process other authors do not take it into account. CaCO
3
concentration in the dynamic
model is calculated on the basis of equation (3b),
(
)
38
18
8
o
Ca
10
X
X
X
S
X
+
+
−
=
,
(31)
Values in the right hand side (30) and (31) are known since X
8
is measured and
X
18
and X
38
were calculated above. Calculation results by (30) and (31) are shown in
fig. 14 – point and 15 curve 1.
Data in fig. 14 and 15 were not compared to the experiments since direct
measurements of crystallized CaCO
3
were not carried out. However, one can calculate
the crystallization rate using the alternative approach based on reactions (19) and
compare it to the obtained here, see curve in Fig. 14.
Final phase of CaCO
3
formation. Consider in details the experimental kinetic
curve of crystallization at the section of Ca
2+
crystallization reduction. For this purpose,
we use special function [1],
−
=
dt
dX
ln
Ls
8
8
,
(32)
that is shown in Fig.16 according to experiments data. We can see that starting
from measurement i = 90 the function (32) is approximated well by the line
10.02
b
;
10
1.59
a
90),
(v
a
b
y
2
v
=
=
−
+
=
−
(33)
resulting in values dependence of X
8
upon the time that is described by equation
(
)
8
8
8
8
X
X
a
dt
dX
−
=
,
(34)
і
X'
10
Figure 14. CaCO
3
crystallization rate
calculated by (30), points and by the
equation (19) – continues curve.
і
X
10
2
1
Figure15. Crystallized CaCO
3
concentra-
tion calculated by (31), curve 1 and by
equation (19), curve 2.
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