Agriculture Reference
In-Depth Information
source covers a length 2
a
along the inlet boundary at
z
=
0 and is located symmet-
rically about the coordinate
x
=
0. The transport region of interest is the half-plane
(
z
≥
0; -
∞≤
x
≤∞
). The boundary condition may be written as
=
−
≤
≤
c
(
x
,0,
t
)
c
0
a
x
a
c
(
x
,0,
t
)
=
0
other values of
x
∂
c
z
=
lim
z
0
(7.10)
∂
→∝
∂
c
lim
x
=
0
∂
x
→±∝
7.4.5 One-Dimensional Solute Transport with Nitrification Chain
One special group of degradation reactions involves decay chains in which solutes
are subject to sequential (or consecutive) decay reaction. Problems of solute
transport involving sequential first-order decay reactions frequently occur in soil
and groundwater systems. Examples are the migration of various radionuclides,
the simultaneous movement of interacting nitrogen species, organic phosphate
transport, and the transport of certain pesticides and their metabolities.
For solute transport in a homogeneous, isotropic porous medium during steady-
state unidirectional groundwater flow, the solute transport Eqs. (
3.1
) and (
3.2
)
reduces to
2
c
1
∂
R
1
∂
c
1
∂
D
∂
v
∂
c
1
∂
t
=
−
x
−
μ
1
R
1
c
1
(7.11)
x
2
2
c
1
∂
R
1
∂
c
1
∂
D
∂
v
∂
c
1
∂
t
=
−
x
+
μ
i
−
1
R
i
−
1
c
i
−
1
−
μ
i
R
i
c
i
i
=
2, 3
(7.12)
x
2
where
μ
is a first-order degradation constant,
D
is the dispersion coefficients,
ν
is the
average pore water velocity (
q
x
/
) in the flow direction,
x
is the spatial coordinate
in the direction of flow, and where it is assumed that three solutes participate in the
decay chain. For this specific three-species nitrification chain:
θ
NH
4
NO
2
NO
3
→
→
The boundary condition may be written as
vc
1
D
∂
c
i
∂
−
x
+
=
vc
0,1
(0,
t
)
vc
i
D
∂
c
1
∂
−
x
+
=
0
i
=
2, 3
(7.13)
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