Thermoeconomic analysis and simulation of a combined... - circe ...

THERMOECONOMIC ANALYSIS AND 

SIMULATION OF A COMBINED POWER 

AND DESALINATION PLANT 

Departamento de Ingeniería Mecánica 

Ph. D. Thesis 

Francisco Javier Uche Marcuello 

Universidad de Zaragoza

THERMOECONOMIC ANALYSIS AND 

SIMULATION OF A COMBINED POWER 

AND DESALINATION PLANT 

Departamento de Ingeniería Mecánica 

Universidad de Zaragoza 

Ph. D. Tesis 

Francisco Javier Uche Marcuello 

Zaragoza, Mars 2000

D. Antonio Valero Capilla, Catedrático del Departamento de Ingeniería Mecánica 

de la Universidad de Zaragoza, y D. Luis Serra De Renobales, Profesor Titular del 

Área de Máquinas y Motores Térmicos de la Universidad de Zaragoza 

CERTIFICAN 

que la memoria titulada Thermoeconomic Analysis and Simulation of a Combined 

Power and Desalination Plant presentada por el Ingeniero Industrial 

D. Francisco Javier Uche Marcuello para optar al grado de Doctor en el programa de 

Optimización Energética del Departamento de Ingeniería Mecánica, ha sido realizada 

bajo su dirección. 

Zaragoza, 20 de Marzo de 2000 

Fdo: Antonio Valero Capilla Fdo: Luis Serra de Renobales

a Sonia

Agradecimientos 

Quiero agradecer especialmente la realización de esta tesis doctoral a mis padres Luis 

y Pilar, y a mi hermano José Luis por su paciencia y ánimos para realizarla, a pesar de 

no entender a veces muy claramente la finalidad de la misma. 

Por supuesto, Natalia es la que más me ha tenido que aguantar y animar en los malos 

momentos que a veces he tenido. Además, ella ha tenido siempre un interés especial 

para que yo la realizara. 

Los directores de mi tesis, Antonio y Luis, han estado siempre a mi lado disponibles 

para cualquier duda o sugerencia en su realización. Nuestras reuniones periódicas han 

servido para enriquecerme personalmente. Esta tesis también ha servido para establecer 

una relación especial de amistad y confianza con Luis, que para mí es fundamental 

en el trabajo diario. 

También quiero agradecer al personal de la Central Térmica Teruel (ENDESA) por su 

flexibilidad de horarios, que me ha permitido desarrollar gran parte de mi tesis doctoral 

durante mi estancia en Andorra. Y a mis compañeros de piso durante dicha estancia, 

que me dejaron trabajar en todo momento sin impedimento alguno. 

Finalmente, quiero agradecer a Rosa y a Morris su ayuda en la edición. Y a esa gran 

familia que es CIRCE, y al gran ambiente que existe dentro de ella. 

Acknowledgements 

The financial support provided by ICWES (International Center for Water and Energy 

Systems, United Arab Emirates) is gratefully acknowledged. Sincere appreciation is 

expressed to D. M. K. Al-Gobaisi, Director of ICWES, for his continued support and 

encouragement during the course of this thesis. The discussions that the author and 

my directors had with him and Ali El-Nashar and Asghar Husain were very helpful. 

Thanks are also extended to Hanif Sultan and John Nynam who provided the technical 

information essential to the design of my simulator.

Resumen 

La desalación de aguas de mar o salobres es una de las formas más utilizadas para 

dotar con la calidad suficiente a la población de los recursos hídricos necesarios para 

su manutención y desarrollo. En un sector industrial en constante crecimiento, ya que 

el consumo humano per cápita sigue aumentando constantemente con el incremento 

del nivel de vida, a pesar de las campañas buscando el ahorro y la racionalidad en el 

consumo, sobre todo en la agricultura intensiva. 

España es país que cuenta con un claro déficit de agua en las zonas costeras del 

Levante y Sur, así como en los dos archipiélagos principales (Baleares y Canarias), 

dichas zonas coinciden con ser las más turísticas del país, lo que significa que la 

demanda se multiplica en verano. Sin tener en cuenta la posibilidad de efectuar trasvases 

de otras cuencas hidrográficas no deficitarias, el problema está siendo resuelto 

principalmente por plantas de Osmosis Inversa, plantas cuyas dimensiones y producción 

se adecuan mucho mejor a las necesidades de los diferentes tamaños de los 

núcleos ó asentamientos estables de población. El coste del agua producida sigue 

siendo muy alto en comparación con la obtención por medios naturales, pero sin 

embargo es menor que otros métodos de desalación. 

Sin embargo, la situación de España no es extrapolable a las zonas con verdaderos 

problemas de escasez de agua: los países desérticos del Golfo Pérsico. Su escasísima 

pluviometría, sus elevadas temperaturas durante todo el año y la casi nula impermeabilidad 

de sus suelos disparan su consumo de agua. Son además países de relativamente 

reciente creación, por lo que la demanda de energía eléctrica también debe 

ser resuelta. La instalación de grandes plantas de cogeneración permite a la vez resolver 

los dos problemas, con la utilización de los inmensos recursos petrolíferos y gas 

de la zona. Las plantas duales de generación de potencia acopladas con las unidades 

de desalación por destilación flash multietapa producen el 80% del agua desalada en 

el mundo. Pero ello no significa que sea el método más eficiente de producir esos dos 

productos necesarios para toda sociedad. 

El análisis termoeconómico permite conocer el funcionamiento interno de dichas 

plantas de generación de electricidad y agua dulce, las posibilidades de ahorro que 

ofrece este modo combinado de producción. Es esencial realizar dicho análisis de 

Thermoeconomic analysis and simulation of a combined power and desalination plant

12 

Resumen 

forma conjunta, cosa que normalmente no se hace en este tipo de instalaciones: cada 

planta es gestionada independientemente. 

Esta Tesis Doctoral desarrolla el análisis termoeconómico completo de la planta de 

cogeneración más grande que actualmente existe (en cuanto a la producción de agua 

por unidad desaladora), que consta de una planta con una turbina de vapor para la 

generación de electricidad y una desaladora por destilación flash de un único efecto 

por cada una de sus etapas. Es una tesis eminentemente práctica, es decir, trata de 

aplicar las metodologías que la Termoeconomía actualmente está aplicando a otros 

sistemas tales como plantas de potencia a un sistema muy complejo en el cual los 

procesos químicos también son importantes en el balance de la instalación, no sólo 

los procesos mecánicos y térmicos. 

El análisis termoeconómico comprende cuatro partes principales que se detallan a 

continuación: 

• En primer lugar, el análisis de costes permite conocer los costes físicos de los flujos 

más importantes de las dos plantas, así como los costes finales de producción 

de agua y energía, teniendo en cuenta los costes de operación y de adquisición y 

mantenimiento de los equipos de la planta. Dicho análisis se basa en la creación 

de un modelo termoeconómico que representa de una forma funcional los procesos 

que ocurren dentro de la planta de potencia y de agua. Los resultados obtenidos 

son comparados con métodos tradicionales de contabilidad de costes que se 

han usado para asignar costes a los productos industriales. 

• Después, el análisis desarrolla el diagnóstico de la planta combinada, es decir, 

analiza los efectos provocados por una o varias ineficiencias simuladas dentro de 

la planta. Para ello, se ha construido un simulador de los dos procesos a partir de 

un modelo matemático y datos reales de una planta de cogeneración, que permite 

conocer los estados termodinámicos de referencia y con la ineficiencia con una 

precisión suficiente para nuestro análisis. Dichos efectos se traducen a un consumo 

adicional de fuel, incremento en la irreversibilidad de los diferentes procesos 

y una menor eficiencia en los mismos, además de ayudar a conocer las relaciones 

de los diferentes componentes de una instalación. En este análisis se demuestra 

que la planta de potencia los parámetros guía de funcionamiento de cada componente 

son locales, es decir, una variación de ellos no significa prácticamente al 

resto de componentes del sistema. Sin embargo, en la unidad MSF todos elementos 

principales están interconectados a través de los flujos principales que circulan 

por los destiladores, y por lo tanto los fallos ó mejoras sufridas en el 

funcionamiento de la planta afectan a toda ella, no sólo al equipo en el que están 

ocurriendo. 

• La tercera parte del análisis termodinámico es la optimización de la planta de potencia 

a partir de la optimización local de sus componentes. En la planta destiladora 

de agua la optimización local no es posible al no estar sus componentes 


Resumen 

termodinámicamente aislados, como ya se vió en la diagnosis de la planta. Esta 

metodología es muy valida para el diseño de nuevas plantas o la readaptación de 

plantas existentes hacia un mayor ahorro en las mismas. 

• Finalmente, un nuevo apartado conteniendo los conceptos de coste, precio y beneficio 

obtenidos se desarrolla brevemente, para aclarar errores que normalmente se 

cometen en la contabilización de los costes de una instalación. 

La Tesis Doctoral también incluye dos partes introductorias, la primera contiene la 

situación en los países con escasez de agua y los métodos de desalación más comunes 

utilizados actualmente. La segunda parte introductoria incluye el estado actual de la 

teoría termoeconómica necesaria para el análisis termoeconómico de la planta. 

Thermoeconomic analysis and simulation of a combined power and desalination plant 13

Abstract 

Desalination is the most important source of drinking water in arid zones, especially 

in the Gulf Area. Desalination consumes a lot of energy and, unfortunately, mostly 

from oil or natural gas. Co-generation plants providing freshwater and electricity are 

used in the arid areas. The combination of steam turbine plants and MSF (Multi-stage 

Flash) units is one of the most common schemes to meet water and energy 

requirements, providing almost 80% of all desalinated water in the world. 

A dual-purpose plant is a very complex system. Its behaviour is difficult to model, 

especially when all the available configurations of both sub-systems are considered. 

Usually plant performance is analysed separately, neglecting component interactions 

and possible savings from the combined systems. 

Thermoeconomic analysis techniques are the most convenient tools to analyze these 

systems, because they can: 

• Calculate the costs of the flows and products of a plant based on physical criteria 

(Second Law of Thermodynamics). 

• Assess alternatives to save energy. 

• Optimize operations. 

• Locally optimize subsystems. 

• Perform energy audits and assess the fuel impact of malfunctions (operation 

diagnosis) 

This Ph. D. Thesis develops the complete thermoeconomic analysis applied in an 

existing steam power plant and MSF desalination unit, including cost analysis, 

diagnosis and local optimization of the plant. Cost analysis provides the physical 

costs of the main flows of the dual plant depending on operating conditions. Special 

emphasis was made on the interactions between the plant components of both 

subsystems: new concepts such as induced or intrinsic malfunction, dysfunction or 

the malfunction matrix were included. The results demonstrate the effect of different 

conditions or inefficiencies in terms of water and energy costs and additional fuel 

consumption during an inefficiency. Operation recommendations were also included 


16 

Abstract 

in the analysis. Local optimization of the dual plant locates the optimum point for 

each operating condition and is a very powerful tool for the design analysis. 

Thermoeconomic analysis was developed using a validated model (simulator) of the 

plant to determine the thermodynamic reference state at design conditions for any 

load point, ambient condition, operating mode etc. Plant data from a dual-plant in the 

Gulf were used to adapt the mathematical models. The simulator also obtained the 

thermodynamic state of the plant when an inefficiency is estimated in the plant 

diagnosis. 


CHAPTER 1 

Introduction 

Water scarcity will soon be a serious problem, especially considering the rapidly 

increasing world population and water consumption per capita. Fortunately, part of 

this problem may be alleviated by desalting seawater, although this process consumes 

a lot of energy and may be difficult to use in non-developed countries. This Ph. D. 

Thesis contributes to searching for a way to reduce the energy required by desalting 

plants and provides tools to improve desalination technology. 

Several studies and international organizations focus on energy and others on water, 

but there seems to be a marked lack of attention on combined water and energy issues. 

The interaction between water production and energy is the main topic in this thesis. 

The main objective is to determine the validity of the thermoeconomic analysis in 

very complex systems like a dual-purpose power and desalination plant. 

This thesis considers the behavior of one of the most developed systems for providing 

water within the following framework: 

• Increasing human consumption and its consequences. 

• Water quality and the uses derived from its quality. 

• The world water crisis is mostly focused on water stressed areas. In these areas 

the water problem may also be solved by using desalting plants. 

• The interactions among the methods required to provide energy to desalt water. 

• The reasons for studying the steam turbine power plant + Multi-Stage Flash 

(MSF) desalination unit from thermodynamic point of view. 

• How Thermoeconomic techniques as the most useful to study complex systems. 

The final section of this chapter includes the structure of this Ph. D. Thesis. 


18 

Introduction 

1.1 Water requirements 

According to Al-Gobaisi (1999), all life depends on water and all terrestrial species, 

including humans, depend on fresh or non-saline water. Although the oceans 

represent the largest water reservoir on earth (covering three-quarters of its surface), 

it contains a high concentration of dissolved salts (more than the 3% of its weight). 

This makes it unsuitable for humans, industry and even irrigation. Less than 3% of 

the earth's water is non-saline, and the vast majority of it is locked up in glaciers and 

ice sheets. Water is moved around the earth in global cycles (evaporation-cloud 

formation-rain-percolation), but only when it is non-saline and in the liquid state, can 

it be used by humans. Human development and indeed civilization requires a reliable 

supply of even greater volumes of fresh water for drinking, cooking, washing and 

sanitation. Furthermore, industry consumes on average 200 tons of water per ton of 

manufactured product (Al-Gobaisi, 1997). Water also makes up more than half of the 

human body. An average adult drinks about 2.5 liters of water per day and needs 

0.75 liters a day just to stay alive. According to the World Health Organization, about 

150 liters of water are needed per day for a satisfactory hygienic life (Al-Gobaisi, 

1999). But in the South more than 1,500 million people do not have drinking water 

(Intermón, 1998). 

The imbalance between the available water resources and demand is clear, especially 

in arid areas like the Arabian Gulf or Northern Africa. Human water consumption per 

capita in this region is very high (including domestic, agricultural and industrial uses) 

ranging from 300 to 1,500 liters per day. Rapidly rising incomes in some countries, 

with the resultant increase of living standards, and water losses in the network have 

led to even higher per capita water consumption. Intensive agriculture under arid 

conditions increases this demand. The available water resources from perennial 

surface water, renewable ground water and reclaimed wastewater are insufficient to 

meet the demand. Overexploitation of ground-water decreases ground-water levels 

and deteriorates water quality, including salt-water intrusion. On the basis of the past 

experiences in arid zones, renewable freshwater resources of 1,000 cubic meters per 

capita per year have been considered the limit for a chronic water scarcity that will 

impede development and harm human health. In terms of resources deficiency, water 

stress is defined as an annual renewable resource less than 1,000 cubic meters per 

capita per year. All the countries of the Arabian World suffer from water stress 

(Al-Gobaisi, 1999). 

1.2 Water quality and uses 

Water use depends on its quality. The salinity of average seawater is 34,800 ppm, 

although it may vary between oceans. For example, the total dissolved solids (TDS) 

in Arabian Gulf seawater is between 43,000 and 50,000 ppm, while the Atlantic 


World water resources and demand 

Ocean has an average TDS of 36,000 ppm, and 33,600 ppm for the Pacific Ocean 

water (Abu Qdais, 1999). 

The highest limit for human consumption is 1,000 ppm (Spiegler and El-Sayed, 

1994), although the maximum permissible salt concentration in drinking water 

depends on the type of salt, the total daily water consumption and the climate (e.g., if 

the climate is hot and the salt is mainly sodium chloride, excess salt can even be 

beneficial to the human body). On average humans consume 2-8 liters per day. Thus, 

salt-water rejection for drinking water does not present a serious economic problem 

in the future, if compared with the water demand for agricultural or industrial 

purposes. 

The purity of water for industry strongly depends on the use. Sometimes brackish 

water (water with less than 5,000 ppm) is enough for industrial purposes, but 

ultrapure water is needed for specific processes like cooling power generation plants. 

The amount of water for industry is several times human water consumption which 

is why we need more research on saving water in industrial processes and reusing 

waste water. 

Non-natural irrigation (that is, not provided by rainfall) consumes the most amount of 

the world's water. For example, in China agriculture uses up 87% of the total water 

demand. In arid areas irrigation consumes enormous amounts of water. Desalination 

processes are so expensive that they are not feasibly introduced to irrigate land. 

However, brackish waters with a moderate salinity (about 2,000 ppm) are acceptable 

for some crops. The tolerance limits of each plant must be examined as a function of 

the soil, climate, saltwater composition, irrigation method and additional treatments 

(fertilizers). 

1.3 World water resources and demand 

Seawater desalination is most common in the countries bordering the Persian- 

Arabian gulf, the north of Africa and the Canary islands, the Caribbean islands, the 

Pacific region (Australia, Japan, Korea and China), and the south and east of Spain, as 

well as various locations in the American south-west and Florida. The following is a 

brief explanation of water demand and disposal in these areas in order to introduce 

the reader to the world’s water scarcity problem. 

1.3.1 Gulf Region 

The annual per capita annual water resources of countries in the Gulf region (United 

Arab Emirates, Saudi Arabia, Bahrain, Oman, Qatar and Kuwait. Iran and Iraq are 

excluded in the study) are very scarce. The fast growing population and increasing 


20 

Introduction 

per capita water demand (over 500 l per capita per day, Abdel-Jawad and Al- 

Tabtabaei, 1999) to meet the huge socio-economic developments since the 70s have 

recently magnified the problem. These countries are characterized by scanty rainfall 

and high evaporation and consumption which leads to deficits in their water budget. 

All these factors classify these countries as arid to semi-arid because of their limited 

conventional water resources and generally absent reliable surface water. 

Arabian Gulf seawater is quite different from other oceans: 

• The Arabian Gulf is roughly rectangular, surrounded by Iraq and Kuwait on the 

northwest, Saudi Arabia, Qatar, United Arab Emirates (UAE) and Oman on the 

west and south and by Iran on the east. The Gulf is approximately 100 Km long 

and 300 Km wide, with a surface area of 2.39× 

105 

Km2. 

Average water depth is 

35 meters, so its volume is 8.63× 

103 

Km3. 

Water circulates very slowly between 

the Arabian Gulf and the Gulf of Oman via the Strait of Hormuz: the average 

residence time of water is 2-5 years. 

• The Gulf Region has an arid sub-tropical climate with very limited annual rainfall. 

Water temperature varies seasonally from 18 ºC to 33 ºC. Therefore, evaporation is 

very high most of the year, exceeding the total river runoff by approximately a 

factor of 10. The effect of the river runoff, temperature and evaporation explain the 

gradually increasing salinity (from 36,300 to 50,000 ppm). 

• The Gulf ecosystem is seriously endangered and it is located in a region with 

political conflicts (two major wars in the last 15 years). It is also the largest oil 

route in the world; 20% of the total world production of oil passes through the 

Gulf. The serious environmental impact of large desalination units should be 

considered. 

Water stores are gradually depleting since it is extracted faster than refilled: 

approximately 17,000 million cubic meters are used per year and 3,000 million cubic 

meters recharged, and 4,000 million cubic meters are available from surface water. The 

total current water demand is about 20,000 Mm3/y, 

with non renewable resources 

satisfying approx. 75% with the rest supplied by renewable conventional sources, 

desalination plants and recycled wastewater. Table 1.1 shows the ground water 

resources and the amount of renewable water resources in 1994 per year in the Gulf 

Countries. 

Table 1.1 informs that the water stress in the Gulf countries is one of the main 

problems that needs to be solved. Water withdrawal or water demand is shown in 

table 1.2. The total demand is divided in domestic, agricultural and industrial uses. 


TABLE 1.1 

Country 


Ground water disposal and renewable water resources in the Gulf Countries in 1994 (Alawadhi, 

1999). 

Population 

(millions) 

Ground water 

resources 

(Mm3/y) 

Conventional 

Renewable water resources (Mm3/y) 

Non conventional 

Desalination Wastewater 

Saudi Arabia 18.18 14,430 4,550 874 217 

UAE 2.15 1,000 490 385 110 

Kuwait 1.62 114 161 514 83 

Qatar 0.53 185 50 108 25 

Bahrain 0.55 190 90 75 32 

Oman 2.05 728 1,929 39 25 

Total 25.08 16,647 7,270 1,995 492 

TABLE 1.2 

Water demand for the Gulf Countries in 1990 (ESCWA, 1994). 

Country 

Total demand 

(Mm3/y) 

Withdrawal in various sectors (Mm3/y) 

Domestic Agricultural Industrial 

Saudi Arabia 16,300 1,508 14,600 192 

UAE 1,490 513 950 27 

Kuwait 383 295 80 8 

Qatar 194 76 109 9 

Bahrain 223 86 120 17 

Oman 1,236 81 1,150 5 

Total 19,826 2,559 17,009 258 

Desalination is a means of augmenting fresh water resources to remove or at least 

reduce water stress. The number of desalination plants in the Gulf Council Countries 

(GCC) states increases daily. Table 1.3 summarizes the production and capacity of 

the Middle East countries. 


TABLE 1.3 

TABLE 1.4 

22 

Introduction 

Total installed capacity and production in the seawater desalination plant of the Gulf Area in year 

1994 (Alawadi, 1999; Al-Gobaisi, 1999). 

Country Total capacity (m3/d) 

Total production (Mm3/y) 

Saudi Arabia 4,179,882 874.2 

UAE 2,066.340 385 

Kuwait 1,409,000 514 

Qatar 295,000 108 

Bahrain 220,571 75 

Oman 105,000 39 

Total 8,275,793 1,995 

Water production in Gulf countries represented the majority of the worldwide 

capacity. Table 1.4 shows representative values of freshwater produced in different 

processes. As seen in the table, large-scale Multi-stage Flash (MSF) plants installed 

in the Gulf produce the maximum quantity of freshwater and are the most 

competitive with more than 20,000 m3/d. 

Desalted seawater per capita per day is very 

high in some countries such as UAE and Qatar: 1.2 and 1.7 cubic meters per person 

and day. 

Contracted capacity of freshwater production from seawater and all waters with the existing 

process. The total capacity is 12.8 million cubic meters per day and 21 million cubic meters per 

day, respectively. Data collected in 1996 (Alawadhi, 1999). 

Seawater All waters 

World Gulf World Gulf 

% MSF 77.3 64.8 47.6 39.5 

% RO 13.3 4.7 38.6 10.9 

% ED — — 5.2 1.0 

% VC 4.6 1.5 4.3 1.0 

% ME 4.6 0.7 4.3 0.5 

Total 100 71.7 100 52.9 

Gulf countries actually recycle no more than 35% of their total treated wastewater, 

which contributes about 2.2% to the total water supply. Treated seawater is currently 

used mainly for landscaping, fodder crop irrigation and some very specific industrial 

uses. There are a total of 105 sewage water treatment plants in the Gulf countries with 


TABLE 1.5 


a total capacity of about 2 Mm3/d. 

There is no doubt that this water source is 

underused due to the lack of wastewater plants. More of these plants are needed make 

better use of this water source and minimize the serious impact on the environment as 

a result of its uncontrolled and unsafe disposal. Salt intrusion, ground water quality 

and the saline interface between sea and ground water are some of the problems that 

could be avoided with these plants. 

1.3.2 Pacific Region and India 

The Pacific Region is diverse in terms of desalination. Japan and Korea have 

developed their own desalination technology which competes on the world market. 

Australia and China also have their own technology and the rest of countries import 

plants from overseas. Here we will consider the first two categories. 

Table 1.5 shows the water resources in these four countries. Water resource per capita 

is one of the fundamental indexes of water abundance. However, they only express 

part of the potential availability since in some cases the transportation cost is too 

high. Australia, for example, has the highest water value per capita because it has a 

small population with rather little and irregular precipitation, and high evaporation. 

Japan has the most precipitation but also the largest population. In China water 

availability is irregular due to the climate and population distribution. Korea has the 

least water per capita despite of a lot of precipitation. 

Natural resources in the pacific region in the year 1998 (Goto et al., 1999). 

Country 

Precipitation 

(mm/y) 

Population 

(millions) 

Available water 

(Mm3/y) 

Water per capita 

(m3/y) 

Australia 465 18.1 100 5,520 

China 648 1,224 2,813 2,340 

Japan 1,714 125.6 422 3,360 

Korea 1,274 46.4 69.7 1,500 

Agricultural use occupies the largest portion in the region, whereas the consumption 

for living is dependent of the area (standard of living, life-style and climate determine 

the water consumption). Industrial water consumption is increased by industrial 

development but can be decreased by efforts such as recycling. Table 1.6 summarizes 

the fresh water consumption in the four countries. 


TABLE 1.6 

TABLE 1.7 

24 

Country 

Introduction 

Water use trends in the Pacific region (Goto et al., 1999). 

Country (year) Total (Mm3/y) 

% Agriculture % Living % Industry 

Australia (1995) 18,600 82.17 10,35 7.47 

China — 87 11 2 

Japan (1995) 90,700 58.7 17.2 14.8 

Korea (1996) 23,668 62.85 26.23 10.91 

Desalination in the Pacific region is not as important as in the Gulf region. Table 1.7 

explains the capacity, process, use and feed water of the desalination plants in the 

Pacific area. 

Desalination installations in the Pacific region. Data from 1998 (Goto et al., 1999). 

Capacity 

(m3/d) 

Australia 84,000 

China 182,000 

Japan 129,885 

Korea 180,000 

Process Use Feed water 

64% RO 

18% VC 

12% MSF + ME 

85% RO 

15% MSF + ME 

88% RO 

6.5% ED 

3.5% MSF 

1.8% ME 

> 90% RO 

Rest ED 

45% Industry 

33% Power gen. 

15% Municipal 

55% Industry 

40% Power gen. 

5% Living 

53% Industry 

47% Water supply systems 

100% Industry including 

power generation 

70% brackish 

18% wastewater 

10% seawater 

50% brackish 

20% pure water 

30% river, wastewater 

Seawater and brackish mainly 

Pure > brackish > 

wastewater > river water 

In conclusion, water shortage will increase with the development of industry and an 

improved standard of living in the coming century, especially in the more populated 

areas like China. 

There are more than 200,000 villages in India with inadequate drinking water, out of 

which about 50,000 suffer from brackishness problems affecting a population of 

about 60 million. Approximately one third of these villages are acutely affected by 

salinity levels above 4,000 ppm. Villages with an average population of about 500 to 

1,500 are mostly separated either by mountainous terrain or long stretches of barren 

land and can be broadly categorized into inland and coastal. Provision of safe 

drinking water to the villages inland has been given high priority in recent years, with 


TABLE 1.8 

TABLE 1.9 

Country 


hundreds of small Reverse Osmosis and Electrodialysis (RO/ED) plants (10-30 m3/d) 

installed in the affected villages. Only two Multi-Effect Distillation (MED) plants of 

more than 10,000 m3/d 

were installed to supply process water in their industrial 

complex by seawater desalination (Prabhakar et al., 1997). 

1.3.3 North Africa 

In this region, water resources seem to be limited in time and space, unequally 

distributed and remote with respect to centers suffering from a continuous increase in 

demand. The annual renewable water resources in this region are shown in table 1.8 

(Al-Gobaisi, 1997). 

Water disposal in the African region in 1995. 

Country 

Annual renewable water resources 

Total (Mm3/y) 

Per capita (m3/y) 

Algeria 14.8 528 

Egypt 58.1 923 

Libya — — 

Morocco 30.0 1,110 

Tunisia 3.9 443 

Water extracted from the ground is very high in some of these countries, as seen in 

table 1.9. 

Water withdrawal in North African countries. Data collected in 1990 for Algeria and Tunisia; for 

Egypt and Morocco data from 1992 (Al-Gobaisi, 1997). 

Annual withdrawal 

% water resources Per capita (m3/y) 

% Agriculture % Industrial % Living 

Algeria 30 180 60 15 25 

Egypt 97 956 85 9 6 

Libya — — — — — 

Morocco 36 427 92 3 5 

Tunisia 78 381 89 3 9 


TABLE 1.10 

26 

Introduction 

In the future, desalination should be the alternative saving solution when the 

mobilization of non-conventional water resources is impossible or very costly 

(essentially in coastal zones). In this regard, five North African countries (Morocco, 

Algeria, Tunisia, Libya and Egypt) requested in 1989 technical assistance from the 

International Agency of Atomic Energy (IAAE) to study the feasibility of 

desalination using nuclear power. The aim was to reuse the treated water in 

wastewater plants and provide an important resource to agriculture. 

There is little information about desalination plants in Northern Africa, although the 

water production there is almost negligible with respect to the Middle East Countries. 

Desalination in Egypt is the most important in the region, but the total capacity 

contracted is now reported to be 95,000 m3/d 

(Hassan and Florido, 1999). The MSF 

desalination technology switched to reverse osmosis for large plants over 5,000 m3/d 

in the last few years The proportion is 55% for the RO plants, 40% for the MSF plants 

and the rest in Vapor Compression (VC). Libya has two MSF plants of 24,000 and 

10,000 m3/d 

(VA Tech, 1999), and in the south of Tunisia there are two brackish RO 

plants with a capacity of 12,000 m3/d 

(Cadagua, 1999). Morocco has only one RO 

plant with an installed capacity of more than 1,000 m3/d: 

the Laayoune Seawater 

Reverse Osmosis (SWRO) plant produces 7,000 m3/d 

of freshwater (NOPW, 1996). 

1.3.4 US experience and the Caribbean Islands 

California, Texas and Florida, the three states considered as the most arid and coastal 

areas of the country, will account for more than 45% percent of the nation’s total 

population growth between now and 2025. They are already experiencing the highest 

overall water deficit and droughts are also very common. As the population will 

continue growing in these areas, progressive approaches to meet water demands will 

be necessary (Ponce and Jankel, 1999). 

The total water use in the US has fallen since the 80’s since water is now used more 

efficiently. Table 1.10 shows the total water consumption and the use by each sector. 

Water use in the U.S. in 1995 (Gleick, 1998). 

Total use (Mm3/y) 

% Public % Irrigation % Thermo-industrial 

552,1 10.9 39.2 49.9 

Thermal technologies were used in the early years of desalination prior to 

development of RO, beginning in the 60’s with two MSF plants in Southern 

California and Florida. After that experience, RO technology has been successfully 

introduced in several plants. The use of desalination plants is steadily growing in the 


TABLE 1.11 


US. The desalination growth rated based on increased contracted capacity was the 

highest in the world from 1996-1997, with about 120,000 m3/d 

of new freshwater. 

This implies a rate of growth between 10-20% per year, with a total installed capacity 

of more than 900,000 m3/d. 

(Wangnick, 1998). Much of the potable supplies utilize 

brackish water. 

Many of the island nations of the world are in warm sunny environments and have 

two significant items in common: beautiful beaches and a pernicious lack of potable 

water. Major economic growth is inhibited since the island’s population cannot 

enhance its agriculture and stimulate the tourist trade without a suitable and 

consistent supply of useable water. The Caribbean sea is a good example. In Antigua, 

about 50% of the total drinking water requirements are supplied by a SWRO plant of 

9,500 m3/d 

which substitutes an old MED plant (Barendsen and Moch, 1999). Other 

examples are a 10,000 m3/d 

SWRO plant in Nassau (Bahamas) (Andrews and 

Shumway, 1999), a SWRO plant in Curaçao producing 9,000 m3/d 

and the Virgin 

Islands with 9 MED units and a combined production of 30,000 m3/d 

(Elovic and 

Willocks, 1999). 

1.3.5 Mediterranean area and Europe 

Desalination in Spain started in the early 70’s in places with little water and near the 

coast. Here it was the only way to supplement natural water resources needed for 

domestic uses in highly populated isolated territories. The current and future 

development of the tourism industry is assured by the seawater desalination plants in 

those areas. 

The total capacity of Spanish desalination plants is now above 600,000 m3/d, 

and new 

projects for another 400,000 m3/d 

for urban uses are being developed and should be 

in operation in two years. Table 1.11 shows the seawater desalinated in Spain in 1998. 

Desalinated water in Spain during the year 1998 (Torres and Medina, 1999). 

Total (Mm3/y) 

% Urban & Tourism % Agriculture % Industry 

Seawater 95.3 94.4 5.6 — 

Brackish 126.57 20.4 47.6 32.0 

The desalination industry is located in dry Spain, that is, the southern part of the 

country: Balearic Islands, Canary Islands, Ceuta and the Costa del Sol. Three MSF 

plants were installed in Ceuta (1) and Las Palmas (2) in the 70’s, and small vapor 

compression units (VC) were the water supply in public delivery systems and private 


TABLE 1.12 

28 

Introduction 

tourist resorts in the 80’s. Since then, reverse osmosis process (RO) is being used in 

big plants. Table 1.12 resumes the biggest desalination plants in Spain. 

Some of the RO desalination plants installed in Spain (Cadagua, 1999; Sánchez et al., 1997; 

Fayas and Novoa, 1997; Torres et al., 1999; AECYR, 1999). 

Plant Location Capacity (m3/d) 

Feed water 

Son Tugores Mallorca 35,000 Brackish 

Maspalomas Las Palmas 35,000 Brackish/Sea 

Marbellaa 

Málaga 56,000 Sea 

Bahía de Palma Mallorca 42,000 Sea 

Arrecife Lanzarote 32,500 Sea 

Las Palmas III Las Palmas 38,000 Sea 

Alicante 50,000 Sea 

Alicantea 

a. Not in operation 

The use of wastewater in agriculture irrigation, landscape improvement, leisure needs 

and aquifer recharge is another way to supply the increasing water demand in Spain. 

The Republic of Cyprus is an island at the eastern end of the Mediterranean Sea 

plagued by draught and water shortages in recent years. Seawater desalination has 

been the main solution. It has two little MSF plants, a MED plant and a RO plant with 

a capacity of 20,000 m3/d 

(Echaniz et al., 1997). A new RO plant with a capacity of 

40,000 m3/d 

will be built by the year 2000. 

Desalination in the rest of Mediterranean countries is less important. There are small 

old MSF plants and VC units in the south of Italy to cover the local demand (Ophir 

and Gendel, 1999; Italimpianti, 1999). Greece, Turkey, Jordan, Israel and Lebanon 

(VA Tech, 1999) also have small desalination RO plants. 

Germany and Austria have several desalination plants to recycle wastewater or 

produce pure water for industrial processes including power generation (VA Tech, 

1999). They do not produce drinking water. 

Humanity has developed non-conventional sources of potable water in order to 

remove or at least reduce water stress. Seawater desalination is the most important of 

the non-conventional ways of producing water and several processes have been 

developed in the last few years to produce fresh water for human consumption. Yet 

desalinated water makes up only one part in a thousand of the fresh water used 

worldwide. Desalination costs several times more than conventional means and is 

therefore mostly used in developed countries with water scarcity (i.e. Arab countries). 


TABLE 1.13 

Desalination and energy 

1.4 Desalination and energy 

Desalination is highly energy intensive and should not be considered in isolation 

from energy. The power requirements of seawater desalination plants is also 

increasing. There is a theoretical minimum power needed to desalt water but much 

more power is required in practice (El-Sayed and Silver, 1980). Unfortunately, most 

of the energy used is obtained from oil and natural gas. The Arab World desalinates 

using their large fossil fuel reserves. Consequently, the specific consumption of a 

desalination process must be accounted in fuel not electrical consumption as usually 

given when measuring plant efficiency. Table 1.13 shows the primary energy or fuel 

consumed in most desalination methods in the world. Note that the specific 

consumption has strongly decreased as desalting technology has developed. 

Specific consumption of desalination processes. Data obtained from several sources (Fisia- 

Italimpianti, 1999; I.D.E., 1999). 

Process MSF MED VCa 

Specific consumption 

(kJ fuel/ kg water ) 

400-500 

200-300 b 

350-400 

200-250 b 

a. Electrical energy produced in a conventional power plant at 30% efficiency. 

b. Desalination process in a co-generation plant. 

c. Including energy recovery system in the RO process. 

100-200 

ROa 

70-90 

30-50 c 

As seen in the previous table, thermal distillation consumes more than other methods 

and more or less recovers (in the worst case) 80% of the latent heat of boiling water at 

atmospheric conditions (about 2,257 kJ/kg). In the previous table, specific 

consumption strongly depends on way the required energy is obtained (converting the 

primary energy from the fossil fuels into thermal or electrical energy to supply the 

plant). Up until recently power plant technology has developed separately from the 

technology used to desalt sea or brackish water. However, when the co-generation 

concept is applied to combine the two processes, the consumption of the desalination 

process can be reduced more than 50%. Including combined cycles in new MSF/ 

MED plants considerably reduces consumption and also provides electricity in areas 

with energy demand. Co-generation fuels could be substituted by biomass or refuse 

fuels (Tadros and Tadros, 1997). The energy-water interaction should be investigated 

further and improved in order to provide water to water stressed areas at minimum 

cost. 

Desalination is almost entirely powered by the combustion of fossil fuels. Their finite 

supply is rapidly being depleted and they also pollute the air and contribute to global 

climate change. Assuming that all desalinated water in the world (total installed 

capacity of 13 Mm3/d) 

is produced at an average fuel consumption of 200 kJ/kg, and 


Introduction 

that the current annual global consumption of oil is 25 billion barrels (rising 2% per 

annum, Al-Gobaisi, 1997), 0.17% of world oil consumption is consumed in 

desalination. To underline how important energy is in desalination, if all the water 

consumed in the world came from desalination plants (remember that it is actually 

only one part in a thousand, Al-Gobaisi, 1999) the required oil would surpass the 

current yearly oil consumption. 

The development of renewable-driven desalination is still severely impeded (if not 

stopped) by the pressure from contemporary economic factors and political inertia. If 

our technology continues along the present unsustainable path, not only it is essential 

to have an orderly transition in the energy used for desalination (from fossil fuels to 

renewable resources) but the whole industry needs to gear itself towards enhanced 

efficiency, waste minimization and less environmental impact (Menéndez, 1997). In 

short, the philosophy of industrial ecology needs to be applied for desalination. The 

concept of industrial ecology considers an industrial system together with its 

surrounding systems. This systems view of industrial operations seeks to optimize the 

total materials cycle from raw material to manufactured material, from component to 

product and waste to ultimate disposal. Energy, resources and capital are the factors 

that have to be optimized. 

1.5 Why a MSF and power plant? 

The demand for electricity increases every day in arid and warm areas where air 

conditioning is used to improve living standards. A dual-purpose plant is one of the 

best solutions to supply water and energy demands (although is not the most efficient 

method to produce fresh water, see table 1.13). As the nuclear or coal power plants 

are not very common in the Gulf Area, the more abundant fossil fuels like natural gas 

or fuel oil are consumed in new co-generation plants. Solar powered desalination is 

an insignificant proportion because of the costs of using renewable energy are very 

dependent on the scale of the infrastructure. 

Several power generation configurations can be coupled with a desalination unit: 

steam turbine plants, gas turbine plants, combined cycle power plant (gas turbine, 

heat recovery steam generator and steam turbine). Some desalination processes only 

require electrical power (not exhaust gas or steam) and co-generation is not possible. 

In those cases, desalination and power generation can be studied separately although 

the way of producing electricity is the same. 

This thesis aims to demonstrate the scope of Thermoeconomic Analysis when applied 

to a very complex system. One of the most important configurations of dual-purpose 

desalination plants is the multi-stage flash desalination unit (MSF) coupled with a 

steam turbine power plant fuelled by natural gas (fuel is also available in exceptional 

conditions and startups). This type of configuration is used in a plant containing the 

30 Thermoeconomic analysis and simulation of a combined power and desalination plant

Why a MSF and power plant? 

largest single desalination units in the world, in the United Arab Emirates (UAE). 

MSF units provide almost 77% of all desalinated seawater and nearly 82% of that 

production is from the Gulf Area (Alawadhi, 1999). MSF plants with unit capacity up 

to the unit studied here are likely to dominate the scene in the Gulf countries for at 

least another 10 years. The other predominant method of obtaining freshwater, 

reverse osmosis (RO), is not in favor due to the high salinity and temperatures of Gulf 

seawater. MSF desalination is energy intensive and inefficient especially if the steam 

turbine plant does not include a reheater in the boiler. It is therefore a good example 

to study from the thermodynamic point of view, following the Second Law 

perspective. The conventional energy analysis methods based on the First Law of 

Thermodynamics are implicitly compared here. 

The reason for studying an MSF plant is not only its dominant position in the world 

desalination market. In terms of energy consumption, MSF is the worst desalination 

process (see table 1.13). However, from a thermodynamic point of view it offers 

many more possibilities to reduce energy consumption in the process. The minimum 

power requirement (or thermodynamic limit) to desalt water is consumed in rejecting 

the difference of the equilibrium vapor pressure between saltwater and freshwater 

(this difference depends on the process temperature). All practical processes are 

non-ideal, performed by imperfect devices, and are accompanied by auxiliary nonideal 

processes. So, the minimum power requirement is higher for all desalination 

processes. In RO or VC processes, the power requirement is electrical energy 

produced in external power plants. Reducing the energy consumption of the process 

is only possible in the desalination process. But when a thermal desalination plant 

like a MSF unit is combined with a power plant, MSF technology can be oriented to 

improve the thermal efficiency of vertical tube evaporators (VTE) that allow the use 

of low temperature heat sources such as turbine reject steam (Sephton, 1999; Sephton 

and Salomon, 1997), normally rejected to the environment (through the steam cycle 

condenser). In the limit, the cooling tower of a conventional power plant can be 

substituted by a low-temperature MSF unit to highly improve the efficiency of the 

steam cycle. Thermoeconomic analysis connects the Second Law of Thermodynamic 

and Economics and is especially recommended for these two combined processes. 

This is the first time an in depth thermoeconomic study has been made of a 

desalination plant, a system combining thermal and chemical processes. Interestingly 

the first thermoeconomic ideas were applied to desalination processes in the sixties 

and early seventies (Evans, 1962; Tribus et al., 1960; Tribus and Evans, 1963; 

El-Sayed and Aplenc, 1970; El-Sayed and Evans, 1970), but were most developed in 

the eighties and nineties when Thermoeconomics was applied in power plants. 

Several exergy analyses of MSF plants have already been made (Hamed et al., 1999; 

Darwish, Al-Najem and Al-Ahmad, 1993; Al-Sulaiman and Ismail, 1995; El-Nashar, 

1993), and the optimization of thermal desalting systems has also been considered 

(El-Sayed, 1996). In this Ph. D. Thesis, thermoeconomic techniques previously 

applied only to power plants were successfully used for a combined power generation 


Introduction 

and desalination process. Chemical exergy was successfully introduced in a most 

complex installation, in the global exergy balance. Furthermore, no thermodynamic 

analysis has been done for a dual-purpose plant with two different products: water 

and electricity. The interactions between the two processes were analyzed in this 

Ph. D. Thesis. New methodologies are introduced in this complex system, allowing a 

better understanding of the real relationships between the plant equipment. 

1.6 Thermoeconomic analysis 

A dual-purpose plant is a very complex system that is difficult to analyze, especially 

when all the available configurations of both sub-systems are considered. Usually the 

plants are analyzed separately, neglecting component interactions and the energy 

savings possible from the combined analysis. When two different products are 

obtained in a co-generation plant, it is very difficult to quantify the real cost of each 

product and redistribute the costs over the rest of upstream flows inside the dualpurpose 

plant by applying conventional energy analysis techniques based on the First 

Law of Thermodynamics. 

Thermoeconomic analysis techniques are the most convenient tools to analyze these 

systems, because they can: 

• Calculate the costs of the flows and products of a plant based on physical criteria 

(Second Law of Thermodynamics). 

• Assess alternatives for energy savings. 

• Optimize operation. 

• Locally optimize subsystems. 

• Perform energy audits and assess fuel impact of malfunctions (operation 

diagnosis) 

Thermoeconomic analysis uses the First and Second law of Thermodynamics in 

combination with economic data and introduces new concepts such as Fuel-Product, 

productive structure, exergy savings, cost of irreversibilities, additional fuel 

consumption, malfunction and others. The degradation mechanisms of the energy 

quality in each component require a comprehensive approach that encompasses 

resources, generation of products, specific unit consumption and cost, plant/system 

malfunction, impact on fuel consumption, etc. A better understanding of the actual 

plant performance increases the potential for improvements in operation and/or 

design. 

When applied to analyze an existing dual plant, thermoeconomic analysis requires a 

validated model (simulator) of the plant to determine the thermodynamic reference 

state at design conditions for any load point, ambient conditions, operating mode, etc. 

Data from a dual plant in Abu Dhabi were used to adapt the models to reproduce the 


Ph. D. Thesis development 

states of the plant (therefore, the data obtained by the simulator are considered 

measured data). As in this case, the data acquisition, processing and storage system is 

not operative to be used in the thermoeconomic analysis. The simulator can obtain the 

thermodynamic state of the plant when an inefficiency is detected or estimated. 

1.7 Ph. D. Thesis development 

The structure of the Ph. D. Thesis is summarized as follows. First, world water 

resources and demand are reviewed, especially for the Gulf area. Water quality and 

uses are also included to inform the non-specialist readers. A brief description is then 

made of the most important desalination methods (Chapter 2). When the desalination 

unit follows a thermal principle it is usually coupled with a power generation plant. 

In Chapters 3 and 4 the mathematical models applied to the power and desalination 

plant are developed. The results are compared and readapted with operational data 

from the data acquisition system of the plant. The mathematical model was validated 

as a tool that widely reproduces the real state of the plant under different operating 

conditions, as if the results were real plant data. An interactive steady-state simulator 

was made that can be used on a personal computer to help obtain output data. 

The simulator (Chapter 5) supplied the main part of this Ph. D. Thesis: the complete 

thermoeconomic analysis of a dual-purpose power and desalination plant (Chapter 7). 

After explaining the fundamental concepts of Thermoeconomics (Chapter 6), the first 

step was to build the thermoeconomic model. The most convenient productive 

structure was chosen for the power and desalination plant. The thermodynamic 

operation and economic costs of every flowstream of the plant were calculated and 

analyzed. Those costs allow cost assessment of the plant products based on physical 

criteria. Then, the thermoeconomic diagnosis was applied. The steady-state diagnosis 

of the dual-purpose plant helped us obtain a more cost-effective operation and a better 

understanding of plant performance. The mathematical model was applied for a given 

operating condition characterized by operational data (previously validated and 

processed) to quantitatively analyze the following steps: 

• Comparison with a reference case (target) with the same operating conditions. 

• Identification of inefficiencies, and the performance degradation of sub-systems 

or components. These inefficiencies were simulated. 

• Evaluation of the causes of cost generation and component inefficiencies. 

• Assessment of the extra-operating cost due to malfunctions with respect to the 

most feasible operation and the cost impact of appropriate maintenance actions. 

The previous cost analysis is therefore essential to perform the diagnosis of the 

system. 


Introduction 

• Operation recommendations for the plant managers, taking into account the 

experience from the analysis (assessment of alternatives). 

A new method is introduced to develop the thermoeconomic diagnosis, including the 

matrix formulation and some new concepts like induced and intrinsic malfunction, 

and dysfunction. 

Once the diagnosis was completed, a global optimization of the plant was performed 

from locally optimizing the system units. The local optimization of a unit consists in 

finding the minimum cost of the product of each component. The thermoeconomic 

model was also used in this process. 

Finally, the idea of maximum benefit in water and electricity production was 

analyzed using practical examples. The contribution of the price policy applied in the 

final benefit is considered by separating the methods of assessing product price and 

cost. 

The last chapter (Chapter 8) contains the conclusions of the Ph. D. Thesis and future 

lines of research. 


CHAPTER 2 

Desalination processes 

In chapter 1, the great problem of water scarcity and desalination as the way to solve 

it is remarked. Desalination is the process that convert brackish or seawater in water 

for human consumption, there are several processes technologically developed 

providing water in arid areas. 

This chapter includes a general review of desalination methods, in order to have an 

overall perspective of the state of the art in desalination technology. The importance 

of the MSF with respect to the other methods is also argued in this chapter. 

The most reliable techniques of seawater desalination are rated into three categories 

depending on the principle applied: 

• Processes involving a change of phase: Freezing or distillation. 

• Processes using membranes: Reverse osmosis or electrodialysis. 

• Processes acting on chemical bonds: Ion exchange. 

Among the processes above, distillation and reverse osmosis processes show high 

performances in seawater desalination; thus they are the most marketable in the 

world. Next, we develop the following processes in detail: 

• Multi-Stage Flash (MSF). 

• Multi-Effect Distillation (MED). 

• Reverse Osmosis (RO). 

• Vapor Compression (VC). 

We also mentioned the other techniques, which have not been developed in the field 

of desalination due to problems generally, related to energy consumption and/or to the 

high investments required. These techniques are: 



• Solar Distillation. 

• Freezing. 

• Electrodialysis. 

• Ion Exchange. 

2.1 Phase change processes: distillation and freezing 

More than 85% of the world’s desalted water is obtained by distillation. Desalination 

by distillation involves boiling water seawater to release water vapor and dissolved 

gasses, leaving behind the salts (which are only volatile above 300 ºC). Pure water is 

collected by condensing the vapor inside or on the outside of tubes which may be 

arranged horizontally or vertically depending on the installation. Every distillation 

system must also be ventilated to extract air and non-condensable gases in the 

seawater, and a vacuum pump or steam ejector is required when the evaporatorcondenser 

system is at lower than atmospheric pressure. 

2.1.1 Multi-stage flash process (MSF) 

Multi-Stage Flash is the most widely used evaporation process (Wangnick, 1998). 

It is especially common wherever the temperature, salt content, biological activity or 

pollution level of raw water is high, as in the Middle East. MSF also be used if the 

desalination plant is coupled to a power station or if waste heat is present (e.g. from 

gas turbine effluents). In general, MSF plants are more common because they are 

simple and robust, although their specific consumption may be higher than other 

3 

methods (12-24 kWh/m ). 

Flash evaporation takes place when a fluid is heated to a certain temperature and 

evaporates both above and below the atmospheric pressure: under gradual decreasing 

pressure, flashing by pressure reduction is called flash evaporation. In multi-stage 

flash plants seawater (pumped through heat exchanger tubes installed in the various 

evaporator stages) is heated to a certain temperature. Final heating is performed by 

steam in a final heater. The hot seawater then goes into flash chambers where the 

pressure is maintained below the equilibrium pressure corresponding to the 

temperature at which the brine enters. Part of the brine flashes into vapor and after 

passing a demister, it condenses outside the tubes while heating the seawater flowing 

through the tubes. The multi-flash distillation unit contains cells assembled in series, 

at a different pressure. The water produced in each stage is collected in a trough 

mounted below the tube bundle which collects the fresh water end product. These 

widely used units perform recycle brine (50% to 70% of the brine quantity within the 

last stage is collected and discharged through the seawater feeding pipe of the unit) in 

order to reduce the quantity of the make-up seawater needed to produce fresh water. 

The concentrated seawater is also removed from the last stage by a pump or by 

gravity. Figure 2.1 shows a general scheme of a conventional MSF unit. 


FIGURE 2.1 

Phase change processes: distillation and freezing 

General outlay of MSF distillation with brine recycling. 

Thermoeconomic analysis and simulation of a combined power and desalination plant 

37


Seawater with 40,000 to 50,000 ppm dissolved solids is converted into distillate and 

fresh water with a few ppm of solids. An MSF type plant operates between two 

temperatures: the top brine temperature (brine heater outlet temperature, or TBT) and 

the last stage temperature. The top brine temperature depends on: 

a) Available steam quality. 

b) Scale prevention technique. 

c) Brine concentration and nature of dissolved salts 

The last stage temperature depends on: 

a) Cooling water inlet temperature. 

b) Absolute pressure maintained in the last stage by the ejector system. 

In practice, MSF plants are designed for various gain outputs ratios (GOR, tons of 

fresh water produced per tons of steam supplied to the brine heater). In practice, a 

G.O.R of 12:1 being the upper limit. Obviously, the production rate is a direct 

function of the flashing brine flow and the flash range (brine top temperature-last 

stage temperature). Also, in theory, the actual number of stages is not important for a 

given ratio. 

However, the number of stages determines the total exchange area required for heat 

recuperation. More stages will decrease the total exchange area required thereby 

limiting the maximum number of stages per plant. In practice, however, stage number 

increases at increasing gain ratios but also depends on the plant’s capacity. The 

number of stages is generally about 20 and sized to keep the temperature difference 

constant between stages (the temperature difference is estimated to be about 3 ºC). 

2.1.2 Multi-effect distillation (MED) 

Contrary to MSF, in Multi-Effect Distillation (MED) evaporation takes place on 

surfaces, by exchanging the latent heat through the heat transfer surface between 

condensing vapor on one side and evaporating brine on the other. The MED plant 

also has several stages, each with a heat exchanger tube bundle (see fig. 2.2). 

Seawater is sprayed onto the tubes and the condensing heating steam inside the 

tubes evaporates part of the seawater on the outside. The steam produced is used as 

heating steam in the next stage, where it condenses inside the tubes. The condensate 

is the water product. Obviously the boiling temperatures (and pressures) in the 

different evaporators cannot be the same. The specific consumption depends on the 

steam conditions supplied to the first stage, but is usually lower than in MSF 

3 

(10-15 kWh/m ). 


FIGURE 2.2 


Flow diagram of Multi-Effect Distillation (MED) with thermal vapor compression (TVC). 


39

FIGURE 2.3 


MED process with vertical tube evaporators (VTE). 



The first stage is heated by external steam from a heat recovery system or a 

back-pressure steam turbine. But in most cases, MED plants are equipped with 

thermal vapor compressors for better efficiency. A steam ejector driven by mediumpressure 

steam removes a part of the steam produced in the last stage and compresses 

it to use as the heating steam. The steam produced in the last stage is condensed on 

the outside of exchanger tubes in a separate condenser, which is cooled by incoming 

seawater. Part of the heated seawater is then used as feedwater. Product water and 

concentrated seawater are then pumped out from the last stage of the evaporator. 

Most MED plants have horizontal evaporators. Vertical tube evaporators (VTE) are 

also available: In vertical tube evaporation, salt water falls in a thin film through 

vertical tubes in a large chamber (figure 2.3). As it falls, it is heated by steam that 

condenses on the outer surface of the tubes. This heat exchange converts some of the 

salt water in the tubes into steam and some of the steam around the tubes into fresh 

water (condensate). 

Steam generated inside the tubes in the first chamber flows to the second chamber, 

and condenses on the tubes there. The process is repeated in several chambers and is 

sometimes called “multiple-effect falling-film” distillation, because each bundle of 

tubes is an “effect”, and because a thin film of water falls down the inside surface of 

the tubes. Vertical tube evaporators are most cost-effective in large plants requiring 

high efficiency. They have an improvement over older systems since less heat transfer 

surface is required and the water need only be circulated once. 

2.1.3 Vapor compression (VC) 

Thermocompression (TVC) or vapor compression distillation (VC) involves boiling a 

liquid (seawater in this case) on one side of the heat transfer surface, and directing the 

compressed vapor to the other side of the heat transfer surface to be condensed (see 

flow diagram, figure 2.4). 

In the specific design described here as an example, a single-stage VTE type seawater 

is boiled inside a bank of enhanced surface tubes. The generated vapor then passes 

through a mist separator to remove any entrained salt-water droplets. In a vertical 

tube evaporator, the pure vapor enters the compressor at 101,5 ºC and 1 psig for a 

compressed steam temperature of 106 ºC and 3.6 psig (the pressure is therefore 

increased 0.18 bar). The compressor is a centrifugal, single-stage type designed for 

high-volumetric flows. This higher-energy compressed steam is discharged into the 

evaporator onto the outside of the enhanced surface tubes, where it condenses and 

provide its latent heat energy to the boiling seawater inside the tubes. 

Note that the process is very efficient thermodynamically, because most of the shaft 

work required by the compressor is used to avoid the boiling point elevation of 

seaweater (BPE). Additional vapor is generated and the process continues. The 

vapor, which condenses on the outside of the tubes, is collected, and drawn off by 


41

FIGURE 2.4 


the distillate pump and pumped through a three-stream heat exchanger. The excess 

feed water, called blowdown, which is concentrated, is also pumped through the 

same heat exchanger. The distillate and blowdown are cooled therein while 

preheating the incoming feedwater. This heat exchanger helps to minimize energy 

consumption of the system, in a VC system the specific electric consumption is 

3 

lower than 10 kWh/m . 

Flow diagram of a vapor compression system with vertical tube evaporators (VTE). 



Distilled water is made by condensing above atmospheric pressure at 106 ºC. A small 

amount of make-up heat is required for continuous operation to replace the heat lost 

to radiation and venting and the portion not reclaimed in the three-stream heat 

exchanger. Electric immersion heaters, a steam coil, or heat recovery exchangers to 

recover waste heat from engine jacket water or exhaust gas when available can 

provide this make-up heat. The distillate must be sterilized to meet Health Service 

requirements and may also be chlorinated for storage purposes. 

2.1.4 Solar distillation 

Solar stills use can be an ideal source of fresh water for drinking and agriculture in 

arid, isolated zones. Solar energy has a definite advantage over fossil energy, for 

small stand-alone units in rural and isolated areas (India). However, solar distillation 

is not widely used since installation costs are high and only a few liters can be 

produced per day, per square meter of pan area in the stills. Of course any economic 

or energetic comparison should not be considered. 

Several different configurations can be used to recycle the recuperated heat from the 

vapor condensation in solar stills. But we will only consider the conventional solar 

still (figure 2.5). The sun heats salt water in a black pan covered with a sloping glass 

roof. Water vapor rises to the glass where it condenses, forming a film which runs off 

into a collecting trough and is stored. The water does not boil but vaporizes slowly 

through a layer of water-saturated air and reaches the cooler glass by convection. The 

rate of evaporation is primarily controlled by the intensity of the incoming solar 

radiation which creates both temperature and water vapor concentration differences 

between the water and glass surface. Additional solar radiation can be obtained using 

lenses, mirrors and other focusing devices, but also heat losses increase when the 

temperature inside the solar still change. Finally, wind velocity has a negative effect 

on the cooling of the heating surface. 

The principle of the thermal energy extraction from a solar pond or other methods 

could be used as the energy source for seawater desalination processes. For example, 

the use of parabolic trough collectors (PTC) could make competitive the use of solar 

energy for desalination processes (MSF, García and Gómez, 1999; MED, García, 

Palmero and Gómez, 1999), depending on conventional energy costs, the solar 

collectors cost and the climatic conditions that determine the attainable fresh water 

2 

3 

production per m of solar collector (the PTC collectors provide on average 10 m of 

2 

fresh water per m of solar collector), and the solar fraction SF that determines the 

percentage of the day in which the desalination plant consumes solar energy. 


43

FIGURE 2.5 


Diagram model of a solar still. 

Solar energy 

2.1.5 Freezing process 

Glass 

Condensed vapor 

Vapor 

Salt water 

Insulation 

Distilled water Distilled water 

This process, also based on phase change, is independent of the water salt content. 

Seawater is cooled and the ice is collected (ice crystals are essentially salt free). Ice 

formation is analogous to distillation in this respect since salt-free vapor is produced 

while the liquid may have a high salt concentration. The ice is melted to obtain fresh 

water (the fusion temperature is less than that of salts contained in the ice). 

The freezing process is different from distillation since the latter is carried out well 

above ambient temperature and the equipment is designed for minimal heat losses. 

In freezing methods, the system must be protected against heat gains or cold losses, 

and ice needs to be transported and purified, which is somewhat more complex than 

handling fluids alone. Although the low operating temperature of freezing processes 

greatly reduces scale and corrosion problems, refrigeration technology may be 

adapted. So that water is the first or secondary refrigerant. This secondary refrigerant 

system could be mixed or separated from water by a heat transfer surface. 

Freezing methods are not widely used in the desalination industry, and to calculate 

their power consumption, we still have to rely on experiments in relatively small and 

medium-sized plants and extrapolation to larger plants. 


Processes using membranes 

2.2 Processes using membranes 

2.2.1 Reverse osmosis 

Osmosis is a physical process which occurs naturally in animals and plants 

(figure 2.6). Osmotic pressure is measured using a recipient divided into 2 

compartments by a semi-impermeable membrane. Saline solution is poured into one 

half and freshwater into the other. Part of the fresh water will flow through the 

membrane into the saline solution. The excess height at the saline solution over the 

fresh water is a measure of the osmotic pressure of the solution. 

If external pressure greater than osmotic pressure is applied to the saline solution, the 

water will flow through the membrane in the other direction, leaving behind a more 

highly concentrated salt solution. This process is called reverse osmosis (RO). The 

osmotic pressure of a solution is directly proportional to the solute concentration, and 

the permeated water flow is proportional to the difference between the applied 

pressure and the osmotic pressure of the concentrated solution. 

RO can be used to demineralize brackish water with 1-10 gr/l salinity. It is also used 

for seawater desalination and has lower energy consumption, investment cost, space 

requirements and maintenance than other processes. However, RO seawater plants in 

the Gulf Area need an intensive water pre-treatment process with a lower product 

quality, and are not often used. 

In RO desalination (figure 2.7) seawater is pretreated to avoid membrane fouling. 

It then passes through filter cartridges (a safety device) and is sent by a high-pressure 

pump through the membrane modules (permeators). Because of the high pressure, 

pure water permeates through the membranes and the seawater is concentrated. The 

water product flows directly from the permeators into a storage tank, and the 

concentrated seawater (at high pressure) is sent via an energy recovery system back 

into the sea. The four main parts of the RO installation are: 

Preliminary treatment unit 

The treatment has the following steps: 

• 

• 

• 

• 

• 

Chlorination: 

To reduce bacteriological and organic loads found in raw water. 

Filtration on a sand bed: 

To reduce raw water turbidity. 

Acidification: 

Acid is added to clarified raw water to lower its pH and limit the 

formation of calcareous deposits. 

Inhibition by polyphosphates: 

Polyphosphates delay the formation of precipitates 

such as calcium and barium sulfate. 

Dechlorination: 

To remove the residual chlorine from the pre-treatment. 


45

FIGURE 2.6 


Reverse osmosis process. 


FIGURE 2.7 

Processes using membranes 

Reverse osmosis (RO) desalination with Pelton turbine. 


47


• 

Cartridge filtering: 

To catch the particles obtained by oxidation of dissolved ions 

(Fe++) in raw water. 

Note that distillation methods only need a light chlorination process and some scale 

inhibitors (addition of polyphosphates). Sometimes acid is added to prevent the 

scaling problem. 

High-pressure pumping system 

This stage is the least problematic and normally involves centrifugal pumps. 

RO modules 

The main modules used for RO seawater desalination are made out of hollow fibers 

and spiral fibers provided by several manufacturers. The spiral-wound and hollow 

fiber designs were developed to contain the high-pressure fluid in the lowest possible 

volume for a given membrane surface. 

In spiral-wound elements membranes and backing are wound similar to a jelly roll 

around a central perforated tube which collects the product. Saline water flows 

through separate channels in one direction; the membrane elements are typically 

30-120 cm long and 10-30 cm in diameter. They can be mounted in series with antitelescoping 

devices between adjacent elements to form modules. Separate modules 

can readily be connected in series or in parallel. 

The hollow fiber units have a very large number of hollow fibers, thinner than human 

air, with their ends potted in epoxy resin, are held in a pressure vessel. Pressurized 

saline water circulates on the outside of the fibers while the hyperfiltrate flows within 

the fibers toward the open ends of the fibers held in position by the epoxy resin. 

Desalted water emerging from millions of open fiber ends is collected there. The 

hollow fibers are made by methods similar to those developed in the textile fiber 

industry. These units pack more membrane surface per unit volume than spiralwound 

unit and are extensively used for seawater RO. 

The brine energy recovery system 

In the last years, investigators have tried to reduce the energy requirements 

3 

(6-8 kWh/m ) of RO seawater desalination using two main devices: 

• 

• 

Pelton turbines: 

The high-pressure concentrate from membranes pushes on the 

Pelton blades to provoke a pair in a common shaft. Energy recovery for RO plants 

results in energy savings of 40% (Calder, 1999). 

Pressure exchangers (PE) 

: The PE unit uses the principle of positive 

displacement to pressurize low-pressure raw seawater by direct contact with the 

concentrate stream from a seawater membrane system. A cylindrical rotor with 

longitudinal ducts parallel to its rotational axis is used to transfer the pressure 


Processes acting on chemical bounds 

energy from the concentrate stream to the feed stream. The energy recovery with 

PE is in the range of 50-65% (Hauge and Ludvigsen, 1999). 

2.2.2 Electrodialysis (ED) 

This process is used to demineralize brackish water by making different ions 

migrate through selective membranes in electric field made by the dirct difference of 

voltage potential between two electrodes connected at the boundaries of the 

membranes. 

Whenever salt water is flowing in a cell, the cations are attracted by the anode and the 

anions by the cathode. If not constrained, these ions discharge on the electrodes of 

opposite sign. In return, if a set of selective and permeable membranes is placed 

between the electrodes, salt concentration decreases in some compartments of the cell 

where water is desalinated, while this concentration increases in the other 

compartments where salt water becomes even more concentrated. This process 

(shown in fig. 2.8) is suitable for desalinating brackish waters with an average salt 

3 

content between 1 to 3 g/l with a very low power consumption (about 1 kWh/m ) and 

a salt rejection of 75% (data obtained from De Armas, Torrent and Von Gottberg, 

1999). Above this it becomes more costly than competitive processes (its energy 

consumption for seawater desalination is much higher). 

2.3 Processes acting on chemical bounds 

2.3.1 Ion exchange 

Ion-exchanging resins are insoluble substances. In contact with a solution, they 

exchange some ions with the dissolved salt. 

Two types of resins can be used: anionic resins that substitute water anions by 

OH-- ions (hydroxil permutation); and cationic resins substitute cations by H+ ions 

(acidic permutation). 

Ion exchange demineralization provides high purity water if the salt concentration 

does not exceed 1 g/l. It is often used for water preparation of boilers from water of 

streams or aquifers, characterized by their low salt content, and for softening water 

with excessive calcium and magnesium. Resins must be regenerated regularly with 

chemical reagents to substitute its original ions and those fixed by the resin. 

The resins and chemicals must be substituted regularly, which raises the cost and 

makes it unpractical for seawater desalination. 


49

FIGURE 2.8 


Electrodialysis process. 


Summary 

2.4 Summary 

A general review of desalination technology has been written in this chapter. The 

review includes the principle of operation, description of the necessary installation, 

advantages/disadvantages, characteristic parameters (including specific consumption) 

and application range of each desalination method that is now available in 

desalination market. 

MSF is not only the most dominant process in desalination. It offers the possibility to 

be connected to several heat sources: steam turbines, gas turbines, solar storage, 

combined cycles. So, it allows applying techniques oriented to produce the MSF 

product with the lowest cost. This Ph. D. Thesis develops one of those techniques, 

nd based on 2 Law of Thermodynamics. 


51

CHAPTER 3 

MSF desalination 

steady-state model 

The daily world production of drinkable water from Multi-Stage Flash plants (MSF) 

far exceeds that of other desalination methods. This is particularly the case where 

power generation is linked to water production to use the process steam. 

In this chapter I will describe a mathematical model used in the SIMTAW program, to 

simulate a MSF plant under different operating conditions. 

MSF plant design data were included in the mathematical model, which is not 

oriented for design analysis. Several operating variables can be modified by the user 

to observe changes in plant behavior, such as consumed steam, inlet water 

temperature, water mass flow rates, TBT value, fouling factors and more variables 

explained below. The inverse calculation procedure option can evaluate the fouling 

factor of the stages instead of the distillate temperature profile. 

This model provides information to perform the exergy and thermoeconomic analysis 

of the whole dual-purpose plant, i.e. power generation plant and MSF plant, in order 

to analyze plant efficiency and cost savings. 

The structure of this section is as follows: 

• First, brief descriptions of the physical processes in a MSF plant. 

• Second, an explanation of the mathematical model, including the equations used 

to solve the model. 

• Third, a description of the solution algorithm of the system of model equations. 

• Finally an explanation of the simulation options and the design data. 


FIGURE 3.1 

54 

MSF desalination steady-state model 

3.1 Process description 

Many multi-stage flash plant arrangements and operational techniques are available. 

Each evaporator is usually described by defining the three main plant characteristics: 

the flashing flow system, the chemical treatment and the tube configuration. The MSF 

Plant studied here is a brine recirculation flow, high-temperature (HT) antiscale 

treatment, and cross tube configuration, the most typical of the MSF plant types. It 

3 

has six 20-stage condensing lines which deliver up to 14,400 m /h of water with a 

steam turbine cycle to provide electrical power. 

The plant has a single effect MSF evaporator with recycled brine (see figure 3.1). 

Recycled brine plants contain three main sections from left to right: the ‘heat input 

section’ (or brine heater), the ‘heat recovery section’ , and the ‘heat rejection section’ . 

The recovery and rejection sections both have a series of stages. Each stage has a 

flash chamber and a heat exchanger/condenser, where vapor (flashed off in the flash 

chamber) is condensed. The flash chamber is separated from the condenser by a 

demister, where entrained brine droplets are removed from the flashing vapor, and a 

distillate trough catches the condensate from the condenser above. 

Schematic diagram of a single effect MSF evaporator with recycled brine. 

A brief description of the MSF desalination flow process follows (see figure 3.1). The 

plant feed, SR, is allowed to pass through the heat rejection section, which rejects the 

excess thermal energy from the plant and cools the product and brine to the lowest 

possible temperature when it comes from the last recovery section stage. 

At the output of the first (warmest) rejection stage the feed stream splits into two parts, 

reject seawater CW (which is returned back to the sea) and a make up stream F (which 

is then combined with the recycle stream). The combined stream R passes through the 

heat exchangers of the recovery section, where its temperature increases as it proceeds 

towards the heat input section of the plant. In the brine heater, the brine temperature is 

raised from TF,1 

to a maximum value TB,o 

( = Top Brine Temperature TBT) 


FIGURE 3.2 

Process description 

approximately equal to the saturation temperature at the system pressure. If the 

seawater temperature is lower than 25 ºC, the temper system takes part of the cooling 

reject seawater, so that the distiller feed temperature is at least the above mentioned 

temperature. 

The brine then enters the first heat recovery stage where it is flashed by reducing the 

pressure in a throttling valve. As the brine was already at its saturation temperature 

for a higher pressure, superheated water vapor is generated in the throttling process. 

This vapor passes through a wire mesh (demister), to remove any entrained brine 

droplets before condensing onto a heat exchanger where cold brine passes through 

and recovers the latent heat (as shown in figure 3.2). The condensed vapor drips onto 

a distillate tray. 

The process is repeated all the way down the plant as both brine and distillate enter 

the next stage at a lower pressure. The concentrated brine is divided into two parts as 

it leaves the plant, the blowdown BD, which is pumped back to the sea, and a recycle 

stream R, which returns to the recovery section. 

From a mathematical point of view, the once-through design (with no reject section), 

and the recycle design can be represented by the same model if the zero value is set to 

the mass flow rates of the recycle R and the reject seawater CW streams. 

Furthermore, there is no distinction between heat recovery and heat rejection sections 

in the once-through plant. 

Cross-section of a stage in a typical MSF plant. 

Vapor 

Tube bundle 

Distillated 

Flashing brine 

Roof 

Demister 

Flash box 

For the recycled brine plants, the mass flow rates of the recycled brine and cooling 

water loops are typically 10 times greater than the distillate production rate. The latter 

is, in turn, approximately an order of magnitude greater than the steam supply mass 

flow rate. 


55

FIGURE 3.3 

56 


MSF plant operation can be better analyzed by temperature profiles and sorting out 

the main parameters. The temperature profiles of a recycled brine plant are illustrated 

in figure 3.3. The first obvious parameter is the temperature range, ∆T, 

which is the 

difference between the top temperature (TB,o) 

of the incoming feed and cooling 

water, i.e. seawater, Tsea. 

Another important parameter is the temperature rise in the 

brine heater, (= TB,o 

– TF,1). 

Temperature profile of a recycle brine MSF plant. 

Brine 

heater Heat recovery 

T S 

T F1 

T Bo 

Brine recirculation 


Distillate 

A non-uniform temperature difference is assumed over the entire flash range, but this 

does not imply a different design for each stage. This means that the interstage 

temperature differences will vary slightly down the plant and may vary significantly 

between stages of different designs. Specifically, the interstage temperature 

differences in the recovery and reject sections may differ considerably. 

The total temperature drop in each stage may have a number of causes, including: 

a) Interstage temperature difference ( δT): 

the drop temperature of all fluids at each 

stage. As a first assumption, all the fluids of an MSF plant have the same 

interstage temperature difference. 

b) Condenser terminal difference ( δTC): 

the temperature difference between the 

recycled brine flow being heated inside the evaporator tubes (being heated) and 

the flashed vapor temperature at each stage. This value strongly depends on the 

heat exchanger type (design, material, fouling effect, etc.). A high heat transfer 

coefficient value means a lower δT 

value. 


C 

Cooling 

reject 

Heat rejection 

Make-up 

Blowdown + distillate 

Feedwater T sea 

c) Demister pressure losses ( δTP): 

the frictional pressure loss when the vapor is 

passed through the demister, to remove any entrained brine droplets, results in a 

further decrease in saturation temperature. The resulting saturation temperature 

drop can be estimated either using the Clausius-Clayperon relationship or the 

steam tables.

Mathematical model of MSF unit 

d) Condenser pressure losses: vapor undergoes a frictional pressure loss in the 

condenser tube bundle as when passing through the demisters. 

e) Boiling point elevation (BPE): Non-volatile solutes (i.e. sodium chloride) 

dissolved in water, raise its boiling point. The size of this raise may be predicted 

by considering the equilibrium between the solution and the water vapor, whose 

value is a function of the brine temperature and salinity. The BPE value is most 

often less than 1 ºC. 

f) Non equilibrium allowance (NEA): When the flashing brine stream enters a 

stage, it undergoes a pressure reduction. If this brine had an infinite residence 

time in the stage, the whole lot would cool down to the saturation temperature 

corresponding to the flash chamber pressure and a maximum amount of distillate 

would flashed off. 

The energy consumption of an MSF plant is usually expressed in terms of the 

performance ratio PR, sometimes also called Gained Output Ratio, GOR defined 

previously. PR is commonly defined as kg of distillate per kg of dry saturated heating 

steam condensed in the brine heater without condensate subcooling. MSF plants 

normally have a PR value of 8 in the nominal case. The cleaning ball system is not 

normally installed in MSF plants but helps to avoid fouling in heat exchanger tubes, 

so the PR is also increased. 

Another measure of the energy consumption in MSF plants is sometimes expressed 

as the energy input to the brine heater per unit mass of distillate produced, often 

called the specific energy consumption (NC). This can be converted into a 

performance ratio, as defined above, by providing the steam condensing temperature 

in the brine heater. 

A large flash range as possible is desirable. Since the performance ratio improves as 

flash range increases, either for a fixed performance ratio (the operational efficiency 

increases due to a reduction in the required heat transfer surface area) or for a 

constant surface area. The recycled ratio is also reduced as the flash range increases, 

which results in a larger temperature rise in the heat input section for a fixed heat 

input, and a larger logarithmic mean temperature differences in the recovery section, 

with the corresponding reduction in the required heat transfer surface area. 

Seawater temperature limits the lowest temperature value in the plant. The only way 

to increase flash range is by raising the top temperature. This is limited by the onset 

of calcium sulphate scaling, and the increasing costs of additional stages. 

3.2 Mathematical model of MSF unit 

Several models of a single effect MSF plant are available (Barba, Liuzzo and 

Tagliaferri, 1973; Darwish and Arazzini, 1989; Itahara and Stiel, 1968; Beamer and 

Wilde, 1971; Coleman, 1971; Al Owais, Nijhawan and Budhijara, 1989; Helal, 


57

FIGURE 3.4 

58 


Medani and Soliman, 1986; Al-Mutaz, 1989; Alhumaizi, 1997; Hayakawa, Satori and 

Konishi, 1973; Glueck and Bradshaw, 1970; Rautenbach and Buchel, 1979; Husain et 

al., 1993; Husain et al., 1994; Falcetta and Sciuba, 1997). In the SIMTAW model 

presented here, the energy and mass balances are applied to each stage of the MSF 

plant and guidelines and nomenclature following Helal et al. (1986), although all of it 

with significant modifications. 

Apart from assumptions considered in the next two sections, the following 

assumptions were introduced in the SIMTAW model: 

a) The product leaving any stage is salt free (distillate concentration = 0 ppm). No 

mist is entrained with the flashing vapor. 

b) No subcooling of condensate leaving the brine heater is considered. Furthermore, 

inlet steam to the brine heater is assumed to be saturated vapor, even though it 

can be slightly superheated, i.e., desuperheater model in the brine heater was not 

considered. 

c) There is no interstage model in SIMTAW. So, the effect of the flashing brine level 

per stage is not taken into account. 

Hence the mathematical equations —i.e., mass, energy and heat transfer equations— 

for a single stage (figure 3.4) and brine heater model (figure 3.5) are basically as 

follows: 

3.2.1 Stage model 

Referring to figure 3.4, the following equations can be written for stage number j at 

steady state. 

A general stage in a MSF plant. 

R 

T F,j 

C R 

Dj–1 TD,j–1 Bj–1 TB,j–1 CB,j–1 Cooling brine 

Distillate 


j th Stage 

R 

T F,j+1 

C R 

Dj TD,j Bj , flow rate 

TB,j, temperature 

CB,j , concentration 



Enthalpy balance on flashing brine: 

where B 

j 

Bj–1 

Hbj–1 

= Bj 

Hbj 

+ (Bj–1 

– Bj) 

Hvj 


(3.1) 

is the flashing brine flowstream in jth flash chamber (stage j), Hbj 

is the 

flashing brine enthalpy, which is a function of temperature and concentration. This 

property is calculated as a saturated liquid, Hvj 

is the saturated vapor enthalpy of 

water in jth stage. 

Total material balance (water + salt): 

Bj–1 

+ Dj–1 

= Bj 

+ Dj 

where Dj 

is the distillate in the jth stage. 

Salt balance: 

Bj–1 

CB,j–1 

= Bj 

CB,j 

where CB,j 

is the salt concentration in the jth stage. 

Overall enthalpy balance: 

R CPR,j 

(TF,j 

– TF,j+1) 

= Dj 

CPD,j–1 

(TD,j–1 

– T*) 

+ Bj–1 

CPB,j–1 

(TB,j–1 

– T*) – Dj 

CPD,j 

(TD,j 

– T*) 

(3.2) 

(3.3) 

– Bj 

CPB,j 

(TB,j 

– T*) (3.4) 

where R is the recycled brine mass flow rate. In the Recovery Section, R depends on 

the required distillate and seawater temperature, but in the Reject Section the value 

corresponds to feed water supply (SR). CPR,j 

is the heat capacity of cooling brine, 

passing through the heat exchanger tubes, this property is a function of temperature 

and concentration. Although cooling brine is under high pressure, (to allow 

circulation inside the tubes), this property is calculated as if cooling brine were 

saturated liquid. CPD,j 

is the heat capacity of distillate, in this case, it is considered to 

be saturated liquid water; CPB,j 

is the heat capacity of flashing brine, which is 

assumed to be saturated liquid at flash chamber pressure in each stage. This property 

is calculated in a similar way to the cooling brine. T* is the temperature reference 

(273.15 K); TF,j 

is the cooling brine temperature in the jth stage; TD,j 

is the distillate 

temperature in the jth stage, and TB.j 

is the flashing brine temperature in the jth stage. 

59

60 


Heat transfer equation (condenser): 

TD, j– 

TF, j+ 1 

--------------------------------- 

TD, j– 

TF, j 


(3.5) 

where A j is the total evaporator/condenser heat exchange area; U j is the overall heat 

transfer coefficient of the evaporator in each stage. Its value depends on the various 

heat transfer resistance in the plant. The overall heat transfer coefficient is then: 

U j 

where R bi is the inside tube heat transfer resistance, given by 

(3.6) 

(3.7) 

where OD and ID are the outside and inside tube diameters respectively and h i is the 

convective heat transfer coefficient for fully-developed turbulent flow inside a tube. 

Assuming a small temperature difference between the wall surface and the bulk of the 

fluid, 

(3.8) 

where E is the ‘Enhancement factor’ (for smooth tubes this is 1.0, but is much greater 

for enhanced tubes); Re is the Reynolds number of the tube flow, Pr is the Prandtl 

number of the tube flow. 

R w is the tube wall resistance, given by 

⎛ Uj ⋅ Aj ⎞ 

exp ⎜---------------------- ⎟ 

⎝R⋅CPR, j⎠ 

where d lm is the logarithmic mean diameter of the tube, defined as: 

= 

1 

= ---------------------------------------------- 

Rbi + Rw + Rc + Rf R bi 

= 

1 

-----hbi 

OD 

⋅ -------- 

ID 

hbi E 0.023 k 

----- Re 

ID 

0.8 Pr 0.4 

= ⋅ ⋅ 

R w 

d lm 

t ⋅ OD 

= -----------------kw 

⋅ dlm OD – ID 

= 

-------------------- 

OD 

ln-------- 

ID 

(3.9) 

(3.10) 

k w is the thermal conductivity of the wall and t is the wall thickness. Note that the 

tube wall resistance can be reduced, by either reducing the wall thickness or 

increasing the thermal conductivity of the wall.


R c is the resistance from the condensate film on the vapor-side, given by 

(3.11) 

where h c is the condensing film heat transfer coefficient obtained from the wellknown 

Nusselt equation: 

h c 

(3.12) 

where k is the condensate thermal conductivity; ρ is the condensate density; λ fg is the 

latent heat of evaporation; n represents the number of tubes in a vertical row; µ refers 

to the condensate viscosity; ∆T fm is the temperature difference across the film 

(=T s-- T w) where T s and T w are the saturated vapor and outside wall temperatures; g is 

the acceleration due to gravity. 

The condensate properties are usually evaluated at the film temperature T fm given by 

T fm = T s – 0.5 (T s – T w) (3.13) 

R f is the overall fouling resistance, which includes the inside and outside fouling 

resistance and the non-condensable gas resistance. It is usually provided by the heat 

exchanger designer and depends on the material and acid treatment applied to both 

sides of the tube walls and the cleaning ball system. 

Distillate and flashing brine temperatures correlation: 

TB, j 

R c 

= 

1 

---hc 

k 

= 0.729 

3 ρ 2 ⎛ g λfg ⎞ 

⎜--------------------------------- ⎟ 

⎝n µ OD ∆Tfm⎠ 0.25 

= 

TD, j+ 

BPE + NEA + PL 

(3.14) 

where BPE is the boiling point elevation of brine with respect to pure water. As 

explained below, it is a function of brine temperature and concentration; NEA 

represents the non equilibrium allowance, which is the temperature drop due to the 

non infinite residence time of flashing brine in the flash chamber. PL refers to the 

pressure losses and includes demister and condenser pressure losses. 



3.2.2 Brine Heater Model 

FIGURE 3.5 Heat input section. 

Brine heater performance (figure 3.5) can be described by the following equations: 

Saturated steam 

Brine heater 

Saturated liquid 

m ST 

T S 

Mass and salt balance (brine): 

= R , and CBo , = CR (3.15) 

where B o is the mass flow in the Brine Heater outlet; C B,o is the salt concentration in 

the Brine Heater outlet; C R is the salt concentration in recovery section. 

Overall enthalpy balance: 

Heat recovery section 

R 

T F,1 

C R 

Bo 

T B,o 

C B,o 

B 0 

Stage 1 

RCPH( TBo , – TF1 , ) = mST λST 62 Thermoeconomic analysis and simulation of a combined power and desalination plant 

(3.16) 

where T B,o is the brine temperature in the Brine Heater outlet; CP H is the mean heat 

capacity of brine flowing inside the brine heater; m ST is the steam mass flow rate to 

the brine heater leaving the power generation plant; λ ST is the latent heat of steam to 

the brine heater. 

Heat transfer equation in the brine heater evaporator: 

TS – TF1 , ⎛UH⋅AH⎞ ----------------------- = 

exp ⎜------------------- ⎟ 

TS – TBo , ⎝R⋅CPH⎠ (3.17) 

where A H is the total heat exchange area of the brine heater; U H is the overall heat 

transfer coefficient of the brine heater. It contains the same terms (explained in 

section 3.2.1), as the overall heat transfer coefficient of the evaporator in the jth stage; 

T S is the saturation temperature of the vapor entering to the brine heater.


3.2.3 Mixer and splitter model 

This model takes into account the MSF Plant configuration and the model proposed 

by Helal et al. (1986). In the SIMTAW model the mixing process is considered after 

the last stage of the reject section. As a result this last stage is considered another 

distillation stage with exactly the same model as the other MSF stages. For this 

reason, the SIMTAW model contains an explicit mixer and splitter model, completely 

separate from the desalination stages (see figure 3.6) which can be modeled with the 

equations below. Note that even though it does not exactly reflect the real physical 

conditions in the plant, the results are accurate enough. 

Mass balance (salt + water) on mixer: 

(3.18) 

where B N is the flashing brine flow in the last stage of the reject section; BD is the 

blowdown mass flow rate. 

FIGURE 3.6 Mixing and splitting points in the MSF desalination plant. 

R, Recycle brine 

Mass balance on mixer: 

Enthalpy balance on mixer: 

( BN – BD)CBN 

, + FCF = R CR 18 19 20 SR 

Seawater inlet 

Rejection section 

BD 

Blowdown 

D, Distillate 

F, Make-up 

Deareator 

CW 

Reject seawater 

R = F + B N – BD (3.19) 

R · Hb R = (B N – BD) Hb N + F · Hb DR 

(3.20) 

where Hb N, Hb R, Hb DR are respectively the enthalpy of brine leaving the reject 

section, recycle stream and deaerator. 



Mass balance on reject seawater splitter: 

CW = SR – F (3.21) 

where SR is the inlet seawater into the reject section. The temper water is neglected 

here. 

3.3 Auxiliary equations 

Correlations of various properties used to solve the MSF SIMTAW model are 

included in this section. Most of thermodynamic and transport properties of pure 

water and steam are calculated with the same correlations used in the steam power 

plant model, described in Chapter 4. Correlations for calculating the brine and 

seawater properties in the SIMTAW model are described below, but most properties 

can be found in technical handbooks (Fabuss and Korosi, 1968; Hömig, 1978). The 

correlations used in the simulator are accepted here because results that they gave are 

reasonable when other mathematical models have been developed (Helal et al., 

1986). 

3.3.1 Density 

The expression for the brine density ρ b (lb/ft 3 ) given here is valid for the range of 

0-26% C b concentration and 40-300 ºF temperature. Pure water density was 

calculated (Mothershed, 1966) from the equation below with C b = 0. 

ρ b 

Another correlation can be found in Chen et al. (1973). 

3.3.2 Viscosity 

= 62.707172 + 49.364088Cb– 

0.43955304 10 2 

⋅ 

– 0.032554667CbTb– 

0.46076921 10 4 

⋅ 

+ 0.63240299 10 4 – ⋅ 

Cb Tb – 2 

Tb – T b 

64 Thermoeconomic analysis and simulation of a combined power and desalination plant 

2 

(3.22) 

Tabulated and interpolated data (Lewis and Randal, 1961) for a given concentration 

C b and temperature T b are extrapolated between the range 0 < C b < 20%, 

0 ºC < T b < 120 ºC, to obtain brine viscosity µ b (N·s/m 2 ). Other correlations can be 

found in Leyendekkers (1979); Isdale, Spence and Tudhope (1971).

Auxiliary equations 

3.3.3 Thermal conductivity 

(3.23) 

Tabulated data (Lewis and Randal, 1961) are used, interpolating with three 

concentrations C b (0%, 10%, 20% weight) at different temperatures T b (up to 

120 ºC). As we can see in the formula, brine thermal conductivity k b (W/mK) is close 

to pure water conductivity (brine is about 2% less than pure water). 

Yusufova et al. (1978) also provides a correlation for thermal conductivity of brine. 

3.3.4 Heat capacity 

(3.24) 

Specific water heat capacity CP d is the equation (3.26). The correlation of brine 

specific heat (BTU/lb ºF) is obtained (Helal et. al, 1986) by applying a factor 

dependent upon the solid concentrations and temperature to the heat capacity of pure 

water CP d at the desired temperature (Bromley et al., 1970): 

where 

(3.25) 

(3.26) 

where T b is the brine temperature (50 ºF < T b < 200 ºF); C b the percentage of salt 

concentration. 

3.3.5 Enthalpy 

µ b ( 1.745 + 2.5Cb)10 3 – 

( 5.26 + 4Cb)10 5 – = 

– 

Tb 9 10 7 2 – 9 3 

8 10 Tb 3 10 11 

+ ⋅ – ⋅ + ⋅ 

4 

– T b 

– T b 

kb 0.569118 0.00184086 Tb 7.289 10 6 – = ( + 

– ⋅ Tb) ( 1 – 0.2 Cb) CPb = 1.0 – Cb ( 0.011311 – 0.0000146 Tb) CPd CPd 1.0011833 6.1666652 10 5 – T 1.3999989 10 7 

= – ⋅ + ⋅ 

+ 

1.3333336 10 9 – T 3 

⋅ 

For a given concentration C b, integration of the heat capacity from the reference 

temperature T* = 273.15 K gives the specific enthalpy (BTU/lb) of brine solution H b 

at T b: 

Thermoeconomic analysis and simulation of a combined power and desalination plant 65 

2 

– T 2


where 

a = 1 – C b · 0.011311 

a 1 = a · 1.0011833 

3.3.6 Vapor pressure 

Hb a1 ( Tb – T* ) a2 ( Tb – T* ) a3 ( Tb – T* ) 3 

= 

+ + 

a 2 

a 3 

a 4 

a 5 

= 

= 

= 

= 

a4 ( Tb – T* ) 4 

+ + 

a5 ( Tb – T* ) 5 

1.1473561 10 5 – 

⋅ 6.1666652 10 5 – 

– ⋅ ⋅a 

---------------------------------------------------------------------------------------------- 

2 

1.3999989 10 7 – 

⋅ 7.0669983 10 10 – 

– ⋅ ⋅a 

------------------------------------------------------------------------------------------------ 

3 

1.3333336 10 9 – 

⋅ 1.6043987 10 12 – 

– ⋅ ⋅a 

------------------------------------------------------------------------------------------------ 

4 

1.5296 10 14 – 

⋅ 

--------------------------------- 

5 


(3.27) 

The following equation (Antoine correlation) describes how the vapor pressure p s of 

saturated steam is dependant on temperature T (using the water coefficients, Reid, 

Prausnitz and Sherwood, 1977): 

ln ps = 23.196452 

3816.44 

– ---------------------- 

T – 46.13 

(3.28) 

Equation (3.28) is used until 441 K. Above this temperature (and the critical point), 

the Harlacher & Braun vapor-pressure correlation is used, with the coefficients 

proposed by Reid et al. (1977). 

68695 

ln ps = 60.228852 – -------------- – 5.115 T + 7.875 10 

T 

3 – ps ⋅ 

T 2 

ln----- 

(3.29) 

Equation (3.29) needs an iteration algorithm, for example a Newton-Raphson 

method. SI units must be used. No correlation is used to calculate the vapor pressure 

of brine solutions.

Auxiliary equations 

3.3.7 Boiling point elevation 

Data from Stoughton and Lietzke (1965) were correlated (Friedrich and Hafford, 

1971) to represent the boiling point rise BPE (ºF) as a function of temperature T K and 

salt concentration C: 

BPE 

= 

565.757 

------------------ – 9.81559 + 1.54739 ln T 

T K 

k 

⎛337.178 ⎞ 

– ⎜------------------– 6.41981 + 0.922753lnT T K⎟C 

⎝ K 

⎠ 

32.681 

--------------- – 0.55368 0.079022 T 

T K C 

K 

2 

⎛ ⎞ 

+ ⎜ + ln ⎟ 

⎝ ⎠ 

⎧ C 

⎫ 

⎪---------------------------------------------------------------------------- 

⎪ 

⎨266919.6 

379.669 

⎪ 

--------------------- – ------------------ + 0.334169 

⎬ ⋅ 1.8 

2 

⎩ T T ⎪ 

K 

K 

⎭ 

where T K = (T b + 460)/1.8 (K); C = (19.819 C b)/(1 – C b). 

(3.30) 

Brandoni, del Re, and Di Giacomo (1985) include correlations for BPE and other 

seawater properties. 

3.3.8 Non-equilibrium allowance 

Burns and Roe correlation (Omar, 1981) reported the following empirical equation 

for the non-equilibrium allowance (NEA), expressed as temperature loss (ºF): 

NEA ( 352) 

( Hj) 1.1 ( ∆TB, j) 

0.25 – 

ωj 10 3 – 

( ⋅ ) 0.5 ( TD, j) 

2.5 – 

= 

(3.31) 

where Hj is the height of brine pool in each stage (in.); ∆TBj , is the flash down per 

stage (TB,j–1 – TB,j), expressed in ºF; ωj the chamber load per unit width (lb·h/ft). 

3.3.9 Demister and other losses 

Omar (1981) suggests the following empirical equation to calculate the temperature 

loss due to the pressure drop in the demister and condenser tubes. 

∆TL = 

exp ( 1.885 – 0.0263TD, j) 

where ∆T L is expressed in ºF, and T D,j is the distillate temperature (ºF) in stage j. 

(3.32) 



3.4 Solution algorithm 

MSF can be classified as a steady-state and lumped parameter model (Husain, 1999). 

A wide variety of iterative solution procedures for solving non-linear algebraic 

equations exist in the literature. In such procedures the equations are usually split into 

groups and then ordered by carefully choosing the iteration variables so that the large 

system of equations is decomposed into simpler subsystems. 

The methods usually applied to solve the multistage countercurrent separation 

problems encompassing large systems of non-linear equations are: 

a) Stage by stage calculations, i.e., iterative methods, 

b) Global methods, e.g. Newton and quasi-Newton methods, 

c) Linear methods (Helal et al., 1986), 

d) Other mathematical procedures, such as relaxation methods or a combination of 

several methods. 

The procedure to simulate a MSF plant with the SIMTAW model is a global one, i.e., 

the Powell hybrid method (Powell, 1964), which was also used to solve the power 

plant model in Chapter 4. The subroutines implemented for this method are available 

in internet (UTK and ORNL, 1999). 

FIGURE 3.7 Solution algorithm of a MSF desalination plant model. 


Solution algorithm 

Figure 3.7 shows how the Powell hybrid model is applied to solve the MSF model. 

First, the variable array is built with the initial values included in SIMTAW, taking 

into account the chosen program options. Then, the Jacobian matrix is calculated 

using the differences of the array function, which contains the equations that perform 

the MSF model, included in the above sections. Finally, the variable array is updated 

by multiplying the Jacobian and the array function. If the values do not vary with 

respect to the latest iteration (that is, they are lower than the specified tolerance), the 

process is finished, or new updates are made until a new value of the Jacobian matrix 

is needed. The condition leading to a new calculation of the Jacobian matrix depends 

on the convergence of the iterations. Usually the Jacobian matrix is calculated when 

the variable array is updated five times. 

The criteria for convergence applied in SIMTAW has been imposed by the Powell 

method (Powell, 1964). The simulation is completed when the relative error between 

two consecutive iterations satisfies the specified tolerance: 

where 

m 

xj (3.33) 

is the calculated value of the variable j in the iteration m; is the calculated 

value of the variable j in the iteration m–1; x is the variable array, containing the 

dependent variables needed to perform the MSF plant simulation. The variable array 

contains the following terms: 

• Flashing brine temperature in each stage (T B,j). 

• Cooling brine temperature in each stage (T F,j). 

• Distillate temperature in each stage (T D,j) (it is not a variable in the inverse 

problem, see Section 3.6.3). 

• Flashing brine concentration in each stage (C B,j). 

• Flashing brine flow rate in each stage (B j). 

• Distillate flow rate in each stage (D j). 

• Top brine temperature (T B,o). In the TBT option this variable is not considered 

(see Chapter 5). 

• Recovery section concentration (C R). 

• Deaerator temperature (T DR). 

max ∆x ⎛ j ⎞ 

⎜-------- m ⎟ ≤ 

⎝ ⎠ 

∆x j 

= 

x j 

10 3 – 

m m– 1 

xj – xj 

m– 1 

xj Thermoeconomic analysis and simulation of a combined power and desalination plant 69


3.5 Simulation cases 

The MSF brine recycle flowchart (figure 3.1) has 7 (NRC + NRJ) + 13 degrees of 

freedom as demonstrated by the number of independent equations and unknowns. 

The following variables are defined for an existing plant: 

• Number of recovery stages NRC (=17 in our case). 

• Number of rejection stages NRJ (3 stages). 

The following five variables (design data) are fixed for each stage (assuming the 

number and arrangement of tubes): 

a) heat transfer area of evaporators A j, 

b) tube length L j, 

c) stage width w j, 

d) outside diameter OD j; and 

e) inside diameter ID j (or tube thickness t). 

The four brine heater variables (A H, L H, OD H, and ID H) are also known. The defined 

variables mentioned above sum up to 5 · (NRC + NRJ) + 6 specifications. Thus, if the 

fouling factor is also fixed in every different stage as well as the brine heater, this will 

result in (NRC + NRJ+1) more specifications. Furthermore, if the brine levels in the 

different stages are defined (NRC + NRJ variables), then the total number of 

specifications is 

= 

5( NRC+ NRJ) 

+ 6 + ( NRC+ NRJ+ 1) 

+ ( NRC + NRJ) 

7( NRC+ NRJ) 

+ 7 


(3.34) 

The above specifications limit the degrees of freedom to only 6; obtained by 

subtracting 7 (NRC + NRJ) + 7 from 7 (NRC + NRJ) + 13. Since the feed 

temperature T sea and concentration C sea will be known, only four remaining 

variables will have to be specified to solve the problem. 

Different combinations of variables can be chosen to simulate the MSF plant, 

depending on the objective of the simulation study. Each set (different case) has four 

specifications. For example, three cases are explained below: 

a) The first is called performance calculation. In this case the following operating 

variables are specified: R, CW, F, T S, T sea, C sea; distillate production, steam

Simulation cases 

consumption and Top Brine Temperature are solved. This case is most useful for 

sensitivity analysis studies, it is the simulation case implemented in SIMTAW. 

Two new simulation options, explained in Section 3.5.1 and 3.5.2, were also 

included in the SIMTAW program: TBT option and the inverse problem option, 

where the fouling factors were obtained by substituting in the distillate 

temperature profile. 

b) In the second case, the operating parameters F, CW, T sea, C sea, T B,o and the plant 

capacity D N are specified; steam consumption, steam temperature and recycle 

brine are solved. This case may be used to investigate the possibility of 

maintaining a specified plant capacity when the feed temperature is modified. 

This case it is not considered in the SIMTAW program because the recycle brine 

is determined by the MSF plant (design curves). 

c) In the third case, the parameters F, C sea, CW/R, m ST and T sea are specified. The 

behavior of the whole plant is analyzed when a specified amount of steam is 

supplied to the desalination plant by a coupled power plant. This case is not 

included in the SIMTAW program, taking into account the control implemented 

in the combined power and MSF plant. 

3.5.1 TBT control 

The MSF Plant has a TBT control (from 84 to 112 ºC), to avoid the tube scaling, 

which was included in the simulator option with a fixed TBT value. The rest of the 

variables can be affected by this option, e.g., distillate output is close to the initial 

value, due to the TBT/distillate correspondence (initial curves). 

This option reduces the number of equations. The equation governing heat transfer in 

the heater is rejected because the TBT is not a constraint in this equation. This is the 

only equation removed from the MSF plant model. As a result, a new system of 

equations is obtained. 

3.5.2 Inverse problem 

This problem involves calculating the global heat transfer coefficient, U, and the 

fouling factor of all distillation stages of the MSF plant. In this simulation option the 

distillation temperature profile is a user variable. As a consequence, the results 

obtained in the brine heater are less accurate than in other simulation modes. 

The heat transfer equations used to calculate the distillate temperature in each stage 

of the recovery and reject section are omitted, when solving the inverse problem 

because the user should provide the distillate profile. The other equations included in 

the MSF model remain unchanged. 



Taking into account the four possibilities in the simulation of the MSF process (TBT 

control, inverse problem, both or none options), there are four mathematical models 

implemented in SIMTAW. 

3.6 Initial data and simulation 

Internal parameters of the MSF plant were calculated in the simulation model, using 

some design curves provided by the manufacturers (Fisia-Italimpianti, 1996): 

• Top Brine Temperature (TBT) as a function of seawater temperature (SWT in 

figure 3.8) and distillate D. 

• Recycle brine R as a function of seawater temperature T sea and distillate D 

(figure 3.9). 

• Feedwater (make-up F) as a function of distillate D and seawater concentration 

(figure 3.10). 

• Seawater to reject section as a function of distillate D and seawater temperature 

T sea (≡ SWT) (figure 3.11). 

FIGURE 3.8 Correspondence between the Top Brine Temperature and distillate output. 

Top Brine Temperature (º C) 

115 

110 

105 

100 

95 

90 

85 

80 

65 % 

SWT 32º C 

TBT 84 ºC 

SWT 28º C 

TBT 112 º C 

SWT 25º C 

100 % 125 % 

1200 1400 1600 1800 2000 2200 2400 

Distillate output (T/h) 


Initial data and simulation 

FIGURE 3.9 Brine recirculation as a function of the distillate output. 

Brine recirculation (T/h) 

20000 

19500 

19000 

18500 

18000 

17500 

17000 

16500 

16000 

1000 1200 1400 1600 1800 2000 2200 2400 


FIGURE 3.10 Make-up feed water as a function of the distillate output. 

Make-up feed (t/h) 

8500 

8000 

7500 

7000 

6500 

6000 

5500 

5000 

4500 

65 % 

SWT 28º C 

SWT 25º C 

SWT 32º C 

100 % 

FIGURE 3.11 Seawater to reject section as a function of the distillate output. 

Sea Water to Reject (T/h) 

18000 

17500 

17000 

16500 

16000 

15500 

15000 

14500 

14000 

Sea water inlet TDS: 45,000 

125 % 

1200 1400 1600 1800 

Distillate output (t/h) 

2000 2200 2400 

65 % 

SWT 25º C 

SWT 32º C 

SWT 28º C 

100 % 

125 % 

1000 1200 1400 1600 1800 2000 2200 2400 




These curves contain the limits and the feasible operation ranges in the MSF plant. 

But those graphics also could be correlated by using the real data obtained from the 

plant managers in 1997 (WED, 1997). Figures 3.12 to 3.15 show how the correlations 

have been made using regression lines in a range of 2 ºC of seawater temperature. 

This possibility is available in SIMTAW with the option ‘Sim. with real data’. 

FIGURE 3.12 Top brine temperature depending on the seawater temperature and distillate production. Data 

collected during the year 1997. 

TBT (ºC) 

FIGURE 3.13 Recycle brine flow as a function of the seawater temperature and production. Real data collected 

in the MSF distillers during 1997. 

R (T/h) 

112 

108 

104 

100 

96 

92 

88 

20000 

19500 

19000 

18500 

18000 

17500 

TBT 26ºC 

TBT 28ºC 

TBT 30ºC 

TBT 32ºC 

TBT 34ºC 

TBT 36ºC 

1350 1550 1750 1950 2150 D (T/h) 2350 

R 26ºC 

R 28ºC 

R 30ºC 

R 32ºC 

R 34ºC 

R 36ºC 

1350 1550 1750 1950 2150 D (T/h) 2350 

Therefore, only three input parameters are needed to run the program (note that the 

model has only 6 degrees of freedom): distillate or Top Brine Temperature, seawater 

temperature and concentration (the seawater salinity concentration C sea in Arabian 

Gulf area is 45,000 TDS). Steam to brine heater conditions is also requested by 

SIMTAW, and the temper system takes into account the seawater intake temperature 

and flow rate. 


Initial data and simulation 

FIGURE 3.14 Make-up feed flow obtained for each range of seawater temperature when real data are 

computed. Average data of 1997. 

F (T/h) 

FIGURE 3.15 Seawater to reject flow correlations for different seawater temperatures entering the MSF plant. 

Data collected during the year 1997. 

SR (T/h) 

6600 

5600 

4600 

3600 

17900 

17700 

17500 

17300 

3.6.1 Fouling effect 

F 26ºC 

F 28ºC 

F 30ºC 

F 32ºC 

F 34ºC 

F 36ºC 

1350 1550 1750 1950 2150 D (T/h) 2350 

SR 26ºC 

SR 28ºC 

SR 30ºC 

SR 32ºC 

SR 34ºC 

SR 36ºC 

1350 1550 1750 1950 2150 D (T/h) 2350 

Design curves account for the fouling inside and outside of the tubes, without a 

cleaning ball system. Although the fouling values are very difficult to evaluate, they 

are input data in the program. 

The cleaning ball system can reduce the design fouling factor by five (Barthelmes and 

Bolmer, 1996), depending on the tube material. Overall heat transfer coefficient of 



the evaporator is increased from ≈2,500 to ≈3,500 W/m 2 ·K, then the Performance 

Ratio and the steam consumption are also improved. 

TABLE 3.1 Fouling factors of the heat sections in MSF Plants. 

3.7 Summary 

Tube material Fouling factor (m 2 K/W) 

Cooper alloys 0.00005 

Titanium or Stainless Steels 0.00003 

Without On-Load Cleaning System 0.00020 

Thermoeconomic analysis of a system requires knowledge of thermodynamic states 

of the system under different operating conditions and circumstances of the plant. 

If the data acquisition system of the plant does not provide those data or the system is 

not an existing plant, the state of the system could be obtained by using a 

mathematical model describing system behavior. 

Energy and mass balance, and heat transfer equations compose the mathematical 

model of the MSF process, so it is not necessary to apply additional equations to 

obtain a reasonable agreement in the model results. Correlations providing 

thermodynamic properties of seawater are essential for accurate results. The model is 

solved using conventional methods and software. Mathematical method differs form 

the original if some important parameters of the plant are introduced. Thus, the state 

of the plant could be achieved below different perspectives. Finally, the model has 

been adjusted as much as possible, in order to respond the design but also the real 

behavior of the MSF plant. 

When the thermodynamic state of the MSF plant is obtained, the state of the steam 

power plant is also demanded if the thermoeconomic analysis is going to be 

performed. It will be obtained by using equations described in Chapter 4. 


CHAPTER 4 

Steam power plant 

steady-state model 

In this chapter the mathematical model of the power generation system of a dualpurpose 

plant is described, which is implemented in the SIMTAW program (the 

simulator included in Chapter 5). This model can perform both a conventional energy 

analysis and a thermoeconomic analysis of a power plant. Thermophysical properties, 

such as temperature, pressure, viscosity, specific enthalpy, specific exergy, and so on, 

are calculated for the most significant mass and energy flow streams, together with 

operating parameters of different plant units, e.g., isoentropic efficiencies, heat 

transfer coefficients, etc. Different operating scenarios can be simulated by varying 

the input data and the simulation options to analyze plant behavior and the 

interactions among equipment. 

Power plants produce both electricity and process steam used in the MSF plant to 

produce desalted water from seawater. The co-generation concept considers the 

varying demands for power generation and process steam in the production of 

drinking water. Continuous water production is required throughout the year, whereas 

the generation of electricity will be higher in summer than in winter. 

In the first part of this Chapter I will describe the power plant. Later, the mathematical 

model together with the most significant formulae and the solution algorithm of the 

system of equations are explained. Finally, the model solution is given in the third 

section. The operating modes of the co-generation plant lead to different models that 

are also described in the last section of this chapter. 


FIGURE 4.1 

78 

Steam power plant steady-state model 

4.1 Model description 

The power generation plant is a co-generation plant providing both electrical power 

and the steam required by the seawater desalination plant (MSF plant). The selected 

power plant had six turbojets, each of them at the co-generation design point 

3 

produced 122 MW of electricity and 198 MJ/s of process heat to provide 57,600 m 

of drinking water per day. A maximum of 6× 

146 MW can be delivered in generator 

terminals in pure condensing mode. 

Extraction/condensing turbines in each unit operated under constant pressure (that is, 

pressure at the high-pressure (HP) turbine inlet is always constant). Each of the 

turbines has two sections, a single flow HP section and a single flow low-pressure 

(LP) section. Steam extraction outlets for the seawater desalination plant and 

extraction points for the feedwater heaters (points 3,4,5,6 and 8 in figure 4.1) are 

available on both turbine sections. 

Steam flow is an important variable determining the behavior of the power plant. If 

there is no steam supply for the MSF plant, the steam flows through the LP section 

and is returned (via a damper and bypass line). 

Schematic diagram of the power generation plant. Main significant flows are numbered for later 

descriptions and equations. 

Main HP steam flows from the steam generator —point 1 in figure 4.1— through the 

steam supply lines to the main steam emergency and control valves, which are 

flange-mounted onto the lower section of the HP outer casing. The steam from the 

valve casings to the valve chests welded onto the HP inner casing is supplied by the 


Model description 

lower section, and via bypass lines between the valve and turbine casing in the upper 

section. 

Afterward, the steam enters the valve chests which house the nozzle segments. It then 

flows via the control wheel of the HP rotor into the impulse chamber of the turbine 

casing. The steam expands through the reaction blading and enters the exhaust steam 

chamber of the HP section. The steam required for the seawater desalination plant is 

extracted via the extraction outlets in the lower exhaust section —point 6 in 

figure 4.1—. 

A certain percentage of the steam flows through the exhaust nozzles in the upper 

exhaust section and then through the downstream damper and bypass line to the LP 

section. It then flows into the LP reaction blading via the steam inlet nozzles and, 

after expansion, enters the condenser at the exhaust nozzles. 

The simple design of the high-pressure casing is based on a single shell construction 

with perfect rotational symmetry. All the components of the HP section are secured 

so that concentric alignment and unrestricted movement is maintained under all 

operating conditions. 

First and second HP turbine extractions —points 3 and 4 in figure 4.1— are fed to the 

HP heaters. The first HP extraction goes to the vacuum system of the MSF plant, and 

is condensed in the condenser. The third HP extraction —point no. 5— feeds the 

deaerator; and finally a smaller quantity of the lowest extraction is sent to the first LP 

heater (the main part is sent to the desalination plant). 

The LP section is a standard single-flow design with an upstream inlet section. 

Depending on the operating mode of the turbojet, the steam is directed to the first 

blade carrier via a vertically mounted inlet steam nozzle —point no. 7— and led to 

the second blade carrier via a bypass, when the amount of steam to the LP turbine is 

large enough. The automatically controlled water injection system in the upper 

section of the casing provides the cooling required in specific operating modes. A 

rupture disc is fitted in the outer casing as a safeguard against over pressure. LP 

extraction —point no. 8— feeds the second LP heater. 

The Power Generation Plant also contains a live steam reduction pressure station, to 

extract the steam flow to desalination in case of turbine system failure. As seen in 

figure 4.1, E1 and E2 are the live steam extractions to the two connected desalination 

units. The reduction pressure station mixes the live steam with water feed from the 

feed pump (S1 to S4 in figure 4.1), to reach the optimum pressure for the MSF plant. 

When the turbine does not work, a new extraction E3 is needed to feed the vacuum 

system of the MSF units, and a fourth one, called E4 in figure 4.1, feeds the deaerator, 

where it is mixed with the condensate returned to the MSF units. In this way, the 

steam cycle is closed, via the HP feed flow to the boiler. 


79

FIGURE 4.2 

80 


4.2 Mathematical model 

4.2.1 Steam turbines 

Simulation of admission properties (Salisbury, 1974) is based on the determination of 

the mass flow coefficient, which was defined according to the Cooke’s model 

(Cotton, 1993; Spencer, Cotton and Cannon, 1974) and the Stodola’s Ellipse model 

(Stodola, 1927; Cooke, 1985). The mass flow coefficient φ is defined as: 

m 

m 

φ = ------- or φ = ------- 

(4.1) 

p 

------p 

-- 

T 

v 

where m is the mass flow rate (kg/s), p is the pressure (bar), T is the temperature (K) 

3 

and v is the specific volume (m /kg). The mass flow coefficient under operating 

conditions can be calculated as a function of the design parameters (subscript d). 

Thus, the admission values can be solved: 

2 

m md 1– rpd φ --------------p p 

------- d 

--------- 1 rp 

T 

2 

= = -------------------- 

– 

T d 

where rp = ---- is the pressure ratio at each turbine section (see figure 4.2): 

Schematic diagram of a turbine section. 

p i 

m i 

T i 

p 0 

p i 

p 0 

T 0 


(4.2) 

The admission properties of the steam turbine are evaluated using a model in which 

the mass flow coefficient is a function of the pressure ratio in each turbine section, 

and is a characteristic value for each type of turbine. This model cannot be applied to 

the first section, due to the fixed pressure mode which controls the steam turbine 

operation. Therefore,

FIGURE 4.3 

Mathematical model 

φ K 1 rp 2 

= ⋅ – 


(4.3) 

Values of the constant K are obtained using the turbine admission properties for the 

design conditions supplied by the manufacturer. For example, the value of K4 

for the 

4th 

section of the high-pressure turbine can be obtained as follows: 

φ 4d 

m 4d 

= ------------ = K 

p 4 ⋅ 1– rp4d 4d 

------------ 

T 4d 

(4.4) 

rd 

where the subscript ‘4d’ refers to the steam properties at the 3 extraction of the high 

pressure turbine, taken from a performance data case (ABB, 1996b). 

The efficiency model is also based on the mass flow coefficient. A correlation was 

proposed to obtain the isoentropic efficiency of a turbine section as a function of this 

coefficient. The design mass flow coefficients were used to solve this correlation for 

the different operation loads of the plant. Polynomial formulae were obtained for 

nd 

each section of the turbine. The formula corresponding to the 2 section of the highpressure 

turbine is a linear function of the mass flow coefficient φ2d, 

obtained from 

nd 

the pressure, temperature and flow of the performance data cases in the 2 section of 

the high-pressure turbine: 

η 2 

= f( φ2d) = 0.013985 ⋅ φ2d + 0.1002 

Isoentropic and real expansion of the steam in a turbine section. 

h 

h 1 

h 2s 

p 1 

h 2 

p 2 

s 

2 

(4.5) 

Finally, the thermodynamic properties of the steam at each turbine section are 

calculated as follows (see figure 4.3): 

η i 

hi – hi+ 1 

= 

-----------------------hi 

– hi+ l, s 

(4.6) 

81

FIGURE 4.4 

82 


where hi 

is the enthalpy of the inlet section, hi+1 

is the enthalpy of the outlet section, 

and hi+1,s 

is the enthalpy of the outlet section in an isoentropic process. 

The steam pressure in the lowest section of the high-pressure turbine was a fixed 

value, due to the pressure control applied to the desalination units. Hence, HP and LP 

turbines can be considered two different pieces of equipment. 

4.2.2 HP heat exchangers 

HP heat exchangers have desuperheating, condensation, and subcooling sections 

(ABB, 1996c). Thus, feed water is heated by exchanging the maximum quantity of 

heat with the steam bled from the HP extractions. 

The model of the HP heat exchangers is based on a correlation of the terminal 

temperature differences (TTD) for the different existing loads, see figure 4.4. The 

overall heat balances are used to calculate the amount of extracted steam from the HP 

turbine. The overall heat transfer coefficient in each section cannot be used because 

of the lack of design data, except for the heat transfer coefficient in the condensing 

zone, which is a design data that varies with the requested load. Moreover, it is 

assumed that the condensate is a saturated liquid, even though some sub-cooling may 

occur. 

TTD differences in an HP heater. 

T 

TTD o 

Condensation section 

TTDi 

Desuperheating section Subcooling section 

Numerical correlations proposed by Erbes (Erbes and Gay, 1989) were used to solve 

the terminal temperature differences TTD (inlet/outlet) in HP heaters: 

∆Ti ⎛ m ⎞ 

--------- ⎜------ ⎟ 

∆Td ⎝md⎠ x 

⎛ T ⎞ 

⎜----- ⎟ 

⎝Td⎠ y 

⎛ p ⎞ 

⎜---- ⎟ 

⎝pd⎠ z 

= 

⋅ ⋅ 


L 

(4.7)

TABLE 4.1 


where ∆Ti 

is the inlet TTD in an HP exchanger (usually called Drain Cooling 

Advantage (DCA)), and m, T and P are the feedwater properties at the HP inlet. The d 

subscript refers to the design conditions. The x, y and z exponents were obtained 

from the heat balances for different loads supplied by the manufacturer (ABB, 

1996b). Typical x, y and z values are shown in table 4.1: 

Typical x, y and z coefficient values for the inlet TTD’s in an HP heater. 

The outlet TTD ( ∆To) 

(or simply called TTD) correlation contains more factors. 

Thus, the mass flow rate and steam pressure of the turbine extraction are also needed, 

in order to model the correct behavior in all cases. Typical values for the five 

coefficients needed in a HP heater are shown in table 4.2. 


(4.8) 

The Erbes and Gay model (Erbes and Gay, 1989) also provides the pressure losses in 

the feed waterside of the HP heat exchangers: 

4.2.3 LP heat exchangers 

x y z 

0.64 –0.29 0.52 

∆T 0 

--------- 

∆T d 

⎛ m ⎞ 

⎜------ ⎟ 

⎝md⎠ x 

⎛ T ⎞ 

⎜----- ⎟ 

⎝Td⎠ y 

⎛ p ⎞ 

⎜---- ⎟ 

⎝pd⎠ z 

⎛ mex ⎞ 

⎜------------- ⎟ 

⎝mex, d⎠ 

a 

⎛ pex ⎞ 

⎜----------- ⎟ 

⎝pex, d⎠ 

d 

= ⋅ ⋅ ⋅ ⋅ 

TABLE 4.2 Typical x, y, z, a and b coefficient values for the outlet TTD’s in an HP heater. 

x y z A b 

–2.395 4.407 –0.713 0.584 0 

∆p 

-------- 

∆pd ⎛ m 

------ ⎞ 

⎝m⎠ d 

1.8 ⎛ T ⎞ ⎛ p ⎞ 

⎜----- ⎟ ⎜---- ⎟ 

⎝Td⎠ ⎝pd⎠ 1 – 

= 

(4.9) 

LP heat exchangers in the Steam Power Plant only have a condensation and a 

subcooling section (ABB, 1996c). Usually the steam flow is saturated vapor or 

contains a humidity fraction. Thus the feedwater is heated by extracting the maximum 

quantity of steam heat from the LP extraction and the lowest HP extraction. 

83


Correlations similar to those used in the HP heaters to calculate the TTD’s (see 

figure 4.5) and the pressure losses were also used to model the LP heater behavior. 

The exponent values were also obtained from the heat balances for different loads 

supplied by the manufacturer (ABB, 1996b), they are shown in tables 4.3 and 4.4. 

FIGURE 4.5 TTD differences in an LP heater. 

T 

TTD o 

4.2.4 Deaerator 

Condensation 

section 

Subcooling 

section 

TABLE 4.3 Typical x, y and z coefficient values for the inlet TTD’s in an LP heater. 

x y z 

0.43 –0.02 0.10 

TABLE 4.4 Typical x, y, z, a and b coefficient values for the outlet TTD’s in a LP heater. 

x y z z b 

–0.04 18.97 –0.12 1.11 4.33 

A whole plant energy balance is included when modeling the deaerator and feedwater 

tank behavior (ABB, 1996c). Feedwater from the LP heaters, condensate from the 

desalination units and cooled drain from the HP heaters enter the feedwater tank, but 

the operating pressure is controlled by the 3 rd HP extraction. 

The mass flow leaving the extraction must be correlated to assure some saturated 

liquid is entering the feed pump. Several parameters were included to calculate the 

3 rd HP extraction mass flow rate, to cover the operating range designed by the 

manufacturer (ABB, 1996b). The proposed correlation is: 


TTD i 

L


mex, 3 

-------------mex, 

3d 

(4.10) 

where m 1 is the live steam mass flow rate generated in the boiler; T 5 and P 5 are the 

admission properties leaving the 3 rd section, m 1,des is the difference between m 1 and 

desalination mass flow rate m des, m 1,LS is the difference between m 1 and Live Steam 

extraction sent to the reducing pressure station m LS, and m 1,LS,des m 1 minus 

desalination and live steam (to the reduction pressure station). The last three variables 

have a strong influence on the rest of the plant process units, which is why they were 

included in the above-proposed correlation. Table 4.5 shows the coefficients 

calculated in the last correlation. 

TABLE 4.5 x, y, z, a, b and c coefficient values in deaerator. 

4.2.5 Condenser 

4.2.6 Boiler 

⎛ m1 ⎞ 

⎜-------- ⎟ 

⎝m1d⎠ x ⎛ T5 ⎞ 

⎜------- ⎟ 

⎝T5d⎠ y 

⎛ p5 ⎞ 

⎜------- ⎟ 

⎝p5d⎠ z ⎛ mdes ⎞ 

⎜--------------- ⎟ 

⎝mdes, d⎠ 

a ⎛ mLS ⎞ 

⎜-------------- ⎟ 

⎝mLS, d⎠ 

b ⎛ m1LSdes , , ⎞ 

⎜--------------------------- ⎟ 

⎝m1LSdesd , , , ⎠ 

c 

= ⋅ ⋅ ⋅ ⋅ ⋅ 

x y z a b c 

Deaerator 0.121 1.091 1.905 0.206 2.588 –0.211 

A global energy balance was applied to develop the condenser model. Three streams 

enter the vapor side of the condenser: (i) exhaust steam from the low-pressure 

turbine, (ii) condensate from the MSF vacuum system and (iii) discharge from the 

ejectors. The maximum cooling seawater flow rate is at the seawater temperature. 

The condensate presumably discharges at the saturation temperature (ABB, 1996d). 

A model was used including the heat balance of the waterside of the boiler to 

simulate performance of the boiler (figure 4.1). The energy needed to heat the 

feedwater leaving the high-pressure heater No. 1 to the fixed conditions of the steam 

leaving the boiler was used to calculate the natural gas consumption of the boiler 

(LHV of natural gas is 8026 kcal/Nm 3 ). Boiler efficiency was introduced using the 

design data provided by the contractors (ABB, 1996a) for different operating 

conditions. Pressure losses on the waterside of the boiler were computed using the 

following equation: 

∆P 

--------- 

∆Pd ⎛ m ⎞ 

⎜------ ⎟ 

⎝md⎠ 0.463 

⎛ T ⎞ 

⎜----- ⎟ 

⎝Td⎠ 0.436 – 

⎛pd⎞ ⎜---- ⎟ 

⎝ p ⎠ 

3.917 – 

= 

(4.11) 



A more detailed model could calculate the intermediate properties inside the boiler 

(the boiler in study has two economizers and three superheaters, and a non reheat 

process inside the boiler). A detailed boiler model clearly surpasses the scope of this 

Ph. D. Thesis and is not necessary to perform a thermoeconomic analysis of a whole 

plant. 

4.2.7 Valves 

Pressure losses in valves were calculated using the BBC Thermal kit correlations 

(BBC, 1979): 


(4.12) 

where p is the pressure of the flow entering the valve; Z is the pressure drop 

coefficient (constant value); DV, is the main stop valve seat diameter (m) Sa = , 

the sonic area (m 2 ), with v, specific volume (m3 m 

/kg), α, sonic velocity (m/s), and m 

the mass flow inside the inside the valve. 

v 

-- 

α 

4.2.7.1 Turbine control valves 

The inlet of the HP turbine has four control valves with some pressure losses (about 

4-5 bars). The main steam mass flow in the boiler is equally divided into four parts, 

each flowing through one of the valves. The pressure drop coefficient value (Z) was 

taken to be 0.38. 

4.2.7.2 Boiler outlet stop valve 

The security valve fixed at the boiler outlet had a pressure drop coefficient Z of 2.31. 

4.2.7.3 Boiler inlet control valve 

4.2.8 Pipes 

∆p 

------ = Z 

p 

⎛ Sa ⎞ 

⎜---------- ⎟ 

⎝ ⎠ 

2 

DV 2 

This valve, used to control the pressure entering the boiler, had a pressure drop 

coefficient Z of 1.30. 

Significant pressure losses occur in the pipelines, e.g., pipes to the deaerator, 

extraction pipes or pipes to the boiler. These are calculated by applying the 

correlation proposed by Erbes and Gay (1989):


(4.13) 

The value of the a coefficient depends on the type of pipe and operating conditions. 

Table 4.6 lists the values of the applied a coefficient. 

TABLE 4.6 Values of the a coefficient for each pipe of the power model. 

1 st HP extraction 

4.2.9 Pumps 

∆p 

-------- 

∆pd 2 nd HP extraction 

3 rd HP extraction (to deaerator) 

4 th HP extraction 

Pipe description a 

The pump model is based on the efficiency versus mass flow rate curves provided by 

the power plant manufacturers (ABB, 1996f). Energy consumption is derived from 

the energy balance applied to the pump, when the conditions of the water entering 

and leaving the pump are known. 

The thermodynamic properties of the water at the inlet/outlet of the feedwater and 

condenser pump can be calculated using the isoentropic efficiency (see figure 4.6): 

1.95 

1.95 

1.95 

LP extraction 1.95 

Waterside of LPH No. 2 1.5 


LPH2 to deaerator 1.5 

Feed pump to HPH No. 2 1.8 



LPH No. 1 to Boiler 1.85 

1 st HP extraction 

η i 

⎛ m 

------ ⎞ 

⎝m⎠ d 

a ⎛ T ⎞ ⎛ p ⎞ 

⎜----- ⎟ ⎜---- ⎟ 

⎝Td⎠ ⎝pd⎠ 1 – 

= ⋅ ⋅ 

– hi = 

------------------------- 

– 

hi+ 1, s 

hi+ 1 

h i 

(4.14) 


1.8 

1.95


where h i is the enthalpy of the inlet water, h i+1 is the enthalpy of the outlet water, and 

h i+1,s is the outlet water enthalpy in an isoentropic pumping process. 

FIGURE 4.6 Isoentropic and real compression process in a pump. 

h 

4.2.10 Gland and seal steam system 

All steam flow leakages are considered and accounted for in the heat balance 

calculations. Gland steam system of the power plant is described in figure 4.7. 

FIGURE 4.7 Gland and seal steam system. 

h 1 

h 2s 

Live steam 

h 2 

p 2 

Martin’s formula (Martin, 1919) for steam leakage through labyrinth seals was used 

to calculate the leakage flows for representative designs with normal running 

clearances (figure 4.8): 


p 1 

HP LP 

m1 + m2 = Kd m 2 

= 

K′ d 

s 

( pt – pl)pt --------------------------- 

273.15 + Tt ( p1 – p2)p1 ---------------------------- 

273.15 + T1 Ejector 

(4.15) 

(4.16)


where Kd and K′ d are constants, obtained from the design data (ABB, 1996b), and 

1, 2 and t subscripts refer to the first and second seal in a leakage and the steam 

conditions inside the turbine. 

FIGURE 4.8 Leakage flows and seals of a steam turbine. 

m 2 

p 2 

The valve connecting the high and low pressure lines of the gland steam system (see 

figure 4.7) is only opened in the condensing operation mode, i.e. when the turbine is 

working without desalination flow and only producing electricity, due to the high 

amount of steam lost in the HP leakage. 

Finally, the energy balances in the high and low pressure lines of the gland steam 

system are used, to evaluate the properties of the steam flowing to the ejector. 

Table 4.7 shows the Kd and K′ d 

values obtained for the four parts of the turbine 

interacting with the gland and seal steam system. 

TABLE 4.7 K d and K d’ constants of the gland and seal steam system. 

HP Turbine. Inlet 0.02 1.392 

HP Turbine. Outlet 0.83 1.448 

LP Turbine. Inlet 1.4288 2.962 

LP Turbine. Outlet 1.4288 2.962 

4.2.11 Generator 

m 1 

shaft 

p 1 

K d 

turbine 

Generator losses were accounted for in the model to more precisely calculate the 

plant’s output power, using manufacturer design data (ABB, 1996e). Generator 

efficiency is therefore included in equation (4.17) as a function of the output power 

in MW: 

η gen (%) = (0.941 + 9.701 · 10 –4 · MW + 7.071 · 10 –6 · MW 2 

+ 1.771 · 10 –8 · MW 3 ) · 100 (4.17) 


p t , T t 

m t 

K d’


The excitation system was also included, using plant performance data. The 

excitation system losses (ESL) are calculated by a formula that depends on the output 

power in kW: 

ESL = 0.00152 * kW – 5.01645 (4.18) 

Therefore, the simulator can calculate the electrical and net output power produced in 

the power plant. 

4.3 Auxiliary equations 

The thermodynamic and transport properties in a steam power plant simulation 

involve pure water and steam. 

4.3.1 Thermodynamic properties 

The thermodynamic properties of water can be calculated by a group of functions 

using equations from the IFC-1967 formulae for industrial applications. Those 

formulae was accepted in the Sixth International Conference about Water Properties 

(1967). Since then, they have become the standard for ASME, JSME, etc. (also see 

ASME, 1967; JSME, 1968). 

Detailed numerical methods used to solve the inverse functions can be found in Pina 

(1979). 

4.3.2 Transport properties 

Specific heat at constant pressure was obtained by numerical integrating the enthalpy 

function. Formulae used to calculate the thermal conductivity and dynamic viscosity 

were taken from Sangers and Watson (1986) and Yata and Minamiyama (1979). 

Vargaftik (1978) covers the entire range of the properties, and numerical interpolation 

methods were used to complete them at the proper conditions. 

4.4 Solution algorithm 

The mathematical model of the power plant is also a set of non-linear algebraic 

equations. There are a wide variety of iterative procedures to solve this kind of 

problem; splitting the equations into subgroups and then solving each subsystem to 

create an iteration loop. Our model was not portioned into subsystems. 

The power plant model is solved using the Powell hybrid method (Powell, 1964), also 

used by SIMTAW simulator to solve the MSF plant model. It is a derivation of the 


Solution algorithm 

Newton method supported by an iterative technique where non-linear terms, such as 

variable products and properties, are set to constant values from the latest iteration. 

The Powell hybrid method is applied to the whole set of equations. It requires a 

considerable programming effort and computer storage. Despite this, a global method 

provides the best solution. Solving the whole system sequentially (where it is 

decomposed in a set of subsystems), or linearally (where some variables are 

considered a linear combinations of others), does not provide a better convergence of 

the whole system of equations. 

The Powell hybrid method calculates the Jacobian by a forward-difference formula, 

and uses a relaxation technique to update the values in a new iteration, i.e. the 

Jacobian does not need to be calculated in each iteration. The applied solution 

algorithm is available in the Subroutine HYBRID, in the NETLIB mathematical 

libraries (UTK and ORNL, 1999). The user should provide a subroutine containing 

the model functions, which are, in turn, the functions needed in the subroutine 

HYBRID to calculate the Jacobian applying the forward-difference approximation. 

In the power plant, the number of equations is much higher than the system 

developed to solve the desalination unit: the variable array, (with the dependant 

variables needed for the power plant simulation) includes the following terms 

corresponding to the main flowstreams of the model: 

• Admission properties (m, p, h, T, η, K, φ) in each section of the HP and LP turbine. 

• Gland and seal steam system properties (m, h, T). 

• HP and LP heaters properties (m ex, p, h, T). 

• Condenser and deaerator values (m, X, p, h, T). 

• Boiler parameters (m, p, h, T). 

• Pressure losses in pipes and heat exchangers (∆p). 

Live Steam properties are kept constant to take into account the plant operation 

strategy (sliding pressure control is avoided). The applied convergence criterion was 

the same as in the SIMTAW model to solve the MSF plant: the relative error of each 

variable included in the variable array between two consecutive iterations must be 

lower than the specified tolerance. Usually, this value is set to 10 -3 but it could be 

considerably reduced: 

where 

max ∆x ⎛ j ⎞ 

⎜-------- ⎟ ≤ 

m 

⎝ ⎠ 

∆x j 

= 

x j 

10 3 – 

m m– 1 

xj – xj 

(4.19) 

(4.20) 



m 

xj m– 1 

xj represents the calculated value of the variable j in the iteration m. 

is the calculated value of the variable j in the iteration m-1. 

The solution algorithm adopted to solve the mathematical model by using the Powell 

hybrid method is shown in figure 4.9. 

FIGURE 4.9 Algorithm to solve the power plant model using the Powell hybrid method. 

4.5 Operating modes and mathematical models 

A wide variety of operating modes are available in the power plant, depending on the 

amount of required steam for the MSF desalination units, (either via the live steam 

reduction pressure station or via the fourth extraction of the HP turbine). Moreover, if 

it is not necessary to produce electricity, the system live steam-deaerator-boiler can 

be used to obtain the required steam for one or two desalination units. 

The operating modes of the steam power plant are as follows: 

a) Extraction mode. The most common operation mode where the plant produces 

electricity and also supplies steam to the MSF unit. 

b) Parallel mode: When the power output is less than 75 MW, the live steam reduction 

pressure station supplies steam with enough pressure to the MSF unit. 

c) Condensing mode: In this case no distilled water is produced and the plant operates 

as a conventional steam power plant (the power output is maximum). 


Operating modes and mathematical models 

d) Desalination mode: The opposite of the condensing mode. The plant only produces 

distilled water and the steam turbine does not work. Thus the boiler provides 

the required steam to the MSF units via the steam reduction pressure 

station. 

e) Twin desalination mode: Here the boiler is in full load operation and produces 

steam for two MSF desalination units. This mode is unusual and the steam turbine 

plant does not operate either. 

f) Twin extraction mode: Similar to the extraction mode, but the boiler also provides 

steam for a second MSF desalination unit using a portion of the live steam 

derived from the live steam reduction pressure station. 

Three different mathematical models were implemented to simulate all the different 

operating modes included in the boiler performance data (ABB, 1996a). 

The models included in the power plant simulation program were the following: 

(i) Normal Turbine Load Model (NTL MODEL): Mass flow entering the LP turbine 

is between 3-125 kg/s; then the Stodola’s model is applied to simulate the LP 

turbine. The amount of steam required via the live steam reducting pressure 

station is not important if the mass flow to LP turbine is more than the 

specified lower limit. This model is more complex, and has the maximum 

number of equations. 

(ii) Low Turbine Load Model (LTL MODEL): Mass flow entering the LP turbine is 

less than the lower limit imposed previously. The Stodola´s model cannot be 

applied to the LP turbine, there is a compressor action at high exhaust 

pressures and low loads, illustrated by the stream lines in figure 4.10: 

FIGURE 4.10 Last stage of LP turbine acting as a compressor. 



This model determines entry conditions at the condenser. A parametric model 

based on the thermal balances is then used to solve the admission properties in 

the LP turbine. Thus, the number of equations in the LTL model is reduced 

when the LP values are solved differently. However, the model has a poor 

stability because negative mass flows could appear during the iteration process 

and the program must be aborted. 

(iii)Non Turbine Working Model (NTW MODEL): The Power Plant is only used to 

supply steam to the MSF desalination units, and the HP and LP turbines are 

off. Therefore, the power plant scheme is reduced to a very simple model, 

composed of the boiler, live steam reduction pressure station and deaerator. 

HP heaters are bypassed, and pressure losses are neglected. This final scheme 

is shown in figure 4.11: 

FIGURE 4.11 Power plant scheme in the NTW Model. Some flowstreams are renumbered with respect fig. 4.1. 

The third model is the simplest one used to describe the power plant as the number of 

equations is considerably reduced. 

Operating conditions should be classified in one of the three simulation models 

outlined above (see table 4.8). Performance data cases included in the Design Data of 

the Boiler (ABB, 1996a) are: 

1. MSL1 (Minimum stable load at 20% boiler MCR) 

Load at which the boiler is still able to operate continuously with rated steam 

properties, without the bypass system in operation and without extraction heat 

flow to desalination and pressure reduction station. 


Operating modes and mathematical models 

2. MSL2 (Minimum stable load) 

Load corresponding to unit operation at 45 MW and with combined heat flow of 

145 Gcal/h from parallel operation of turbine extraction and live steam reducing 

pressure station (118.66 and 26.34 Gcal/h respectively). 

3. MSL3 (Minimum stable load with two distillers) 

The turbine is at minimum stable load and the extraction heat flow is 145 Gcal/h 

plus 150 Gcal/h through HP pressure reduction station. 

4. MSL4 (Winter operation) 

The turbine is at minimum stable load with an extraction heat flow of 170 Gcal/h 

to desalination unit. 

5. PL65 

The turbine generator load is 65 MW and the extraction heat flow is 145 Gcal/h. 

6. PL85 

The turbine generator is at 85 MW and an extraction heat flow of 145 Gcal/h. 

7. PL115 

The turbine generator at 115 MW and an extraction heat flow of 145 Gcal/h. 

8. MCR (Maximum Continuous Rating) 

The turbine generator at rated steam parameters with a power output of 115 MW 

and an extraction heat flow of 170 Gcal/h. 

9. VWO 

Turbine swallowing capacity (all control valves open) with extraction heat flow 

of 170 Gcal/h. 

10. MR (Maximum Rating) 

The turbine generator at rated steam parameters, nominal control valve spindle 

position and no extraction heat flow to desalination. 

11. Boiler MCR 

Maximum continuous rating of boiler to be 10% above the requirement of unit 

MCR test mentioned in item 8. 

12. Boiler peak load (COC) 

Boiler peak load at least 5% more than boiler MCR. The extraction heat flow is 

170 Gcal/h to desalination and 50.8 Gcal/h to live steam reduction pressure 

station. 



13. ODOB (One desalination and one boiler only) 

170 Gcal/h extracted through the HP reduction pressure station (a desalination 

unit), turbine is not in use. 

14. TDOB (Two desalination and one boiler only) 

340 Gcal/h extracted through the HP reduction pressure station (two desalination 

units), turbine is not in use. 

Table 4.8 shows the type of model applied to simulate each operating mode in the 

performance data: 

TABLE 4.8 Operating mode and mathematical model corresponding to the performance data cases. 

Performance data case Mathematical Model Operating mode 

4.6 Summary 

MSL1 LTL a 

a. Live steam temperature is 460 ºC. 

Condensing 

MSL2 LTL Parallel 

MSL3 LTL Twin Extraction 

MSL4 LTL Extraction 

PL65 NTL Extraction 



MCR NTL Extraction 

VWO NTL Extraction 

MR NTL Condensing 

MCR NTL Extraction 

COC NTL Twin Extraction 

ODOB NTW Desalination 

TDOB NTW Twin Desalination 

The thermodynamic states of the co-generation plant with the steam turbine plant and 

the MSF unit are now permissible thanks to the mathematical models described in the 

previous and this chapter. The mathematical model of the steam turbine plant is in 

some cases very unstable, especially when the operating conditions provoke the 

deviation of the steam to the MSF unit and LP turbine is forced to work in unexpected 

conditions. 


Summary 

The set of equations composing the mathematical model depending on the operation 

mode of the plant is solved with a global method in which the variables are 

simultaneously calculated. 

These two chapters contain the mathematical models introduced in the simulator, 

which is the tool that allows the use of the model’s results in the thermoeconomic 

analysis of the dual-purpose plant. 


CHAPTER 5 

Simulator 

Mathematical models used to simulate a dual-purpose plant are quite complex (see 

Chapters 3 and 4), so a solid basis is needed to solve them. Despite this, the SIMTAW 

program has been built in such way that only a few input data are essential to simulate 

the power and desalination plants in order to analyze plant performance. Hence, no 

highly qualified background is needed to use the program, although we only 

recommend its use to obtain a correct understanding of the results to technicians and 

plant managers that have an in depth knowledge of the dual plant. 

Simulation of the thermodynamic processes in a dual-purpose plant is the first step to 

develop the Thermoeconomic Analysis of the Plant. Thermodynamic properties of the 

flowstreams in the plant are needed to apply the exergy balance, and to calculate the 

exergy costs of these flows. In this way, the complete analysis of the irreversibilities 

and malfunctions can be done, and the causes that generate these faults can be 

detected. 

SIMTAW is the thermoeconomic software that can provide these results. It is the 

result of a complex project with several model developments of different complexity. 

A Visual Basic coded program is the user friendly interface. SIMTAW was built 

following those stages: 

1. To solve the mathematical models using an Equation Solver. In this case the EES 

program was used (Klein and Alvarado, 1999). Mathematical models were 

solved in blocks, then the whole model was connected. Relationships between 

variables, and independent blocks of equations were found, then the mathematical 

model was translated to a high-level programming language such as Fortran. 


Simulator 

2. The dual-plant was simulated with a Fortran coded program (Microsoft Corporation, 

1997). This program has several files including the design data, steam and 

brine properties, subroutines to initialize and calculate the variables, subroutines 

to solve the system of equations, and the algorithm which controls the whole 

program. 

3. The Dynamic Link Libraries, usually named ‘DLL’s’, are the interface between 

the Fortran and Visual Basic programs. Seven ‘DLL’s’ were built to develop four 

mathematical models included in the MSF Plant and three Power Plant models - 

all these mathematical models correspond to the operating modes explained in 

the previous chapters-. 

4. Finally, a Visual Basic coded program (Microsoft Corporation, 1997) was built 

to make the program more user friendly. This program is described in the following 

section. 

The first section of the chapter describes how to use the simulator when the 

thermoeconomic state of the MSF or the steam power plant is requested. But in 

Chapters 3 and 4 the accuracy of the mathematical models is not analyzed. Model 

validation is therefore included in this section, when the data flowsheets obtained 

from plant designers are compared with the results given by the simulator. In general, 

simulator calculates the properties of the main flowstreams of the dual-plant, the 

associated error in the calculations is very low. 

5.1 SIMTAW structure 

SIMTAW is the program that simulates the two processes involved in a well-known 

dual-purpose plant: the MSF and the Power Generation units. SIMTAW has a userfriendly 

interface that (through a set of more than 20 windows) allows the user to 

proceed by clicking the specified buttons. SIMTAW is built in Visual Basic 5.0, a new 

version only useful for 32 bits, and requires at least Windows’95. A user guide 

explaining how to manage the program has been implemented (Villalon, 1995), and 

includes a very strict control over the input data introduction in order to avoid 

inconsistencies in the mathematical models. 

The two processes can be simulated independently and are driven by two different 

windows. The window that manages the MSF simulation is shown in figure 5.1, 

containing the MSF unit scheme, and seven text boxes and control buttons. In the text 

boxes, the user must introduce an allowed value for the following variables: 

1. Distillate mass flow rate (1,200-2,400 T/h) or Top Brine Temperature (84-112 ºC) 

in the MSF plant. 

2. Seawater to reject temperature (25-36 ºC). 


FIGURE 5.1 

SIMTAW structure 

3. Seawater concentration at the seawater inlet (40,000-50,000 TDS). 

4. Steam to brine heater temperature (80-150 ºC). 

5. Steam to brine heater pressure (0.8-3.0 bar). 

6. Sea water temperature (18-36 ºC) 

7. Seawater inlet flow (12,000-20,500 T/h). 

SIMTAW MSF process window. 

After these values are correctly introduced, the user must choose the TBT control 

option—clicking the corresponding box—, to fix the Top Brine Temperature value 

during the simulation. The inverse problem option also calculates the fouling factor in 

each stage. The third option, called Sim. With real data, 

includes a correlation with 

real data of the main mass flow rates of the MSF unit collected during the year 1997 

(WED, 1997). 

The window that manages the power plant (figure 5.2) contains the plant scheme and 

four text boxes where the user introduces input variables needed to perform the power 

plant simulation: 


101

Simulator 

1. Generator output (including generator losses, 50-147 MW). 

1 

2. Live Steam extractions to the reduction station (0-340 Gcal/h). 

3. Steam mass flow rate to the desalination units (0-189 kg/s). 

4. Condenser pressure (0.02-0.14 bar). 

Then, the user must choose one of the six operating modes in the dual-plant, 

depending on the power and steam demanded to the MSF unit(s), the operation 

modes are (see section 4.6 relating the operating and mathematical models of the 

process): 

• Extraction mode. 

• Parallel mode. 

• Condensing mode. 

• Desalination mode. 

• Twin desalination mode. 

• Twin extraction mode. 

The four input variables must be consistent with the selected operating mode, anyway 

the program will inform you which variable is out of the range specified for each 

operating mode. 

The simulation results of both processes are also presented in several windows, and 

are resumed here: 

• Relevant parameters corresponding to the whole plant and to different 

components (fuel consumption, performance ratio, plant efficiency, specific 

consumption, steam consumption, etc). 

• Thermophysical properties of the mass flowstreams considered in the simulation 

(the flowstreams are numbered in figures 5.1 and 5.2 respectively). In the power 

plant process the values of the gland steam leakage system are also available (see 

section 4.3.10 for specifications). The properties are: 

– 

– 

– 

– 

– 

– 

Temperature. 

Pressure. 

Mass flow rate. 

Steam quality. 

Specific enthalpy. 

Specific entropy. 

1. Taking into account for the two extraction units (E1, E2) —see figure 4.1— with the same thermodynamic 

properties. 


FIGURE 5.2 

SIMTAW structure 

SIMTAW power plant window. 

– 

– 

– 

– 

– 

Specific exergy (thermal, mechanical and chemical contributions). 

Dynamic viscosity. 

Thermal conductivity. 

Specific heat. 

Density. 

• Some charts of different variables plotted by using a graphic server in SIMTAW: 

temperature profiles in the MSF stages, distillation per stage, expansion line of 

the steam turbine. 

• The exergy costs of the main components of the power plant and water are shown 

in a window, if the fuel cost is introduced (in dollars per unit of energy) the 

exergoeconomic costs are also included. 

All these results can be saved in a text file than can be accessed by conventional 

applications (MS Office). The file also includes the input values and some interesting 

design values introduced in the simulator (tube characteristics and fouling factor in 


103

Simulator 

distillers in the MSF plant, for example), and the exergy cost of the products of each 

component, following the productive structure that will be explained in Chapter 7. 

5.2 Model validation 

The simulator should predict the most important values of the main flowstreams of 

the power and desalination plant with an accuracy that allows reproducing the 

operating conditions of the plant without using a data flowsheet for each situation. 

The accuracy of the simulator is tested with the data flowsheets provided by the plant 

managers, also called model validation of the simulator. Furthermore, when the data 

acquisition system of a plant is not enough to provide the data necessary for the 

diagnosis of the plant, a good simulator could substitute the acquisition system. 

The model validation is separately applied to the power and desalination plant, note 

that the way to calculate the thermodynamic properties in the design flowsheets is 

unknown, therefore an indeterminate error is structurally included in the comparative 

analysis (or model validation). 

Only a few values calculated in the simulator are also available in the data acquisition 

system of the power plant (this does not means that there are more signals than the 

system can measure, but that the recording system is limited by the plant managers): 

temperature and pressure of some turbine extractions, live steam conditions and 

feedwater temperature in some heaters. Furthermore, the live steam properties are not 

maintained under operating conditions, and the data collected is every four hours. 

Consequently, no adjustment has been made to the simulator in order to achieve a 

more realistic set of values of the main flowstreams of the power plant. 

The data acquisition system of the MSF plant only provides a few data of the main 

controlling variables of the process every four hours (temperatures and flow rates 

entering and leaving the heater, recovery and reject section, and the internal 

parameters mentioned above). Therefore no comparison is included between the real 

data and the results obtained when the simulator operates with the ‘ Sim. with real 

data’ 

option, that is, using the correlated internal parameters based on real 

experience. 

5.2.1 Power plant 

Most of the performance data cases are simulated and compared with the data 

provided by the plant contractors (ABB, 1996b). The first table of each comparative 

study shows (in different rows) the inputs of the simulation (output power W, steam to 

MSF unit Md, condenser pressure Pc and Live steam extraction LS); note that the 

output power is not exactly the same as that proposed by the contractors. This is 


Model validation 

because the input power value inserted in the simulator window is only a first step to 

calculate the main steam flow to the boiler. Therefore, the output results try to find out 

the minimum difference in both live steam mass flow and the final output power for 

each performance case. The feed pump consumption is also included in this table 

(W FP). The third row shows the relative error observed in the input process. 

The second table shows in its first part the pressure p, temperature T and mass flow 

rate m of the main flowstreams of the power plant. The second part includes the 

values ( p′ , T′ and m′ 

) obtained by the simulator. Finally, the third part introduces 

the relative error of each property of the flowstreams ( εp, 

εT, 

εm). 

Each flow is 

numbered according to the scheme followed in figure 5.2. The meaning of each 

performance data case is described in section 4.6. Only the values that are provided 

by the contractors have been compared in the table. 

Analyzing the model results, when the steam to LP turbine is not close to zero, that is, 

in performance data cases which represent partial or full load in extraction or twin 

extraction mode (MCR, MR, VWO, COC, PL115, PL85 performance data cases), the 

highest relative error is detected in the LP extraction (< 3% in any case), but the 

absolute difference between the simulator and data flowsheet is minimum. 

However, when the NTW mathematical model is applied, i.e. a minimum amount of 

steam passes through the LP turbine (this situation correspond to MSL3 and MSL4 

cases, the last one is the most usual in winter operation in the Gulf Area, when the 

water demand is always high but the energy consumption decrease to the 30% of the 

plant capacity), the relative error could reach to a 10% in the LP extraction and the 

steam derived to the condenser, although in those limit cases the absolute difference 

detected is very low. It is clear that the mathematical model applied when the steam 

to LP turbine is close to zero (NTW model) is more unstable than other 

mathematical models applied when some amount of steam passes through the LP 

turbine (LTW model). 


105

TABLE 5.1 

TABLE 5.2 

Simulator 

5.2.1.1 MCR case 

Input variables for the MCR (maximum continous rating, producing both electricity and water) 

case. 

W (MW) W FP (kW) Md (kg/s) Pc (bar) LS (Gcal/h) 

Design 122 2308 89.68 0.072 0 

Simulation 122.75 2262.4 89.68 0.072 0 

Rel. error (%) 0.611 –2.016 0.000 0.000 0.000 

Model validation for the MCR case. 

No. p (bar) T (ºC) m (kg/s) p' 

(bar) T' 

(ºC) m' 

(kg/s) 

εp 

(%) 

εT 

(%) 


εm 

(%) 

1 93 535 156.187 93 535 156.09 0.00 0.00 0.06 

3 28.46 365.4 10.839 28.39 363.5 10.8 0.25 0.52 0.36 

4 14.79 282.1 8.303 14.73 278.1 8.24 0.41 1.42 0.76 

5 7.235 203.2 10.989 7.213 198.6 10.94 0.30 2.26 0.45 

6 2.76 130.7 3.321 2.76 130.7 3.32 0.00 0.00 0.03 

8 0.482 80.4 2.278 0.482 80.4 2.21 0.00 0.00 2.99 

9 0.072 39.5 29.631 0.072 39.5 29.75 0.00 0.00 –0.40 

11 39.6 36.545 39.8 36.59 –0.51 –0.12 

12 41 36.545 41.2 36.59 –0.49 –0.12 

24 5.599 5.53 1.23 

14 78.2 36.545 78.2 36.59 0.00 –0.12 

23 84.2 3.321 84.4 3.32 –0.24 0.03 

15 128.2 36.545 128.3 36.59 –0.08 –0.12 

16 162.9 156.355 162.8 156.25 0.06 0.07 

18 164.8 156.187 164.7 156.09 0.06 0.06 

22 168.8 19.142 168.7 19.04 0.06 0.53 

19 194.6 156.187 194.4 156.09 0.10 0.06 

21 198.6 10.839 198.4 10.8 0.10 0.36 

20 230.1 156.187 230 156.09 0.04 0.06 

30 27.18 10.839 27.106 10.8 0.27 0.36 

31 14.12 8.303 14.08 8.24 0.28 0.76 

32 6.655 10.989 6.634 10.94 0.32 0.45 

33 2.677 3.321 2.677 3.32 0.00 0.03 

34 0.467 2.278 0.467 2.21 0.00 2.99

TABLE 5.3 

TABLE 5.4 


5.2.1.2 MR case 

Input variables for the MR (maximum rating, producing only electricity) performance case. 


Design 146.693 2,274 0 0,135 0 

Simulation 146.73 2,331.4 0 0.135 0 

Rel. error (%) –0.025 –2.524 0.000 0.000 0.000 

Model validation for the MR case. 


(bar) T' 

(ºC) m' 

(kg/s) 

εp 

(%) 

εT 

(%) 


εm 

(%) 

1 93 535 156.187 93 535 156.2 0.00 0.00 –0.01 

3 30.58 374.5 9.254 30.52 374 9.22 0.20 0.13 0.37 

4 17.7 302.8 5.492 17.61 298.6 5.49 0.51 1.39 0.04 

5 11.23 248.9 6.012 11.17 243.3 5.92 0.53 2.25 1.53 

6 8.232 218.8 13.291 8.232 213.6 13.35 0.00 2.38 –0.44 

8 1.913 118.8 11.778 1.916 118.9 11.65 –0.16 –0.08 1.09 

9 0.135 51.9 110.043 0.135 51.8 110.26 0.00 0.19 –0.20 

11 52 135.429 52 135.58 0.00 –0.11 

12 53.6 135.429 53.5 135.58 0.19 –0.11 

24 25.069 25 0.28 

14 108 135.429 107.6 135.58 0.37 –0.11 

23 118 13.291 117.8 13.35 0.17 –0.44 

15 162.4 135.429 162.3 135.58 0.06 –0.11 

16 184.5 156.187 184.2 156.2 0.16 –0.01 

18 186.6 156.187 186.3 156.2 0.16 –0.01 

22 190.6 14.476 190.2 14.7 0.21 –1.55 

19 205.3 156.187 205.1 156.2 0.10 -0.01 

21 209.3 9.254 209 9.22 0.14 0.37 

20 235 156.187 234.8 156.2 0.09 -0.01 

30 29.71 9.254 29.62 9.22 0.30 0.37 

31 17.45 5.492 17.349 5.49 0.58 0.04 

32 11.11 6.012 11.038 5.92 0.65 1.53 

33 7.676 13.291 7.674 13.35 0.03 -0.44 

34 1.799 11.778 1.78 11.65 1.06 1.09 

107

TABLE 5.5 

TABLE 5.6 

Simulator 

5.2.1.3 PL115 case 

Input variables for the PL115 performance case (partial load with 115 MW of electricity and a 

heat extraction to MSF of 145 Gcal/h). 


Design 122 2162 75.96 0.065 0 

Simulation 122.12 2063.1 75.96 0.065 0 

Rel. Error (%) –0.098 4.574 0.000 0.000 0.000 

Model validation for the PL115 performance data case. 


(bar) T' 

(ºC) m' 

(kg/s) 

1 

3 

4 

5 

6 

8 

9 

11 

12 

24 

14 

23 

15 

16 

18 

22 

19 

21 

20 

30 

31 

32 

33 

34 

εp 

(%) 

εT 

(%) 


εm 

(%) 

93 535 148.923 93 535 148.11 0.00 0.00 0.55 

26.99 360.5 10.252 26.791 358.4 10.17 0.74 0.58 0.80 

13.97 277.4 8.03 13.848 273.2 8.07 0.87 1.51 –0.50 

6.749 198 10.897 6.705 193.3 10.59 0.65 2.37 2.82 

2.39 126 3.317 2.39 126 3.29 0.00 0.00 0.81 

0.588 85.4 3.237 0.587 85.4 3.13 0.17 0.00 3.31 

0.065 37.5 36.083 0.065 37.7 35.75 0.00 –0.53 0.92 

37.6 43.949 37.7 43.48 –0.27 1.07 

38.8 43.949 37.7 43.48 2.84 1.07 

6.553 6.51 0.66 

82.2 43.949 82.2 43.48 0.00 1.07 

88.7 3.317 88.9 3.29 –0.23 0.81 

123.2 43.949 123.4 43.48 –0.16 1.07 

159.7 149.087 158.9 148.27 0.50 0.55 

161.6 148.923 160.6 148.11 0.62 0.55 

165.5 18.282 164.5 18.24 0.60 0.23 

191.9 148.923 191.4 148.11 0.26 0.55 

195.8 10.252 195.3 10.17 0.26 0.80 

227.3 148.923 226.9 148.11 0.18 0.55 

25.79 10.252 25.598 10.17 0.74 0.80 

13.32 8.03 13.188 8.07 0.99 –0.50 

6.141 10.897 6.135 10.59 0.10 2.82 

2.295 3.317 2.299 3.29 –0.17 0.81 

0.563 3.237 0.562 3.13 0.18 3.31

TABLE 5.7 

TABLE 5.8 


5.2.1.4 PL85 case 

Input variables for the PL85 performance case (partial load with 85 MW of electricity and 145 

Gcal/h of extraction heat flow). 


Design 91 1,649 75.62 0.055 0 

Simulation 91.24 1,540.4 75.62 0.05 0 

Rel. error (%) –0.264 6.586 0.000 0.000 0.000 

Model validation for the PL85 performance case. 


(bar) T' 

(ºC) m' (kg/s) εp (%) εT (%) εm (%) 

1 93 535 117.391 93 535 117.03 0.00 0.00 0.31 

3 21.15 340.7 7.331 21.064 340.4 7.29 0.41 0.09 0.56 

4 11.1 261.7 5.719 11.036 259.2 5 .83 0.58 0.96 –1.94 

5 5.56 187.7 7.875 5.538 184.6 7.68 0.40 1.65 2.48 

6 2.39 126 2.21 2.39 126 2.18 0.00 0.00 1.36 

8 0.261 66 0.993 0.262 66.1 0.95 –0.38 –0.15 4.33 

9 0.055 34.6 16.478 0.055 34.6 16.63 0.00 0.00 –0.92 

11 34.6 20.993 34.7 20.76 –0.29 1.11 

12 37 20.993 37.1 20.76 –0.27 1.11 

24 3.203 3.12 2.59 

14 65 20.993 65 20.76 0.00 1.11 

23 69.7 2.21 70.1 2.18 -0.57 1.36 

15 124.4 20.993 124.5 20.76 -0.08 1.11 

16 153.2 117.539 152.5 117.18 0.46 0.31 

18 155 117.391 154.1 117.03 0.58 0.31 

22 158.5 13.051 157.6 13.12 0.57 -0.53 

19 182.4 117.391 182.3 117.03 0.05 0.31 

21 185.9 7.331 185.8 7.29 0.05 0.56 

20 215 117.391 215 117.03 0.00 0.31 

30 20.39 7.331 20.31 7.29 0.39 0.56 

31 10.7 5.719 10.62 5.83 0.75 –1.94 

32 5.186 7.875 5.185 7.68 0.02 2.48 

33 2.348 2.21 2.347 2.18 0.04 1.36 

34 0.257 0.993 0.258 0.95 –0.39 4.33 


109

Simulator 

5.2.1.5 MSL2 case 

TABLE 5.9 MSL2 performance case (minimum stable load with 45 MW of electricity and a combined heat 

extraction flow of 145 Gcal/h). Main input data. 


Design 51 1,305 60.4 0.048 26.34 

Simulation 51.57 1,250.7 60.4 0.048 26.34 

Rel. error (%) –1.118 4.161 0.000 0.000 0.000 

TABLE 5.10 Model validation for the MSL2 performance case. 

No. p (bar) T (ºC) m (kg/s) p' (bar) T' (ºC) m' (kg/s) εp (%) εT (%) εm (%) 

1 93 535 86.5 93 535 86.49 0.00 0.00 0.01 

3 13.75 324.9 4.477 13.714 322.9 4.49 0.26 0.62 –0.29 

4 7.442 251.2 3.355 7.411 247.4 3.38 0.42 1.51 –0.75 

5 4.074 186.8 4.971 4.061 182.6 4.89 0.32 2.25 1.63 

6 2.39 137.9 0.454 2.39 135.8 0.46 0.00 1.52 –1.32 

8 0.054 34.4 0 0.055 34.7 0 –1.85 –0.87 0.00 

9 0.048 80 1.751 0.048 80 1.75 0.00 0.00 0.06 

11 32.4 3.466 32.2 3.55 0.62 –2.42 

12 46.9 3.466 47.4 3.52 –1.07 –1.56 

24 0.454 0.46 –1.32 

14 47.3 3.466 47.7 3.52 –0.85 –1.56 

23 49.6 0.454 50.2 0.46 –1.21 –1.32 

15 125.7 3.466 125.7 3.52 0.00 –1.56 

16 142.4 90.218 142 90.19 0.28 0.03 

18 144.3 86.5 143.7 86.49 0.42 0.01 

22 147.4 7.832 146.7 7.87 0.47 –0.49 

19 166.4 86.5 166.1 86.49 0.18 0.01 

21 169.5 4.477 169.2 4.49 0.18 –0.29 

20 194.5 86.5 194.4 86.49 0.05 0.01 

30 13.32 4.477 13.288 4.49 0.24 –0.29 

31 7.235 3.355 7.206 3.38 0.40 –0.75 

32 3.871 4.971 3.864 4.89 0.18 1.63 

33 2.388 0.454 2.387 0.46 0.04 –1.32 

34 0.108 0 0.055a 0 49.07 0.00 

a. Note that the simulator does not suppose a pressure loss in the 5 th extraction if any vapor is extracted. 



5.2.1.6 MSL3 case 

TABLE 5.11 Input data of the MSL3 performance case (minimum stable load with two extractions of 150 and 

145 Gcal/h to MSF units). 


Design 72.44 2,975 75.13 0.048 150 

Simulation 73.6 3,122.2 75.2 0.048 150 

Rel. error (%) –1.601 –4.948 –0.093 0.000 0.000 

TABLE 5.12 Model validation for the MSL3 performance case. 


1 93 535 163 93 535 163.1 0.00 0.00 –0.06 

3 18.22 333 9.851 18.176 329.8 9.94 0.24 0.96 –0.90 

4 9.344 252.4 7.883 9.314 247.4 7.69 0.32 1.98 2.45 

5 4.891 179.6 10.272 4.687 174.6 10.02 4.17 2.78 2.45 

6 2.39 126 0.461 2.39 126 0.5 0.00 0.00 –8.46 

8 0.054 34.3 0 0.055 34.7 0 –1.85 –1.17 0.00 

9 0.048 80 1.727 0.048 80 1.91 0.00 0.00 –10.60 

11 32.4 3.462 32.2 3.75 0.62 –8.32 

12 47 3.462 46.4 3.72 1.28 –7.45 

24 0.461 0.5 –8.46 

14 47.3 3.462 46.7 3.72 1.27 –7.45 

23 49.6 0.461 49.3 0.5 0.60 –8.46 

15 125.7 3.462 125.7 3.72 0.00 –7.45 

16 142.8 183.567 142 183.61 0.56 –0.02 

18 144.6 163 144.2 163.1 0.28 –0.06 

22 148.7 17.514 148.4 17.63 0.20 –0.66 

19 171.6 163 171.3 163.1 0.17 –0.06 

21 175.6 9.851 175.5 9.94 0.06 –0.90 

20 204 163 204.1 163.1 –0.05 –0.06 

30 16.6 9.851 16.62 9.94 –0.12 –0.90 

31 8.465 7.663 8.505 7.69 –0.47 –0.35 

32 3.907 10.272 4.026 10.02 –3.05 2.45 

33 2.388 0.461 2.387 0.5 0.04 –8.46 

34 0.108 0 0.055a 0 49.07 0.00 

a. The same argumentation of the MSL2 case. 


Simulator 

5.2.1.7 MSL4 case 

TABLE 5.13 Input data of the MSL4 performance case (minimum stable load with the maximum heat flow 

extraction to MSF unit: 170 Gcal/h). 


Design 75.52 1,543 88.63 0.021 0 

Simulation 76.36 1,501.5 88.63 0.021 0 

Rel. error (%) –1.112 2.690 0.000 0.000 0.000 

TABLE 5.14 MSL4 performance case. Model validation. 


1 93 535 109.5 93 535 109.64 0.00 0.00 –0.13 

3 19.87 340.3 6.537 19.821 338.1 6.55 0.25 0.65 –0.20 

4 10.58 262.9 4.956 10.534 258.9 5.04 0.43 1.52 –1.69 

5 5.514 192.5 6.789 5.495 188.1 6.68 0.34 2.29 1.61 

6 2.76 130.7 0.424 2.76 131.1 0.45 0.00 –0.31 –6.13 

8 0.025 20.9 0 0.024 20.5 0 4.00 1.91 0.00 

9 0.021 80 1.004 0.021 79.8 1.14 0.00 0.25 –13.55 

11 18.3 2.743 18.3 2.92 0.00 –6.45 

12 36.7 2.743 36.6 2.92 0.27 –6.45 

24 0.424 0.45 –6.13 

14 37.1 2.736 36.9 2.9 0.54 –5.99 

23 39.2 0.424 39.1 0.45 0.26 –6.13 

15 130.5 2.736 130.5 2.9 0.00 –5.99 

16 153.6 109.649 153 109.79 0.39 –0.13 

18 155.3 109.5 154.7 109.64 0.39 –0.13 

22 158.8 11.493 158.2 11.58 0.38 –0.76 

19 180.8 109.5 180.7 109.64 0.06 –0.13 

21 184.2 6.537 184.1 6.55 0.05 –0.20 

20 212.2 109.5 212.2 109.6 0.00 –0.09 

30 19.23 6.537 19.176 6.55 0.28 –0.20 

31 10.26 4.956 10.207 5.04 0.52 –1.69 

32 5.233 6.789 5.22 6.68 0.25 1.61 

33 2.759 0.424 2.758 0.45 0.04 –6.13 

34 0.063 0 0.024a 0 61.90 0.00 

a. No pressure losses are associated to the final extraction 



5.2.1.8 ODOB case 

TABLE 5.15 Main input data of the ODOB case (one desalination-one boiler). 


Design 0 ? 88.45 0 170 

Simulation 0 1,222.6 88.45 0 170 

Rel. error (%) 0.000 ? 0.000 0.000 0.000 

TABLE 5.16 Model validation of the ODOB case. 


1 93 535 70.383 93 535 70.38 0.00 0.00 0.00 

3 0 0 0 0 0 0 

4 0 0 0 0 0 0 

5 0 0 0 0 0 0 

6 0 0 0 0 0 0 

8 0 0 0 0 0 0 

9 0 0 0 0 0 0 

11 0 0 0 0 

12 0 0 0 0 

24 0 0 

14 0 0 0 0 

23 0 0 0 0 

15 0 0 0 0 

16 138.9 93.841 138.9 94.94 0.00 –1.17 

18 140.7 70.383 140.5 70.38 0.14 0.00 

22 0 0 0 0 

19 140.7 70.383 140.5 70.38 0.14 0.00 

21 0 0 0 0 

20 140.7 70.383 140.5 70.38 0.14 0.00 

30 0 0 0 0 

31 0 0 0 0 

32 0 0 0 0 

33 0 0 0 0 

34 0 0 0 0 


Simulator 

5.2.1.9 TDOB case 

TABLE 5.17 Main input data of the TDOB case (two desalination-one boiler). 


Design 0 ? 140.766 0 340 

Simulation 0 764.8 140.76 0 340 

Rel. error (%) 0.000 ? 0.004 0.000 0.000 

TABLE 5.18 Model validation data for the TDOB case. 


1 93 535 140.766 93 535 140.76 0.00 0.00 0.00 

3 0 0 0 0 0 0 

4 0 0 0 0 0 0 

5 0 0 0 0 0 0 

6 0 0 0 0 0 0 

8 0 0 0 0 0 0 

9 0 0 0 0 0 0 

11 0 0 0 0 

12 0 0 0 0 

24 0 0 

14 0 0 0 0 

23 0 0 0 0 

15 0 0 0 0 

16 138.9 187.682 138.9 187.38 0.00 0.16 

18 140.8 140.766 139.7 140.76 0.78 0.00 

22 0 0 0 0 

19 140.8 140.766 139.7 140.76 0.78 0.00 

21 0 0 0 0 

20 140.8 140.766 139.7 140.76 0.78 0.00 

30 0 0 0 0 

31 0 0 0 0 

32 0 0 0 0 

33 0 0 0 0 

34 0 0 0 0 



5.2.1.10 VWO case 

TABLE 5.19 Main input data of the VWO performance case (maximum capacity of the steam turbine with and 

extraction heat flow of 170 Gcal/h to MSF). 


Design 126.587 2,412 89.69 0.074 0 

Simulation 126.78 2,425.9 89.68 0.074 0 

Rel. error (%) –0.152 –0.576 0.011 0.000 0.000 

TABLE 5.20 Model validation data for the VWO case. 


1 93 535 161.038 93 535 160.21 0.00 0.00 0.51 

3 29.36 368.1 11.317 29.158 365.4 11.17 0.69 0.73 1.30 

4 15.23 284.3 8.665 15.11 279.6 8.59 0.79 1.65 0.87 

5 7.419 204.7 11.473 7.368 199.5 11.33 0.69 2.54 1.25 

6 2.759 130.7 3.485 2.76 130.7 3.44 –0.04 0.00 1.29 

8 0.533 82.9 2.623 0.528 82.7 2.4 0.94 0.24 8.50 

9 0.074 40 32.64 0.074 40.1 32.44 0.00 –0.25 0.61 

11 40.1 40.064 40.1 39.63 0.00 1.08 

12 41.3 40.064 42.2 39.6 –2.18 1.16 

24 6.109 5.85 4.24 

14 80.4 40.064 80.3 39.6 0.12 1.16 

23 86.6 3.485 86.8 3.44 –0.23 1.29 

15 128 40.064 128.1 39.6 –0.08 1.16 

16 163.8 161.209 163.5 160.38 0.18 0.51 

18 165.7 161.038 165.5 160.21 0.12 0.51 

22 169.7 19.982 169.5 19.76 0.12 1.11 

19 195.8 161.038 195.6 160.21 0.10 0.51 

21 199.9 11.317 199.6 11.17 0.15 1.30 

20 231.8 161.038 231.4 160.21 0.17 0.51 

30 28.01 11.317 27.817 11.17 0.69 1.30 

31 14.53 8.665 14.41 8.59 0.83 0.87 

32 6.8 11.473 6.758 11.33 0.62 1.25 

33 2.667 3.485 2.671 3.44 –0.15 1.29 

34 0.515 2.623 0.512 2.4 0.58 8.50 


Simulator 

5.2.1.11 COC case 

TABLE 5.21 Input data of the COC performance case (boiler peak load at least 5% more than the MCR case). 


Design 124.41 3,103 89.72 0.072 50.8 

Simulation 124.65 3,350 89.72 0.072 50.8 

Rel. error (%) –0.193 –7.960 0.000 0.000 0.000 

TABLE 5.22 Model validation data for the COC case. 


1 93 535 180.556 93 535 179.58 0.00 0.00 0.54 

3 29.02 366.9 12.704 28.77 363.7 12.6 0.86 0.87 0.82 

4 14.93 282.3 9.723 14.786 277 9.7 0.96 1.88 0.24 

5 7.219 202.2 12.96 7.17 196.8 12.55 0.68 2.67 3.16 

6 2.76 130.7 3.314 2.76 130.7 3.29 0.00 0.00 0.72 

8 0.479 80.3 2.258 0.471 79.9 2.17 1.67 0.50 3.90 

9 0.072 39.5 29.449 0.072 39.5 29.14 0.00 0.00 1.05 

11 39.6 36.335 39.6 35.92 0.00 1.14 

12 41 36.335 40.7 35.92 0.73 1.14 

24 5.572 5.46 2.01 

14 78.1 36.335 77.7 35.92 0.51 1.14 

23 84 3.314 83.9 3.29 0.12 0.72 

15 128.2 36.335 128.3 35.92 –0.08 1.14 

16 161.4 187.942 160.3 186.94 0.68 0.53 

18 163.5 180.556 162.8 179.58 0.43 0.54 

22 167.7 22.427 167 22.3 0.42 0.57 

19 193.8 180.556 193.3 179.58 0.26 0.54 

21 198 12.704 197.5 12.6 0.25 0.82 

20 230 180.556 229.6 179.58 0.17 0.54 

30 27.28 12.704 27.06 12.6 0.81 0.82 

31 14.02 9.723 13.888 9.7 0.94 0.24 

32 6.398 12.96 6.415 12.55 –0.27 3.16 

33 2.677 3.314 2.678 3.29 –0.04 0.72 

34 0.464 2.258 0.457 2.17 1.51 3.90 



5.2.2 MSF Plant 

Distiller design data in the most characteristic operating conditions have been 

provided by the plant manufacturers (Italimpianti, 1997). Only a few cases contain 

the temperature profile of the three flows inside each stage of the distiller. They 

correspond to the guarantied conditions of the contractors: 

• Nominal production in summer (normal-temperature operation in summer, 

NTOS): 1,900 T/h of freshwater produced (or a TBT of 100 ºC) and a seawater 

temperature of 32 ºC. 

• Maximum production in summer (high-temperature operation in summer, 

HTOS): distillation of 2,258 T/h (112 ºC TBT) with a seawater entering at 32 ºC. 

• Minimum production in summer (low-temperature operation in summer, LTOS): 

distillation of 1,232 T/h (84 ºC TBT), seawater enters at 32 ºC. 

• Maximum production in winter (high-temperature operation in winter, HTOW): 

distillation of 2,400 T/h (112 ºC TBT) with a seawater entering at 18 ºC. Seawater 

to reject section enters at 25 ºC by using the temper system by the way of 

deviating a quantity of cooling seawater rejected to the sea. 

The first table of each comparative study shows some inputs of design data and 

simulation in the first and second rows respectively (seawater intake flow SW and 

temperature T sea). Some other inputs (steam to heater conditions, seawater intake 

temperature) needed for the simulator are not included because they must be the same 

quantity as the proposed design value. The distillate produced in the two cases is 

maintained in the same quantity too. Other operating parameters that are obtained in 

the simulation are also compared in the table: seawater to reject and recycle brine 

flows (SR and R), Top Brine Temperature (TBT), Performance Ratio (PR) and steam 

consumption (m ST). The third row shows the relative error observed in the table, the 

highest error is in the steam consumed. This error can be due to the absence of a 

desuperheater before the brine heater in the mathematical model applied to the MSF 

distillers, and the error introduced when the steam properties (the latent heat of 

vaporization) below two different perspectives are calculated. 

The second table shows in its first part the chamber pressure p, temperature profile 

(cooling brine TF, distillate TD and flashing brine TB) and distillate flow rate (D) of 

each stage of the MSF plant. The second part includes the values ( p′ , TF′ , TD′ , TB′ and D′ 

) obtained by the simulator. Finally, the third part introduces the relative error 

of the stage values (εp, εTF, εTD, εTB, εD). Each stage is numbered according to the 

scheme followed in figure 5.1. 


Simulator 

In Gulf Area the water demand in summer is the 100% of the plant capacity, and 

covers the 80% in winter. So, the most realistic performance data cases are (in this 

order) HTOS and HTOW. The error analysis is going to be underlined in these two 

cases. 

The main error source in HTOS case is detected in the pressure of the reject stages 

and the last stage of the recovery section (a maximum of 9% of relative error). The 

contractors for absolute pressure of the MSF chambers give an accuracy of two 

decimals, therefore the error associated to the numeric presentation could be 

important. The correlation to calculate the absolute pressure of a flash chamber also 

should improve the error detected in those values. 

The distillate produced in the first stages of the recovery section has a maximum 

relative error of 5%. This error is due to the correlations for calculating both brine and 

steam properties and the global heat transfer coefficient of each condenser. The 

temperatures of the three main flows of each distiller do not exceed in any case a 

relative error of 1.5%. 



5.2.2.1 NTOS case 

TABLE 5.23 Input data and performance parameters of the NTOS case (normal-temperature operation in 

summer). 

SW (T/h) SR (T/h) R (T/h) TBT (ºC) m ST (T/h) PR T sea (ºC) 

Design 19,900 17,700 19,650 100 239.6 8 32 

Simulator 19,965 17,396.8 19,584.5 100.4 247.9 7.85 32 

Rel. Error (%) –0.33 1.71 0.33 –0.40 –3.46 1.88 0.00 

TABLE 5.24 Model validation of the NTOS performance case. 

Stage 

p 

(bar) 

T F 

(ºC) 

T D 

(ºC) 

T B 

(ºC) 

D 

(T/h) 

p’ 

(bar) 

T F’ 

(ºC) 

T D’ 

(ºC) 

T B’ 

(ºC) 

D’ 

(T/h) 

1 0.87 93.1 95.7 96.7 109 0.883 93.3 96.2 97.1 114.2 –1.49 –0.21 –0.52 –0.41 –4.77 

2 0.77 90 92.5 93.5 219 0.781 89.9 92.9 93.8 226.3 –1.43 0.11 –0.43 –0.32 –3.33 

3 0.68 86.7 89.3 90.2 328 0.688 86.6 89.5 90.4 338.9 –1.18 0.12 –0.22 –0.22 –3.32 

4 0.59 83.5 86 86.9 437 0.605 83.3 86.2 87.1 449.4 –2.54 0.24 –0.23 –0.23 –2.84 

5 0.52 80.1 82.7 83.6 545 0.531 80 82.8 83.7 557.9 –2.12 0.12 –0.12 –0.12 –2.37 

6 0.46 76.8 79.4 80.3 652 0.465 76.7 79.5 80.5 664.3 –1.09 0.13 –0.13 –0.25 –1.89 

7 0.4 73.5 76.1 77 757 0.407 73.4 76.3 77.2 768.7 –1.75 0.14 –0.26 –0.26 –1.55 

8 0.35 70.2 72.8 73.8 861 0.355 70.2 73 74 871 –1.43 0.00 –0.27 –0.27 –1.16 

9 0.3 67 69.5 70.5 963 0.309 67 69.8 70.8 971.4 –3.00 0.00 –0.43 –0.43 –0.87 

10 0.26 63.7 66.3 67.3 1064 0.269 63.8 66.6 67.6 1069.7 –3.46 –0.16 –0.45 –0.45 –0.54 

11 0.22 60.4 63 64 1160 0.234 60.6 63.5 64.5 1165.9 –6.36 –0.33 –0.79 –0.78 –0.51 

12 0.19 57.3 59.9 60.9 1255 0.203 57.5 60.4 61.4 1260.4 –6.84 –0.35 –0.83 –0.82 –0.43 

13 0.17 54.2 56.8 57.8 1347 0.175 54.4 57.3 58.3 1352.6 –2.94 –0.37 –0.88 –0.87 –0.42 

14 0.14 51.1 53.7 54.8 1437 0.152 51.4 54.2 55.3 1442.6 –8.57 –0.59 –0.93 –0.91 –0.39 

15 0.12 48 50.7 51.8 1527 0.131 48.4 51.2 52.3 1530.3 –9.17 –0.83 –0.99 –0.97 –0.22 

16 0.105 45 47.7 48.8 1614 0.113 45.4 48.3 49.4 1615.4 –7.62 –0.89 –1.26 –1.23 –0.09 

17 0.09 42.1 44.7 45.9 1698 0.097 42.5 45.4 46.6 1698 –7.78 –0.95 –1.57 –1.53 0.00 

18 0.08 39.5 42.5 43.7 1761 0.086 39.6 43 44.4 1763.5 –7.50 –0.25 –1.18 –1.60 –0.14 

19 0.07 37.1 40.2 41.5 1826 0.076 37.1 40.6 42.1 1829.7 –8.57 0.00 –1.00 –1.45 –0.20 

20 0.06 34.7 37.9 39.2 1896 0.067 34.6 38.2 39.7 1896.2 –11.67 0.29 –0.79 –1.28 –0.01 


εP 

(%) 

εT F 

(%) 

εT D 

(%) 

εT B 

(%) 

εD 

(%)

Simulator 

5.2.2.2 HTOS case 

TABLE 5.25 Input data and performance parameters of the HTOS case (high-temperature operation in 

summer). 


Design 19,900 17,700 19,850 112 294.1 8 32 

Simulator 19,975 17,509.1 19,850 112.3 301.3 7.86 32 

Rel. Error (%) –0.38 1.08 0.00 –0.27 –2.45 1.75 0.00 

TABLE 5.26 Model validation of the HTOS performance case. 

Stage 

p 

(bar) 

T F 

(ºC) 

T D 

(ºC) 

T B 

(ºC) 

D 

(T/h) 

p’ 

(bar) 

T F’ 

(ºC) 


T D’ 

(ºC) 

T B’ 

(ºC) 

D’ 

(T/h) 

1 1.3 103.8 107.2 108.2 131 1.311 103.9 107.4 108.4 138.5 –0.85 –0.10 –0.19 –0.18 –5.73 

2 1.14 100.2 103.5 104.5 261 1.147 100 103.5 104.5 274.1 –0.61 0.20 0.00 0.00 –5.02 

3 1 96.4 99.7 100.7 390 0.997 96.2 99.5 100.5 409.9 0.30 0.21 0.20 0.20 –5.10 

4 0.87 92.7 95.9 96.9 521 0.865 92.2 95.6 96.6 542.8 0.57 0.54 0.31 0.31 –4.18 

5 0.75 88.8 92 93 649 0.748 88.3 91.7 92.7 672.9 0.27 0.56 0.33 0.32 –3.68 

6 0.65 85 88.2 89.2 776 0.646 84.5 87.9 88.8 800.3 0.62 0.59 0.34 0.45 –3.13 

7 0.56 81.1 84.4 85.3 902 0.556 80.6 84 85 924.9 0.71 0.62 0.47 0.35 –2.54 

8 0.48 77.2 80.5 81.5 1025 0.478 76.8 80.2 81.2 1047 0.42 0.52 0.37 0.37 –2.15 

9 0.41 73.4 76.7 77.7 1146 0.41 73 76.4 77.4 1166.3 0.00 0.54 0.39 0.39 –1.77 

10 0.35 69.6 72.9 73.9 1266 0.35 69.3 72.7 73.7 1283.3 0.00 0.43 0.27 0.27 –1.37 

11 0.3 65.8 69 70 1381 0.299 65.6 69 70 1397.6 0.33 0.30 0.00 0.00 –1.20 

12 0.25 62 65.4 66.4 1493 0.254 61.9 65.3 66.3 1509.7 –1.60 0.16 0.15 0.15 –1.12 

13 0.21 58.4 61.7 62.7 1603 0.215 58.3 61.7 62.7 1619.1 –2.38 0.17 0.00 0.00 –1.00 

14 0.18 54.7 58.1 59.1 1711 0.182 54.7 58.1 59.2 1725.8 –1.11 0.00 0.00 –0.17 –0.86 

15 0.15 51.1 54.5 55.5 1817 0.154 51.1 54.6 55.7 1829.7 –2.67 0.00 –0.18 –0.36 –0.70 

16 0.12 47.5 50.9 52 1920 0.13 47.6 51.1 52.2 1930.7 –8.33 –0.21 –0.39 –0.38 –0.56 

17 0.1 44 47.4 48.5 2021 0.109 44.2 47.6 48.9 2028.6 –9.00 –0.45 –0.42 –0.82 –0.38 

18 0.09 40.5 44.6 45.9 2096 0.095 40.9 44.9 46.2 2104.2 –5.56 –0.99 –0.67 –0.65 –0.39 

19 0.08 38.1 41.9 43.2 2173 0.083 38 42.2 43.6 2180.7 –3.75 0.26 –0.72 –0.93 –0.35 

20 0.07 35.1 39.2 40.5 2258 0.071 35 39.3 40.8 2257.9 –1.43 0.28 –0.26 –0.74 0.00 

εP 

(%) 

εT F 

(%) 

εT D 

(%) 

εT B 

(%) 

εD 

(%)


5.2.2.3 LTOS case 

TABLE 5.27 Some input data and performance parameters of the LTOS case (low-temperature operation in 

summer). 


Design 17,000 14,800 16,450 84 148.1 8.1 32 

Simulator 17,000 14,900.2 16,476.9 84.6 150.5 8.14 32 

Rel. Error (%) –0.00 –0.68 –0.16 –0.71 –1.62 –0.49 0.00 

TABLE 5.28 Model validation. LTOS performance case in MSF distillers. 

Stage 

p 

(bar) 

T F 

(ºC) 

T D 

(ºC) 

T B 

(ºC) 

D 

(T/h) 

p’ 

(bar) 

T F’ 

(ºC) 

T D’ 

(ºC) 

T B’ 

(ºC) 

D’ 

(T/h) 

1 0.475 78.7 80.48 81.4 72 0.495 79.2 81.1 81.9 73.9 –4.21 –0.64 –0.77 –0.61 –2.64 

2 0.428 76.2 77.97 78.9 143 0.445 76.6 78.5 79.3 146.6 –3.97 –0.52 –0.68 –0.51 –2.52 

3 0.385 73.6 75.37 76.3 215 0.399 74 75.8 76.7 219.7 –3.64 –0.54 –0.57 –0.52 –2.19 

4 0.345 71 72.79 73.7 286 0.357 71.3 73.2 74.1 291.5 –3.48 –0.42 –0.56 –0.54 –1.92 

5 0.309 68.4 70.21 71.1 356 0.32 68.7 70.6 71.5 362.2 –3.56 –0.44 –0.56 –0.56 –1.74 

6 0.277 65.9 67.65 68 426 0.286 66.2 68 68.9 431.6 –3.25 –0.46 –0.52 –1.32 –1.31 

7 0.247 63.3 65.08 66 494 0.255 63.6 65.4 66.3 499.7 –3.24 –0.47 –0.49 –0.45 –1.15 

8 0.22 60.7 62.53 63.5 562 0.228 61.1 62.9 63.8 566.6 –3.64 –0.66 –0.59 –0.47 –0.82 

9 0.196 58.2 60.01 61 629 0.203 58.6 60.4 61.3 632.1 –3.57 –0.69 –0.65 –0.49 –0.49 

10 0.175 55.7 57.49 58.4 695 0.181 56.1 57.9 58.9 696.3 –3.43 –0.72 –0.71 –0.86 –0.19 

11 0.154 53.2 54.9 55.8 756 0.161 53.6 55.5 56.4 759.2 –4.55 –0.75 –1.09 –1.08 –0.42 

12 0.138 50.8 52.56 53.3 816 0.143 51.2 53.1 54.1 820.7 –3.62 –0.79 –1.03 –1.50 –0.58 

13 0.123 48.5 50.23 51.2 876 0.127 48.9 50.7 51.7 880.8 –3.25 –0.82 –0.94 –0.98 –0.55 

14 0.109 46.1 47.91 48.9 934 0.113 46.5 48.3 49.4 939.7 –3.67 –0.87 –0.81 –1.02 –0.61 

15 0.098 43.9 45.64 46.6 992 0.101 44.2 46 47.2 996.1 –3.06 –0.68 –0.79 –1.29 –0.41 

16 0.087 41.6 43.36 44.4 1048 0.09 42 43.7 45 1051.2 –3.45 –0.96 –0.78 –1.35 –0.31 

17 0.077 39.3 41.11 42.2 1104 0.08 39.8 41.5 42.8 1104.3 –3.90 –1.27 –0.95 –1.42 –0.03 

18 0.071 37.1 39.44 40.5 1145 0.072 37.6 39.7 41.1 1146.9 –1.41 –1.35 –0.66 –1.48 –0.17 

19 0.064 35.8 37.71 38.8 1187 0.066 35.8 37.9 39.4 1189.5 –3.13 0.00 –0.50 –1.55 –0.21 

20 0.058 33.9 35.94 37.1 1232 0.059 33.9 36 37.7 1231.9 –1.72 0.00 –0.17 –1.62 0.01 


εP 

(%) 

εT F 

(%) 

εT D 

(%) 

εT B 

(%) 

εD 

(%)

Simulator 

5.2.2.4 HTOW case 

TABLE 5.29 Some input data and performance parameters of the HTOW case (high-temperature operation in 

winter). 


Design 11,231.5 16,400 19,850 112 313.3 8 18 

Simulator 11,231 17,000 19,850 111.4 320.6 7.84 18 

Rel. Error (%) 0.00 –3.66 0.00 0.54 –2.33 2.00 0.00 

TABLE 5.30 Model validation of HTOW case of the MSF plant. 

Stage 

p 

(bar) 

T F 

(ºC) 

T D 

(ºC) 

T B 

(ºC) 

D 

(T/h) 

p’ 

(bar) 

T F’ 

(ºC) 


T D’ 

(ºC) 

T B’ 

(ºC) 

D’ 

(T/h) 

1 1.28 103.2 106.8 107.9 142 1.258 102.4 106.2 107.1 148.5 1.72 0.78 0.56 0.74 –4.58 

2 1.12 99.3 102.8 103.8 284 1.088 98.2 102 103 294.1 2.86 1.11 0.78 0.77 –3.56 

3 0.97 95.2 98.7 99.7 424 0.935 94.1 97.8 98.7 439.6 3.61 1.16 0.91 1.00 –3.68 

4 0.83 91 94.5 95.5 565 0.801 89.8 93.5 94.5 581.9 3.49 1.32 1.06 1.05 –2.99 

5 0.71 86.9 90.3 91.3 703 0.684 85.7 89.4 90.3 721 3.66 1.38 1.00 1.10 –2.56 

6 0.6 82.7 86.2 87.2 840 0.583 81.5 85.2 86.1 857.1 2.83 1.45 1.16 1.26 –2.04 

7 0.51 78.5 82 83 975 0.495 77.4 81.1 82 990.1 2.94 1.40 1.10 1.20 –1.55 

8 0.43 74.3 77.8 78.8 1107 0.42 73.3 77 78 1120.3 2.33 1.35 1.03 1.02 –1.20 

9 0.36 70.1 73.7 74.7 1237 0.354 69.2 73 73.9 1247.5 1.67 1.28 0.95 1.07 –0.85 

10 0.3 66 69.6 70.6 1365 0.298 65.2 69 69.9 1371.7 0.67 1.21 0.86 0.99 –0.49 

11 0.25 61.8 65.4 66.4 1487 0.25 61.3 65 66 1493.1 0.00 0.81 0.61 0.60 –0.41 

12 0.21 57.8 61.4 62.5 1605 0.21 57.3 61.1 62.1 1611.8 0.00 0.87 0.49 0.64 –0.42 

13 0.17 53.9 57.5 58.6 1721 0.175 53.4 57.2 58.2 1727.5 –2.94 0.93 0.52 0.68 –0.38 

14 0.14 50 53.6 54.8 1833 0.146 49.6 53.4 54.4 1840 –4.29 0.80 0.37 0.73 –0.38 

15 0.12 46.2 49.8 51.1 1943 0.121 45.8 49.6 50.7 1949.2 –0.83 0.87 0.40 0.78 –0.32 

16 0.1 42.4 46.1 47.4 2049 0.1 42.1 45.9 47.1 2055 0.00 0.71 0.43 0.63 –0.29 

17 0.08 38.7 42.3 43.8 2150 0.083 38.5 42.2 43.5 2157 –3.75 0.52 0.24 0.68 –0.33 

18 0.07 35.2 39.5 41.1 2229 0.071 34.9 39.4 40.7 2236.8 –1.43 0.85 0.25 0.97 –0.35 

19 0.06 32.3 36.5 38.2 2310 0.06 31.7 36.4 37.9 2317.9 0.00 1.86 0.27 0.79 –0.34 

20 0.05 28.8 33.6 35.2 2400 0.051 28.4 33.3 34.9 2400 –2.00 1.39 0.89 0.85 0.00 

εP 

(%) 

εT F 

(%) 

εT D 

(%) 

εT B 

(%) 

εD 

(%)

CHAPTER 6 

Thermoeconomics 

Fundamentals, applications of thermoeconomic diagnosis 

and optimization of complex energy systems 

As the human population grows, our finite world is becoming smaller and natural 

resources are more and more scarce. We must conserve them in order to survive and 

Thermoeconomics plays a key role in this endeavor. We should find out how energy 

and resources degrade, which systems work better, how to improve designs to reduce 

consumption and prevent residues from damaging the environment. Thermoeconomics 

and its application to engineering energy systems can help to answer these 

questions. 

The production process of a complex energy system (e.g., a dual-purpose power and 

desalination plant) can be analyzed in terms of its economic profitability and 

efficiency with respect to resource consumption. 

An economic analysis can calculate the cost of fuel, investment, operation and 

maintenance for the whole plant but provides no means to evaluate the single 

processes taking place in the subsystems nor how to distribute the costs among them. 

On the other hand, a thermodynamic analysis calculates the efficiencies of the 

subsystems and locates and quantifies the irreversibilities but cannot evaluate their 

significance in terms of the overall production process. 

Thermoeconomic analysis combines economic and thermodynamic analysis by 

applying the concept of cost (originally an economic property) to exergy (an energetic 

property). Most analysts agree that exergy is the most adequate thermodynamic 

property to associate with cost since it contains information from the second law of 

thermodynamics and accounts for energy quality (Tsatsaronis, 1987, 1998; Gaggioli 

and El-Sayed, 1987; Moran, 1990). Exergetic efficiency compares a real process to a 

reversible one, (i.e. an ideal process of the same type). An exergy analysis locates and 



quantifies irreversibilities in a process. Exergy based thermoeconomic methods are 

also referred to as “exergoeconomics” (Tsatsaronis and Winhold, 1985). 

In his seminal book, The Entropy Law and the Economic Process, 

Nicholas 

Georgescu-Roegen (1971) pointed out that “…the science of thermodynamics began 

as physics of economic value and, basically, can still be regarded as such. The 

Entropy Law itself emerges as the most economic in nature of all natural laws… the 

economic process and the Entropy Law is only an aspect of a more general fact, 

namely, that this law is the basis of the economy of life at all levels…”. 

Hence, the physical magnitude connecting physics (thermodynamics) and economics 

is entropy generation or, more specifically, irreversibility. This represents the “useful” 

or available energy lost or destroyed (exergy destruction) in all physical processes. 

All real processes in a plant are non-reversible and, as a consequence, some exergy is 

destroyed and some natural resources are consumed and lost forever, which creates 

cost. All natural resources have an economic cost: the more irreversible a process, the 

more natural resources are consumed (higher energetic cost) and the higher the 

required investment (higher thermoeconomic cost). If we can measure this 

thermodynamic cost by identifying, locating and quantifying the causes of 

inefficiencies in real processes, we can provide an objective economic basis using the 

cost concept. 

Thus, thermoeconomics assesses the cost of consumed resources, money and system 

irreversibilities in terms of the overall production process. Consumed resource cost 

involves resources destroyed by inefficiencies and helps to point out how resources 

may be used more effectively to save energy. Money costs express the economic 

effect of inefficiencies and are used to improve the cost effectiveness of production 

processes. 

Assessing the cost of the various streams and processes in a plant helps to understand 

the process of cost formation, from the input resource(s) to the final product(s). This 

process can solve problems in complex energy systems that cannot normally be 

solved using conventional energy analysis based on the First Law of Thermodynamics 

(mass and energy balances only), for instance: 

1. Rational price assessment of plant products based on physical criteria. 

2. Optimization of specific component variables to minimize final product costs and 

save resource energy, i.e., global and local optimization. 

3. Detection of inefficiencies and calculation of their economic effects in operating 

plants, i.e., plant operation thermoeconomic diagnosis. 

4. Evaluation of various design alternatives or operation decisions and profitability 

maximization. 

5. Energy audits. 


Specific examples of these applications will be given here and applied to a real dualpurpose 

power and desalination plant. Many reports also provide specific information 

about thermoeconomic applications (Lozano and Valero, 1993; Tsatsaronis, 1994; 

Lozano, Valero and Serra, 1996; Valero et al., 1994; Bejan, Tsatsaronis and Moran 

1997, Valero and Lozano, 1997; Valero, Correas and Serra, 1999; Lozano et al., 1994; 

Frangopoulos, 1987; Von Spakovsky and Evans, 1993; El-Sayed and Tribus, 1983; 

El-Sayed, 1988; Pisa, 1997). 

Thermoeconomic methods can generally be subdivided into two categories 

(Tsatsaronis, 1987), those based on cost accounting (e.g. Exergetic Cost Theory, 

Lozano et al., 1993; Average-Cost-Approach, Bejan et al., 1997; Last-In-First-Out 

Approach; Lazzareto and Tsatsaronis, 1997) and those based on optimization 

techniques (e.g. Thermoeconomic Functional Analysis, Frangopoulos, 1987; 

Engineering Functional Analysis, von Spakovsky and Evans, 1993; Intelligent 

Functional Approach, Frangopoulos, 1990). Cost accounting methods help to 

determine actual product cost and provide a rational basis for pricing, while 

optimization methods are used to find the optimum design or operating conditions. 

Unfortunately, there are almost as many nomenclatures as theories. This causes 

confusion, complicates method comparison and impedes the development of 

Thermoeconomics in general (Tsatsaronis, 1994). The Structural Theory of 

Thermoeconomics (Valero, Serra and Torres, 1992; Valero, Serra and Lozano, 1993) 

provides a general mathematical formulation using a linear model which 

encompasses all thermoeconomic methodologies. The most systematic and 

widespread methodologies (see above) use exergy to linearly apportion costs when 

two or more coproducts appear, and their results can be reproduced using the 

Structural Theory (Erlach, 1998; Erlach, Serra and Valero, 1999). For this reason, all 

concepts and procedures explained here are based on the general and common 

mathematical formalism of the Structural Theory. 

This chapter on the fundamentals of thermoeconomics is divided into three parts. 

First the basic concepts needed to perform and understand the thermoeconomic 

analysis of complex energy systems are presented. Special attention has been paid to 

explaining the thermoeconomic cost concept. Once the average and marginal costs 

are defined, in the second part their meaning, relationship and calculation procedures 

are fully explained with examples. Finally, the third part describes some applications 

of thermoeconomic analysis as applied to operation diagnosis and optimization of 

complex energy systems. 


125

FIGURE 6.1 


6.1 Basic concepts 

All thermoeconomic theories use costs based on the Second Law of thermodynamics 

when solving engineering problems. In this section, the cost concept is explained 

together with all the new basic concepts, including fuel, product and thermoeconomic 

models needed to perform a thermoeconomic analysis of a plant. 

Physical structure of the co-generation plant. 

Compressor 

2 

0 

6.1.1 The concept of cost 

2 

1 

Air 

Gases 

Natural gas 

Work 

Water/Steam 

Combustor 

1 

HRSG 

The cost of a flow in a plant represents the external resources that have to be supplied 

to the overall system to produce this flow. Thermoeconomic analysis distinguishes 

between exergetic costs and monetary costs. 

The exergetic cost of a mass and/or energy flow is the units of exergy used to produce 

it, e.g. the exergetic cost of the net power is the exergy provided by the natural gas to 

generate the electrical power delivered to the net by the cogeneration plant (see figure 

6.1). These costs are a measure of the thermodynamic efficiency of the production 

process generating these flows. The unit exergetic cost of a mass and/or energy flow 

represents the amount of resources required to obtain one unit. Thus, if the unit 

exergetic cost of the electricity is three, three units of plant exergy resources (natural 

gas in the case of the cogeneration plant) are consumed to obtain one exergy unit of 

electrical power. 

The monetary cost takes into account the economic cost of the consumed fuel (i.e., its 

market price) as well as the cost of the installation and the operation of the plant and 

defines the amount of money consumed to generate a mass and/or energy flow. These 

costs are a measure of the economic efficiency of a process. Similarly, the unit 


3 

5 6 

Turbine 

3 

4 

8 

4 

7

Basic concepts 

monetary cost (also called unit exergoeconomic cost or unit thermoeconomic cost) 

of a 

mass and/or energy flow is the amount of monetary units required to obtain one unit. 

We can further distinguish between average costs, 

which are ratios and express the 

average amount of resources per unit of product, and marginal costs, 

which are a 

derivation and indicate the additional resources required to generate one more unit of 

the product under specified conditions. Mathematically they are defined as: 

unit average cost = ----- 

(6.1) 

⎛ ) 

* ∂B 

⎞ 

o 

unit marginal cost k = ⎜ 

(6.2) 

⎜ 

⎟ 

⎝ ∂B 

⎟ 

i ⎠ 

The average costs are only known after production, when we know how many 

resources were used and the production obtained. The average cost is not predictive. 

Knowing the average unit cost of a product does not provide the cost of a production 

process P + ∆P. 

Thermoeconomic cost accounting theories calculate average costs 

and use them as a basis for a rational price assessment, under physical criteria, of the 

internal flows and the products of the plant. 

Marginal costs can be used to calculate additional fuel consumption when the 

operating conditions are modified. Thermoeconomic optimization methods 

(Frangopoulos, 1997, 1990; Von Spakovsky and Evans, 1993) are based on marginal 

costs when solving optimization problems. 

The relationship between average and marginal costs will be analyzed in more detail 

in section 6.3.1. 

6.1.2 Fuel, product and unit exergetic consumption 

k * 

B0 Bi conditions 

A productive purpose, a certain good or service to be produced, can be defined for 

every plant. In order to generate this product, some resources have to be supplied to 

the plant and are consumed in the process. For example, in the co-generation plant, 

natural gas is supplied to the plant to generate electric power and process steam. 

A productive purpose expressing component function in an overall production 

process can be defined for each component. The productive purpose of a component 

measured in terms of exergy is called product. 

To create this product, another exergy 

flow(s) is consumed. The flow of exergy which is consumed in the component during 

the generation of its product is called fuel (s) . 


127


Real process exergy is destroyed in any process. That is, part of the fuel exergy is 

destroyed during product generation. Using the definitions of fuel and product, the 

exergy balance for a component can be formulated as: 

F = P + I (6.3) 

Therefore, the fuel required to generate a certain amount of a product depends on the 

amount of irreversibility (exergy destroyed). 

The fuel exergy required to generate one exergy unit of product is defined as unit 

exergetic consumption k: 

k 

= 

F 

-- 

P 


(6.4) 

It is a measure of the thermodynamic efficiency of the process and equals one for 

reversible processes and is greater than one for all real processes. The more 

irreversible a process, the higher the value of the unit exergetic consumption. 

Combining equation (6.4) with the exergy balance on a fuel/product basis (Equation 

6.3), the unit exergetic consumption k can also be formulated as: 

I 

k = 1+ 

-- 

P 

(6.5) 

The reciprocal of the unit exergy consumption is defined as the exergetic efficiency η. 

It is equal to one for reversible processes and is less than one for all real processes. 

P I 

η = -- = 

1– 

-- 

F F 

(6.6) 

Fuel and product definitions for some typical components in a dual-purpose power 

and desalination plant are shown in table 6.1. The fuel-product definition for the 

components of the cogeneration plant (figure 6.1) are shown in table 6.2.

TABLE 6.1 


Fuel and product definitions for typical dual-purpose power and desalination plant units. 

Component Fuel Product 

Boiler 

Pump 

Turbine 

without 

extraction 

Turbine 

with 

extraction 

Generator 

Heat 

exchanger/ 

brine heater 

MSF stage 

B 1 

fuel 

B 1 

W mech 

B 1 

B 1 

B 1 

cold 

stream 

B 4 

B 1 

W 

B 2 

B 2 

B 2 water 

B 3 

steam 

B 3 

W 

W 

B 2 

W el 

B4 B2 B 3 

hot stream 

D 

B 3 

B 2 

Natural gas 

B 

1 

Work to drive pump/compressor 

W 

Exergy removed from working 

fluid during the expansion 

B1 

– B2 

Exergy removed from working 

fluid during the expansion 

B1 

– B2 

– B3 

Mechanical work 

W 

mech 

Exergy removed from the hot 

flow 

B3 

– B4 

Exergy removed from the 

flashing brine (B1 

– B2) 

minus 

exergy provided to the cooling 

brine (B4 

– B3) 

Exergy difference between the 

generated steam flow and the 

entering water flow 


B 

3 

– B 

2 

Exergy supplied to the working fluid 

B 

2 

– B 

1 

Generated work 

W 

Generated work 

W 

Electric Work 

W 

el 

Exergy supplied to the cold flow 

B2 

– B1 

Distilled water in the stage 

D 

129

FIGURE 6.2 


6.1.3 Physical and thermoeconomic plant models 

A plant is analyzed using a physical model with a group of equations to describe the 

physical behavior of the components. It calculates parameters such as temperatures, 

pressures, efficiencies, power generated etc. to describe the physical state of the plant. 

Depending on the analysis, a decision has to be taken on the detail required i.e., 

which flows and components are to be considered. The components for the analysis 

do not necessarily correspond to physical units. Various parts of the installation can 

be combined into one component and physical units can be further disaggregated. It 

is important to chose an appropriate aggregation level that properly defines the 

behavior of each component and its purpose in the overall production process. The 

physical structure (see figure 6.1) depicts the components, mass and connecting 

energy flows considered in the physical model. 

The minimum physical data required in a thermoeconomic analysis are temperatures, 

pressures, mass flow rates and compositions of all mass flows together with the heat 

and power rates of the energy flows considered. Usually all this information is fully 

or partially obtained from the physical model of the plant. But it is not strictly 

indispensable if all the required data are measured plant data, collected directly from 

the plant data acquisition system. 

Productive structure of the cogeneration plant. 

Compressor 

P 2 = B 2 – B 0 

P 1 = B 3 – B 2 

F 1 = B 1 

Combustor 

Pj1 = B3 j1 

F 3 = B 3 – B 4 

F 2 = B 5 = W Cp 

F 4 = B 4 

Turbine 

HRSG 

P 4 = B 7 = B heat 

Nevertheless, when pricing all mass and energy flows in the thermoeconomic 

analysis, it is absolutely necessary to define a thermoeconomic model of the plant 

which considers the productive purpose of the components, i.e. the definitions of 

fuels and products and the distribution of the resources throughout the plant. The 

productive model can be graphically depicted by the productive structure diagram 

(figure 6.2). 


b1 

P 3 

b2 

W net = B 6

TABLE 6.2 


In this scheme, the flows (lines connecting the equipment) are the fuel and the 

product of each subsystem. Each “real“ piece of equipment in the plant has an outlet 

flow (product) and an inlet flow (fuel). The capital cost of the units is also considered 

as an external plant resource and is represented as inlet flows coming directly from 

the environment (not considered in figure 6.2). Since the fuel of a process unit can be 

the product of another and the product of a process unit can be the fuel of several 

subsystems, two types of fictitious devices are introduced: junctions (rhombs) and 

branching points or branches (circles). In a junction, the products of two or more 

components are joined to form the fuel of another component. In a branching point, 

an exergy flow (fuel or product in the productive structure –see figure 6.2-) is 

distributed between two or more components. Sometimes the productive structure 

can be simplified (with the same results) by merging the junctions and branches in a 

new fictitious component called junction-branching point. Figure 6.5 in section 6.3.1 

shows a similar productive structure as figure 6.2, where the junction j1 and the 

branching point b1 have been merged in a junction-branching point. For the sake of 

simplicity, the explanation of the fundamentals of thermoeconomics will be made 

using the productive structure depicted in figure 6.2. 

Fuels and Products of the components of the co-generation plant. 

No Subsystem Fuel Product 

Technical 

production 

coefficients 

1 Combustor F 

1 = B 1 P 1 = B 3 – B 2 k cb = F 1 /P 1 

2 Compressor F 2 = B 5 = W cp P 2 = B 2 – B 0 k cp = F 2 /P 2 

3 Turbine F 3 = B 3 – B 4 P 3 = B 5 + B 6 = W cp + W net k gt = F 3 /P 3 

4 HRSG F 4 = B 4 P 4 = B 7 = B heat k HRSG = F 4/P 4 

5 Junction 

P 1 = B 3 – B 2 

P 2 = B 2 – B 0 

6 Branching 1 P j1 = B 3 

7 Branching 2 P 3 = B 5 + B 6 = W cp + W net 

P j1 = B 3 

F 3 = B 3 – B 4 

F 4 = B 4 

F 2 = B 5 = W cp 

B 6 = W net 

r 1 = P 1/P j1 

r 2 = P 2 /P j1 

The productive structure is a graphical representation of resource distribution 

throughout the plant. Thus, its flows are fictitious and are not necessarily physical 

flows. While each plant has only one physical structure to describe the physical 

relations between the components, various productive structures can be defined 


131


depending on the fuel and product definitions as well as decisions on how the plant 

resources are distributed among the components. 

Thus, the thermoeconomic model (mathematical representation of the productive 

structure) is a set of mathematical functions called characteristic equations, which 

express each inlet flow as a mathematical function of the outlet flows for all the 

productive structure components and a set of internal parameters x l: 

B i = g i (x l, B j) i = 1,…, m–s (6.7) 

where the index i refers to the input flows of the component l, the index j refers to the 

output flows of the component l, and m is the number of flows considered in the 

productive structure. Every flow is an input flow of a component and an output flow 

of another component or the environment. For the flows interacting with the 

environment, we define: 

B m–s+1 = ω i i = 1,…, s (6.8) 

where s is the number of system outputs, and ω i is the total system product, i.e., an 

external variable which determines the total product. The characteristic equations for 

the system in figure 6.2, are shown in table 6.3: 

TABLE 6.3 Characteristic equations a of the cogeneration plant. 

No Component Entry Outlet Equation 

1 Combustor F 1 P 1 F 1 = g F1 (x 1 , P 1 ) = k cb P 1 

2 Compressor F 2 = W cp P 2 F 2 = g F2 (x 2 , P 2 ) = k cp P 2 

3 Turbine F 3 P 3 = W gt F 3 = g F3 (x 3 , P 3 ) = k gt P 3 

4 HRSG F 4 P 4 = B heat = ω 4 

5 Junction 1 P 1 , P 2 P j1 

F 4 = g F4 (x 4 , P 4 ) = k HRSG P 4 = k HRSG ω 4 

= k HRSG B heat 

P1 = gP1 (x5 , Pj1 ) = r1 Pj1 = r1 (F3 + F4 ) 

P2 = gP2 (x5 , Pj1 ) = r2 Pj1 = r2 (F3 + F4 ) 

6 Branching 1 P j1 F 3 , F 4 P j1 = g Pj1 (x 6 , F 3 , F 4 ) = (F 3 + F 4 ) 

7 Branching 2 P 3 F 2 , W net 

P 3 = g P3 (x 7 , F 2 , ω 3 ) = F 2 + ω 3 

= W cp + W net 

a. Variables in these characteristic equations are from the Exergetic Cost Theory, corresponding to the PF representation 

(Torres, 1991, Valero and Torres, 1990). Note that the Exergetic Cost Theory is a particular case 

(Serra, 1994) of the Structural Theory which is the thermoeconomic mathematical formalism presented in 

this Ph. D. Thesis. 



The inlet and outlet flows of the productive structure units are extensive magnitudes, 

which are the product of a quantity (usually mass flow rate) and a quality (specific 

magnitude). The magnitudes applied by most thermoeconomic methodologies are 

exergy (Tsatsaronis, 1987), negentropy (Frangopoulos, 1983) and money. Other 

magnitudes, like enthalpy or entropy, can also be used. 

The internal variables appearing in the thermoeconomic model depend on the 

behavior of the subsystem and they are presumably independent of mass flow rates. 

This implies that relations like efficiencies or pressure and temperature ratios — 

which are mainly independent of the quantity of the exiting flows— can be used as 

internal parameters. 

Note, that the main objective of the productive structure, and hence of the 

thermoeconomic model, consists on sorting the thermodynamic magnitudes related 

to the physical mass and energy flow-streams connecting the plant subsystems, in a 

different way that the equations modeling the physical plant behavior do, in order to 

explicitly determine for each subsystem its energy conversion efficiency. 

It is important take in mind that, as it was already explained, thermoeconomics 

connects thermodynamics, which is a phenomenological (black box analysis) 

science, with economics. That is, by sorting the thermodynamic properties of the 

physical mass and energy flow-streams of a plant, which in turn provide the energy 

conversion efficiency of each subsystem, thermoeconomics analyzes the degradation 

process of energy quality through an installation, i.e., thermoeconomics evaluates the 

process of cost formation. 

Depending on the analysis scope each subsystem can be identified with a separate 

piece of equipment, a part of a device, several process units or even the whole plant. 

Sometimes the objective consists on analyzing a plant in a deep detail. In this case it 

is advisable, if possible, to identify each subsystem with a separate physical process 

(heat transfer, pressure increase or decrease and chemical mixture or reaction) in 

order to locate and quantify, separately if possible, each thermal, mechanical and 

chemical irreversibility occurring in the plant. If the objective consists on analyzing a 

macro-system composed of several plants, probably in this case the more convenient 

approach is consider each separate plant as a subsystem. 

Thus, thermoeconomics always performs a systemic analysis, no matter how 

complex the system is, basically oriented to locate and quantify the energy 

conversion efficiency. It is out of the scope of thermoeconomics to model the 

behavior of the components, which is made by the mathematical equations of the 

physical model. 

Even though (it is out of the scope of thermoeconomics simulate the behavior of the 

subsystems), it is very important build the thermoeconomic model with physical 

meaning. This is the reason, as already explained, of defining different 



thermoeconomic models for the same plant. Depending on the aggregation level and 

on the nature of the thermoeconomic equations the model will content physical 

information about the actual system behavior with different accuracy degrees. The 

obtained results from a very rough thermoeconomic model, without any physical 

sensitivity related with the actual behavior of the plant, probably will be useless. 

The more extended thermoeconomic methodologies use linear equations in their 

thermoeconomic models, because they present practical (the model is simpler and for 

this reason much more powerful when applied to very complex energy systems) and 

conceptual advantages, as it will be explained before. Moreover, in many real plants it 

is possible to find an aggregation level where the system and subsystems linearly 

behave with accuracy enough, under an engineering point of view (Valero, Torres and 

Lerch, 1999; Martínez, Serra and Valero, 2000). This is also the case of the dual 

power and desalination plant analyzed in this work, as it is proved in next chapter. 

Thus, if the characteristic equations are first grade homogeneous functions with 

respect to the subset B, of independent variables (as linear equations do), that is: 

λ B i = g i (λ B 1,… λ B j, x l) λ∈ℜ (6.9) 

Euler’s Theorem states that the homogeneous function of first order verify: 

gi 

gi 

gi 

Bi 

= Bl 

Bl 

Bl 

Bl 

Bl 

Bls 

∂ 

⎛ ⎞ 

⎜ ⎟ + 

⎜ ∂ ⎟ 

⎝ ⎠ 

∂ 

⎛ ⎞ 

⎜ ⎟ + + 

⎜ ∂ ⎟ 

⎝ ⎠ 

∂ 

⎛ ⎞ 

... ⎜ ⎟ 

1 

2 ⎜ ∂ ⎟ 

1 

2 ⎝ ⎠ 

or using the marginal consumption notation, 

κ ij 

gi 

= 

B 

∂ 

∂ 

B = ∑κ B 

i ij j 

j∈Sl j 

l 1,…,l s in S l 


(6.10) 

(6.11a) 

i = 1,...,m l = 1,...,n. (6.11b) 

This property means that the input of a component varies at the same rate as its 

outputs. Note that this property does not imply that the function must be linear. For 

instance, a Cobb-Douglas function z = a x α y (1–α) , is also a homogeneous first order 

function. 

κ ij are the technical production coefficients and represent the portion of the i-th 

component production: 

κ ij 

gi 

= 

B 

∂ 

∂ 

j 

s 

(6.12a)


The sum of κ ij coefficients of a unit is the unit exergy consumption of that unit: 

k 

Fi 

n 

i= 

0 Fj 

= ∑ κ = = 

P P 

j ij 

i= 

0 

n 

∑ 

j 

j 

(6.12b) 

In thermoeconomics there are three types of characteristic equations, which are 

linear: 

1. Those connecting each fuel of a component to its corresponding product: 

F i = κ ij P j as for instance F 1 = g F1 (x 1, P 1) = k cb P 1 

(6.13a) 

There is one such equation for each component’s fuel. These types of equations 

are generated in the pieces of equipment and they inform about: 

– the productive function of each component, i.e., its production (product) 

– what the component needs (fuel) to develop its productive purpose, and 

– the thermodynamic efficiency of the process in the component 

2. Structural equations model how the resources consumed by the plant are distributed 

through the plant components. They show how the process units are connected 

from a productive point of view. Structural equations are characteristic 

equations to describe the productive model of junctions and branches, e.g.: 

P 1 = g P1 (x 5, P j1) = r 1 P j1 = r 1 (F 3+F 4) (6.13b) 

3. When the capital cost of the equipment is also considered in the analysis, a third 

type of characteristic equation is required; costing equations. These equations are 

very often not linear, but in the case of these equations this is a minor problem, 

because they can be linearized for different operation intervals. They relate the 

investment cost of the component with thermodynamic variables and its product. 

They express the amount of resources needed to build, install, maintain (etc.) a 

component. For example, a costing equation proposed by El-Sayed (1996), see 

section 7.3.3.1 for details: 

Z = 002 . ⋅10⋅Q⋅∆T ⋅∆T ⋅∆P 

−075 . −05 . −01 

. 

n t t 

(6.13c) 

The diagram of the productive structure is also called a Fuel/Product diagram (Torres 

et al., 1999) because in most cases the lines connecting the pieces of equipment 

represent the fuels and products of the different units. Thus, the characteristic 

equations (see table 6.3) using the Fuel–Product notation can also be written as: 

P = B + B 

i i0 ij 

j= 

1 

n 

∑ 

i = 0,1,…, n (6.14) 



This equation shows how the production of a process unit is used as fuel by another 

unit or as a part of the total plant production. In the above expression, B ij is the 

production portion of the i-th component that fuels the j-th component, and B i0 

represents the production portion of the component i leading to the final plant product 

(the subscript 0 refers to the environment, which is considered another process unit 

interacting with the plant). 

Equation (6.14) can be expressed in terms of the unit exergetic consumptions as: 

P = B + κ P 

i i0 ij j 

j= 

1 

n 

∑ 

In matrix notation it can also be expressed as: 

P = Ps + KP P 

i = 0,1,…, n (6.15) 


(6.16) 

where P s is a (n×1) vector whose elements contain the contribution to the final 

production of the system P i0 obtained in each component, and 〈KP〉 is a (n×n) matrix, 

whose elements are the unit exergy consumption κ ij. This expression helps to relate 

the production of each component as a function of the final production and the unit 

consumption of each component: 

⎛ ⎞ 

P = P Pswhere 

P ≡⎜UD− KP ⎟ 

(6.17) 

⎝ ⎠ 

In the same way, we can express the irreversibility of each component as: 

( D D) 

I = I Pswhere 

I ≡ K −U 

P 

(6.18) 

while the total resources of the system may be obtained as: 

t 

t 

FT =κe P Ps 

(6.19) 

where κe 

≡ 

( κ01, …κ , 0n) 

, is a (n×1) vector whose elements contain the unit 

consumption of the system-input resources. 

6.2 Calculating thermoeconomic costs 

Once the thermoeconomic model has been defined and the characteristic equations 

corresponding to the productive structure of the system are known, the costs of all 

flows in the productive structure can be easily calculated. 

There are two different types of thermoeconomic costs: average costs and marginal 

costs (equations 6.1 and 6.2). It is important to note that (as discussed below) the 

−1

Calculating thermoeconomic costs 

average and marginal costs coincide when the characteristic equations of the 

thermoeconomic model are first grade homogeneous functions. 

This result is very important since both costs can be calculated using the same 

procedure. Marginal costs are a derivative (see equation 6.2) and can be calculated by 

applying the chain rule of the mathematical derivation. Similarly, average costs can 

also be obtained from the rules of the mathematical derivation applied to the 

thermoeconomic model when the characteristic equations are first grade 

homogeneous functions. 

According to the previous premises, the cost of the plant resources can be defined as: 

e 

0 = ∑ 0, 

i 

i= 

1 

* 

B k B 

i 

(6.20) 

where e, is the number of system inputs, and k * 0,i is the unit cost of the –i– external 

resource. 

Each flow, as a component input, is a function (defined by the characteristic equation) of a 

set of internal variables, x, external variables ω and the output flows of the component. 

The cost of the plant resources is then a function of each flow, the set of internal 

variables of each component and the final product of the plant B 0 = B 0 (B i , x, ω), 

according the relations (6.7) and (6.8). 

When calculating the variation of the resources consumed in the plant concerning a 

flow, the chain rule can be applied: 

∂B 

∂B 

0 

i 

∂B 0 

--------- 

∂B i 

= k 

= 

* 

0, i 

m 

∑ 

j = 1 

∂B 0 

i = 1,…, e (6.21a) 

∂B 0 

--------- ∂g j 

-------- 

∂B j 

∂B i 

i = e + 1,…, m (6.21b) 

The expression --------- represents the marginal costs which evaluate the additional 

∂B i 

consumption of the resources, when an additional unit of the flow –i– is produced, 

under the conditions that the internal variables, x, do not vary throughout this process. 

We can denote these marginal costs as k* i , and κij = -------- the marginal consumption 

of flow –i– to produce the flow –j–, then we can rewrite the previous expressions, as: 

* 

i = 0, 

i 

* 

k k 

i = 1,…, e (6.22a) 


∂g i 

∂B j


i = e + 1,…, m (6.22b) 

Note that the unit exergetic cost of each fuel entering the plant is unity because there 

is no energy quality degradation nor exergy destruction at the very beginning of the 

productive process. Hence, the amount of exergy consumed to obtain each plant’s 

fuel is its own exergy content and therefore its unit exergetic cost equals one. 

It can easily be proved that the cost of each flow Pij of the productive structure using 

the Fuel/Product notation is: 


(6.23) 

And the exergetic cost of the product of each component is the same as the cost of the 

resources needed to obtain it, hence: 

i = 1,…, n (6.24) 

This cost equation can also be expressed in terms of the unit exergetic consumptions: 

i = 1,…, n (6.25) 

which can be used to obtain the unit exergetic cost of the flows appearing in the 

productive structure diagram as a function of the unit exergetic consumption of each 

process unit. 

Then, if the characteristic equations and the marginal consumptions for each 

component are known, the marginal cost k * for each flow can be obtained by solving 

the system of linear equations (6.25). 

Example 1 

m 

∑ 

k* * 

i = κ ji k j 

j = 1 

j≠i * * 

P = k B 

ij P, i ij 

n 

i i ∑ P j ji 

0 

* * 

* 

P = F = k , B 

j= 

n 

Pi i ji 

* 

Pj , 

∑ 

* 

k , = κ0+ κ k 

j= 

1 

For the example of a co-generation plant (figure 6.2), equations 6.21a, 6.21b can be 

written as: 

* ∂B 

k F = 1 ∂F 

k 

k 

1 

1 

B 

= 

F 

∂ 

∂ 

B 

= 

P 

∂ 

∂ 

∂P 

∂F 

= k 

* 1 1 3 * 

F2 P3 

2 3 2 

B B P 

1 1 j1 

= k 

F P F 

∂ 

= 

∂ 

∂ ∂ 

= 

∂ ∂ 

* * 

F3 

Pj1 3 j1 

3 

*


k 

k 

k 

k 

k 

k 

k 

B 

= 

F 

∂ 

∂ 

B 

= 

P 

∂ 

∂ 

∂Pj 

∂F 

= k 

* 1 1 1 * 

F4 

Pj1 4 j1 

4 

B 

= 

P 

∂ 

∂ 

B 

= 

F 

∂ 

∂ 

∂F1 

k k 

∂ P 

= 

* 1 1 

* 

P1 F1 cb 

1 1 1 

B 

= 

P 

∂ 

∂ 

B 

= 

F 

∂ 

∂ 

∂F 

∂P 

= k k 

* 1 1 2 * 

P2 F2 cp 

2 2 2 

B 

= 

P 

∂ 

∂ 

B 

= 

F 

∂ 

∂ 

∂F 

∂P 

= k k 

* 1 1 3 * 

P3 F3 gt 

3 3 3 

B 

= 

P 

∂ 

∂ 

B 

= 

F 

∂ 

∂ 

∂F 

∂P 

= k k 

* 1 1 4 * 

P4 F4 HRSG 

4 4 4 

B 

= 

P 

∂ 

∂ 

B 

= 

P 

∂ 

∂ 

∂P 

∂P 

B 

+ 

P 

∂ 

∂ 

∂P 

∂P 

= k r + k r 

* 1 1 2 1 1 * * 

Pj1 

P2 2 P1 

1 

j12j11j1 B 

= 

W 

∂ 

∂ 

B 

= 

P 

∂ 

∂ 

∂P 

∂W 

= k 

* 1 1 3 * 

Wnet 

P3 

net 3 net 

The thermoeconomic model (characteristic equations) of an energy system contains 

the mathematical dependence between the resources consumed and plant flows 

(products and internal flows). It is therefore possible to define a set of linear equations 

to calculate the costs of every flow of the plant's productive structure. Note that these 

equations show the process of cost formation on the productive structure. 

The proposed procedure to calculate the marginal cost of all the flows of a plant is 

general and valid for any thermoeconomic formulation that uses equations 

connecting inlet and outlet flows of each component. 

Just as k * was defined as a marginal cost when production is modified, we can also 

obtain the marginal cost when the internal variables x are modified. Similarly, 

applying the chain rule, we get: 

∂B 

∂x 

0 

i 

= 

m 

∑ 

j= 

1 

k 

* 

j 

∂g 

∂x 

j 

i 

(6.26) 

This equation expresses the effect on additional resource consumption when an 

internal parameter x i is modified and is the basis for the thermoeconomic diagnosis 

(explained in detail below). 

To determine the physical model of the system, a set of equations must be defined 

which relate the internal and external variables to the thermodynamic laws: mass, 

energy and entropy balances. 



The most developed thermoeconomic optimization methodologies (Frangopoulos, 

1987, 1990; Von Spakovsky et al., 1993), use the Lagrange multipliers optimization 

method to calculate the marginal costs defined in the previous section. It can easily be 

proved (Serra, 1994; Reini, 1994) that the Lagrange multipliers are the marginal costs 

defined in equation (6.2), i.e: 

i = 1,..., m (6.27) 

This multiplier represents the variation of the objective function B 0 concerning the 

state variable B i. 

6.2.1 Marginal and average thermoeconomic costs 

Now, we will show that the marginal and average costs coincide when the 

characteristic equations of the system are first grade homogeneous functions 

concerning the extensive magnitude B. This is a very important result since the 

marginal and average costs can be calculated using the same procedure. This unifies 

accounting and optimization theories in a common mathematical formulation. The 

most important advantage is that variables and costs with different conceptual 

significance can be compared and better understood. Thus, the Exergetic Cost Theory 

(Valero, Lozano and Muñoz, 1986a), a cost accounting methodology which provides 

average costs, and Thermoeconomic Functional Analysis (Frangopoulos, 1983, 

1987), an optimization methodology which provides marginal costs, are particular 

cases of the Structural Theory. As a result of the integration of different approaches, 

some useful thermoeconomic applications have been developed, e. g. diagnosis 

operation and thermoeconomic optimization using the same mathematical formalism. 

As an illustration, consider a generic component or subsystem with several inlet and 

outlet flows. For the sake of simplicity we will use a general subsystem with two inlet 

flows and two outlet flows (figure 6.3). 

FIGURE 6.3 Generic component scheme. 

B 1 

B 2 

λ i 

B 

= 

B 

∂ 

∂ 

0 

i 

4 

B1 3 

B1 4 

B2 140 Thermoeconomic analysis and simulation of a combined power and desalination plant 

3 

B2 B 3 

B 4


The characteristic equations that describe component behavior are: 

B 1 = k 13 B 3 + κ 14 B 4 

B 2 = k 23 B 3 + κ 24 B 4 

(6.28) 

(6.29) 

These equations provide the amount of inlet resources (B 1, B 2) consumed to obtain 

each one of the outlet flows (B 3, B 4). This idea is easily understood if the component 

is made up of two subsystems. The equations modeling each subsystem are: 

B 13 = κ 13 B 3 

B 14 = κ 14 B 4 

B 23 = κ 23 B 3 

B 24 = κ 24 B 4 

(6.30a) 

(6.30b) 

(6.31a) 

(6.31b) 

Equations (6.30a, 6.31a) represent the resources needed to produce B 3 and Equations 

(6.30b, 6.31b) are the resources consumed to produce B 4. The total amount of 

resources required to obtain B 3 is thus: 

and to obtain B 4: 

B 13 + B 23= κ 13 B 3 + κ 23 B 3 

B 14 + B 24 = κ 14 B 4 + κ 24 B 4 

According to Equation (6.1) the average cost of the outlet flows are: 

* κ13 B3 + κ23 B3 = ------------------------------------- = κ13 + κ23 k 3 

k 4 

B 3 

* κ14 B4 + κ24 B4 = ------------------------------------- = κ14 + κ24 B 4 

And the marginal cost of the outlet flows are: 

k 

k 

g 

B k 1 = ∂ 

∂ 

g 

+ 

B ∂ 

∂ 

k = k + k 

* * 2 * 

3 

1 

2 13 23 

3 

3 

g 

B k 1 = ∂ 

∂ 

g 

+ 

B ∂ 

∂ 

k = k + 

k 

* * 2 * 

4 

1 

2 14 24 

4 

4 

(6.32) 

(6.33) 

(6.34a) 

(6.34b) 

(6.35a) 

(6.35b) 

considering that the value of the marginal cost of the input flows (B 1, B 2) is equal to 

one. Since equations (6.34) are the same as equations (6.35), the average and 

marginal costs of B 3 and B 4 coincide. Both kinds of costs coincide because the 

equations modeling the component are homogeneous functions of first order 

concerning the extensive magnitudes characterizing the outlet flows. 



In this proof, the cost of the inlet flows was unity. This is equivalent to considering 

that the subsystem was at the beginning of the productive process. The general 

mathematical formulation of the cost generated in a component is the same for each 

one and is not dependent on the position in the productive process. Thus, the results 

obtained are general. 

The average and marginal costs coincide because the equations modeling the 

components are first grade homogeneous functions concerning the extensive 

magnitude characterizing the outlet flows. The mass is the property determining 

whether a magnitude is extensive or not. If all equations modeling a system are first 

grade homogeneous functions concerning the mass, a simple substitution can 

transform those equations in homogeneous functions with respect to any extensive 

property. Thus, the marginal and average costs coincide if all equations modeling the 

behavior of the system are first grade homogeneous functions concerning the mass 

flow rate. 

6.2.2 Economic resources and thermoeconomic costs 

Thermoeconomic cost calculation considering the component capital cost Z, is 

similar to the above method but should be explained in more detail. The capital cost 

of each component Z can be considered an external flow of plant resources from the 

environment to the component (see figure 6.4). This will represent the monetary units 

per second needed to compensate the depreciation, maintenance cost and so on, of the 

component. 

FIGURE 6.4 Economic resources scheme. 

B 0 

Economic resources 

B i 

Z 1 = Z 1 (B 1 , B j , B h ) 

According to marginal cost analysis, Z represents an environmental resource and can 

be handled in the same mathematical way as energy resources. The amount of 

resources consumed when manufacturing a device are, in fact, resources consumed to 

obtain the plant products. Some authors (Brodyansky et al., 1993; Le Goff, 1979) 

have developed methodologies to evaluate the total amount of resources consumed 

when building a process unit. Then the marginal unit cost ∂Z/∂B, can be considered a 

marginal consumption κ Zj. 


x 1 

B j 

B h

Thermoeconomic applications to thermoeconomic operation diagnosis and the optimization of 

For the component depicted in figure 6.4 the characteristic equations are: 

B i = f (B j, κ ij) (6.36a) 

Z j = Z (B j, κ Zj) (6.36b) 

And the cost of the product is: 

k 

B 

B k i = ∂ 

∂ 

Z 

+ 

B 

∂ 

∂ 

= k κ + κ 

* * j * 

j 

i 

i ij Zj 

j 

j 

If Z j is proportional to the production of the unit, or in other words its characteristic 

function is first order homogeneous, the marginal cost is equal to the average cost. 

But, unfortunately Z j is a non-linear function of the production in most cases. 

6.3 Thermoeconomic applications to thermoeconomic 

operation diagnosis and the optimization of complex 

energy systems 

Having defined the tools needed for a thermoeconomic analysis of a complex system, 

some applications to thermoeconomic diagnosis and optimization can be presented. 

The methodology is presented together with a simple application. 

6.3.1 Operation thermoeconomic diagnosis 

Diagnosis is the art of discovering and understanding signs of malfunction and 

quantifying their effects. In the case of Thermoeconomics, the effect of a malfunction 

is quantified in terms of additional resources consumed to obtain the same 

production, both in quality and in quantity. 

The main problem in energy system diagnosis can be summarized in the following 

question: Where, how and which part of the consumed resources can be saved by 

keeping the quantity and quality of the final products constant? To answer these 

questions, we need: 

• Procedures that accurately determine the state of the plant. 

• A theory to provide the concepts and tools to understand and explain the causes 

of this state. 

The methodology presented in this paper applies Structural Theory to provide the 

tools to investigate the causes of the irreversibilities and the cost formation process. 



In order to clarify the explanation of the proposed method we use a simple example (a 

more complex one can be found in Lerch, Royo and Serra, 1999), the co-generation 

plant depicted in figure 6.1, whose design and operational exergy flow values are 

shown in table 6.4. The plant has a co-generation gas turbine cycle and uses the 

turbine outlet gases as thermal energy in a heat recovery steam generator that 

produces steam (flow #7) together with the electric energy produced in the turbogenerator 

(flow #6). 

TABLE 6.4 Design and operation exergy flow values of the cogeneration plant (figure 6.1). 

Flow (kW) 1 2 3 4 5 6 7 8 

Design 11781 2704 9614 3831 2977 2500 2355 388 

Operation 11914 2758 9753 3887 3056 2500 2355 424 

6.3.1.1 Technical exergy saving 

Once the exergy flows have been supplied by an appropriate performance test or a 

model simulator, the irreversibilities in each productive unit can be obtained from the 

exergy balance. But not all exergy losses can be saved in practice. In fact, the 

potential exergy saving is limited by technical and/or economic constraints. It also 

depends on the decision level that limits the actions to be undertaken. In contrast to 

conventional thermodynamic analysis, Thermoeconomics assumes a reference 

situation of the plant operating under design conditions. From this perspective, in the 

plant of figure 6.1, we see that only 133 kW, of the 7.06 MW of total irreversibilities 

can be saved with respect to design conditions. 

Therefore, the additional fuel consumption can be expressed as the difference 

between the resource consumption of the operating plant and the resource 

consumption for a reference or design condition with the same production objectives: 

∆FT = FT −FT 0 

and it can be broken up into the sum of the irreversibilities of each component: 

n 

∆FT = ∆IT = ⎛Ij 

−I 

⎞ 

⎝ j⎠ 

∆I 

= 

0 

∑ ∑ 

j= 

1 j= 

1 


n 

(6.37a) 

(6.37b) 

However, even though the methods based on Second Law Analysis (Kotas, 1985) and 

Technical Exergy Saving are useful to quantify the additional fuel consumption, they 

fail when trying to identify the real causes of the additional resources consumption. 

j


6.3.1.2 Impact on resources consumption 

The Fuel/Product diagram of the cogeneration plant is shown in figure 6.2. This 

diagram can be simplified by merging junction 1 and branching point 1 in a new 

fictitious component called junction–branching point (see figure 6.5). This new 

productive structure is slightly different than figure 6.2, and is more compact. 

The characteristic equations of this new productive structure are obtained as in the 

previous section applying equation (6.15) 

P = Ps + KP P 

FIGURE 6.5 Fuel / Product diagram and fuel and product exergy flows (kW) in design conditions for the cogeneration 

plant shown in figure 6.1. 

1 

1 

2 

2 

3-2 

F 0 F 1 F 2 F 3 F 4 Total 

P 0 0 11781 0 0 0 11781 

P 1 0 0 0 4156 2474 6631 

P 2 0 0 0 1627 968 2595 

P 3 2500 0 2977 0 0 5477 

P 4 2355 0 0 0 0 2355 

Total 4855 11781 2977 5783 3443 

8 

For the sake of simplicity we did not consider thermal and mechanical exergies as 

separate entities. Two auxiliary variables also appear r 1 = (B 3 – B 2)/B 3 and r 2 = B 3/B 2, 

which correspond to the part of the fuel of the turbine and HRSG coming from the 

combustor and the compressor respectively. Flow #8, produced in part in the 

combustor and in the compressor, also leaves the system as a residue. Only a part of 


5 

3-4 

4-8 

3 

4 

6 

7


the entering gases to the turbine: B 3 – B 8 are used as a fuel of other components of the 

system. Therefore, only a part of the combustor’s and compressor’s product is used as 

a fuel for other components (useful product). Accordingly, figure 6.5 shows the chosen 

disaggregation scheme of the system and the Fuel/Product values for the design 

conditions. 

TABLE 6.5 Fuel/Product definition corresponding to figure 6.5 

No. Component Fuel Product Residue 

1 Combustor B 1 B 3 – B 2 

2 Compressor B 5 B 2 

3 Turbine B 3 – B 4 B 6 

4 HRSG B 4 – B 8 B 7 B 8 

In order to bring together the problem of the impact of resources consumption with 

thermoeconomic diagnosis we need to know the increase of the unit exergy 

consumption of each component of the plant. A performance test or a simulator 

provides the real values of the unit consumptions which are then compared with the 

design values. 

TABLE 6.6 Increase of unit consumption. (100 ∆κ ij ). 

∆κ e 0.4006 0.0000 0.0000 0.0000 

∆ KP 

0.0000 0.0000 –0.1667 0.3857 

0.0000 0.0000 0.1593 0.4636 

0.0000 1.1147 0.0000 0.0000 

0.0000 0.0000 0.0000 0.0000 

∆k 0.4006 1.1147 -0.0074 0.8493 

The values of the unit exergetic consumption increase are found as: ∆κ ij = κ ij (x) – κ ij 

(x 0 ). Table 6.6 shows the ∆κ ij values for the plant in figure 6.1. 

Equation (6.19) is used to obtain the increment of the total resources of an operating 

plant regarding the reference conditions: 

t 0 

t 

∆ = ∆ κ P + κ ∆P 

F T 

e 


e 

(6.38)


The increase of the component production from equation (6.16) may be expressed in 

terms of the unit exergy consumption as: 

hence, applying equation (6.17), we obtain: 

(6.39) 

(6.40) 

If we want to analyze the fuel impact due to an increment of the exergy unit 

consumption of the components, equation (6.38) could be written as: 

If no change in the total production of the plant is assumed, then: 

or in scalar format: 

0 

∆P = ∆P + ∆ KP P + KP ∆P 

s 

∆P | P〉 

∆Ps ∆ 〈 KP〉 

P 0 

= ⎛ + ⎞ 

⎝ ⎠ 

t 0 t * 0 t * 

∆ = ∆ κ P + κ ∆ KP P + κ ∆P 

F T 

e 

⎛ t t ⎞ 

∆FT= ⎜∆ 

κe+ κ P ∆ ⎟ 

⎝ 

⎠ 

* KP P 0 

n ⎛ n ⎞ 

* 

∆FT = ∑ ⎜ k j ∆ ji Pi 

⎜∑ 

P, κ ⎟ 

i = 1 ⎝ j= 

0 ⎠ 

P 

0 

P s 

(6.41) 

(6.42a) 

(6.42b) 

Using the above equation, the additional resource consumption ∆F T (also called Fuel 

Impact; Reini, 1994) can be expressed as the sum of the contributions of each 

component. 

The variation of the exergetic unit consumption of each component increases its 

resources consumption and its irreversibilities in a quantity ∆κ ji Pi , which we call, 

malfunction. Consequently, this implies an additional consumption of external 

resources given by , which is also named the malfunction cost. 

Therefore, the total fuel impact can be written as the sum of the fuel impact or 

malfunction cost of each component, as shown in equation (6.42b). 

0 

* 0 

kP, j ∆κ ji Pi 

The proposed method provides the exact values of the additional resource 

consumption of each component malfunction for any operational state. Other 

methods, such as the Theory of Perturbations (Lozano et al., 1996), only provide an 

approximate predictive value, based on marginal costs (Lagrange multipliers) which 

is valid for an operating state close to the reference conditions. 



FIGURE 6.6 Fuel impact and technical saving. 

80 

60 

40 

20 

0 

Figure 6.6 compares the fuel impact and the increase of irreversibilities or the 

technical exergy saving of each component and also compares (first column) the 

malfunction and the fuel impact for each component. Three malfunctions in the plant 

are shown in the combustor, the compressor and the HRSG. The largest 

irreversibilities increase is in the combustor, but the largest fuel impact is in the 

compressor. The question that arises is: What causes the irreversibilities increase and 

the fuel impact, and how are they related? 

6.3.1.3 Malfunction and dysfunction analysis 

We have shown that there is no direct relationship between the increase of the 

irreversibilities and fuel impact. The more advanced the production process is, the 

greater the cost of the irreversibility malfunction and, as a consequence, the greater 

its fuel impact. 

Furthermore, the degradation of a component will force other components to adapt 

their behavior in order to maintain their production conditions and modify their 

irreversibilities. Figure 6.7 shows how an increase of the unit consumption of a 

component will not only increase the irreversibilities on it but also the irreversibilities 

of the previous component. 

FIGURE 6.7 Malfunction and fuel impact. 

Combustor Compressor Turbine HRSG 

∆F 1 

F 1 

∆I 1 

I 1 

∆P 1 

P 1 

Fuel Impact 

Malfunction 

Technical Saving 


∆F 2 

F 2 

∆I 2 

I 2 

P 2


The irreversibility increase of a generic system’s component is given by: 

∆I = ∆K D P 0 + (K D – U D) ∆P (6.43) 

From the above expression, we can distinguish two types of irreversibilities: 

Endogenous irreversibility or malfunction produced by an increase of the unit 

consumption of the component itself: 

Exogenous irreversibility or dysfunction induced in the component by the 

malfunction of other subsystems, which forces it to consume more local resources to 

obtain the additional production required by the other components: 

The malfunction only affects the behavior of the components; the dysfunction is a 

result of how the components adapt themselves to maintain the total production. 

Now we will consider the causes and effects of the irreversibilities systems and 

introduce a new method to compute the fuel impact of a malfunction and its effect. In 

other words, how to compute the dysfunction on the rest of the system components. 

If we substitute ∆P from equation (6.40) then the irreversibility increase of each 

component, equation (6.43) is written in terms of the unit consumption as: 

or in scalar format: 

0 0 

MF = P ∆k= P ∆κ i 

j= 

i i i ji 

0 

DF = ( k −1) 

∆P 

i i i 

n 

∑ 

⎛ 

⎞ 

∆I= ⎜∆KD+ 

I ∆ KP ⎟P 

⎝ 

⎠ 

n 

∑ ∑ 

∆I = P ∆κ + φ ∆κ 

P 

i i ji 

j= 

1 

jh , = 1 

n 

0 

ih hj 

0 

j 

(6.44) 

i = 1,…, n (6.45) 

The first part of the previous expression corresponds to the component malfunction, 

and the last part to the dysfunction. If we denote: 

n 

DFij ∑ φih ∆κhj 

Pj 

= 

h= 

1 

0 

(6.46) 

DFij represents the part of i–th component dysfunction generated by component –j–, 

where φih are the coefficients of the irreversibility matrix operator | I〉 

for the actual 

operation values. The above expression shows how a malfunction Pj ∆κhj, on the j-th 

component, generates a dysfunction on the i–th component proportional to the φih coefficients, which represent the weight of the malfunction effect. The coefficient φih Thermoeconomic analysis and simulation of a combined power and desalination plant 149


does not depend on the malfunction amount, but only on the unit consumption of the 

components in the operating state. Therefore, the dysfunction cannot be corrected by 

itself but decreases the malfunction which generated it. 

The technical exergy saving of component –i–, equation (6.45) can be written as the 

sum of its malfunction and the dysfunction generated by other components of the 

system: 

i i ∑ ij 

1 

∆I = MF + DF 

j= 

i = 1,…, n (6.47) 

The graph in figure 6.8 describes the cause of the irreversibilities increase in the gas 

turbine cycle (of the example) as the sum of the malfunctions and the dysfunction 

generated by the rest of the components 

FIGURE 6.8 Analysis of the irreversibility causes (kW). 

80 

60 

40 

20 

0 

∆ I1 

Fuel impact and dysfunction 

n 

∆ I2 

For a specified constant quality and quantity of total production, the fuel impact 

(6.42b) could be written as the sum of the malfunctions and dysfunctions of all the 

plant components: 


(6.48) 

If we rearrange the previous expression, grouping by component production, we 

obtain: 

∆ I3 

n 

n ⎛ 

n ⎞ 

∆FT = ∑ ∆Ii 

= ∑ ⎜MFi 

+ DFij 

⎜ ∑ ⎟ 

i= 

1 i= 

1 

⎝ j= 

1 ⎠ 

HRSG 

Turbine 

Compressor 

Combustor 

Malfunction 

∆ I4


n ⎛ 

n ⎞ 

∆FT= ∑ ⎜∆ki+ 

jh ∆ hi Pi 

⎜ ∑φ 

κ ⎟ 

i= 

1 ⎝ jh , = 1 ⎠ 

(6.49) 

Therefore, the fuel impact or the malfunction cost of each component is given by the 

sum of the malfunction and the dysfunction: 

i i ∑ hi 

h= 

1 

* 

MF = MF + DF 

i = 1,…, n (6.50) 

If we compare the previous equations with the fuel impact equation (6.42b), we find a 

relationship between the unit cost of production and the irreversibility dysfunction 

coefficients, given by: 

n 

* 

k Pj , = 1 + ∑ φij 

i= 

1 

j = 1,…, n (6.51) 

The above expression is an alternative method to compute the unit cost of the product 

as the sum of the contribution of the irreversibilities of each component. Table 6.7 

shows the irreversibility matrix operator coefficients and unit cost of the component 

product for an operating gas turbine plant. 

TABLE 6.7 Irreversibility matrix and unit cost of product. 

| I〉 

k P * 

n 

0.7807 1.0469 0.9037 1.2586 

0.0000 0.2422 0.0723 0.1007 

0.0000 0.0988 0.0853 0.0411 

0.0000 0.0000 0.0000 0.4704 

1.7807 2.3880 2.0614 2.8708 

A graph of the fuel impact for each component is shown in figure 6.9. Note that the 

dysfunction becomes even greater than its own malfunction as the production process 

proceeds. The cost of the malfunction in the compressor and HRSG includes the 

dysfunction generated, for the most part, in the combustor. 

The sum of the dysfunctions generated by a component: 

n 

i = ∑ ji 

j= 

1 

DI DF 

n 

i = 1,…, n (6.52a) 

could be written as: DIi = ⎛ * 

k P j − ⎞ 0 

∑ ⎝ , 1 

⎠ 

∆κ 

ji Pi 

(6.52b) 

j= 

1 


0


FIGURE 6.9 Analysis of fuel impact (kW). 

80 

60 

40 

20 

0 

∆ I4 

∆ I3 

∆ I2 

∆ I1 

MF 

Combustor Compressor Turbine HRSG 

Therefore, the dysfunction generated by a component (as with the fuel impact) 

depends on the malfunction and the position of the component in the productive 

process, which is, in turn, characterized by the unit cost of the resources required by 

the component. 

The relationship between irreversibility increase and fuel impact can be represented 

by a double input table (see table 6.8). The dysfunction table containing the DF ij 

elements can be computed in a compact matrix form using the expression: 

[ DF] I KP P 

= ∆ 0 

D 

TABLE 6.8 Malfunction and dysfunction table in (kW). 

Combustor Compressor Turbine HRSG DF Malfunction Total 

∆I 1 0.000 26.140 2.004 18.520 46.664 26.562 73.226 

∆I 2 0.000 2.092 2.113 2.644 6.849 28.925 35.774 

∆I 3 0.000 2.467 0.862 1.079 4.408 –0.408 4.000 

∆I 4 0.000 0.000 0.000 0.000 0.000 20.000 20.000 

DI 0.000 30.699 4.979 22.243 57.921 

Malfunction 26.562 28.925 –0.408 20.000 75.079 

Total 26.562 59.624 4.571 42.243 133.000 



Each cell represents the DF ij dysfunction. The DI column represents the sum of the 

dysfunctions generated by each component, and the DF row is the sum of the 

dysfunctions generated in each component. The total sum by columns represents the 

Fuel Impact of each component, and the total sum by rows is the irreversibility 

increase. The methodology proposed in this section is summarized in the table 

mentioned above. It is a powerful tool to find the causes and effects of variations from 

the design conditions of a plant and to study, classify and assign the role of each 

system unit. 

6.3.1.4 Intrinsic and induced malfunctions 

Using the above method we can identify and quantify malfunction effects. For 

example, we found three malfunctions in the gas turbine cycle (figure 6.1): one each 

in the combustor, compressor and HRSG. But, What are the causes of the 

malfunctions? In fact, the actual operation values shown in table 6.4 correspond to a 

1% decrease in compressor isoentropic efficiency. This means that HRSG and 

combustor efficiencies can be changed by varying compressor efficiency. 

How do we approach this problem? The relationship between operation and 

efficiency of the components could be analyzed using a simulator. If all the pant 

components were isolated, the efficiencies of those components would be 

independent variables (Lozano et al., 1996). So we will assume that there is an 

operating parameter x r affecting the efficiency of the i-th component of the plant and 

thus, in most cases, also indirectly affecting the efficiencies of the other plant process 

units. 

Once the relationship between unit exergy consumption and the operating parameters 

is known, the above methodology can be applied to distinguish the effect of an 

operating parameter on the internal economy of a component, i.e. its malfunction and 

the cost of its malfunction. 

Plant operating parameters could be classified according to their effect on the 

efficiency of the components of the system: 

Local variables: They mainly affect the behavior of the component related to the 

variable, e.g, the isoentropic efficiency of a turbine. From a practical point of view, a 

variable is considered local and therefore related to a subsystem. The total fuel impact 

due to its perturbation is basically located in this component. 

Global and/or zonal variables: This is the case when an operating parameter cannot 

be associated with a specific component. We must identify them as operating set 

points, environmental parameters and the production load or fuel quality. 

In this thesis we will focus our analysis on local variables and how they affect 

additional fuel consumption and the other plant components. This analysis is, in fact, 

the next step in the thermoeconomic diagnosis. 



Unfortunately the problem of locating causality of losses in a structure is rather more 

complex than locating malfunctions and dysfunctions. 

When a plant unit deteriorates (when its behavior is degraded) its physical variables 

are modified, its efficiency is decreased and its unit exergy consumption increases. 

The unit exergy consumption increase of each component, due to the variation of an 

operating parameter x r, is: 

r 

∆κ = κ ( x + ∆x) 

−κ 

( x ) 

ij 

ij 0 r ij 0 

Therefore, it will be possible to approximate the malfunction of a component as the 

sum of the contributions of each operating parameter: 

r 

MFi ≅ ∑ ∑ ∆κ ji Pi 

r 

n 

j= 

1 


0 

(6.53) 

According to the classification of operating parameters, the intrinsic malfunction is 

that part of the component malfunction due to the degradation/improvement of the 

component itself, which is, in turn, due to variation of local operating parameters: 

L 

r 

MFi ≡ ∑ ∑ ∆κ ji Pi 

n 

r∈Lij= 1 

0 

(6.54) 

A system malfunction or improvement does not only have consequences upstream 

(by trying to see the variation in consumption of used resources) but also 

downstream. Clearly the degradation or improvement of a system’s flow entry 

conditions will affect its efficiency to a greater or lesser extent. This will modify the 

production and affect the next component. 

Not only are there dysfunctions when there is an intrinsic malfunction. There are also 

induced malfunctions, that can decisively affect the system's behavior. For example, 

using the throttle valve in a power plant can destroy a small additional amount of 

exergy but the downstream effects on turbine efficiencies can be quite serious. 

Thus, the difference between total component malfunction and intrinsic malfunction 

is called induced malfunction. It is due to the degradation of other plant components 

which provoke a variation in the unit consumption of that component: 

G 

MF = MF −MF 

i 

L 

i i 

(6.55) 

This phenomenon is not foreseen in classic linear thermoeconomic theory. The 

average cost obtained from the most rigorous disaggregation analysis can never 

predict induced malfunctions and dysfunctions will only be predicted in cases where 

the hypothesis of linearity and continuity holds.


Malfunction matrix 

It is important to know the fuel impact associated with the variation of each physical 

parameter when a malfunction occurs. 

The fuel impact of an operating parameter on the whole plant can be calculated using 

the simulator but the latter does not provide information about the effects on other 

plant components. A deterioration in a component (intrinsic malfunction) can modify 

the efficiencies of other plant components. 

Information about interactions among different plant components can be obtained 

with the methodology presented here. It is basically contained in the so called 

malfunction matrix, or 〈∆KP〉 matrix. This matrix can relate any operating parameter 

with all the possible malfunctions. Note that the overall impact on resources (fuel 

impact) can be written as: 

* r 0 

* r 

∆F ≡ k ∆κ P + k ∆κ 

P 

T P, j ji i 

r∈ Li 

j= 

0 

r∉Li j= 

0 

(6.56) 

Where the first term is the fuel impact associated with the intrinsic malfunction and 

the last term is the fuel impact associated with the induced malfunctions and ∆κ ij are 

elements of the ∆ 〈KP〉 matrix. The ∆ 〈KP〉 matrix has been built for each parameter 

(see Chapter 7) in a variational analysis. 

In a real power plant, the most general case is when several plant components suffer 

simultaneous efficiency deviations. The total fuel impact can be calculated from the 

∆ 〈KP〉 matrix associated with each physical parameter and its causes can be 

explained and quantified component by component. 

This operation is completely new in Thermoeconomics or in any energy analysis 

technique. Thus, the malfunction matrix has a very important engineering application 

and also introduces new theoretical ideas in Thermoeconomics (see Chapter 7). 

6.3.2 Thermoeconomic optimization 

n 

∑ ∑ ∑ ∑ 

n 

Pj , ji 

Here we describe strategies for optimizing complex systems as proposed by Lozano 

et al. (1996). They are based on sequential optimization from component to 

component using the Thermoeconomic Isolation Principle (Evans, 1980). 

A component of a thermal system is thermoeconomically isolated from the rest of the 

system if the product of the component and the unit cost of its resources (internal 

product and/or external resources) are constant and known quantities. If a unit of a 

thermal system is thermoeconomically isolated, the unit may be optimized by itself 

(without considering the modifications of other variables of the rest of the system) 

and the optimun solution obtained for the unit coincides with the optimum solution 

for the whole system. 


0 

i


Of course, TI (Thermoeconomic Isolation) is an ideal condition which cannot be 

achieved in most of the real systems: Pj and k * P,i change when design variables of 

other components change, due to feedback. But the more constant Pj and k * P,i are, the 

closer to TI conditions and the fewer iteration loops needed to achieve the optimal 

solution for the whole system. Thus, the goal is not to achieve TI but to approach it as 

much as possible in order to obtain maximum advantages, which include: 

1. Improvements and optimal design of individual units in highly interdependent 

complex systems are greatly facilitated, as well as of whole systems. 

2. The designers can be specialized and their efforts concentrated on designing the 

variables of single units, while resting assured that these efforts yield optimum 

design and/or improve the overall system. 

3. The convergence of the solution is faster. 

To optimize individual units, the objective function of the cost of product of the 

component –j– could be defined as: 

Min 

κ 

n 

⎛ * ⎞ 

⎜∑κij kPi , ⎟ Pj 

⎝ ⎠ 

i = 0 


(6.57) 

where the unit cost of the input resources kPi , and the production Pj are known and 

constant. 

In real world optimization problems, the design free variables do not necessarily 

coincide with the technical production coefficients. In practice there will be a 

function of the actual design free variables which can be named –x–. 

We say that a free variable x is a local variable of a subsystem –j– when the 

production coefficients κ ij of this subsystem only depend on x. When a design 

variable is attached to several subsystems, the previous expression must be extended 

to all concerned subsystems. 

To determine whether a design free variable is local or not and which components are 

involved, the cost resource impact of the design variables to each component can be 

computed: 

x 

∆C0, j 

* 

kPi , 

∂κ n 

ij 

∑ -------- 

∂x 

i = 0 

∂κZP, j 

⎛ ⎞ 

= 

⎜ + ------------- ⎟ P ∆x 

⎝ ∂x ⎠ 

* 

(6.58)


and the ratio calculated: 

x 

εj ∆ C0, j 

= 

------------------------ 

n 

∑ 

i = 1 

(6.59) 

If this ratio is equal (or close) to 1, the design variable is local for component –j–, if it 

is equal (or close) to zero, the design variable is independent of the referred j 

component. In other cases the design variable involves several components. 

These ideas could be used to design a strategy for global optimization problems: 

1. Determine which variables are local and which are regional (involve several components) 

2. Determine a sequence for local optimization of each component 

3. Take an initial value of the design variables 

4. Calculate technical production coefficients and unit product cost 

5. Find optimum values for local variables 

x 

x 

∆ C0i , 

6. Find optimum values for global variables 

7. Iterate from (3) to convergence when design variables or unit product cost do not 

vary in the next iteration. In each iteration the unit cost of total product must 

decrease. 


CHAPTER 7 

Thermoeconomic analysis of 

a dual-purpose power and 

desalination plant 

The basic concepts and fundamentals of Thermoeconomics were explained in 

Chapter 6 and will now be applied to a dual-purpose power and desalination plant; the 

most important contribution of this Ph. D. Thesis. During the 60’s and early 70’s 

Evans (1962), Tribus (Tribus et al., 1960; Tribus and Evans, 1963) and El-Sayed (El- 

Sayed and Aplenc, 1970; El-Sayed and Evans, 1970) laid down the seminal ideas of 

Thermoeconomics and applied them to the desalination processes. Tribus first 

proposed the term ‘ Thermoeconomics’. 

Since then, Thermoeconomic techniques have 

been developed and applied mostly to power plants. This thesis represents the most 

complete and rigorous thermoeconomic analysis ever made on a complex energy 

system and more specifically on a dual-purpose power and desalination plant. It 

encompasses the whole range between an energy audit based on a detailed cost 

analysis, up to a thermoeconomic optimization, via a thermoeconomic diagnosis of 

several plant component failures. 

The first section of this chapter includes the resolution of the thermoeconomic model 

for the power and desalination plant. The steps to build and solve the thermoeconomic 

model are described in detail. 

The second section contains an in depth cost analysis of the most significant operating 

modes governing the power and desalination plant (including operational and 

investment capital costs) in order to quantify the efficiency of each operation mode. 

This is used to calculate the physical (and therefore more realistic) value of the 

resources consumed to produce every flowstream inside the plant, which is the key to 

an energy audit. An inefficient process can be located and quantified in terms of fuel 

plant consumption. Eight different operating modes were considered in the dualpurpose 

plant, covering the whole range of the diverse combinations: 


160 

Thermoeconomic analysis of a dual-purpose power and desalination plant 

• In the first case, the plant only produced electricity. The second case was the 

opposite: the plant was like a pure distillation unit, producing only desalted 

water. 

• The third to sixth cases studied the effect of partial load operation on the 

efficiency of the installation, starting from maximum production to the minimum 

load of water and electricity demand. 

• The seventh and eighth cases considered the effect of the cleaning ball system on 

the MSF evaporators. In both cases, some live steam was throttled in the HP 

reduction station corresponding to the maximum load of extracting live steam to 

a second MSF unit. 

Non-operating costs were added to the calculated exergy costs. We compared our 

thermoeconomic method with other indirect methods that calculate product costs as 

the accounting of expenses in plant exploitation: fuel, maintenance, amortization, 

etc., divided by the total plant production. 

The third section of this chapter describes a complete thermoeconomic diagnosis of 

the inefficiencies in the units of the power and desalination plant. Not only was the 

additional fuel consumption due to the inefficiency calculated (impact on fuel 

analysis), but also the effect on the behavior of other plant units. This effect was 

separated in different contributions over the rest of devices: malfunctions (induced 

and intrinsic malfunctions) and dysfunctions. Four different loads in the power plant 

were considered and two distillate productions in the MSF plant. These examples 

encompass the most significant operating conditions. Each study considered five 

inefficiencies corresponding to five components of the power plant and three 

inefficiencies in the MSF plant. 

The fourth section applies the thermoeconomic technique based on local 

optimization. The local optimization of energy systems is very valuable to find the 

optimum operating conditions. The plant can be optimized by minimizing the cost of 

the product of each unit, starting from real operating conditions. 

The fifth section analyzes the concepts of price and cost. They were distinguished in 

order to obtain the maximum benefit in plant exploitation. 

Finally, the last section contains the conclusions and some ‘ operation recommendations’ 

from the thermoeconomic analysis. These are very useful to guide managers in 

saving energy and achieving a more cost-effective operation of a dual-purpose plant 

operation. 


FIGURE 7.1 

Thermoeconomic model 

7.1 Thermoeconomic model 

A thermoeconomic model mathematically represents the productive structure of a 

plant. This structure is a graphical representation of the resource distribution. Its 

flows describe the productive relationship among components based on the physical 

structure, although they are not forced to coincide with the existing physical flows of 

the plant. 

The thermoeconomic model should logically be defined after the physical structure 

(section 7.1.2). Then the productive structure is built (section 7.1.3) along with the 

system of characteristic equations that mathematically describe the productive 

structure of the plant (section 7.1.4). Before considering the complex thermoeconomic 

model of the dual plant, a very simple thermoeconomic model of a cogeneration 

system is included in section 7.1.1. It is a simple example of how to build 

a thermoeconomic model and calculate the cost of live steam, water and electricity. 

These can be compared with other methodologies that only account for the cost of the 

final products (water and electricity) with external information or other 

simplifications (see section 7.2.5). 

7.1.1 A simple co-generation system 

A steam generator (boiler), a steam turbine and the MSF plant can represent a very 

simple dual-purpose desalination plant. Auxiliary non-producer elements like heaters, 

pumps or condensers are not included in the scheme. The productive structure in 

figure 7.1 can be built using the F-P definitions in table 7.1. The availability of the 

steam generated in the boiler is sent to the two productive units (steam turbine and 

MSF desalination unit). The fuel and product definition and the characteristic and 

exergy cost equations of every component of the system are included in table 7.1. 

Productive structure of the simple co-generation system. 

C 1 

1 

Boiler 

B 1 

A 

B 1 – B 2 

B 2 

2 

Steam turbine 


3 

MSF unit 

W 

D 

161

TABLE 7.1 

TABLE 7.2 

162 


Fuel, product, characteristic equation and exergy cost balance in the simple co-generation 

system. 

1 Boiler C 

1 

The results of the model (table 7.2) were obtained under maximum continuous rating 

–6 

(MCR). The cost of fuel cf was 2.23× 

10 $/kJ, and the cost of water and electricity 

was also expressed in the most commercial units. 

The values are very similar to the results of the thermoeconomic model explained 

below. This simple model can easily calculate the cost of the two main products using 

thermoeconomic principles. The only requirement is to introduce the quality of the 

steam derived to the MSF unit (from the simulator or an owner’s data sheet). 

7.1.2 Physical structure 

Fuel Product Ch. Equation Cost equation 

B 

1 

C1 

= k1 

B1 

A Branching k * 

A 

2 Turbine B1 

– B2 

3 MSF B 

2 

W 

B1 

– B2 

= k2 

D B2 

= k3 

Results of the simple co-generation system model, MCR case. 

k* 

1 = k 1 cf 

The physical structure of a plant is similar to a set of subsystems or units linked 

among themselves and to the environment by another set of matter, heat, and work 

that express plant behavior more or less accurately, or, in general: 

= k* 

1 

W k* 

2 = k2 

D k* 

3 = k3 

Fuel or product (kW) Unit consumption Exergy cost 

C1 

= 455,000 k1 

= 2.244 k* 

1 = 2.244 

B1 

= 202,800 k2 

= 1.293 

B2 

= 45,000 k3 

= 6.553 

W = 122,000 

D = 6,867 

k* 

2 = 2.902 (= 0.0233 ($/kWh) 

energy system = subsystems or units + matter and/or energy flows 


k * 

A 

k * 

A 

k* 

3 

3 =14.7 (=151.4 kJ/kg, 0.3377 $/m ) 

(7.1)

FIGURE 7.2 


The relationship between the flows and subsystems can be set up in a matrix 

formulation (Lozano and Valero, 1993; Valero et al., 1993), that describes the 

balances of matter, energy and exergy in a very compact form. 

The more detailed the definition of the physical structure, the better the possibilities 

of analyzing the installation. However, a more detailed physical structure implies 

increasing both the number of measurements to be taken in a performance test 

(temperatures, pressures, mass flow rates…) and the complexity of calculations. The 

goal is to find an optimum level of aggregation, i.e. level of detailed description in the 

physical structure corresponding to the depth of analysis. 

The physical structure of the power plant analyzed thermoeconomically is very 

similar to the mathematical model in the simulator (chapter 5). The thermophysical 

properties of the main flowstreams calculated in a simulation can be used as 

reasonable initial values for a thermoeconomic analysis in an operating condition. 

Only the gland steam leakage flow is neglected, which is not significant. Figure 7.2 

shows the physical structure of the power plant. If the power plant is working in 

parallel or twin-extraction mode (that is, the reducing pressure extraction is working), 

the pressure reduction station is included in the physical model. Table 7.3 describes 

the nomenclature adopted in the previous figure. 

Physical structure of the power plant considered for the thermoeconomic model. 


163

TABLE 7.3 

164 


Description of components appearing in figure 7.2. 

Component no. Initials Description 

1 CP Condenser Pump 

2 LPH2 Low Pressure Heater No. 2 

3 LPH1 Low Pressure Heater No. 1 

4 DRT Deaerator 

5 FP Feed Pump 

6 HPH2 High Pressure Heater No. 2 

7 HPH1 High Pressure Heater No. 1 

8 VEX4 th 4 extraction valve 

9 VEX3 rd 3 extraction valve 

10 VEXD Extraction valve to deaerator 

11 VEX2 nd 2 extraction valve 

12 VEX1 st 1 extraction valve 

13 VF Feed valve 

14 BOI Boiler 

15 VB Boiler valve 

16 VST Stop valve 

17 BHP Brine heater pump 

18 HPT1 st 

High pressure turbine (1 section) 

19 HPT2 nd 


20 HPT3 rd 


21 HPT4 th 


22 LPT1 st 


23 LPT2 nd 


24 CND Condenser 

25 GEN Generator 

26 MSF Desalination unit (multistage flash) 

27 VS1 st 

1 Reducing pressure valve (steam) 

28 VS2 nd 2 Reducing pressure valve (vac.) 

29 VS3 rd 

3 Reducing pressure valve (FP) 


FIGURE 7.3 

TABLE 7.4 


However, the physical model considered for the thermoeconomic analysis of the 

MSF unit (figure 7.3) differs from the mathematical model implemented in the 

simulator. The physical model treats the recovery and reject sections as a unique 

component. If these sections are divided into stages, a huge productive structure is 

generated in the plant. Since the functionality of each stage is identical, this 

possibility of plant dissagregation is not considered. Consequently, the input/output 

values of the recovery and reject sections in the simulator can be used as the basis of 

the analysis (their operating data are also available). The pump system of the 

distillation unit is also considered. Exit conditions of these pumps are calculated in 

the thermoeconomic model with their characteristic charts. 

Physical structure of the MSF plant considered for the thermoeconomic analysis. 

Table 7.4 further describes the meaning of figure 7.3. 

Components description from figure 7.3. Note that component no. 1 is not described in physical 

model but is included in other schemes. 

Component no. Initials Description 

2 BH Brine heater 

3 RP Recycle brine pump 

4 BDP Blowdown pump 

5 RCS Recovery section 

6 MIX Mixer 

7 RJS Reject section 

8 SWP Seawater pump 

9 DP Distillate pump 

10 MXT Mixer (temper water) 

11 TP Tempering pump 


165

166 


7.1.3 Productive structure 

A plant is more than a set of flows and units. Each unit has a particular productive 

function which contributes to final production. We will clearly indicate which flow or 

combination of flows constitute the product of the unit (P), which ones are the 

resources or fuel consumed (F) and which flows are the losses (L), i.e. those that 

leave the unit and plant and are not subsequently used. 

The productive structure contains the mathematical definition of the function of each 

component. The production objective (product) and the resources needed (fuel) to 

develop its function are defined for each device, which is equivalent to defining 

efficiency. The productive structure also includes the distribution of consumed 

resources in the different units and how plant products are obtained. 

The best F-P-L definition to represent unit productive function is obtained by 

simultaneously examining their own energy transformation. Using the F-P-L 

definition and the data from the design and operation, it is possible to carry out the 

energy and exergy analysis of the plant. 

The productive structure can be explained in a diagram with squares representing 

physical plant units (productive and dissipative physical processes), and circles and 

rhombuses that are not physical components of the plant. The lines connecting the 

different productive units are exergy resources (fuels and products). The inlet arrows 

going into squares are the fuels of the corresponding components and outlet arrows 

represent products. The circles are branching points where the exergy resource is 

distributed to other components. In every junction (rhombus), a significant exergy 

resource is obtained by the addition of others of the same nature but different origin. 

To apply an on-line thermoeconomic analysis (as presented in Chapter 7) to the dual 

plant, the thermoeconomic model should be disaggregated to a deep enough decision 

level to make use of the most important data provided by the data acquisition system. 

The data acquisition system of the plant is clearly insufficient to provide the data 

required by the productive structure defined in section 7.1 for the power and 

desalination plant. For this reason all required data were provided by the model 

presented in chapters 3 to 5, as if they were measured data provided by the plant 

acquisition system. 

7.1.3.1 Steam power plant 

Depending on the analysis, a productive structure can be designed in different detail 

or aggregation levels. 

For instance, in a thermoeconomic analysis of a power plant, 

the MSF plant is considered a single plant unit in the productive structure. 

The minimum aggregation level is considered for the MSF plant in the productive 

structure of the power plant. The F-P definition used for the power plant follows the 

trend adopted in conventional steam power plants. The difference between thermal, 


FIGURE 7.4 


mechanical and chemical exergy was not considered in the power and desalination 

plant when the productive structure of the system was built. However, a lower 

aggregation level was used in the thermoeconomic analysis of the MSF unit with 

several plant units. The F-P-L definition of the steam power plant components is 

presented in figure 7.4, where B is the exergy flow of a stream (its mass flow rate m 

multiplied by its specific exergy b), W is the work consumed or generated in a 

component, DB is the exergy flow of fresh water leaving the MSF, S is the entropy 

flow of a stream (mass flow m multiplied by the specific entropy s). Exergy losses (L) 

are considered but do not explicitly appear in the productive structure. 

F-P description in steam power plant. 

The fuel and product of each device is defined depending on the functionality of the 

component (Frangopoulos, 1990). Thus, the heater is a component installed to heat 

feedwater (B4 

– B1) 

in a Rankine cycle, with extracted steam supplied by the turbine, 

which is condensed inside the heater (B2 

– B5). 

If the heater has a drain from another 

heater, the fuel also incorporates its exergy flow (B3). 

The job of a steam turbine is to 

produce work (W) by exhausting the steam from a boiler (B1 

– B2). 

A pump has the 

inverse functionality: it uses work (W) as the fuel to increase the pressure of a fluid 

(B2 

– B1). 

A generator is an energy converter, therefore, the fuel is the primary 

(mechanical) energy (W1) 

and the product is secondary (electrical) (W2). 

A valve is a 


167


dissipative component. It undergoes exergy losses when the fuel (B 2) passes through 

the valve (B 1). The fuel and product in a boiler are very clear. A boiler uses primary 

energy like natural gas (B gas) to boil and superheat the feedwater in a steam cycle 

(B 2 -- B 1). The deaerator is a heater with a mixing process of several flows. The 

product is the heating of the colder streams ((m 1 + m 2) b 3 – m 1 b 1 – m 2 b 2) and the 

fuel is the heat released by hotter streams (m 4 b 4 + m 5 b 5 – (m 4 + m 5) b 3). 

The condenser is a dissipative unit which condensates the steam coming from the 

steam turbines to produce liquid water. The heat released (Q) has a low temperature 

and is thus rejected to the atmosphere without any further application. From a 

thermodynamic point of view, the condenser function allows the working fluid 

(water) to reach the physical conditions to perform a new thermodynamic cycle. For 

this reason, several authors (Frangopoulos, 1983; Von Spakovsky, 1986; Benelmir, 

1989) propose negentropy as the condenser product. The negentropy is a 

thermodynamic function (Frangopoulos, 1983) with exergy or energy dimensions but 

with entropy reduction of water/steam in the condenser. The water/steam entropy is 

increased in other plant components. As a result, their negentropy consumption is 

primarily produced in the condenser. The amount of negentropy consumed in a 

component is proportional to its entropy increase. In summary, the exergy losses of 

the different flows entering the condenser are the fuel of the device (B 1 + B 2 + B 3 – 

B 4). The negentropy produced is the condenser product (T 0 (S 4 – S 3 – S 2 – S 1)). 

Finally, the MSF is treated as a component whose main purpose is to produce 

freshwater (DB) using different flows of steam and electricity (B 1 + B 2 – B 3 + W). As 

the steam (B 3) is condensed in the heater of the distillation unit, some negentropy is 

generated in this process (S) which is a secondary product of the MSF (auxiliary 

product or byproduct). 

From the point of view of the diagnosis, the selected productive structure is 

independent of the final results (Valero et al., 1999). The maximum aggregation level 

provides the product and fuel formation cost of each component in the steam plant. 

Although it is complicated to construct a productive structure with a maximum 

aggregation level, it provides the best information to understand the behavior of the 

individual components of a power plant. 

The productive structure is made up of components with exergy added to the working 

fluid of the power plant (steam/water). In this case, the components of the exergy 

addition are the boiler, heaters, deaerator and pumps. The amount of exergy supplied 

to the working fluid is added in a junction and then redistributed (using branching 

points) to the components where the exergy is removed from the working fluid to be 

mixed with another flow or used as fuel of a component. The components of exergy 

removal in the steam cycle with co-generation are the turbine sections, the condenser, 

the MSF unit and the pressure losses in tubes. Finally, a junction is settled to pick up 

the work produced in the turbine sections and, after passing the generator, is 

redistributed to the components that need the electrical consumption as fuel (pump or 



MSF unit). Only two streams leave the plant: distillate flow (DB) and net output 

power, and one stream enters (the exergy flow of fuel). 

Different productive structures were defined for each operating mode because 

different plant units depend on it. For instance, the F-P formulation applied to the 

productive structure generated for the more realistic mode, generating power and 

fresh water (extraction mode, see figure 7.5) does not use the live steam reducing 

pressure station. 

FIGURE 7.5 Productive structure of the power plant in extraction mode. 

When the power plant is working in condensing mode (only electricity is produced), 

brine heater pump and MSF components must be removed, and consequently, the J3 

junction. Figure 7.6 shows the small changes needed to perform the productive 

structure of the condensing mode. 

When the power plant is working in extraction mode at low loads, the low-pressure 

turbine is acting as a compressor. As a result, the condenser and 2 nd section of the 

low-pressure turbine are treated as a component with two fuels: work needed to move 

the turbine and the exergy flow lost in the condenser. Figure 7.7 shows the changes 

applied to this operating mode with respect to the first structure (figure 7.5). 



FIGURE 7.6 Changes applied to extraction mode productive structure (figure 7.5) when the plant operates in 

condensing mode. 

BHP 

17 

J3 

Vacuum 

Steam to MSF 

When the power production is less than a minimum (the outlet pressure of the fourth 

section of the high-pressure turbine is very low), the reduction pressure station is 

automatically opened to maintain steam conditions to the MSF heater (this is the 

parallel mode). The productive structure in figure 7.7 includes the reduction pressure 

valve. Figure 7.8 shows the additional structure added to figure 7.5, which is also 

valid for the twin extraction mode. 

FIGURE 7.7 Productive structure corresponding to extraction mode with low energy production in a dualpurpose 

plant. Changes with respect to figure 7.5. 

Finally, in desalination or twin desalination mode (steam power plant not working), 

the productive structure is quite simple because only six components need to be 

considered to perform the productive structure (see figure 7.9), i.e., those operating in 

this mode. 


MSF 

26


FIGURE 7.8 Productive structure of the steam power plant in parallel and twin extraction mode. Changes with 

respect to figure 7.5. 

FIGURE 7.9 Productive structure of the steam power plant in desalination or twin desalination mode. 

7.1.3.2 MSF unit 

The F-P-L definition of the MSF components is the first step in building the 

productive structure, depending on the aggregation level used to solve the 

thermoeconomic model. In this case, recovery and reject sections are considered one 

component, independently of the number of their stages. This case could be 

considered an intermediate aggregation level, following the physical model 



previously defined in figure 7.3. Figure 7.10 resumes the F-P-L definition applied to 

the MSF plant units. For more information of brine exergy calculation see Annex 2. 

The recovery and reject sections are complex devices. Their products are very clear: 

the distillate produced (DB or DB 2 – DB 1) in each distiller. The resources consumed 

are the exergy released by the flashing brine, which is partially recovered by the 

cooling brine ((B 1 – B 2) – (F 2 – F 1)), and the steam consumed to hold the distillers 

below atmospheric pressure (vacuum). Distillate from the recovery section (DB 1) is 

also a fuel component of the reject section. The brine heater gives the final heating to 

the brine (B 4 – B 3) by condensing vapor bled from the turbine (B 1 – B 2). The mixer 

device produces an outlet stream (B 3) by merging two or more inlet streams 

(B 1 + B 2). 

FIGURE 7.10 F-P definition in the MSF unit. 



Some other interpretations of the F-P definitions were considered to select the 

appropriate productive structure. The objective was to obtain the exact value of the 

exergy cost of the final product (whose value is independent of the productive 

structure) and the F-P definition. But the exergy cost of the intermediate flowstreams 

is obviously different when the fuel and product definition of each component and/or 

the aggregation level is changed. The most important point is to find out the physical 

sense of the flowstreams in the productive structure, in order to explain and study the 

exergy cost of each flow. Several productive structures were studied in this thesis. 

• One possibility is to consider that the exergy recovered in the cooling brine 

(F 2 -- F 1) is a component of the product of these components. The fuel of these 

sections is the exergy released by the flashing brine (B 1 – B 2) and the product is 

the two effects obtained in the sections (F 2 – F 1) + DB. This results of this 

definition are similar to the final F-P definition chosen but it contradicts the 

functionality of the components. 

• The heated cooling brine could be considered a subproduct of the recovery and 

reject sections while maintaining the fuel as in the previous case. The high value 

of the subproduct (F 2 – F 1), (several times the value of distilled water in these 

sections) gives nonsense values for the calculated exergy costs. 

• Consider a zero exergy cost of the MSF plant residues (fourth proposition of the 

exergy cost theory, Valero et al., 1986a). The cost of the rejected cooling 

seawater and blowdown is not charged over the rest of the MSF plant 

flowstreams. This avoids introducing the fictitious device in the productive 

structure of the distillation plant. This consideration is a price allocation because 

the residues are final products external to the system and have zero cost. 

• The distilled water in the recovery section may not be considered a fuel of the 

reject section. The product of the reject section should only be the quantity of 

distilled water produced in that section, not the total amount of freshwater 

produced. This scenario only varies the cost of reject section. 

• The system recovery-reject section could be considered a component, in order to 

avoid the effect of recycling flows in the MSF plant and the modeling of a 

fictitious mixer in the final stage of the distillation plant. This is a higher 

aggregation level than adopted in this thesis. 

• It would not be adequate to consider the chemical exergy of the distillate leaving 

the reject section as the final product of the MSF plant. Its low value would 

imply huge exergy operating costs of the rest of the flowstreams inside the 

distillers. Furthermore, the analysis of a thermal inefficiency in a distiller cannot 

be performed with the F-P definition adopted in this hypothetical assumption. 

The chemical exergy of freshwater only depends on salt concentration and does 

not vary under thermal inefficiency. The only consequence of a thermal 

inefficiency is a thermal exergy variation. 



The formation of the productive structure of the MSF unit is not easily explained with 

the F-P definition considered in the thermoeconomic model (several junctions are 

needed to obtain component fuel and product). As the flows circulating by the MSF 

unit are pumped, the main flows of the plant are added to a junction in which the 

exergy added by the pump is incorporated to the flow. The most significant branching 

points of the MSF plant redistribute their product as a fuel for some components of 

the MSF unit. The first one is the cooling brine heated in the brine heater, the second 

branching has the cooling seawater to reject. But the most amazing situation of this 

structure is the non-physical component or fictitious device (FD). It was included at 

the beginning of the structure to account for residue costs (blowdown and reject 

cooling seawater) in the thermoeconomic model. The cost of steam to brine heater 

(considered to be the main fuel of the plant) is overcharged by the effect of the two 

useless flows sent to sea. The exergy costs of the blowdown and discharged cooling 

brine are used and conveniently incorporated into the rest of the internal costs and the 

final product of the MSF unit. 

Figure 7.11 shows the productive structure of the MSF plant corresponding to the F-P 

definition explained above (figure 7.10), the number of junctions and branches are a 

result of the F-P definition adopted for the recovery and reject sections. The operating 

modes of the power plant do not affect the productive structure of the desalination 

unit, unless the condensing mode is selected (in this case there is no freshwater 

production). 

FIGURE 7.11 Productive structure of the MSF unit. 



7.1.4 Thermoeconomic model 

The thermoeconomic model is the mathematical representation of the productive 

structure. It consists of a group "characteristic equations" which express (for all 

components in the productive structure) each inlet flow as a function of the outlet 

flows and a set of internal parameters, i.e.: 

Unit j: F i = κ ij · P j (7.2) 

Junction j: F i = r ij · P j (7.3) 

Branching point j: F j = ∑ P i (7.4) 

where κ is the technical production coefficient of the unit and r is a structural 

parameter in the junctions or exergy ratio. Equation (7.2) provides information about: 

• the productive function of each commoponent, i.e. its production (P), 

• what the component needs (F) to develop its productive purpose, and 

• the thermodynamic efficiency (κ) of the process taking place in the component. 

The structural equations (7.3) and (7.4) contain the distribution of the resources 

consumed by the plant components, i.e. how the components are interconnected from 

a productive viewpoint. 

The Thermoeconomic model of the steam power plant (extraction mode) has one 7.2type 

equation for each fuel entering a component (57 equations in total), four 

equations for the four junctions and four equations derived from the four branching 

points in the productive structure (figure 7.5). There are 19 characteristic equations in 

the MSF unit model and seven and three equations corresponding to the junctions and 

branching points. 

The characteristic equations (equations 7.2–7.4) can easily be written using the 

productive structure diagram. The subscript numbers of the fuel and products 

correspond to the flow diagram of Chapter 4 (power plant scheme) and Chapter 3 

(diagram of the MSF plant). Table 7.5 includes the equations that describe the 

thermoeconomic model of the steam power plant. 



TABLE 7.5 Exergy flows and characteristic equations of components in the steam power plant (extraction 

mode). 

Dev. Exergy Flows Characteristic equation(s) 

CP 

PCP FSCP = m12 (b12 –b11 ) 

= m12 T0 (s12 –s11 ) 

WCP FSCP = kBCP * PCP = kSCP * PCP LPH2 

LPH1 

DRT 

FP 

HPH2 

HPH1 

VEX4 

VEX3 

VEXD 

PLPH2 = m12 (b14 –b12 ) 

FB1LPH2 = m34 (b34 –b25 )+ mci (bci –b25 ) 

FB2LPH2 = m33 (b23 –b25 ) 

FS LPH2 

= T 0 {m 12 (s 14 –s 12 ) – m 34 (s 34 –s 25 ) 

– m 33 (s 33 –s 25 )– m ci (s ci –s 25 )} 

PLPH1 = m12 (b15 –b14 ) 

FBLPH1 = m33 (b33 –b23 ) 

FSLPH1 PDRT = T 0 {m 12 (s 15 –s 14 )– m 33 (s 33 –s 23 )} 

= m12 (b16 –b15 )+ mdes (b16 –brdes ) 

FB1DRT = m32 (b32 –b16 ) 

FB2DRT = (m30 + m31 ) (b22 –b16 ) 

FSDRT = T0 {m20 s16 –(m30 + m31 ) s22 –m12 s15 – m32 s32 – mdes srdes} PFP FSCP = m20 (b17 –b16 ) 

= m20 T0 (s17 –s16 ) 

PHPH2 = m20 (b19 –b17 ) 

FB1HPH2 = m31 (b31 –b22 ) 

FB2HPH2 = m30 (b21 –b22 ) 

FS HPH2 = T 0 {m 20 (s 19 –s 17 )–m 31 (s 31 –s 22 ) 

– m 30 (s 21 –s 22 )} 

PHPH1 = m20 (b20 –b19 ) 

FBHPH1 = m30 (b30 –b21 ) 

FSHPH1 = T0 {m20 (s20 –s19 )–m30 (s30 –s21 )} 

PVEX4 = m34 (b34 –b25 ) + mci (bci –b25 ) 

FBVEX4 = m34 (b8 –b25 ) + mci (bci –b25 ) 

FSVEX4 = T0 m34 (s34 –s8 ) 

PVEX3 = m33 (b33 –b23 ) 

FBVEX3 = m33 (b6 –b23 ) 

FSVEX3 = T0 m33 (s33 –s6 ) 

PVEXD = m32 (b32 –b16 ) 

FBVEXD = m32 (b5 –b16 ) 

FSVEXD = T0 m32 (s32 –s5 ) 

FB1LPH2 = kB1LPH2 * PLPH2 FB2LPH2 = kB2LPH2 * PLPH2 FSLPH2 = kSLPH2 * PLPH2 FBLPH1 = kBLPH1 * PLPH1 FSLPH1 = kSLPH1 * PLPH1 FB1DRT = kB1DRT * PDRT FB2DRT = kB2DRT * PDRT FSDRT = kSDRT * PDRT 176 Thermoeconomic analysis and simulation of a combined power and desalination plant 

W FP 

FS FP 

= kB FP * P FP 

= kS FP * P FP 

FB1HPH2 = kB1HPH2 *PHPH2 FB2HPH2 = kB2HPH2 * PHPH2 FSHPH2 = kSHPH2 * PHPH2 FBHPH1 = kBHPH1 * PHPH1 FSHPH1 = kSHPH1 * PHPH1 FB VEX4 = kB VEX4 * P VEX4 

FS VEX4 = kS VEX4 * P VEX4 

FB VEX3 = kB VEX3 * P VEX3 


FB VEXD = kB VEXD * P VEXD 

FS VEXD = kS VEXD * P VEXD

VEX2 

VEX1 

VF 

BOI 

VB 



mode). 


VST 

BHP 

HPT1 

HPT2 

HPT3 

HPT4 

LPT1 

LPT2 

CND 

PVEX2 = m31 (b31 –b22 ) 

FBVEX2 = m31 (b4 –b22 ) 

FSVEX2 = T0 m31 (s31 –s4 ) 

PVEX1 = m30 (b30 –b21 ) 

FBVEX1 = m30 (b3 –b21 ) 

FSVEX1 = T0 m30 (s30 –s3 ) 

PVF FBVF FSVF PBOI FSBOI PVB FBVB FSVB PVST FBVST FSVB PBHP FSBHP = m12 (b28 –b11 ) + (m20 –m12 ) (b28 –b16 ) 

= m12 (b20 –b11 ) + (m20 –m12 ) (b20 –b16 ) 

= T0 m20 (s28 –s20 ) 

= m20 (b29 –b28 ) 

= T0 m20 (s29 –s28 ) 

= m12 (b1 –b11 ) + (m20 –m12 ) (b1 –b16 ) 

= m12 (b29 –b11 ) + (m20 –m12 ) (b29 –b16 ) 

= T0 m20 (s1 –s29 ) 

= m12 (b1’ –b11 ) + (m20 –m12 ) (b1’ –b16 ) 

= PVB = T0 m20 (s1’ –s1 ) 

= mdes (brdes –bdes ) 

= T0 mdes (srdes –sdes ) 

FBHPT1 = m20 (b1’ –b3 ) 

= T0 m20 (s3 –s1’ ) 

FS HPT1 

FBHPT2 = (m20 –m30 –mva ) (b3 –b4 ) 

= T0 (m20 –m30 –mva ) (s4 –s3 ) 

FS HPT2 

FBHPT3 = (m20 –m30 –mva–m31 ) (b4 –b5 ) 

= T0 (m20 –m30 –mva –m31 ) (s5 –s4 ) 

FS HPT3 

FBHPT4 = (m20 –m30 –mva –m31 –m32 ) (b5 –b6 ) 

= T0 (m20 –m30 –mva –m31 –m32 ) (s6 –s5 ) 

FS HPT4 

FBLPT1 FSLPT1 FBLPT2 FSLPT2 P CND 

FB CND 

= (m9 + m34 ) (b6 –b8 ) 

= T0 (m9 + m34 ) (s8 –s6 ) 

= m9 (b8 –b9 ) 

= T0 m9 (s9 –s8 ) 

= T0 {m9 s9 + (m34 + m33 + mci ) s25 + mva sva –m12 s11 } 

= m9 b9 + (m34 + m33 + mci ) b25 + mva bva – m12 b11 FB VEX2 = kB VEX2 * P VEX2 


FB VEX1 = kB VEX1 * P VEX1 


FB VF 

FS VF 

C 1 

FS BOI 

FB VB 

FS VB 

FB VST 

FS VST 

W BHP 

FS BHP 

= kB VF * P VF 

= kS VF * P VF 

= kB BOI * P BOI 

= kS BOI * P BOI 

= kB VB * P VB 

= kS VB * P VB 

= kB VST * P VST 

= kS VST * P VST 

= kB BHP * P BHP 

= kS BHP * P BHP 

FB HPT1 = kB HPT1 * W HPT1 

FS HPT1 

= kS HPT1 * W HPT1 


FS HPT2 



FS HPT3 



FS HPT4 

FB LPT1 

FS LPT1 

FB LPT2 

FS LPT2 

FB CND 


= kB LPT1 * W LPT1 

= kS LPT1 * W LPT1 

= kB LPT2 * W LPT2 

= kS LPT2 * W LPT2 

= kB CND * P CND 


GEN 

MSF 

W T 



mode). 

= W HPT1 + W HPT2 + W HPT3 

+ W HPT4 + W LPT1 + W LPT2 

FB1MSF = mdes (b6 –bdes ) 

FB2MSF = mva (b3 –bva ) 

FS MSF 

A FB J3 = m des (b 6 –b 16 ) 

= T 0 {m des (s des –s 6 )+ m va (s va –s 3 )} 

The physical model of the thermoeconomic analysis differs from the mathematical 

model presented in Chapter 3. Figure 7.12 shows the exergy flows considered in the 

thermoeconomic model of the MSF plant (which also appear in the characteristic 

equations in table 7.6). We used the flow nomenclature adopted in Chapter 3. 

FIGURE 7.12 Physical model considered in the thermoeconomic analysis of the MSF plant. 


W T 

= k GEN * P GEN 

WMSF = kB3MSF * PD FB1MSF = kB1MSF * PD FB2MSF = kB2MSF * PD FSMSF = kSMSF * PD P VST = FB VEX4 + FB VEX3 + FB VEX2 + FB VEX1 

+ FB VEXD + FB2 LPH2 + FB2 DRT + FB2 HPH2 

+ FB HPT1 + FB HPT2 + FB HPT3 + FB HPT4 

+ FB LPT1 + FB LPT2 + FB J3 + FB CND +FB2 MSF 

B P DRT = m 12 (b 16 –b 15 ) + m des (b 16 –b rdes ) 

C P GEN = W TN + W FP + W CP +W MSF +W BHP 

J1 


F VF 

= r FP * P FP + r LPH2 * P LPH2 + r LPH1 

* P LPH1 + r DRTj1 * m 12 (b 16 –b 15 ) 

+ r CP * P CP + r HPH2 * P HPH2 + r HPH1 * P HPH1 

J2 FVB = rVF * PVF + rBOI * PBOI J3 

FB1MSF = rJ3 * FBJ3 + rDRTj3 * mdes (b16 –brdes ) + rBHP * PBHP WT = rHPT1 * WHPT1 + rHPT2 * WHPT2 J4 

+ rHPT3 * WHPT3 + rHPT4 * WHPT4 + rLPT1 * WLPT1 + rLPT2 * WLPT2


TABLE 7.6 Exergy flows and characteristic equations for the components of the MSF plant. 

Devices Exergy flows Characteristic equation(s) 

FD 

BH 

P FD = m des (b 6 – b des ) ≡ FB1 MSF 

F1 FD = P FD 

F2 FD = BD b 10 

F3 FD = CW b 13 

PBH = R (b4 – b3 ) 

FBH = PFD F1 FD = k1 FD * P FD 

F2 FD = k2 FD * P FD 

F3 FD = k3 FD * P FD 

P BH = k BH * P BH 

RP P RP = R (b 7 – b 8 ) W RP = k RP * P RP 

BDP P BDP = BD (b 10 – b 8 ) W BDP = k BDP * P BDP 

RCS 

MIX 

RJS 

PRCS = Drcs b5 F1RCS = R b4 – (R – Drcs ) b6 – R (b3 – b7 ) 

F2RCS ≡ 0.5 FB2MSF F3 RCS = 0.5 m vent b 15 

P MIX = R b 8 

F1 MIX = (R – D – BD) b 9 

F2 MIX = F b 13 

P RJS = D b 11 

F1RJS = (R – Drcs ) b6 – (R – D) b9 + Drcs b5 – SR (b13 – b17 ) 

F2RJS = 0.5 FB2MSF F3RJS = 0.5 mvent b15 F1 RCS = k1 RCS * P RCS 

F2 RCS = k2 RCS * P RCS 

F3 RCS = k3 RCS * P RCS 

F1MIX = k1MIX * PMIX F2MIX = k2MIX * PMIX F1RJS = k1RJS * PRJS F2RJS = k2RJS * PRJS F3RJS = k3RJS * PRJS SWP P SWP = SW (b 15 – b 16 ) W SWP = k SWP * P SWP 

DP P DP = D (b 12 – b 11 ) W DP = k DP * P DP 

MXT 

P MXT = SR b 17 

F1 MXT = TP b 14 

F2 MXT = (SW – m vent ) b 15 

F1 MXT = k1 MXT * P MXT 

F2 MXT = k2 MXT * P MXT 

TP P TP = TP (b 14 – b 13 ) W TP = k TP * P TP 

JA 

P JA = F2 FD 

F1 JA = P BDP 

F2 JA = BD b 8 

P JA = r1 JA * F1 JA + r2 JA * F2 JA 



TABLE 7.6 Exergy flows and characteristic equations for the components of the MSF plant. 

Devices Exergy flows Characteristic equation(s) 

JB 

C 

JD 

7.2 Cost analysis 

PJB = R b4 – R (b3 – b7 ) 

F1JB = PBH F2JB = PRP F3JB = PMIX F1JD = (R – Drcs ) b6 – (R – D) b8 – SR (b13 – b17 ) 

F1JI = SR (b13 – b17 ) 

P JD = F1 RJS 

F2 JD = P RCS 

P JB = r1 JB * F1 JB + r2 JB * F2 JB 

+ r3 JB * F3 JB 

P JB = F2 JA + F1 JD + F1 RCS + F1 JI 

+ F1 MIX 

P JD = r1 JD * F1 JD + r2 JD * F2 JD 

E F1 JK = TP b 13 P JI = F3 FD + F1 JK + F2 MIX 

JG 

P JG = SR b 15 

F1 JG = P SWP 

F2 JG = SR b 16 

P JG = r1 JG * F1 JG + r2 JG * F2 JG 

H P JG = F3 RCS + F3 RJS + F2 MXT 

JI 

JJ 

JK 

P JI = SR b 13 

F2 JI = P MXT 

P JJ = P D = D b 12 

F1 JJ = P RJS 

F2 JJ = P DP 

P JK = F1 MXT 

F2 JK = P TP 

P JI = r1 JI * F1 JI + r2 JI * F2 JI 

P JJ = r1 JJ * F1 JJ + r2 JJ * F2 JJ 

P JK = r1 JK * F1 JK + r2 JK * F2 JK 

Thermoeconomic analysis combines the First and Second Law of Thermodynamics 

along with monetary cost balances at the system component level. It helps to 

understand the process of cost formation, minimize overall product costs and assess 

costs of the different products obtained in the processes. The cost accounting method 

can calculate costs using rough data from an energy system control room (pressures, 

temperatures, mass flow rates, electrical production, fuel consumption, excess of 

oxygen etc. and the economic data). 

The costs of all significant mass and energy flowstreams is a very powerful and 

interesting piece of information about the amount of resources used to obtain each 


Cost analysis 

significant mass and energy flowstream. Knowing the costs of the mass and energy 

flowstreams is the key to thermoeconomic analysis. The first consequence is price 

assessment of the products based on physical criteria. 

7.2.1 Exergy costs allocation 

Valero et al. (1986a) present the fundamental problem of cost allocation as follows: 

Given a system whose limits have been defined and a level of aggregation that 

specifies the subsystems which constitute it, how to obtain the cost of all the flows that 

become interrelated in this structure. 

The origin of every cost lies in the irreversibility of the processes. This is a 

cornerstone in thermoeconomics. But how do we link the variation in the local 

irreversibility (∆I i) to the increase of resources consumed (∆F T)? 

Two factors are added to consider the economic: market prices (cf), which are not 

necessarily linked to the exergy of the processed resources and depreciation, and 

maintenance costs of the productive process (Z). The thermoeconomic cost of a flow 

can be calculated after the second factor is introduced (section 7.2.3). The exergy 

costs calculated in this section only take into account the fuel consumed to produce 

each flowstream. 

Valero et al (1986a) also propose a rational procedure to determine the cost of all 

mass and energy flowstreams based on four propositions presented in the ‘Theory 

of exergetic cost’. Consider a plant with n units and m flows with known exergy 

flows. The set of balances of exergy costs (P1 proposition) of the n units provides a 

system of n equations. The number of flows will be higher than the number of 

units, and (m – n) auxiliary equations will be needed to determine flow cost. Serra 

(1994) demonstrated that the rest of the required equations are obtained from the 

productive structure of the plant through the F-P-L definition of its units and the 

subsequent application of the Theory of exergetic cost. 

The Structural Theory of Thermoeconomics (Valero et. al, 1993) based on the rules of 

mathematical derivation provides exactly the same system of cost equations. 

Consequently, this theory can calculate flow cost of the above four propositions by 

simply applying the chain rule of derivatives to the characteristic equations of the 

thermoeconomic model (as explained in Chapter 6). The system of equations 

providing the exergy costs of the steam power plant (cost of the flows appearing in 

the productive structure depicted in figure 7.5) is shown in table 7.7. Note that 

negentropy is included in the cost equation of each component as a second fuel. The 

negentropy generated in the condenser must be allocated to the rest of the plant 

components as a function of their entropy increase. 



TABLE 7.7 System of equations providing the unit exergy costs of the steam power plant (extraction mode). 

Device Exergy cost balance 

* 

* 

CP kCP = kBCP kCPw + kSCP * 

* 

* 

LPH2 kLPH2 = kB1LPH2 kVEX4 + kB2LPH2 kLPH2v + kSLPH2 * 

* 

LPH1 kLPH1 = kBLPH1 kVEX3 + kSLPH1 * 

* 

* 

DRT kDRT = kB1DRT kVEXD + kB2DRT kDRTv + kSDRT * 

* 

FP kFP = kBFP kFPw + kSFP * 

* 

* 

HPH2 kHPH2 = kB1HPH2 kVEX2 + kB2HPH2 kHPH2v + kSHPH2 * 

* 

HPH1 kHPH1 = kBHPH1 kVEX1 + kSHPH1 * 

* 

VEX4 kVEX4 = kBVEX4 kVEX4v + kSVEX4 * 

* 


* 

VEXD kVEXD = kBVEXD kVEXDv + kSVEXD * 

* 


* 


* 

VF kVF = kBVF kJ1 + kSVF * 

* 

BOI kBOI = kBBOI kFUEL + kSBOI * 

* 

VB kVB = kBVB kJ2 + kSVB * 

* 

VST kVST = kBVST kVB + kSVST * 

* 

BHP kBHP = kBBHP kBHPw + kSBHP * 

* 

HPT1 kHPT1 = kBHPT1 kHPT1v + kSHPT1 * 

* 


* 


* 

HPT4 kHPT4 = kBHPT4 kHPT4v + kSHPT4 182 Thermoeconomic analysis and simulation of a combined power and desalination plant 

* 

kCPs * 

kFPs * 

kVFs * 

kVBs * 

kBOIs * 

kVSTs * 

kLPH1s * 

kHPH1s * 

kBHPs * 

kVEX4s * 

kVEX3s * 

kVEXDs * 

kVEX2s * 

kVEX1s * 

kHPT1s * 

kHPT2s * 

kHPT3s * 

kHPT4s * 

kDRTs * 

kLPH2s * 

kHPH2s


TABLE 7.7 System of equations providing the unit exergy costs of the steam power plant (extraction mode). 

Device Exergy cost balance 

* 

* 

LPT1 kLPT1 = kBLPT1 kLPT1v + kSLPT1 * 

* 

LPT2 kLPT2 = kBLPT2 kLPT2v + kSLPT2 * 

CND kCND = kBCND * 

GEN kGEN = kBGEN * 

* 

* 

* 

MSF kMSF = kB3MSF kMSFw + kB1MSF kJ3 + kB2MSF kMSFv + kSMSF J1 

* * 

J2 kJ2 = rVF kVF + rBOI * 

* 

* 

J3 kJ3 = rDRTj3 kDRTJ3 + rVA kJ3v + rBHP J4 

A 

* 

* 

* 

* 

= rHPT1 kHPT1 + rHPT2 kHPT2 + rHPT3 kHPT3 + rHPT4 kHPT4 + rLPT1 + r LPT2 

* * * * 

B kGEN = kFPw = kCPw = kMSFw = 

* * 

C kDRT = kDRTJ1 = 

D 

* 

kJ1 * 

kJ4 * 

kCNDv * 

kJ4 * 

kLPT1s * 

kLPT2s * 

kMSFs * 

* 

* 

* 

* 

= rFP kFP + rLPH2 kLPH2 + rLPH1 kLPH1 + rDRTj1 kDRTJ1 + rHPH2 kHPH2 * 

* 

+ rHPH1 kHPH1 + rCP kCP * 

kLPT2 * 

kBOI * 

kBHP * 

kLPT1 * * * * 

* 

* 

* 

* 

kVST = kLPH2v = kDRTv = kHPH2v = kVEX4v = kVEX3v = kVEX2v = kVEX1v * * * * * * * 

= kHPT1v = kHPT2v = kHPT3v = kHPT4v = kLPT1v = kHPT2v = kCNDv * * 

= kMSFv = kJ3v * 

kDRTJ3 * 

kBHPw * * * * * * * * 

kCND = kCPs = kLPH1s = kLPH2s = kDRTs = kFPs = kHPH1s = kHPH2s * 

* 

* 

* 

* 

* * 

= kVEX4s = kVEX3s = kVEXDs = kVEX2s = kVEX1s = kVFs = kBOIs * * * * * * * 

= kVBs = kVSTs = kBHPs = kHPT1s = kHPT2s = kHPT3s = kHPT4s * * * 

= kLPT1s = kLPT2s = kMSFs In the system of equations providing the exergy costs of the MSF plant (table 7.8), the 

negentropy does not appear, although the brine heater is acting as a plant condenser. 

The negentropy decreases energy waste in the condenser and improves the power 

plant efficiency. 



TABLE 7.8 System of equations providing the exergy costs of the MSF plant (figure 7.11). 

Components Exergy cost equations 

* 

* 

* 

FD kFD = k1FD kST + k2FD kJA + k3FD * 

BH kBH = kBH * 

RP kRP = kRP * 

BDP kBDP = kBDP * 

* 

* 

RCS kRCS = k1RCS kRCSf1 + k2RCS kVA + k3RCS * 

* 

MIX kMIX = k1MIX kMIXf1 + k2MIX * 

* 

* 

RJS kRJS = k1RJS kJD + k2RJS kVA + k3RJS * 

SWP kSWP = kSWP * 

DP kDP = kDP * 

* 

MXT kMXT = k1MXT kJK + k2MXT * 

TP kTP = kTP * 

kFD * 

kW * 

kW * 

kW * 

kW * 

kW * 

* 

JA kJA = r1JA kBDP + r2JA * 

* 

* 

JB kJB = r1JB kBH + r2JB kRP + r3JB * 

* 

JD kJD = r1JD kJDf1 + r2JD * 

* 

JG kJG = r1JG kSWP + r2JG * * 

JI kJI = r1JI kJIf1 + r2JI * * 

JJ kJJ = r1JJ kRJS + r2JJ * 

* 

Jk kJK = r1JK kJKf1 + r2JK * * * * * 

C kJB = kJAf2 = kJDf1 = kRCSf1 = kJIf1 = 

* * * 

E kJI = kMIXf2 = kFDf3 = 

* 

kJAf2 * 

kRCS * * * 

F kJG = kRCSf3 = kRJSf3 = 

* 

kMIXf2 * 

kMXTf2 * 

kMIX * 

kFDf3 * 

kRCSf3 * 

kRCSf3 184 Thermoeconomic analysis and simulation of a combined power and desalination plant 

* 

kSW * 

kMXT * 

kDP * 

kTP * 

kJKf1 * 

kMXTf2 * 

kMIXf1


7.2.2 Exergy cost analysis 

We calculated the exergy costs for the productive structure in figure 7.5 and analyzed 

them under eight different operating conditions with equations in table 7.7. They are 

expressed in energy units and represent the amount of resources (usually natural gas) 

consumed to obtain each significant mass and energy flowstream. These only 

represent the operation costs (they do not include the cost of each plant device) in 

terms of energy. 

The thermodynamic properties of the mass and energy flowstreams (figures 7.2 

and 7.3) were obtained by the simulator. The main features of each case are shown in 

table 7.9. Most of them correspond to a performance data case of the power plant, 

already described in Chapter 4. 

TABLE 7.9 Case studies of the exergy cost analysis (PTC: Performance Test Case of the dual plant; Gc: 

Natural gas consumed; CBS: Cleaning Ball System was used). 

Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 

PTC MR ODOB MCR MSL4 PL85 — MSL3 — 

W (kW) 146,693 — 122,000 75,440 91,000 53,500 76,500 71,000 

mls (kg/s) 156.187 70.38 156.187 109.5 117.39 70.0 170.0 160.0 

Gc (Nm 3 /h) 43,090 22,780 43,460 31,560 33,650 20,850 49,340 49,390 

LS (GCal/h) 0.0 150.0 0.0 0.0 0.0 0.0 150.0 150.0 

mdes (kg/s) 0.0 88.5 89.68 88.63 75.62 41.7 83.0 73.5 

Pc (bar) 0.135 — 0.072 0.021 0.055 0.048 0.048 0.048 

D (T/h) — 2,418.0 2,418.0 2,418.0 2,060.0 1,216.3 2,260.5 2,309.5 

TBT (º C) — 112.0 112.0 112.0 100.0 84.0 112.0 112.0 

SW (º C) — 25.0 25.0 25.0 25.0 32.0 32.0 32.0 

CBS NO NO NO NO NO NO NO YES 

Most case studies corresponded to the limited operating conditions. The operating 

mode in each study was as follows: 

Case 1 The plant was only working as a full load power plant with no distilled 

water production (condensing mode). 

Case 2 The opposite of case 1. The plant was working as a pure distillation 

unit, producing only fresh water (desalination mode). 

Case 3 The nominal case: the plant was working at full load producing the 

maximum distilled water and maximum power (extraction mode). 

Case 4 The more usual operating conditions in winter (parallel mode). 



Case 5 Partial load operating conditions (extraction mode). 

Case 6 Minimum load operating conditions (parallel mode). 

Cases 7&8 The effect of the cleaning ball system was analyzed. In both cases some 

live steam was throttled in the reducing pressure station: the maximum 

load extracting live steam to a second MSF unit (twin extraction mode). 

The exergy and exergoeconomic costs of the most significant mass and energy 

* 

flowstreams (live steam generated in the boiler kBOI , steam to MSF vacuum system 

* 

* 

* 

kVST , steam to MSF brine heater kMSF , electric power kGEN and distilled water 

* 

kD ) appear in tables 7.10 and 7.11 respectively. No other energy analysis based on 

the First Law of Thermodynamics can provide this information, i.e., the amount 

(exergy or $) of the fuel plant consumed to obtain a flow. 

The unit costs in this section (the cost per unit exergy of the considered flow) only 

refer to the operating costs since they do not take into account the capital cost 

investment of the plant units. 

Afgan, Darwish and Carvalho (1999) quantified the primary energy or fuel needed to 

produce 1 kg of freshwater in a single purpose MSF desalination plant (case 2 in our 

analysis) and a dual purpose MSF desalination plant (case 3). These values (445 kJ 

and 225.7 kJ respectively) are based on an energy analysis of the dual-plant products 

and are quantitatively similar. 

Both tables provide the same information expressed in different units. The calculated 

costs are operating costs, discounting investment capital costs. The exergoeconomic 

costs c* were obtained by considering the natural gas market price (cf) of 2.35 ($/ 

MBTU). 

TABLE 7.10 Exergy (kW fuel/kW product) unit costs k* of most significant flows of the dual plant. 

* 

kBOI * 

kVST * 

kMSF * 

kGEN k D * 

k * Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 

a 

2.733 2.371 2.604 2.590 2.576 2.572 2.677 2.559 

2.842 3.147 2.657 2.620 2.616 2.611 2.714 2.600 

— 3.871 2.693 2.644 2.667 2.650 3.650 3.615 

3.286 — 2.938 2.955 2.938 3.149 3.042 2.935 

— 416.511 221.67 224.99 227.67 261.02 549.48 526.38 

bD (kJ/kg) — 10.35 10.35 10.35 9.81 11.62 13.29 12.98 

a. 

* 

Exergy of water kD measured in a more realistic unit: (kJ fuel/kg water), therefore is included the exergy of water leaving the MSF 

unit (bD, in kJ/kg). 



TABLE 7.11 Exergoeconomic (monetary) unit costs ($/GJ) of most significant flows of a dual power and 

desalination plant. Cost of water c* D is expressed in $/m 3 , and electricity cost of is also 

expressed in $/kW·h (c* GEN*). 

c* BOI 

c* VST 

c* MSF 

c* GEN 

c* * 

GEN 

c D * 

c * Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 

6.087 5.281 5.799 5.770 5.738 5.728 5.964 5.699 

6.331 7.010 5.913 5.835 5.827 5.816 6.046 5.792 

— 8.621 5.997 5.888 5.940 5.902 8.130 8.052 

7.319 — 6.543 6.583 6.545 7.014 6.775 6.537 

0.0263 — 0.0235 0.0237 0.0235 0.0252 0.0244 0.0235 

— 0.9277 0.4937 0.5011 0.5071 0.5814 1.223 1.172 

These values only contain the irreversibilities, the destruction of exergy or useful 

energy in the productive process. The live steam cost is always lower because it is 

generated at the very beginning of the production process. The irreversibilities during 

natural gas combustion and heat transfer inside the boiler increase the cost of this 

steam. 

Flowstreams further down the productive process were more costly. All processes in 

the plant were irreversible (see table 7.12) and the total exergy destroyed 

continuously increased throughout the productive process. The amount of exergy 

required to obtain a flow (exergy cost) also increased. For this reason, the final 

products had the highest costs. 

The effect of irreversibilities in the cost generation process is clearly shown by 

comparing studies 7 and 8. The cleaning ball system directly decreases distilled water 

cost by decreasing the irreversibility in the MSF plant (see table 7.12) and increasing 

efficiency (table 7.14). This benefit in the MSF plant also affects the power plant. The 

amount of steam needed in the MSF plant brine heater decreases (see table 7.9), 

increasing the steam mass flow rate expanded in the LP turbine and the electrical 

power produced. Modifying the operating conditions of the MSF affects the electrical 

cost. 

Irreversibilities (table 7.12) may have different costs. For example, boiler 

irreversibilities (I BOI) are much higher than MSF plant irreversibilities (I MSF), but live 

steam cost is lower than distilled water cost. 



TABLE 7.12 Irreversibilities (exergy destruction, kW) in the different components of the dual plant. MSF unit is 

considered a component. 

I Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 

I CP 89.26 58.44 13.93 16.53 13.84 4.94 7.94 16.52 

I LPH2 2,125.1 — 277.6 38.40 118.0 148.8 26.34 42.77 

I LPH1 1,687.8 — 363.0 80.85 279.0 268.2 28.97 219.7 

I DRT 306.0 655.5 990.4 544.1 1,362.4 638.7 821.1 2,317.7 

I FP 265.0 — 212.3 124.7 123.4 229.5 601.9 549.8 

I HPH2 243.2 — 505.4 274.1 329.7 77.61 454.3 566.6 

I HPH1 513.8 — 688.7 368.2 430.6 204.2 661.9 737.6 

I BOI 265,908.9 — 268,206.6 195,921.1 208,749.0 130,195.6 306,254.9 306,605.8 

I VST 89.62 — 1,157.2 394.8 493.7 105.0 423.0 442.7 

I HPT1 2,206.0 — 2,254.8 4,870.4 4,379.7 5,983.7 4,734.6 4,698.4 

I HPT2 250.5 — 637.2 451.1 489.8 112.8 467.1 479.8 

I HPT3 303.5 — 813.9 508.4 595.6 240.1 512.8 539.4 

I HPT4 955.4 — 2,369.5 1,097.1 1,464.0 583.0 912.5 1,054.3 

I LPT1 4,265.0 — 1,888.0 470.0 945.6 1,097.2 131.0 1,139.1 

I LPT2 9,598.9 — — — — 732.3 — 230.1 

I CND 37,816.7 — — — — 3,260.5 — 1,769.3 

I GEN 2,041.7 — — — — 1,372.9 — 1,489.5 

I VS1 — 38,198.1 — — — — 33,892.9 35,451.4 

I VS2 — 314.4 — — — — — — 

I VS3 — 1,750.2 — — — — — — 

I TOT-PP 329,734.2 185,880.0 292,042.4 206,923.9 226,061.2 145,255.9 351,501.1 358,339.3 

I TOT-MSF — 67,482.6 67,014.5 66,954.5 56,843.2 35,350.0 117,924.4 106,596.9 

The reasons for the impressive cost of distilled water are: 

• The large amount of exergy destruction (irreversibility) in the MSF plant, 

considering the high fuel value of the MSF unit (steam exhausted in brine heater 

and ejectors, electrical consumption) and the low value of the product 

(freshwater exergy flow). The energy and exergetic cost balance must be fulfilled 

(Valero, Muñoz and Lozano, 1986c). 



• The low distillate exergy flow is due to the low freshwater temperature leaving 

the MSF unit (see the last row in table 7.10. The different values stem from the 

different distilled water temperatures in different operating conditions (which 

strongly depends on the seawater temperature entering the desalination unit). 

The contribution of chemical and mechanical exergy to the global exergy flow of 

seawater flows is minimum. Consequently, the final exergy cost is very low but 

the intermediate flows inside the distiller can be extremely high (the flashing 

brine, cooling brine, etc). The relationship between the inlet/outlet exergy flows 

which determine the exergy unit consumption k in the characteristic equations 

that model MSF thermoeconomics, is quite elevated in this example. The exergy 

unit consumption k propagates the exergy cost of the final product increasing the 

cost of water from the exergetic point of view. 

• The resources consumed in the MSF units are not primary energy. The electricity 

and steam produced to the distiller were produced in the power plant and the cost 

of the fuels of the MSF do not have a unit exergy cost. Only primary energy has 

an exergy cost equal to one (as natural gas entering the boiler). 

Another important result was the significantly higher water cost when the live steam 

was throttled through the HP reduction station (cases 2, 7 and 8). This has a physical 

explanation related with energy quality degradation. When the live steam expands 

through a throttle valve, its energy content remains stable while its exergy decreases 

(pressure is dramatically reduced in the reduction pressure station). The exergy 

destruction in the pressure reduction station correspond to I VS1, I VS2 and I VS3 

(table 7.12). 

Regarding component efficiencies, the more efficient a process the lower cost 

generated. Consider, for example, turbine efficiencies (table 7.13). 

TABLE 7.13 Isoentropic efficiencies of pumps and turbine sections of the power plant. 

η (%) Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 

HPT1 0.733 — 0.719 0.546 0.581 0.430 0.558 0.560 

HPT2 0.939 — 0.949 0.913 0.919 0.885 0.921 0.922 

HPT3 0.978 — 0.950 0.950 0.950 0.978 0.950 0.950 

HPT4 0.968 — 0.938 0.941 0.939 0.947 0.940 0.938 

HPT5 0.812 — 0.847 0.865 0.857 0.857 0.864 0.864 

LPT1 0.873 — 0.752 < 0 0.820 0.815 0.070 0.802 

LPT2 0.738 — 0.729 < 0 0.737 0.746 < 0 0.756 

FP 0.861 0.807 0.861 0.855 0.870 0.692 0.735 0.737 

CP 0.778 — 0.773 0.113 0.627 0.588 0.077 0.377 



The live steam generated in the boiler is expanded in the HP turbines, before being 

extracted to the brine heater of the MSF plant. For this reason, the difference between 

the cost of steam to brine heater and the cost of live steam for the analyzed cases is 

directly related to the HP turbines efficiencies. Thus, the higher the HP turbine 

efficiency, the lower the cost difference in brine heater and live steam. 

A similar result is obtained for the cost difference between live steam and power 

generated. In the analysis, the low-pressure turbine efficiencies also influenced the 

observed differences. 

Table 7.14 contains global efficiency parameters for the whole plant and for the 

power and MSF plants. As in the device analysis, the more efficient the global 

process, the lower the cost of the final product. For example, in cases 7 and 8 the 

cleaning ball system clearly increases the exergy efficiency of the MSF plant and the 

whole plant. The distilled water and power cost decrease as a result. The exergetic 

efficiency we obtained for the MSF plant is similar to other estimate (Hamed 

et. al, 1999). 

TABLE 7.14 Product and fuel (kW), and exergetic efficiency (%) values for the power and MSF plants. Note: 

The efficiency of the boiler is not included in the final efficiency. 

Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 

P PP 144,260.4 64,712.9 186,024.8 140,244.6 144,096.3 87,113.3 191,289.9 184,994.0 

P MSF — 6,951.78 6,951.78 6,951.78 5,613.4 3,925.9 8,344.9 8,326.9 

F PP 473,994.6 250,592.9 478,067.2 347,168.5 370,157.5 229,369.2 542,791.0 543,333.3 

F MSF — 74,434.4 73,966.4 73,906.3 62,456.6 39,275.9 126,269.3 114,923.8 

η PP 30.4 0.0 38.9 40.4 38.9 36.7 35.2 34.0 

η MSF — 9.3 9.4 9.4 9.0 10.0 6.6 7.2 

η TOT 30.4 2.7 24.9 21.1 23.6 21.3 13.5 14.4 

Finally, product costs of different plant components were also calculated (see 

table 7.15). 

The steam leaving the boiler has a lower exergy cost since the fuel plant exergy only 

degraded in the boiler tubes (the combustion and heat transfer process is non-ideal). 

As the steam passes through the turbine section, its energy quality gradually 

degrades: the exergy cost increases from the first to the last turbine section. The 

exergy cost of the electricity is a weighted sum of the exergy costs of the turbine 

sections. The inefficiencies of the pumps increase the exergy cost of the electricity. 



The energy quality of the steam extracted for the heaters is degraded in this heating 

process. Although the live steam is the cheapest in desalination mode (case 2), the 

exergy cost of the steam to the MSF unit has a higher cost than the steam provided 

when the plant is producing electricity. The reduction pressure station is more 

inefficient than the set of components turbine-heaters-condenser. 

TABLE 7.15 Unit exergy costs k* (kW/kW) of component products in the steam power plant coupled with a 

MSF unit. 

k* Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 

* 

kCP 4.942 — 3.957 20.67 4.960 3.396 16.45 8.020 

* 

kLPH2 3.851 — 3.476 8.106 3.465 3.664 5.363 3.824 

* 

kLPH1 3.389 — 3.177 3.592 3.230 3.249 3.393 3.400 

* 

kDRT 3.040 4.306 3.021 2.944 3.283 3.280 3.059 3.473 

* 

kFP 3.764 3.151 3.282 3.272 3.223 4.077 3.771 3.560 

* 

kHPH2 2.992 — 2.850 2.793 2.796 2.729 2.926 2.822 

* 

kHPH1 3.034 — 2.853 2.796 2.797 2.789 2.930 2.813 

* 

kBOI 2.733 2.371 2.604 2.590 2.576 2.572 2.677 2.559 

* 

kVST 2.842 — 2.657 2.620 2.616 2.611 2.714 2.600 

* 

kHPT1 3.001 — 2.794 2.988 2.925 3.261 3.074 2.926 

* 

kHPT2 2.881 — 2.739 2.706 2.701 2.648 2.807 2.686 

* 

kHPT3 2.910 — 2.778 2.735 2.735 2.706 2.841 2.719 

* 

kHPT4 3.282 — 3.029 2.935 2.951 2.952 3.049 2.918 

* 

kLPT1 3.373 — 3.533 10.434 3.191 3.350 15.711 4.164 

* 

kLPT2 3.858 — 3.660 — 3.577 3.505 — 3.506 

* 

kVS1 — 3.851 — — — — — 4.591 

* 

kVS2 — 3.017 — — — — — — 

* 

kVS3 — 3.527 — — — — — — 

7.2.3 Thermoeconomic costs 

The thermoeconomic cost of a flow has two parts, one from the monetary cost of the 

fuel (natural gas) exergy needed to produce this flow, i.e., its exergoeconomic cost 

(Valero, Muñoz and Lozano, 1986b) and the other from the rest of the costs generated 

in the productive process (capital, maintenance, etc). 



The balance of thermoeconomic costs for any individual unit has one more term than 

the exergy cost balances (tables 7.7 and 7.8). The term Z/ϕ represents the contribution 

of the non-energetic production factors (investment capital costs). The balance of 

thermoeconomic cost ($/s) is expressed in equation 7.5: 

c f F + Z/ϕ = cp P (7.5) 

where cf and cp are the unit thermoeconomic costs ($/kJ) of the fuel (F) and product 

(P) respectively. As the term Z is usually calculated in US dollars ($) it must be 

divided by a temporary factor, called amortization factor (ϕ). The amortization factor 

takes into account the economic life period of the plant and is also called the capital 

cost of an installation (see section 7.2.3.2 for more information on capital costs). 

7.2.3.1 Investment costs 

According to Bejan et al. (1997), an investment cost is a one-time cost, in contrast to 

fuel costs and O&M costs which are continuous or repetitive in nature. Investment 

costs are treated differently than fuel and O&M expenses in an economic analysis. 

Some concepts are necessary to understand these costs: 

• Fixed capital investment, the total system capital cost assuming a zero-time 

design and construction period, i.e., the capital to purchase the land, build all the 

necessary facilities and purchase and install the required machinery and 

equipment. 

• Total capital investment, the sum of the fixed-capital investment and other 

outlays, i.e., startup costs, working capital, costs of licensing, research and 

development, and allowance for funds used during construction. 

• Direct costs, the costs of all permanent equipment, materials, labor and other 

resources involved in the fabrication, erection, and installation of the permanent 

facilities. 

• Indirect costs, not a permanent part of the facilities but required for the orderly 

completion of the project: engineering and supervision, construction costs, 

contingencies. The fixed capital investment is the sum of direct and indirect costs. 

In our case, purchased-equipment costs provided by the plant managers are quite 

different from other studies (El-Sayed, 1996; Boehm, 1987; Frangopoulos, 1991; 

Lozano et al., 1996). This is due to the magnitude of the components considered in 

the dual plant. Several authors propose costing equations for most of the components 

used in our analysis, but the main parameters used in the proposed correlations are 

outside the specified range (our power plant and desalination units were very large). 

Other costs not included in the capital costs of the components (but that also 

constitute a part of the direct costs of the fixed-capital investment) include the 

purchased-equipment installation, piping, instrumentation and controls, electrical 

equipment and materials, land, civil and structural work and service facilities. 



El-Sayed (1996) calculates the cost (in thousands of dollars, k$) of the main 

components of the equipment used in a MSF and steam power plant using the 

following equation: 

Z = ca A, (7.6) 

where the area A is calculated using an exponential formula as a function of four 

parameters, i.e.: 

A = 

k x1 n1 n2 n3 n4 

x2 x3 x4 

These parameters are shown in table 7.16. 

TABLE 7.16 Costing equation parameters for an MSF and power plant (El-Sayed, 1996). Units: ca k$/ft 2 , 

A ft 2 , M lb/s, Q kW, P i , P e psia, T i R, ∆T F, ∆P, dP psi, e = η/1– η. Subscripts: i, inlet; e, exit; t, 

tube; s, shell; m, mean (LTMD). 

Component ca k x 1 x 2 x 3 x 4 n1 n2 n3 n4 

Steam turbine 50 0.45 M T i /P i P e e 1 0.05 –0.75 0.9 

Feed pump 3 0.0025 M ∆P e — 1 0.55 1.05 — 

C.W. pump 3 0.0063 M ∆P e — 1 0.1 0.7 — 

Economizer 0.015 310 Q ∆T m dP t dP s 1 –1 –0.16 –0.12 

Boiler 0.015 340 Q ∆T m dP t dP s 1 –1 –0.33 –0.26 

Superheater 0.015 310 Q ∆T m dP t dP s 1 –1 –0.15 –0.14 

Heater 0.02 3.3 Q ∆T t dP t dP s 1 –0.7 –0.08 –0.04 

MSF 0.02 10 Q ∆T n ∆T t dP t 1 –0.75 –0.5 –0.1 

(7.7) 

Boehm (1987) introduces the size effect of the units into a simple cost equation that 

only depends on a variable, S. Thus, a complete tabulation of data for a particular 

piece of equipment could contain reference cost and size (Z r and S r), and the factor m 

responsible for the economies of scale. 

Z = Z r (S/S r) m (7.8) 

In the cost equation, Boehm normally uses a range of 0.5-1.0. Sometimes m is greater 

than 1.0 (boilers, heaters…), which produces unexpected results. Table 7.17 includes 

the main parameters of the above mentioned equation. 

Finally, the more accurate equations, in comparison with the cost estimation provided 

by the plant managers, are those proposed by Frangopoulos (1991). They are usually 

a correlation with three or four main parameters and correction factors depending on 

the device (see table 7.18). 



TABLE 7.17 Component parameters in Boehm (1987) equations. 

Component Z r S S r m 

Pump 47 M 10 0.03 

Steam turbine 25 W 1000 0.68 

Heater 21 A 100 0.71 

Condenser 3 Q 10 0.55 

Boiler 340 M 12 0.67 

TABLE 7.18 Costing equations proposed by Frangopoulos (1991). 

Component Cost equation 

Boiler 20.1552224 * exp (0.0014110546 * P1 ) * exp (0.7718795 * ln (M1 )) * FAR * FAN * FAT 

Steam Turbine 5240.378 * exp (0.569323 * ln (FB1 * (F2T + F2P))) * FBN * FBT 

Condenser 1.11 * A * 426.2632633 * exp (–0.4556513 * ln (A)) * FCR * FCPW * FCP * FCB 

Pump 1969.2325 * exp (0.4838546 * ln (7.279088e – 5 * M1 * 0.018 * (P2 –P1 ) * FDN 

Heater a 

Exp (8.202 + 0.01506 * ln (A) + 0.06811 * (ln (A)) 2 ) * FD * FP * FM 

Factor Correction factor 

FAR FAR = 1.0 + ((1–∆P r )/(1–∆P)) 8 

FAN FAN = 1.0 + ((1 – η1 r )/(1– η1)) 7 

FAT FAT = 1.0 + 5 * exp ((T1 – 1100)/18.75) 

FB1 FB1 = 0.0003929119 * η * M1 F2T F2T = 0.55 * (T1 – T2 – T2 * ln (T1 /T2 )) 

F2P F2P = 0.1102109 * T2 * ln (P1 /P2 ) 

FBN FBN = 1 + ((1 – η r )/(1 – η)) 3 

FBT FBT = 1.0 + 5 * exp ((T 1 – 1100)/18.75) 

FCR FCR = (P 3 * ((1/∆P s ) – 1)/14.7) –0.11 

FCPW FCPW = (∆P t /14.7) –0.38 

FCP FCP = 0.93 + 2.6380952 e –4 * P2 + 1.352381 e –6 2 

* P2 FCB FCB = exp (0.10/(TTD–5)) 

FDN FDN = 1 + ((1 – 0.8)/(1 – η)) 3 

FD FD = exp (–0.7844 + 0.083 * LN (A)) 

FP FP = 0.8955 + 0.04981 * LN (A) 

FM FM = 1.4144 + 0.23296 * LN (A) 

a. From Chemical Engineering (Corripio, Chrien and Evans, 1982). P 1 , T 1 and M 1 are the inlet conditions, T 2 , P 2 the exit conditions, 

A area, η and η1 efficiency and First principle efficiency, TTD terminal temperature difference, ∆P s , ∆P t pressure losses in tubes and 

shell. 



Lozano et al. (1996) also propose a set of equations for a wide range of values to 

obtain a reasonable equipment cost (see table 7.19): 

TABLE 7.19 Cost equations proposed by Lozano et al. (1996). η exergetic efficiency, B exergy flow of 

product, S negentropy, vw velocity of tubes , W power, e eficiency of the condenser (= T 0 (s 2 –s 1 )/ 

(h 2 –h 1 )). 

Component Cost equation 

Boiler 740 * exp ((P 1 –28)/150) * (1 + 5 * exp ((T 1 –866)/10.42)) * (1 + ((0.45–0.405)/(0.45–η)) 7 ) * B 0.8 

St. Turbine 3000 * (1 + 5 * exp ((T 1 –866)/10.42)) * (1 + ((1–0.953)/(1–η)) 3 ) * W 0.7 

Condenser (1/(T 0 * e)) (217 * (0.247 + 1/(3.24 * vw 0.8 )) * ln (1/(1–e)) + 138) * (1/(1–η)) * S 

Pump 378 * (1 + ((1–0.808)/(1–η)) 3 ) * B 0.71 

Purchase cost provided by the plant managers is much more complete than the 

individual components. It includes the price breakdown per section of each unit, and 

the direct costs of the installation. Table 7.20 includes a list with the percentages of 

each unit or subsystem with respect the total purchase cost (direct cost) of a power 

and desalination plant. Land cost is neglected in the Gulf Area. 

The price breakdown in table 7.20 does not contain the cost of each component in the 

productive structure. As a result, the thermoeconomic cost can only be calculated for 

the final products in the power and desalination plant, knowing the exergy cost of the 

electricity and distillate, the economic investment cost and the thermoeconomic cost 

of the products. The thermoeconomic cost can be expressed in units of money per 

unit of time ($/s), or units of money per unit of product: $/kW·h or $/m 3 . All cost data 

must have the same reference year as a basis for calculations. This is done with an 

appropriate cost index, an inflation indicator from technical journals (e.g. Chemical 

Engineering) that corrects the cost of equipment. We did not apply the cost index 

since the purchase costs of our installation were updated in 1997. 



TABLE 7.20 Price breakdown per section in a dual-purpose plant. 

Component system Portion 

Steam Turbine Plant 12,25 

HP heater, LP heater, feedwater storage tank with deaerator, cold condensate 

storage tank 

1,13 

Steam generating plant 13,15 

HP feeding system 0,12 

LP feeding system 0,30 

Boiling feed pump sets with hydraulic coupling 1,66 

Generator complete with air cooling and excitation systems 2,63 

Others: Transformers, busbars, switchboards, cabling and cable laying, 

rectifiers, batteries, electrical control equipment, instrumentation and control, 

service water and drainage system. 


14,08 

Total for the steam power plant 45,32 

MSF unit: Evaporator shell and tube bundles 20,38 

Brine heater 1,06 

Deaerator 0,04 

Vacuum system 0,63 

Cooling water recircul. pump set including isolating, non-return valves 0,29 

2 Brine recirculating pump sets, complete 0,87 

Blow down pump set, complete 0,22 

2 Distillate pump units 0,22 

2 Brine heater condensate pump sets, complete 0,07 

Others: Protective coating, make-up water strainers, cranes, seawater, brine 

recirculation, blowdown and distillate pipeline, HP, MP and LP reducing 

stations, antiscaling, antifoaming and sodiumsulfite systems, on-load tube 

cleaning system, lighting system, instrumentation and control, switchgear, 

switchboards, transformer. 

Total for the desalination unit 32,79 

General services: Circulating water and seawater supply system, seawater 

cleaning plant, fuel oil and gas system, power transformers, bus duct systems, 

cables, lighting and power outlets, earthing system, common instrumentation 

and control, water treatment, lifts, buildings, fire fighting systems, chemicals 

and chlorination system, town water storage, DPS system, chemical storage. 

9,01 

21,89 

Total for the dual plant 100


7.2.3.2 Capital costs 

The average capital cost for the system was assumed to be 3.47×10 –9 $/s·$. It was 

calculated based on 8% capital recovery per calendar year (8,000 hours operation a 

year) and 15% allowance for the fixed part of O&M (El-Sayed, 1996). The average 

capital cost takes into account the effect of inflation: price increases associated with 

increase in available currency and credit without a proportional increase in available 

goods and services of the same quality. This cost also includes the effect of escalation 

(resource depletion, increased demand and technological advances); and depreciation 

(decrease in equipment value due to physical deterioration, technological advances 

and replacement). Some assumptions were made to assess the average capital cost. 

For example, land costs and total capital investment were placed at the beginning of 

the design and construction period so that the end of this period is considered the 

beginning of commercial operation (economic-life period). 

7.2.4 Thermoeconomic cost analysis 

The exergy and economic costs of a system provide the real plant operating costs. 

Tables 7.21 and 7.22 show the thermoeconomic cost in the eight cases (see table 7.9 

for details). 

TABLE 7.21 Thermoeconomic costs of distilled water and electricity of the analyzed dual-purpose plant. 

Cost ($/s) Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 

Electricity 1.5798 0.5068 1.3046 1.0030 1.1019 0.8818 1.0248 0.9706 

Water 0.3571 0.9798 0.6885 0.6935 0.6471 0.5534 1.1251 1.1088 

TABLE 7.22 Thermoeconomic cost of electricity ($/kW·h) and water ($/m 3 ) for the cases studied in the 

exergetic cost analysis. 

Cost Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 

Electricity 0.0388 0 0.0385 0.0479 0.0436 0.0593 0.0482 0.0492 

Water 0 1.5026 1.0558 1.0635 1.1648 1.6871 1.8456 1.7802 

El-Sayed (1996) proposes the following costs for the products of a typical dualpurpose 

power and desalination plant: 

• Electricity: 0.045 $/kW·h. 

• Water: 1.3 $/m 3 . 



The results of the thermoeconomic analysis were very close to the values given by El- 

Sayed, especially in the most representative cases (in hours of operation per year, 

cases 3, 4 and 5). Note that the thermoeconomic cost was not zero in case 1 for water 

nor for electricity in case 2 (see table 7.21) despite the lack of production. This was 

due to the effect of amortization of the purchase costs in the first table. The effect on 

quantity production is clear in table 7.22 (the cost of electricity per unit of energy is 

reduced in case 1 and is lower than other costs, although this is the worst case if we 

analyze exergy costs). In Case 6 (with partial load) the investment costs overcharge 

the cost per unit of production. The use of the reduction pressure station to produce 

freshwater is not recommended even with a high freshwater demand (see cases 2, 7 

and 8 in table 7.22). Case 3 is the most interesting case to maintain the best operation 

mode. 

7.2.5 Cost allocation: Indirect methods 

Some cost allocation methods allocate the total cost of owning and operating the 

plant among two products, without having to split the total cost in two products 

(direct methods). Other methods allocate the main factory costs (e.g. manpower, 

material, fuel and capital depreciation) among the two products (indirect methods). 

Some criterion is usually needed to help in cost allocation. For example, the exergy 

cost method is an indirect method that allocates the cost of producing the two 

products in terms of fuel consumption. 

Although cost allocation methods are a rational basis for pricing the two products, the 

cost is the amount of resources needed to obtain these products. The price imposed on 

a product is independent of the efficiency of the formation process of that product. 

7.2.5.1 WEA method 

The method proposed by El-Nashar (1999) and the Water and Electricity Department 

of the UAE (WEA method) is indirect and allocates all cost components among water 

and electricity according to functional considerations. The annual cost for a cogeneration 

plant can usually be separated into three cost components: fixed capital 

charges, fuel costs and O&M costs. Each one can be separated into costs for 

electricity production, costs for heat production and common costs to both products. 

The methods differ in how they separate annual costs into the three components and 

in allocating common costs between electricity and heat. 

The total costs are divided into five cost departments: fuel, personnel, maintenance 

contracts, spares and consumables and depreciation of fixed capital. Personnel costs 

are divided among those directly involved in the co-generation plant (such as 

operation and maintenance work), or those that serve several plants. The cost of fuel 

consumed by the steam turbines is split between electricity and water since the steam 

derived to the MSF unit has the potential to generate a certain amount of electrical 



power if allowed to expand through a hypothetical condensing turbine. Since this 

steam is used for desalination instead of additional power generation, the fuel 

consumed for this amount of non-produced electrical power should be charged to 

water. The amount of additional power (W CT) which could have been generated by 

this hypothetical turbine (in our case is the low pressure turbine) may be expressed 

as: 

W CT = Q η B η CT 

(7.9) 

where Q is the amount of heat supplied to the hypothetical steam turbine, η B is the 

efficiency of boiler and η CT is the thermal efficiency of the condensing steam turbine 

cycle. The fuel consumption Gc could be allocated to electricity and water according 

to the following equations, taking into account the power generated in the real steam 

turbine (W ST): 

Gc e = Gc W ST /(W ST + W CT) (7.10) 

Gc w = Gc W CT /(W CT + W CT) (7.11) 

The fuel allocation problem could also be solved using the difference in output power 

produced when the amount of fuel consumed is the same in both cases. The MR (no 

desalination) and MCR (co-generation) cases are a good example. The total 

personnel cost consists of directly assessable costs (e.g. operating and maintenance 

staff) and indirect or common service personnel. The directly assessable portions are 

charged to either electricity or water, depending on the case. The cost of common 

service personnel is allocated to electricity and water according to the ratio of the 

capital cost of the plant and equipment associated with electricity production and 

desalination. Maintenance contracts for specialized maintenance work is priced and 

electricity and water are finally allocated. Depreciation of capital cost between 

electricity and water is allocated according to the function of the equipment in 

operation. The depreciation cost is allocated to electricity in the steam turbine power 

plant and water in the desalination plant. Depreciation costs of common equipment 

and facilities are allocated according to the capital cost of equipment related to 

electricity and water, as done for the common personnel costs. 

The WEA method is widely used in the UAE to allocate the cost of producing water 

and electricity in co-generation plants (starting from the yearly electrical and water 

production) and the cumulative number of operating hours of power and desalination 

plants. Those data are confidential and cannot be presented here. Other characteristics 

include: 

• Average yearly cost (with a wide range of operating modes) of the co-generation 

plants (with several configurations of dual plants) operating in the country. It is 

not valid for calculating an instantaneous cost of water and electricity. 

• Applied fuel and capital costs (which are unknown). 



Compared with exergy cost methodology, the trend of water and electricity costs is 

the following: 

• The WEA method tends to overvalue electricity and undervalue water by 

charging all the capital and O&M costs of the steam turbine (except fuel) to 

electricity. 

• The WEA costing methodology only allocates fuel cost to steam turbines. 

• The WEA method suffers from a certain degree of arbitrariness with regard to 

the efficiency of a hypothetical condensing steam turbine. The assumptions 

could cause fluctuations in the resulting cost of electricity and water. The 

difference in production between operating modes could partially avoid this 

problem (see next section). 

• The exergy/thermoeconomic method charges each product of a multi-product 

unit to the appropriate portion of capital and O&M costs involved in operating 

the unit. 

• The exergy/thermoeconomic method is based on a solid accounting and 

thermodynamics. Therefore, it will be used in our studies. 

As a result of the above, El-Nashar (1993; 1999) developed a model based on exergy 

analysis to predict the final costs of the two products. Other authors propose cost 

redistribution using the exergy analysis of the dual-purpose plant (Evans, Crellin and 

Tribus, 1980; Breidenbach, Rautenbach and Tusel, 1997; Slesarenko and Shtim, 

1986). The energy efficiency of the dual-purpose plant is also used to allocate the 

fuels to power and desalination and the relevant specific fuel costs for power 

generation and water production (Saeed, 1992). 

7.2.5.2 Fuel cost of water in dual plants 

Fuel energy for desalting depends on fuel allocation rules between the power and 

desalted water produced in a dual-purpose plant (Darwish, Yousef and Al-Najem, 

1997). Kronenberg and Dvornikov (1999) argues that the steam cost of desalting 

should be calculated by defining the heat rate difference between the power plant 

coupled and uncoupled to the desalination plant (also called the Lost Kilowatts 

Method, see Gaggioli and El-Sayed, 1987; El-Saie and El-Saie, 1989). This heat rate 

difference is defined by the Fuel Cost of Water (FCW) in a dual-purpose installation. 

The fuel cost of water largely depends on the overall efficiency of the power plant, 

and is calculated as: 

FCW $ m 3 

( ⁄ ) 

( W1 – W2) HR1 cf 

= 

---------------------------------------------- 

Qf D 


(7.12)


where W 1 and W 2 are the electric power output of the uncoupled and coupled plant 

(kW), HR 1 is the heat rate of the uncoupled power plant (the inverse of the efficiency, 

kJ/kW·h), cf is the fuel cost ($/kg), Qf is the heat value of fuel (kJ/kg) and D is the 

water production (m 3 /h). 

Fuel cost of water can be calculated in the dual-purpose plant. For instance, the FCW 

of the MCR case was calculated using natural gas with a high heating value 

(HHV = 9,500 kcal/m 3 ), a density of 0.75 kg/m 3 and an energy cost of 2.23×10 –6 $/kJ 

(applied in the cost analysis). The gas consumption in the MR case (the uncoupled 

power plant in our case) was 43,500 Nm 3 /h. The final values to be introduced in 

formula (7.12) for our example are also introduced after the FCW value: 

FCW = 0.271 $/m 3 

W 1 = 146,700 kW 

W 2 = 122,000 kW 

HR 1 = 43,500 · (9,500 · 4.1868)/146,700 = 11,794 ·1 kJ/kW·h 

cf = 2.23 ·10 –6 (9,500 · 4.1868)/0.75 = 0.1182 $/kg 

Q = (9,500 · 4.1868)/0.75 = 53,032.8 kJ/kg 

D = 2,400 m 3 /h 

Note that the exergy analysis and the lost kilowatts method are similar (see section 

7.1.1 for the exergy analysis of the simple co-generation plant), although the latter 

uses the energy analysis to calculate the cost of fuel consumed in the co-generation 

plant. The resulting cost of water is very similar in both methods. 

If the FCW is compared with the exergoeconomic cost of case 3 in table 7.11 (i.e., the 

exergoeconomic cost of the MCR case), the FCW is more or less 55% of the 

thermoeconomic cost (0.493 $/m 3 ). The difference is mainly due to several factors: 

The exergoeconomic cost also includes the cost of electricity needed to pump the 

MSF flows and the steam derived to the vacuum system of the distillers. 

The FCW assumes a constant efficiency in the power plant (the heat rate of the plant 

in condensing mode). The overall efficiency of the dual-purpose plant is lower when 

the plant is only generating electricity (see table 7.14 for the exergetic efficiency of 

the whole plant). Therefore, the amount of additional electricity generated in the 

condensing mode is not a valid index to calculate the fuel cost in co-generation mode, 

with a higher efficiency. 



7.3 Thermoeconomic diagnosis 

Diagnosis is the identification of something that is not working properly. 

Thermoeconomic diagnosis is the only operation analysis based on the Second Law. 

It uses the exergy balance of an installation to allocate and calculate irreversibilities 

in the production process and identify the equipment affecting overall efficiency. In 

practice, however, this useful information is not sufficient since some irreversibilities 

cannot be avoided. The technical possibilities for saving energy are always lower than 

the theoretical limit of thermodynamic energy losses. Moreover, the local exergy 

savings in different units or processes are not equivalent. The same local 

irreversibility decrease in two different components generally produces different 

variations in the total energy consumption. 

The final objective of Thermoeconomic diagnosis is to describe how malfunctions 

affect additional resource consumption (see Chapter 6 for a review of 

Thermoeconomic theory and its applications). In this section, we analyze a power and 

desalination plant according to the principles outlined in the previous chapter. The 

entire diagnosis is presented using the Structural Theory of Thermoeconomics 

(Valero et al., 1993). It provides information about component fuel consumption 

during equipment degradation (inefficiency), how each component increases fuel 

consumption and how a component's inefficiency affects the behavior of other plant 

units. 

We will only consider the direct problem of thermoeconomic diagnosis (Valero, 

Torres and Lerch, 1999), where inefficiencies are quantified in terms of irreversibility 

increase, while distinguishing between efficiency deterioration (intrinsic and induced 

malfunctions) and component dysfunction (generated by the malfunction). The 

inefficiencies were previously simulated and the causes of the behavior deviation 

provoked by this inefficiency are not searched here. 

The inverse problem is to identify and quantify malfunctions (the origin of new 

irreversibilities). Classical thermoeconomic analysis does not elucidate the cause of 

irreversibilities, although an effort is made to detect and stop malfunctions. The 

inverse problem finds the cause of the deviation between two states of the plant 

(actual and reference conditions). It requires a data acquisition system (for the 

reference conditions), a simulator (to provide the reference state for the same 

operating conditions) and conventional methods of the thermoeconomic diagnosis 

(the direct problem). One of the main difficulties with the inverse problem is 

recognizing and separating effects not intimately related with the inefficiencies of the 

plant components, such as load variation, set points or ambient conditions. 

The impact on fuel predicted by the simulator is exactly the same as that calculated 

by the Structural Theory of Thermoeconomics. This plant diagnosis reproduces the 

deviation of the physical values when one or more inefficiencies are detected. 


Thermoeconomic diagnosis 

Although the simulator calculates the thermodynamic state of the dual plant with 

reasonable accuracy under different operating conditions, it might not be able to 

respond as well to unexpected non-linear inefficiencies. The diagnosis involves a 

sensitivity analysis of the mathematical model of the dual-purpose plant (simulator) 

with respect to a parameter (in this case, one or several inefficiencies in a component 

of the system). The simulator could be avoided in the diagnosis if the data acquisition 

system of the dual plant were available. 

We will first summarize the different inefficiencies, loads and operating modes 

simulated in the plant diagnosis. Then, the ‘direct problem’ of diagnosing one or 

several inefficiencies is analyzed for a defined load (corresponding to an operating 

mode) in the power and/or desalination plant. The analysis involves a new technique 

(see Chapter 6, Torres et al., 1999) based on Structural Theory and Symbolic 

Thermoeconomics to provide a huge quantity of information, including: 

1. The irreversibility generated in each component. 

2. The exergetic cost of each component's product. 

3. The intrinsic malfunction in each component (i.e. the efficiency decrease of a 

component due to its own inefficiency). 

4. The induced malfunction in each component (i.e. the efficiency decrease of a 

component due to inefficiencies in other components). 

5. The dysfunction induced in the component due to the malfunction or 

inefficiency of other subsystems, which forces it to consume more local 

resources to attain the additional production required by the other components. 

6. The fuel impact or malfunction cost of each component due to an inefficiency, 

and the total impact on fuel. 

7. A compact and easy to understand malfunction matrix containing the cost of 

inefficiencies and the effect of a component inefficiency on all other 

components. 

7.3.1 Thermoeconomic diagnosis of a power and desalination 

plant: case studies 

System operating parameters can be classified according to their effect on component 

efficiency: 

• Local variables, which mainly affect the behavior of the component related to 

the variable (e.g. the isoentropic efficiency of a turbine). 

• Global or zonal variables, where the operating parameter cannot be associated 

with a specific component (e.g. live steam conditions of a steam power plant). 



A variable is considered local if the total impact on fuel associated with a subsystem 

is basically located in this component. 

We simulated the device inefficiencies and considered the different simulation data as 

plant data under different conditions (including inefficiencies). All the analyzed 

inefficiencies were associated with local plant variables and were chosen in terms of 

their effect on energy: 

• Degradation of the isoentropic efficiency of the high-pressure turbine (1st section, 

HPT1, and 4th section HPT4). 

• Degradation of the isoentropic efficiency of the low-pressure turbine (1st section, 

LPT1). 

• Heat transfer problems in HP heaters were analyzed by varying the Terminal 

Temperature Difference TTD (temperature difference between the saturation 

temperature of the steam extracted from the turbine and feedwater leaving the 

heater). Only the HP heater no. 1 (HPH1) was treated. 

• By varying the feed pump isoentropic efficiency, operating inefficiencies were 

simulated in the feed pump. 

The effect of a global variable such as live steam temperature can be studied if the 

simulator supports a non-fixed condition in the live steam leaving the boiler. In the 

case of the MSF unit, the analyzed inefficiencies refer to fouling at different stages: 

• brine heater, 

• recovery section, and 

• reject section 

Neither the MSF pumping process nor the brine level in each flash chamber were 

diagnosed since they were not simulated in the mathematical model. The analysis 

could be performed with respect to thermal problems inside the distillers, vapor 

conditions to the brine heater or the TBT/distillate. 

As we will see in later sections, fouling in distillers was considered a global variable 

if it affected other distillers. 

The effect of these eight inefficiencies was measured on: 

• the behavior of the rest of the plant devices (intrinsic/induced malfunction and 

dysfunction analysis), 

• additional fuel plant consumption (impact on fuel), 

• the thermoeconomic cost of electricity and distilled water, 

• the irreversibility increase of each unit. 

Thermoeconomic analysis should cover as much of the maximum range of electricity 

and water production as possible so that intermediate demands can be predicted from 



acquired experience. Four loads were considered under the most usual operating 

situations: 

• Full load in condensing mode (no extraction to MSF unit): 140 MW of power 

generated. 

• Full load in extraction mode (electricity and water production): 122 MW of 

output power (89.68 kg/s of steam extracted to the desalination unit). 

• Partial load in extraction mode at 90 MW output power (60 kg/s steam extracted 

to the MSF unit). 

• Parallel mode (the reduction pressure station is opened to maintain the pressure 

to the MSF unit): 60 MW of output power (50 kg/s extraction to desalination). 

The first situation is a high-electricity demand when the distiller has been stopped for 

repair, the two intermediate productions are the most common and the fourth is 

typical in winter. 

Two freshwater productions were analyzed under the following specific conditions: 

• 1,900 T/h distillate with 32 ºC seawater (the nominal production under Gulf 

seawater conditions in spring or autumn). 

• 2,400 T/h distillate with 25 ºC feedwater to the reject section (the maximum 

winter production). Seawater can be less than 25 ºC (the minimum temperature 

operation for the reject section), so the temper system uses a part of the reject 

cooling brine and stay secure in the last stage of the reject section. 

Loads and inefficiencies may be combined in many ways. We analyzed all of these 

possibilities but only present two: an inefficiency in the fourth section of the highpressure 

turbine and an inefficiency in the MSF unit (with the cleaning ball system in 

the heater) at a prefixed load. These examples represent a local and global variable in 

two separate systems. We subsequently considered the ‘upstream’ effect of fouling in 

the recovery section of the MSF plant on the steam power plant. Finally, the most 

general situation was analyzed when several inefficiencies in the power or 

desalination plant occurred together. The rest of the combinations (i.e. the analysis of 

the individual inefficiencies presented above) are presented in Annex 1 for a 122 MW 

load in the power plant and the NTOS case of the MSF plant, including figures and 

matrices calculated in the analysis of each inefficiency. The effect of the load in the 

above inefficiencies is summarized in section 7.3.4. 

7.3.2 Analysis of individual inefficiencies 

7.3.2.1 Inefficiency in the fourth section of the high-pressure turbine 

As defined by Royo (1994), an intrinsic malfunction in a steam turbine is expressed 

as the damage in the steam expansion process and energy transmission to the shaft 



due to several factors including erosion, fractures, ruptures, sediments, surface finish, 

friction, steam path, seals and diaphragm deterioration, control valve and heat losses. 

An inefficiency can also be an induced malfunction due to the variation of external 

factors apart from component damage. These external factors include changes in 

admission temperature, exhaust pressure or extraction mass flows of a steam turbine 

(Zaleta, 1997). 

We simulated that the fourth section of the high-pressure turbine underwent behavior 

degradation and, as a result, the isoentropic efficiency decreased by 10% (at 122 MW 

total output power). The three upstream turbine sections are insensitive to and 

incapable of responding to this inefficiency and the vapor conditions entering the 

inefficient section were maintained with respect to the design condition. A lower 

isoentropic efficiency means that the outlet steam vapor conditions have a higher 

enthalpy, if the exhaust pressure of the high-pressure turbine is controlled by the MSF 

system. Thus, the first induced malfunction in the MSF unit was due to the variation 

of external factors; the steam conditions entering the MSF plant were changed by an 

inefficiency (or intrinsic malfunction) in the fourth section of the high-pressure 

turbine. 

The output power of this section was also considerably lower because of the 

reduction in the enthalpy drop. The three sections of the high-pressure turbine 

maintained their power production. The steam pressure entering the low-pressure 

turbine was maintained and the exhaust pressure must be the same as in the design 

(we assumed that the ambient conditions remained unchanged and constant 

condenser pressure). Therefore, the efficiency of the low-pressure turbine should not 

vary considerably and the two sections of the low-pressure turbine do not produce 

additional power to maintain the final production. 

Consequently, additional live steam was needed to maintain final production. The 

three sections of the high-pressure turbine and the two sections of the low-pressure 

turbine provided the extra power not supplied by the inefficient section. The 

additional live steam affected the whole system, but the latter generally readapts to 

maintain design values: design feedwater system values were maintained by 

increasing the extraction mass flows. Pump consumption increased in proportion to 

the additional mass flow required by the boiler. As a result, no significant induced 

malfunctions were provoked by the inefficiency in the high-pressure turbine. 

The total impact on the fuel was 6.035 MW, but 6.015 MW in the inefficient 

component. Thus, the effect of the inefficiency could be considered local to the 

component with the intrinsic malfunction. Next we considered the contribution of 

each component. 

The physical consequences of inefficiencies will be reviewed using the symbolic 

diagnosis notation of this Ph. D. Thesis (see Chapter 6 for nomenclature). The same 

methodology was used for each example. First the target conditions and the 



inefficient situations were simulated (see Chapter 5). The design and inefficient 

situation include the most significant flowstreams, which are the basis of the 

thermoeconomic analysis. Following the F-P definitions adopted for the 

thermoeconomic model (section 7.1), the fuel and product table was prepared. 

table 7.23 corresponds to the design and table 7.24 to the inefficient condition. The 

unit exergy consumption κ of each component is very easy to calculate using the F-P 

tables (by dividing the fuels entering the plant by their product). Then the reference 

〈KP〉 matrix (table 7.25) and the 〈KP〉 matrix (table 7.26) are made for the inefficient 

mode. If these two matrices are subtracted, we obtain the ∆ 〈KP〉 matrix with the unit 

exergy consumption increase of each component (table 7.27). The ∆ 〈KP〉 matrix is 

the basis for calculating the endogenous irreversibility or malfunction. If the two 

matrices are multiplied, we obtain the irreversibility matrix |I〉 (table 7.28) with the 

irreversibility increase (or dysfunction coefficients) of each component. The first 

factor is the diagonal matrix K D–U D, where K D is the array containing the sum (by 

columns) of the 〈KP〉 matrix and U D is the unitary matrix. The second factor is the 

inverse of the unitary matrix minus the 〈KP〉 matrix, i.e., (U D–KP) –1 . The unit exergy 

cost of a product is the column sum of the dysfunction coefficients in the |I〉 matrix 

plus one (table 7.28). Finally, the dysfunction matrix [DF] needed to build the 

malfunction and dysfunction table is calculated by multiplying the |I〉 matrix by 

∆ 〈KP〉 P, where P is the array containing the product of each component. Thus, the 

irreversibility increase in each unit is connected to the increase in unit exergy 

consumption of each component. The malfunction of each component MF is the 

product ∆ 〈KP〉 P and is located at the end of the table. The column sum is the fuel 

impact of a component, i.e., the additional fuel plant consumption provoked by the 

considered unit and the row sum is the irreversibility increase of a component (see 

table 7.29). 

After having explained the most relevant matrices to analyze a plant inefficiency 

(table 7.29), we will now consider the results and explain the values using physical 

reasons. Figure 7.13 shows the impact on fuel analysis from the malfunction/ 

dysfunction table (included in table 7.29) and figure 7.14 includes the irreversibility 

increase of each component of the power plant. 

The intrinsic malfunction is the easiest to explain. When the fourth section of the 

high-pressure turbine was working at 10% less isoentropic efficiency than normal, the 

output power (P in the F-P table 7.24) decreased but the section's steam conditions 

were maintained. The irreversibility increased (the turbine section increased its 

irreversibility to 3,270 kW, table 7.29), and the resources required to produce the 

same output power increased as well as the unit exergy consumption of the 

component ∆k (∆k = 0.2144, see table 7.27). Multiplying by the product in this 

section (19.23 MW), the malfunction was 4.12 MW (see table 7.29). The fuel impact 

due to the inefficient component was 6.01 MW (see also the table 7.29). 


FIGURE 7.13 Impact on fuel analysis when the efficiency of the HPT4 is decreased 10%. 



FIGURE 7.14 Irreversibility increase analysis with the inefficiency in the HPT4.

TABLE 7.23 F-P diagram in design, output power of 122 MW . 



TABLE 7.24 F-P values with inefficiency in HPT4 (10% lower efficiency). 



TABLE 7.25 KP matrix in design (122 MW). 



TABLE 7.26 KP matrix with inefficiency in HPT4 (10%). 



TABLE 7.27 Variation de KP with inefficiency in HPT4. 



TABLE 7.28 Irreversibility matrix I with an inefficiency in HPT4. 



TABLE 7.29 Dysfunction/malfunction matrix with inefficiency in HPT4 (10% isoentropic eff.). 



TABLE 7.30 Malfunction matrix with inefficiency in HPT4 (1% isoentropic eff. is varied). 




As mentioned, the inefficiency also affected MSF unit behavior. This induced 

malfunction was expected because the steam leaving the HPT4 section is consumed 

in the MSF unit. Since the MSF product (exergy flow of distilled water) is constant, 

the variation of the steam conditions entering the MSF unit directly affects its 

behavior (we assumed that the condensate returned to the deaerator maintains its 

properties independent of inlet conditions). A higher enthalpy in the exhaust vapor of 

the high-pressure turbine should imply a higher specific consumption per freshwater 

unit produced, as seen in the variation of the unit exergy consumption (∆k = 0.075, 

see the corresponding value in table 7.27). But the thermoeconomic model gives an 

important function to the MSF unit: the negentropy generated in the MSF heater. The 

inefficiency in the fourth section of the high-pressure turbine generated a higher 

negentropy in the MSF unit (the entropy of exhaust vapor from the turbine increases 

with a lower isoentropic efficiency). This negentropy is a secondary product of the 

MSF unit. Its increase implies a decrease in unit exergy consumption of the 

component (the ∆k variation due to negentropy generation is –0.154, see table 7.27). 

Balancing the two terms, the increase in unit exergy consumption in the MSF was 

negative, provoking –537 kW induced malfunction. In conclusion, the value of the 

induced malfunction in this component was due to the thermoeconomic model. It did 

not correspond to the expected response to an intrinsic malfunction in the fourth 

section of the high-pressure turbine. In other words, the negentropy generated in the 

MSF unit reduced the cost of water because the negentropy generated in the MSF unit 

reduced the cost of the condenser. 

The physical analysis of the inefficiency did not detect any more induced 

malfunctions in the system, although two components had a higher induced 

malfunction than the accuracy of the simulator: the boiler (–128 kW) and the first 

section of the HPT (–331 kW). These values are the consequence of a very high 

component product since unit exergy consumption increase was almost zero in both 

cases. This consumption varied only slightly because the steam needed to produce the 

required power increased with the simulated inefficiency. 

The irreversibility increase in each component (table 7.29) was calculated by 

subtracting the fuel-product differences in tables 7.23 and 7.24, or by adding the unit 

malfunction to the unit dysfunction generated by the malfunction of the rest of units 

in the system. In our example, the boiler dysfunction was the highest, mainly due to 

the malfunctions in HPT1, HPT4 and MSF (see table 7.29), the most important ones 

detected in this case. The dysfunction generated in the condenser was also important, 

but the cause was again the three components undergoing the malfunction. Boiler and 

condenser production increased by about 3 MW (this additional production was 

required by the rest of components to maintain the final production of the steam 

power plant with the inefficiency simulated in the fourth section of the HPT). In the 

productive structure (figure 7.5), the two products generated by these two 

components (the availability of the steam generated in the boiler and the negentropy 

generated in the steam cycle) were easily apportioned to the rest of the plant 



components. Figure 7.13 shows the irreversibility increase analysis of this 

inefficiency. 

Some explanations are required regarding the malfunction and dysfunction values of 

the non-physical components of our thermoeconomic model. A junction is a nonphysical 

device and is fictitious in the productive structure. Its function, similar to that 

of branching points, is structural, i.e. junctions and branches show how the resources 

are distributed among the plant devices. The malfunction and the dysfunction 

generated in a junction must be zero: in equation (6.45) the unit exergy consumption 

increase in a junction is zero and the dysfunction coefficients φ responsible for the 

dysfunction generated by other components are also zero (remember that the 

dysfunction coefficients φ only depend on the unit exergy consumption k of the 

component in operating conditions). However, a junction can generate a dysfunction 

in other system components (see equation 6.46). The value of the dysfunction 

strongly depends on the dysfunction coefficients φ of each component where the 

dysfunction is generated. For example, the unit exergy consumption k of junction J4 

varies with a change in the unit exergy consumption of its exergy ratios r (the 

electricity produced in the turbine sections). All the boiler φ coefficients were nonnegative 

(the dysfunction generated by the junction in the boiler was not zero, –445 

kW). The junction usually generates dysfunctions due to the variation in the fuels 

(i.e., the product of the units that enter the junction) but the components that have 

non-zero values in all their φ coefficients also suffer from the junction dysfunction. 

These special components are the boiler and condenser, which are interrelated with 

the rest of components in the productive structure of the power plant (see figure 7.5). 

The impact on fuel analysis is similar to the previous analysis, but here the impact on 

fuel consumption is the sum of the malfunction and the dysfunction generated by 

each component in all others (see figure 7.14). Logically, the dysfunctions generated 

by HPT1, HPT4 and MSF in the boiler and the condenser were the most important. 

One of the most useful applications of the thermoeconomic diagnosis is the 

malfunction matrix. It provides information about the malfunction associated with 

each component during an inefficiency. It is a very valuable tool to predict system 

behavior without using the simulator (recall that the same results were obtained using 

either the diagnosis or simulator). We want to predict the additional fuel consumption 

with an inefficiency and maintain the equations that model the physical behavior of 

the plant in the simulator (performing each individual analysis for an operating 

condition). At least two premises are required to create the malfunction matrix: 

The response of the system must be proportional to the degree of inefficiency (impact 

on fuel, associated malfunctions, etc.). To calculate the fuel impact of a known 

inefficiency, the corresponding malfunction matrix need only be multiplied or 

divided, depending on the ratio of the real inefficiency and the inefficiency defined in 

the malfunction matrix. 



To predict the effect of several malfunctions, the inefficient components must be local 

to their subsystems. The total impact on fuel can then be calculated as the sum of the 

malfunction matrices associated with the individual inefficiencies. 

The second assumption is not necessary here because we only analyzed an individual 

inefficiency. The first premise could be checked by analyzing the graphic impact on 

fuel analysis versus the degree of inefficiency applied. In this case, the isoentropic 

efficiency of the fourth section of HPT was varied from –10% to +10% with respect 

to the design efficiency (around 85%). Figure 7.15 shows how the linearity of the 

sensitivity analysis varies while the plant load is kept constant (122 MW of output 

power in extraction mode and 2,400 T/h freshwater production). 

FIGURE 7.15 Additional fuel consumption when varying the isoentropic efficiency in HPT4. 

Inc. fuel consumption 

6000 

kW 

4000 

2000 

-10 -8 -6 -4 -2 

-2000 

0 2 4 6 8 10 

-4000 

-6000 

0 

% eff. in HT4 

Plant behavior was linear when we varied this inefficiency (figure 7.15). The 

malfunction matrix in table 7.30 is very useful to calculate the malfunctions 

associated with each inefficiency (by summing the columns and multiplying each 

component by its product). The high unit exergy consumption of the condenser pump 

was the result of the mathematical model (as were the high values of the low-pressure 

heater no. 2). In these two cases, the low product values minimized the previously 

mentioned effect in the malfunction analysis. The MSF components of this matrix 

were very high but the low exergy value of its product (freshwater) induced a low 

malfunction. All sections of the high-pressure turbine were affected by the 

inefficiency but, as expected, the fourth section had the highest value. The values of 

the first section of the high and low-pressure turbine were also considerable since 

they had to readapt their products to maintain final production. 

The effect of the inefficiency can be quantified as the total cost (including capital cost 

of devices) of electricity and water, which is especially illustrative for plant 

managers. Electricity increases 0.000033 $/kWh per 1% variation in efficiency 

(figure 7.16) or a yearly savings of 35,200 $/y. 



FIGURE 7.16 Unit electricity cost when the isoentropic HPT4 efficiency is modified. 

Electricity cost 

0,0383 

$/kWh 

0,0381 

0,0379 

0,0377 

0,0375 

0,0373 

% eff. in HT4 

-10 -8 -6 -4 -2 0 2 4 6 8 10 

Surprisingly, the effect on the cost of water was even greater –in absolute terms- than 

for electricity (0.00047 $/m 3 per 1% inefficiency, or almost 10,000 $/y; figure 7.17), 

although the relative cost of electricity varied more. This is because the apparently 

local inefficiency changes the steam conditions sent to MSF unit, which implies an 

additional cost, mainly due to the high exergetic cost associated with water (see 

table 7.28). 

FIGURE 7.17 Unit distilled water cost when the isoentropic HPT4 efficiency is modified. 

Water cost 

1,278 

$/m3 

1,274 

1,270 

1,266 

% eff. in HT4 

-10 -8 -6 -4 -2 0 2 4 6 8 10 

The main conclusions of our analysis of an inefficiency in the final section of the 

high-pressure turbine are: 

• The isoentropic efficiency only affected the behavior of the inefficient 

component and provoked a small malfunction in the MSF plant by changing 

exhaust vapor conditions leaving the HPT. 



• The steam power plant could not readapt its behavior to maintain the final 

production. Additional live steam was required to produce the electricity 

demanded, consuming more fuel (6,035 kW). The dysfunction analysis was 

useful to observe how the components that provide the energy quality to the 

steam cycle (boiler and condenser) have to increase their productions that are 

distributed to the rest of plant components, producing the additional power not 

supplied by the inefficient section of the turbine. 

• The effect of this inefficiency was quite significant and represented an additional 

water and electricity cost of 0.00047 $/m 3 and 0.000033 $/kWh respectively, per 

unit of efficiency (or 45,200 $/y in both products). The nature of the inefficiency 

should be studied carefully, taking into account several factors including repair 

time, personnel costs and the price of the components if they need to be replaced 

to avoid extra natural gas consumption. 

• The sensitivity analysis applied in a reasonable range revealed a linear response 

by the simulator mathematical model. Thus, the malfunction matrix can substitute 

new simulations with this inefficiency and predict its effect on a real plant. 

• The value of the induced MSF unit malfunction demonstrates that plant 

diagnosis strongly depends on the thermoeconomic model. Sometimes the 

physical consequences of an inefficiency cannot be translated into a table of 

expected values for fuel impact or irreversibility increase of a process or 

component. 

7.3.2.2 Using the cleaning ball system in the brine heater 

The fouling resistance R f (for definition see section 3.2.1) involves three resistances: 

• Resistance due to fouling or scale inside the tube. 

• Resistance due to fouling outside the tube. 

• Resistance due to the accumulation of non-condensable gases in the vapor. 

The cleaning ball system can only reduce tube fouling or scale in a heat exchanger, 

one of the main causes of performance loss in MSF plants in the high-temperature 

sections. In general, fouling occurs when deposits are laid down on the heat transfer 

surfaces (Hanbury, Hodgkiess and Morris, 1993). These deposits can be due to scale 

from the reverse solubility of salts in the brine, dirt from corrosion products or 

biological growths on the surface. The latter only occurs in the rejection section and 

can be controlled by feed chlorination. The scale type depends on the brine chemistry, 

plant conditions, chemical additives to the feed and the type of cleaning. In general, 

calcium carbonate and calcium sulfate are the most common forms of scale. 


TABLE 7.31 F-P values (design) for the MSF plant. Nominal production in summer. 



TABLE 7.32 F-P values without fouling in heater. Nominal production, 32 ºC seawater. 



TABLE 7.33 KP matrix in design. 



TABLE 7.34 KP matrix without fouling in heater. NTOS data case. 



TABLE 7.35 Variation of the KP matrix without fouling in heater. NTOS case. 



TABLE 7.36 Irreversibility matrix without fouling in heater. 1,900 T/h and 32 ºC seawater temp. 



TABLE 7.37 Malfunction/dysfunction matrix without fouling in heater. NTOS case. 



TABLE 7.38 Malfunction matrix varying fouling in heater 0,00001 m2 K/W in NTOS case. 




The fouling effect in the MSF plant was simulated, quantified and analyzed for the 

brine heater. The cleaning ball system was assumed to be working at maximum and 

fouling in brine heater was set to zero (fouling factor in heater at design conditions 

was 0.00025 m 2 ·K/W), although this is impossible in practice since outside fouling 

and non-condensable gas phenomena cannot be avoided. The reference case had the 

same operating conditions without the cleaning ball system. For this reason, most 

malfunctions associated with the cleaning ball system are negative (they should be 

called ‘benefunctions’), i.e., they save fuel. The malfunction analysis was performed 

at 1,900 T/h water production with 32 ºC seawater (the first of the two examples). 

Water production was constant although but this does not imply a constant product 

exergy flow. 

To explain how fouling in the brine heater affects MSF behavior, first the recycle 

brine, seawater to reject and make-up flows (R, SR, F) were maintained at designed 

levels. The condensation temperature of the steam provided by the steam power plant 

also remained constant. A lower fouling inside the brine heater improved the overall 

heat transfer coefficient, which implied that: 

• The interstage temperature difference in the heater was reduced, i.e. the cooling 

brine temperatures entering (TF,1) and leaving (TBT = TB,O) the heater were 

increased. 

• The temperature rise of the cooling brine in the heater was also increased. 

A higher Top Brine Temperature (TBT) implies a higher flash range ∆T and more 

freshwater production. The temperature profile of the recovery and reject section is 

altered if the temperatures entering and leaving the recovery section are increased. If 

the final production is to be maintained, R, SR and F must be decreased. But even the 

TBT and T F,1 reach higher than design temperatures (and therefore the temperatures 

profile in recovery and reject sections). Brine fouling is a global variable in the MSF 

unit since it affects the rest of the system. 

About 1,411 kW of fuel was saved with the benefunction in different plant 

components (not only in the heater). Less steam was consumed, affecting the 

behavior of the steam power plant when less steam is required for this extraction, as 

in the next example. 

Inefficiency was diagnosed using the symbolic notation explained in Chapter 6. The 

simulator in Chapter 5 was used to obtain the F and P values for the reference 

conditions and inefficient situation. Following the productive structure of the MSF 

unit (see figure 7.11) with 1,900 T/h water production, the F and P values are 

included in tables 7.31 and 7.32 respectively, using the nomenclature in table 7.4 for 

the components. In this case, the matrix was 18×18 (11 components and 7 junctions) 

whereas the matrix was 30×30 (26 components and 4 junctions) in the power plant 

analysis. The ∆ 〈KP〉 matrix (table 7.35) was built by subtracting the 〈KP〉 reference 

matrix (table 7.33) and the 〈KP〉 matrix (table 7.34) corresponding to an inefficient 



operation. The latter were obtained by dividing the F-P tables. The irreversibility 

matrix |I〉 (table 7.36) contains the irreversibility and unit exergy costs of each 

component. Finally, the dysfunction table (table 7.37) contains the dysfunction 

coefficients φ and the malfunction array MF. The column sum is the fuel impact of a 

component and the row sum is the irreversibility increase of a component. Figure 

7.18 shows the impact on fuel analysis in the malfunction/dysfunction table. Figure 

7.19 includes the irreversibility increase of each component of the power plant. 

Having obtained the dysfunction matrix (which provides information about the state 

of a given plant with an inefficiency), we analyzed the malfunctions in the 

desalination plant components. The physical variations in the MSF plant with the 

benefunction were translated into malfunctions. The first important conclusion is that 

the malfunction generated in the brine heater was not the highest. The malfunction 

induced in other components was more important than the intrinsic malfunction 

provoked by heater inefficiency. Therefore, each malfunction should be analyzed 

separately. 

The intrinsic malfunction is quite easy to explain. Using the cleaning ball system in 

the heater improves the heat transfer process in the tubes. This reduces the thermal 

irreversibility, assuming that the mechanical and chemical irreversibility is 

maintained. The irreversibility was reduced by 865 kW in this component (see table 

7.37), increasing its exergetic efficiency. The reference unit exergy consumption was 

reduced with respect to the inefficient condition (respectively 1.096 and 1.075 in 

tables 7.33 or 7.34), or the change in unit exergy consumption ∆k decreased with 

respect to the reference state. The decrease of the unit exergy consumption (–0.02) is 

included in the ∆ 〈KP〉 matrix (table 7.35). The product of the heater is the cooling 

brine heated to the TBT (42,021 kW), then the intrinsic malfunction of –875 kW. The 

impact on fuel saved in this component was 2,419.6 kW (both values are in 

table 7.37). 

The induced malfunction in the recovery section was positive (203 kW) and the 

irreversibility increase was 247 kW in the process (see both values in table 7.37). 

Consequently, the variation in unit energy consumption in this component with heater 

fouling was positive (∆k = 0.025, see table 7.35), i.e. the process was more inefficient 

in this section. Assuming that the distillate quantity and quality is maintained, an 

uncontrolled TBT increases due to the effect of the cleaning ball system in the brine 

heater. Although cooling brine was also increased, the temperature rise was lower 

than the TBT (because of the two effects of fouling in the brine heater). Thus, the 

amount of energy needed to produce the distillate in the recovery section was higher 

than in the design situation. The efficiency of the component decreased and provoked 

an additional fuel consumption of 494 kW. 


FIGURE 7.18 Impact on fuel analysis when the fouling in BH is neglected. 



FIGURE 7.19 Irreversibility increase in the MSF with BH=0. NTOS case.


On the other hand, the temperature profile in the reject section remained almost 

unchanged because the effect of the heater fouling is far away from the reject section. 

A higher TBT also implies lower recycled brine R flowing toward the reject section to 

maintain final production. This flow is the main contribution of the reject section to 

produce distilled water, which was maintained constant (the reject section product is 

practically the final product of the MSF unit). Less energy was needed to produce 

freshwater. The efficiency was increased and the variation of the unit exergy 

consumption and irreversibility generated were reduced in the inefficient case (∆k = – 

0.013, ∆I = –91 kW, resulting in a negative malfunction of 91 kW (see tables 7.35 and 

7.37) and 725 kW in fuel savings. 

The induced malfunction associated with the mixer was quite substantial (-- 942 kW). 

The make-up F and recirculation R flows were decreased by the cleaning ball system 

in the heater under constant final production of freshwater. The mechanical and 

thermal irreversibility of the mixing process is logically reduced if the two flows 

entering the mixing chamber are reduced. The unit exergy consumption of the 

process or the irreversibility increase was reduced (∆k = - 0.0159, ∆I = –912 kW, see 

tables 7.35 and 7.37) and 1,360 kW (table 7.37) of fuel was saved. 

The fictitious device is a non-physical component intercalated at the beginning of the 

productive structure of the MSF unit (see figure 7.11). It charges the exergy costs of 

the distiller flows with the plant residues: brine blowdown and reject cooling 

seawater. There is no physical explanation for malfunction of this device but the 

thermoeconomic model suggests two causes: 

• The exergy flow of the residues is higher (the fuel of this unit). The specific 

energy or mass flow rate of one of the two streams must be increased by an 

inefficiency in the MSF unit. 

• The steam to the brine heater decreases (here the unit product corresponds to the 

fuel of the brine heater). 

The second cause provoked a positive malfunction of 938 kW in the FD and 

1,222 kW of extra fuel consumption (table 7.37). The same MSF residues are sent out 

to sea at a higher cost to the distiller when less fuel is consumed to produce water. 

The amount of irreversibility in each component is the sum of its own malfunction 

plus the dysfunctions generated by the malfunction of other components. Only the 

fictitious device had a considerable dysfunction value (–764 kW), generated by 

malfunctions in the brine heater, recovery and reject sections, mixer and several 

junctions (see table 7.37). As above (tables 7.31 and 7.32), the product of the 

fictitious device decreased more than 700 kW to readapt the use of the cleaning ball 

system in the brine heater under constant freshwater production. The dysfunction 

depends on the φ coefficients of the component. Since the fictitious device is at the 

beginning of the productive structure, most of its φ coefficients were non-zero values. 

In conclusion, dysfunction analysis is clearly unrelated to the physical behavior of the 



plant, i.e., the MSF components do not vary production to maintain the final distillate 

due to the malfunctions. 

The impact on fuel analysis was similar to the previous analysis. In this case, the 

impact on fuel consumption was the sum of the malfunction and dysfunction 

generated by each component on others (table 7.37). As expected, the dysfunction 

generated by the brine heater, recovery and reject section and the mixer are important. 

Note that the malfunction/dysfunction analysis considers an unchanged final product. 

This is quite easy when the product is electricity, since the simulator can control the 

power output. However, the exergy flow of freshwater as the final product has two 

terms: the mass flow and the specific exergy of water leaving the distiller unit 

(quantity * quality, see Structural Theory, Valero et al., 1993). The mass flow must be 

controlled in the simulator but the specific distillate exergy is a function of the 

distiller temperature. The latter temperature depends on the operating conditions of 

the MSF unit: seawater temperature and concentration, fouling in each section, etc. In 

our example, the water temperature leaving the distillate pump did not vary with the 

brine heater fouling. If the temperature changed, the impact on fuel associated with 

the change in total production is k * ∆P, where k * is the exergy cost of the product and 

∆P is the variation of the total production (the value is shown in the right-bottom 

corner of the DF/MF table). The impact on fuel associated with the variation of the 

final product can be more important than the impact on fuel associated with the 

variation of the unit exergy consumption ∆k in each component (the total contribution 

due to both variations is also shown at the end of the DF/MF table). 

Having explained the most important results of MSF plant diagnosis without heater 

fouling, we can consider one of the most useful applications. Figure 7.20 can be used 

to study the linearity of the simulator (and a real plant, since the simulator was 

validated using data collected from a physical plant) to validate the malfunction 

matrix. Changing the design fouling factor in the brine heater (25×10 –5 m 2 ·K/W) 

gradually to zero saves fuel when the plant was operating to produce the same 

quantity of water as in the example. 

The model was reasonably linear when heater fouling was varied, at least for nominal 

production conditions in summer. However, at maximum operation, some internal 

flows like the recirculation flow R, make-up F or seawater to reject SR reached a 

maximum and the effect of the cleaning ball system was lower than expected for that 

load. 

Table 7.38 shows the malfunction matrix associated with each component when the 

fouling factor in the brine heater was changed by 0.00001 m 2 K/W. The most 

important terms of the matrix are associated with the above mentioned components: 

fictitious device, brine heater, recovery and reject sections and the mixer. These values 

can also be explained by analyzing the malfunctions associated with this inefficiency. 

As expected, pumps were not affected by brine heater fouling. The impact on fuel due 



to changes in brine heater fouling can be calculated by multiplying the components of 

the malfunction matrix by the product of each component and their unit exergy cost 

(obtained from the irreversibility matrix). Sometimes the malfunction matrix has 

components with high values, but the low product or low exergy cost associated with 

this component results in a lower impact on fuel. 

FIGURE 7.20 Impact on fuel analysis when the fouling in heater is varied. 

-500 

-1000 

-1500 

-2000 

-2500 

-3000 


Knowing the monetary cost of fresh water as a function of an inefficiency helps plant 

managers take decisions on using the cleaning ball system, depending on the 

compromise between consumption, operating costs and energy saved. Note that the 

cost of water decreased when heater fouling was decreased (figure 7.21). 

FIGURE 7.21 Monetary cost of distillate when the fouling in heater is varied. 

1,475 

1,470 

1,465 

1,460 

0 

fouling*10-5 in BH 

0 5 10 15 20 25 

kW 

$/m3 

Water cost 

fouling*10-5 in BH 

0 5 10 15 20 25 

In the nominal case, 0.00045 $/m 3 was saved when fouling was decreased by 

10 -- 5 m 2 ·K/W (or 7,650 $/y). Although the effect of the cleaning ball system was very 

difficult to translate into a constant fouling variation, the system reduced the fouling 



factor several times over (see section 3.6.1) when the cleaning system was 

periodically connected (for example in a four-hour cycle). At maximum production, 

the cost decreases due to the effect of purchase costs and because the increase in 

exergy cost is lower than in the nominal case (remember that the internal flows reach 

a maximum during maximum winter production). 

The sensitivity analysis of the monetary cost and fuel impact takes into account that 

the exergy costs k * of the steam to the brine heater and the electricity for the MSF 

pumps are different from unity (unit exergy cost of steam to heater and vacuum system 

was 2.55 and 2.5 respectively and exergy cost of electricity was 2.85). So, the real cost 

of producing water and the consequences of an inefficiency can be dealt with correctly. 

In summary, using the cleaning ball system in the heater had the following 

consequences: 

• It changed the temperature profiles of the cooling, flashing brine and distillate in 

the MSF unit. As the brine heater is settled at the beginning of the process, the 

temperatures of the recycle brine before and after the heater were affected. As 

those temperatures enter and leave the recovery section, the whole system was 

influenced by this inefficiency. 

• As a consequence of the last point, the induced malfunctions in the rest of 

components were higher than the intrinsic malfunction in the heater, taking into 

account the dimensions of each component. However, the dysfunction analysis 

did not provide any interesting information on how the components readapted 

their production to maintain the final production of freshwater. The non-physical 

components cannot be explained from a physical viewpoint. 

• The model was linear under changes in heater fouling. So, the malfunction 

matrix can be used to predict the fuel saved with the cleaning ball system or 

component malfunctions. 

• The cleaning ball system in heater increased the TBT of the unit. This implies a 

lower consumption to produce the same amount of freshwater, but also provokes 

scale formation due to the high-operation temperatures. Consequently, the 

cleaning ball system should be continuously maintained in the heater to keep the 

fouling factor low. If the system is not operating, scale formation will reduce the 

effectiveness of the condenser and the whole MSF unit. 

7.3.2.3 The effect of recovery section fouling on steam power plant behavior 

An inefficiency in a power plant or desalination unit will provoke additional fuel 

consumption. The analysis was performed separately for both plants. But if an 

inefficiency in the MSF unit provokes an increase/decrease in steam consumption by 

the brine heater, how does the steam power plant readapt?. If the electricity and water 

production are kept constant, the inefficiency in the MSF unit is an inlet parameter 

that seriously affects power plant behavior. This parameter is the amount of steam 



diverted to the MSF unit. Our analysis considered an inefficiency detected 

‘downstream’ and the MSF unit can induce the malfunctions; an inefficiency detected 

downstream should also be quantified upstream. So, we considered the ‘co-lateral’ 

effects of a co-generation plant with this example. 

In this example, electricity production was held at 122 MW in MCR operating 

conditions. The fouling in the recovery section was reduced to zero by the cleaning 

ball system and the live steam leaving the boiler was maintained. The first physical 

consequence (the effects of the cleaning ball system in the recovery section are 

explained in section 6 of Annex 1) of an inefficiency was a reduction in steam 

consumption from 89.1 to 71.1 kg/s (corresponding to a freshwater production of 

2,400 T/h, the maximum distillated in a MSF unit). Extraction to the MSF unit is at 

the end of the high-pressure turbine, so the latter was not affected by the different 

uses of the exhaust steam from this turbine. If the steam leaving the high-pressure 

turbine is not diverted to the MSF unit when some of it is saved with the cleaning ball 

system, an extra quantity of steam goes to the low-pressure turbine. Although the 

final section of the turbine has to maintain the exhaust pressure (we maintain the 

external parameters of the plant), at least the efficiency of the first section of the lowpressure 

turbine is improved with a higher entering mass flow rate (remember that the 

low-pressure turbine is designed to work in condensing mode, that is, when no steam 

is derived to the MSF unit). 

But the electricity production increases since the amount of steam and the efficiency 

of the low-pressure turbine have been improved. To maintain the final production, the 

amount of steam leaving the boiler must decrease from 156.1 to 146.6 kg/s. The 

redistribution of the flows inside the steam cycle was similar to the previous analysis; 

the low-pressure turbine produces the electricity that the high-pressure turbine 

cannot. This produces a negative impact when more steam is forced to flow in the 

low-pressure cycle (that is, passing through the condenser and not through the MSF 

heater). The feedwater system cools and additional fuel is required to reach the set 

point conditions of live steam in the boiler. Finally, the steam conditions leaving the 

high-pressure turbine are slightly varied (recall that the exhaust pressure is controlled 

by the MSF unit). 

Tables 7.39 and 7.40 show the F-P values for the steam power plant in design and 

operation (when the inefficiency occurs in the recovery section of the MSF unit). The 

〈KP〉 matrix is shown in tables 7.41 and 7.42 for the design and inefficient case, 

respectively. The ∆ 〈KP〉 matrix is the key to analyze the system with this inefficiency 

(table 7.43). Table 7.44 contains the |I〉 matrix and the exergy cost array. The 

dysfunction matrix [DF] including the malfunction array MF is shown in table 7.45. 

Figures 7.22 and 7.23 include the impact on fuel analysis and irreversibility increase. 


TABLE 7.39 F-P values in design, 122 MW output power. 



TABLE 7.40 F-P values without fouling in recovery section. MCR case. 



TABLE 7.41 KP matrix in design. MCR case. 



TABLE 7.42 KP matrix without fouling in recovery section. MCR case. 



TABLE 7.43 Variation of KP without fouling in recovery section. MCR case. 



TABLE 7.44 Irreversibility matrix without fouling in recovery section (MCR case). 



TABLE 7.45 Malfunction/dysfunction matrix without fouling in recovery section (MCR case). 



TABLE 7.46 Malfunction matrix when the fouling in recovery is varied 0,00001 m2·K/W in MCR case. 



FIGURE 7.22 Impact on fuel analysis without fouling in RCS, MCR case. 



FIGURE 7.23 Irreversibility increase analysis of section 7.4.2.3.


The first analysis compared the fuel impact associated with the whole plant (a fuel 

savings of 24.00 MW), with the fuel saved in the MSF 1 unit (26.47 MW). This means 

that the steam power plant is forced to work under less-efficient operating conditions. 

We will now explain the most significant values in the malfunction array of table 

7.45, relating the physical consequences to the matrix values. 

The deaerator component mixes and preheats the feedwater from the condenser. 

Irreversibility in the mixing process is lower because the mass flows entering the 

deaerator are lower during operation (where the live steam mass flow rate is reduced 

to maintain the final production) than in the design. Thermal irreversibility was lower 

because the cold flow entering the mixer was increased and its irreversibility was 

reduced by 828 kW (see table 7.45). The efficiency of the component should thereby 

increase, i.e., the variation of the unit exergy consumption was negative in the 

component (∆k = –0.085, see the ∆ 〈KP〉 table 7.43), implying an induced 

malfunction of –682 kW. 

The feedwater temperature entering the boiler was reduced because the low-pressure 

cycle increased its contribution to the whole system. The boiler consumed additional 

resources to reach the set point of the steam turbine (93 bar, 535 ºC). The increased 

exergy unit consumption in the boiler was ∆k = 0.004, and the malfunction associated 

with the component was finally 858 kW (see tables 7.45 and 7.43 respectively), with 

an associated fuel impact of 576 kW. 

The first section of the high-pressure turbine had a 1,320 kW induced malfunction as 

a consequence of the mathematical model. The efficiency of the Curtis blade was 

correlated as a function of the live steam from the boiler under different operating 

conditions, as in this case this amount has been decreased considerably, the 

isoentropic efficiency in the section decreases (and consequently the exergy and 

entropy properties of steam leaving the section). Consequently, ∆ 〈KP〉 in table 7.43 

was positive (∆k = 0.0267) with a 1,320 kW malfunction and a 1,954 kW fuel impact. 

Surprisingly, the fourth section of the high-pressure turbine had a decreased 

isoentropic efficiency but a negative induced malfunction (–484 kW, see table 7.45) 

and 1,500 kW fuel was saved. This abnormal behavior is explained by the exhaust 

pressure of the high-pressure turbine which decreased with the amount of live steam, 

allowing the output power (produced in the section) to increase. Since the product of 

this component is the output power (according to the thermoeconomic model), the 

unit exergy consumption was lower during the inefficiency, resulting in a ∆k value of 

–0.025 (see table 7.43 with the ∆ 〈KP〉 components). 

1. In this case the MSF unit is the component inserted in the structure productive of the steam power plant. 

Exergy product of the MSF unit is kept constant. 



As mentioned above, the efficiency of the first section of the low-pressure turbine 

increased because the amount of entering steam increases considerably and its 

∆ 〈KP〉 component was negative (∆k = –0.319, table 7.43). The irreversibility of the 

process was reduced by 1,965 kW, with a –2,177 kW induced malfunction and 2,970 

kW fuel savings. 

The malfunction associated with the MSF was positive, although the fuel impact 

saved was very high in this component. The dysfunction generated by this component 

achieved the desired fuel savings (a large negative value). The reason for the 12,491 

kW induced malfunction (table 7.45, which coincides with the irreversibility increase 

of the process in this case) was the drastic reduction in negentropy (which was 

introduced in the thermoeconomic model of the steam cycles to account for the heat 

rejected in the condenser). This negentropy is a subproduct in the productive 

structure. The unit exergy consumption of the unit increased (∆k = 1.837, table 7.43). 

The most important dysfunctions in the boiler and condenser were caused by the 

components with the most important malfunctions (figure 7.24). The boiler and 

condenser suffered dysfunctions of 1,620 kW and 752 kW from the deaerator; 

1,812 kW and –1,215 kW from the first section of the high pressure turbine, 

-- 1,391 kW and 404 kW from the fourth section of this turbine and –24.55 MW and 

--13.68 MW from the MSF unit, respectively. The final product in the boiler was 

reduced by more than 10 MW to maintain the total production at a lower steam 

consumption (total boiler dysfunction, –22.65 MW). The condenser also increased 

production by 16 MW (total condenser dysfunction, –13.71 MW). The high φ 

coefficients promote high dysfunction since they are related to the position of the 

components in the productive structure of the system. 

Following the methodology in Chapter 6 for the diagnosis of complex systems, the 

DI array is the column sum of the dysfunctions. The values of the main components 

are described in the previous paragraph (2.43 MW for the deaerator, 634 kW for the 

HPT1, and –38.9 MW for the MSF unit!). The impact on fuel associated with each 

component (table 7.45) was obtained by adding the malfunction array MF. This is the 

additional fuel consumed due to the change in the operation of each unit with respect 

to the operating conditions and no inefficiency. 

Having obtained the most relevant results in the inefficiency analysis, the malfunction 

matrix can be used as a predictive tool to diagnose the effects of the inefficiency. 

Figure 7.24 shows the total impact on fuel associated with the inefficiency variation 

in the recovery section (the effect of fouling in the recovery section when fouling is 

varied). Here the malfunction matrix did not exactly predict the malfunctions because 

the response of the mathematical model was not perfectly linear when varying the 

steam to the MSF unit (under maximum production, some internal flows of the 

distiller are forced to keep a constant value). However, the MSF model behaved 

linearly at nominal production. 



FIGURE 7.24 Impact on fuel depending on fouling in recovery section. 

-6000 

-12000 

-18000 

-24000 

0 


Since the model responded in a non-linear way to the efficiency, the most rigorous 

diagnosis should separate simulate each case (avoiding the malfunction matrix). The 

malfunction matrix in table 7.46 provides the ‘linearized’ malfunction induced in 

each component when the fouling in the recovery section is changed by 

0.00001 m 2 ·K/W. The condenser pump and low-pressure heater coefficients were 

again high (as are the brine heater and feed pump values), although the low product 

did not induce an important malfunction. As expected, the MSF coefficients were the 

highest and the HPT1 and HPT4 were also elevated. 

FIGURE 7.25 Monetary cost of electricity depending on the fouling in recovery section. 

0,03796 

0,03794 

0,03792 

0,03790 

0,03788 

0 36 9 12 15 

kW 

$/kW·h 


fouling*10-5 in RCS 

0 3 6 9 12 15 

The ‘monetary diagnosis’ (figures 7.25 and 7.26) involves the cost of electricity and 

water as a function of recovery section fouling during maximum production in winter 

(which was the load requested in the example). The cost of electricity increased a bit 

(4×10 –6 $/kW·h) when the fouling was decreased. The malfunction analysis proved 



that the steam power plant decreases its global efficiency with an inefficiency in the 

recovery section of the MSF unit (as explained at the beginning of this section). 

Water cost followed the expected results, 0.0057 $/m 3 was saved with a 0.00001 m 2 

K/W decrease in recovery section fouling (see figure 7.26) or 120,000 $/y. 

FIGURE 7.26 Cost in $ per cubic meter of water when recovery section fouling is varied. 

1,05 

1,03 

1,01 

0,99 

0,97 

0,95 

$/m3 

In summary: 

Water cost 

0 36 9 12 15 

• The results of the inefficiency diagnosis imply that fouling in the recovery 

section considerably reduces the amount of steam needed to produce freshwater. 

The cost of water was drastically reduced (see figure 7.26) when the cleaning 

ball system operates in the recovery section of the MSF distillers. But a 

reduction in the derived steam did not imply improved plant performance (for 

this particular case, the electricity cost was even higher). 

• A consequence of this example is that the co-generation plant should operate at 

an optimum ratio between the steam to MSF and the live steam produced in the 

boiler. The installation of the cleaning ball system in the MSF distillers should 

be taken into account in the design in the co-generation plant, because the 

optimum point of the performance in the dual plant is seriously affected by the 

use of this system. 

• An inefficiency in the MSF unit provokes induced malfunctions in several 

components of the steam power plant (boiler, deaerator, some turbine 

sections…). Therefore, this type of inefficiency detected ‘downstream’ has a 

more global effect than an inefficiency local to a component in the steam power 

plant. 



7.3.3 Analysis of several inefficiencies 

7.3.3.1 Analysis of several simultaneous inefficiencies in the steam power plant 

We will now consider the combined effect of several simultaneous inefficiencies in 

different components and the effect of induced malfunctions. This exercise reinforces 

the concept of local and intrinsic malfunctions. We simulated the physical effect of 

these inefficiencies (changing main flowstreams) and describe related malfunctions, 

dysfunctions, and additional fuel consumption in the steam power plant (the direct 

problem). 

The analyzed inefficiencies were: 

• TTD in high-pressure heater no. 1 increases 5 ºC 

• Isoentropic efficiency of the feed pump decreases 10%. 

• Isoentropic efficiency of the first section of the high-pressure turbine 

decreases 5%. 

• Isoentropic efficiency of the first section of the low-pressure turbine decreases 

15%. 

• Isoentropic efficiency of the fourth section of the high-pressure turbine 

decreases 10%. 

If the TTD of the HPH1 increases, the feedwater leaves the heater at a lower 

temperature and the turbine extraction temperature increases. If the heater does not 

need to preheat the feedwater the same amount, the extraction mass flow should be 

reduced. The boiler is also affected because feedwater enters the economizers at a 

lower-than-design temperature. 

The mechanical irreversibility of the feed pump increases if the isoentropic efficiency 

is lower than expected. The pump responds by consuming more power and the 

feedwater temperature increases. 

The exhaust conditions of the high and low-pressure turbine are more or less 

maintained with the MSF unit and ambient conditions. When the isoentropic 

efficiency of several sections of the steam turbine decreases, the steam conditions are 

not significantly affected by inefficiencies in other sections. The output power in each 

inefficient section is not enough to maintain final production but other sections cannot 

produce this extra power since their efficiency was maintained constant. Thus, 

although the system demands more live steam, the efficiency of the boiler does not 

necessarily decrease. 


TABLE 7.47 F-P values in design, 122 MW output power. 



TABLE 7.48 F-P values with inefficiencies in five components (MCR case). 



TABLE 7.49 KP matrix in design (MCR Case). 



TABLE 7.50 KP matrix with several inefficiencies in MCR case. 



TABLE 7.51 Variation of KP matrix with several inefficiencies in MCR case. 



TABLE 7.52 Irreversibility matrix with five inefficiencies in power plant (MCR case). 



TABLE 7.53 Malfunction/dysfunction matrix with five inefficiencies in MCR case. 



FIGURE 7.27 Impact on fuel analysis in section 7.3.3.1. 


FIGURE 7.28 Irreversibility increase in section 7.3.3.1. 


CHAPTER 8 

Synthesis, contributions and 

perspectives 

8.1 Synthesis 

This Ph. D. Thesis brings together three topics that have never been thoroughly 

interrelated. 

• Desalination processes. 

Water scarcity is a serious problem for humanity now and in the future. Water 

resources are being depleted by excessive consumption and polluted by human 

development. Fortunately, the problem can be solved by desalting seawater or 

reusing wastewater. Chapter 1 describes the current situation in arid countries and 

how to solve some water shortages. Chapter 2 summarizes the most common 

methods to produce freshwater for human consumption. 

• Energy consumed in desalination. 

The detailed description of desalination processes in Chapter 2 including the 

consumption and energy producing process in desalination. It is very energy 

intensive and should not be isolated from energy production processes. 

Desalination designers normally present the energy consumption of different 

3 

desalination processes in terms of electrical consumption (kW·h/m ) even if they 

consume thermal energy. The current trend is to separate the two processes. The 

existence of big companies that only produce electricity or only water widens the 

gap between desalination and energy communities. This thesis demonstrates that 

energy and water suppliers interact in a co-generation installation to provide both 

products and that both systems should not be analyzed separately. 


324 

Synthesis, contributions and perspectives 

• Thermoeconomic analysis of the most common desalting and power installations. 

We used thermoeconomic techniques normally applied to power plants. In this 

way, we took advantage of everything that thermoeconomics provides to obtain 

an in depth knowledge of a very complex system. The energy supplier was also 

analyzed since the desalting plant is coupled with the power plant. We analyzed 

one of the most common processes used in arid regions with important water 

scarcity problems: multi-stage flash desalting plants that use fossil fuels to also 

produce electricity with the help of a conventional power plant. The 

thermoeconomic analysis was also applied to a steam power plant providing 

steam to the MSF unit. 

The main contribution of the thesis is contained in Chapter 7. The thermoeconomic 

analysis of the dual plant included cost analysis, diagnosis, and optimization. The 

results of the different thermoeconomic techniques applied in each case are as 

follows: 

1. The cost analysis is very useful to find the enormous possibilities of energy 

savings under different configurations of the co-generation plant. A detailed 

analysis of the internal costs pin-points the component responsible for 

irreversibilities. New processes can also be combined to produce minimum water 

and electricity costs. 

2. Plant diagnosis helps to elucidate component interaction. The different 

relationships and effects of component inefficiencies on other subsystems can be 

successfully quantified by considering both plants together. The interaction can 

also be separated by varying component efficiency (malfunction) and the 

subsequent additional component production (dysfunction). This thesis includes 

one example of a thermodynamically isolated (power plant) and non-isolated 

(MSF unit) system. However, the diagnosis cannot be used as a predictive tool in 

the control systems because the theory cannot yet recognize the origin of the 

inefficiencies. 

3. Local optimization optimizes the operating conditions by calculating the 

minimum product cost of each plant unit. It is very valuable to design new cogeneration 

plants or to readapt existing ones. 

4. Product cost and price must be calculated from their origin. Cost is the resources 

consumed to produce something and price is the value obtained when this product 

is sold. Benefit is the difference between both concepts. Once the price is known, 

the cost must be minimized to obtain the maximum benefit (plant operating 

conditions of the plant can be changed intentionally depending on demand and 

price). 


Main contributions 

8.2 Main contributions 

This Ph. D. Thesis applies the most recent thermoeconomic techniques (normally 

only applied to power generation systems) to a power and desalination plant. The 

main contributions of the thesis are listed here: 

8.2.1 Simulator of a dual-purpose power and desalination plant 

A simulator was used to provide the thermodynamic states of desalination and power 

generation process. Thermal desalination processes have been simulated by chemical 

engineers (Jernqvist, Jernqvist and Aly, 1999; Ettouney and El-Dessouky, 1999), but 

the steam producing system is not considered. The two processes were separately 

introduced in the simulator to independently analyze each process. A combined state 

can be modelled by introducing the same quantity of steam sent to the MSF unit. The 

simulator was validated using performance data cases and real operating data for the 

dual-plant with a MSF unit and a steam power plant. It can model the effect of 

inefficiencies in the two systems for diagnosis. 

The mathematical model applied under different operating modes accurately 

reproduces (for engineering purposes) the real state of the plant, despite the scarcity 

of data for each operating mode. The most difficult case is when the amount of steam 

entering the low-pressure turbine is so low that the system has to consume 

mechanical energy to move the blades. In this case, the input conditions of the 

mathematical model have to be continuously restricted in order to preserve the 

stability of the model. The mathematical models of the MSF and steam turbine power 

plant were solved using a solution algorithm that simultaneously handles the whole 

set of model equations. The packages containing the sequential scheme to solve the 

flowsheeting of a plant are discarded here, although this threatens model stability 

under different operating conditions. 

8.2.2 State of the art in Thermoeconomics 

An effort was made in Chapter 6 to review and summarize Thermoeconomic 

methodologies. The Structural Theory was finally adopted to explain the concepts, 

procedures and applications of these techniques, including the matrix formulation 

and new terms like induced malfunction, intrinsic malfunction and dysfunction. The 

thermoeconomic analysis of the dual plant was based on this theory and its latest 

improvements. 


325

326 


8.2.3 F-P definition for a MSF unit 

The F-P definition of the thermoeconomic analysis of the MSF unit (see section 

7.1.3.2) highlights the cost of water production in the recovery and reject section, 

taking into account the thermodynamic processes in the plant. Several F-P definitions 

solved the model but none gave appropriate costs of device functionality nor for the 

main flow degradation in the MSF plant. 

8.2.4 Cost analysis of a dual-plant 

A detailed cost analysis of the power and desalination plant was carried out under 

different operating modes (see section 7.2). The physical (or formation) costs of the 

main components were calculated. Exergy operating costs are available for each 

component as well as the thermoeconomic costs of water and electricity. These latter 

costs were successfully compared with other methodologies (EL-Nashar, 1999; 

Kronenberg et al., 1999) that do not use the thermoeconomic model and provide 

much less information. 

8.2.5 Diagnosis of a complex system 

The thermoeconomic diagnosis in section 7.3 was based on Structural Theory and 

Symbolic Thermoeconomics (Torres et al., 1999). This is the first time that a 

malfunction/dysfunction analysis is applied to a complex energy system (26 

components and 4 junctions for the power plant and 11 components and 7 junctions 

for the MSF plant). Usually the matrix formulation is only used to study simpler 

systems like the gas turbine co-generation plant in Chapter 6. The malfunction/ 

dysfunction table provides a lot of information that should be carefully analyzed 

when an inefficiency is simulated in the plant (exergy costs, impact on fuel, 

irreversibility increase in each component...). The relationships between components 

are rapidly found with in terms of efficiency variation (intrinsic or induced 

malfunction) or additional production (dysfunction). This method does not find the 

nature of the malfunction. Whether it is intrinsic or induced depends on user 

knowledge. 

The symbolic notation and Structural Theory also helps to formulate the malfunction 

matrix to find the quantity of additional resources consumed due to an inefficiency 

(without using the simulator). This matrix is used when the system responds linearly 

to the applied inefficiencies. If the inefficiency is local to the component, individual 

matrices of different inefficiencies may be added to make one large malfunction 

matrix with the same effect. 

To date, most analyzed systems demonstrate additivity of diagnosis: several 

inefficiencies can be disaggregated. However, the MSF did not fulfil this requirement 


Perspectives 

in the diagnosis of complex systems. As seen above, this fulfilment strongly depends 

on the physical structure of the system. 

8.2.6 Local optimization of the steam power plant 

Local optimization of the main components of the steam power plant also provides a 

global minimum final cost of electricity and water. Global optimization of the steam 

power plant (based on local optimization, see section 7.5) has never been applied to a 

set of 14 free-design variables that govern plant behavior. Local optimization can be 

applied to the steam power plant because it is thermodynamically isolated, i.e. local 

perturbations only affect one component (demonstrated in the diagnosis of the steam 

power plant). 

8.2.7 Cost, price and benefit 

Finally, a new methodology is included to assign product cost, price and benefit using 

examples to demonstrate that cost and price are independent. The main objective of 

an investment is to obtain maximum benefit, which does not always imply minimum 

cost. 

8.3 Perspectives 

8.3.1 Improving existing plants. Process integration 

One of the immediate consequences of this work is to increase the ways existing 

plants may reduce energy consumption. After analyzing one of the most developed 

methods to produce freshwater and electricity, some areas were found lacking. Our 

suggestions include: 

• Promoting the simulation of both processes (water and energy production) 

integrated in specific simulators. 

• Applying our methodology to other desalination processes. Our objective was to 

find the most efficient process at the lowest energy consumption, the best way to 

produce both energy and water and not contribute to fossil fuel depletion, air 

pollution and climate change. The importance of hybrid configurations, i.e. the 

integration of other processes to produce energy (wind, solar, tides, even nuclear) 

and water (MSF/RO or MED/RO units, heat absorption pumps) will possibly be 

the trend in the next decades. 'Building-block’ software will be required to 

thermoeconomically analyze any process producing water or electricity. 

• Thermoeconomics only considers the costs of operation, installation and 

maintenance, but processes also involve other costs that should be taken into 


327

328 


account including environmental (pollution, brine discharges...), costs of 

producing materials, biological costs, building costs, etc. All these are less 

developed than the costs evaluated in the thermoeconomic analysis. Since 

thermoeconomic techniques can consider any type of costs, they should be 

introduced in the global theory when they are more or less available. 

8.3.2 Improvements in thermoeconomic diagnosis 

Cost analysis provides a lot of information about how processes degrade and the 

energy quality of fluids in a plant. It is very useful to quantify the efficiency of plant 

processes. Diagnosis is directly oriented to an on-line implementation in the control 

system. In this regard, a big effort is needed to improve thermoeconomic techniques 

related to plant diagnosis (the ‘ inverse problem’) 

when the data acquisition system 

(DAS) finds deviations from the target conditions for each operating mode and load. 

The diagnosis should detect the inefficiency from the data collected by the DAS to 

take corrective actions. New communication technologies (Internet) allow remote 

control of the on-line implementation of system diagnosis, so plant managers can also 

see the benefits of the implementation. The on-line system can also be installed 

higher up in the control system, i.e. it can be used for all units. The units respond as a 

whole unit when a deviation is detected. Regarding maximizing benefit, the higher 

level of hierarchy can help decide the most profitable configuration and the 

possibility of connecting the hybrid systems installed in the plants for additional 

water or energy in peak or low-demand periods. 

Some previous steps may be needed to solve the inverse problem of the 

thermoeconomic diagnosis: 

• Analyze the problem of ‘noise’ provoked by the real boundary conditions in an 

installation: set points, ambient conditions, fuel quality, different loads and 

operating modes. We should consider the way to isolate the system from these 

boundary conditions or their effects. Once the problem is solved, the diagnosis 

finds the real causes of the deviations. 

• Thermoeconomics should be used to investigate the development of new 

techniques to study component interdependence during induced malfunctions in a 

complex system. The non-additivity of the diagnosis in these interrelated systems 

opens an interesting new line of investigation. 

• Clarifying the application and interpretation of dysfunctions generated in/by plant 

components. We could consider performing the analysis under a constant final 

production (of the complex system), depending on the finality of the analysis. 


Perspectives 

8.3.3 Integrating attitudes 

Thermoeconomic analysis provides enormous amounts of information about plant 

functioning and possible savings. This information should be clearly integrated in a 

vertical structure, i.e. a different kind of information should go to each level in the 

plant staff hierarchy. For example, if we divide the organization of the plant in three 

levels, we have: 

Operator level 

The information derived from the diagnosis is the most important at this level. The 

physical and economic effects of the inefficiencies and the control strategies (security 

versus economy) are the main issues for operators. 

Technician level 

This field includes optimizing existing systems and investigating and developing 

more efficient systems, and new control systems to handle inefficiencies. 

Managers level 

Cost analysis must be the main tool used by the plant managers since they manage 

the whole plant (assuming there are many units per plant). Cost, price and benefit 

must be clearly differentiated at this level. 

Training seminars are necessary for all levels to inform staff about the 

“thermoeconomic culture” and its benefits for humanity. 

8.3.4 Sustainable desalination 

Desalination is one of the most promising means of producing drinkable water with a 

low impact on the environment. The tendency of the desalination scientific 

community is to reduce energy consumption and substitute primary energy sources 

by renewable sources on a large scale. This tendency should be followed in all areas 

that influence our future. A more global analysis, like the Life Cycle Analysis (LCA), 

including additional aspects (residues, product use, materials, etc) is also necessary to 

provide an overall perspective of desalination processes. 

Research on desalination using solar energy for existing or new methods, should be 

encouraged. As solar technology develops, the cost of producing water (on a large 

scale) will decrease as will the strong dependence on energy. 

Promoting the installation of simple devices to provide water in acceptable conditions 

at a very low (or zero) cost in non-developed/isolated areas (Africa, India), is another 


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330 


means of redistributing world resources and promoting a more equal development in 

the world community. 

8.3.5 Promote energy and water interactions 

Water and energy are both limited resources, vital to the quality of the human life. 

The rapidly growing human population increases the demand for these resources 

every day. Several international organizations are dedicated to energy and several 

others to water, but there is a marked lack of attention to combined water and energy 

issues. 

This Ph. D. Thesis demonstrates that energy and water cannot be studied separately. 

A multi-disciplinary group of water and energy specialists has been formed 

(International Study Group for Water and Energy Systems (ISGWES), settled at the 

University of Zaragoza) to promote the interchange of ideas, scientific knowledge 

and sustainable development of water and energy systems. Some of the investigation 

lines commented above will be promoted by ISGWES. 


ANNEX 1 


The thermoeconomic diagnosis of the dual plant in section 7.3 considered several 

inefficiencies described at the beginning of the chapter. Each inefficiency requires 

many tables and figures, all of which are included in this annex. Thus, this annex is 

an overall view of the effects provoked by one or more inefficiencies in the power 

and desalination plant. 

The following individual inefficiencies (described but not analyzed in section 7.3) 

were applied: 

• Inefficiency in the HPH1: variation in terminal temperature difference of heater. 

• Inefficiency in the feed pump: reduced efficiency. 

• Inefficiency in the high-pressure turbine: efficiency analysis in the first section. 

• Inefficiency in the low-pressure turbine: efficiency variation in first section. 

• Inefficiency in the recovery section: effect of reduced fouling in MSF. 

• Inefficiency in the reject section: effect of the fouling factor. 

The analysis was performed under different operating conditions but is only 

presented for one load, the MCR case for the power plant and NTOS performance 

case for the MSF unit. The effect of the different loads in the two systems is 

summarized in sections 7.3.4 and 7.3.5. 


332 


A1.1 Effect of an inefficiency in the high-pressure heater 

no.1 (HPH1) 

The TTD of the HPH1 was varied to analyze the effect on the steam power plant. 

The heater TTD is the difference between the temperature of saturated vapor 

extracted from the turbine and the feedwater leaving the heater. Since the conditions 

of the steam extracted in the turbine are maintained, a higher TTD implies a poorer 

heat transfer inside the heater tubes. The feedwater therefore leaves the heater at a 

lower temperature than expected. Consequently, the extraction mass flow to this 

heater decreases and the boiler produces less live steam. Although the live steam 

needed for the electricity demand is reduced, the boiler heats the feedwater from a 

lower temperature and natural gas consumption increases. An excessive change in 

heater TTD may also sharply vary the levels inside the heater, leading to dangerous 

problems or even drains in the heaters. The consequences are very difficult to 

evaluate with conventional component analysis since the model does not incorporate 

the security system layout of the power plants. 

The mathematical explanation of varying TTD involves the malfunction and 

dysfunction matrices detailed in section 7.3. Tables A1.1 and A1.2 include the F-P 

definition of the steam power plant in design and operation with an inefficiency in 

the HPH1: the TTD increases 5 ºC. The output power used was 122 MW, but other 

examples were at 60, 90 and 140 MW, corresponding to the parallel mode, 

extraction mode with partial load and condensing mode, respectively (section 7.3.4). 

These are the most important operating modes (the most operating hours per year) in 

the power and desalination plant. Tables A1.3 and A1.4 include the 〈 KP〉 

tables 

corresponding to the design and inefficient operation, and table A1.5 is the ∆ 〈 KP〉 

matrix. Table A1.6 contains the φ coefficients of the irreversibility matrix | I〉 

with 

exergy cost of components. Finally, table A1.7 is the malfunction/dysfunction table 

built using table A1.6. Table A1.8 is the malfunction matrix when we vary the TTD 

of the HPH1 1 ºC. Figures A1.1 and A1.2 show the impact on fuel analysis and the 

irreversibility increase per component. 

The highest malfunctions in table A1.7 corresponded to the boiler, HPH1 (the 

inefficient component) and HPT1. The rest of the components were within simulator 

accuracy (< 100 kW). Varying the heater TTD only affected the components 

interacting with the heater. This inefficiency did not induce malfunctions in other 

components. 


TABLE A1.1 F-P values in design (MCR case). 

Effect of an inefficiency in the high-pressure heater no.1 (HPH1) 


333

TABLE A1.2 F-P values in operation with 5º C TTD respect to design . 

334 



TABLE A1.3 KP matrix in design (MCR case). 



335

TABLE A1.4 KP matrix with inefficiency in HPH1 (MCR case). 

336 



TABLE A1.5 Variation of KP matrix when TTD in the HPH1 is 5 ºC higher than the expected. 



337

TABLE A1.6 Irreversibility matrix with the inefficiency in HPH1. 

338 



TABLE A1.7 Malfunction/Dysfunction matrix when the TTD in HPH1 is 5º C higher. 



339

TABLE A1.8 Malfunction matrix when TTD in HPH1 is varied 1 ºC 

340 



FIGURE A1.1 Impact on fuel analysis with an inefficiency in HPH1. 


FIGURE A1.2 Irreversibility analysis when the TTD in HPH1 is increased 5 ºC. 


341

342 


In the simulated intrinsic malfunction, increasing the TTD of the HPH1 by 5 ºC 

(which could be interpreted as a problem in the heat transfer mechanism of the 

heater), decreases more than expected the feedwater temperature leaving the heater. 

The extraction flow to this heater also decreases (to meet the energy balance of the 

heater). In any case, the inefficiency increases the irreversibility in the heater 

( ∆I 

= 16.5 kW, see table A1.7) when the temperature difference in the water tubes 

increases. The first effect (a lower heating process in the heater) is more important 

than the second (a lower extraction flow). Unit exergy consumption varied by 

∆k 

= 0.020 (see table A1.5). The result of the inefficiency was a 223.6 kW intrinsic 

malfunction (or an associated 272 kW impact on fuel). 

The effect induced in the boiler is clear: if the feedwater leaves the heater at a lower 

temperature, the boiler consumes additional fuel to maintain the live steam 

conditions (which are fixed in the simulator and the real plant). The ∆ 〈 KP〉 

component, i.e. the variation of component unit exergy consumption (table A1.5) 

was ∆k 

= 0.005. As the boiler product was very high (the heat transferred to the 

feedwater was about 210 MW), the malfunction was 1,179 kW with an associated 

830 kW impact on fuel. The total impact on fuel associated with this inefficiency 

was 1,048 kW. In this case, the malfunction induced in the boiler was more 

important than the intrinsic malfunction in the heater. 

The amount of steam flowing in HPT1 was lower than in design, although this effect 

disappears when HPH1 extraction was reduced. The steam flowing through the 

second section of the HPH is maintained. The energy production in this section is 

maintained, but the efficiency in this section is lightly decreased (the efficiency of 

the Curtis blade is higher as the live steam flow grows), then the variation of the unit 

exergy consumption of the section is ∆k 

= 0.0026, then we have a little malfunction 

induced in this section of 130 kW, and an impact on fuel associated of 209 kW. 

The dysfunctions due to the HPH1 inefficiency emphasizes the results of other 

inefficiencies in the steam power plant: only the boiler and the condenser suffer 

dysfunctions generated by component malfunctions (HPH1, boiler or HPT1). The 

dysfunction generated in the boiler was positive. The φ coefficients were positive but 

negative for the condenser, provoking a negative dysfunction. The junction J2 

produced a –393 kW dysfunction in the boiler associated with its exergy unit 

consumption variation. This variation is explained by the productive structure of the 

steam power plant (see figure 7.5): feedwater heated in the boiler in one of the inlets 

of that junction. 

The power plant model varied linearly to a one degree change in the heater TTD 

when comparing the amount of fuel saved. Figure A1.3 shows this effect for 

electricity production in the extraction mode of the example (122 MW). The effect is 

non-linear when TTD is negative and close to zero (the design TTD for this 

operating condition is –1.7 ºC). The analysis could be performed avoiding this range 


FIGURE A1.3 

FIGURE A1.4 


of temperature differences since the impact on fuel associated with the whole plant 

can be less than 200 kW and the mathematical model cannot diagnose the 

inefficiency with less than 100 kW accuracy. 

Impact on fuel associated with a variation in the TTD of HPH1. 122 MW power plant production. 


1200 

kW 

800 

400 

-5 -4 -3 -2 -1 0 1 2 3 4 5 

-400 

-800 

-1200 

0 

In any case, the observed trend could be used to apply the malfunction matrix to this 

inefficiency. Some matrix components had large values. The condenser pump and 

low-pressure heater No.2 were high due to the behavior of the mathematical model 

at the condenser exit area (see section 4, mathematical model of the power plant). 

The feed pump and deaerator also had considerable values due to the decrease in 

feed water flow in the high-pressure zone (provoked by the HPH1 inefficiency). 

Cost of electricity when varying TTD in HPH1 (MCR performance case). 


0,03790 

0,03785 

0,03780 

0,03775 

$/kwh 

TTD (º C) in HPH1 

-5 -4 -3 -2 -1 0 1 2 3 4 5 


The effect on the cost of electricity and water was not as important as the impact on 

fuel associated with the inefficiency in the turbine section. It implied an additional 

3 

0.000009 $/kW·h in electricity and 0.00017 $/m in freshwater per degree Celsius in 

the TTD of the HPH1. This could save 9,600 $ and 3,570 $ if the plant were 


343

FIGURE A1.5 

344 


operating yearlong at these loads. Figures A1.4 and A1.5 refer to this assumption, 

emphasizing the linearity of the model (except from –2 to 0 ºC). 

Cost of water when varying TTD in the first HPH (MCR performance case). 

In summary: 

Water cost 

1,2730 

$/m3 

1,2725 

1,2720 

1,2715 

1,2710 

-5 -4 -3 -2 -1 0 1 2 3 4 5 


• the heater TTD affects heater behavior and components receiving feedwater 

heated by the inefficient heater (the boiler). The inefficiency did not result only 

local to its component, and the associated malfunctions were higher in other 

components than the intrinsic one. The rest of the components were not 

considerably affected compared to an inefficiency in the steam turbine sections. 

• The impact on fuel associated with the additional cost of water or energy due to 

the inefficiency was not important when compared with other inefficiencies (the 

total saving of 14,000 $/y in both products could be obtained by decreasing the 

TTD of the HPH1 by 1 ºC). This only refers to the range where the model 

responds linearly to TTD variation (the variational analysis was assumed to be 

linear). If the TTD is abnormally high, an excess heater level or excessive 

heating in the economizers can lead to extreme induced malfunctions that can 

not be calculated in the diagnosis (Valero, Torres and Lerch, 1999). Therefore, 

heater TTD should be carefully controlled. A by-pass in one of the HPHs is a 

very good example of heater inefficiency, but it is very difficult to simulate. The 

model needs to be modified considerably to consider this inefficiency. 

• The results of the HPH1 inefficiency could be extrapolated to HPH2, taking into 

account the amount of heat transferred in the two heaters (usually the HPH2 uses 

less steam to heat the feedwater). The effect on the boiler should also be 

reduced. 


Effect of feed pump isoentropic efficiency 

A1.2 Effect of feed pump isoentropic efficiency 

The feed pump pressurizes the feedwater before it enters the boiler. An inefficiency 

inside the pump mechanism (assuming that the pump can supply the specified 

pressure) only slightly increases feedwater temperature since the temperature rise in 

pumping a liquid is also low. Therefore, this inefficiency should not induce 

important malfunctions in other components. The most important consequence is 

the significant increase in feed pump power consumption. Additional live steam is 

required to maintain the net output power. 

If the feed pump is coupled with an auxiliary turbine providing energy, an 

inefficiency should affect other components because an abnormally functioning 

auxiliary turbine would redistribute the flows in the steam/water cycle of the power 

plant. 

Feed pump behavior can be studied considering an isoentropic efficiency, a variable 

that appears in our mathematical model. Pump efficiency decreased 12% with 

respect to its characteristic curve at 122 MW (MCR performance case). The 

inefficiency was also analyzed under different operating conditions (see 

section 7.3.4). Tables A1.9 and A1.10 show the F-P values for design and operating 

conditions. The 〈 KP〉 

matrices are written dividing fuels and the product of each 

component (tables A1.11 and A1.12). After these matrices are built, the ∆ 〈 KP〉 

matrix and irreversibility matrix I are immediately processed, containing the unit 

exergy costs of the components (tables A1.13 and A1.14). The malfunction/ 

dysfunction matrix with the dysfunction coefficients is included in table A1.15. The 

malfunction matrix with the extra consumption when the pump isoentropic 

efficiency increases 1% is finally included (table A1.16). Figures A1.6 and A1.7 

show the impact on fuel and the irreversibility increase in all components for this 

simulated inefficiency. 

We will now explain the physical analysis using results from the inefficiency 

diagnosis. The malfunction array demonstrates that the feed pump does not induce 

any malfunction in the rest of the components. Only the boiler and the inefficient 

component have a malfunction greater than 30 kW. The mechanical irreversibility 

increases when the pump has serious problems to reach the demanded pressure. 

These internal frictions also increase the temperature of the pressurized feedwater 

leaving the pump. So, the thermal irreversibility also appears in the inefficiency and 

the final reversibility increase was ∆I 

= 475 kW (see table A1.15). The unit exergy 

consumption increase was obvious ( ∆k 

= 0.200, see table A1.13). The intrinsic 

malfunction was therefore 409 kW, and the impact on fuel associated with the 

inefficiency is 608 kW (the total impact on fuel taking for the whole system is 

750 kW). 


345

TABLE A1.9 F-P design values. 

346 



TABLE A1.10 F-P values with inefficiency in FP: -12% in its efficiciency. 



347


348 



TABLE A1.12 KP matrix when the inefficiency in FP is detected. 



349

TABLE A1.13 Variation of the KP matrix when the FP is working improperly. 

350 



TABLE A1.14 Irreversibility matrix with -12% in the FP efficiency. 



351

TABLE A1.15 Dysfunction table and malfunction array when the FP is working with 12% lower efficiency. 

352 



TABLE A1.16 Malfunction matrix when the efficiency of the FP varies 1%. 



353

FIGURE A1.6 Impact on fuel analysis when a inefficiency in FP is detected. 

354 


FIGURE A1.7 Irreversibility analysis with the irreversibility in FP. 



The malfunction induced in the boiler was mainly due to the large amount of 

product it generates (210 MW), since its efficiency and unit exergy consumption are 

not varied (the ∆k component is close to zero, see the ∆ 〈KP〉 matrix in table A1.13). 

This provokes a malfunction of –80 kW and an impact on fuel of only –69 kW. 

The irreversibility analysis shows that the dysfunctions associated with the boiler 

and condenser were the highest (754 and –472 kW respectively) and were generated 

by the feed pump. The weight coefficients φ ij (see table A1.14) were quite high in the 

rows corresponding to boiler and condenser (the unit consumption was changed in 

this case because the final products of these components had to increase 370 and 

550 kW respectively to maintain the net output power). In these rows, the pump 

inefficiency dysfunction was provoked by varying the unit exergy consumption of 

components more related to other components (i.e., the boiler and the condenser). 

Since the feed pump does not induce malfunctions and the model reacts linearly to 

variations in pump efficiency, the malfunction matrix is an exact tool to quantify 

additional fuel consumption for this inefficiency. Figure A1.8 demonstrates this 

linear behavior at the extraction mode load (122 MW). 

FIGURE A1.8 Effect of feed pump efficiency on fuel consumption. Variational study in the MCR performance 

case. 


800 

kW 

600 

400 

200 

0 

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 

-200 

-400 

-600 

% eff. in FP 

The cost of electricity and water as a function of feed pump inefficiency was very 

clear and linear (see figures A1.9 and A1.10). We can save 0.000003 $/kW·h and 

0.00006 $/m 3 in electricity and freshwater production with a 1% increase in pump 

efficiency. The relative effect on electricity (the effect per unit produced) is 

supposedly greater than the effect on water. For a constant yearly production, a 1% 

isoentropic efficiency implies a savings of 3,530 $/y in electricity and 1,260 $/y in 

water. 



FIGURE A1.9 Effect of pump inefficiency on electricity cost (MCR performance case). 


0,03784 

0,03782 

0,03780 

0,03778 

0,03776 

% eff. in FP 

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 

FIGURE A1.10 Water cost when the efficiency of the feed pump is varied. 

The main results of the inefficiency analysis were: 

• As expected, the effect of the feed pump inefficiency was only local. The 

increase in feedwater temperature leaving the pump was almost insignificant. 

The additional electrical consumption of the pump did not change the steam 

cycle behavior. The additional fuel supplied the extra electrical consumption of 

the feed pump. The effect of this inefficiency is not as important as inefficiencies 

in other components, such as the steam turbine sections (less than 5,000 $/y in 

the combined production of water and electricity). 

• The feed pump is not strategic in a power plant. Its effects need only be 

considered if an inefficiency stops the plant because of a broken pump 

component (i.e. the linearity of the variational analysis is not valid). 

• The product of the steam power plant must be the net output power. The effect of 

this inefficiency is not clearly noted in the system if gross output power is 

maintained. 


$/kWh 

Water cost 

1,2730 

1,2725 

1,2720 

1,2715 

1,2710 

$/m3 

% eff. in FP 

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Effect of an inefficiency in the first section of the high-pressure turbine (HPT1) 

A1.3 Effect of an inefficiency in the first section of the 

high-pressure turbine (HPT1) 

The physical effects of an inefficiency in a turbine section are described in section 

7.3.2.1 as intrinsic malfunctions (steam path degradation, etc). HPT1 contains the 

governing section which is also affected by the control valves. Although the steam 

power plant always works at constant pressure, an intrinsic malfunction in the Curtis 

blade or wheels induces malfunctions downstream (see section 7.3.2.1). This varies 

steam conditions downstream because the steam conditions exiting HPT1 are 

changed, even though the HPT exhaust pressure remains constant. As this steam 

passes through the rest of turbine sections, they should also be affected, although 

their isoentropic efficiencies remain almost constant due to a constant pressure ratio. 

Conditions of low-pressure steam are slightly varied as the HPT exhaust values are 

sent to the MSF unit. The exhaust pressure remains constant by definition. The 

system can only respond to the inefficiency by producing additional live steam to 

maintain output power. This extra steam is proportionally spread over the steam 

cycle so no new induced malfunctions (in pre-heaters or pumps) arise. The noninefficient 

turbine sections produce the power that the inefficient section cannot 

produce. 

HPT1 efficiency was varied to observe its effect on other plant components and 

additional consumption. We considered a production of 122 MW in extraction mode 

with a 5% decrease in isoentropic efficiency. The diagnosis was also developed at a 

similar degree of inefficiency for 60 MW (parallel mode), 90 MW (extraction mode) 

and 140 MW (condensing mode). 

Tables A1.17-A1.24 show, step by step, the methodology applied in the previous 

sections. Tables A1.17 and A1.18 are the F-P definition tables of the design and 

inefficient situation, tables A1.19 and A1.20 are the 〈KP〉 matrices. The ∆ 〈KP〉 

matrix and the irreversibility matrix are depicted in tables A1.21 and A1.22, and the 

[DF] matrix and the malfunction matrix are shown in tables A1.23 and A1.24. 

Figures A1.11 and A1.12 show the impact on fuel and irreversibility increase 

analysis of the inefficiency. 

An inefficiency in an component producing an important part of the final product 

should have important consequences. Other components have to readapt the turbine 

section to maintain electricity production and improve their efficiency (turbine 

sections) or consume more resources (boiler). A inefficiency diagnosis will explain 

these ideas. 


TABLE A1.17 F-P values without any inefficiency. MCR case. 



TABLE A1.18 F-P values when the HPT1 decreases 5% its efficiency (MCR case). 






TABLE A1.20 KP matrix when the inefficiency in HPT1 is 5% in its efficiency. 



TABLE A1.21 Variation of the KP with the inefficiency in HPT1 (MCR case). 



TABLE A1.22 Irreversibility matrix with the inefficiency in HPT1 (MCR case). 



TABLE A1.23 Dysfunction/malfunction table when the efficiency of the HPT1 is decreased 5%. 



TABLE A1.24 Malfunction matrix when the efficiency of the HPT1 is varied 1%. 



FIGURE A1.11 Impact on fuel analysis when the HPT1efficiency is 5% less than the expected. 



FIGURE A1.12 Irreversibility analysis with the inefficiency in HPT1.


The malfunctions of this inefficiency will be analyzed using table A1.23. The 

components with a malfunction that surpasses a non-negligible quantity are the 

inefficient component (HPT1), the boiler and the MSF unit. First we will explain the 

inefficient component. If the isoentropic efficiency of a turbine section decreases, 

the expansion line is moved away from the reversible process. The irreversibility in 

the section increases by 1,667 kW. Since the turbine exhaust has a higher enthalpy 

(see the h-s diagram), the output power strongly decreases with respect to the design 

situation (2,220 kW). This means that unit exergy consumption increases and the 

product decreases. The ∆ 〈KP〉 component of HPT1 was ∆k = 0.039 (see table 

A1.21). The intrinsic malfunction was 1,948 kW, and the impact on fuel due to the 

inefficiency was 2,825 kW. Since the total impact on fuel in the plant was 3,732 kW, 

this parameter could be considered local to the system. 

However, the malfunction associated with the MSF unit is negative 

(MF = --280 kW), if we assume that the water produced and the condensate returned 

to the deaerator are constant. The is because the end point of the expansion line is 

located in HPT. Steam leaving HPT has a higher enthalpy but also a higher entropy. 

The energy needed by the MSF unit also increases, decreasing efficiency. The 

generated negentropy in the MSF unit is considered a secondary product of the 

component and is beneficial (see section 7.3.2.1), so the final variation of the unit 

exergy consumption is negative (∆k = –0.041). 

The malfunction associated with the boiler is also negative. As its product exergy 

flow is huge, the induced malfunction is –242 kW, although its unit exergy 

consumption did not change very much (∆k = –0.0011, see table A1.21). The reason 

is the increased feedwater temperature entering the boiler due to the additional 

steam required by the steam power plant to maintain the electricity production in the 

inefficient situation. The additional fuel consumed is not used for the same 

temperature rise in the boiler with respect to the design conditions. The impact on 

fuel associated with the boiler is –175 kW, but the irreversibility in the component 

increases 3,341 kW. The last assumption is a consequence of the dysfunction 

analysis explained below. 

The dysfunction analysis is quite similar to when other components suffer 

inefficiencies. Once again, the two components suffering from the dysfunctions 

generated by the components with an inefficiency are the boiler and the condenser. 

In both components the highest dysfunction is provoked by the inefficient 

component (2,616 kW for the boiler and –1,795 kW for the condenser), that is, the 

component with the intrinsic and greatest malfunction. The sum of the dysfunctions 

generated by the other components is the irreversibility increase associated with 

each component. For example, the total dysfunction generated in the boiler is 

3,583 kW and its production is increased by 1,790 kW to maintain the final 

production of the power plant. 



Figure A1.13 shows the linearity of the model when the isoentropic efficiency is 

varied from –5 to +5 %, in extraction mode under MCR (122 MW), in this figure the 

total impact on fuel associated to this inefficiency is analyzed. 

FIGURE A1.13 Model linearity with respect to an inefficiency in HPT1. 


4000 

kW 

3000 

2000 

1000 

-5 -4 -3 -2 -1 0 1 2 3 4 5 

-1000 

-2000 

-3000 

-4000 

0 

% eff. in HPT1 

The model behaved more of less linearly to variations of the inefficiency using the 

simulator. Thus, the malfunction matrix can be used to predict the impact on fuel. 

Since the inefficiency does not provoke any important induced malfunctions in other 

components, the malfunction matrix could also be used when several inefficiencies 

are occurring in different components. 

FIGURE A1.14 Cost of electricity depending on the degree of inefficiency applied to HPT1 (MCR case). 



0,0381 

$/kWh 

0,0380 

0,0379 

0,0378 

0,0377 

0,0376 

0,0375 

-5 -4 -3 -2 -1 0 1 2 3 4 5 

The cost of electricity and water as a function of the isoentropic efficiency of HPT1 

illustrates its effect (see figures A1.14 and A1.15). A 1% decrease in the isoentropic 

efficiency in HTP1 means an additional cost of 0.00004 $/kW·h (44,900 $/y) in 

electricity and 0.0005 $/m 3 in water (11,800 $/y). Clearly the inefficiency should be 


Effect of inefficiency in the first section of the low-pressure turbine (LPT1) 

corrected to avoid additional costs, because the first section is responsible for a high 

percentage of the total electricity produced in the steam power plant. 

FIGURE A1.15 Cost of water when the isoentropic efficiency is varied from –5% to 5% with respect to design 

efficiency (MCR case). 


Water cost 

1,275 

$/m3 

1,274 

1,273 

1,272 

1,271 

1,270 

1,269 

1,268 

-5 -4 -3 -2 -1 0 1 2 3 4 5 

The most important results derived from the analysis of this inefficiency include: 

• HPT1 is very important in terms of additional fuel consumption and cost of 

water and electricity (more than 55,000 $/y savings in the two products when the 

inefficiency is improved by only 1%). 

• The steam conditions exiting HPT1 also affect (to a lesser degree) some other 

components receiving that steam, i.e. the MSF unit. In any case, the inefficiency 

could be considered local to the turbine section. 

• The HPT1 inefficiency should be avoided, even if the turbine needs repair to 

prevent against inefficiencies or failures, since the savings would be quickly 

recovered. 

A1.4 Effect of inefficiency in the first section of the lowpressure 

turbine (LPT1) 

The low-pressure turbine has only two sections in the power plant configuration. 

Unless the plant is working at condensing mode, the amount of steam sent to this 

turbine is very low. Thus, an inefficiency in this section should have less effect than 

other inefficiencies in the turbine sections. The induced malfunctions should be 

detected in the second section of the low-pressure turbine. The degradation process 

could be accelerated if the last section of the low-pressure turbine has to work as a 

compressor when the amount of steam diverted to this section is so low that the 

steam cannot overcome the mechanical losses of the turbine. But this section also 



suffers from induced malfunctions form HPT (according to the definition of induced 

and intrinsic malfunctions by Royo (1994) for a steam turbine). The amount of 

steam to the MSF unit gives the pressure of the steam leaving the high-pressure 

turbine. Some part of this steam is also introduced in the low-pressure turbine. 

Finally, the atmospheric conditions control the exhaust pressure of the turbine 

making the behavior of this section strongly dependent the ambient temperature. 

This inefficiency analysis was performed for the MCR case (122 MW power 

production with an extraction to the MSF unit of 89.68 kg/s). The physical effects of 

these inefficiencies were translated into malfunctions and additional fuel 

consumption. The isoentropic efficiency of this section was 15% lower than the 

design efficiency (about the 76%). 

Tables A1.25 and A1.26 show the F-P values of the simulation corresponding to the 

design and inefficient cases. If we apply the analysis for other operating modes 

(condensing or parallel mode, or 140 and 60 MW of output power, respectively), the 

productive structure changes (see section 7.1), and the F-P definitions and the rest of 

matrices are different than in these examples. Tables A1.27 and A1.28 include the 

〈KP〉 matrices dividing the fuels and products of each component. Table A1.29 is the 

∆ 〈KP〉 matrix composed by the subtraction of the two last matrices, and table A1.30 

is the irreversibility matrix |I〉. Finally, table A1.31 is the dysfunction/malfunction 

table, and table A1.32 is the malfunction matrix associated with the inefficiency in 

LPT1. Figures A1.16 and A1.17 include the impact on fuel and the increase of 

irreversibility. 

An inefficiency in LPT1 is less important than in HPT1 in a co-generation plant. The 

HPT does not detect an inefficiency. The conditions of the steam downstream the 

inefficient component do vary but the exhaust pressure is controlled by the external 

temperature and does not vary, although the exhausted vapor to the condenser can 

vary its humidity. Some other turbine sections have to readapt their production to 

produce the electricity required, as their efficiencies do not vary when some amount 

of extra live steam is demanded to the boiler. 

In the malfunction array of this inefficiency, the inefficient component (LPT1) and 

the first section of the high-pressure turbine have a higher malfunction than the 

minimum accuracy of the simulator. The physical interpretation of these 

malfunctions will be connected. The irreversibility of the steam expansion increases 

in the inefficient component of LTP1 (∆I = 2,062 kW, see table A1.31), when the 

isoentropic efficiency decreases. The electricity production of the component 

reduces by 1,230 kW, and its variation of unit exergy consumption is ∆k = 0.522 

(see table A1.29). The last assumptions result in an intrinsic malfunction (that is, the 

malfunction created in the inefficient component of a system) of 3,408 kW. The total 

malfunction associated with the whole plant is 3,260 kW. Clearly this inefficiency 

does not provoke any induced malfunctions in the rest of the plant components. 


TABLE A1.25 F-P values in design (MCR case). 



TABLE A1.26 F-P values with the inefficiency in LPT1, MCR case. 



TABLE A1.27 KP matrix in design, MCR case. 



TABLE A1.28 KP matrix when the efficiency in the LPT1 is decreased 15%, MCR case. 



TABLE A1.29 Variation of the KP matrix with an inefficiency in LPT1, MCR case. 



TABLE A1.30 Irreversibility matrix with the efficiency of the LPT1 decreased 15%, MCR case. 



TABLE A1.31 Dysfunction/malfunction table for an inefficiency in the LPT1 (15%), MCR case. 



TABLE A1.32 Malfunction matrix when the efficiency of the LPT1 is varied 1%, MCR case. 



FIGURE A1.16 Impact on fuel analysis, section A1.4. 


FIGURE A1.17 Irreversibility analysis in section A1.4. 



HPT1 has a negative malfunction of 215 kW and ∆k = –0.004 (see table A1.29). 

This negative value is explained in the mathematical model of the steam turbine. The 

amount of steam entering the Curtis blade is higher than expected and the section 

operates more efficiently when the steam leaving this section is slightly increased. 

The total impact on fuel associated with this effect was –281 kW. 

The dysfunction analysis applied to this inefficiency is very illustrative. Only the 

boiler and condenser suffer dysfunctions generated by the components with 

malfunctions: HPT1 and LTP1. In both cases these components have to readapt 

production by 1,470 and 2,430 kW respectively, to maintain the additional 

production required by the first section of the low-pressure turbine. Since these two 

components redistribute their products over the rest of the components, their φ ij 

coefficients are not zero. If there is a ∆k ij coefficient whose value is not zero, the 

dysfunction generated by the last component in the first two components is 

significant. The rest of components do not have any important dysfunction worth 

mentioning in our analysis. 

Figure A1.18 shows the effect of varying the efficiency in this turbine section around 

the design point. The efficiency was varied from –15 to +15% with respect to this 

point. Since the model was linear with respect to the inefficiency, the malfunction 

matrix (table A1.32) can be used to quantify the additional fuel consumption by 

multiplying this matrix by the product and the unit exergy cost of every component. 

With this inefficiency there were no induced malfunctions (isolated component), 

making the malfunction matrix an exact guide to predict the increment on fuel 

consumption. 

FIGURE A1.18 Effect on the fuel consumption when the degree of inefficiency in the LPT1 is varied from the 

design point (MCR case). 


4000 

2000 

-2000 

-4000 

0 

% eff. in LPT1 

-15 -12 -9 -6 -3 0 3 6 9 12 15 

The monetary cost (including the capital cost and device maintenance) of water and 

electricity is one of the consequences of the diagnosis of the plant with respect to an 

component inefficiency. Figures A1.19 and A1.20 show how the cost in electricity 


kW


increases 0.000015 $/kWh and the water increases 0.00006 $/m 3 when the LTP1 

isoentropic efficiency decreases by 1%. In a year, at 122 MW and 2,400 T/h, 

15,000 $ and 1,280 $ are saved in electricity and water costs. 

FIGURE A1.19 Cost of electricity for inefficiencies in LPT1 (MCR case). 


0,0381 

$/kWh 

0,0379 

0,0377 

0,0375 

-15 -12 -9 -6 -3 0 3 6 9 12 15 

FIGURE A1.20 Water cost per cubic meter for inefficiencies in LPT1. 122 MW in extraction mode (MCR case). 


Water cost 

1,2730 

$/m3 

1,2725 

1,2720 

1,2715 

1,2710 

1,2705 

This section demonstrated that: 


-15 -12 -9 -6 -3 0 3 6 9 12 15 

• The behavior of LPT1 is linear when its efficiency is varied within allowable 

limits. It does not induce any significant malfunctions in other plant components, 

following the trend in other examples. 

• As predicted in the first paragraph of this section, the cost of water and 

electricity were not affected as much as by inefficiencies in HPT (only 16,300 $/ 

y are saved in both products if the isoentropic efficiency is improved 1%). 

Therefore, the effect of an inefficiency in the turbine is proportional to the 

amount of steam entering the turbine section. 



• The most dangerous problem associated with inefficiencies in LPT is the steam 

quality when the efficiency is increased. Low quality steam can damage the 

wheels of the condensing turbine. The variational analysis can also be broken 

when the inefficiency provokes a non-linear system response. 

A1.5 Effect of the cleaning ball system in the recovery 

section 

The recovery section is the most important component of the MSF unit. Therefore, 

the cleaning ball system inside the distiller tubes could provoke several malfunctions 

in other plant components. In this section we analyze the fouling reduction effect. 

The benefits of reducing fouling in the reject section can be translated into the 

physical response of the MSF unit. First, an analysis was done keeping the control 

parameters constant (SR, R, F). If the fouling is decreased in the recovery section, 

heat transfer inside the tubes is increased and the inter-stage temperature difference 

between the vapor and cooling brine decreases. This raises the temperature of 

cooling brine and decreases the flashing brine and released vapor. But the cooling 

brine goes to the brine heater since it is hotter than in design. Finally, the cooling 

brine flow enters the recovery section at a higher temperature than expected. In the 

final stages of the recovery section, both distillate and flashing temperatures are 

reduced by the effect of the fouling inside the recovery tubes. The flash range of the 

distillers is increased in the two limits and the distillate produced in the MSF unit is 

higher than in design. The control parameters of the MSF unit (seawater to reject 

SR, recycle brine R or make-up feed F) must be reduced if the distillate product is to 

be maintained (although the distillate temperature leaving the unit could be reduced) 

and, indirectly, the amount of steam consumed in the heater. The diagnosis 

mathematically explains the physical effects. 

Tables A1.33 and A1.34 show the F-P definition matrices following the productive 

structure in section 7.1. Then, the 〈KP〉 matrices from the last two matrices (tables 

A1.35 and A1.36) are shown. The ∆ 〈KP〉 matrix (table A1.37) is obtained by 

subtracting tables A1.35 and A1.36. The irreversibility matrix |I〉 (table A1.38) and 

the malfunction/dysfunction table is shown in table A1.39. The example analyzed 

produced 1.900 T/h with 32 ºC seawater (nominal-temperature operation of the MSF 

distillers in summer). Figures A1.21 and A1.22 show the impact on fuel analysis and 

the increase of the irreversibility in the MSF components. 


TABLE A1.33 F-P values in design, NTOS case. 

Effect of the cleaning ball system in the recovery section 


TABLE A1.34 F-P values with fouling in RCS=0, NTOS case. 



TABLE A1.35 KP matrix in design, NTOS case. 



TABLE A1.36 KP matrix with an inefficiency in RCS, NTOS case. 



FIGURE A1.21 Impact on fuel analysis in section A1.5. 


FIGURE A1.22 Irreversibility increase in section A1.5. 



In the malfunction analysis, only the inefficient component has an intrinsic 

malfunction of –1,570 kW. This low value can be explained physically. The fouling 

reduction inside the recovery tubes improves the heat transfer coefficient in those 

stages, reducing the thermal irreversibility (∆I = –2,132 kW, see table A1.39) and 

also the flows recirculating in the recovery section in order to maintain final 

production. This means that the variation of the unit exergy consumption is 

∆k = --0.194, see table A1.37. The impact on fuel associated with the inefficient 

component is –4,279 kW. 

The brine heater has an induced malfunction of –626 kW. The brine entering the 

heater has a higher temperature due to improved heat transmission in the recovery 

section, but the temperature entering the distiller is reduced by 0.3 ºC. The brine 

heater needs less steam to heat the cooling brine, considering that the recycle brine 

flow is also reduced to maintain distillate production. This means that the 

irreversibility generated in the heater is also reduced by ∆I = –1,131 kW, and 

therefore the variation of the unit exergy consumption (the ∆ 〈KP〉 coefficient is 

∆k = –0.0149, see table A1.37). 

The inefficiency in the recovery induces a –540 kW malfunction in the reject 

section. The distillate flow leaving the section depends on the temperature of the 

flashing brine and distillate entering the plant (both temperatures decrease 2.6 ºC) 

and the recycle brine to the distiller (which is reduced 263 T/h). The energy required 

to produce the distillate is lower than the design value and the irreversibility 

generated in this section (∆I = –554 kW, see table A1.39). The unit exergy 

consumption of the reject is reduced because the amount of resources to distillate 

the freshwater is lower (∆k = –0.079, see table A1.37). As the distillate is produced 

at a considerable exergy cost (see the last row of table A1.38 for the exergy cost of 

each component), 5,408 kW of fuel was saved with this induced malfunction. 

The component suffering the highest malfunction is the fictitious device (FD), 

included in the productive structure to quantify the flows sent to sea: blowdown and 

reject cooling seawater. The malfunction associated with this component (7,850 kW, 

see table A1.39) can only be explained by the thermoeconomic model. Its product 

(the fuel consumed in the MSF unit to produce freshwater, i.e. the steam coming 

from the steam power plant) is obviously decreased with the use of the cleaning ball 

system. The exergy flow of the steam to the MSF unit decreases 9,250 kW. The 

increase in unit exergy consumption is ∆k = 0.170 and the impact on fuel associated 

with this component is 13,249 kW. It is clearly not convenient to use non-physical 

components in the productive structure of the system because their associated 

malfunctions and dysfunctions are quite difficult to explain physically. 


TABLE A1.37 Variation of the KP matrix when the fouling in RCS is neglected. 



TABLE A1.38 Irreversibility matrix without fouling in RCS. 



TABLE A1.39 Dysfunction/malfunction table without fouling in RCS, NTOS case. 




The mixer is also a non-physical device in the last stage of the reject section. It 

models the mixing process between the make-up feed and the brine flashing in the 

last stage of the reject section. It has a negative induced malfunction of 765 kW due 

to the reduction of irreversibility generated (∆I = –735 kW, see table A1.39) in the 

mixing process (the two mixed flows are reduced in quantity and energy). The 

efficiency of the process is therefore improved, with a unit exergy consumption 

variation of ∆k = –0.013 (see table A1.37). The impact on fuel associated with the 

‘benefunction’ in the mixer is –996 kW. 

Now the dysfunction analysis will be introduced. Components suffering a important 

malfunction clearly induce a large dysfunction in the rest of components. For 

example, the main dysfunctions in the fictitious device are generated by itself 

(5,016 kW), the heater (–1,226 kW), the recovery section (–2,534 kW), the mixer 

(--212 kW) and the reject section (–3,022 kW). The value of the dysfunction is 

proportional to the malfunction in each component. The dysfunction in a component 

due to the junctions of the productive structure must be distributed to the 

components supplying the junction. The total dysfunctions generated by each 

component were 5,398 kW for the FD, –1,263 kW for the heater, –2,708 kW for the 

recovery section, –230 kW for the mixer and finally –4,867 kW for the reject 

section. The temperature profile change in the distillers provokes differences in the 

exergy of products leaving each component to readapt the final production of 

distilled water. 

The previous analysis kept the final product of the system constant (distillate water). 

As mentioned in previous sections, the simulator can maintain the mass flow rate in 

the distiller but it cannot maintain the exergy of this flow. As in this case, the 

temperature of distillate leaving the MSF unit is reduced by 1.3 ºC. The impact on 

fuel associated with the variation of the final product is an astonishing –4,337 kW! 

This value is similar to the total impact on fuel associated with the unit exergy 

consumption variation inside the MSF unit (–5,336 kW). 

The variational analysis of this inefficiency involves the linear behavior of the 

model, as in the figure A1.23, where the total impact on fuel saved (including the 

final product variation) with decreased fouling is depicted from the design value to 

total absence. In this section we analyzed nominal production (1,900 T/h) with 32 ºC 

seawater and the typical exergy costs of electricity and steam obtained in the power 

plant analysis. 

The inefficiency diagnosis can also be quantified in monetary terms. The cost of 

water depending on fouling helps plant managers develop a maintenance plan to 

operate under the best conditions. In this case (see figure A1.24) the cost of a cubic 

meter of water decreased 0.0069 $ when the fouling in this section decreased 

0.00001 m 2 ·K/W. This value is very high (115,000 $ a year) and implies that the 

cleaning ball system should always operate in the recovery section. 



FIGURE A1.23 Effect on fuel consumption when the fouling in recovery section is gradually decreased. 1,900 T/ 

h and 32º C seawater. 

0 

fouling*10-5 in RC 

0 3 6 9 12 15 

-4000 

-8000 

-12000 

-16000 

-20000 

-24000 


FIGURE A1.24 Cost of a cubic meter of water depending on the fouling in the recovery section. 

1,48 

1,45 

1,42 

1,39 

1,36 

$/m3 

kW 

Water cost 

fouling*10-5 in RC 

0 3 6 9 12 15 

The malfunction matrix (table A1.40) of the MSF unit with this inefficiency is a 

good tool to calculate the effect on natural gas. The malfunction matrix can be used 

because the model is linear with respect to the fouling in recovery. But the induced 

malfunctions produced by this inefficiency imply that the malfunction matrix can 

only be used for individual malfunctions. 


TABLE A1.40 Malfunction matrix when the fouling in RCS is varied 0.00001 m 2 K/W. 



Effect of reject section fouling 

Summarizing the results: 

• The change of the temperature profile by the fouling in the main flows of the 

MSF plant is responsible for the induced malfunctions in the distillers. Thus, 

each malfunction should be dealt individually. The values of the induced 

malfunctions surpass the intrinsic malfunction because the flows leaving and 

entering the recovery section also pass through the reject or brine heater. The 

dysfunctions generated in the different components are also very important. 

• The increased heat transfer increases the production rate per stage in the distiller. 

This reduces the amount of resources to produce the same distillate. Since the 

cleaning ball system obviously saves fuel (115,000 $/y), it should operate 

continuously. 

• A large part of fuel saved with this inefficiency is due to the lower temperature 

of the distillate leaving the plant. But, in fact, the distillate temperature is now 

irrelevant (unless this energy is used by another process). So, this effect should 

not be considered during the analysis, although that temperature has a direct 

relationship with the other distiller temperatures. 

A1.6 Effect of reject section fouling 

Usually the cleaning ball system is not installed in the reject section since its 

seawater operating temperatures do not produce any scaling problems. But the 

biological activity of seawater intake can lead to dangerous bio-fouling in this 

section. The effect of installing a cleaning ball system here is similar to the recovery 

section. It reduces the interstage difference because the distillate temperature 

decreases and the cooling brine is heated to a higher temperature. Since the seawater 

temperature is imposed by the environment, the distillate temperature is forced to 

decrease when the heat transfer coefficient of each stage is increased, because the 

fouling inside the tubes is neglected. In this case, the flash range of the plant ∆T is 

higher because the lower limit of this range is decreased. A higher flash range 

implies a higher distillation per stage. If the control parameters of the plant are 

maintained, it can only produce additional freshwater with the help of the cleaning 

ball system. A lower recycle (R), seawater to reject (SR) and make-up feed (F) flow 

are needed to maintain the distillate production. 

As the brine heater is so far from the reject section, the temperature profiles of the 

cooling brine entering and leaving the heater do not vary considerably. The 

performance indexes or steam consumption of the plant are not expected to greatly 

improve. 

This system should not be used for several reasons based on thermoeconomic 

criteria. The example is the same as in previous sections: a water production of 



1.900 T/h with 32 ºC seawater and a fouling factor reduced to zero. Tables A1.41 

and A1.42 show the F-P definition applied to the design and inefficient case, tables 

A1.43 and A1.44 are the ∆ 〈KP〉 matrix made by using the previous tables, table 

A1.45 is the ∆ 〈KP〉 matrix and table A1.46 is the irreversibility matrix I containing 

the dysfunction coefficients and the exergy cost array. The dysfunction/malfunction 

matrix [DF]/MF is the table that resumes the final results of the thermoeconomic 

diagnosis applied to this inefficiency (table A1.47). The impact on fuel and the 

increase of irreversibility per component are shown in figures A1.25 and A1.26 

respectively. 

Although the reject section has three stages, the effect of fouling should be identical 

to the effect observed in the recovery section (17 stages). In this case, the 

temperature of cooling brine entering the distiller is given by the ambient 

conditions. The flashing and distillate temperatures would try to reach the cooling 

temperature flowing inside the tubes if the heat transfer were an ideal process. The 

symbolic formulation of thermoeconomics will give us the effects provoked by this 

inefficiency in the MSF unit. 

The most significant malfunctions are yet again located in the fictitious device, 

heater, recovery and reject sections and the mixer. The inefficient component 

analysis considers the cleaning ball system installed in the reject section. 

Suprisingly, the associated malfunction with no fouling in the reject is positive 

(49 kW). The ∆ 〈KP〉 component corresponding to its exergy unit consumption is 

∆k = 0.007 (see table A1.45). But this result is provoked by the assumptions adopted 

in the thermoeconomic model of the reject section. The part of the unit exergy 

consumption corresponding to the efficiency of the process (or the heat transfer 

improvement) is logically lower than the design situation (∆k 1 = –0.024). But the 

steam and brine needed for maintaining the vacuum inside the chambers is more or 

less independent from the distillate produced (i.e. is a constant value). As the 

product of the reject section decreases (the distillate temperature leaves the section 

at a lower temperature), the unit exergy consumption due to the vacuum system is 

∆k 2 = 0.031. Clearly the general services of the MSF unit are not affected by an 

intrinsic inefficiency but they have to consider product variation in order to account 

for its contribution to the final cost of water. 

The brine heater is located on the other side of the MSF plant. The effect of the 

inefficiency in the reject section also affects this component because the recycled 

brine heated in the brine heater comes from the reject section. The recycle brine 

flowing in the recovery section is reduced by 195 T/h and the cooling brine heating 

is reduced by 227 kW. The temperature difference in the first stage of the recovery 

section is improved by 0.1 ºC. So, heater efficiency decreases and the variation of 

the unit exergy consumption is positive (∆k = 0.0044, see table A1.45). The 

malfunction is MF = 185 kW and an irreversibility increase in the heater of 

∆I = 468 kW (see table A1.47). 


TABLE A1.41 F-P values in design, NTOS case. 



TABLE A1.42 F-P values when the fouling in RJS=0, NTOS case. 



TABLE A1.43 KP matrix in design, NTOS case. 



TABLE A1.44 KP matrix with the inefficiency in RJS, NTOS case. 



TABLE A1.45 Variation of the KP matrix when the inefficiency in RJS is detected. 



TABLE A1.46 Irreversibility matrix corresponding to reject fouling in RJS, NTOS case. 



TABLE A1.47 Dysfunction/malfunction table when the fouling in RJS=0. 



FIGURE A1.25 Impact on fuel analysis, section A1.6. 



FIGURE A1.26 Increase of irreversibility in section A1.6.


As seen for the brine heater, the cleaning ball system in the reject section induces an 

unexpected 1,800 kW positive malfunction in the recovery section. This result will 

be described analytically. The temperature of water leaving the distiller is reduced 

by 1.7 ºC (remember that the cleaning ball system in the reject decreases the 

distillate profile in the reject section and, therefore, in the last section of the recovery 

distiller). In general, since the heat transfer coefficient is higher at high 

temperatures, the thermal irreversibility increases in the recovery section 

(∆I = 2,079 kW, see table A1.47). As the product of the section decreases, the 

variation of the unit exergy consumption is positive (∆k = 0.223, see table A1.45). 

The impact on fuel associated with this induced malfunction is 4,248 kW. 

The malfunction associated with the fictitious device is –788 kW. Two fuels enter 

this component in the productive structure of the MSF unit, one is the exergy of the 

blowdown leaving the recovery section. This exergy is reduced because the 

temperature of the flashing brine decreases 1.8 ºC when leaving the reject section. 

So, the unit exergy consumption of the component is lower than in design 

(∆k = --0.017, see table A1.47). As demonstrated, a lower temperature of the 

blowdown rejected to the sea at least implies a lower cost in the water production. 

Finally, the mixer has an induced malfunction of 1,208 kW, with a very clear 

physical explanation. The temperatures of the make-up and flashing brine to 

blowdown are similar in the reference case but these temperatures are separated with 

the cleaning ball system in the reject section. The irreversibility generated in the 

mixing process is higher although those two flows are reduced to maintain the final 

production in the MSF plant (∆I = 1,191 kW, see table A1.47). The variation of the 

unit exergy consumption in the idealized component was ∆k = 0.0204 (see table 

A1.45). The additional fuel necessary for this component provoked by the cleaning 

ball system in RJS was 1,868 kW. 

In the dysfunction analysis, only the fictitious device had an important dysfunction 

generated by the inefficient components (total dysfunction was 3,283 kW). This 

component reduces its product by only 64 kW, however the final reduction in the 

distillate exergy flow is 482 kW. 

Although the plant diagnosis suggests that the MSF unit is working at a poorer 

efficiency (the impact on fuel associated with the unit exergy consumption variation 

was 6,394 kW), this analysis considered a constant total production. The 

temperature of the distillate leaving the MSF unit is 1.8 ºC lower than expected in 

design. This means that total production is not constant and the last term in equation 

(6.41) cannot be neglected. The impact on fuel associated with this variation is 

calculated by multiplying the total product variation by the exergy unit cost of the 

product. In this case 6,768 kW of fuel were saved (in the case of the power plant, the 

term of the product variation can usually be neglected because it is normally less 

than 20 kW). The total amount of fuel saved with this inefficiency is 374 kW, by 



combining the two effects. Therefore, the cleaning ball system also benefits the MSF 

unit, as well as the heater and recovery section. 

Figure A1.26 shows the effect of fouling in the reject section when we gradually 

decrease to zero the design value (0.000018 m 2 K/W). If the thermoeconomic model 

is linear with respect the variational analysis of the fouling, the malfunction matrix 

could be used to predict the impact on fuel associated with the desired variation of 

the fouling of this component (if known). 

If the model responds linearly, the total cost of water (includes capital and 

maintenance costs) must also increase linearly depending on the degree of 

inefficiency (see figure A1.27). Each cubic meter of water increases 0.00012 $ when 

the fouling factor in the reject distiller increases 0.00001 m 2 K/W. Yearly freshwater 

production would involve an additional cost of 2,000 $ with this small variation in 

reject fouling. 

FIGURE A1.27 Effect on fuel consumption when the fouling in reject is varied. Nominal-temperature operation in 

summer (NTOS, i.e., 1,900 T/h and 32 ºC seawater temperature). 

-100 

-200 

-300 

-400 

-500 

fouling*10-5 in RJ 

0 

kW 

0 3 6 9 12 15 18 


The linearity of the model with respect to fouling variation is shown in figure A1.28. 

The malfunction matrix (table A1.48) can be used to predict the impact on fuel 

consumed with the inefficiency. But the induced malfunctions provoked by 

temperature variation in the rest of components implies that the analysis for several 

inefficiencies has different results than the individual analysis of those inefficiencies. 

So, the malfunction matrix can only be used to predict specific inefficiencies. 

Important errors may arise if it is used for several inefficiencies. 

The most important results derived from the analysis of the fouling in recovery 

section are : 

• Fouling increases the flash range of the plant and, therefore, the distillate 

production if the same control parameters of the plant are maintained. Input 

conditions must be relaxed to maintain the final production of freshwater. 


Summary 

FIGURE A1.28 Variation of the water cost when fouling in the reject section is decreased from the design value 

to zero. 

1,474 

1,473 

1,472 

1,471 

$/m3 

• The inefficiency negatively affects the rest of the MSF components (see the 

malfunctions induced in other components in table A1.47). Furthermore, the 

benefit is due to the lower temperature of the freshwater produced, although the 

plant is not working more efficiently (the impact on fuel associated with the unit 

exergy consumption variation is positive). The cost of water is not reduced very 

much with the cleaning ball system. 

• The cleaning ball system is not recommended for the reject section. It is very 

difficult to install there (it is an open circuit in which some of the cooling brine is 

rejected to the sea), and the low temperatures do not provoke serious scaling 

problems in this section. Feed chlorination is a simpler solution to avoid possible 

biological fouling (which depends on seawater intake conditions). 

A1.7 Summary 

Water cost 

fouling*10-5 in RJ 

0 3 6 9 12 15 18 

Thermoeconomic diagnosis of the dual-purpose plant for the inefficiencies in 

section 7.3 was completed in this annex for the most representative load in the 

power and desalination plant. The symbolic formulation of the Structural Theory of 

Thermoeconomics provides a lot of information and explains the physical 

consequences expected with the inefficiency. 

Inefficiencies studied in steam power plant are local to the components suffering the 

inefficiency, but in the desalination plant the main units of the system are connected 

by the cooling brine, flashing brine and distillate, where any inefficiency is easily 

distributed over the rest of the plant components. 


TABLE A1.48 Malfunction matrix when the fouling in RJS is varied 0.00001 m 2 K/W. 



ANNEX 2 

Thermodynamic properties 

of seawater 

Below are the models and correlations of the thermodynamic properties needed to 

simulate the MSF desalination plant, except for the properties previously described 

by the auxiliary equations (Chapter 3). 

A2.1 Specific enthalpy h of superheated or saturated vapor 

We used equations from Badr, Probert and O’Callaghan (1990), from formulations 

by Keenan and Keyes (1955, 1969) and conveniently expressed for computer 

calculation (Schnakel, 1958). The temperature and pressure range was valid below 

the critical point. 

Units: International System 

where 

p 

h F 101.31558 F0 --------------------- 

101325.0 

B0 ----- ⎛ p 

------------------------- ⎞ 

2 ⎝101325.0T⎠ 2 

⎧ 

= + 

⎨ + 

⎩ 

⎛ p ⎞ ⎫ 

– B6 + B0⎜B2– B3 + B0 B7 ------------------------- ⎟ ⎬ 

⎝ 101325.0T ⎠ ⎭ 

B0 p 

B B01 101325T 2 

----------------------- B2 – B ⎛ 

B0 p 

3 --------------------- ⎞ 

⎝101325T⎠ 2 

⎧ ⎫ 

⎪ ⎪ 

– 

⎨ + 

+ ( B4– B5) ⎬ 

⎪ ⎪ 

⎩ ⎭ 


2

410 

Thermodynamic properties of seawater 

B0 

= 1.89 – B1 

B2 

= 82.546 

B4 

= 0.21828 T 

B6 

= B0 

B3 

– 2 F0 

(B2 

– B3) 

B7 

= 2 F0 

(B4 

– B5) 

– B0 

B5 

2 

F = 1804036.3 + 1472.265 T + 0.37789824 T + 47845.137 ln T. 

A2.2 Specific entropy of superheated or saturated vapor 

Term ß was added to those in section A2.1. The specific entropy s of superheated 

vapor was: 

where 

B 1 

B 3 

B 5 

= 

= 

= 

s = 1472.626 ln T – 461.4874 ln p + 0.7557174 T + 3830.4065 

– 

2641.62 80870 ⁄ T2 

------------------ 10 

T 

162470 

----------------- 

T 

126970 

----------------- 

T 

372420 

F0 = 1.89 – B ⎛ 

1 ----------------- + 2⎞ 

⎝ ⎠ 

β 

= 

T 2 

47845.076 

------------------------ – 101.31344 β 

T 

1 

p 

-- ( B0 – F0) ----------------- 

T 

101325 

B ⎧ 

0 

⎨ 

+ ----- 

⎩ 

2 

⎫ 

B0 ( B4 – B5) – 2B7 ⎬ 

⎭ 

⎛ p 

--------------------- ⎞ 

⎝101325T⎠ 2 1 

B6 -- ⎛ 

B0 p 

--------------------- ⎞ 

2 ⎝101325T⎠ 2 

⎛ + 

⎞ 

⎝ ⎠ 


Specific volume of superheated or saturated vapor 

A2.3 Specific volume of superheated or saturated vapor 

Using B from section A2.1, the specific volume v of pure water was: 

A2.4 Latent heat vaporization of water as a function of 

boiling temperature 

Below the atmospheric boiling point (373.15 K), latent heat of vaporization 

(SI units): 

where h was solved in section A2.1 and ps 

in section 3.3.6. 


λs 

was 

The Fish & Lielmezs correlation (Reid, Prausnitz and Sherwood, 1977) was used in 

the range 373.15 < T < 450 K: 

where 

⎛ T ⎞ 

−3 

461539. 453 

v = 1. 00035⋅ 10 ⎜ 

+ B⎟ 

⎝ p ⎠ 

λ s s 

= ( ) 

( ) 

h T, p ( T) −4. 186 T−273. 

15 

ℵ + ℵ0.35298 

λs 6051.1583 

1 ℵ 0.13856 

⎛ ⎞ 

= ⎜------------------------------ ⎟ T 

⎝ + ⎠ 

647.3 T 

ℵ 1.3615467 – 

= ⎛---------------------- ⎞ 

⎝ T ⎠ 

The Carruth & Kobayashi correlation (Reid et al., 1977) was used for 

450 < T < 647.3 K: 

λ s 

2115173.3 ⎛ T 

1 – ------------ ⎞ 

⎝ 647.3⎠ 

0.354 

1125343.9 ⎛ T 

1 – ------------ ⎞ 

⎝ 647.3⎠ 

0.456 

= 

+ 

411

412 


A2.5 Seawater exergy 

A2.5.1 Theory 

Mass flow and five parameter measurements characterize the different stages of 

seawater: pressure, temperature, altitude, velocity and composition (Zaleta, Ranz 

and Valero, 1998). The exergy method associates each parameter with its exergetic 

component: mechanical, thermal, potential, kinetic and chemical, respectively. 

These components help to quantify some quality and quantity aspects of seawater. 

The information provided by the exergy method also clarifies concepts related to the 

seawater availability. 

Ambient reference 

The first step in developing the analytic exergy methodology is to establish the 

ambient reference (AR) for seawater comparison. The AR must be relatively 

abundant with respect to the rest of the systems or subsystems. The thermodynamic 

equilibrium conditions of AR must resemble a closed system; therefore, the system 

brought to AR conditions will undergo a series of physical-chemical changes. 

Authors sometimes call this the ‘dead state’, because it is a zero exergy state 

(although its energy is different than zero). 

AR may be chosen in different ways to establish thermodynamic equilibrium. 

Ahrendts (1980) proposes an approximation of the “dead” ambient of Earth if it 

were thermodynamically isolated from the rest of the universe. When we impose 

restrictions on the method (excluding HNO 3 formation and its products), the 

resulting AR composition is very similar to the real physical ambient. Liquid AR is 

mainly seawater with more than 99% of the system's total mass. On the other hand, 

Szargut (1980) proposes an AR that is more similar to the real physical ambient in 

nature and independent of the process or system under consideration. This is more 

convenient to exegetically analyze systems classified as natural resources. 

We used the AR proposed by Szargut to analyze seawater. The AR in the liquid 

phase corresponded to seawater composition at main ambient temperature and sea 

level atmospheric pressure. The seawater composition for the AR proposed by 

Szargut (1989) is shown in the next table. 


Seawater exergy 

TABLE A2.1 Liquid phase composition of Reference Ambient (Szargut, 1989; Morris, and Szargut, 1986). 

Chemical element Molality (mol/kg) 

Ag (s) 2.7 × 10 –9 

As (s) 2.1 × 10 –8 

Au (s) 5.8 × 10 –11 

B (s) 3.4 × 10 –4 

Ba (s) 1.4 × 10 –7 

Bi (s) 1.0 × 10 –10 

Br 2 (l) 8.7 × 10 –4 

Ca (s) 9.6 × 10 –3 

Cd (s) 6.9 × 10 –11 

Cl2 (g) 0.5657 

Co (s) 6.8 × 10 –9 

Cs (s) 2.3 × 10 –9 

Cu (s) 7.3 × 10 –10 

F 2 (g) 3.87 × 10 –5 

Hg (l) 3.4 × 10 –10 

I 2 (s) 5.2 × 10 –7 

K (s) 1.04 × 10 –2 

Li (s) 2.5 × 10 –5 

Mg (s) 4.96 × 10 –2 

Mn (s) 7.5 × 10 –9 

Mo (s) 1.1 × 10 –7 

Na (s) 0.474 

Ni (s) 1.2 × 10 –7 

P (s) 4.9 × 10 –7 

Pb (s) 4.2 × 10 –11 

Rb (s) 1.42 × 10 –6 

S (s) 1.17 × 10 –2 

Se (s) 1.2 × 10 –9 

Sr (s) 8.7 × 10 –5 

W (s) 5.6 × 10 –10 

Zn (s) 1.7 × 10 –8 



Seawater availability: exergy function 

The availability of a renewable resource can be understood as ‘how accessible is it’. 

In order to be used, a resource must be changed chemically and physically to the 

required conditions (e.g., for human consumption, water must be extracted from a 

river or sea, be purified and sent to end users). 

The analogy between the availability of a natural resource and exergy helps relate 

each resource parameter with its exergy components. As the exergy method is 

conditioned by a Stable Reference Environment (SRE) —dead state conditions— 

the SRE proposed by Szargut (1980) is the most convenient (the most similar to the 

real physical environment of Earth). 

In the case of seawater, the exergy method is useful to quantify the ‘availability’ of a 

sea, with respect to the defined SRE. By applying the exergy model (Gaggioli, 1980) 

in terms of temperature, pressure, height, velocity and composition, and assuming 

seawater is an incompressible liquid and dilute substance, the specific exergy can be 

used in terms of its components for each seawater property (thermal, mechanical, 

chemical, kinetic and potential components, respectively): 

bar , CPH2O Ta Tr Tr Ln Ta = 

– ----- 

Tr + 

∑ 

i 

xir , 

– vH2OPaP + ( – r) 

( µ ia , – µ ir , ) 1 2 2 

-- ( ca – cr ) + g( za– zr) 2 


(A2.1) 

According to equation (A2.1), the thermal exergy component depends on the heat 

capacity of the aqueous solution and its absolute temperature T a. The mechanical 

exergy component is calculated from the specific volume of the solution (seawater) 

and the pressure difference between the sea and the SRE. The specific heating value 

CP H2 O and the specific volume v H2O of the solution can be calculated without 

serious error if it is considered pure water (Perry and Chilton, 1984). We used the 

correlations described in Chapter 4. The potential exergy component requires the 

altitude z above sea level (almost negligible in a MSF plant). It is used to calculate 

the maximum mechanical work obtained from a waterfall, such as a hydroelectric 

station. The kinetic exergy component is of relatively little exergetic importance in 

comparison with other exergetic components (taking into account the low velocity c a 

of brine inside the tubes or in the flash chambers). Its mean velocity must be 

calculated, which depends on flow and operation conditions. The chemical exergy 

component is the most complex to calculate. It may be broken down into the 

following components: (i) the chemical exergy of the water, (ii) the chemical exergy 

of the dissolved inorganic substances, (iii) the chemical exergy of the organic 

substances.


i) The chemical exergy of pure water in the sea. This component provides information 

about the thermodynamic degradation process; pure water availability under 

different conditions such as pollution (the presence of substances other than pure 

water like salts, organic material, etc.). The magnitude of the exergetic component 

µ can be calculated from its activity as a pure substance in a solution equation 

(equation A2.2): 

, xH2O µ H2O µ ( – H2Or , ) xH2O RTr Ln 

⎛ ⎞ 

= = 

⎜-------------- ⎟ 

⎝aH2O, r⎠ 

b qH2O 

(A2.2) 

where x H2O is the molar fraction of pure water in seawater, and a H2O, a H2O,r can 

be estimated from measuring coligative properties, such as osmotic pressure, π. 

In the case of seawater, the osmotic pressure of a diluted solution with respect to 

its pure solvent is typically calculated using equation A2.3, 

π H2O 

= – -------- Ln ( a and (A2.3) 

v H2O) 

π H2O, r = – -------- Ln ( a 

v H2O, r) 

where π is obtained by measuring the Electrical Conductivity (EC) of seawater 

and considering that the osmotic pressure is a function of the salt concentration 

(binary) in solution (without any serious errors, as in the case of a very diluted 

substance, such as seawater). 

π H2 O 

= 0.36 EC (A2.4) 

where π is the osmotic pressure (atmospheres) and EC the electrical conductivity 

in dS/m (1 dS/m = 640 ppm, Medina (2000)) of ionized electrolytic components 

in a solution. 

ii) The chemical exergy of the dissolved inorganic substance is determined by the 

well-known procedure for an electrolytic solution (equation A2.5): 

b qi 

(A2.5) 

where the activity for each chemical substance i in the sea and in the SRE can be 

expressed in terms of the activity coefficient, γ, and its molality, m: 

a i = γ i m i 

RT r 

, = xi ( µ i – µ ir , ) = 

xi RTr Ln ⎛------- ⎞ 

⎝ ⎠ 

RT r 

a H2O 

(A2.6) 

The activity coefficient, γ, of each of the electrolytic species is determined using 

the equation obtained by Debye-Hückel (equation A2.7). 


a i 

air ,


Log( γ i) 


(A2.7) 

where A, B are constants depending on the solvent and temperature, z i is the ionic 

charge, d i is the ionic diameter of specie i and I is the ionic dissolution force, 

∑ 

2 

I = mizi. For diluted solutions (seawater is a good example), this equation can 

i 

be expressed as: 

= 

– 

1 2 

Azi I ⁄ 

1 2 

1+ BdiI ⁄ 

---------------------------- 

1 2 ⁄ 

Log ( γ i) 

= – [ Azi I ] 

(A2.8) 

The activity coefficient of non-electrolytic inorganic substances is always γ =1. 

iii) The chemical exergy of organic substances. It is difficult to determine the presence 

of organic substances in seawater due to the diversity of species involved 

(including biological organisms). However, organic substances are not present in 

the Szargut (1980) definition of SRE, but are purified naturally in rivers. This 

means that the oxygen (from photosynthesis or atmospheric) dissolved in water 

oxidizes the organic substances. This process may be slow or fast depending on 

the substance. One way to quantify the exergetic content of an organic substance 

is by proposing a single organic molecule to represent the “organic substance 

mean”. 

For practical sea analysis, our representative substance was a fat molecule, as shown 

in equation A2.9. This enabled us to calculate the order of magnitude of the exergy 

organic component to be determined qualitatively. 

115 

C39 H80 O3 + -------- O2 ↔ 39 CO2 + 40 H2O 2 

(A2.9) 

The laboratory measurement of Chemical Oxygen Demand (COD, mg. of O 2/lt of 

seawater consumed in the reaction is estimated) was used to obtain the amount of 

moles of mean organic substance per liter of water. The exergy of the organic 

substance was obtained from the definition of exergy reaction in the standard state, 

according to the expression in equation A2.10. 

b o 

o 

∆hf = 

∑ 

o o o 

o 

∆hf – T s – xj µ j 

o 

µ j 

where , s o and are well known for industrial substances. 

(A2.10)


A2.5.2 Practice: Brine exergy as a function of temperature, pressure 

and salt concentration 

Brine exergy only includes thermal, chemical and mechanical terms (kinetic and 

potential terms are neglected, see equation A2.1). Although it is impossible to know 

the chemical analysis of seawater entering the MSF unit, the chemical term only 

considers seawater concentration due to sodium chloride. 

This means that the chemical energy of the organic compounds is not considered 

and the contribution of inorganic substances is only calculated for Na + and Cl – ions. 

Chemical exergy of pure water depends on the osmotic pressure difference with 

respect to reference seawater. The AR used was 0 ºC and 45,000 TDS (average 

seawater concentration in the Arabian Gulf). The results were similar to other 

studies (Zaleta et al., 1998). For more detailed information about how to calculate 

these terms, see Barner and Scheuerman (1978), Newman (1980) and Marín and 

Turégano (1985). 


ANNEX 3 

Technical data 

This annex includes the most important design and constructive values provided by 

the contractors. Most of those values are introduced in the simulator, but they cannot 

be changed unless requested by the author. 

A3.1 MSF plant 

MSF: Guarantee figures (112 ºC TBT, 25 ºC SWT) 

Seawater temperature (Tsea) 

25 (ºC) 

Distillate production per hour (D) 2,400 (T/h) 

Distillate temperature at pump suction 38 (ºC) 

3 

Distillate density at production temperature 994 (kg/m ) 

Discharge pressure at distillate pump 3.5 (bar) 

Distillate purity expressed as TDS 10 (ppm) 

pH value of distillate before caustic soda injection 5.5-6.0 

Fe content in distillate 0.05 (ppm) 

Cu content in distillate 0.05 (ppm) 

Vapor velocity at the smallest path in last stage 14 (m/s) 


420 


Performance ratio (PR) not less than 8 

Quantity of heating steam at reducing valve before brine heater (mST) 

313.400 (kg/h) 

Steam pressure at heater inlet 1.8 (bar) 

Steam temperature at heater inlet 120 (ºC) 

Heater condensate temperature at pump suction 117 (ºC) 

Net specific heat consumption (NC) 290.75 (kJ/t distillate) 

Total specific heat consumption 295 (kJ/kg distillate) 

–3 

Specific electric power consumption 4.0 (kWh/kg dist. x 10 ) 

O2 

content in heater condensate (at 20 ºC) 0.03 (ppm) 

Fe content in heater condensate 0.04 (ppm) 

Cu content in heater condensate 0.04 (ppm) 

Conductivity of heater condensate 5 (µs/cm) 

Temperature of ejector condensate 40 (ºC) 

PH of ejector condensate 5.5-6.0 

T.D.S in brine blow down 71,000 (ppm, máx.) 

T.D.S in recirculated brine in the heater tubes 62,000 (ppm) 

Temperature of the sea water outlet from heat rejection section 36 (ºC) 

Sea water velocity inside tubes of heat rejection section 2.0 (m/s) 

Brine velocity inside tubes of heat recovery section 2.1 (m/s) 

Brine velocity inside tubes of brine heater 2.1 (m/s) 

Pressure inside the heater space 1.8 (bar) 

Brine pressure after the heater 1.9 (bar) 

Brine temperature in first stage (TBT) 108 (ºC) 

Brine temperature in last stage 35.5 (ºC) 

Vapor temperature in first stage 106.5 (ºC) 

Vapor temperature in last stage 34.5 (ºC) 

Absolute pressure in first stage 1.305 (bar) 

Absolute pressure in last stage 0.055 (bar) 


MSF plant 

Temperature of make-up feed entering deaerator 36 (ºC) 

Temperature of make-up feed leaving deaerator 36 (ºC) 

Absolute pressure in deaerator space 0.05 (bar) 

O2 

content in feed make-up leaving deaerator (without sulphite inj.) 0.03 (ppm) 

O2 

content in feed make-up leaving deaerator (with sulphite inject.) 0.04 (ppm) 

–6 

Specific chemical consumption (antiscale with sponge ball cleaning) 12 (kg/kg dist. x 10 ) 

–6 

Specific chemical consumption (antiscale without sponge ball clean.) 27.2 (kg/kg dist. x 10 ) 

7 

Heat losses due to radiation, venting or other losses 5 x 10 (kJ/h) 

Evaporators 

GENERAL 

2 

Recovery section: heat exchange surface 110,200 (m ) 

2 

Reject section: heat exchange surface 15,150 (m ) 

2 

Brine heater: heat exchange surface 10,272 (m ) 

2 

Recovery section: Fouling factor (design) 0.00015 (m K/W) 

2 

Reject section: Fouling factor (design) 0.00018 (m K/W) 

2 

Brine heater: Fouling factor (design) 0.00025 (m K/W) 

2 

Recovery section: Heat transfer coefficient (design) 2,673 (W/m K) 

2 

Reject section: Heat transfer coefficient (design) 2,211 (W/m K) 

2 

Brine heater: Heat transfer coefficient (design) 2,147 (W/m K) 

2 

Demisters: Total area 640 (m ) 

Total width 19 (m) 

Total length 87 (m) 

Total height 17 (m) 

Total weight-empty 3,000,000 (kg) 

Tube Pitch (pattern: triangular) 1.25 


421

422 


BRINE HEATER 

Number of tubes 3060 (2 passes) 

Tube internal diameter 33 (mm) 

Tube thickness 1.2 (mm) 

Tube effective length 15.1 (m) 

Tube material CuNi 66/30 2 Fe 2 Mn 

Tube conductivity 28.0 (W/m K) 

RECOVERY SECTION: Stages 1-2 

Number of tubes 3060 




Tube material CuNi 70/30 ASTM B107 







Tube material CuNi 90/10 ASTM B111 







Tube material Titanium B338Gr2 



MSF plant 

REJECT SECTION: Stages 18-20 


Tube internal diameter 33.6 (mm.) 

Tube thickness 0.7 

Tube effective length 19.2 

Tube material Titanium B338Gr2 


EFFECTIVE STAGE LENGTHS AND WIDTHS FOR BRINE FLOW 

Stage no. Length (m) Width (m) 

1 3.800 19.000 

2 3.800 19.000 

3 3.800 19.000 

4 3.800 19.000 

5 3.800 19.000 

6 4.000 19.000 

7 4.000 19.000 

8 4.000 19.000 

9 4.200 19.000 

10 4.200 19.000 

11 4.400 17.500 

12 4.400 17.500 

13 4.500 17.500 

14 4.500 17.500 

15 4.800 17.500 

16 4.800 17.500 

17 4.000 17.500 

18 4.800 17.500 

19 4.300 17.500 

20 5.100 17.500 


423

424 


DEMISTERS 

Stage no. 2 Area (m ) 

Height (m) 

1 26.89 2.8 

2 22.00 2.8 

3 22.00 2.8 

4 22.00 2.8 

5 22.00 2.8 

6 25.75 2.8 

7 25.75 2.8 

8 25.75 2.8 

9 29.50 2.8 

10 29.50 2.8 

11 33.30 2.8 

12 33.30 2.8 

13 35.20 2.8 

14 35.20 2.8 

15 40.80 2.8 

16 40.80 2.8 

17 40.80 2.8 

18 35.10 2.8 

19 38.80 2.8 

20 52.33 2.8 


MSF plant 

BRINE ORIFICES (112 ºC TBT, 25 ºC SW) 

Stage no. Height (mm) Width (mm) 3 Area (m ) 

1 77 16.134 19.000 

2 80 16.134 19.000 

3 83 16.134 19.000 

4 87 16.134 19.000 

5 91 16.134 19.000 

6 95 16.134 19.000 

7 99 16.134 19.000 

8 104 16.134 19.000 

9 108 16.134 19.000 

10 113 16.134 19.000 

11 131 14.420 17.500 

12 137 14.420 17.500 

13 144 14.420 17.500 

14 150 14.420 17.500 

15 156 14.420 17.500 

16 163 14.420 17.500 

17 169 14.420 17.500 

18 175 14.420 17.500 

19 182 14.420 17.500 

20 200 14.420 17.500 


425

426 


A3.2 Power Plant 

Boiler 

GENERAL 

Length x width x height (furnace) 9.825 x 10.875 x 19.9 (m) 

Length x width x height (steel structure) 23.0 x 15.5 x 45.5 (m) 

Total weight of boiler unit 3,500 (T) 

Shipping volume of largest item 3 

120 (m ) 

Total gross weight of the largest item to be shipped 80 (T) 

Weight of the largest item to be dismantled during maintenance 15 (T) 

ECONOMIZERS 

Effective heating surface (ECO 1/ ECO 2) 2 

10,890/4,390 (m ) 

Number of stages in line (ECO 1/ ECO 2) 7/3 

Number of parallel streams (ECO 1/ ECO 2) 1/1 

Location (ECO 1/ ECO 2) rd rd nd 

3 /3 -2 pass 

Design pressure 129 (bar) 

Design temperature (ECO 1/ ECO 2) 260/355 (ºC) 

Effective height of one stage 1,555 (mm) 

Pitch across the gas flow (ECO 1/ ECO 2) 65/75 (mm) 

Pitch parallel to the gas flow 75/110 (mm) 


Power Plant 

AIR WATER HEATER 

Number of heaters per boiler 2 

Design pressure (airside) 1,300 (mm WG) 

Design pressure (waterside) 129 (bar) 

Design temperature (airside) 250 (º C) 

Design temperature (waterside) 260 (º C) 

Design air throughput 3 

463,740 (Nm /h) 

Design water throughput 211 (t/h) 

Effective surface heating 2 

20,920 (m ) 

Fouling factor considered (air/water side) 5/2 % 

STEAM WATER DRUM 

Type 3 

48 (m ) 

Water content 3 

24 (m /h) 

Steam space rating 3 3 

470 (m /m ·h) 


Design temperature 330 (º C) 

Total length 14,000 (mm) 

Shell length 12,800 (mm) 

Shell thickness 82 (mm) 


427

428 


Combustion chamber 

WALL HEATING SURFACES 

Nominal height 19.9 (m) 

Nominal width 10.875 (m) 

Nominal depth 9.825 (m) 

Volume 3 

2.123 (m ) 

Total effective heat absorbing surface of the combustion chamber 2 

1,454 (m ) 

Total length 14,000 (mm) 

Shell length 12,800 (mm) 

Shell thickness 82 (mm) 

Heat input (natural gas at MCR, 40º C air temperature) 6 

422.22 × 10 (kcal/h) 

Evaporators 

Total effective heat absorbing surface 2 

2,740 (m ) 


Design temperature 375 (ºC) 

Maximum local heat flux 2 

290,000 (kcal/m ·h) 

Evaporator headers 

Number 40 


Design temperature 330 (ºC) 


Power Plant 

SUPERHEATERS 

Number of stages in line 3 

Number of parallel streams 2 

Number of spray attemperators 4 


Design temperature (máx.) (SH1/SH2/SH3) 580/590/590 (ºC) 

Effective heating surface (SH1/SH2/SH3) 2 

3,090/860/360 (m ) 

Number of elements over the width (SH1/SH2/SH3) 144/72/72 

SPRAY ATTEMPERATORS 

Number 2 

Design steam flow (inlet/outlet) (AT1/AT2) 270-295/295-310 (t/h) 

Calculated spray water flow (AT1/AT2) 27/18 (t/h) 

Design spray water flow (AT1/AT2) 41/27 (t/h) 


Design temperature (AT1/AT2) 500/550 (ºC) 

DOWNCOMERS 

Number 2 

Outside diameter 508 (mm) 

Wall thickness 16 (mm) 


429

430 


Condensing Plant 

Condenser surface (between tube sheets and related to steam side) 2 

6,725 (m ) 

Condenser vacuum at MCR 0.072 (bar abs) 

Specific condenser surface demand at MCR 2 67.5 (m ·h/t) 

Condenser hotwell useful capacity 3 25 (m ) 

Circulating water velocity within tube bundle 2.2 (m/s) 

Associated hydraulic loss of CW 0.37 (bar) 

Basic heat transfer coefficient at MCR 2 

2,732 (kcal/m ·h·K) 

Applied cleanliness factor 90 % 

Associated maximum temperature difference 6.7 (ºC) 

Thermal conductivity 14 (kcal/m·h·K) 

Number of tubes per total cond. for one turbine 7124 

Condensate Pumps 

Number of pumps 2 + 2 

Specific gravity of fluid (MCR) 3 

992.5 (kg/m ) 

Suction pressure (MCR) 0.071 (bar) 

Suction temperature (MCR) 39.2 (ºC) 

Discharge pressure (MCR) 18 (bar abs.) 

Discharge temperature (MCR) 39.2 (ºC) 

Flow at discharge nozzle (MCR) 2 x 131 (T/h) 

Overall efficiency according to DIN 1944 of equiv. (MCR) 71.6 % 

Pump speed 1485 (l/min) 

Critical speeds of pump and motor unit > 1800 (rpm) 

Nameplate rating (MCR) 130 (kW) 


Power Plant 

HP1 Heater 

Overall dimensions of feed heater 1,300 x 8,600 (mm) 

Main steam flow (feedwater side, MCR) 562.9 (t/h) 

Inlet pressure (feedwater side, MCR) 119.05 (bar) 

Inlet/outlet temperature (feedwater side, MCR) 194.6/230.1 (ºC) 

Heating steam flow 39.0 (t/h) 

Pressure incl. vacuum if appl. 27.2 (bar) 

Temperature (heating side, MCR) 369 (ºC) 


Overall heat transfer coefficient (condensing zone) 2 

3,280 (kcal/m ·h·K) 

LMTD (condensing zone) 11.6 (ºC) 

Heat transfer surface (desuperheating section) 2 

65.3 (m ) 

Heat transfer surface (condensing section) 2 

531.6 (m ) 

Heat transfer surface (condensate cooling section) 2 

64.4 (m ) 

Velocity of main condensate or feed water inside tubes 1.54 (m/s) 

HP2 Heater 


Main steam flow (feedwater side, MCR) 562.3 (t/h) 





Temperature (heating side, MCR) 282 (ºC) 



3,200 (kcal/m ·h·K) 


Heat transfer surface (desuperheating section) 2 

37.8 (m ) 


525.2 (m ) 


101.3 (m ) 



431

432 


LP1 Heater 


Main steam flow (feedwater side MCR) 131.6 (t/h) 





Temperature (heating side, MCR) 129.7 (ºC) 



3,200 (kcal/m ·h·K) 



341.4 (m ) 


54.1 (m ) 


LP2 Heater 


Main steam flow (feedwater side MCR) 131.6 (t/h) 





Temperature (heating side, MCR) 79.7 (ºC) 



2,840 (kcal/m ·h·K) 



316.4 (m ) 


124.8 (m ) 



Nomenclature 

Abbreviatures/ Symbols/Acronyms 

a Cost parameter, activity, or constant of Cobb-Douglass equation. 

A Exchange area of the evaporator/condenser or constant of Debye-Hückel 

equation. 

AR Reference Ambient. 

AT Atemperator. 

b Specific exergy. 

B Flashing brine flow in j-th flash chamber, exergy flow, constant of Debye- 

Hückel equation, or constant for calculating vapor enthalpy. 

BD Brine Blowdown. 

BDP Blowdown Pump. 

BH Brine Heater. 

BHP Brine Heater Pump. 

BOI Boiler. 

BPE Boiling Point Elevation of brine with respect the pure water. 

c Velocity. 

C Salt concentration, or total monetary cost. 

c* Exergoeconomic cost. 

ca Cost per unit of area. 

CBS Cleaning Ball System. 

cf Fuel cost. 

CND Condenser. 

COC Boiler Peak Load. 

COD Chemical Oxygen Demand. 

CP Condensate Pump or Heat Capacity. 

cp Product cost. 

CW Cooling rejected Water. 

d Ionic diameter. 

D Distillate flow. 


434 

Nomenclature 

DAS Data Acquisition System. 

DB Exergy flow of distillate. 

DCA Drain Cooling Advantage. 

DF Dysfunction generated in a component. 

DI Dysfunction generated by a component. 

DLL Dynamic Link Library. 

DP Distillate Pump. 

DRT Deaerator. 

DV Main stop valve seat diameter. 

e Condenser efficiency. 

E Enhancement factor. 

EC Electrical Conductivity. 

ECO Economizer. 

ED Electrodyalisis. 

EDS European Desalination Society. 

EES Engineering Equation Solver. 

ESL Excitation System Losses. 

f Generic function. 

F Fuel, Make-up feed or constant for calculating vapor enthalpy. 

FCW Fuel Cost of Water. 

FD Fictitious Device. 

FP Feed Pump. 

g Acceleration due to gravity, or characteristic equation. 

Gc Gas consumption. 

GCC Gulf Council Countries. 

GEN Generator. 

GOR Gain Output Ratio. 

h Heat transfer coefficient or enthalpy. 

H Height. 

Hb Flashing brine (seawater) enthalpy. 

HHV High Heating Value. 

HT High-Temperature. 

HP High-Pressure. 

HPH High-Pressure Heater. 

HPT High-Pressure Turbine. 

HR Heat Rate of a power plant. 

HRSG Heat Recovery Steam Generator. 

HTOS High-Temperature Operation in Summer. 

HTOW High-Temperature Operation in Winter. 

Hv Saturated vapor enthalpy of water. 


Nomenclature 

I Irreversibility or Ionic dissolution force. 

IAAE International Agency of Atomic Energy. 

ID Inside Diameter. 

IDA International Desalination Association. 

k Thermal conductivity or unit exergy consumption. 

K Constant for mass flow coefficient or gland steam system. 

k* Exergy unit cost. 

L Length or Exergy Losses. 

LP Low-Pressure. 

LPH Low-Pressure Heater. 

LPT Low-Pressure Turbine. 

LS Live Steam Extraction. 

LTL Low Turbine Load. 

LTMD Logarithmic Temperature Mean Difference. 

LTOS Low-Temperature Operation in Summer. 

m Mass flow or molality. 

MCR Maximum Continuous Rating. 

Md Steam flow to MSF unit. 

MED Multi-Effect Distillation. 

MF Malfunction of a component. 

MF* Malfunction cost (impact on fuel). 

MFl Intrinsic malfunction. 

MFg Induced malfunction. 

MIX Mixer. 

MR Maximum Rating. 

MSL Minimum Stable Load. 

MSF Multistage Flash. 

MXT Mixer Temper water. 

n number of tubes in a vertical row. 

NC Net energy Consumption. 

NEA Non Equilibrium Allowance. 

NRC Number of Recovery Stages. 

NRJ Number of Reject Stages. 

NTL Normal Turbine Load. 

NTOS Nominal-Temperature Operation in Summer. 

NTW Non Turbine Working. 

OD Outside Diameter. 

ODOB One Desalination One Boiler. 

O&M Operating and Maintenance 

p Pressure. 


436 

Nomenclature 

P Product. 

Pc Condenser pressure. 

Pr Prandtl number. 

PE Pressure Exchanger. 

PL Pressure losses, or Partial Load. 

PR Performance Ratio. 

PTC Performance Test Case or Parabolic Trough Collector. 

Q Heat flow. 

Qf Heat value of fuel. 

r Exergy ratio. 

R Thermal resistance or recycle brine. 

RCS Recovery Section. 

Re Reynolds number. 

RJS Reject Section. 

RO Reverse Osmosis. 

rp Pressure ratio in a turbine section. 

RP Recycle Pump. 

s Specific entropy. 

S Entropy flow or size. 

Sa Sonic area. 

SF Solar Factor. 

SH Superheater. 

SR Seawater to Reject section flow. 

SRE Stable Reference Environment 

SW Seawater feed flow. 

SWP Seawater Pump. 

SWRO Seawater Reverse Osmosis. 

t Thickness. 

T Temperature. 

T* Temperature reference, 273.15 K. 

TBT Top Brine Temperature. 

TDOB Two Desalination One Boiler. 

TDS Total Dissolved Solids. 

To Ambient Temperature. 

TP Temper water Pump (also TPP). 

TTD Terminal Temperature Difference. 

TVC Thermal Vapor Compression. 

UAE United Arab Emirates. 

U Overall heat transfer coefficient. 

US, USA United States of America. 


Nomenclature 

VC Vapor Compression. 

VEX Extraction valve (pressure loss simulation). 

VF Feed valve. 

vw Tube velocity. 

VS Reducing pressure station valve. 

VST Stop valve. 

VTE Vertical Tube Evaporator. 

VWO Valve Wide Open. 

x 

Variable or molar fraction. 

X Steam quality. 

w Width. 

W Power. 

z Ionic charge. 

Z Pressure drop coefficient or Capital Cost of a component. 

Greeks 

α 

β 

γ 

δ 

∆ 

ε 

η 

κ 

λ 

µ 

ν 

π 

ρ 

φ 

ℵ 

ϕ 

ϖ 

Sonic velocity or constant of Cobb-Douglass equation. 

Constant for calculating vapor entropy. 

Activity coefficient. 

Interstage (temperature) difference. 

Difference, increment, variation (or loss). 

Relative error or ratio. 

Efficiency. 

Technical production coefficient. 

Latent heat, real number or Lagrange multiplier. 

Viscosity or chemical exergy component. 

Specific volume. 

Osmotic pressure. 

Density. 

Arrays/Matrices 

B 

[DF] 

DF 

DI 

∆FT 

Mass flow coefficient of a turbine section, or dysfunction coefficient. 

Constant for calculating latent heat of vapor. 

Amortization factor. 

Chamber load or total final product. 

Exergy flows set. 

Dysfunction matrix. 

Array of dysfunctions generated in the components. 

Array of dysfunctions generated by the components. 

Impact on fuel array. 


438 

Nomenclature 

κe 

KD 

〈 KP〉 

MF 

I 

| I〉 

P 

P 

S 

| P〉 

U 

D 

Subscripts 

Unit exergy consumption array of the system input resources. 

Diagonal matrix of the unit exergy consumption. 

Unit exergy consumption matrix. 

Malfunction array. 

Irreversibility array. 

Irreversibility matrix operator. 

Product array. 

Final product array. 

Product matrix operator. 

Unitary matrix. 

a Absolute. 

b Exergy flow or brine. 

B Brine. 

bi Brine inside the tubes. 

c Condensate. 

C Condenser. 

ci Steam to Ejector from leakage system. 

CT Condensing Turbine. 

d Distillate, design. 

D Distillate. 

des Low-Pressure Steam to MSF unit. 

DR Deaerator. 

e Exit or electricity. 

es Interstage. 

ex Extraction. 

f Fouling, formation or fuel relative. 

F Cooling brine. 

fg Evaporation. 

fm Film. 

gen Generator. 

H Brine Heater. 

H2O 

Pure water. 

i Inlet, i-section or array index. 

j j-Stage, index, variable or specie. 

K Kelvin. 

L Loss. 

ls Live Steam Flow. 

LS Live Steam Extraction from reduction pressure station. 


Nomenclature 

lm Logaritmic mean. 

m Mean. 

msf MSF plant. 

N Last stage of MSF unit. 

NRC Last stage of recovery section. 

o Outlet. 

P Demister pressure losses, or product. 

q Chemical. 

r Reference. 

rcs Recovery section (exit). 

rdes Condensate returned from the MSF unit (heater), after passing brine heater 

pump. 

s Isoentropic, shell or entropy flow. 

S Saturated. 

sea Seawater. 

ST Steam or Steam Turbine. 

t Turbine or tube. 

T Total. 

va Steam to vacuum system of MSF unit (condensate returning to condenser). 

vent Venting system. 

w Wall or water. 

Z Capital cost. 

0 To the environment. 

Superscripts 

a, b, c, x, y, z Exponents for calculations of TTDs in heaters or deaerator, pressure losses or 

gland steam system. 

L Local. 

G Induced. 

m m-Iteration or scaling factor. 

n1, n2, n3, n4 Exponents for capital costing equation. 

´ Extraction mass flow rate. 

o Standard state. 

r Operating parameter. 

t Transpose (matrix notation). 

–1 Inverse (matrix notation). 

0 Reference or design (matrix notation). 


References 

Asea Brown Bovery (ABB) (1996a). 

Details. Private Communication. 

Boiler Performance Data. Construction 

Asea Brown Bovery (ABB) (1996b). Diagram Charts, and Heat Balance of 

Al Taweelah B Power Generation Unit. Private Communication. 

Asea Brown Bovery (ABB) (1996c). HP and LP Heaters, Feedwater Storage Tank, 

Cold Storage Tank. Private Communication. 

Asea Brown Bovery (ABB) (1996d). Steam, Condensate and Feedwater Piping 

System. Private Communication. 

Asea Brown Bovery (ABB) (1996e). Generator System. Private Communication. 

Asea Brown Bovery (ABB) (1996f). Pump Curves. Private Communication. 

Asea Brown Bovery (ABB) (1997). Private communication. 

Abdel-Jawad, M., Al-Tabtabaei, M. (1999). Impact on Current Power Generation 

and Water Desalination Activities on Kuwait Marine Environment. Proceedings of 

the IDA World Congress on Desalination and Water Reuse. San Diego, USA. 

Abu Qdais, H. A. (1999). Environmental Impacts of Desalination Plants on the 

Arabian Gulf. 

Proceedings of the IDA World Congress on Desalination and Water 

Reuse. San Diego, USA. 

Afgan, N. H., Darwish, M., Carvalho, M. G. (1999). Sustainability Assessment of 

Desalination Plants for Water Production. Desalination 124, pp. 19-32. Presented at 

the European Conference on Desalination and the Environment. Las Palmas, Spain. 


442 

References 

Alawadhi, A. A. (1999). Regional Report on Desalination. Proceedings of the IDA 

World Congress on Desalination and Water Reuse. San Diego, USA. 

Al-Gobaisi, D. M. K. (1999). Water for Sustainable Development of the Arab World. 

Private Communication. 

Al-Gobaisi, D. M. K. (1997). Sustainable Augmentation of Fresh Water Resources 

through Appropriate Energy and Desalination Technologies. Proceedings of the IDA 

World Congress on Desalination and Water Reuse. Madrid, Spain. 

Alhumaizi, K. (1997). Modeling, Simulation and Control of Multistage Flash 

Desalination Plant, 

Proceedings of the IDA World Congress on Desalination and 

Water Reuse. Madrid, Spain. Vol. III, pp. 111-130. 

Al-Mutaz, I. S., Soliman, M. A. (1989). Simulation of MSF Desalination Plants. 

Desalination 74, pp. 317-326. 

Al-Owais, A. A., Nijhawan, R. K., Budhiraja, P. K. (1989). Operational Experience 

of Once Through MSF Desalination Units. Desalination 73, pp. 327-340. 

Al-Sulaiman, F. A., Ismail, B. (1995). Exergy Analysis of Major Recirculating 

Multi-stage Flash Desalting Plants in Saudi Arabia. Desalination 103, pp. 265-270. 

3 

Andrews, T., Shumway, S. A. (1999). Design Study of a 20,000 m /day Seawater 

Reverse Osmosis Work Exchanger Energy Recovery System. Proceedings of the IDA 

World Congress on Desalination and Water Reuse. San Diego, USA. 

Ahrendts, J. (1980). Reference States. Energy 5, Vol. 8, pp. 667-677. 

American Society of Mechanical Engineers (ASME) (1967). 1967 ASME Steam 

Tables. The American Society of Mechanical Engineers. New York, USA. 

Badr, O., Probert, S. D., O’Callaghan, P. (1990). Rankyne Cycles for Steam Power- 

Plants. Applied Energy 36, pp. 191-231. 

Barba, D., Liuzzo, G., Tagliaferri, G. (1973). Mathematical Model for Multiflash 

th 

Desalting Plant Control. 4 International Symposium on Fresh Water from the Sea. 

Vol. 1, pp. 153-168. 

Barendsen, W. C., Moch, I. (1999). Privatization of Seawater Reverse Osmosis 

Plants in Antigua. Proceedings of the IDA World Congress on Desalination and 

Water Reuse. San Diego, USA. 

Barner, H. E., Scheuerman, R. V. (1978). Handbook of Thermochemical Data for 

Compounds and Acqueous Species. John Wiley and Sons Inc. 


References 

Barthelmes, J., Bolmer, H. (1996). Fouling and Scaling Control in MSF 

Desalination Units by “On-Load” Tube Cleaning. Desalination and Water Reuse, 

Vol. 7/2, pp. 27-33. 

Brown Boveri Co. (BBC) (1979). Thermal Kit, Simplified Instructions for the 

Thermal Calculation of the Antikokan Units. 

HTGD 12246 E. 

Beamer, J. H., Wilde, J. D. (1971). The Simulation and Optimization of a Single 

Effect Multi-Stage Flash Desalination Plant. 

Desalination 9, pp. 259-275. 

Bejan, A., Tsatsaronis, G., Moran, M. (1997). Thermal Design and Optimization. 

John Wiley and Sons Inc., New York. 

Benelmir, R. (1989). Second Law Analysis of a Co-generation Cycle. Ph. D. Thesis. 

Georgia Institute of Technology. 

Boehm, R. F. (1987). Design Analysis of Thermal Systems. Ed. John Wiley and 

Sons. New York. 

Brandani, V., Del Re, G., Di Giacomo, G. (1985). A New Model for Predicting 

Thermodynamic Properties of Sea Salt Solutions. Desalination 56, pp. 299-313. 

Breidenbach, L., Rautenbach, R., Tusel, G. F. (1997). Thermoeconomic Assessment 

of Fossil Fuel Fired Dual Purpose Power/Water Plants. 

Proceedings of the IDA 

World Congress on Desalination and Water Reuse. Madrid, Spain. Vol. IV, 

pp. 167-180. 

Bromley, L. A., Diamond, A. E., Salam, E., Wilkins, D. G. (1970). J. Chem. Eng. 

Data 15, pp. 246. 

Brodyansky, V., Bandura, A. (1993). The Prognosis for Macroeconomical 

Development and Exergy. 

Proceedings of the International Symposium on energy 

systems and ecology ENSEC’93. Cracow, Poland. pp. 153-161. 

Cadagua (1999). Private Communication. 

Calder (1999). Pelton Wheel Energy Recovery Turbines. Private Communication. 

Chen, S. F., Chan, R. C., Read, S. M., Bromley, L. A. (1973). Viscosity of Sea Water 

Solutions. Desalination 13, pp. 37-51. 

Coleman, A. K. (1971). Optimization of a Single Effect, Multi-Stage Flash 

Distillation Desalination System. Desalination 9, no. 4, pp. 315-331. 

Cooke, D. H. (1985). On prediction of Off-Design Multistage Turbine Pressures by 

Stodola’s Ellipse. Journal of Engineering for Gas Turbines and Power. Transactions 

of the ASME. Vol. 107, pp. 596-606. 


443

444 

References 

Corripio, A. B., Chrien, K. S., Evans, L, B. (1982). Estimate Costs of Heat 

Exchangers and Storage Tanks Via Correlations. Chemical Engineering, January 

1982, pp. 125-127. 

Cotton, K. C. (1993). Evaluating and Improving Steam Turbines Performance, 

Edit. 

Cotton Factory Inc. New York, USA. 

Darwish, M. A., Al-Najem, N. M., Al-Ahmad, M. S. (1993). Second-Law Analysis of 

Recirculating Multi-stage Flash System. Desalination 89, pp. 289-309. 

Darwish, M. A., Yousef, F. A., Al-Najem, N. M. (1997). Energy Consumption and 

Costs with a Multi-stage Flashing (MSF) Desalting System. Desalination 109, 

pp. 285-302. 

Darwish, M. K., Arazzini, S. (1989). Description and Mathematical Model of a 

Large MSF Desalination Plant in Scada Configuration. 

Private Communication, 

pp. 91-106. 

De Armas, J. C., Pérez, J. L., Von Gottberg, A. J. M. (1999). Desalination of 

Municipal Sewage Effluent with Electrodialysis Reversal in Tenerife. 

Proceedings of 


Echaniz, J., Rodero, A., Sallangos, O., Santamaria F. J. (1997). Dhekelia (Cyprus) 

Seawater Desalination Plant Design, Construction and Commissioning of the 

3 20,000 m /day R.O. Plant. Proceedings of the IDA World Congress on Desalination 

and Water Reuse. Madrid, Spain. Vol. II, pp. 371-392. 

El-Nashar, A. M. (1999). Cost Allocation in a Cogeneration Plant for the 

Production of Power and Desalted Water – Comparison of the Exergy Cost 

Accounting Method with the WEA Method. 

Private Communication. 

El-Nashar, A. M., Qamhiyeh, A. A. (1993). Optimal Performance of MSF Distillers 

for UANW 9 and 10 Power Plant: A Thermoeconomic Study. 

Desalination 93, 

pp. 323-342. 

Elovic, P., Willocks, G. (1999). Case Study of Operating Experience of 9 Low 

Temperature MED plants in the U.S. Virgin Islands. Proceedings of the IDA World 

Congress on Desalination and Water Reuse. San Diego, USA. 

El-Saie, M. H., El-Saie, Y. M. H. (1989). Optimization of Dual-Purpose Steam 

Power and MSF Desalination Plant. Desalination 76, pp. 155-175. 

El-Sayed, Y. M., Aplenc, A. J. (1970). Application of the Thermoeconomic Approach 

in the Analysis and Optimization of Vapor-Compression Desalting System. 

Transactions of the ASME. Journal of Engineering and Power, Vol. 92 no. 1, 

pp. 17-26. 


References 

El-Sayed, Y. M., Evans, R. B. (1970). Thermoeconomics and the Design of Heat 

Systems. 

Transactions of the ASME. Journal of Engineering and Power, Vol. 92 

no. 1, pp. 27-35. 

El-Sayed, Y. M., Silver, R. S. (1980). Fundamentals of Distillation. 

Principles of 

Desalination, Chapter 2. Academic Press Inc. 

El-Sayed, Y. M., Tribus, M. (1983). Strategic use of Thermoeconomics for Systems 

Improvement. ACS Symposium Series, no. 235, pp. 215-238. Washington D.C., 

USA. 

El-Sayed, Y. M. (1988). A Decomposition Strategy for Thermoeconomics 

Optimization of a Given New Configuration, 

Approaches to the Design and 

Optimization of Thermal Systems. Wepfer and Moran eds. ASME, pp. 41-47. New 

York, USA. 

El-Sayed, Y. M. (1996). Second-Law-Based Analysis and Optimization of Seawater 

Desalting Systems. Private Communication. 

Erbes, M. R., Gay, R. B. (1989). Gate/cycle Predictions of the Off-Design 

Performance of Combined Cycle Power Plants. ENTER Software, Inc. ASME 1989 

WAM. 

Erlach, B. (1998). Comparison of Thermoeconomic Methodologies: Structural 

Theory, AVCO and LIFO. Application to a Combined Cycle. University of Zaragoza. 

Dept. of Mechanical Engineering. 

Erlach, B., Serra, L., Valero, A. (1999). Structural Theory as Standard for 

Thermoeconomics. Energy Conversion and Management 40, pp. 1627-1649. 

Ettouney, H. M., El-Dessouky, H. T. (1999). A Simulator for Thermal Desalination 

Processes. Desalination 125, pp. 277-292. Presented at the European Conference on 

Desalination and the Environment. Las Palmas, Spain. 

Evans, R. B. (1962). A Contribution to the Theory of Thermo-Economics. Sea Water 

Research Project S. W. 604. Report no. 62-36. Department of Engineering. 

University of California. 

Evans, R. B., Crellin, G. L., Tribus, M. (1980). Thermoeconomic Considerations of 

Sea Water Demineralization. 

Principles of Desalination, Chapter 1. Academic Press 

Inc. 

Evans, R. B. (1980). Thermoeconomic Isolation and Essergy Analysis. 

Energy, 

Vol. 5, no. 8-9, pp. 805-822. 

Fabuss, B. M., Korosi, A. (1968). Properties of Sea Water and Solutions Containing 

Sodium Chloride, Potassium Chloride, Sodium Sulfate and Magnesium Sulfate. 


445

446 

References 

Research and Development Progress Report no. 384. U.S. Department of the 

Interior. 

Falceta, F., Sciubba, E. (1997). Modelling and Simulation of Multi-Stage Flash 

Desalination Plants. 

Private Report. 

Fayas, J., Novoa, J. (1997). The Desalination Process in the Balearic Islands. 

Proceedings of the IDA World Congress on Desalination and Water Reuse. Madrid, 

Spain. Vol I, pp. 41-54. 

Fisia Italimpianti (1996). Private Communication. 

Fisia Italimpianti (1997). 

Communication. 

Diagram charts of the MSF Plant. 

Fisia-Italimpianti (1999). Water Desalination Plants. Private Communication. 


Private 

Frangopoulos, C. (1983). Thermoeconomic Functional Analysis: A method for the 

Optimal Design or Improvement of Complex Thermal Systems. Ph. D. Thesis. 

Georgia Institute of Technology. 

Frangopoulos, C. A. (1987). Thermoeconomic Functional Analysis and 

Optimization. Energy Vol. 12, no. 7, pp. 563-571. 

Frangopoulos, C. A. (1988). Optimal Design of a Gas Turbine Plant by a 

Thermoeconomic Approach. ASME COGEN-TURBO, pp. 563-571. ASME, New 

York, USA. 

Frangopoulos, C. A. (1990). Intelligent Functional Approach: A Method for Analysis 

and Optimal Synthesis-Design-Operation of Complex Systems. Proceedings of the 

International Symposium: A future for energy. Florence, Italy. Pergamon Press, 

pp. 805-815. 

Frangopoulos, C. A. (1991). Private Communication. 

Frangopoulos, C. A. (1994). Application of the Thermoeconomic Functional 

Approach to the CGAM Problem. 

Energy Vol. 19, no. 13. 

Friedrich, R. O., Hafford, J. A. (1971). Report ORNL-TM-3489. 

Gaggioli, R. A. (1980). Thermodynamics: Second Law Analysis. 

ACS Symposium 

Series 122. American Chemical Society. Washington D.C., USA. 

Gaggioli, R. A., El-Sayed, Y. M. (1987). A Critical Review of Second Law Costing 

Methods. 

Proceedings of the IV International Symposium on Second Law Analysis 

of Thermal Systems (ASME Book I00236). ASME, pp. 59-73. New York, USA.

References 

García, L., Gómez, C. (1999). Conditions for Economical Benefits of the Use of 

Solar Energy in Multi-stage Flash Distillation. Desalination 125, pp. 133-138. 

Presented at the European Conference on Desalination and the Environment. Las 

Palmas, Spain. 

García, L., Palmero, A. I., Gómez, C. (1999). Application of Direct Steam 

Generation into a Solar Parabolic Trough Collector to Multieffect Distillation. 

Desalination 125, pp. 139-145. Presented at the European Conference on 


Gleick, P. H. (1998). The World’s Water – The Biennial Report on Freshwater 

Resources, 1998/1999. 

Island Press. Washington DC, USA. 

Glueck, A. R., Bradshaw, R. W. (1970). A Mathematical Model for a Multistage 

rd 

Flash Distillation Plant. 3 International Symposium on Fresh Water from the Sea. 

Vol. 1, pp. 95-108. 

Georgescu-Roegen, N. (1971). The Entropy Law and the Economic Process. 

Harvard University Press. Cambridge MA. USA. 

Goto, T., MacCormick, T., Congjie, G., Guoling, R., Chung Y.-T. 

(1999). Overview 

of Desalination in the Pacific Region. 

Proceedings of the IDA World Congress on 

Desalination and Water Reuse. San Diego, USA. 

Hamed, O. A., Al-Sofi, M. A. K., Iman, M., Mustafa, G. M., Ba-Mardouf, K., Al- 

Washmi, H. (1999). Thermal Performance of Multistage Flash Distillation Plants in 

Saudi Arabia. Proceedings of the IDA World Congress on Desalination and Water 


Hanbury, W. T., Hodgkiess, T., Morris, R. (1993). Desalination Technology 93. An 

Intensive Course. 

Porthan Ltd., Easter Auchinloch. Lenzie, Glasgow, UK. 

Hassan, A. S., Florido, P. C. (1999). Feasibility of Nuclear Desalination Costs in 

Egypt. Proceedings of the IDA World Congress on Desalination and Water Reuse. 

San Diego, USA. 

Hauge, L. J., Ludvigsen, F. (1999). Field Installation of Pressure Exchanger in a 

3 80 m /d SWRO Plant. Proceedings of the IDA World Congress on Desalination and 


Hayakawa, K., Satori, H., Konishi, K. (1973). Process Simulation on a Multi-Stage 

Flash Distillation Plant. 4 th International Symposium on Fresh Water from the Sea. 

Vol. 1, pp. 303-312. 

Helal, A. M., Medani, M. S., Soliman, M. A. (1986). A Tridiagonal Matrix Model 

for MultiStage Flash Desalination Plants. Computers & Chemical Engineering Vol. 

10, pp. 95-108. 


447

References 

Hömig, H. E. (1978). Seawater and Seawater Distillation (Fichtner Handbook). 

Vulkan-Verlag. Essen, Germany. 

Husain, A., Hassan, A., Al-Gobaisi, D. M. K., Al-Radif, A., Woldai, A., Sommariva, 

C. (1993). Modelling, Simulation, Optimization and Control of Multistage Flashing 

(MSF) Desalination Plants. Part I: Modelling and Simulation. Desalination 92, 

pp. 21-41. 

Husain, A., Woldai, A., Al-Radif, A., Kesou, A., Borsani, R., Sultan, H., 

Deshpandey, P. B. (1994). Modelling, and Simulation of a Multistage Flash (MSF) 

Desalination Plant. Desalination 97, pp. 555-586. 

Husain, A. (1999). Computational Aspects in Process Simulation. International 

Center for Water and Energy Systems (ICWES). Private Communication. 

I.D.E. Technologies ltd. (1999). Private Communication. 

Intermón (1998). Relaciones Norte-Sur. Conceptos Clave. Dossiers para entender el 

mundo. Ed. Octaedro. 

Isdale, J. D., Spence, C. M., Tudhope, J. S. (1972). Physical Properties of Sea Water 

Solutions: Viscosity. Desalination 10, pp. 319-328. 

Itahara, S., Stiel, L. Y. (1968). The Optimal Design of Multi-Stage Flash 

Evaporators by Dynamic programming. Desalination 4, pp. 248-257. 

Jernqvist, A., Jernqvist, M., Aly, G. (1999). Simulation of Thermal Desalination 

Processes. Desalination 126, pp. 147-152. Presented at the European Conference on 


JSME (1968). 1968 JSME Steam Tables. The Japan Society of Mechanical 

Engineers. Tokyo, Japan. 

Keenan, J. H., Keyes, F. G. (1955). Thermodynamic Properties of Steam. John Wiley 

and Sons Inc., New York, USA. 

Keenan, J. H., Keyes, F. G., Hill, F., Moore, K. (1955). Steam Tables (SI Units). John 

Wiley and Sons Inc., New York, USA. 

Klein, S. A., Alvarado, F. L. (1992). EES Engineering Equation Solver. F-Chart 

Software. Middleton, USA. 

Kotas, T. (1985). The Exergy Method of Thermal Plant Analysis. Butteerworth eds., 

London, UK. 

Kronenberg, G., Dvornikov, V. (1999). Fuel Cost of Water (FCW) in Dual Plants. 

Proceedings of the IDA World Congress on Desalination and Water Reuse. San 

Diego, USA. 


References 

Lazzaretto, A., Tsatsaronis, G. (1997). On the Quest for Objective Equations in 

Exergy Costing. Proceedings of the ASME Advanced Energy Systems Division. 

ASME. AES-Vol. 37, pp. 197-210. 

Le Goff, P. (1979). Energetique Industrièlle. Tecnique et Documentation. Paris, 

France. 

Lerch, F., Royo, J., Serra, L. (1999). Structural Theory and Thermoeconomic 

Diagnosis. Part II: Application to an Actual Power Plant. Proceedings of the 

ECOS’99 Conference. ASME, pp. 374-379. Tokyo, Japan. 

Lewis, G. N., Randal, M. (1961). Thermodynamics. Mc-Graw Hill Company. 

Leyendekkers, J. V. (1979). Prediction of the Density and Viscosity of Seawater its 

Concentrates and other Multicomponents Solutions Using the Tamman-Tait-Gibson 

(TTG) Model. Desalination 29, pp. 263-274. 

Lozano, M. A., Valero, A. (1993). Theory of the Exergetic Cost. Energy, Vol. 18, 

no. 3, pp. 939-960. Elsevier Science Ltd., UK. 

Lozano, M. A., Valero, A., Serra, L. (1993). Theory of the Exergetic Cost and 

Thermoeconomics Optimization. Proceedings of the International Symposium 

ENSEC’93. Cracow, Polland. 

Lozano, M. A., Bartolomé, J. L., Valero, A., Reini, M. (1994). Thermoeconomic 

Diagnosis of Energy Systems. Flowers 94, Florence World Energy Research 

Symposium, pp. 149-156. Florence, Italy. 

Lozano, M. A., Valero, A., Serra, L. (1996). Local Optimization of Energy Systems. 

Proceedings of the ASME Advanced Energy System Division. Atlanta, Georgia. 

AES-Vol. 36, pp. 241-250. 

Marín, J. M., Turégano, J. A. (1985). Contribution to the Calculation of Chemical 

Exergy in Industrial Processes (Electrolyte Solutions). Energy Vol. 11, pp. 231-236. 

Martin, M. H. (1919). Articles on Leakage of Steam Through Dummy Pistons. 

Engineering Jan 3. 

Martínez, A., Serra, L., Valero, A. (2000). Cost Assessing in Entrained Flow 

Gasifiers Based on Physical Models. Paper accepted to ECOS’2000 Conference. 

Enschede, Netherlands. 

Menéndez, E. (1997). Las Energías Renovables. Los Libros de la Catarata Eds. 

Medina, J. A. (2000). Desalación de Aguas Salobres y de Mar. Osmosis Inversa. 

Mundi-Prensa Eds. Madrid, Spain. 

Microsoft Corporation (1997). Microsoft Fortran Developer Studio. 


References 

Microsoft Corporation and Cooper Software Inc. (1997). Microsoft Visual Basic 

Version 5.0. 

Moran, M. J. (1990). Second Law Analysis. What is the State of the Art? 

International Symposium: A future for energy. Florence (Italy). Pergamon Press, 

pp. 249-260. 

Morris, D. R., Szargut, J. (1986). Standard Chemical Exergy of some Elements and 

Compounds on the Planet Earth. Energy Vol. 11, pp. 733-749. 

Mothersed, C. T. (1966). Report ORNL-TM-1560, August 1966. 

National Office of Potable Water (NPOW) (1996). Non Conventional Waters Use for 

Drinking Water Supply/Seawater Desalination. Kingdom of Morocco. Private 


Newman, A. (1980). Thermodynamics of Acqueous Systems with Industrial 

Applications. American Chemical Society. Washington DC, USA. 

Omar, A. M. (1981). M. Sc. Thesis. UPM Dharan (Saudi Arabia). 

Ophir, A., Gendel, A. (1999). Development of the World’s Largest Multi-Effect 

Mechanical Vapor Compression (M.E.M.V.C.) Desalination Plants. Proceedings of 


Perry, R. H., Chilton, C. (1984). Manual del Ingeniero Químico. Ed. McGraw-Hill, 

5 th edition. Vol. I, pp. 446. 

Pina, H. L. G. (1979). A Computer Program for the Calculation of the 

Thermodynamic Properties of Water. Revue Generale de Thermique, no. 215, 

pp. 689-693. 

Pisa, J. (1997). Thermoeconomic Analysis of IGCC plants. Ph. D. Thesis. 

Department of Mechanical Engineering. University of Zaragoza. 

Ponce, S. L., Jankel, L. H. (1999). The Value of Water in the 21 st Century – Impact 

on U.S. Desalination. Proceedings of the IDA World Congress on Desalination and 


Powell, M. J. D. (1964). An Efficient Method for Finding the Minimun of a Function 

of Several Variables without Calculate Derivatives. Computer J. Vol. 7, pp. 155-162. 

Prabhakar, S., Hanra, M. S., Misra, B. M., Sadhukan, H. K. (1997). Small 

Desalination Units to Provide Safe Drinking Water in Remote Rural Areas in India. 

Proceedings of the IDA World Congress on Desalination and Water Reuse. Madrid, 

Spain. Vol. I, pp. 3-16. 


References 

Rautenbach, R., Buchel, H. G. (1979). Modular Program for Design and Simulation 

of Desalination Plants. Desalination 31, pp. 71-83. 

Reid, R. C., Prausnitz, J. M., Sherwood, T. K. (1977). The Properties of Gases and 

Liquids. McGraw-Hill. New York, USA. 

Reini, M. (1994). Analisi e Sviluppo dei Metodi Termoeconomi per lo Studio degli 

Impianti di Conversione dell’Energia. Ph. D. Thesis. Università di Padova. 

Royo, F. J. (1994). Las Ecuaciones Características de los Sistemas Térmicos. La 

energía Libre Relativa. Ph. D. Thesis. Dept. of Mechanical Engineering. University 

of Zaragoza. 

Saeed, M. N. (1992). Fuel Efficiencies, Allocation of Fuels and Fuel Cost for Power 

and Desalination in Dual Purpose Plants: A Novel Methodology. Desalination 85, 

pp. 213-229. 

Salisbury, J. K. (1974). Steam Turbines and their Cycles. Krieger Publishing 

Company. New York, USA. 

Sánchez, J. M., Velasco, J., Kindelan, J. M., Andreu, J. (1997). Marbella Seawater 

Desalination Plant: Construction and Start-up Experience. Proceedings of the IDA 

World Congress on Desalination and Water Reuse. Madrid, Spain. Vol. V, 

pp. 463-478. 

Schnakel, H. C. (1958). Formulations for the Thermodynamic Properties of Steam 

and Water. Trans. ASME 80, pp. 959-966. 

Sengers, J. V., Watson, J. T. R. (1986). Improved International Formulations for the 

Viscosity and Thermal Conductivity of Water Substance. Journal of Physical & 

Chemical Reference Data, Vol. 15, no. 4, pp. 1291-1314. 

Sephton, H. H., Solomon, R. L. (1997). Use of Power Plant Turbine Reject Steam to 

Drive Desalination with Enhanced Heat Transfer Performance. Proceedings of the 

IDA World Congress on Desalination and Water Reuse. Madrid, Spain. Vol. IV, pp. 

299-308. 

Sephton, H. H. (1999). Turbine Exhaust Steam Driven Desalination. Proceedings of 


Serra, L. (1994). Optimización Exergoeconómica de Sistemas Térmicos. 

Ph. D. Thesis. Department of Mechanical Engineering. University of Zaragoza. 

Slesarenko, V. N., Shtim, A. S. (1987). Exergy Analysis of Multi-Stage Desalination 

Plants. Desalination 61, pp. 1-5. 


References 

Slesarenko, V. N. (1999). Desalination Plant with Absorption Heat Pump for Power 

Station. Desalination 126, pp. 281-286. Presented at the European Conference on 


Spanish Desalination and Water Reuse Association (AEDyR) (1999). Private 


Spencer, R. C., Cotton, K. C., Cannon, C. N. (1974). A Method of Predicting the 

Performance of Steam Turbine Generators 16.500 kW and Larger. General Electric 

Corp., Publication GER-2007C. 

Spiegler, K. S., El-Sayed, Y. M. (1994). A Desalination Primer. Balaban 

Desalination Publications. Italy. 

Stodola, A. (1927). Steam and Gas Turbines. McGraw Hill Company, Vol. 1, 

pp. 316. New York, USA. 

Stoughton, R. W., Lietzke, M. H. (1965). J. chem. Engng. Data 10, pp. 254. 

Szargut, J. (1980). International Progress in Second Law Analysis. Energy Vol. 5, 

pp. 709-718. 

Szargut, J. (1989). Chemical Exergies of the Elements. Applied Energy 32, pp. 269- 

286. 

Tadros, S., Tadros, N. (1997). Power and Seawater Distillation From Biomass and 

Refuse Fuels. Proceedings of the IDA World Congress on Desalination and Water 

Reuse. Madrid, Spain. Vol. IV, pp. 309-332 

Torres, C. (1991). Exergoeconomía Simbólica. Metodología para el Análisis 

Termoeconómico de los Sistemas Energéticos. Ph. D. Thesis. Department of 

Mechanical Engineering. University of Zaragoza. 

Torres, C., Valero, A., Serra, L., Royo, J. (1999). Structural Theory and 

Thermoeconomic Diagnosis. Part I: On Malfunction and Dysfunction Analysis. 

Proceedings of the ECOS’99. ASME. Tokyo, Japan. pp. 368-373. 

Torres, M., Medina, J. A. (1999). Desalination in Spain, a Race for Lowering Power 

Consumption. Proceedings of the IDA World Congress on Desalination and Water 


Tribus, M., Asimow, R., Richardson, N., Gustaldo, C., Elliot, K., Chambers, J., 

Evans, R. B. (1960). Thermodynamic and Economic Considerations in the 

Preparation of Fresh Water from the Sea. Report no. 59-34. Department of 

Engineering. University of California. 


References 

Tribus, M., Evans, R. B. (1963). The Thermo-Economics of Sea Water Conversion. 

Report no. 62-53. Department of Engineering. University of California. 

Tsatsaronis, G., Winhold, M. (1985a). Exergoeconomic Analysis and Evaluation of 

Energy Conversion Plants, Part I: A New General Methodology. Energy Vol. 10, pp. 

69-80. 

Tsatsaronis, G., Winhold, M. (1985b). Exergoeconomic Analysis and Evaluation of 

Energy Conversion Plants, Part II: Analysis of a Coal Fired Steam Power Plant. 

Energy Vol. 10, pp. 81-94, 1985. 

Tsatsaronis, G. (1987). A Review of Exergoeconomic Methodologies. International 

Symposium on Second Law Analysis of Thermal Systems. Rome (ASME Book 

I00236). ASME, pp. 81-87. New York, USA. 

Tsatsaronis, G. (1994). Invited Papers of Exergoeconomics. Energy Vol. 19, pp. 279. 

Tsatsaronis, G. (1998). Recent Development in Energy Economics. Proceedings of 

ECOS’98. Nancy, France. Vol. I, pp. 37-38. 

United Nations Economic and Social Commission for Western Asia (ECSWA), 1994 

and 1995. Private communication. 

University of Tennessee and Oak Ridge National Laboratory (ORNL) (1999). Netlib 

Repository. A Collection of Mathematical Software. Web page: http://www.netlib.org. 

Valero, A., Lozano, M. A., Muñoz, M. (1986a). A General Theory of Exergy Saving. 

Part I: On the Exergetic Cost. ASME Book H0341A. WAM 1986. AES-Vol 2-3, 

pp. 1-8. 

Valero, A., Lozano, M. A., Muñoz, M. (1986b). A General Theory of Exergy Saving. 

Part II: On the Thermoeconomic Cost. ASME Book H0341A. WAM 1986. AES- 

Vol. 2-3, pp. 9-16. 

Valero, A., Lozano, M. A., Muñoz, M. (1986c). A General Theory of Exergy Saving. 

Part III: Energy Saving and Thermoeconomics. ASME Book H0341A. WAM 1986. 

AES-Vol 2-3, pp. 17-22. 

Valero, A., Torres, C. (1990). On Causality in Organized Energy Systems, Part II: 

Symbolic exergoeconomics. International Symposium: A future for energy. Florence, 

Italy. Pergamon Press, pp. 393-401. 

Valero, A., Serra, L., Torres, C. (1992). A General Theory of Thermoeconomics: Part 

I: Structural Analysis. International Symposium ECOS’92. Zaragoza, Spain. ASME 

Book I00331, pp. 137-145. 


References 

Valero, A., Serra, L., Lozano, M. A. (1993). Structural Theory of Thermoeconomics. 

International Symposium on Thermodynamics and the Design, Analysis and 

Improvement of Energy Systems. Richter H. J. eds. ASME Book no. H00874. New 

Orleans, USA. pp. 189-198. 

Valero, A., Lozano, M. A., Serra, L., Torres, C. (1994). Application of the Exergy 

Cost Theory to the CGAM problem. Energy Vol. 19, no. 13, pp 365-381. 

Valero, A., Lozano, M. A. (1997). An Introduction of Thermoeconomics. Published 

in Developments in the design of thermal systems (Boehm Editor). Cambridge 

University Press. pp. 203-233. 

Valero, A., Correas, L., Serra, L. (1999). On-Line Thermoeconomic Diagnosis of 

Thermal Power Plants. Thermodynamics and Optimization of Complex Energy 

Systems. Klumer Academic Publishers (Bejan and Mamut eds.), pp. 117-136. 

Valero, A., Torres, C., Lerch, F. (1999). Structural Theory and Thermoeconomic 

Diagnosis. Part III: Intrinsic and Induced Malfunctions. Proceedings of the 

ECOS’99 Conference (ASME). Tokyo, Japan. pp. 35-41. 

Vargaftik, N. B. (1978). Handbook of Physical Properties of Liquids and Gases. 

Hemisphere Publishing Corporation. 

VA Tech Wabag (1999). List of References, Thermal Desalination Plants and 

Reverse Osmosis Desalination. Private Communication. 

Villalon, C. (1995). VB Automatic Help Author Version 1.25. 

Von Spakovsky, M. R. (1986). A Practical Generalized Analysis Approach to the 

Optimal Thermoeconomic Design and Improvement of Real-World Thermal 

Systems. Ph. D. Thesis. Georgia Institute of Technology. 

Von Spakovsky, M. R., Evans, R. B. (1993). Engineering Functional Analysis. 

Part I. ASME Journal of energy resources technology, Vol. 115, pp. 86-92. 

Von Spakovsky, M. R. (1994). Application of Engineering Functional Analysis to 

the Analysis and Optimization of the CGAM Problem. Energy Vol. 19, no. 13. 

Wangnick, K. (1998). 1998 IDA Worldwide Desalting Plants Inventory Report 

no. 15. 

Water and Electricity Department (WED) of the United Arab Emirates (UAE) 

(1997). Private Communication. 

Yata, J., Minamiyama, T. (1979). An Equation for Thermal Conductivity of Water 

and Steam. JSME Vol. 22, no. 171, pp. 1234-1242. 


References 

Yusufova, V. D., Pepinov, R. I., Nicolayev, V. A., Zokhrabbekova, G. U., Lobcova, 

N. V., Tuayev, T. D. (1978). Thermophysical Properties of Softened Seawater and 

Salt Solutions Over a Wide Temperature and Pressure Range. Desalination 25, 

pp. 269-280. 

Zaleta, A., Ranz, L., Valero, A. (1998). Towards an Unified Measure of the 

Renewable Resources Availability: The Exergy Method Applied to the Water of a 

River. Energy Conversion and Management 39, 16-18, pp. 1911-1917. 

Zaleta, A. (1997). Conceptos sobre el Diagnóstico y la Evaluación Termoecónomica 

de Turbinas de Vapor. Ph. D. Thesis. Department of Mechanical Engineering. 

University of Zaragoza. 


List of figures 

FIGURE 2.1 General outlay of MSF distillation with brine recycling .................................................... 

FIGURE 2.2 Flow diagram of Multi-Effect Distillation (MED) with thermal vapor compression (TVC) 

FIGURE 2.3 MED process with vertical tube evaporators (VTE) .......................................................... 

FIGURE 2.4 Flow diagram of a vapor compression system with vertical tube evaporators (VTE) ....... 

FIGURE 2.5 Diagram model of a solar still ............................................................................................ 

FIGURE 2.6 Reverse osmosis process..................................................................................................... 

FIGURE 2.7 Reverse osmosis (RO) desalination with Pelton turbine .................................................... 

FIGURE 2.8 Electrodialysis process........................................................................................................ 

FIGURE 3.1 Schematic diagram of a single effect MSF evaporator with recycled brine ....................... 

FIGURE 3.2 Cross-section of a stage in a typical MSF plant ................................................................. 

FIGURE 3.3 Temperature profile of a recycle brine MSF plant ............................................................. 

FIGURE 3.4 A general stage in a MSF plant........................................................................................... 

FIGURE 3.5 Heat input section ............................................................................................................... 

FIGURE 3.6 Mixing and splitting points in the MSF desalination plant................................................. 

FIGURE 3.7 Solution algorithm of a MSF desalination plant model...................................................... 

FIGURE 3.8 Correspondence between the Top Brine Temperature and distillate output....................... 

FIGURE 3.9 Brine recirculation as a function of the distillate output..................................................... 

FIGURE 3.10 Make-up feed water as a function of the distillate output .................................................. 

FIGURE 3.11 Seawater to reject section as a function of the distillate output.......................................... 

FIGURE 3.12 Top brine temperature depending on the seawater temperature and distillate 

production. Data collected during the year 1997................................................................ 

FIGURE 3.13 Recycle brine flow as a function of the seawater temperature and production. 

Real data collected in the MSF distillers during 1997........................................................ 

FIGURE 3.14 Make-up feed flow obtained for each range of seawater temperature when real 

data are computed. Average data of 1997 .......................................................................... 

FIGURE 3.15 Seawater to reject flow correlations for different seawater temperatures entering 

the MSF plant. Data collected during the year 1997 .......................................................... 


37 

39 

40 

42 

44 

46 

47 

50 

54 

55 

56 

58 

62 

63 

68 

72 

73 

73 

73 

74 

74 

75 

75

458 


FIGURE 4.1 Schematic diagram of the power generation plant. Main significant flows are 

numbered for later descriptions and equations ................................................................... 

FIGURE 4.2 Schematic diagram of a turbine section .............................................................................. 

FIGURE 4.3 Isoentropic and real expansion of the steam in a turbine section........................................ 

FIGURE 4.4 TTD differences in an HP heater ........................................................................................ 

FIGURE 4.5 TTD differences in an LP heater......................................................................................... 

FIGURE 4.6 Isoentropic and real compression process in a pump.......................................................... 

FIGURE 4.7 Gland and seal steam system .............................................................................................. 

FIGURE 4.8 Leakage flows and seals of a steam turbine........................................................................ 

FIGURE 4.9 Algorithm to solve the power plant model using the Powell hybrid method ..................... 

FIGURE 4.10 Last stage of LP turbine acting as a compressor................................................................. 

FIGURE 4.11 Power plant scheme in the NTW Model. Some flowstreams are renumbered 

with respect fig. 4.1............................................................................................................. 

FIGURE 5.1 SIMTAW MSF process window ........................................................................................ 

FIGURE 5.2 SIMTAW power plant window .......................................................................................... 

FIGURE 6.1 Physical structure of the co-generation plant...................................................................... 

FIGURE 6.2 Productive structure of the cogeneration plant ................................................................... 

FIGURE 6.3 Generic component scheme ................................................................................................ 

FIGURE 6.4 Economic resources scheme ............................................................................................... 

FIGURE 6.5 Fuel / Product diagram and fuel and product exergy flows (kW) in design 

conditions for the co-generation plant shown in figure 6.1 ................................................ 

FIGURE 6.6 Fuel impact and technical saving ........................................................................................ 

FIGURE 6.7 Malfunction and fuel impact............................................................................................... 

FIGURE 6.8 Analysis of the irreversibility causes (kW)......................................................................... 

FIGURE 6.9 Analysis of fuel impact (kW).............................................................................................. 

FIGURE 7.1 Productive structure of the simple co-generation system ................................................... 

FIGURE 7.2 Physical structure of the power plant considered for the thermoeconomic model ............. 

FIGURE 7.3 Physical structure of the MSF plant considered for the thermoeconomic analysis ............ 

FIGURE 7.4 F-P description in steam power plant.................................................................................. 

FIGURE 7.5 Productive structure of the power plant in extraction mode ............................................... 

FIGURE 7.6 Changes applied to extraction mode productive structure (figure 7.5) when 

the plant operates in condensing mode ............................................................................... 


78 

80 

81 

82 

84 

88 

88 

89 

92 

93 

94 

101 

103 

126 

130 

140 

142 

145 

148 

166 

150 

152 

161 

163 

165 

167 

169 

170


FIGURE 7.7 Productive structure corresponding to extraction mode with low energy production 

in a dual-purpose plant. Changes with respect to figure 7.5............................................... 

FIGURE 7.8 Productive structure of the steam power plant in parallel and twin extraction mode. 

Changes with respect to figure 7.5 ..................................................................................... 

FIGURE 7.9 Productive structure of the steam power plant in desalination or twin desalination mode 

FIGURE 7.10 F-P definition in the MSF unit............................................................................................ 

FIGURE 7.11 Productive structure of the MSF unit.................................................................................. 

FIGURE 7.12 Physical model considered in the thermoeconomic analysis of the MSF plant ................. 

FIGURE 7.13 Impact on fuel analysis when the efficiency of the HPT4 is decreased 10% ..................... 

FIGURE 7.14 Irreversibility increase analysis with the inefficiency in the HPT4.................................... 

FIGURE 7.15 Additional fuel consumption when varying the isoentropic efficiency in HPT4 ............... 

FIGURE 7.16 Unit electricity cost when the isoentropic HPT4 efficiency is modified............................ 

FIGURE 7.17 Unit distilled water cost when the isoentropic HPT4 efficiency is modified ..................... 

FIGURE 7.18 Impact on fuel analysis when the fouling in BH is neglected ........................................ 

FIGURE 7.19 Irreversibility increase in the MSF with BH = 0. NTOS case ........................................ 

FIGURE 7.20 Impact on fuel analysis when the fouling in heater is varied ............................................. 

FIGURE 7.21 Monetary cost of distillate when the fouling in heater is varied......................................... 

FIGURE 7.22 Impact on fuel analysis without fouling in RCS. MCR case .......................................... 

FIGURE 7.23 Irreversibility increase analysis of section 7.3.2.3 .......................................................... 

FIGURE 7.24 Impact on fuel depending on fouling in recovery section .................................................. 

FIGURE 7.25 Monetary cost of electricity depending on the fouling in recovery section ....................... 

FIGURE 7.26 Cost in $ per cubic meter of water when recovery section fouling is varied...................... 

FIGURE 7.27 Impact on fuel analysis in section 7.3.2.4 ....................................................................... 

FIGURE 7.28 Irreversibility increase in section 7.3.2.4............................................................................ 

FIGURE 7.29 Additional fuel consumption due to inefficiencies in several components 

of the power plant ............................................................................................................... 

FIGURE 7.30 Electricity cost with five inefficiencies in the power plant ................................................ 

FIGURE 7.31 Water cost under different degrees of inefficiency in five components ......................... 

FIGURE 7.32 Impact on fuel analysis without fouling in distillers ......................................................... 

FIGURE 7.33 Increase of irreversibility when fouling is neglected in MSF plant ................................ 

FIGURE 7.34 Impact on fuel due to several inefficiencies in the MSF plant. 

Unit exergy cost of steam and electricity is 2.55 and 2.85 respectively............................. 

FIGURE 7.35 Water cost when the fouling in three distillers is varied .................................................... 

FIGURE 7.36 Malfunctions with an inefficiency of 5 ºC in the TTD of HPH1 heater under 

varying loads in the steam power plant .............................................................................. 


170 

171 

171 

172 

174 

178 

208 

208 

219 

220 

220 

232 

232 

235 

235 

246 

246 

249 

249 

250 

259 

259 

264 

264 

265 

274 

274 

277 

279 

280

460 


FIGURE 7.37 Malfunctions generated when the FP is working with an isoentropic efficiency 

12% lower than the expected under four different loads in the steam power plant ............ 

FIGURE 7.38 Malfunctions generated by an inefficiency of 5% in the isoentropic efficiency 

of the HPT1 under varying loads in the steam power plant................................................ 

FIGURE 7.39 Malfunctions generated in the fourth section of the HPT under a 10% decrease 

in its isoentropic efficiency................................................................................................. 

FIGURE 7.40 Malfunctions in LPT1 under varying loads in the steam power plant and a 15% 

decrease in isoentropic efficiency ....................................................................................... 

FIGURE 7.41 Malfunctions provoked by the fouling reduction in heater at different loads..................... 

FIGURE 7.42 Malfunctions generated in the MSF plant at different loads with no fouling 

in the recovery section ........................................................................................................ 

FIGURE 7.43 Malfunctions generated in the MSF plant when the fouling in reject section 

is neglected for the two analyzed loads .............................................................................. 

FIGURE 7.44 Impact on fuel in the MSF plant when the fouling is neglected in the three distillers. 

Three loads at 32 ºC seawater are included ........................................................................ 

FIGURE 7.45 Physical model applied to the thermoeconomic optimization ............................................ 

FIGURE 7.46 Productive structure of the thermoeconomic model applied to the 

thermoeconomic optimization ............................................................................................ 

FIGURE 7.47 Optimization algorithm to find the minimum cost of the plant using local optimization... 

FIGURE 7.48 Speed of convergence of the local variables that are efficiencies....................................... 

FIGURE 7.49 Evolution of the local variables that are TTD in heaters .................................................... 

FIGURE 7.50 Minimization of the global cost of the system.................................................................... 

FIGURE 7.51 Sensitivity analysis of the energetic efficiency of the boiler around 

the optimum point ( η = 0.8608) ........................................................................................ 

1 

FIGURE 7.52 Sensitivity analysis of the efficiency of the first section of the high-pressure 

turbine around the optimum point ( η = 0.924).................................................................. 

FIGURE 7.53 Exergy cost of water (k* of steam and electricity entering the MSF is the unity), 

and distillate temperature at different loads at 32 ºC seawater ........................................... 

2 

FIGURE A1.1 Impact on fuel analysis with an inefficiency in HPH1 ................................................... 341 

FIGURE A1.2 Irreversibility analysis when the TTD in HPH1 is increased 5 ºC .................................. 341 

FIGURE A1.3 Impact on fuel associated with a variation in the TTD of HPH1. 

122 MW power plant production ........................................................................................ 343 

FIGURE A1.4 Cost of electricity when varying TTD in HPH1 (MCR performance case)........................ 343 

FIGURE A1.5 Cost of water when varying TTD in the first HPH (MCR performance case) ................... 344 

FIGURE A1.6 Impact on fuel analysis when a inefficiency in F in detected ......................................... 354 

FIGURE A1.7 Irreversibility analysis with the irreversibility in FP ...................................................... 354 


281 

281 

282 

282 

283 

283 

284 

284 

297 

297 

304 

305 

305 

306 

309 

309 

315


FIGURE A1.8 Effect of feed pump efficiency on fuel consumption. Variational study in the 

MCR performance case ...................................................................................................... 355 

FIGURE A1.9 Effect of pump inefficiency on electricity cost (MCR performance case) ......................... 356 

FIGURE A1.10 Water cost when the efficiency of the feed pump is varied................................................ 356 

FIGURE A1.11 Impact on fuel analysis when the HPT1 efficiency is 5% less than the expected .......... 366 

FIGURE A1.12 Irreversibility analysis with the inefficiency in HPT1 .................................................... 366 

FIGURE A1.13 Model linearity with respect to an inefficiency in HPT1 ................................................... 368 

FIGURE A1.14 Cost of electricity depending on the degree of inefficiency applied to HPT1 (MCR case) 368 

FIGURE A1.15 Cost of water when the isoentropic efficiency is varied from –5% to 5% with 

respect to design efficiency (MCR case) ............................................................................ 369 

FIGURE A1.16 Impact on fuel analysis, section A1.4 ............................................................................. 379 

FIGURE A1.17 Irreversibility analysis in section A1.4 ........................................................................... 379 

FIGURE A1.18 Effect on the fuel consumption when the degree of inefficiency in the LPT 

is varied from the design point (MCR case)....................................................................... 380 

FIGURE A1.19 Cost of electricity for inefficiencies in LPT1 (MCR case)................................................. 381 

FIGURE A1.20 Water cost per cubic meter for inefficiencies in LPT1. 122 MW in extraction 

mode (MCR case) ............................................................................................................... 381 

FIGURE A1.21 Impact on fuel analysis in section A1.5 .......................................................................... 387 

FIGURE A1.22 Irreversibility increase in section A1.5 ........................................................................... 387 

FIGURE A1.23 Effect on fuel consumption when the fouling in recovery section is 

gradually decreased. 1,900 T/h and 32º C seawater ........................................................... 393 

FIGURE A1.24 Cost of a cubic meter of water depending on the fouling in the recovery section ............. 393 

FIGURE A1.25 Impact on fuel analysis, section A1.6 ............................................................................. 404 

FIGURE A1.26 Increase of irreversibility in section A1.6 ....................................................................... 404 

FIGURE A1.27 Effect on fuel consumption when the fouling in reject is varied. Nominal-temperature 

operation in summer (NTOS, i.e., 1,900 T/h and 32 ºC seawater temperature)................. 406 

FIGURE A1.28 Variation of the water cost when fouling in the reject section is decreased from 

the design value to zero ...................................................................................................... 407 


List of tables 

TABLE 1.1 Ground water disposal and renewable water resources in the Gulf Countries in 1994 

(Alawadhi, 1999) .............................................................................................................. 

TABLE 1.2 Water demand for the Gulf Countries in 1990 (ESCWA, 1994)...................................... 

TABLE 1.3 Total installed capacity and production in the seawater desalination plant of the 

Gulf Area in year 1994 (Alawadi, 1999; Al-Gobaisi, 1999) ............................................ 

TABLE 1.4 Contracted capacity of freshwater production from seawater and all waters with the 

existing process. The total capacity is 12.8 million cubic meters per day and 21 million 

cubic meters per day, respectively. Data collected in 1996 (Alawadhi, 1999) ................ 

TABLE 1.5 Natural resources in the pacific region in the year 1998 (Goto et al., 1999).................... 

TABLE 1.6 Water use trends in the Pacific region (Goto et al., 1999)................................................ 

TABLE 1.7 Desalination installations in the Pacific region. Data from 1998 (Goto et al., 1999)....... 

TABLE 1.8 Water disposal in the African region in 1995................................................................... 

TABLE 1.9 Water withdrawal in North African countries. Data collected in 1990 for Algeria 

and Tunisia; for Egypt and Morocco data from 1992 (Al-Gobaisi, 1997) ....................... 

TABLE 1.10 Water use in the U.S. in 1995 (Gleick, 1998)................................................................... 

TABLE 1.11 Desalinated water in Spain during the year 1998 (Torres and Medina, 1999) ............. 

TABLE 1.12 Some of the RO desalination plants installed in Spain (Cadagua, 1999; Sánchez 

et al., 1997; Fayas and Novoa, 1997; Torres et al., 1999; AECYR, 1999) ...................... 

TABLE 1.13 Specific consumption of the thermal desalination processes. Data obtained from 

several sources (Fisia-Italimpianti, 1999; I.D.E., 1999)................................................... 

TABLE 3.1 Fouling factors of the heat reject section in MSF Plants .................................................. 

TABLE 4.1 Typical x, y, and z coefficient values for the inlet TTD’s in an HP heater ...................... 

TABLE 4.2 Typical x, y, z, a, and b coefficient values for the outlet TTD’s in an HP heater ............ 

TABLE 4.3 Typical x, y, and z coefficient values for the inlet TTD’s in an LP heater ...................... 

TABLE 4.4 Typical x, y, z, a, and b coefficient values for the outlet TTD’s in a LP heater............... 

TABLE 4.5 x, y, z, a, b, and c coefficient values in deaerator............................................................. 

TABLE 4.6 Values of the a coefficient for each pipe of the power model .......................................... 


21 

21 

22 

23 

23 

24 

24 

25 

25 

26 

27 

28 

29 

76 

83 

83 

84 

84 

85 

87

464 


TABLE 4.7 Kd and Kd’ constants of the gland and seal steam system ............................................... 

TABLE 4.8 Operating mode and mathematical model corresponding to the performance 

data cases .......................................................................................................................... 

TABLE 5.1 Input variables for the MCR (maximum continous rating, producing both electricity 

and water) case.................................................................................................................. 

TABLE 5.2 Model validation for the MCR case.................................................................................. 

TABLE 5.3 Input variables for the MR (maximum rating, producing only electricity) 

performance case .............................................................................................................. 

TABLE 5.4 Model validation for the MR case .................................................................................... 

TABLE 5.5 Input variables for the PL115 performance case (partial load with 115 MW 

of electricity and a heat extraction to MSF of 145 Gcal/h) .............................................. 

TABLE 5.6 Model validation for the PL115 performance data case ................................................... 

TABLE 5.7 Input variables for the PL85 performance case (partial load with 85 MW 

of electricity and 145 Gcal/h of extraction heat flow) ...................................................... 

TABLE 5.8 Model validation for the PL85 performance case............................................................. 

TABLE 5.9 MSL2 performance case (minimum stable load with 45 MW of electricity 

and a combined heat extraction flow of 145 Gcal/h). Main input data ............................ 

TABLE 5.10 Model validation for the MSL2 performance case ........................................................... 

TABLE 5.11 Input data of the MSL3 performance case (minimum stable load with two 

extractions of 150 and 145 Gcal/h to MSF units)............................................................. 

TABLE 5.12 Model validation for the MSL3 performance case ........................................................... 

TABLE 5.13 Input data of the MSL4 performance case (minimum stable load with the maximum 

heat flow extraction to MSF unit: 170 Gcal/h) ................................................................. 

TABLE 5.14 MSL4 performance case. Model validation...................................................................... 

TABLE 5.15 Main input data of the ODOB case (one desalination-one boiler) ................................... 

TABLE 5.16 Model validation of the ODOB case................................................................................. 

TABLE 5.17 Main input data of the TDOB case (two desalination-one boiler).................................... 

TABLE 5.18 Model validation data for the TDOB case ........................................................................ 

TABLE 5.19 Main input data of the VWO performance case (maximum capacity of the steam 

turbine with and extraction heat flow of 170 Gcal/h to MSF).......................................... 

TABLE 5.20 Model validation data for the VWO case ......................................................................... 

TABLE 5.21 Input data of the COC performance case (boiler peak load at least 5% more than 

the MCR case) .................................................................................................................. 

TABLE 5.22 Model validation data for the COC case........................................................................... 


89 

96 

106 

106 

107 

107 

108 

108 

109 

109 

110 

110 

111 

111 

112 

112 

113 

113 

114 

114 

115 

115 

116 

116


TABLE 5.23 Input data and performance parameters of the NTOS case (normal-temperature 

operation in summer)........................................................................................................ 

TABLE 5.24 Model validation of the NTOS performance case ............................................................ 

TABLE 5.25 Input data and performance parameters of the HTOS case (high-temperature 


TABLE 5.26 Model validation of the HTOS performance case ............................................................ 

TABLE 5.27 Some input data and performance parameters of the LTOS case (low-temperature 


TABLE 5.28 Model validation. LTOS performance case in MSF distillers.......................................... 

TABLE 5.29 Some input data and performance parameters of the HTOW case (high-temperature 

operation in winter) .......................................................................................................... 

TABLE 5.30 Model validation of HTOW case of the MSF plant ......................................................... 

TABLE 6.1 Fuel and product definitions for typical dual-purpose power and desalination 

plant units ..................................................................................................................... 

TABLE 6.2 Fuels and Products of the components of the co-generation plant ................................... 

TABLE 6.3 Characteristic equations of the cogeneration plant........................................................... 

TABLE 6.4 Design and operation exergy flow values of the cogeneration plant (figure 6.1) ............ 

TABLE 6.5 Fuel/Product definition corresponding to figure 6.5 ........................................................ 

TABLE 6.6 Increase of unit consumption. (100 


119 

119 

120 

120 

121 

121 

122 

122 

129 

131 

132 

144 

146 

∆κij) 

......................................................................... 146 

TABLE 6.7 Irreversibility matrix and unit cost of product.................................................................. 

TABLE 6.8 Malfunction and dysfunction table in (kW) ..................................................................... 

TABLE 7.1 Fuel, product, characteristic equation and exergy cost balance in the simple 

co-generation system ........................................................................................................ 

TABLE 7.2 Results of the simple co-generation system model, MCR case........................................ 

TABLE 7.3 Description of components appearing in figure 7.2 ......................................................... 

TABLE 7.4 Components description from figure 7.3. Note that component no. 1 is not described 

in physical model but is included in other schemes ......................................................... 

TABLE 7.5 Exergy flows and characteristic equations of components in the steam power plant 

(extraction mode).............................................................................................................. 

TABLE 7.6 Exergy flows and characteristic equations for the components of the MSF plant ........... 

TABLE 7.7 System of equations providing the exergy cost of the steam power plant 

(extraction mode).............................................................................................................. 

TABLE 7.8 System of equations providing the exergy costs of the MSF plant (figure 7.11) ............. 

151 

152 

162 

162 

164 

165 

176 

179 

182 

184

466 


TABLE 7.9 Case studies of the exergy cost analysis (PTC: Performance Test Case of the dual 

plant; Gc: Natural gas consumed; CBS: Cleaning Ball System was used) ...................... 

TABLE 7.10 Exergy (kW fuel/kW product) unit costs k* of most significant flows of the dual plant . 

TABLE 7.11 Exergoeconomic (monetary) unit costs ($/GJ) of most significant flows of a dual 

power and desalination plant. Cost of water c* 

D is expressed in $/m3, 

and electricity 

cost of is also expressed in $/kW·h (c* 

GEN* ) ................................................................... 

TABLE 7.12 Irreversibilities (exergy destruction, kW) in the different components of the dual 

plant. MSF unit is considered a component...................................................................... 

TABLE 7.13 Isoentropic efficiencies of pumps and turbine sections of the power plant...................... 

TABLE 7.14 Product and fuel (kW), and exergy efficiency (%) values for the power and 

MS plants. Note: The efficiency of the boiler is not included in the final efficiency....... 

TABLE 7.15 Unit exergy costs k* (kW/kW) of component products in the steam power plant 

coupled with a MSF unit................................................................................................... 

TABLE 7.16 Costing equation parameters for an MSF and power plant (El-Sayed, 1996). 

Units: ca k$/ft2 

2 

, A ft , M lb/s, Q kW, Pi, 

Pe 

psia, Ti 

R, ∆T 

F, ∆P, 

dP psi, e = η/1– 

η. 

Subscripts: i, inlet; e, exit; t, tube; s, shell; m, mean (LTMD) ........................................ 

TABLE 7.17 Component parameters in Boehm (1987) equations......................................................... 

TABLE 7.18 Costing equations proposed by Frangopoulos (1991) ...................................................... 

TABLE 7.19 Cost equations proposed by Lozano et al. (1996). η exergetic efficiency, B exergy 

flow of product, S negentropy, vw velocity of tubes , W power, e eficiency of the 

condenser (= T0 

(s2 

– s1)/(h2 

– h1)) 

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

TABLE 7.20 Price breakdown per section in a dual-purpose plant ....................................................... 

TABLE 7.21 Thermoeconomic costs of distilled water and electricity of the analyzed 

dual-purpose plant............................................................................................................. 

TABLE 7.22 Thermoeconomic cost of electricity ($/kW·h) and water ($/m3) 

for the cases 

studied in the exergetic cost analysis................................................................................ 

TABLE 7.23 F-P diagram in design, output power of 122 MW ........................................................... 209 

TABLE 7.24 F-P values with inefficiency in HPT4 (10% lower efficiency) .................................... 210 

TABLE 7.25 KP matrix in design (122 MW) ....................................................................................... 211 

TABLE 7.26 KP matrix with inefficiency in HPT4 (10%) ................................................................... 212 

TABLE 7.27 Variation de KP with inefficiency in HPT4...................................................................... 213 

TABLE 7.28 Irreversibility matrix I with an inefficiency in HPT4 ...................................................... 214 

TABLE 7.29 Dysfunction/malfunction matrix with inefficiency in HPT4 (10% isoentropic eff.) ....... 215 

TABLE 7.30 Malfunction matrix with inefficiency in HPT4 (1% isoentropic eff. is varied) ........... 216 

TABLE 7.31 F-P values (design) for the MSF plant. Nominal production in summer. .................... 222 

TABLE 7.32 F-P values without fouling in heater. Nominal production, 32 ºC seawater ................ 223 


185 

186 

187 

188 

189 

190 

191 

193 

194 

194 

195 

196 

197 

197


TABLE 7.33 KP matrix in design ...................................................................................................... 224 

TABLE 7.34 KP matrix without fouling in heater. NTOS data case .................................................... 225 

TABLE 7.35 Variation of the KP matrix without fouling in heater. NTOS case .............................. 226 

TABLE 7.36 Irreversibility matrix without fouling in heater. 1,900 T/h and 32 ºC seawater temp ..... 227 

TABLE 7.37 Malfunction/dysfunction matrix without fouling in heater. NTOS case ..................... 228 

TABLE 7.38 Malfunction matrix varying fouling in heater 0.00001 m 2 K/W in NTOS case .......... 229 

TABLE 7.39 F-P values in design, 122 MW output power .................................................................. 238 

TABLE 7.40 F-P values without fouling in recovery section. MCR case ............................................ 239 

TABLE 7.41 KP matrix in design. MCR case ...................................................................................... 240 

TABLE 7.42 KP matrix without fouling in recovery section. MCR case ............................................ 241 

TABLE 7.43 Variation of KP without fouling in recovery section. MCR case .................................... 242 

TABLE 7.44 Irreversibility matrix without fouling in recovery section (MCR case) .......................... 243 

TABLE 7.45 Malfunction/dysfunction matrix without fouling in recovery section (MCR case) ......... 244 

TABLE 7.46 Malfunction matrix when the fouling in recovery is varied 0.00001 m 2 K/W 

in MCR case ................................................................................................................. 245 

TABLE 7.47 F-P values in design, 122 MW output power ............................................................... 252 

TABLE 7.48 F-P values with inefficiencies in five components (MCR case) ................................... 253 

TABLE 7.49 KP matrix in design (MCR Case) ............................................................................... 254 

TABLE 7.50 KP matrix with several inefficiencies in MCR case ..................................................... 255 

TABLE 7.51 Variation of KP matrix with several inefficiencies in MCR case ................................. 256 

TABLE 7.52 Irreversibility matrix with five inefficiencies in power plant (MCR case ............................ 257 

TABLE 7.53 Malfunction/dysfunction matrix with five inefficiencies in MCR case ............................... 258 

TABLE 7.54 Comparison of individual inefficiencies and combined inefficiencies in the 

power plant. The first five columns are individual inefficiencies, the sixth is 

the sum of the five inefficiencies and the seventh is the malfunctions generated 

with the five combined inefficiencies. MCR conditions .................................................. 261 

TABLE 7.55 Intrinsic and induced malfunctions (MF) and impact on fuel (MF*) of the power 

plant. 122 MW load.......................................................................................................... 262 

TABLE 7.56 The first column represents the X-axis in charts, corresponding to the inefficiency 

associated with each component ...................................................................................... 263 

TABLE 7.57 F-P values in design, nominal production with 32 ºC seawater ...................................... 267 

TABLE 7.58 F-P values without fouling in heater, recovery and reject section. NTOS case ............. 268 

TABLE 7.59 KP matrix in design (NTOS case) ............................................................................... 269 

TABLE 7.60 KP matrix with three inefficiencies in distillers (NTOS case) ...................................... 270 



TABLE 7.61 Variation of KP when the fouling in distillers is zero (NTOS case). ........................... 271 

TABLE 7.62 Irreversibility matrix with three inefficiencies in distillers. NTOS case ...................... 272 

TABLE 7.63 Malfunction/dysfunction matrix when fouling in distillers is zero (NTOS case). ...... 273 

TABLE 7.64 Correspondence between the X-label and fouling ............................................................ 276 

TABLE 7.65 Comparison between the sum of individual inefficiencies and three combined 

inefficiencies in the MSF unit. The first three columns are individual inefficiencies, 

the fourth is the sum of the three inefficiencies and the fifth is the malfunctions 

generated with the three combined inefficiencies. Nominal production with 32 ºC 

seawater (NTOS case) ...................................................................................................... 277 

TABLE 7.66 Intrinsic (MFl) and induced (MFg) malfunctions of the MSF plant and their costs 

(impact on fuel, MF*) under nominal production (32 ºC seawater temperature)............. 278 

TABLE 7.67 Impact on fuel associated with the inefficiencies in the power plant in extraction 

mode (MCR case) ............................................................................................................. 285 

TABLE 7.68 Cost variation associated with the inefficiencies in the power plant in co-generation 

mode (MCR) ..................................................................................................................... 286 

TABLE 7.69 Impact on fuel associated with the inefficiencies in the MSF plant (isolated from 

the power plant). 32 ºC Seawater...................................................................................... 286 

TABLE 7.70 Additional cost associated with the inefficiencies in the MSF plant (isolated from 

the power plant). 32 ºC Seawater (NTOS case)................................................................ 287 

TABLE 7.71 Impact on fuel associated with the inefficiencies in the MSF plant (coupled with 

the power plant) ................................................................................................................ 287 

TABLE 7.72 Additional cost associated with the inefficiencies in the MSF plant (coupled with 

the power plant) ................................................................................................................ 287 

TABLE 7.73 Intrinsic and induced malfunctions at 122 MW ............................................................... 290 

TABLE 7.74 Intrinsic and induced malfunctions at 140 MW ............................................................... 291 

TABLE 7.75 Intrinsic and induced malfunctions at 90 MW ................................................................. 292 

TABLE 7.76 Intrinsic and induced malfunctions at 60 MW ................................................................. 293 

TABLE 7.77 Intrinsic and induced malfunctions at 1,900 T/h ............................................................. 294 

TABLE 7.78 Intrinsic and induced malfunctions at 2,400 T/h .......................................................... 295 

TABLE 7.79 Resources and products in the productive structure of the thermoeconomic model. 

The superscript (´) is extraction mass flow rate, mdes is the steam flow to MSF unit 

(89.7 kg/s), D is the distilled water mass flow (2000 T/h) and b w is the exergy of 

water leaving the MSF plant (7 kJ/kg·K).......................................................................... 298 

TABLE 7.80 Equations of the thermoeconomic model applied in the local optimization..................... 299 

TABLE 7.81 Values of parameter a in the capital cost equation of a heater ......................................... 303 

TABLE 7.82 Results of the local variables in the optimization process ............................................. 304 

TABLE 7.83 Main physical variables after the optimization process.................................................... 306 



TABLE 7.84 Results for the optimization of the dual-purpose plant in the MCR performance 

case. Exergy flows are described in figure 7.45. c is the cost (10 –6 $/kJ), with a 

fuel cost cf of 2×10–6 $/kJ and includes the capital cost factor kZ (kZ = ϕ·Z/P); 

Z (10 6 $) is the capital cost of the component.................................................................. 307 

TABLE 7.85 Different configurations in a dual power plant with 6 co-generation units, applied 

to two different power and water demands ...................................................................... 311 

TABLE 7.86 Price for water and electricity depending on the policy applied ...................................... 312 

TABLE 7.87 Benefit obtained in the two examples with five different price policies see 

previous table) .................................................................................................................. 312 

TABLE A1.1 F-P values in design (MCR case) ................................................................................ 333 

TABLE A1.2 F-P values in operation with 5 ºC TTD respect to design ............................................. 334 

TABLE A1.3 KP matrix in design (MCR case) ................................................................................ 335 

TABLE A1.4 KP matrix with inefficiency in HPH1 (MCR case) ...................................................... 336 

TABLE A1.5 Variation of KP matrix when TTD in the HPH1 is 5 ºC higher than the expected ........ 337 

TABLE A1.6 Irreversibility matrix with the inefficiency in HPH1 .................................................... 338 

TABLE A1.7 Malfunction/Dysfunction matrix when the TTD in HPH1 is 5 ºC higher....................... 339 

TABLE A1.8 Malfunction matrix when TTD in HPH1 is varied 1 ºC ................................................ 340 

TABLE A1.9 F-P design values ........................................................................................................ 346 

TABLE A1.10 F-P values with inefficiency in FP: –12% in its efficiciency ........................................... 347 

TABLE A1.11 KP matrix in design (MCR case) ............................................................................. 348 

TABLE A1.12 KP matrix when the inefficiency in FP is detected ...................................................... 349 

TABLE A1.13 Variation of the KP matrix when the FP is working improperly.................................... 350 

TABLE A1.14 Irreversibility matrix with –12% in the FP efficiency .................................................. 351 

TABLE A1.15 Dysfunction table and malfunction array when the FP is working with 12% 

lower efficiency ......................................................................................................... 352 

TABLE A1.16 Malfunction matrix when the efficiency of the FP varies 1% ............................................ 353 

TABLE A1.17 F-P values without any inefficiency. MCR case ......................................................... 358 

TABLE A1.18 F-P values when the HPT1 decreases 5% its efficiency (MCR case) ............................ 359 

TABLE A1.19 KP matrix in design (MCR case) ..................................................................................... 360 

TABLE A1.20 KP matrix when the inefficiency in HPT1 is 5% in its efficiency ................................. 361 

TABLE A1.21 Variation of the KP with the inefficiency in HPT1 (MCR case) ................................... 362 

TABLE A1.22 Irreversibility matrix with the inefficiency in HPT1 (MCR case) ................................. 363 

TABLE A1.23 Dysfunction/malfunction table when the efficiency of the HPT1 is decreased 5% ........ 364 



TABLE A1.24 Malfunction matrix when the efficiency of the HPT1 is varied 1% ................................ 365 

TABLE A1.25 F-P values in design (MCR case) ..................................................................................... 371 

TABLE A1.26 F-P values with the inefficiency in LPT1, MCR case ..................................................... 372 

TABLE A1.27 KP matrix in design, MCR case ....................................................................................... 373 

TABLE A1.28 KP matrix when the efficiency in the LPT1 is decreased 15%, MCR case ..................... 374 

TABLE A1.29 Variation of the KP matrix with an inefficiency in LPT1, MCR case ............................. 375 

TABLE A1.30 Irreversibility matrix with the efficiency of the LPT1 decreased 15%, MCR case ......... 376 

TABLE A1.31 Dysfunction/malfunction table for an inefficiency in the LPT1 (15%), MCR case ......... 377 

TABLE A1.32 Malfunction matrix when the efficiency of the LPT1 is varied 1%, MCR case .............. 378 

TABLE A1.33 F-P values in design, NTOS case ..................................................................................... 383 

TABLE A1.34 F-P values with fouling in RCS=0, NTOS case .............................................................. 384 

TABLE A1.35 KP matrix in design, NTOS case ..................................................................................... 385 

TABLE A1.36 KP matrix with an inefficiency in RCS, NTOS case ....................................................... 386 

TABLE A1.37 Variation of the KP matrix when the fouling in RCS is neglected .................................. 389 

TABLE A1.38 Irreversibility matrix without fouling in RCS .................................................................. 390 

TABLE A1.39 Dysfunction/malfunction table without fouling in RCS, NTOS case .............................. 391 

TABLE A1.40 Malfunction matrix when the fouling in RCS is varied 0.00001 m 2 K/W ...................... 394 

TABLE A1.41 F-P values in design, NTOS case ..................................................................................... 397 

TABLE A1.42 F-P values when the fouling in RJS = 0, NTOS case ...................................................... 398 

TABLE A1.43 KP matrix in design, NTOS case ..................................................................................... 399 

TABLE A1.44 KP matrix with the inefficiency in RJS, NTOS case ....................................................... 400 

TABLE A1.45 Variation of the KP matrix when the inefficiency in RJS is detected ............................. 401 

TABLE A1.46 Irreversibility matrix corresponding to reject fouling in RJS, NTOS case ...................... 402 

TABLE A1.47 Dysfunction/malfunction table when the fouling in RJS = 0 ........................................... 403 

TABLE A1.48 Malfunction matrix when the fouling in RJS is varied 0.00001 m 2 K/W ..................... 408 

TABLE A2.1 Liquid phase composition of Reference Ambient (Szargut, 1989; Morris, and 

Szargut, 1986)................................................................................................................... 413 


Índex 

Resumen ..................................................................................................................................................... 11 

Abstract ..................................................................................................................................................... 15 

CHAPTER 1. Introduction ..................................................................................................................... 17 

1.1 Water requirements ................................................................................................................. 18 

1.2 Water quality and uses ............................................................................................................ 18 

1.3 World water resources and demand ........................................................................................ 19 

1.3.1 Gulf Region ................................................................................................................. 19 

1.3.2 Pacific Region and India ............................................................................................. 23 

1.3.3 North Africa ................................................................................................................. 25 

1.3.4 US experience and the Caribbean Islands ................................................................... 26 

1.3.5 Mediterranean area and Europe ................................................................................... 27 

1.4 Desalination and energy .......................................................................................................... 29 

1.5 Why a MSF and power plant? ................................................................................................. 30 

1.6 Thermoeconomic analysis ....................................................................................................... 32 

1.7 Ph. D. Thesis development ...................................................................................................... 33 

CHAPTER 2. Desalination processes ..................................................................................................... 35 

2.1 Phase change processes: distillation and freezing ................................................................... 36 

2.1.1 Multi-stage flash process (MSF) ................................................................................. 36 

2.1.2 Multi-effect distillation (MED) ................................................................................... 38 

2.1.3 Vapor compression (VC) ............................................................................................. 41 

2.1.4 Solar distillation ........................................................................................................... 43 

2.1.5 Freezing process .......................................................................................................... 44 

2.2 Processes using membranes .................................................................................................... 45 

2.2.1 Reverse osmosis .......................................................................................................... 45 

2.2.2 Electrodialysis (ED) .................................................................................................... 49 

2.3 Processes acting on chemical bounds ...................................................................................... 49 

2.3.1 Ion exchange ................................................................................................................ 49 

2.4 Summary ................................................................................................................................. 51 


Índex 

CHAPTER 3. MSF desalination steady-state model ............................................................................ 53 

3.1 Process description ..................................................................................................................... 54 

3.2 Mathematical model of MSF unit ............................................................................................... 57 

3.2.1 Stage model .................................................................................................................... 58 

3.2.2 Brine Heater Model ........................................................................................................ 62 

3.2.3 Mixer and splitter model ................................................................................................. 63 

3.3 Auxiliary equations ..................................................................................................................... 64 

3.3.1 Density ............................................................................................................................ 64 

3.3.2 Viscosity ......................................................................................................................... 64 

3.3.3 Thermal conductivity ...................................................................................................... 65 

3.3.4 Heat capacity .................................................................................................................. 65 

3.3.5 Enthalpy .......................................................................................................................... 65 

3.3.6 Vapor pressure ................................................................................................................ 66 

3.3.7 Boiling point elevation ................................................................................................... 67 

3.3.8 Non-equilibrium allowance ............................................................................................ 67 

3.3.9 Demister and other losses ............................................................................................... 67 

3.4 Solution algorithm ...................................................................................................................... 68 

3.5 Simulation cases ......................................................................................................................... 70 

3.5.1 TBT control .................................................................................................................... 71 

3.5.2 Inverse problem .............................................................................................................. 71 

3.6 Initial data and simulation .......................................................................................................... 72 

3.6.1 Fouling effect .................................................................................................................. 75 

3.7 Summary ..................................................................................................................................... 76 

CHAPTER 4. Steam power plant steady-state model .......................................................................... 77 

4.1 Model description ....................................................................................................................... 78 

4.2 Mathematical model ................................................................................................................... 80 

4.2.1 Steam turbines ................................................................................................................ 80 

4.2.2 HP heat exchangers ......................................................................................................... 82 

4.2.3 LP heat exchangers ......................................................................................................... 83 

4.2.4 Deaerator ......................................................................................................................... 84 

4.2.5 Condenser ....................................................................................................................... 85 

4.2.6 Boiler .............................................................................................................................. 85 

4.2.7 Valves ............................................................................................................................. 86 

4.2.7.1 Turbine control valves ...................................................................................... 86 

4.2.7.2 Boiler outlet stop valve ..................................................................................... 86 

4.2.7.3 Boiler inlet control valve .................................................................................. 86 

4.2.8 Pipes ................................................................................................................................ 86 

4.2.9 Pumps ............................................................................................................................. 87 

4.2.10 Gland and seal steam system .......................................................................................... 88 

4.2.11 Generator ........................................................................................................................ 89 

4.3 Auxiliary equations ..................................................................................................................... 90 

4.3.1 Thermodynamic properties ............................................................................................. 90 

4.3.2 Transport properties ........................................................................................................ 90 


Índex 

4.4 Solution algorithm ...................................................................................................................... 90 

4.5 Operating modes and mathematical models ............................................................................... 92 

4.6 Summary ..................................................................................................................................... 96 

CHAPTER 5. Simulator .......................................................................................................................... 99 

5.1 SIMTAW structure ..................................................................................................................... 100 

5.2 Model validation ......................................................................................................................... 104 

5.2.1 Power plant ..................................................................................................................... 104 

5.2.1.1 MCR case .......................................................................................................... 106 

5.2.1.2 MR case ............................................................................................................ 107 

5.2.1.3 PL115 case ........................................................................................................ 108 

5.2.1.4 PL85 case .......................................................................................................... 109 

5.2.1.5 MSL2 case ......................................................................................................... 110 

5.2.1.6 MSL3 case ........................................................................................................ 111 

5.2.1.7 MSL4 case ........................................................................................................ 112 

5.2.1.8 ODOB case ....................................................................................................... 113 

5.2.1.9 TDOB case ........................................................................................................ 114 

5.2.1.10 VWO case ......................................................................................................... 115 

5.2.1.11 COC case .......................................................................................................... 116 

5.2.2 MSF Plant ....................................................................................................................... 117 

5.2.2.1 NTOS case ........................................................................................................ 119 

5.2.2.2 HTOS case ........................................................................................................ 120 

5.2.2.3 LTOS case ........................................................................................................ 121 

5.2.2.4 HTOW case ...................................................................................................... 122 

CHAPTER 6. Thermoeconomics. Fundamentals, applications of thermoeconomic diagnosis 

and optimization of complex energy systems .................................................................... 123 

6.1 Basic concepts ............................................................................................................................ 126 

6.1.1 The concept of cost ......................................................................................................... 126 

6.1.2 Fuel, product and unit exergetic consumption ................................................................ 127 

6.1.3 Physical and thermoeconomic plant models ................................................................... 130 

6.2 Calculating thermoeconomic costs ............................................................................................. 136 

6.2.1 Marginal and average thermoeconomic costs ................................................................. 140 

6.2.2 Economic resources and thermoeconomic costs ............................................................ 142 

6.3 Thermoeconomic applications to thermoeconomic operation diagnosis and 

the optimization of complex energy systems .............................................................................. 143 

6.3.1 Operation thermoeconomic diagnosis ............................................................................ 143 

6.3.1.1 Technical exergy saving ................................................................................... 144 

6.3.1.2 Impact on resources consumption .................................................................... 145 

6.3.1.3 Malfunction and dysfunction analysis .............................................................. 148 

6.3.1.4 Intrinsic and induced malfunctions ................................................................... 153 

6.3.2 Thermoeconomic optimization ....................................................................................... 155 


Índex 

CHAPTER 7. Thermoeconomic analysis of a dual-purpose power and desalination plant ............. 159 

7.1 Thermoeconomic model ............................................................................................................. 161 

7.1.1 A simple co-generation system ....................................................................................... 161 

7.1.2 Physical structure ......................................................................................................... 162 

7.1.3 Productive structure ........................................................................................................ 166 

7.1.3.1 Steam power plant ............................................................................................ 166 

7.1.3.2 MSF unit ........................................................................................................... 171 

7.1.4 Thermoeconomic model ................................................................................................. 175 

7.2 Cost analysis ............................................................................................................................... 180 

7.2.1 Exergy costs allocation ................................................................................................... 181 

7.2.2 Exergy cost analysis ....................................................................................................... 185 

7.2.3 Thermoeconomic costs ................................................................................................... 191 

7.2.3.1 Investment costs ............................................................................................... 192 

7.2.3.2 Capital costs ...................................................................................................... 197 

7.2.4 Thermoeconomic cost analysis ....................................................................................... 197 

7.2.5 Cost allocation: Indirect methods ................................................................................... 198 

7.2.5.1 WEA method .................................................................................................... 198 

7.2.5.2 Fuel cost of water in dual plants ....................................................................... 200 

7.3 Thermoeconomic diagnosis ........................................................................................................ 202 

7.3.1 Thermoeconomic diagnosis of a power and desalination plant: case studies .............. 203 

7.3.2 Analysis of individual inefficiencies .............................................................................. 205 

7.3.2.1 Inefficiency in the fourth section of the high-pressure turbine ......................... 205 

7.3.2.2 Using the cleaning ball system in the brine heater ........................................... 221 

7.3.2.3 The effect of recovery section fouling on steam power plant behavior ............ 236 

7.3.3 Analysis of several inefficiencies ................................................................................... 251 

7.3.3.1 Analysis of several simultaneous inefficiencies in the steam power plant ....... 251 

7.3.3.2 Analysis of several inefficiencies in the MSF plant ......................................... 265 

7.3.4 Thermoeconomic diagnosis and load influence in the dual plant ................................... 279 

7.3.4.1 Effect of inefficiencies in the power plant for different loads .......................... 280 

7.3.4.2 Effect of MSF unit inefficiencies under different loads ................................... 283 

7.3.5 Summary of applying thermoeconomic diagnosis to power and desalination plants .. 285 

7.4 Thermoeconomic optimization ................................................................................................... 288 

7.4.1 Introduction ..................................................................................................................... 288 

7.4.2 Thermoeconomic isolation ............................................................................................. 288 

7.4.3 Physical model ................................................................................................................ 296 

7.4.4 Thermoeconomic model ................................................................................................. 296 

7.4.5 Local and global variables .............................................................................................. 299 

7.4.6 Local optimization of subsystems .................................................................................. 301 

7.4.7 Local optimization results ............................................................................................... 303 

7.5 Economic analysis. Cost, price and benefit ................................................................................ 309 

7.5.1 Case study ....................................................................................................................... 311 

7.6 Conclusions and operation recommendations ............................................................................ 313 

7.6.1 Cost analysis ................................................................................................................... 313 

7.6.1.1 Results .............................................................................................................. 313 

7.6.1.2 Conclusions and operation recommendations .................................................. 316 


Índex 

7.6.2 Thermoeconomic diagnosis ............................................................................................ 317 

7.6.2.1 Results .............................................................................................................. 317 

7.6.2.2 Conclusions and final considerations ............................................................... 318 

7.6.3 Local optimization .......................................................................................................... 321 

7.6.4 Operating management ................................................................................................... 322 

CHAPTER 8. Synthesis, contributions and perspectives ..................................................................... 323 

8.1 Synthesis ..................................................................................................................................... 323 

8.2 Main contributions ..................................................................................................................... 325 

8.2.1 Simulator of a dual-purpose power and desalination plant ............................................ 325 

8.2.2 State of the art in Thermoeconomics .............................................................................. 325 

8.2.3 F-P definition for a MSF unit ......................................................................................... 326 

8.2.4 Cost analysis of a dual-plant ........................................................................................... 326 

8.2.5 Diagnosis of a complex system ...................................................................................... 326 

8.2.6 Local optimization of the steam power plant ................................................................. 327 

8.2.7 Cost, price and benefit .................................................................................................... 327 

8.3 Perspectives ................................................................................................................................ 327 

8.3.1 Improving existing plants. Process integration .............................................................. 327 

8.3.2 Improvements in thermoeconomic diagnosis ................................................................. 328 

8.3.3 Integrating attitudes ........................................................................................................ 329 

8.3.4 Sustainable desalination ................................................................................................. 329 

8.3.5 Promote energy and water interactions .......................................................................... 330 

ANNEX 1. Thermoeconomic diagnosis .................................................................................................. 331 

A1.1 Effect of an inefficiency in the high-pressure heater no.1 (HPH1) ............................................ 332 

A1.2 Effect of feed pump isoentropic efficiency ................................................................................ 345 

A1.3 Effect of an inefficiency in the first section of the high-pressure turbine (HPT1) ..................... 357 

A1.4 Effect of inefficiency in the first section of the low-pressure turbine (LPT1) ........................... 369 

A1.5 Effect of the cleaning ball system in the recovery section ......................................................... 382 

A1.6 Effect of reject section fouling ................................................................................................... 395 

A1.7 Summary .................................................................................................................................... 407 

ANNEX 2. Thermodynamic properties of seawater ............................................................................. 409 

A2.1 Specific enthalpy h of superheated or saturated vapor ............................................................ 419 

A2.2 Specific entropy of superheated or saturated vapor ................................................................ 410 

A2.3 Specific volume of superheated or saturated vapor ................................................................. 411 

A2.4 Latent heat vaporisation of water as a function of boiling temperature .................................. 411 

A2.5 Seawater exergy ......................................................................................................................... 412 

A2.5.1 Theory ............................................................................................................................. 430 

A2.5.2 Practice: Brine exergy as a function of temperature, pressure and salt concentration 417 


Índex 

ANNEX 3. Technical data ....................................................................................................................... 419 

A3.1 MSF plant ................................................................................................................................ 419 

A3.2 Power Plant .............................................................................................................................. 426 

NOMENCLATURE ........................................................................................................................................ 433 

REFERENCES ................................................................................................................................................ 441 

LIST OF FIGURES.......................................................................................................................................... 457 

LIST OF TABLES .......................................................................................................................................... 463

Thermoeconomic analysis and simulation of a combined... - circe ...

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