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history of use. The figure indicates that the introduction of new materials can also be considered as a slow diffusion<br />

process.<br />

INDEX [-]<br />

120<br />

100<br />

80<br />

60<br />

40<br />

20<br />

0<br />

1960 1965 1970 1975 1980 1985 1990 1995<br />

[YEAR]<br />

STEEL<br />

CEMENT<br />

ALUMINIUM<br />

PAPER/BOARD<br />

Figure 3 Western European materials production, period 1960-1995 (1990=100)<br />

An additional barrier for materials substitution is the relatively closed life cycle of many materials (contrary to<br />

the energy carrier life cycle). Recycling of waste materials beyond the product life limits the rate of change in<br />

the materials system. In conclusion, the slow dynamics of the materials system makes long term planning<br />

feasible and sensible.<br />

General model description<br />

The MARKAL linear programming model was developed 20 years ago within the international IEA/ETSAP<br />

framework (International Energy Agency/Energy Technology Systems Analysis Programme). More than 50<br />

institutes in 27 countries use nowadays MARKAL [5,6] MARKAL is an acronym for MARKet ALlocation.<br />

The model was originally developed for energy systems analysis. In recent years, the model has been extended<br />

for materials system analysis [7] The model covers now the whole materials life cycle ‘from cradle to grave’.<br />

Figure 4 shows the materials system model structure.<br />

1 PRIMARY<br />

PRODUCTION<br />

MATERIAL<br />

3 PRODUCT<br />

ASSEMBLY<br />

PRODUCT<br />

4 PRODUCT<br />

USE<br />

WASTE PRODUCT<br />

5 REMOVAL<br />

&SEPARATION<br />

2 RECYCLING<br />

6 ENERGY<br />

RECOVERY<br />

Figure 4 Materials system model structure<br />

WASTE<br />

MATERIAL<br />

7 DISPOSAL<br />

PE

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