SOLUTIONS
HOMEWORK NO. 3
CE 3400 – Introduction of Environmental Engineering
Material Covered:
Chapter 6 (REACTORS) in Vesilind et al., 2010
1.
A CSTR is used to treat an industrial waste, using a reaction that destroys the
pollutant according to firstorder kinetics with k = 0.216 day
1
.
The reactor volume
is 500 m
3
, the volumetric flow rate of the single inlet and exit is 50 m
3
/day, and the
inlet pollutant concentration is 100 mg/L.
What is the concentration of the pollutant
in the treated effluent?
Find
:
C
out
Assumptions
:
steady state (Q
in
= Q
out
), consumption of pollutant, perfect mixing,
no concentration or temperature gradients in reactor, firstorder reaction kinetics
Volumetric Mass Balance:
Q
in
= Q
out
so use Q without subscripts in equations
dC
dt
V
=
QC
in
−
QC
out
+
r
1
V
−
r
2
V
Assume steady state so:
dC
dt
V
=
0 because
dC
dt
in reactor not changing w/ time
0
=
QC
in
=
QC
out
−
r
2
V
Since
r
=
kC
, then 0
=
QC
in
−
QC
out
−
kCV
C
o
C
=
1
+
k
V
Q
C
=
QC
o
Q
+
kV
(Equation found on p.184 of textbook)
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 Spring '10
 Colberg
 Environmental Engineering, Steady State, Rate equation, Qin

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