Page 794 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Biological Reactors 749

PROBLEMS
TABLE 23.10
Biological Treatment Equations and Parameters ACTIVATED SLUDGE
Parameter 23.1 Aerated Lagoon Mass Balance
Monod kinetics Given
Figure P23.1 illustrates the conditions
S
m ¼ ^m (22.31) Assume S o ¼ 300 mg BOD=L and that u ¼ 24 h.
K s þ S
Assume for analysis purposes that the aerated lagoon
Substrate utilization rate and cell synthesis rate is ‘‘complete mix.’’
Required

dX dS
(22.29)
¼ Y Formulate a materials-balance–kinetics relation for an
dt g dt
aerated lagoon, such as at Northglenn. From what you

dX
¼ mX (22.30) have done, estimate the effluent BOD at the Northglenn
dt
g aerated lagoon.
m dS=dt
(23.48)
Y ¼ X
Substrate degradation rate Q
Q
θ=24h
dS 1 S =300mg BOD/L S
^ m X (22.32) S o
dt ¼ Y K s þ S
Net rate of cell synthesis
FIGURE P23.1 Aerated lagoon.
½ dX=dtŠ net ¼ m b (22.36)
X
23.2 Conventional Activated-Sludge Wasting
½ dX=dtŠ net (22.37)
m(net) Given
X
Assume the following data apply for complete-mix acti-
m(net) ¼ m b (22.38)
vated-sludge system that treats municipal wastewater
3
Q ¼ 0.066 m =s (1.5 mgd)
Sludge age related to m(net) 3
V(reactor) ¼ 1426 m
V(reactor) X S o ¼ 260 mg=L.
(22.52)
u c ¼
S ¼ 30 mg=L
WX r
1
(22.53) Required
u c
^ m b
Calculate the sludge-wasting rate, R (also called W).
0
1
m (22.54)
c ^ m b
u 23.3 Conventional Activated Sludge for New Conditions
Given
Substrate utilization rate defined and related to m=Y An activated-sludge system treats a municipal waste-
water. Assume the system operates under steady-state
S o S 3
(22.43) conditions. The flow was Q ¼ 0.044 m =s (1.0 mgd).
U
uX
The detention time in the reactor was 6 h. The effluent
m
(22.44) BOD, was measured as S(1.0 mgd) ¼ 20 mg=L.
Y 3
U ¼
The flow is increased to Q ¼ 0.066 m =s (1.5 mgd).
1
¼ YU b (22.58) Calculate S(1.5 mgd), the effluent BOD concentration.
u c
S o does not change.
F=M defined and related to U
Required
3
F S o 1. Effluent BOD for Q ¼ 0.066 m =s.
(22.45)
M uX 2. Calculate the sludge-wasting rate R . 0
23.4 Conventional Activated-Sludge Treatment of

S o S o S
(22.47)
uX S o
U ¼ Toluene
Given

S o S
An activated-sludge system treats toluene at 258C with
E ¼
S o
influent concentration, S o ¼ 60 mg=L. The flow was
3
Net cell yield as affected by sludge age Q ¼ 0.044 m =s (1.0 mgd). The effluent concentration,
is required to be S ¼ 20 mg=L. Assume the system
Y
(22.28)
Y(net) ¼ operates under steady-state conditions. Kinetic coeffi-
1 þ bu c
cients from a study by Chang (1991) and reported in