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Reaction models

Reaction models describe the (net) fluxes \(f_{\mathrm{react}}\) of a reaction mechanism. CADET features one reaction type:

Historically, a chromatography system is modeled as a reaction system without considering any transport phenomenon. We also introduce some reaction-based models that can be solved in CADET:

Dependence on external function

A reaction model may depend on an external function or profile \(T\colon \left[ 0, T_{\mathrm{end}}\right] \times [0, L] \to \mathbb{R}\), where \(L\) denotes the physical length of the unit operation, or \(T\colon \left[0, T_{\mathrm{end}}\right] \to \mathbb{R}\) if the unit operation model has no axial length. By using an external profile, it is possible to account for effects that are not directly modeled in CADET (e.g., temperature). The dependence of each parameter is modeled by a polynomial of third degree. For example, the forward rate constant \(k_{\mathrm{fwd}}\) is really given by

\[\begin{aligned} k_{\mathrm{fwd}}(T) &= k_{\mathrm{fwd},3} T^3 + k_{\mathrm{fwd},2} T^2 + k_{\mathrm{fwd},1} T + k_{\mathrm{fwd},0}. \end{aligned}\]

While \(k_{\mathrm{fwd},0}\) is set by the original parameter XXX_KFWD of the file format (XXX being a placeholder for the reaction model), the parameters \(k_{\mathrm{fwd},3}\), \(k_{\mathrm{fwd},2}\), and \(k_{\mathrm{fwd},1}\) are given by XXX_KFWD_TTT, XXX_KFWD_TT, and XXX_KFWD_T, respectively. The identifier of the externally dependent reaction model is constructed from the original identifier by prepending EXT_ (e.g., MASS_ACTION_LAW is changed into EXT_MASS_ACTION_LAW). This pattern applies to all parameters and supporting reaction models. Note that the parameter units have to be adapted to the unit of the external profile by dividing with an appropriate power.

Each parameter of the externally dependent reaction model can depend on a different external source. The 0-based indices of the external source for each parameter is given in the dataset EXTFUN. By assigning only one index to EXTFUN, all parameters use the same source. The ordering of the parameters in EXTFUN is given by the ordering in the file format specification.

For the configuration of external function dependence and more information on model parameters required to define in CADET file format, see section Reaction models.