(564b) Towards a Complete Solution of Allocation in Life Cycle Inventories

The need for allocation arises in life cycle inventories when a process results in multiple products. In such a situation, resources and emissions embodied in the inputs need to be partitioned between the products. Popular approaches for accomplishing this task involve partitioning the embodied resources in proportion to characteristics of the outputs such as mass, energy, exergy or cost. Given the subjectiveness of this decision, many practitioners apply multiple allocation methods. Recent efforts have proposed the use of regression methods such as ordinary least squares and total least squares to solve the allocation problem. Allocation may be avoided by expanding the system boundary, but this approach can be tedious due to the need for more data.

We show that allocation can be understood as an ill-posed problem, analogous to the situation where the number of variables in simultaneous equations is larger than the number of independent equations. In such a situation, the number of solutions is infinite, and without additional information or assumptions, a single "correct" solution cannot be determined. Using a matrix framework for life cycle inventories, we devise a method of calculation whereby results from all possible allocation methods can be examined.

We use this insight to evaluate the special case where LCA is used to compare products that have the same use but are produced by different processes. Examples of such a case include comparing ethanol from various sources, gasoline, and other transportation fuels. We develop an approach to determine the sensitivity of the comparative LCA to allocation weights and show that sometimes the better product may be independent of the allocation approach. For cases when this does not happen, we propose an optimization approach to determine the "tipping curve" or the boundary across which the product preference changes.

The practical usefulness of this approach is demonstrated with two case studies. The first study compares the LCIs of 1,3-propanediol (PDO) produced from fossil fuels and from biomass. This comparison was found to be robust to allocation for nine resources and emissions out of the eleven considered: biomass PDO was preferred over fossil PDO for all choices of allocation weights. The second case study compared ethanol produced from corn stover hydrolysis, corn stover gasification, and corn grain fermentation. This comparison was not robust to allocation, although the two corn stover processes were preferred over the corn grain process for most choices of allocation weights. More information is needed to decide conclusively which process is preferred. Extension of the framework to incorporate this additional information is proposed.