Environmental Engineering Reference
In-Depth Information
Fig. 8.2 Calcite dissolution
example, equilibrium case
9.8
Equilibrium Calcite Dissolution
9.6
time: 0-5 a
9.4
9.2
9
8.8
8.6
0
20
40
60
80
100
distance [m]
Saaltink et al. ( 2001 ) already consider the case in which the calcite dissolution
reaction (the last in Table 8.2 ) is slow compared to all other processes.
In that case, the reaction matrix for equilibrium reactions contains four rows
only. for S 1 and S 2 results:
0
@
1
A
0
@
1
A
100
1
1000
0010
000
10
011
200
S 1 ¼
S 2 ¼
(8.39)
1
0
110
Using ( 8.20 ) and ( 8.21 ) and MATLAB
it is easy to calculate U:
®
0
@
1
A
100
10
0100111
0010001
11
¼
U
(8.40)
Now the total concentrations are different combinations of the species:
0
@
1
A ¼
0
@
1
A
H þ CO 3 2 þH 2 CO 3 OH
HCO 3 þH 2 CO 3 þCO 3 2 þCaHCO 3 þ
Ca 2 þ þCaHCO 3 þ
TotH
TotC
TotCa
There are three initial and inflow concentrations required for the totals TotH ,
TotC and TotCa . The values proposed by Saaltink et al. ( 2001 ) are provided in
Table 8.4 . The kinetic transfer coefficient
a
varies over 4 orders of magnitude. It is
used in the kinetic rate law given by:
r kin ¼ r ¼ a
ð Þ
1
(8.41)
where
s
denotes the calcite saturation index.
 
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