SCOUT content flow model

This model defines a structure and set of constraints which can be solved to track the flow of different “content types” through a material flow system. There are many ways that such a model could be formulated (within the constraints set by the principle of conservation of mass); this is one particular way, which has some convenient properties:

  • It can describe the main types of process that occur (involving mixing/assembly, conversion, and disassembly).

  • It can do something sensible if more specific information about processes is not available, making it easy to get started.

  • The constraints that are produced are well-posed, giving a unique solution.

Of course, it also has limitations, such as:

  • To ensure the constraints can always be solved, the process characteristics must be defined from upstream to downstream.

Conceptual structure of a process

SCOUT stands for Source, Crossover, OUTput – these are the three types of parameter that are used to describe how different types of material pass through the process.

Process structure and coefficients

  • The crossover matrix βmm describes how content type m is transformed into content type m. If there is no transformation, this is an identity matrix.

  • The source terms Δmdescribehowmuchnewcontentofeachtypem$ is created (or destroyed) within the process. For most processes theses terms will be zero; at the beginning of the material flow model there must be some source terms to define a starting content of certain flows, otherwise the solution will simply be zero content everywhere.

  • The output coefficients αkm describe how much of the content type m is sent to output k. For most processes, these coefficients are set in proportion to the output mass flows, so that all outputs share the same content.

Basic constraint equation

ficim=αim(mβsrc(i)mmkfkckm+Δsrc(i)m)

TODO: details

Ensuring conservation of mass

TODO: explain the conditions that α, β must meet to keep conservation of mass.

Adjustments for imports and exports

TODO: explain how imports and exports are accommodated (they are assumed to have the same content as the main flows).

Higher-level interface to defining these coefficients

This model is quite flexible, but it has too many free parameters to be convenient as a means to specify the intended flow of different material types through the system.

We can describe three higher-level types of process behaviour that can be translated into specific values of α, β and Δ for each process:

  • Output content

  • Output allocation

  • Content transformation

TODO: describe their definitions