Page 247 - Materials Chemistry, Second Edition

L1644_C06.fm Page 220 Monday, October 20, 2003 12:06 PM

2
1
The values of the weighted eco-matrix WE in the diagonals D , D and D 3
M
represent the environmental damage cost or damage indicator of processes 1, 2 and
12
3. If the values of WE are not in the diagonal, such as D , and given the assumption
M
of linearity, they represent the environmental damage cost or damage indicator of
the corresponding process, but in a different region, e.g., the damage cost or damage
indicator that the process 2 would cause in the region 1. Consequently, it is possible
to compare the effects of a certain process in different regions. Each component D kj
of the weighted eco-matrix is obtained by Expression 6.3 and in Expression 6.6 is
given the abbreviated mathematical way of expressing the contents, where k stands
for the region k and j for the process j:

N
D = Â (W M ki . E ) (6.6)
kj
ij
M
i
The weighting matrix components for the EL corresponding to the different
i
processes j and k are equal if the processes are situated in the same region. Indeed,
that is the case for global impacts such as for the GWP, where this simplification
allows working with one eco-vector for all the processes and one weighting vector
for all regions, as shown in Expression 6.7. In the case of global weighting factors,
the weighting matrix has the same components for all processes.

W = W M ki < = = > region (j) = region (k) (6.7)
ji
M
A special topic that must be considered is the question of mobile processes. If
the process is a moving one, different regions may be involved so that Expression
6.8 holds true. By choosing the size of the region, the number of regions to consider
for the corresponding mobile process is determined. If there is a mobile process
with sufficient transport kilometers,
lj
kj
= = > exists at least 1 i; D π D V k π i (6.8)
This mathematical framework delivers a tool for introducing site-specific aspects
in the life-cycle approach. The matrix algebra provides an elegant and powerful
technique for the derivation and formulation of different tools in a life-cycle per-
spective.

6.5 OUTLINE OF THE COMBINED FRAMEWORK
6.5.1 OVERVIEW OF THE METHODOLOGY

With the mathematical framework at our disposal, the next task is to find a way to
determine the eco-technology matrix and the weighting or damage-assigning matrix.
It is proposed to base the environmental damage estimations of industrial process
chains on the results of a conventional LCI analysis and one or more LCIA methods
to answer the environmental management problem of interest.

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