Environmental Engineering Reference
In-Depth Information
Therefore,
d
C
A
d
t
=
k
F
(C
A0
−
C
A
)
−
k
tot
C
A
.
(6.73)
Expressions for individual rate constants are given in Table 6.1. Note that a similar
equation was used in Example 6.2 to illustrate the loss mechanisms in a wastewater
surface impoundment.
E
XAMPLE
6.7 F
ATE OF
T
ETRACHLOROETHENE IN
L
AKE
G
RIEFENSEE
,
S
WITZERLAND
Schwarzenbach et al. (1998) have estimated the following parameters for Lake
Griefensee: Average area
=
2
×
10
6
m
2
, average epilimnion depth
=
5 m, particulate
matter concentration
=
2
×
10
−
6
kg/L, average particulate settling velocity
=
2.5 m/d,
average
K
w
for
tetrachloroethene
(TetCE)
=
0.15 m/d, average load of TetCE per
day to the lake
=
0.1 kg/d, average flow rate of water
=
2.5
×
10
5
m
3
/d. Estimate the
steady-state removal of TetCE in the lake.
Firstly,notethatTetCEisarefractorycompound.Henceforthezerothapproximation,
let us assume that chemical, photochemical, and biological reactions are negligible.
K
aw
for TetCE is 0.6 at 298 K. Log
K
ow
=
2.1. Hence log
K
ow
=
(
0.92
)
(
2.10
)
−
0.23
=
1.70. Hence
K
oc
=
K
c
=
50 L/kg.
φ
p
A
=
(
50
)(
2
×
10
−
6
)/
[
1
+
(
50
)
(
2
×
10
−
6
)
]=
1
×
10
−
4
.
k
voln
=
(
0.15
)(
1
)/
5
=
0.03 d
−
1
,
k
sed
=
(
2.5
)(
1
×
10
−
4
)/
5
=
10
−
5
d
−
1
,
k
F
=
10
5
/(
5
)(
2
10
6
)
=
0.025 d
−
1
. At steady state,
(C
A0
−
5
×
2.5
×
×
C
A
/C
A
)
=
(k
voln
+
k
sed
/k
F
)
=
1.2. Hence 1
−
C
A
/C
A0
=
0.55.
TABLE 6.1
Expressions for First-Order Rate Constants in a CSTR Model
for the Epilimnion of a Lake
Process
Rate Constant
Expression
Flushing
k
F
Q
F
/V
e
K
W
h
e
1
A
p
Volatilization
k
voln
− φ
U
set
h
e
p
A
Reaction loss
k
rxn
+
k
photo
+
k
bio
Specific to chemicals
Notes: Q
F
=
feed rate, m
3
/d;
V
e
=
epilimnion volume, m
3
;
K
w
=
overall liquid-
phase mass transfer coefficient of A, m/d;
h
e
=
height of the epilimnion, m;
ϕ
φ
Sedimentation
k
sed
A
=
fraction of A bound to particulates,
K
oc
C
C
/ (
1
+
K
oc
C
C
)
, where
K
oc
is
the organic carbon-based partition constant of A (L
/
kg),
C
C
is the particulate
organic carbon concentration, L
/
kg, and
U
set
=
average settling velocity of
particulates, m
/
d.
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