Mathematical Modeling of Multicomponent Rectification (on Example of Ethyl Alcohol Distillation)

On the identified models have calculated columns rectification installation and a check of the adequacy of the model to experimental data.

Rectified ethyl alcohol produced by fermentation-rectification installation (FRI), consisting of fermentation, epyuration and distillation columns.

Model [1] (equation 1-15) The calculation of the installation and a check of the adequacy of the model to experimental data obtained from measurements.

1. The equation of material balance of the total installed

(1)

2. The equation of material balance of the total plate:

(2)

3. The equation of material balance of component-wise plate i:

(3)

4. Heat balance equation of the column:

(4)

(5)

(6)

5. Heat balance equation of plate number i:

(7)

6. Equation component-wise material balances for the cube and reflux

(8)

7. Heat balance equation for a cube and reflux:

(9)

8. The equations calculate the enthalpy of the liquid and vapor:

(10)

9. The equation for calculating the temperature of condensation (dew point):

(11)

(12)

10. Composition of the vapor leaving the plate:

(13)

11. The equation relating the concentration of vapor and liquid:

1) for reflux

(14)

2) for columns cube

_or (15)

Adjustment of the model was carried out changing the value of the efficiency of the plate in terms of efficiency Murphy. Measurements were performed every 2 hours for 24 hours. Fixed temperature top and bottom fermentation, epyuration and distillation column, the temperature on the side dishes selections fusel oil fusel alcohols and distillation column. We measured the strength of rectified spirit and efiraldegid fraction. Sampling was conducted in a stationary mode of operation of the unit simultaneously from multiple threads - this thread ferments, epyurats and efiraldegid fraction, fusel fraction and rectified spirit. Scan results are shown below.

Evaluation of measurement errors and mistakes made ​​by the average general work on the initial installation process flowsheet and operating conditions. Measurements were made of the fortress of rectified spirit every 2 hours for 24 hours. Obtain an estimate of measurement errors and errors for the general average of rectified spirit below.

The sample mean:

where g = 5 - number of dimensions.

Sampling variance

The standard deviation of the sample (standard error of a single measurement).

(16)

When the reliability of measurements of 95% probability tables for the Student distribution for the number of degrees of freedom g = 4 and P = 95% is determined that t = 2,78.

The absolute error is:

Consequently, 95 % could be argued that the general average is in the range:

(17)

Based on the results of mathematical modeling was obtained calculated value of ethyl alcohol strength x = 0,96333 vol. fraction.

The deviation of the experimental value of rectified alcohol strength of the calculated values

(18)

This difference is 7.0 • 10^-5 does not exceed the arithmetic mean error equal to about 6.8-10^-4. shares at a confidence level as determined by Student's t distribution and equal to 0.95.

Thus, 95 % could be argued that the Student's criterion for the deviation of the results of theoretical and experimental data does not exceed the experimental error.
Functional analysis of the distillation column and epyuration conducted using the model plant consisting of two columns (epyuration and distillation) with direct flow epyurate the distillation column and the reverse flow of unpasteurized alcohol from the distillation column to epyuration (Fig. 1).

Optimization of the process was carried out using two objective functions: square deviation of the fortress efiraldegid fractions and square deviation of the fortress rectified spirit from their experimental values. The parameters investigated were the functions of the number of theoretical plates distillation column n^p and the number of theoretical plates epyuration clones n_e.

In the optimization process minimizes both the objective function. Observe restrictions on the quality of products. The search for optimal values ​​of the parameters was carried out by the method of descent [2,3]. In the distillation column at least the objective function achieved when the number of theoretical plates n^p = 29, taking into account the condenser (Fig. 2 and 3), and n_e=epyuration 17 (Fig. 4 and 5).

Fig.1. The design scheme epyuration and distillation columns.

The values ​​of minimum deviation for efiraldegid fraction epyurat, rectified spirit and the corresponding number of theoretical plates are shown in Table 1.

Table 1

Calculated and experimental data for the minimum values ​​of squared deviations of the fortress EAF, and the resulting alcohol epyurat

Thus, an adequate description of the installation work is carried out fermentation-rectification = 17 and n^p = epyuratsionnoy 29 in distillation columns.

Figure 2. A plot of the square deviations of calculated and experimental values ​​of the average strength rectification of ethanol on the number of theoretical plates, and distillation columns epyurational rectification installation.

Figure 3. A plot of the square deviations of the fortress of ethanol on the number of theoretical plates epyuration column with n^p = 29

Figure 4. A plot of the square deviations of the calculated and the average
Experimental values ​​of the strength of EAF number of theoretical plates, and distillation columns epyuration rectification installation.

Figure 5. - A plot of the square deviations of the fortress on the number of EAF theoretical plates column with the alcohol = 17

References:

1. Мухитдинов Д.П. Математическое моделирование многокомпонентной ректификации с учётом химической реакции // Журнал «Химическая технология. Контроль и управление». – Ташкент, 2005. – № 5. – С.25-30.

2. Мухитдинов Д.П., Абдулхаков А.А., Матмурадов У.Х. Метод расчета многокомпонентной ректификации // Журнал «Химическая технология. Контроль и управление». – Ташкент, 2005. – № 3. – С.8-11.

3. Мухитдинов Д.П. Обеспечение и ускорение сходимости итерационных схем расчета процесса многокомпонентной ректификации // Тр.XVIII Межд.научн.конф. «Математические методы в технике и технологии–(ММТТ-18)». - Казань, 2005.