Geoscience Reference
In-Depth Information
D
b
at the bed, the pore water in the
sediment bed also exchanges with the water column at a rate
As sediment exchanges at the net rate
E
b
−
p
m
/(
p
m
)
(
E
b
−
D
b
)
1
−
.
Consequently, the dissolved contaminant exchanges at a rate:
p
m
C
db
C
dw
1
q
d
,
ex
=
max
(
E
b
−
D
b
,0
)
p
m
+
min
(
E
b
−
D
b
,0
)
p
m
1
−
1
−
−
s
(12.108)
p
m
and 1
/
/(
−
)
The factors 1
1
s
are used in Eq. (12.108) to convert the net water
p
m
/(
p
m
)
flux
to the volumes of the corresponding water and sediment
mixtures in the sediment bed and water column, respectively, in which
C
db
and
C
dw
are defined. The parameter
p
m
is cancelled in the first term on the right-hand of
Eq. (12.108).
Note that the porosity
p
m
of the bed surface layer in Eq. (12.108) is assumed to have
the same value in cases of erosion and deposition. However, different values might be
used, because the newly deposited material is unconsolidated and the eroded material
may be partially- or fully-consolidated in the case of cohesive sediment.
In addition, the expulsion of pore water due to consolidation of cohesive bed mate-
rial, infiltration, and seepage flow also results in the dissolved contaminant flux
between the water column and the sediment bed. These effects may be included in
the loading terms
q
dw
and
q
sw
, as discussed above.
(
E
b
−
D
b
)
1
−
12.3.2.2 Equilibrium partition model
In cases where the time scale of sorption and desorption processes is much faster than
that of flow and sediment transport, the sorption and desorption may be assumed
to reach the equilibrium state instantaneously. The fractions of the dissolved and
sorbed contaminants can then be determined using Eq. (12.98) or (12.101). This is
called the equilibrium partition model. Because Eq. (12.98) or (12.101) provides an
algebraic relation between
C
dw
and
C
sw
, it is only necessary to compute the total
concentration of contaminant, which is determined in the 1-D and depth-averaged
2-D models by
J
d
,
aw
h
DC
tw
Dt
k
dbw
h
(
q
t
,
ex
h
=
+
q
tw
−
k
tw
C
tw
+
f
db
C
tb
−
f
dw
C
tw
)
+
(12.109)
where
C
tw
is the total concentration of contaminant in the water column,
k
tw
is the total contaminant decay coefficient,
q
tw
is the total loading rate of con-
taminant per unit volume,
f
dw
is the fraction of the dissolved contaminant
over the total contaminant in the water column,
f
db
is the fraction of the dis-
solved contaminant over the total contaminant in the bed surface layer, and
q
t
,
ex
is the total exchange rate of contaminant due to sediment erosion and
deposition.
Eq. (12.109) can be derived by summing Eqs. (12.102) and (12.103). Similarly, the
3-D or width-averaged 2-D equation for the total concentration of contaminant can
