## Mean Retention Time Recycle Ratio and Thickening Ratio as Process Parameters

Figure 6.3 presents the flow sheet of an activated sludge plant. The balance of bacteria X for the CSTR in steady state is:

Corresponding to Eq. (6.35), the balance of substrate S is: P

YX/S

with: kd = ks + ke as the decay coefficient.

kd includes both the specific rate of death ks and that of mass decrease by endogenous respiration ke. The decay coefficient was first proposed by Herbert (1958). kd and ke were already introduced in Chapter 4.23 (see Eq. 4.27). Dividing Eq. (6.36) by Eq. (6.35), we obtain:

For ppkd, Eq. (6.15) follows from Eq. (6.37), which can be interpreted as a relationship between the substrate used and the bacterial mass formed. After introducing Eq. (6.37) and Monod kinetics (Eq. 6.1) in Eq. 6.36, S can be calculated.

Furthermore, a bacterial balance at the mixing point M is necessary (Fig. 6.3). Neglecting Q0X0, we obtain:

With the recycle ratio:

then we can calculate: nRnE

1+nR

After introducing Eqs. (6.1), (6.20), (6.37) and (6.41) into Eq. (6.36), we obtain:

It is interesting that S is not influenced directly by S0. For kd ; 0, it follows that:

If we are interested in the bacterial concentration X, we must introduce Eqs. (6.1) and (6.43) into Eq. (6.37).

Pmax S0

tRC is the critical mean retention time which was already introduced in Section 6.2.2 for the discussion on the chemostat (see Eq. 6.25). For nR = 0, Eq. (6.44) can be transformed into Eq. (6.25). The higher nR is, the lower tRC is for nE> 1. This model was published by Mehring (1979) and by Sundstrom and Klei (1979) among others.

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