Environmental Engineering Reference
In-Depth Information
and the formula (
5.29
) is programmed by the lengthy term:
Also the
‚simpletrans.m'
model can be extended easily by introducing decay as
additional process. Write another submodule, named
'kinetics.m'
that includes only
one command:
In the main module
‚simpletrans.m,'
the command
kinetics
is called before
diffusion
. Appelo and Postma (
1993
) describe a similar procedure.
In dimensionless formulation the solution is:
!
!
!
:::
xt
2
xþt
2
1
2
erfc
1
2
exp
Pe x
cðx;tÞ¼c
0
exp
Da
2
t
p
p
ð
Þ
1
ð
Þ
erfc
t=Da
2
t=Da
2
!
!
!
erfc
erfc
xut
2
xþut
2
c
in
2
1
u
2
x
1
þu
2
x
þ
exp
Pe
p
þ
exp
Pe
p
t=Da
2
t=Da
2
(5.30)
p
1
. Figure
5.7
illustrates the solution for a high P
´
clet
with
u ¼
þ
4
Da
2
=Pe
number
Pe ¼
100 and a moderate second Damkohler number. The front proceeds
in positive
x
-direction from left to right. The time to proceed from one front line to
the next amounts to the 10th part of the mean time which a tracer would need to
migrate through the entire system.
With the intruding front the concentration is reduced. Because of the high P´clet
number, the front line remains relatively steep, which has the additional effect that
1
0.8
0.6
0.4
Fig. 5.7
Steady and transient
solution for transport
equation with degradation;
dimensionless space variable
x
0.2
and dimensionless
concentration
0
0
0.2
0.4
0.6
0.8
1
y
for
Pe ¼
100
Distance
x
[-]
and
Da
2
¼
1