Environmental Engineering Reference
In-Depth Information
Soil surface
Groundwater
flow
NAPL ganglion
x
s
Flow velocity, u
FIGURE 6.52
An NAPL ganglion dissolving in groundwater.
6
[A]
∗
−
[A]
,
d
[
A
]
d
t
=
k
L
u
D
θ
N
D
p
(6.199)
where
f
(
x
,
t)
and
u
D
is the Darcy velocity, defined later in this section. The
above equation is applicable for plug-flow conditions. We assume that the reduction
in NAPL volume is minimal, and hence
D
p
=
[
A
]=
D
0
and
θ
N
= θ
0
(the initial values).The
volume fraction
θ
0
is the spread over a length
X
s
. Integrating the resulting equation
gives us the concentration of A at the edge of the plume,
[
A
]
e
−[
(k
L
/u
D
)(
6
θ
0
/D
0
)X
s
]
.
]
∗
=
1
−
(6.200)
[
A
Numerous correlations exist for
k
L
in the chemical engineering literature. Hunt et al.
(1988) used the correlation
k
L
ε
T
/
1.09
u
D
=
Pe
−
2
/
3
, where
Pe
is the Peclet number
given by
u
D
D
p
/D
w
, and
D
w
is the molecular diffusivity of the NAPL in water.
E
XAMPLE
6.26 NAPL G
ANGLION
S
OLUBILIZATION
Let us consider an initial volume fraction
θ
o
of 0.05 over a total horizontal extent
of 10 m. In this case
θ
o
X
s
=
0.5 m. For a typical Darcy velocity of 1 m/day, and a
D
o
=
0.1 m, and for a typical molecular diffusivity in water of 8.6
×
10
−
5
m
2
/d, we
obtain
Pe
=
1157. If
ε
T
=
0.4,
k
L
=
0.024 m/d. Hence
[
A
]
/
[
A
]
∗
=
0.51.As the globule
dissolves, both its diameter and volume decrease (Powers et al., 1991). To obtain the
actual solubilized mass in water, the change in volume should be taken into account.The
ganglionlifetimesarefoundtobeweakfunctionsoftheflowvelocity.Asaconsequence,
very large volumes of water are necessary to reduce the ganglion size. Therefore, one
ends up with an expensive above-ground treatment system.
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