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
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