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material flow analysis (MFA) substance flow analysis (SFA) dynamic stock modelling industrial ecology
Abstract:
Material flow analysis (MFA) is a core method in industrial ecology that tracks material flows within a system, such as a national economy, across different life cycle stages (Brunner & Rechberger, 2016). It also accounts for material accumulation in stocks, including materials
embodied in products, assets, and infrastructure at a given time. MFA supports resource management, environmental impact assessment, and the evaluation of circular economy strategies, informing policy-making, urban and regional planning, and sustainable product design.
flodym (Flexible Open Dynamic Material Systems Model) is a Python library of objects and functions needed to build dynamic MFA models. From a mathematical perspective, MFA largely involves operations on multi-dimensional arrays. flodym implements the FlodymArray class, which internally manages operations of one or more such arrays. Objects representing flows, stocks, and parameters inherit from this class. Stocks include lifetime models for dynamic stock modelling, i.e. for calculating the relationship between material inflows to a stock and the
resulting mass and age structure of that stock over time. The whole MFA system is realized with an abstract parent class, which users can subclass. The parent class includes routines for checking mass balance consistency and non-negative flows. flodym offers functionality for
efficient data import and export via pandas (McKinney, 2010; The pandas development team, 2020), as well as visualization routines.
flodym is based on the concepts of the Open Dynamic Material Systems Model (ODYM) (Pauliuk & Heeren, 2020). It is a re-implementation with expanded functionality and improved structuring. As a result, flodym enables users to write customized, flexible MFAs, designed for maintainability and future extension.
