Environmental Engineering Reference
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10
−
5
mol/L; an underlying flow of clean water with simplified water chemistry
and a dissolved oxygen concentration of 4
1
×
10
−
4
mol/L were selected as bound-
ary conditions. The simulations were run for a total simulation time of 1200 days,
subdivided into 600 time steps.
In steady state groundwater plumes, a balance between microbial growth and
decay can be considered and the aerobic degradation of toluene can be summarized
by the following redox reaction (Wiedemeier et al.
1999
):
×
7HCO
3
7H
+
C
7
H
8
+
9O
2
+
3H
2
O
→
+
(19.17)
For the present modeling study a so-called double Monod formulation was used
to describe the reaction kinetics. It is a commonly used expression (e.g. Barry et al.
2002
) and it takes into account the reaction rate dependence on both the electron
donor (toluene) and the electron acceptor (oxygen), as follows:
∂
[
C
7
H
8
]
∂
[
C
7
H
8
]
K
C
7
H
8
+
[
O
2
]
K
O
2
+
=−
k
(19.18)
t
[
C
7
H
8
]
[
O
2
]
where
k
is the kinetic rate constant [mol L
−
1
s
−
1
] and
K
C7H8
,
K
O2
are the half-
saturation Monod constants for toluene and oxygen [mol L
−
1
]. A value of 5
10
−
11
mol L
−
1
s
−
1
was selected for the kinetic constant in the base modeling scenario
while the half-saturation constants were set to 1
×
10
−
5
mol L
−
1
for all the simula-
tion runs. The results of the base scenario, after a total simulation time of 1200 days,
are shown in Fig.
19.8a
. It can be observed that despite the continuous supply of
toluene, the plume reaches a steady state length
L
×
712.5 m, when the contaminant
mass flux removed by aerobic degradation equals the contaminant input. Evolving
from this base case a number of additional scenarios was computed to identify and
quantify the influence and sensitivity of individual parameters on steady state plume
length.
Figure
19.9
, for example, shows the effect of transverse dispersivity. This param-
eter largely controls the mixing of reaction partners and, therefore, it is of pivotal
importance for microbially mediated fringe degradation reactions. As shown in
Fig.
19.9
(squares), longer steady state plumes were computed with decreasing
transverse dispersivity (
=
α
T
). A linear relationship between the plume length and the
inverse of the transverse dispersivity was derived also in similar two-dimensional
studies with different boundary conditions compared to the present scenario. For
instance, Liedl et al. (
2005
) derived the following analytical solution of steady
state plume length in a completely contaminated aquifer with supply of the electron
acceptor just from the top, through the water table:
ln
4
π
c
D
+
c
A
4
M
2
π
γ
L
=
(19.19)
2
α
T
c
A
where
c
D
0
and
c
A
0
are the initial concentrations of electron donor and acceptor,
α
T
is the vertical transverse dispersivity,
M
is the source thickness and
γ
is the
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