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.