Geoscience Reference
In-Depth Information
and sorbed components are included here. The details of handling the particulate
contaminant can be found in Lang and Chapra (1982).
Sorption and desorption of contaminants on sediment particles are often described
by the linear isotherm:
s
s
C
d
1
R
ad
=
k
ad
ρ
s
=
k
ad
r
sw
C
d
(12.95)
−
R
de
=
k
de
C
s
(12.96)
m
−
3
s
−
1
), respectively;
where
R
ad
and
R
de
are the sorption and desorption rates (mg
·
k
ad
is the sorption rate coefficient (m
3
kg
−
1
s
−
1
);
k
de
is the desorption rate coefficient
·
(s
−
1
);
m
−
3
);
s
is the volumetric concentration of sediment
(unitless); and
r
sw
is the sediment-to-water phase ratio (kg
ρ
s
is the sediment density (kg
·
m
−
3
), defined as
r
sw
·
=
ρ
s
s
/(
1
−
s
)
. In the water column, usually
s
1, so
r
sw
=
ρ
s
s
. In the sediment bed,
p
m
, and thus
r
sw
=
ρ
s
(
p
m
)/
p
m
. Here,
p
m
is the porosity of bed
s
is equal to 1
−
1
−
material.
In the equilibrium state, the sorption and desorption rates in Eqs. (12.95) and (12.96)
should be equal, thus yielding
C
s
C
d
=
k
ad
r
sw
k
de
=
k
D
r
sw
(12.97)
k
de
(m
3
kg
−
1
).
where
k
D
is the equilibrium partition coefficient, defined as
k
D
=
k
ad
/
Using Eqs. (12.94) and (12.97) yields
C
d
C
t
=
1
C
s
C
t
=
k
D
r
sw
f
d
=
k
D
r
sw
,
f
s
=
(12.98)
1
+
1
+
k
D
r
sw
where
f
d
and
f
s
are the fractions of the dissolved and sorbed contaminants in the
equilibrium state, respectively.
In fact, other models, such as the Langmuir isotherm and Freundlich isotherm, are
also commonly used. The sorption rate in Eq. (12.95) can be replaced by
k
ad
r
sw
C
d
1
C
s
C
s
,max
R
ad
=
−
(12.99)
where
C
s
,max
is the maximum concentration of contaminant sorbed to sediment.
Eq. (12.99) implies that the sorption process is limited by the maximum concentra-
tion of the sorbed contaminant. In the equilibrium state, equating the sorption and
desorption rates in Eqs. (12.99) and (12.96) leads to
C
d
aC
d
C
s
=
C
s
,max
)
=
C
s
,max
(12.100)
C
d
+
C
s
,max
/(
k
D
r
sw
1
+
aC
d
where
a
is the Langmuir sorption coefficient, defined as
a
=
k
D
r
sw
/
C
s
,max
.
