Environmental Engineering Reference
In-Depth Information
1.0
Removal with
tailing
0.5
heoretical
removal
0
0
1
2
Water-filled aquifer volume
FIGURE 6.61
Phenomena of tailing-off in conventional P&T process for groundwater
remediation.
The process can be modeled by considering the aquifer to be a completely mixed
reactor (CSTR). If we consider a total volume
V
T
of the aquifer, the fluid volume is
ε
is the porosity of solids.A mass balance on the continuous reactor gives
the following:
V
T
, where
ε
rate in with water
=
rate out with water
+
accumulation rate (solids
+
pore fluid
)
.
d
[
]
d
t
+
A
d
W
A
d
t
.
Q
[
A
]
in
=
Q
[
A
]+
V
T
(
1
−
)V
T
ρ
s
(6.217)
If local equilibrium between solids and pore fluid is assumed,
W
A
=
K
sw
[A]. More-
over, if pure water is brought into contact from the injection well, [A]
in
=
0.
Hence,
Q
R
F
[
]
V
T
=
A
d
[
]
d
t
,
A
−
(6.218)
where
Q
is the volumetric flow rate and
R
F
= ε +
(
1
− ε
)
ρ
s
K
sw
is the retardation
factor. Integrating the above equation gives
exp
.
[
]
A
Qt
R
F
V
T
]
0
=
−
(6.219)
[
A
Hence, the time taken to flush 50% of the contaminant in porewater will be
t
1
/
2
=
0.693
(R
F
V
T
/Q)
. Thus, cleanup time will increase with increasing
R
F
and decreasing
Q
. Note that
[
A
]
0
=
M
0
/V
T
R
F
, where
M
0
is the total initial mass of the contaminant.
Note that
(Qt/
ε
V
T
)
is the number of pore volumes,
N
PV
flushed in time
t
. Therefore,
[
exp
.
A
]
−
N
PV
R
F
]
0
=
(6.220)
[
A
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