Environmental Engineering Reference
In-Depth Information
Table 8.2 Carbon chemistry equilibrium constants
Reactions and equilibrium constants (log) for T
¼
25
C
H
þ
þOH
$ H
2
O
14
H
þ
þCO
3
2
$ HCO
3
10.329
Ca
2
þ
þHCO
3
$ CaHCO
3
þ
1.106
2
H
þ
þCO
3
2
$ H
2
CO
3
16.7
Ca
2
þ
þCO
3
2
$ CaCO
3
8.48
always possible. When kinetic reactions have to be considered additionally, the
equations remain coupled and the numerical solution is not as easy (Holzbecher
2005
).
The situation is also more complex when species in different phases are
involved. In the mathematical formulation species in different phases can not be
expressed by the same transport operator, as it is assumed in (
8.33
).
For demonstration purposes we selected an example from carbon chemistry.
A formulation is chosen in which seven species are involved in five reactions.
These are ordered in the species vector as follows:
H
þ
; HCO
3
; Ca
2
þ
; OH
; H
2
CO
3
; CO
3
2
; CaHCO
3
þ
The major reactions for the carbon species and the equilibrium constants are
gathered in Table
8.2
. Note that two additional species appear in the reactions:
water,
H
2
O
, and calcite,
CaCO
3
. Those two species are not included in the
model, because it is assumed that both are available from an infinite pool. In
that case their concentrations can be set to unity. Water is the medium within
which other species are dissolved. Concerning calcite, it is assumed that the
flow passes through a calcareous or limy formation, a fracture, a pipe or a karst
system.
The following reaction matrix corresponds with the reaction system:
0
1
1001000
1
@
A
100010
011000
S
¼
1
(8.36)
2000
110
0010010
The matrices S
1
and S
2
are given by:
0
@
1
A
0
@
1
A
10
1
01000
00010
1000
1
01
20
00
S
1
¼
S
2
¼
1
(8.37)
00
110
10010
