Geoscience Reference
In-Depth Information
The contaminant mass balance equations for the underlying layers can be derived
similarly, which are not presented here.
Note that Eqs. (12.114), (12.115), (12.117), and (12.118) are the governing
equations of the non-equilibrium partition model in the sediment bed. In analogy
to the equilibrium partition model in the water column described in Section 12.3.2.2,
the equilibrium partition model in the sediment bed can be established for the cases
where the sorption and desorption processes proceed much faster than other processes.
Thus, the fractions of the dissolved and sorbed contaminants in the sediment bed are
determined using Eq. (12.98) or (12.101), and the equations for the total concentra-
tion of contaminant in bed layers 1 and 2 are obtained by summing Eqs. (12.114) and
(12.115) and summing Eqs. (12.117) and (12.118):
∂(δ
1
C
tb
,1
)
=
Q
tb
,1
−
k
tb
,1
δ
1
C
tb
,1
−
k
dbw
(
f
db
,1
C
tb
,1
−
f
dw
C
tw
)
−
q
t
,
ex
∂
t
+
k
db
12
(
f
db
,2
C
tb
,2
−
f
db
,1
C
tb
,1
)
+
q
tb
12
(12.119)
∂(δ
2
C
tb
,2
)
∂
=
Q
tb
,2
−
k
tb
,2
δ
2
C
tb
,2
−
k
db
12
(
f
db
,2
C
tb
,2
−
f
db
,1
C
tb
,1
)
−
q
tb
12
t
+
k
db
23
(
f
db
,3
C
tb
,3
−
f
db
,2
C
tb
,2
)
+
q
tb
23
(12.120)
where
C
tb
,
i
is the total concentration of contaminant in bed layer
i
;
Q
tb
,
i
is the total
contaminant loading rate in bed layer
i
;
k
tb
,
i
is the total contaminant decay coefficient
in bed layer
i
;
q
tb
12
and
q
tb
23
are the total exchange rates of contaminant between
bed layers 1 and 2 and between layers 2 and 3, respectively, due to interface lowering
or rising; and
f
db
,
i
is the fraction of the dissolved contaminant in bed layer
i
. The
following relations exist:
q
tb
12
=
q
db
12
+
q
sb
12
(12.121)
Q
tb
,
i
=
Q
db
,
i
+
Q
sb
,
i
(12.122)
k
tb
,
i
=
f
db
,
i
k
db
,
i
+
f
sb
,
i
k
sb
,
i
(12.123)
where
f
sb
,
i
is the fraction of the sorbed contaminant in bed layer
i
.
Note that the above multiple-layer flux model is simple, but its application should
be limited to the situations where the effects of groundwater flow are neligible or can
be lumped into the diffusion process between the bed layers.
