Thermodynamical Material Networks for Modeling, Planning, and Control of Circular Material Flows

Material flow analysis (MFA) is the main methodology to assess material flow circularity. It is essentially a data-analysis-based approach whose physical foundations consist of conservation of mass. To improve both the accuracy and the repeatability of MFA models, in this paper we leverage compartmental dynamical thermodynamics merged with graph theory and control theory. The key idea is that the thermodynamic compartments and their connections can be added, removed or modified as needed to achieve a circular material flow. Thus, our methodology consists of designing thermodynamical material networks (TMNs). We also provide a physics-based definition of circularity and implement a nonlinear compartmental control, which has been possible since TMNs are highly dynamic models based on differential calculus (i.e. ordinary differential equations) rather than on arithmetic as is typical for MFA models. As we envision scalable and repeatable designs of TMNs, we made publicly available the paper source code.