Having integrated (34) we obtain the dependence X
8
(t) at the section i > 90.
Calculations by (33) are compared to experimental data in fig. 17 and 18.
As we can see the agreement of experimental data and modeled calculations
(diffusion model by calcium) at the actual section is good. It is interesting that by Fig.18
data this measurement range corresponds to total CaCO
3
crystallization, i.e. the one
when due to intensive crystal nuclei growth oversaturation by calcium carbonate is
reduced.
CONCLUSION
1. On the basis of the laws of conservation of carbonate concentration sum and
calcium components the general formula of mathematical model of solid calcium
carbonate formation from CHCS free of assumptions about crystallization mechanism
has been obtained, see equations (2) and (3).
2. Within quasiequilibrium approximation the expressions for CHCS parameters
calculation have been obtained. Since pH change is not usually large the amount of
solid CaCO
3
is determined by the change of CO
2
concentration resulting from
degassing (water-cooling towers, spray ponds) or may be caused by temperature
gradient, change of CO
2
solubility in heat exchangers. In these cases, the amount of
crystallized CaCO
3
is approximately equal to the amount of CO
2
removed due to its
solubility.
3. Comparison of calculated and measured values unambiguously indicates the
essential non-equilibrium of processes running in CHCS at CO
2
degassing
accompanied by CaCO
3
crystallization. Visible equilibrium in CHCS comes only in
11 minutes after total crystallization start. It follows that it is inadmissible to use
equilibrium relations (8) – (14) to calculate CHCS parameters for the processes with
the relaxation time less than 11 min. Calculations by formulae (8) – (14) at non
equilibrium section give unreal values or error exceeding 50%.
4. From viewpoint of dynamic approach and depending on pH values the
following main phases of crystallization are possible in CHCS: at рH < 5.5 calcium
carbonate is only dissolved; within the range of 6.5 < рH < 9.5 calcium carbonate
crystallization is caused by interaction of Ca
2+
with HCO
3
-
by the scheme (19) with
CO
2
emission (let us call it bicarbonate crystallization), and at рН > 10.5
crystallization occurs due to interaction of Са
2+
with carbonate ions (carbonate
crystallization).
5. Obtained here values of dynamically determined concentrations of ion
CaHCO
3
+
and СаСО
3
0
complexes differ essentially from values calculated by
equilibrium equations. It should be taken into account while forecasting the sequence
of fast processes in CHCS, degassing and deionization at water treatment units in
particular.
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