The received experimental data were approximated by the kinetic equation close
to the known Moser mathematical model [7]:
n
s
n
a
m
k
c
T
T
+
=
0
,
(1)
where T is titrated acidity, %; Tm is the maximum value of titrated acidity that
can be achieved at the end of the fermentation process, %; c
0
– initial concentration of
sugars in birch sap, %; τ –duration of fermentation, hours; a, k
s
, n – kinetic coefficients
determined using experimental data.
Table 3 The research plan and study findings of kinetics of birch sap's
fermentation process
Experiment
number
Conditions
Titrated acidity, %
Fractional
accuracy, %
С, %
τ, hours
experiment
calculation
1
1.4
0
0.00
0.00
-
2
1.4
1
0.12
0.13
5.45
3
1.4
2
0.48
0.49
1.93
4
1.4
3
0.78
0.84
7.10
5
1.4
4
1.09
1.06
2.55
6
1.4
5
1.25
1.20
4.21
7
1.4
6
1.26
1.28
1.48
8
0.9
0
0.00
0.00
-
9
0.9
1
0.10
0.09
9.33
10
0.9
2
0.38
0.35
7.75
11
0.9
3
0.6
0.60
0.24
12
0.9
4
0.75
0.76
1.48
13
0.9
5
0.84
0.86
2.14
14
0.9
6
0.90
0.92
1.80
15
0.4
0
0.00
0.00
-
16
0.4
1
0.05
0.05
1.64
17
0.4
2
0.21
0.19
9.45
18
0.4
3
0.34
0.32
4.51
19
0.4
4
0.44
0.41
6.18
20
0.4
5
0.45
0.47
3.42
21
0.4
6
0.49
0.50
1.42
We determined the aforementioned kinetic coefficients a, k
s
, n (which are
included to the kinetic equation (1)) using experimental data via least-squares method
[2], and according to the received coefficients, the kinetic equation has the following
form:
410
,
2
410
,
2
754
,
0
0
521
,
10
131
,
1
+
=
c
T
,
(2)
The calculations were carried out in MS Excel spreadsheets using the "Decision
Search" procedure.
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