## Sludge Age as Parameter

In activated sludge plants the mean retention time of bacteria (sludge age) tRX is decoupled from that of the water retention time. The sludge age is defined by Eq. (6.45):

QRXR + QexXR

Because of QRXRPQexXR, it is often allowed to write: VX

QR XR

This is the mass of solids inside the aeration tank applied to the production rate of excess solids. The steady-state balance of solids around the settler gives (see Fig. 6.3):

Neglecting QeXe, transforming Eq. (6.47) and considering Eqs. (6.39), (6.40), (6.46) and (6.20), it follows that:

If we introduce this result into the solutions with bacterial decay [Eq. (6.42)] and without bacterial decay (Eq. 6.43) we obtain:

tRX Pmax 1

Substrate removal is only influenced by sludge age tRX, which replaces the three parameters tR, nR and nE. We see here the importance of the parameter "sludge age", which will be used more and more not only in theoretical considerations but also in the practice of activated sludge system control.

The critical sludge age tRXC is the mean retention time of bacteria which must be exceeded in the activated sludge process. Otherwise, the bacteria (the sludge) will be washed out. tRXC follows from Eqs. (6.49) and (6.50) for S = S0:

P-max S0

tRXC

follows, the same relationship as calculated for tRtRX. After this model with tRX was presented as the only process parameter in the early 1970s, it was published, discussed and applied very frequently (Sunstrom and Klei 1979; Benefield and Randall 1980; Winkler 1981; Nasaroff and Alvarez-Cohen 2001). Figure 6.4 presents some theoretical results which were calculated for pmax=7.2 d-1, KS=100 mg L-1 COD, kd = 0.24 d-1 and S0 = 500 mg L-1 COD.

For these conditions nearly 90%, that is S0-S = 500-50 = 450 mg L-1 COD are removed, if a sludge age of about tRX = 0.5 d = 12 h is selected. The real sludge production is obtained from:

for tRX = 0.5 d, YX/S = 0.43 g MLSS (g COD)-1 and pmax = 7.2 d-1 with

it follow a real yield:

If we want to consider oxygen limitation, Eq. (6.10) must be introduced into Eqs. (6.41) and (6.42) and we have to add an oxygen balance:

02 uptake by exhaust air measurements

02 needed for growth keXV Yo

O2 needed for endogeneous respiration

The difference of dissolved O2 in the influent and effluent water is neglected. We want to continue the calculation of activated sludge plants in Chapter 11.

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