CWR 6537 Subsurface Contaminant Hydrology
1
ADVECTIVEDISPERSIVE TRANSPORT OF REACTIVE SOLUTES:
Equilibrium Sorption Cases
A.
Lecture Goal:
To investigate solute transport under the assumption that a contaminant will undergo
equilibrium,
reversible
sorption to the porous medium solid matrix during transient and steady
water flow.
B.
Reactive Solutes:
Equilibrium Models
We will now consider “reactive” or adsorbed solute transport through porous media.
A
reactive solute interacts with the solid matrix during flow, as opposed to an “ideal” solute that is
transported passively through the porous medium with no interactions or reactions with the solid
matrix.
A sorbed solute is one that is sorbed and desorbed (if sorption is reversible) by the
porous medium. The solute is therefore distributed between the fluid (solution and/or gas) and
the sorbed phases.
Note on terminology:
See attached copy of paper for a discussion of various mechanisms
responsible for sorption of solutes by the solid matrix.
You will
see various terms like
“sorption” or “uptake” or “adsorption” or “partitioning” – depending on the mechanism
responsible – to describe the phenomenon of interest to us here.
The distribution of the solute
between the solid phase and the solution phase.
Some refer to it as simply “retention”.
We will
use the term “soption” throughout this course.
(i)
Let, S represent the mass of solute sorbed per gram of solid matrix, M M
1
.
[for example,
µ
g/g solid; meq/g solid; etc].
(ii)
Let
ρ
be the porous medium bulk density; M L
3
[ for example, g solids/cm
3
total].
(iii)
Let C
w
be the solutionphase concentration; M L
3
[for example,
µ
g/ml ; meq/ml].
(iv)
Let
θ
w
be the volumetric water content; L
3
L
3
[for example, ml/cm
3
total]
The total mass of solute, M
T
, per unit volume the porous medium is simply the sum of the
solute mass present in the solutionphase (M
w
) and that in the sorbed phase (M
s
).
Thus,
M
T
= M
w
+ M
s
= (
θ
w
C
w
) + (
ρ
S
)
(
1
)
g
g
cm
g
ml
g
cm
ml
µ
µ
µ
⋅
+
⋅
=
3
3
3
We have shown earlier, from the continuity equation, that
x
J

=
t
M
s
T
∂
∂
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2
Substituting Eq[1] in [2],
x
J

=
S
+
C
t
s
w
w
∂
∂
∂
∂
]
[
ρ
θ
(
3
)
Recall that for advectivedispersive solute transport, the total solute flux is given as:
]
[
]
[
C
q
+
t
C
D

=
J
w
w
w
w
s
∂
θ
For
steady water flow, under saturated or uniformly unsaturated conditions,
in homogeneous
media, (that is, with
θ
w
and q
w
being constant):
x
C
q

x
C
D
=
t
S
+
t
C
w
w
2
w
2
w
w
w
∂
∂
∂
∂
∂
∂
ρ
θ
(
4
)
x
C
v

x
C
D
=
t
S
+
t
C
w
2
w
2
w
w
∂
∂
∂
∂
∂
∂
θ
ρ
(
5
)
where
ν
is the average porewater velocity,
ν
=
(q
w
/
θ
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 Spring '08
 Jawitz
 Solubility, Freundlich isotherm, Subsurface Contaminant Hydrology

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