Comparison Between Tank Cascades and Tube Flow Reactors

How we can compare a tube flow reactor with axial dispersion with a series of tanks in cascade? How many stages of a cascade correspond to the same degree of backmixing of a system with a known Peclet number?

Figure 6.12 presents the response to an impulse-formed input. This response is given by Eq. (6.90). t = tR follows from the correspondence of A1 = A2.

F(t) 0.5

pe=o// i / / \//2°


Fig. 6.11 Retention time distribution F(l) for a CSTR (Pe' = 0) compared with one of real tube flow reactors (Pe' = 2 ... <*>) (Wen and Fan 1975).

The variance according to the property t being investigated is (Froment and Bischoff 1979):

is obtained for a "closed, closed" vessel (Wen and Fan 1975; Levenspiel 1979).

At high Pe' numbers low dispersion results:

If we consider a tank cascade, Eq. (6.97) must be introduced into Eq. (6.104). A simplified result can be estimated:

t2R n

Fig. 6.12 Retention time density distribution E(t) for a tube flow reactor (qualitative drawing).

144 | 6 Aerobic Wastewater Treatment in Activated Sludge Systems Combining Eq. (6.105) and (6.107), we obtain Pe'2

results. This is an approximation and results f.e. in n = 50 for Pe' = 100. The exact solution from Eq. (6.108) is n = 50.55.

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