Page 441 - Civil Engineering Formulas

STORMWATER, WASTEWATER, AND ENVIRONMENTAL PROTECTION 367

X mixed liquor suspended solids (MLSS)
Q return activated sludge pumping rate (Mgd)
r
X concentration of sludge in the return line (mg/L). When lacking site
r
specific operational data, a value commonly assumed is 8000 mg/L.
Q effluent flow rate (Mgd)
e
X concentration of solids in effluent (mg/L). When lacking site specific
e
operational data, this value is commonly assumed to be zero.
Q waste activated sludge (WAS) pumping rate from the reactor (Mgd)
w
Q waste activated sludge (WAS) pumping rate from the return line (Mgd)
w
Other variables are as defined previously.
(a) Waste Activated Sludge (WAS) pumping rate from the return line. If the mean
cell residence time is used for process control and the wasting is from the sludge
return line (Fig. 13.3), the wasting rate is computed using the following:
V r X
c (13.19)
(Q w X r Q e X e )
Assuming that the concentration of solids in the effluent from the settling
tank (X ) is low, then the above equation reduces to:
e
V r X V r X
c Q w (13.20)
Q w X r c X r
To determine the WAS pumping rate using this method, the solids concen-
tration in both the aeration tank and the return line must be known.
If the food to microorganism ratio (F:M) method of control is used, the
WAS pumping rate from the return line is determined using the following:

P x(ss) Q w X r (8.34 lb/Mgal/mg/L) (13.21)

(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 aer-
ation tank (Fig. 13.4 and the solids in the plant effluent (X ) are again
e
neglected, then the WAS pumping rate is estimated using the following:
c Q w V r (13.22)
V r
Q w c
Assuming that the sludge blanket level in the settling tank remains constant
and that the solids in the effluent from the settling tank (X ) are negligible, a
e
mass balance around the settling tank (Fig. 13.3) yields the following equation
for RAS pumping rate:
XQ X r Q w
Q r (13.23)
X r X