Handbook of Civil Engineering Calculations

(b) Waste Activated Sludge (WAS) pumping rate from the aeration tank. If the mean
cell residence time is used for process control, wasting is from the aeration tank (Fig. 2),
and the solids in the plant effluent (Xe) are again neglected, then the WAS pumping rate is
estimated using the following:

VT Vr

9 ~c —- O « —-

n ^

w

Qw VC ft

Using values defined previously:

Qw = °'^833 ^gal = 0.104 Mgd = 104,000 gal/day (393.6 m^3 /d)

8 d

Note that in case (a) or (b) above, the weight of sludge wasted is the same (3933 Ib SS/d)
(1785.6 kg SS/d), and that either wasting method will achieve a Oc of 8 days. As can be
seen, wasting from the aeration tank produces a much higher waste flow rate. This is be-
cause the concentration of solids in the bottom of the settling tank (and hence the return
line) is higher than in the aeration tank. Consequently, wasting a given mass of solids per
day is going to require a larger WAS pumping rate (and larger WAS pumps) if done from
the aeration tank as opposed to the return line. The Return Activated Sludge (RAS) pump-
ing rate is determined by performing a mass balance analysis around either the settling
tank or the aeration tank. The appropriate control volume for either mass balance analysis
is illustrated in Figs. 1 and 2, respectively. Assuming that the sludge blanket level in the
settling tank remains constant and that the solids in the effluent from the settling tank (Xe)
are negligible, a mass balance around the settling tank (Fig. 1) yields the following equa-
tion for RAS pumping rate:

= XQ-X&*

^

r

Xr-X

Using values defined previously, the RAS pumping rate is computed to be

_ (4500 mg/L)(4.0 Mgd) - (8000 mg/L)(0.0584 Mgd)

®r ~ 8000 mg/L - 4500 mg/L

= 5.0 Mgd (18,925 m^3 /d)

As outlined above, the required RAS pumping rate can also be estimated by perform-
ing a mass balance around the aeration tank (Fig. 2). If new cell growth is considered neg-
ligible, then the solids entering the tank will equal the solids leaving the tank. Under con-
ditions such as high organic loadings, this assumption may be incorrect. Solids enter the
aeration tank in the return sludge and in the influent flow to the secondary process. How-
ever, because the influent solids are negligible compared to the MLSS in the return
sludge, the mass balance around the aeration tank yields the following equation for RAS
pumping rate:

n _ X(Q-Q*)

U" x-x

Using values defined previously, the RAS pumping rate is computed to be