Environmental Engineering Reference
In-Depth Information
Fig. 8.1 Sorption
isotherm for species
with stoichiometric
coefficient ¼ 2 (see text)
1
solid phase concentration
0.8
0.6
0.4
0.2
gaseous phase concentration
0
0
0.2
0.4
0.6
0.8
1
@ c
@t ¼ k c s k ! c 2
s
@ s
@t ¼ k c s k ! c 2
(8.31)
s
@ c s
@t ¼ k ! c 2
s k c s
the same arguments as above lead to the isotherm:
Kc s; max c 2
1
c s ¼
(8.32)
þK c 2
Figure 8.1 depicts an example of such a sorption isotherm. Formula ( 8.32 )is
a special case of the so called Langmuir-Freundlich isotherm (Klug et al. 1998 ) with
exponent two.
8.5 Transport and Speciation
The differential equation for multi-species reactive transport has been written in
vector notation (see equation (7.6)):
@
c
@t ¼r
S T r
j
ð
c
Þþ
(8.33)
The system ( 8.33 ) contains one differential equation for each species. It is
a system with N s equations. In case of equilibrium reactions it is not possible to
treat the system ( 8.33 ) directly, because the exchange rates of the equilibrium
reactions r are neither known nor given by an explicit expression. In order to
reach a feasible formulation, the equations have to be summed up in a way that
eliminates the last term on the right side of the equation. The procedure was already
described in Chap. 8.3.
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