CSTRs and PFRs are reactors idealized as either completely mixed or not mixed at all. In a technical scale, all reactors in continuous operation differ from these extreme cases. In a longitudinal open basin, dispersion effects dominate which can be reflected, for example, by a dispersion model or by a model of n completely stirred tank reactors coupled in series, which is called a reactor cascade. Frequently, a reactor with longitudinal dispersion can be described as a cascade with a specific number of completely mixed tanks (see Section 6.2.8). In the following, this model will be discussed shortly.
The model consists of n balances each for substrate and bacteria. It is sufficient to write only the balances for stage number n, which shows the structure of all the other balances for stages < n. We write according to Eqs. (6.35) and (6.36) for stage number n and steady-state conditions:
0 = Qm (Xn-1 Xn) + UnXnVn - kdXnVn (6.69) Xn in Eq. (6.68) can be replaced by:
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