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

ABSTRACT

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.¹

KEYWORDS:

• Compartmental dynamical thermodynamics
• graph theory
• control systems
• material flow design
• industrial ecology
• circular economy

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. https://github.com/fedezocco/TMNbiometh-SciPy.

Additional information

Notes on contributors

Federico Zocco

Federico Zocco received the B.S. in Mechanical Engineering and the M.S. in Robotics and Automation Engineering from University of Pisa in 2013 and 2016, respectively, and the Ph.D. in applied Machine Learning from Queen’s University Belfast in 2021. He is currently a postdoctoral researcher with the School of Mechanical, Electrical and Manufacturing Engineering and with the Centre for Sustainable Manufacturing and Recycling Technologies at Loughborough University. Dr. Zocco’s research merges computer vision, compartmental dynamical thermodynamics, control theory, and network science with the holistic perspective of industrial ecology to define the theoretical foundations of material flow design. The main area of application is the circularity of critical materials such as the atmospheric carbon dioxide and the rare-earth metals.

Pantelis Sopasakis

Pantelis Sopasak is received the Diploma (M.Eng.) degree in chemical engineering and the M.Sc. Degree (Hons.) in applied mathematics from the National Technical University of Athens (NTU Athens), Athens, Greece, in 2007 and 2009, respectively, and the Ph.D. degree from the School of Chemical Engineering, NTU Athens, in 2012. He held post-doctoral positions at IMT Lucca, Lucca, Italy, from 2013 to 2016, ESAT, KU Leuven, Leuven, Belgium, from 2016 to 2018, and KIOS, University of Cyprus, Nicosia, Cyprus, in 2018. He is currently a Lecturer with the School of Electronics, Electrical Engineering and Computer Science (EEECS), Queen’s University Belfast, where he is a member of the Centre for Intelligent Autonomous Manufacturing Systems (i-AMS). His research interests include the development of model predictive control methodologies, numerical algorithms for large-scale stochastic systems, and massive parallelization on general-purpose graphics processing units (GP-GPUs). The outcomes of his research have several applications in automotive and aerospace, microgrids, water distribution networks, and optimal, safe drug administration.

Beatrice Smyth

Beatrice Smyth is a senior lecturer in the School of Mechanical and Aerospace Engineering, Queen’s University Belfast, and is part of the Research Centre in Sustainable Energy. Her research is focused on environmental impacts and circular economy thinking, and specific areas of interest include energy and carbon life cycle analyses, optimisation of energy pathways, resource quantification and mapping, and economic assessment. Ongoing research projects include nutrient management of digestate combined with energy recovery, the use of short rotation coppice willow to reduce agricultural run-off and improve water quality, sustainability indicators for food, hydrogen for heavy duty transport, microplastic pollution in drinking water, and the sustainable use of plastics in a circular economy. Prior to moving to Queen’s in 2013, Beatrice worked in both the public and private sectors, mainly in energy/carbon management and in geotechnical and environmental engineering. Beatrice has wide experience in working in multi-disciplinary teams, with colleagues from psychology, management, public health, politics and sociology.

Wassim M. Haddad

Wassim M. Haddad received the B.S., M.S., and Ph.D. degrees in mechanical engineering from Florida Tech in 1983, 1984, and 1987. From 1987 to 1994 he served as a consultant for the Structural Controls Group of the Government Aerospace Systems Division, Harris Corporation, Melbourne, FL. In 1988 he joined the faculty of the Mechanical and Aerospace Engineering Department at Florida Tech, where he founded and developed the Systems and Control Option within the graduate program. Since 1994 he has been with the School of Aerospace Engineering at Georgia Tech, where he holds the rank of Professor, the David Lewis Chair in Dynamical Systems and Control, and Chair of the Flight Mechanics and Control Discipline. He also holds a joint Professor appointment with the School of Electrical and Computer Engineering at Georgia Tech. He is the Co-Founder, Chairman of the Board, and Chief Scientific Advisor of Autonomous Healthcare, Inc. Dr. Haddad has made numerous contributions to the development of nonlinear control theory and its application to aerospace, electrical, and biomedical engineering. His transdisciplinary research in dynamical systems and control is documented in over 700 archival journal and conference publications, and 8 books in the areas of science, mathematics, medicine, and engineering. Dr. Haddad is an NSF Presidential Faculty Fellow; a member of the Academy of Nonlinear Sciences; an IEEE Fellow; an AAIA Fellow; and the recipient of the AIAA Pendray Aerospace Literature Award.