Geoscience Reference
In-Depth Information
dissolved and sorbed contaminants in the water column are
DC
dw
Dt
=
q
dw
−
k
ad
,
w
r
sw
C
dw
+
k
de
,
w
C
sw
−
k
dw
C
dw
(12.104)
DC
sw
Dt
−
∂(ω
s
C
sw
)
=
q
sw
+
k
ad
,
w
r
sw
C
dw
−
k
de
,
w
C
sw
−
k
sw
C
sw
(12.105)
∂
z
where
s
is the settling velocity of sediment particles.
In each of the above models, two differential equations are used to determine the
concentrations of the dissolved and sorbed contaminants. This approach is generally
applied to simulate the non-equilibrium sorption and desorption processes, and thus
is called the non-equilibrium partition model.
The loading rates
q
dw
and
q
sw
in Eqs. (12.102)-(12.105) account for external
loading or loss due to side inflow, rainfall, infiltration, seepage flow, biochemical
interaction with other constituents, etc.
Many toxic substances, such as PCBs, transfer across the water surface by
volatilization. The interfacial transfer rate of a dissolved gas is modeled by (see
Chapra, 1997)
ω
p
g
H
e
−
C
dw
J
d
,
aw
=
v
(12.106)
ν
s
−
1
),
p
g
is the
partial pressure of gas in the air over the water (atm), and
H
e
is Henry's constant
(atm
where
v
is the net transfer velocity across the water surface (m
·
ν
m
3
mg
−
1
). As described in Section 12.2.2, for dissolved oxygen, Eq. (12.106)
can be rewritten as
J
d
,
aw
=
·
. For substances that are not abundant
in the atmosphere,
p
g
can be assumed to be zero.
Mass may exchange at the bed surface through a variety of mechanisms. The most
common one is the diffusion flux across the bed surface. In particular, in the case of
lakes and reservoirs, the flow is slow, so diffusion is the main mode of bed release.
This diffusion flux across the bed surface is modeled in Eq. (12.102) by the term
k
dbw
(
K
L
(
C
sDO
−
C
DO
)
, which is similar to Eq. (12.89).
The sorbed contaminant exchanges at the bed as sediment erosion or deposition
occurs. This exchange rate is determined by
C
db
−
C
dw
)
C
sb
C
sw
s
q
s
,
ex
=
max
(
E
b
−
D
b
,0
)
p
m
+
min
(
E
b
−
D
b
,0
)
(12.107)
−
1
s
−
1
), defined in
Eqs. (11.14) and (11.19), respectively;
s
is the volumetric concentration of sediment in
the water column; and
p
m
is the porosity of sediment in the bed surface layer. The two
terms on the right-hand side of Eq. (12.107) represent the cases of net erosion and net
deposition, respectively. The factors 1
where
D
b
and
E
b
are the sediment deposition and erosion rates (m
·
p
m
)
/(
−
/
1
and 1
s
are introduced in Eq. (12.107)
to convert the net sediment flux
E
b
−
D
b
to the volumes of the corresponding water
and sediment mixtures in the sediment bed and water column, respectively, in which
C
sb
and
C
sw
are defined.
