This type of reactor is only rarely utilized in biological wastewater treatment. But we can compare the responses shown in retention time distribution measurements of a tube reactor with axial dispersion with those for a tank cascade. This enables us to calculate the theoretical number of stages which a real tube reactor has (see Section 6.3.5).

6.3 Retention Time Distribution in Activated Sludge Reactors 1141 The model for n CSTR tanks consists of n tracer balances:

dci dc2

Vn —- = Qo(Cn-l-Cn) dt with the solution for the probability distribution of residence times: F(t) = l-exp(-nT)

Some results are given in Fig. 6.10.

With inCreasing n, the probability distribution approaChes that of a plug flow reaCtor, whiCh is the same as a CasCade of n=^ stages (Hill 1977; Chow et al. 1979). By differentiation of Eq. (6.96), the probability density follows:

(Froment and BisChoff 1979; Chow et al. 1979). With inCreasing n, the peak beComes more narrow and higher.

/ V \//-10 |
CO |
Fig. 6.10 Retention time distribution F(t) for a CSTR (n = 1) compared with one from a tank cascade system (n = 2 ... <*>) (Wen and Fan 1975). |

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