Environmental Engineering FOURTH EDITION

Wastewater Treatment 191

In a steady-state system, (dX/dt) = 0, and Xo = 0 is assumed. Substituting Eq. (9.15)
into Eq. (9.18), and introducing the mean cell residence time OC,

(9.19)

and

(9.20)

Equation (9.20) is important because it implies that the substrate concentration S is
a function of both the kinetic constants (which are beyond our control for a given
substrate) and the mean cell residence time. The mean cell residence time (or sludge
age, as defined before) influences the substrate S and thus the treatment efficiency.
A system without microorganism recycle is not very efficient, since long hydraulic
residence times are needed to prevent flushing out of the microorganisms. Success-
ful activated sludge systems for wastewater treatment are based on microorganism
recycling, as is shown in Fig. 9-19. Some simplifying assumptions are needed to
model this system, however. We assume Xo = 0, and further, that the microorganism
separator is a perfect device and the effluent contains no microorganisms (Xe = 0).
Steady-state conditions and perfect mixing are also assumed. Excess microorganisms,
or waste activated sludge, are removed from the system at flow rate Qw, and solids
concentration Xt.Xt is the settler underRow concentration and the concentration of
solids being recycled to the aeration tank. Finally, to simplify the model we make the
obviously incorrect assumption that no substrate is removed in the settling tank and
that the settling tank has zero volume, so that all of the microorganisms in the system
are in the aeration tank. The only active volume is that of the aeration tank. The mean
cell residence time in this case is

Ks

/.Lo, - 1'

S=

Mass of solids (microorganisms) in aeration tank

Mass rate of solids leaving the system

0, = (9.21)

vx

Qwxt + (Q - QwWt'

0, =

I Xr 4 I

(9.22a)

xr 1%

Figure 9-19. A biological reactor with microorganism recycle.