available, that is X
10
= 0. It follows from expressions (10) and (11) that the change of
Ca
2+
concentration in quasiequilibrium approximation depends only upon the rate of
concentration change of the dissolved CO
2
and pH system.
The range of Ca
2+
concentration change is determined by subsystem capacity of
calcium hydrocarbonate and carbonate complexes, i.e. does not exceed (6-15%) of
initial concentration of calcium ions.
CaCO
3
formation. Equations (3b) and (4) describe the influence of CaCO3
formation upon the state of CHCS. Integrating the latter, we obtain:
)
t
(
S
)
t
(
S
)
t
(
X
)
t
(
X
o
C
C
o
8
8
dg
2
ΔX
−
−
+
=
,
(12)
(
)
1
t
to
2e
1
2
2
dt
X
)
t
(
X
a
−
−
=
dg
2
ΔX
,
(13)
Combining (12) and (3b) we find the expression for calcium carbonate
concentration for t > t
cr
(the time of crystallization start).
(t))
X
(t),
(X
f
(t)
X
S
(t)
X
7
2
8
8
o
Ca
10
−
=
,
(14)
From (12) and (14) we can see that CaCO
3
formation in quasiequilibrium
approximation is controlled by pH and X
2
(t) dependences. That is, still decisive are
two parameters as in the no crystallization case.
If CO
2
removal does not occur (ΔX
2
dg
(t) = 0), then Ca
2+
concentration change is
determined only by the change of carbonate components concentrations sum, see (8),
which is close to dissolved CO
2
concentration change at small pH drop.
It is such situation that is observed in heat exchangers where while approaching
to hot wall carbon dioxide dissolution is reduced and it is accompanied by the
formation of equivalent amount of solid calcium forms.
If pH drop is considerable, for example, due to alkali addition then calcium ions
concentration change may be essential and the solid calcium carbonate formation is
possible in large amounts even without gas exchange.
The case
)
t
(
dg
2
ΔX
≠ 0, ΔpH = 0 is studied in [5]. There, according to (4), the
change of calcium ions concentration is given by the expression,
(t)
ΔX
)
(X
f
)
(t
X
(t)
X
)
(t
X
(t)
X
(t)
ΔX
dg
2
7
2
o
2
2
o
8
8
8
−
−
=
−
=
, (15)
Since ∆X
2
concentration change of dissolved CO
2
in neutral and poor alkali water
is low then at stable pH the formation of solid calcium is controlled by CO
2
degassing.
Equations (2) – (15) allow us to calculate CHCS parameters: [HCO
3
-
],
[Ca(HCO
3
)
+
], [Ca
2+
], [CaCO
3
] and the others, measuring pH and CO
2
values without
absorbing in the essence of crystallization mechanism. It is usual feature of the
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