Consider that chlorides and sodium ions are neutral with regards to process of
CHCS components transformation. Of course, such assumption is not quite correct,
because, at least, of the fact that these ions concentration changes salt content of the
system and influences the coefficient value of its components activities. But we neglect
it here.
From the law of conservation of total carbonate moles amount we obtain that at
any time the dynamics of changes of carbonate Sc concentrations sum in CHCS is
described by the equations
−
−
−
−
−
=
,
X
X
X
;
X
X
X
S
38
18
10
dg
38
18
dg
X
dt
c
d
2
2
X
dt
dX
,
(2)
dg
X
2
– rate of CO
2
removal from the mother solution;
38
18
10
X
,
X
,
X
- rates of
solid CaCO
3
and appropriate ion complexes formation.
The first (2) equation refers to the processes of CO
2
exchange with atmosphere
when CaCO
3
formation is not available, but ion complexes may be formed. The second
equation takes into account the solid CaCO
3
formation (term X
10
) and parallel
formation of calcium ion complexes.
Relation (2) should be added by equations resulting from the law of conservation
of total compounds moles amount with calcium ions content
o
Ca
38
18
8
S
X
X
X
=
+
+
,
(3a)
without solid carbonates formation and
o
Ca
38
18
10
8
S
X
X
X
X
=
+
+
+
(3b)
with solid CaCO
3
formation;
S
0
Ca
– constant initial sum of components concentrations with calcium content,
mole/dm
3
.
In both cases (with and without crystallization) substituting (3a) and (3b) into (2)
we obtain the kinetic equation for carbonate concentration sum,
8
dg
2
X
X
c
S
+
=
,
(4)
resulting in kinetic equation for calcium without any assumptions regarding the
mechanism of crystallization [6],
)
X
(X
a
X
X
X
X
c
S
X
2e
_
2
2
3
2
1
dg
2
_
8
+
+
+
=
=
,
(5)
In (5) the process of CO
2
(degassing-saturation rates) is modeled by Henry’s
approximation
)
X
(X
a
X
2e
_
2
2
dg
2
−
=
,
(6)
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