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Rate Constant Distribution Theory¶
The rate constant distribution (RCD) theory describes a heterogeneous system by assuming a continuum of different adsorption sites, in contrast to the single site presumed in the Thomas Model. The traditional RCD model assumes that each binding site is governed by a Langmuir isotherm model, while in theory any single-component isotherm models can be used.
The RCD model reads:
where
To solve the above integro-differential equation, the
The discretized RCD model reads:
where
By definition, the total solid phase concentration
Therefore, we obtain a governing equation for each discretized binding site:
This equation is essentially a single-component Langmuir isotherm model. Hence, to configure the entire RCD model, one can utilize the Multi Component Bi-Langmuir implementation and the RCD model is thus not implemented as a standalone model.
The associated mass balance equation is given by:
Similar to the Thomas Model, the RCD model can also be configured in different unit operation models like Continuous stirred tank reactor model (CSTR) and Lumped rate model without pores (LRM).
We note that a significant issue with the RCD model is the difficulty in uniquely determining its parameters. Therefore, careful handling of the model is essential.