Page 246 - Materials Chemistry, Second Edition

L1644_C06.fm Page 219 Monday, October 20, 2003 12:06 PM

the environmental loads must be in the same order for all the processes and that a
certain environmental intervention must be expressed always in the same unit.
By analogy to the multiplication of the eco-vector by a weighting vector, the
eco-matrix can be multiplied by another matrix, the weighting or damage-assigning
matrix W , which contains the fate analysis, impact factors and final weighting.
M
This matrix assigns the damage cost or another damage indicator caused by one
specific EL to each process. In W there are N columns for the N environmental
M
i
loads and M rows for the M linear processes. In this way an M ¥ M matrix is
obtained, the weighted eco-technology matrix WE M, as shown in the following
expression:

W . E = WE M (6.3)
M
M
The main magnitude will be the trace D of WE (Expression 6.4), where E M ij
M
is the specific [EL/kg] of the EL in the process j, W m ji is the specific damage factor
i
j
for the EL in the process j, and D is the environmental cost or another indicator of
i
the process j. D expresses the total environmental damage cost of the life-cycle, if
W represents a weighting by costs, or the damage indicator for the life-cycle, if
M
W represents a weighting by an indicator.
M
M N
M Â
ji
D = tr (WE ) = (W . E ) = Â Â W . E )]
ij
ji
ij
[
M
M
M
M
ji j i
M M
jj
=  D l  D j (6.4)
j j
The algorithm is illustrated in Expression 6.5 for the example of three processes
and two environmental loads SO and Cd.
2
M
N M
1
12
D D D 13
1, SO2 1, Cd
M W M W M SO2, 1 SO2, 2 SO2, 3
N E M E M E M M D D D 23
21
2
2, SO2 2, Cd
W M W M Cd, 1 Cd, 2 Cd, 3
E M E M E M 31 32 3
= D D D
3, SO2 3, Cd
W M W M
1
Ï D = W M 1, SO2 E∑ M SO2, 1 + W M 1, Cd E∑ M Cd, 1
Ô 2 2,SO2 SO2, 2 2, Cd Cd, 2 1 2 3
with D = W M E∑ M + W M E∑ M Æ D = D + D + D
Ì
Ô 3 3,SO2 SO2, 3 3, Cd Cd, 3
Ó D = W M E∑ M + W M E∑ M
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