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Overview

The ODYM model framework is a software library for dynamic material flow analysis (MFA). It can best be described as a framework for modeling biophysical stock-flow relations in socioeconomic metabolism.

Novel Features of ODYM

  • System variables (stocks and flows) can have any number of aspects (time, age-cohort, region, product, component, material, element, …)
  • The software automatically matches the different dimensions during computations. No manual re-indexing of tables and arrays is necessary.
  • The user only specifies those aspects that are relevant for the model. The software handles the data storage and matching of the indices used.
  • The software checks whether a consistent classification is used all across the model.
  • Flexibility regarding different data formats (table and list) and subsets of classifications used (only certain years or chemical elements, for example).
  • Representation of system variables and parameters as objects, general data structures serve as interfaces to a wide spectrum of modules for stock-driven modelling, waste cascade optimisation, etc.

Background

ODYM was developed to handle the typical types of model equations and approaches in a dynamic MFA model in a systematic manner. These approaches include:

  1. Regression models: Socioeconomic parameters, such as in-use stocks or final consumption are required to determine the basic material balance or material flows. They are often determined from regression models fed by exogenous parameters such as GDP. A typical example for a regression model is the Gompertz function, where \(a(p,r)\) and \(b(p,r)\) are product-and region-dependent scaling parameters. Regression models can also be used to determine future scenarios.
\[ \begin{equation} i(p,r,t) = i_{Sat}\cdot exp^{-b(p,r)\cdot exp^{-a(p,r)\cdot t}} \end{equation} \]
  1. Dynamic stock model: The material stock S and outflow o can be estimated from inflow data i, using a product lifetime distribution \(\lambda(t,c)\), which describes the probability of a product of age-cohort c being discarded at time t
\[ \begin{align} o(t) &= \sum_{t'\leq t}i(t')\cdot \lambda(t,c = t') \\ S(t) &= \sum_{t'\leq t}(i(t')-o(t')) \end{align} \]
  1. Parameter equation with transfer coefficients: The distribution of a material flow to different processes is determined by the transfer coefficient. Consider a flow of different end-of-life products p, \(F_p\), with chemical element composition \(\mu\). The products are sent to waste treatment by different technologies w, and each technology has its own element-specific yield factor \(\Gamma\), which assigns the incoming elements to different scrap groups s and which varies depending on when the technology was installed (age-cohort dependency): \(\Gamma = \Gamma(w,e,s,c)\). The flow of chemical elements in the different scrap groups \(F_s\) is then
\[ \begin{equation} F_s(t,s,e) = \sum_{w,p,c}\Gamma(w,e,s,c)\cdot C(w,t,c)\cdot F_p(t,p)\cdot \mu(p,e) \end{equation} \]

Where \(C(w,t,c)\) is the capacity of the different waste treatment technologies $wä of age-cohort \(c\) in a year \(t\).

  1. Optimisation: For a system with a 1:1 correspondence of industries and markets, which is the basis of input-output models, the application of linear optimisation to select between competing technological alternatives is common. This optimisation approach can also be used to determine waste treatment cascades so that non-functional recycling, costs, or GHG emissions are minimized. A waste cascade optimisation problem has the typical form (Kondo and Nakamura 2005)
\[ \begin{align} \min C &= c^T \cdot x \\ \textrm{s.t.} \quad w &= G \cdot x + y \\ x &= S \cdot w \\ x &\geq 0 \end{align} \]

In the above equation, \(x\) is the output vector of the different waste treatment plants, \(c\) is a cost vector, \(y\) is the final demand for waste treatment, \(G\) is the waste generation of waste treatment, and \(S\) is the allocation of waste to treatment processes.