ODYM - Open Dynamic Material Systems Model

Please note that ODYM is still in its inception phase. Documentation on this repo and a scientific publication are in preparation.

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.

The novel features of ODYM include:
• 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.

More information is available:
• Wiki pages in this repository.
• Tutorials (Jupyther notebooks) in the docs folder.
• A journal paper (in preparation).

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:

a) 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.

$$ i(p,r,t) = i_{Sat}\cdot exp^{-b(p,r)\cdot exp^{-a(p,r)\cdot t}} $$

b) 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

$$ \begin{eqnarray} o(t)=\sum_{t'\leq t}i(t')\cdot \lambda(t,c = t') \\ S(t)=\sum_{t'\leq t}(i(t')-o(t')) \end{eqnarray} $$

c) 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

$$ F_s(t,s,e) = \sum_{w,p,c}\Gamma(w,e,s,c)\cdot C(w,t,c)\cdot F_p(t,p)\cdot \mu(p,e)$$

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

d) 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)

$$ \begin{eqnarray} min C = c^t\cdot x\\ s.t.\\ w = G\cdot x+y\\ x = S\cdot w \\ x \geq 0 $$

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.