Environmental Engineering Reference
In-Depth Information
Wind
(Diffusion + Advection)
Soil surface
x
Vadose zone
z
Reaction
Soil
Groundwater
FIGURE 6.58 Transport of a contaminant from the soil to the atmosphere.
there exist both pore air and porewater. The mobile phase is air, while both porewater
and solids are immobile with respect to the contaminant. The advective-dispersion
equation derived is applicable with the stipulation that [A] represents the pore air
concentration and [A] tot is the total concentration (pore air
solid
phase). D should be replaced by the effective molecular diffusivity in partially satu-
rated air, D g , and U g is the advective gas-phase velocity. R A denotes the biochemical
reaction loss of compound A in pore air and porewater.
+
porewater
+
2
] g
∂z 2
[
A
[
] g
∂z R A =
A
[ A ] tot
∂t
D g
U g
.
(6.214)
If the air-filled and water-filled porosities are ε g and ε w , respectively, then a
total mass conservation gives [A] tot =
mass in pore air
+
mass in porewater
+
mass
on soil particles
− ε g − ε w )W A . Since local equilibrium
is assumed between the three phases, [A] w =[
= ε g [
A
] g + ε w [A] w + ρ s ( 1
A
] g /K aw , W A =
K SA [A] g . With
theseexpressions,wehave[A] tot =
R F [A] g ,where R F = ε g + ( ε w /K aw ) +
( 1
− ε g
ε w )
ρ s K SA is the retardation factor. If we further consider the case where R A =
0 and
advective velocity is negligible, we have
2
[ A ] g
∂t =
D g
R F
[ A ] g
∂z 2
.
(6.215)
Thus molecular diffusion through pore air is the dominant mechanism in this case.
The initial condition is [A] g ( z ,0 )
=[
A
] 0 for all z . The following two boundary
D g
] g /∂z +
conditions are applicable: (i) [A] g (
, t)
=[
A
] 0 for all t and (ii)
[
A
k a [A] g (z , t)
0. The second boundary condition states that at the surface
there is a reaction or mass transfer loss of chemical, thus contributing to a resistance to
=
0at z
=
 
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