Environmental Engineering Reference
In-Depth Information
6.4.1.1.2 Transport of the Dissolved Contaminant in Groundwater
Pollutant that solubilizes in the aqueous phase is transported with the groundwater.
As the solubilized pollutant moves through the heterogeneous subterranean soil pore-
water, it adsorbs to the soil particles. Hence, we have to consider both soluble and
adsorbed contaminant mass in ascertaining the transport in the groundwater environ-
ment. Nonideal plug flow is assumed because of the soil heterogeneity. Consider a
volume element in the direction of groundwater flow (Figure 6.53). Advective and
dispersive terms comprise both feed and effluent rates. The advective term is
U
[A]
and dispersion is given by
−
D∂
[
A
]
/∂x
, evaluated at appropriate
x
co-ordinates.Accu-
mulation of mass occurs in both solid and liquid phases. Reaction losses occur in the
liquid phase as a result of chemical or microbiological processes. Note that for the
porous solid the volume is
ε
A
c
Δ
x
. The overall material balance is as follows:
rate in
=
rate out
+
accumulation
+
reaction loss.
x
= ε
x
+Δ
x
A
c
D
∂
[
A
]
A
c
D
∂
[
A
]
ε
A
c
U
[
A
]|
x
− ε
A
c
U
[
A
]|
x
+Δ
x
− ε
∂x
∂x
+ ε
A
c
Δ
x
∂
[
A
]
tot
∂t
+
r
A
ε
A
c
Δ
x
.
(6.201)
Note that [A] is the concentration in the mobile phase (water) and [A]
tot
is the total
concentration (porewater
+
solid). Dividing throughout by
ε
A
c
Δ
x
and taking the limit
as
Δ
x
→
0, we obtain after rearrangement,
D
∂
2
[
]
]
∂x
−
[
[
]
tot
∂t
A
U
∂
A
∂
A
−
r
A
=
.
(6.202)
∂x
2
The above expression is the general
advective-dispersive equation
in the
x
co-
ordinate.Notethatontheright-handsideoftheequation,
[
A
]
tot
= ε[
A
]+
(
1
− ε
)
ρ
s
W
A
,
Reaction loss
Euent
(Advection
+
Dispersion)
Porous
media
Feed
(Advection
+
Dispersion)
Accumulation on solids
Accumulation in liquid phase
FIGURE 6.53
A volume element and transport kinetics in the groundwater environment.
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