Flow programming: adding non-linear behaviour to parameterised process models for prospective Material Flow Analysis and Life Cycle Assessment

Abstract

Industrial ecology modelling commonly aims to understand how the system's processes, stocks and flows would respond to changes, and the consequences for changes in environmental impacts and resource requirements. While marginal changes can be assessed with linear models, discontinuities in behaviour often mean that results for marginal changes cannot be extrapolated to larger shifts. Here, we present a new framework for introducing non-linear behaviour into process-flow models (such as in Material Flow Analysis, or for the foreground inventory of a Life Cycle Assessment), based on the idea of flexibly building up the model from a set of basic building-block operations. The approach is implemented in an open source Python library based on the Sympy computer algebra system. The resulting parameterised model can be expressed as algebraic equations, or translated into computer code to evaluate results, apply uncertainty and sensitivity analysis, or embed into a broader modelling framework. We demonstrate the approach by constructing a stock-driven model of plastics demand and petrochemical production processes, considering recycling loops, co-products and capacity limits. This new framework offers a systematic way to formulate models which respond non-linearly, which is important in understanding the impacts of, and interactions between, systemic changes in the transition to a decarbonised and more circular economy.