Page 118 - Materials Chemistry, Second Edition

102 3 Life Cycle Inventory Analysis

Standards. 91) Price-weighted allocation, uncommon in the early period of LCA, has
been discussed, in particular, by Huppes. 92)
A completely different approach going back to matrix calculations for quanti-
tative descriptions of product systems as developed in economic theory has been
93)
introduced by Heijungs. The most important result is the occurrence of allocation
problems in all cases where the matrix equations describing the system cannot
be solved. 94) Using an example of CLR it can be shown by formal derivation that
an allocation problem does not exist, in accordance with common practice and
experience.
An overview by Curran of the allocation of co-products 95) that also refers to
recycling and disposal, starts with the inventory and the distinction between
foreground and background processes. 96) The former relate to the scope of the
examined product system that can be directly influenced by the decision maker.
For this, specific data are usually available or can easily be procured. Raw material
acquisition, material production, and the supply of energy, transportations, and so
on, are termed background process. For the latter, mostly generic data (see Section
3.4.3.1) that represent averages of many single processes are used. Foreground data
can be investigated by their reaction to (small) changes in technology. A special case
represents the modelling of a profound change of technology-mix called discrete
change, which may follow fundamental changes in society.

3.3.2.5 System Expansion
The basic idea of system expansion and also the subsequent problems of very
large systems have already been described in Section 3.3.2.1 (see Figures 3.11 and
3.12). The following example shows possible solutions for a product comparison
if system expansion is applied. For reasons of clarity Figures 3.14–3.16 illustrate
the production alone. Use and disposal are not integrated but of course have to be
considered in the modelling of a system expansion.
System expansion is illustrated by a comparison of products A and C, where A is
formed together with co-product B (Figure 3.14). The benefit of the systems 1 and
2 is not identical because in system 1 two useful products (A and B) are formed,
whereas in system 2 only one product (C) is formed – the one to be compared
with A. In order to achieve comparability, the fU is changed by an expansion to
A + Band C + B. Due to the co-production of B in system 1, the entire and separate
production of B must be added to C in system 2, yielding the same amount B
as in system 1 (Figure 3.15). A production system for B has to be modelled as
an equivalent system. The system boundary is the same as the one that has been

91) Heintz and Baisn´ ee, 1992; Boustead, 1994b; International Standard Organization (ISO), 1998a;
Frischknecht, 2000; Kim and Overcash, 2000; Werner and Richter, 2000; Ekvall and Finnveden,
2001; Guin´ ee et al., 2002.
92) Huppes and Schneider, 1994; Guin´ ee et al., 2002.
93) Heijungs, 1997, 2001; Heijungs and Suh, 2002.
94) Heijungs and Frischknecht, 1998.
95) Curran, 2007, 2008.
96) First in: SETAC-Europe, 1996.