Geoscience Reference
In-Depth Information
where
M
s
′
=
concentration of sediment in water in segment [kg
s
l
w
−1
]
B
′
=
concentration of dissolved organic carbon in water in segment [kg
B
l
w
−1
]
C
w
′
=
concentration of dissolved chemical in water in segment [mg l
w
−1
]
C
s
=
concentration of sorbed chemical on sediment in segment [mg l
−1
]
C
B
=
concentration of DOC-sorbed chemical in segment [mg l
−1
]
n
=
porosity or volume water per volume segment [l
w
l
−1
]
The forward reaction is sorption and the backward reaction is desorption. These
reactions are usually fast in comparison with the model time step, and can usually
be considered in local equilibrium. The phase concentrations
C
w
,
C
s
, and
C
B
are
governed by the equilibrium partition coefficients
K
ps
0
and
K
pB
(l kg
−1
):
Cn
MC
/
C
C
′
′
K
=
s
′
=
s
(4.52)
ps
0
′ ⋅
s
w
w
Cn
BC
/
C
C
′
′
K
=
B
′
=
B
(4.53)
pB
′ ⋅
w
w
C
B
=
concentration of DOC-sorbed chemical in segment [mg l
−1
]
C
B
′
=
concentration of DOC-sorbed chemical in segment (
C
B
/
B
) [mg kg
−1
]
B
=
concentration of DOC in segment [kg l
−1
]
B
′
=
concentration of DOC in water in segment (
B
/
n
) [kg l
W
−1
]
n
=
porosity or volume water per volume segment [l
W
1
l
−1
]
These two equations describe the linear form of the Freundlich isotherm, appli-
cable when sorption sites on sediment and DOC are plentiful:
C
s
′
=
K
ps
⋅
C
w
′
(4.54)
C
B
′
=
K
pB
⋅
C
w
′
(4.55)
where
K
ps
is the partition coefficient of chemical on sediment in segment [l
w
kg
s
−1
]
and
K
pB
is the partition coefficient of chemical on DOC in segment [l
w
kg
B
−1
]
The total chemical concentration is the sum of the five phase concentrations:
∑
CCn
= ′ ⋅+ ′ ⋅ +′ ⋅
CM CB
(4.56)
w
s
s
B
s
Substituting in equations, factoring, and rearranging terms gives the dissolved
fraction
f
D
:
Cn
C
′ ⋅
n
nK B
f
=
w
=
(4.57)
∑
D
+⋅ + ⋅
K M
pB
ps
s
s
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