearly chemical exergy consumption in <strong>the</strong> US <strong>of</strong> pure copper due to 

copper production throughout <strong>the</strong> 20th century . . . . . . . . . . . . . . 239 

7.5 Cumulative chemical exergy decrease <strong>of</strong> copper mines in <strong>the</strong> US 

throughout <strong>the</strong> 20th century . . . . . . . . . . . . . . . . . . . . . . . . . . 239 

7.6 Yearly concentration exergy consumption in <strong>the</strong> US <strong>of</strong> pure copper due 

to copper production throughout <strong>the</strong> 20th century . . . . . . . . . . . . . 240 

7.7 Cumulative concentration exergy decrease <strong>of</strong> copper mines in <strong>the</strong> US 


7.8 The Hubbert peak applied to US copper production. Best fitting curve. 

Values in ktoe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 

7.9 The Hubbert peak applied to US copper base reserves. Values in ktoe. . 245 

7.10 Ore grade and cumulated exergy consumption <strong>of</strong> Australian gold mines 248 

7.11 The Hubbert peak applied to Australian gold reserves. Values in toe. . 249 

7.12 Ore grade and cumulated exergy consumption <strong>of</strong> Australian copper 

mines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 

7.13 The Hubbert peak applied to Australian copper reserves. Values in ktoe. 251 

7.14 Ore grade and cumulated exergy consumption <strong>of</strong> Australian nickel mines 253 

7.15 The Hubbert peak applied to Australian nickel reserves. Values in ktoe. 253 

7.16 Ore grade and cumulated exergy consumption <strong>of</strong> Australian silver mines 255 

7.17 The Hubbert peak applied to Australian silver reserves. Values in toe. . 256 

7.18 Ore grade and cumulated exergy consumption <strong>of</strong> Australian lead mines 257 

7.19 The Hubbert peak applied to Australian lead reserves. Values in ktoe. . 258 

7.20 Ore grade and cumulated exergy consumption <strong>of</strong> Australian zinc mines 259 

7.21 The Hubbert peak applied to Australian zinc reserves. Values in ktoe. . 260 

7.22 Ore grade and cumulated exergy consumption <strong>of</strong> Australian iron mines 261 

7.23 The Hubbert peak applied to Australian iron reserves. Values in ktoe. . 262 

7.24 The exergy loss <strong>of</strong> Australian coal reserves. Values in ktoe. . . . . . . . . 264 

7.25 The Hubbert peak applied to Australian coal reserves. Values in ktoe. . 265 

7.26 The exergy loss <strong>of</strong> Australian oil reserves. Values in ktoe. . . . . . . . . . 266 

7.27 The Hubbert peak applied to Australian oil reserves. Values in ktoe. . . 267 

7.28 The exergy loss <strong>of</strong> Australian natural gas reserves. Values in ktoe. . . . 268 

7.29 The Hubbert peak applied to Australian natural gas reserves. Values in 

ktoe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 

7.30 Irreversible exergy consumption <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong>s in Australia 

in <strong>the</strong> period from 1884 to 1906 . . . . . . . . . . . . . . . . . . . . 270 


in <strong>the</strong> period from 1907 to 1964 . . . . . . . . . . . . . . . . . . . . 271

List <strong>of</strong> Figures 423 


in <strong>the</strong> period from 1965 to 2004 . . . . . . . . . . . . . . . . . . . . 271 

7.33 Irreversible exergy consumption <strong>of</strong> <strong>the</strong> main fuel and non-fuel <strong>mineral</strong>s 

in Australia in <strong>the</strong> period <strong>of</strong> 1914 to 1968 . . . . . . . . . . . . . . . . . . 272 

7.34 Irreversible exergy consumption <strong>of</strong> <strong>the</strong> main fuel and non-fuel <strong>mineral</strong>s 

in Australia in <strong>the</strong> period <strong>of</strong> 1969 to 2004 . . . . . . . . . . . . . . . . . . 273 

7.35 Relative contribution <strong>of</strong> <strong>the</strong> extraction <strong>of</strong> fuel and non-fuel <strong>mineral</strong>s to 

<strong>the</strong> global exergy degradation <strong>of</strong> Australia in <strong>the</strong> period <strong>of</strong> 1914 to 2004 273 

7.36 <strong>Exergy</strong> countdown <strong>of</strong> <strong>the</strong> main consumed <strong>mineral</strong>s in Australia . . . . . 275 

7.37 <strong>Exergy</strong> countdown <strong>of</strong> metals copper, zinc, nickel, lead and silver in 

Australia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 

8.1 The exergy loss <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong> commodities on earth in 

<strong>the</strong> twentieth century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 

8.2 The actual exergy loss <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong> commodities on 

earth in <strong>the</strong> twentieth century . . . . . . . . . . . . . . . . . . . . . . . . . 287 

8.3 The actual exergy loss <strong>of</strong> <strong>the</strong> main 15 non-fuel <strong>mineral</strong> commodities 

on earth in <strong>the</strong> twentieth century, excluding iron and aluminium . . . . 288 

8.4 Depletion degree in % <strong>of</strong> <strong>the</strong> main non-fuel <strong>mineral</strong> commodity reserves 288 

8.5 The Hubbert peak applied to world iron production. Data in ktoe . . . 289 

8.6 The Hubbert peak applied to world aluminium production. Data in ktoe 290 

8.7 The Hubbert peak applied to world copper production. Data in ktoe . . 290 

8.8 Actual exergy consumption <strong>of</strong> <strong>the</strong> world’s fuel and non-fuel <strong>mineral</strong>s 


8.9 The Hubbert peak applied to world coal production. Data in Mtoe . . . 293 

8.10 The Hubbert peak applied to world natural gas production. Data in Mtoe 293 

8.11 The Hubbert peak applied to world oil production. Data in Mtoe . . . . 294 

8.12 The Hubbert peak applied to <strong>the</strong> world’s conventional fossil fuel production. 

Data in Mtoe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 

8.13 The Hubbert peak applied to <strong>the</strong> world’s main <strong>mineral</strong>s production. 

Data in Mtoe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 

8.14 The exergy countdown <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s extracted on earth . . . . 296 

8.15 Schematic presentation <strong>of</strong> <strong>the</strong> global carbon cycle as estimated by Post 

et al. [270] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 

8.16 Scenarios for GHG emissions from 2000 to 2100 and projections <strong>of</strong> 

surface temperatures [160] . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 

8.17 CO 2 emissions and equilibrium temperature increases for a range <strong>of</strong> 

stabilization levels [162] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 

8.18 <strong>Exergy</strong> loss <strong>of</strong> <strong>the</strong> different types <strong>of</strong> coal as a function <strong>of</strong> <strong>the</strong> CO 2 concentration 

in <strong>the</strong> atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . 303 

8.19 <strong>Exergy</strong> loss <strong>of</strong> <strong>the</strong> different types <strong>of</strong> fuel-oils as a function <strong>of</strong> <strong>the</strong> CO 2 

concentration in <strong>the</strong> atmosphere . . . . . . . . . . . . . . . . . . . . . . . . 304 

8.20 <strong>Exergy</strong> loss <strong>of</strong> natural gas as a function <strong>of</strong> <strong>the</strong> CO 2 concentration in <strong>the</strong> 

atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

424 LIST OF FIGURES 

8.21 Actual exergy consumption <strong>of</strong> <strong>the</strong> main <strong>mineral</strong>s in <strong>the</strong> 21st century 

based on <strong>the</strong> Hubbert peak model. Values in Gtoe . . . . . . . . . . . . . 308 


based on <strong>the</strong> IPCC’s B1 scenario. Values in Gtoe . . . . . . . . . . . . . . 310 


based on <strong>the</strong> IPCC’s A1T scenario. Values in Gtoe . . . . . . . . . . . . . 312 


based on <strong>the</strong> IPCC’s B2 scenario. Values in Gtoe . . . . . . . . . . . . . . 313 


based on <strong>the</strong> IPCC’s A1B scenario. Values in Gtoe . . . . . . . . . . . . . 314 


based on <strong>the</strong> IPCC’s A2 scenario. Values in Gtoe . . . . . . . . . . . . . . 316 


based on <strong>the</strong> IPCC’s A1FI scenario. Values in Gtoe . . . . . . . . . . . . . 317 

8.28 Summary <strong>of</strong> <strong>the</strong> actual exergy degradation <strong>of</strong> <strong>the</strong> main extracted <strong>mineral</strong>s 

in <strong>the</strong> period between years 1900 and 2100 based on <strong>the</strong> Hubbert 

and <strong>the</strong> IPCC’s SRES scenarios . . . . . . . . . . . . . . . . . . . . . . . . . 319 

A.1 The Hubbert peak applied to <strong>the</strong> exergy cost <strong>of</strong> world’s iron production, 

based on <strong>the</strong> world resources. Data in ktoe . . . . . . . . . . . . . . . . . 409 

A.2 The Hubbert peak applied to <strong>the</strong> exergy cost <strong>of</strong> world’s aluminium 

production, based on <strong>the</strong> world resources. Data in ktoe . . . . . . . . . . 409 

A.3 The Hubbert peak applied to <strong>the</strong> exergy cost <strong>of</strong> world’s copper production, 

based on <strong>the</strong> world resources. Data in ktoe . . . . . . . . . . . . . . 410

List <strong>of</strong> Tables 

2.1 Composition <strong>of</strong> <strong>the</strong> main envelopes derived from direct sampling or 

from a chemical translation <strong>of</strong> a direct measurement (density), in <strong>the</strong> 

case <strong>of</strong> <strong>the</strong> core, and <strong>the</strong> corresponding whole earth composition [169]. 21 

2.2 Gaseous chemical composition <strong>of</strong> <strong>the</strong> atmosphere [272]. . . . . . . . . . 24 

2.3 Inventory <strong>of</strong> water at <strong>the</strong> earth’s surface [263]. . . . . . . . . . . . . . . . 25 

2.4 Volume <strong>of</strong> Oceans and Seas. Adapted from [85] . . . . . . . . . . . . . . 26 

2.5 The composition <strong>of</strong> average seawater. Adapted from [224] . . . . . . . 27 

2.6 Predicted Mean Oceanic Concentrations. Adapted from [273]. . . . . . 28 

2.7 Renewable water resources and potential water availability by continents 

[311]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 

2.8 Mean chemical contents <strong>of</strong> world river water [197] . . . . . . . . . . . . 31 

2.9 The average concentrations <strong>of</strong> elements in filtered river water. Concentration 

in ppb. Adapted from Li [196]. . . . . . . . . . . . . . . . . . . 32 

2.10 Constituents <strong>of</strong> ground waters from different rock types. Concentrations 

in µg/g [405]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 

2.11 Area <strong>of</strong> land surface covered by glaciers in different regions <strong>of</strong> <strong>the</strong> 

world, toge<strong>the</strong>r with estimates <strong>of</strong> volume and <strong>the</strong> equivalent sea level 

rise that <strong>the</strong> volume implies [185]. . . . . . . . . . . . . . . . . . . . . . . 35 

2.12 The concentration <strong>of</strong> major ions in glacial run<strong>of</strong>f from different regions 

<strong>of</strong> <strong>the</strong> world. Concentrations are reported in mg/l. Adapted from [43] 36 

2.13 Average composition <strong>of</strong> <strong>the</strong> upper continental crust according to different 

studies. Elements in g/g. . . . . . . . . . . . . . . . . . . . . . . . . . 39 

3.1 Mineral classification based on Dana’s New Mineralogy [103] . . . . . . 44 

3.2 Crustal abundance <strong>of</strong> <strong>mineral</strong>s. Data in percent volume. . . . . . . . . . 47 

3.3 Average <strong>mineral</strong>ogical composition <strong>of</strong> <strong>the</strong> upper continental crust according 

to Grigor’ev [127]. Results are given in mass percentage. . . . 47 

3.4 Comparison <strong>of</strong> Rudnick and Gao’s [292] chemical composition <strong>of</strong> <strong>the</strong> 

upper earth’s crust and <strong>the</strong> one generated by Grigor’ev [127] according 

to Eq. 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 

3.5 Mineralogical composition <strong>of</strong> <strong>the</strong> earth’s crust according to <strong>the</strong> calculations 

<strong>of</strong> this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 

425

426 LIST OF TABLES 

3.6 Crustal abundance <strong>of</strong> <strong>mineral</strong>s according to this and Grigor’ev’s model 

in mass % [127] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 

4.1 World energy use in 1984 [130] . . . . . . . . . . . . . . . . . . . . . . . . 106 

4.2 Estimates <strong>of</strong> bulk continental crust heat production from heat flow data 

[168]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 

4.3 Estimated uranium resources in ores rich enough to be mined for use in 

235 U power plants [317], toge<strong>the</strong>r with estimated rates <strong>of</strong> production 

for 2005 according to <strong>the</strong> BGS [139]. Data reported as ktons <strong>of</strong> metal 

content. No distinctions are drawn between reserves and resources, 

and no data for resources are reported by <strong>the</strong> former URSS countries. . 111 

4.4 Specific exergy on a dry basis <strong>of</strong> representative biomass samples [138] 118 

4.5 Rank <strong>of</strong> coal according to <strong>the</strong> norm ASTM D388. . . . . . . . . . . . . . . 121 

4.6 Rank <strong>of</strong> oil according to <strong>the</strong> British standard BS2869:1998 . . . . . . . 122 

4.7 Physical properties <strong>of</strong> different compositions <strong>of</strong> natural gas [34] . . . . 123 

4.8 Available energy, potential energy use and current consumption <strong>of</strong> natural 

resources on earth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 

4.9 Summary statistics <strong>of</strong> grade-tonnage models. After [66] . . . . . . . . . 132 

4.10 Mineral world reserves, reserve base and world resources in 2006 . . . 136 

5.1 <strong>Exergy</strong> difference <strong>of</strong> selected elements considering ei<strong>the</strong>r as reference 

species <strong>the</strong> most abundant or <strong>the</strong> most stable substances in <strong>the</strong> R.E. 

[367] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 

5.4 Standard chemical exergies <strong>of</strong> <strong>the</strong> elements . . . . . . . . . . . . . . . . . 154 

5.5 Composition <strong>of</strong> <strong>the</strong> three R.E. proposed . . . . . . . . . . . . . . . . . . . 164 

5.6 Calculation <strong>of</strong> <strong>the</strong> chemical potential <strong>of</strong> <strong>the</strong> elements according to 

three different R.E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 

5.7 <strong>Exergy</strong> costs <strong>of</strong> selected substances [371] & [207] . . . . . . . . . . . . . 170 

5.8 Summary <strong>of</strong> <strong>the</strong> methodologies used to predict <strong>the</strong> <strong>the</strong>rmodynamic 

properties <strong>of</strong> <strong>mineral</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 

6.1 Thermodynamic properties <strong>of</strong> <strong>the</strong> atmosphere. Values <strong>of</strong> ∆H 0 , ∆G0 f i f i , 

b 0 

ch i 

in kJ/mole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 

6.2 Thermodynamic properties <strong>of</strong> seawater. Values in kJ/mole . . . . . . . . 190 

6.3 Thermodynamic properties <strong>of</strong> average rivers. Values in kJ/mole . . . . 191 

6.4 Thermodynamic properties <strong>of</strong> glacial run<strong>of</strong>f. Values in kJ/mole . . . . . 192 

6.5 Thermodynamic properties <strong>of</strong> groundwaters. Values in kJ/mole . . . . 193 

6.6 Summary <strong>of</strong> <strong>the</strong> <strong>the</strong>rmodynamic properties <strong>of</strong> <strong>the</strong> hydrosphere. Values 

in kJ/mole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 

6.7 Thermodynamic properties <strong>of</strong> <strong>the</strong> upper continental crust . . . . . . . . 196 

6.8 The standard chemical exergy <strong>of</strong> <strong>the</strong> earth’s outer layers . . . . . . . . . 205 

6.9 High heating value and elementary analysis (% by weight) considered 

in <strong>the</strong> study <strong>of</strong> Valero and Arauzo [366] to define different types <strong>of</strong> coal. 208

List <strong>of</strong> Tables 427 

6.10 Thermodynamic properties <strong>of</strong> <strong>the</strong> different types <strong>of</strong> coal. Values in 

kJ/kg, except for s 0 (kJ/kgK) . . . . . . . . . . . . . . . . . . . . . . . . . 208 

6.11 The exergy <strong>of</strong> <strong>the</strong> world’s coal proven reserves reported in [401]. Values 

in million tonnes if not specified . . . . . . . . . . . . . . . . . . . . . 209 

6.12 High heating value and elementary analysis (% by weight) <strong>of</strong> <strong>the</strong> different 

types <strong>of</strong> oil, according to <strong>the</strong> British standard BS2869:1998 . . . 213 

6.13 Thermodynamic properties <strong>of</strong> <strong>the</strong> different types <strong>of</strong> oil. Values in 

kJ/kg, except for s 0 (kJ/kgK) . . . . . . . . . . . . . . . . . . . . . . . . . 213 

6.14 The exergy <strong>of</strong> <strong>the</strong> world’s oil proven reserves reported in [35]. Values 

in thousand million tonnes if not specified . . . . . . . . . . . . . . . . . . 213 

6.15 Standard volumetric composition <strong>of</strong> natural gas considered in [366] . 215 

6.16 Thermodynamic properties <strong>of</strong> natural gas. Values in kJ/N m 3 , except 

for ∆H f (kJ/kg) and s 0 (kJ/kgK) . . . . . . . . . . . . . . . . . . . . . . . 216 

6.17 The exergy <strong>of</strong> <strong>the</strong> world’s natural gas proven reserves reported in [35] 216 

6.18 The exergy and exergy cost <strong>of</strong> <strong>the</strong> <strong>mineral</strong> reserves, base reserve and 

world resources. Values are expressed in ktoe . . . . . . . . . . . . . . . . 219 

6.19 Available exergy, potential exergy use and current exergy consumption 

<strong>of</strong> natural resources on earth. Letter e denotes electrical consumption, 

while th <strong>the</strong>rmal consumption. . . . . . . . . . . . . . . . . . . . . . . . . 224 

7.1 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> US copper mines 

during <strong>the</strong> 20th century. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 

7.2 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian gold mines. 250 

7.3 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian copper 

mines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 

7.4 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian nickel mines. 254 

7.5 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian silver mines. 256 

7.6 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian lead mines. 258 

7.7 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian zinc mines. 260 

7.8 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy distance <strong>of</strong> Australian iron mines. 263 

7.9 Summary <strong>of</strong> <strong>the</strong> results <strong>of</strong> <strong>the</strong> exergy assessment <strong>of</strong> <strong>the</strong> main Australian 

<strong>mineral</strong>s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 

7.10 Monetary costs <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> reserves depletion suffered in Australia 

due to <strong>mineral</strong> production in year 2004 . . . . . . . . . . . . . . . . 276 

8.1 The exergy loss <strong>of</strong> <strong>the</strong> main <strong>mineral</strong> commodities in <strong>the</strong> world. Values 

are expressed in ktoe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 

8.2 The exergy loss <strong>of</strong> coal, oil and natural gas in <strong>the</strong> 20th century. . . . . . 291 

8.3 Projected global averaged temperature change ( ◦ C at 2090-2099 relative 

to 1980-1999) at <strong>the</strong> end <strong>of</strong> <strong>the</strong> 21st century. After [160] . . . . . 300 

8.4 Characteristics <strong>of</strong> stabilization scenarios and resulting long-term equilibrium 

global average temperature rise above pre-industrial at equilibrium 

from <strong>the</strong>rmal expansion only. After [162] . . . . . . . . . . . . . 301 

8.5 Temperature rise and CO 2 concentration in <strong>the</strong> SRES scenarios . . . . . 302

428 LIST OF TABLES 

8.6 Specific exergy (b in kJ/kg) and <strong>Exergy</strong> loss (%) <strong>of</strong> anthracite, bituminous, 

subbituminous, and lignite coal according to <strong>the</strong> different SRES 

scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 

8.7 Specific exergy (b) and <strong>Exergy</strong> loss (%) <strong>of</strong> fuel-oil 1, fuel-oil 2 and 

fuel-oil 4, according to <strong>the</strong> different SRES scenarios. . . . . . . . . . . . 303 

8.8 Specific exergy (b) and <strong>Exergy</strong> loss (%) <strong>of</strong> natural gas according to <strong>the</strong> 

different SRES scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 

8.9 <strong>Exergy</strong> loss <strong>of</strong> <strong>the</strong> 2006 coal reserves due to <strong>the</strong> increase <strong>of</strong> GHG emissions, 

according to <strong>the</strong> different SRES scenarios. Values in Mtoe . . . . 306 

8.10 <strong>Exergy</strong> loss <strong>of</strong> <strong>the</strong> 2006 fuel-oil reserves due to <strong>the</strong> increase <strong>of</strong> GHG 

emissions, according to <strong>the</strong> different SRES scenarios . . . . . . . . . . . 306 

8.11 <strong>Exergy</strong> loss <strong>of</strong> <strong>the</strong> 2006 natural gas reserves due to <strong>the</strong> increase <strong>of</strong> GHG 

emissions, according to <strong>the</strong> different SRES scenarios . . . . . . . . . . . 306 

8.12 Actual exergy degradation <strong>of</strong> <strong>the</strong> main extracted <strong>mineral</strong>s in <strong>the</strong> 21st 

century based on <strong>the</strong> Hubbert peak model . . . . . . . . . . . . . . . . . . 309 


century based on <strong>the</strong> B1 scenario . . . . . . . . . . . . . . . . . . . . . . . 311 


century based on <strong>the</strong> A1T scenario . . . . . . . . . . . . . . . . . . . . . . 312 


century based on <strong>the</strong> B2 scenario . . . . . . . . . . . . . . . . . . . . . . . 313 


century based on <strong>the</strong> A1B scenario . . . . . . . . . . . . . . . . . . . . . . 315 


century based on <strong>the</strong> A2 scenario . . . . . . . . . . . . . . . . . . . . . . . 316 


century based on <strong>the</strong> A1FI scenario . . . . . . . . . . . . . . . . . . . . . . 318 

8.19 Summary <strong>of</strong> <strong>the</strong> actual exergy degradation <strong>of</strong> <strong>the</strong> main extracted <strong>mineral</strong>s 

in <strong>the</strong> period between years 1900 and 2100 based on <strong>the</strong> Hubbert 

and <strong>the</strong> IPCC’s SRES scenarios . . . . . . . . . . . . . . . . . . . . . . . . . 318 

A.1 Vector ˆε j [78 × 1], according to Rudnick and Gao [292] and vector ε j 

[78 × 1], obtained from Grigor’ev [127]. Values in mole/g . . . . . . . 351 

A.2 Vector ξ i [324 × 1], according to Grigor’ev [127] and vector ˆ ξ i [324 × 

1] obtained in this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 

A.3 Matrix R ′ [324 × 78] (Part 1) . . . . . . . . . . . . . . . . . . . . . . . . . . 360 

A.4 Matrix R ′ [324 × 78] (Part 2) . . . . . . . . . . . . . . . . . . . . . . . . . . 367 

A.5 Summary statistics <strong>of</strong> grade-tonnage models-1. After [66] . . . . . . . . 376 






A.11 Summary statistics <strong>of</strong> grade-tonnage models-7. After [66] . . . . . . . . 382

List <strong>of</strong> Tables 429 


A.13 Chemical exergies <strong>of</strong> <strong>the</strong> elements for gaseous reference substances . . 384 

A.14 Chemical exergies <strong>of</strong> <strong>the</strong> elements for aqueous reference substances . . 384 

A.15 Chemical exergies <strong>of</strong> <strong>the</strong> elements for solid reference substances . . . . 385 

A.16 Coefficients a 1 through a 7 [413] . . . . . . . . . . . . . . . . . . . . . . . . 386 

A.17 The g i and h i <strong>of</strong> each polyhedral type and <strong>the</strong> standard error (%) <strong>of</strong> 

<strong>the</strong> estimate. Values in kJ/mol. [55] . . . . . . . . . . . . . . . . . . . . . 387 

A.18 Values <strong>of</strong> ∆ GO −2 M z+ (clay) for ions located in different sites [382] 

for hydrated clays and phyllosilicates. Values in kJ/mole . . . . . . . . . 388 

A.19 Estimations <strong>of</strong> <strong>the</strong> standard enthalpy and Gibbs free energy <strong>of</strong> <strong>mineral</strong>s. 

Values in kJ/mole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 

A.20 The chemical exergy and exergy cost <strong>of</strong> <strong>the</strong> 2006 world’s <strong>mineral</strong> production, 

<strong>mineral</strong> reserves, base reserve and world resources. Values 

are expressed in ktoe if not specified . . . . . . . . . . . . . . . . . . . . . 398 

A.21 The concentration exergy and exergy cost <strong>of</strong> <strong>the</strong> 2006 world’s <strong>mineral</strong> 

production, <strong>mineral</strong> reserves, base reserve and world resources. Values 

are expressed in ktoe if not specified . . . . . . . . . . . . . . . . . . . . . 400 

A.22 Evolution <strong>of</strong> <strong>the</strong> Australian coal production. Values in ktons . . . . . . . 402 

A.23 Evolution <strong>of</strong> <strong>the</strong> Australian oil production. Values in ktons . . . . . . . . 403 

A.23 Evolution <strong>of</strong> <strong>the</strong> Australian oil production. Values in ktons.– continued 

from previous page. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 

A.24 Evolution <strong>of</strong> <strong>the</strong> Australian natural gas production. Values in millions 

<strong>of</strong> cubic meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 

A.25 Production <strong>of</strong> uranium in western countries and in <strong>the</strong> world. Values 

are expressed in tons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 

A.26 Evolution <strong>of</strong> <strong>the</strong> world’s coal production . . . . . . . . . . . . . . . . . . . 406 

A.27 Evolution <strong>of</strong> <strong>the</strong> world’s oil production . . . . . . . . . . . . . . . . . . . . 407 

A.28 Evolution <strong>of</strong> <strong>the</strong> world’s natural gas production. Data in billion <strong>of</strong> cubic 

meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 

A.29 Primary energy consumption and cumulative resources production in 

<strong>the</strong> IPCC’s B1 scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . . . 410 


<strong>the</strong> IPCC’s A1T scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . . 411 


<strong>the</strong> IPCC’s B2 scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . . . 411 


<strong>the</strong> IPCC’s A1B scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . . 411 


<strong>the</strong> IPCC’s A2 scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . . . 412 


<strong>the</strong> IPCC’s A1FI scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . . 412

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