SOLUTIONS
HOMEWORK NO. 6
CE 3400 – Introduction of Environmental Engineering
Material Covered:
Chapter 11 (Wastewater Treatment) in Vesilind et al., 2010
1.
This is Problem 11.11 in your textbook (reworded slightly for clarification)
Mean cell residence time (MCRT or
θ
c
) is also called ‘sludge age’.
Calculate
the sludge age if an aeration tank in an activated sludge system has a hydraulic
retention time of 2 hours and a suspended solids concentration of 2,000 mg/L.
The flow rate of influent wastewater to the aeration basin is 1.5 m
3
/min, the
return sludge solids concentration is 12,000 mg/L, and the flow rate of waste
activated sludge (WAS) is 0.02 m
3
/min.
Assume that Q
w
= Q
r
. Hint: You need
to calculate values of
θ
c
for sludge wasted from both the aeration basin and the
recycle line.
Start by calculating the volume of the reactor.
It might help to
draw a diagram and label it before starting.
Answers
:
θ
c
(aeration basin) = ~6 days
θ
c
(recycle line) = ~1 day
Known:
Hydraulic retention time = 2 hr
X
r
= 12,000 mg/L
X = 2,000 mg/L (= SS in aeration basin)
X
w
= 2,000 mg/L
Q = 1.5 m
3
/min
Q
w
= 0.02 m
3
/min
NOTE:
X = X
w
but X
≠
X
r
and X
w
≠
X
r
Step 1
: Calculate
V
of aeration basin because you know
t
and
Q
:
t
=
V
Q
so V
=
t
Q
V
=
(2
hr
) (1.5
m
3
/min)
=
120 min (1.5
m
3
/min)
=
180
m
3
Step 2
:
Calculate sludge age (
θ
c
) for sludge wasting from (a) aeration basin and from (b) recycle line:
(
a
)
θ
c
=
VX
Q
w
X
w
=
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 Spring '10
 Colberg
 Environmental Engineering, Activated sludge, MLSS, aeration basin, Θc

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