Proposal of a Construction Method for a Unique Coefficient Matrix in Matrix-based Life Cycle Inventory Analysis

Abstract

Background, Aim and Scope. Matrix-based life cycle inventory analysis is effective to evaluate environmental impacts of systems including closed–loops (e.g. recycling). However, the matrix method has not yet been widely used because it is complicated and difficult for most LCA practitioners to adequately make a regular coefficient matrix from input/output data of processes. Therefore, this study aims to develop a general method to make a unique, regular coefficient matrix for supporting the use of the matrix method.
Methods. First, five types of basic components are newly defined to express a product system. The combination of these five components allows for describing an arbitrary product system. Second, a system that is re-described using the five components can be dealt with as a geometrical figure that is expressed using the abstract concepts of nodes and edges in the graph theory. Finally, a regular coefficient matrix is made by analyzing geometrical relationships between nodes and edges.
Results. It was proved that a unique, regular coefficient matrix can be obtained if the geometrical figure corresponding to a product system is a planar graph. An algorithm to make such a coefficient matrix was formulated using Euler's polyhedron theory, based on balance equations of flows of goods (e.g. energy, materials) in a system studied. The validity of the proposed algorithm was demonstrated by applying the algorithm to a simple, numerical example: a product system including closed recycling.
Discussion and Conclusions. An advantage of the developed method is that the complicated flows of goods in a product system studied can be reduced to an abstract geometrical figure according to mathematically simple rules. This means that computers can easily generate a unique, regular coefficient matrix automatically from input/output data of processes in a product system. We plan to create software based on the proposed algorithm, which enables LCA practitioners to easily perform the matrix-based LCA without making a coefficient matrix on their own.