Geoscience Reference
In-Depth Information
a large number of physical, chemical and biological processes that interact with one
another. Modeling the fate and transport of these pollutants and the resulting water
quality in aquatic systems is an important task in environmental engineering. Some
important aspects of water quality modeling are briefly described here. More details
may be found in Thomann and Mueller (1987), Huber (1993), and Chapra (1997).
12.2.1 Kinetics and rate coefficients
The production or loss of a constituent, with or without interaction with other
constituents, is a kinetic process (Huber, 1993). Examples of kinetic processes
include decay of bacteria, oxidation of carbonaceous materials, and oxidation of
nitrogen compounds. Such processes are usually quantified through the following
equation:
DC
i
Dt
=
S
c
=
f
(
C
i
,
C
j
,
T
)
j
=
1, 2,
...
(12.43)
where
C
i
is the concentration of constituent
i
,
T
is the water temperature,
DC
i
/
Dt
denotes the rate of change in concentration of constituent
i
. In the 1-D model,
DC
/
Dt
is defined as
∂(
E
L
A
∂
DC
Dt
1
A
AC
)
+
∂(
QC
)
−
∂
∂
C
=
(12.44)
∂
t
∂
x
x
∂
x
where
C
is the constituent concentration averaged over the cross-section, and
E
L
is
the longitudinal effective diffusivity (mixing coefficient).
In the depth-averaged 2-D model,
DC
/
Dt
is
∂(
E
x
h
∂
E
y
h
∂
DC
Dt
1
h
hC
)
+
∂(
hU
x
C
)
+
∂(
hU
y
C
)
−
∂
∂
C
−
∂
∂
C
=
∂
t
∂
x
∂
y
x
∂
x
y
∂
y
(12.45)
where
C
is the depth-averaged constituent concentration, and
E
i
(
i
=
x
,
y
)
are the
horizontal effective diffusivities.
In the width-averaged 2-D model,
DC
/
Dt
is
∂(
E
x
b
∂
E
z
b
∂
DC
Dt
1
b
bC
)
+
∂(
bU
x
C
)
+
∂(
bU
z
C
)
−
∂
∂
C
−
∂
∂
C
=
∂
t
∂
x
∂
z
x
∂
x
z
∂
z
(12.46)
where
C
is the width-averaged constituent concentration, and
E
i
(
i
=
x
,
z
)
are the
effective diffusivities in the longitudinal section.
