Page 439 - Civil Engineering Formulas

STORMWATER, WASTEWATER, AND ENVIRONMENTAL PROTECTION 365

3
where V reactor volume (Mgal) (m )
r
mean cell residence time, or the average time that the sludge remains
c
in the reactor (sludge age). For a complete-mix activated sludge
process, ranges from 5 to 15 days. The design of the reactor is
c
based on on the assumption that substantially all the substrate
c
(BOD) conversion occurs in the reactor.
Q average daily influent flow rate (Mgd)
Y maximum yield coefficient (mg VSS/mg BOD ). For the activated
5
sludge process for domestic wastewater Y ranges from 0.4 to 0.8.
Essentially, Y represents the maximum mg of cells produced per mg
organic matter removed.
S influent substrate (BOD ) concentration (mg/L)
5
0
S effluent substrate (BOD ) concentration (mg/L)
5
X concentration of microorganisms in reactor mixed liquor volatile
a
suspended solids (MLVSS) in mg/L. It is generally accepted that the
ratio MLVSS/MLSS 0.8, where MLSS is the mixed liquor sus-
pended solids concentration in the reactor. MLSS represents the sum
of volatile suspended solids (organics) and fixed suspended solids
(inorganics). For a complete-mix activated sludge process, MLSS
ranges from 1000 to 6500 mg/L.
–1
k endogenous decay coefficient (d ) which is a coefficient represent-
d
ing the decrease of cell mass in the MLVSS. The activated sludge
–1
process for domestic wastewater k ranges from 0.025 to 0.075 d .
d
The hydraulic retention time, , is
V /Q (13.12)
r
For a complete-mix activated sludge process, ( is generally 3 to 5 h).
The observed cell yield:
Y obs Y/1 k (13.13)
d c
And the observed cell yield is always less than the maximum cell yield, (Y).
The increase in MLVSS is computed using the following equation:
P x Y obs Q(S O S)(8.34 lb/Mgal/mg/L) (13.14)
where P is the net waste activated sludge produced each day in (lb VSS/d).
x
The theoretical oxygen requirements for the removal of the carbonaceous
organic matter in waste water for an activated-sludge system can be computed
using the following equation:
O /d (lb) (total mass of BOD utilized, lb/d)
2
L
1.42 (mass of organisms wasted, lb/d) (13.15)
Using terms that have been defined previously where f conversion factor
for converting BOD to BOD (0.68 is commonly used):
5
L
lb/Mgal
Q(S O S) 8.34
O 2 /d(lb) mg/L (1.42)(P x ) (13.16)
f