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

### _Библиографическое описание:_

_Мухитдинов Д. П., Авазов Ю. Ш. Mathematical Modeling of Multicomponent Rectification (on Example of Ethyl Alcohol Distillation) // Молодой ученый. — 2012. — №1. Т.1. — С. 24-29._

_On the identified_ _models_ _have calculated_ _columns_ _rectification_ _installation_ _and_ _a check_ _of the adequacy_ _of the model_ _to experimental data_ _._

Rectified ethyl alcoholproducedby fermentation-rectificationinstallation (FRI), consisting of fermentation, epyurationand distillationcolumns.

Model [1] (equation 1-15)The calculation ofthe installationanda checkof the adequacyof the modelto experimental dataobtainedfrommeasurements.

1.Theequationofmaterialbalanceofthetotalinstalled

(1)

2\. The equation ofmaterial balance ofthe totalplate:

(2)

3\. The equationof material balanceof component-wiseplatei:

(3)

4\. Heat balance equationof the column:

(4)

(5)

(6)

5\. Heat balance equation of plate number _i_ :

(7)

6\. Equationcomponent-wisematerial balancesfor the cube andreflux

(8)

7\. Heat balance equationfor a cubeandreflux:

(9)

8\. The equationscalculatethe enthalpy ofthe liquid and vapor:

(10)

9\. The equation forcalculating thetemperature ofcondensation(dew point): 

(11)

(12)

10. Composition of the vaporleaving theplate:

(13)

11\. The equation relating theconcentration of vaporandliquid:

1) forreflux

(14)

2) for columns cube

or (15)

Adjustment ofthe modelwas carried outchanging the value ofthe efficiency of theplatein terms ofefficiencyMurphy. Measurementswere performedevery 2hours for 24hours.Fixedtemperaturetop and bottom fermentation, epyurationanddistillation column,the temperature on thesidedishesselectionsfusel oilfuselalcoholsanddistillation column.We measured thestrengthof rectifiedspirit andefiraldegidfraction.Samplingwas conductedin a stationarymode ofoperation of the unitsimultaneouslyfrom multiple threads-thisthread ferments, epyurats andefiraldegidfraction, fusel fraction andrectifiedspirit.Scan resultsare shown below.

Evaluationof measurement errorsand mistakesmade​​bythe averagegeneralworkonthe initialinstallationprocess flowsheetandoperating conditions.Measurementswere madeof the fortressof rectifiedspiritevery 2hours for 24hours. Obtain an estimate ofmeasurement errorsand errorsforthe generalaverageof rectifiedspiritbelow.

The sample mean:

where _g =__5_ -number of dimensions.

Sampling variance

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

(16)

Whenthe reliability of measurementsof95%probabilitytablesforthe Student distributionfor the numberof degrees of freedomg = 4and P= 95%is determined thatt = 2,78.

The absolute erroris:

Consequently, 95 % could be arguedthat the generalaverageis in the range:

(17)

Based on the resultsof mathematical modelingwas obtainedcalculated valueof ethyl alcoholstrength _x = 0,96333_ _vol. fraction_.

The deviation ofthe experimental value ofrectified alcoholstrengthof the calculatedvalues

(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 processwas carried out usingtwoobjective functions: square deviationof the fortressefiraldegidfractionsandsquare deviationof the fortressrectifiedspiritfromtheirexperimental values.The parametersinvestigatedwere thefunctions ofthe numberof theoretical platesdistillation column _n_ _p_ and the numberof theoretical platesepyurationclones _n_ _e_.

Inthe optimization processminimizesboththe objective function. Observe restrictionson the quality ofproducts.The search for optimalvalues ​​of the parameterswas carried outby the methodof descent[2,3]. In thedistillation columnat leastthe objective functionachievedwhen the numberof 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 schemeepyurationanddistillation columns.

The values​​of minimumdeviationforefiraldegidfractionepyurat, rectifiedspiritand the correspondingnumber oftheoretical platesare shownin Table 1.

Table 1

Calculated and experimental dataforthe minimum values​​of squared deviations ofthe fortressEAF, andthe resultingalcoholepyurat

Name |  n, pcs |  fortress(eksperim.),volumefraction |  fortress(calculation),volumefraction |  squaredeviationfortress, volumefraction  
---|---|---|---|---  
Efiraldegidfraction |  17 |  0.96150 |  0.96153 |  9.006•10-10  
Epyurat |  0.38540 |  0.38636 |  9.228•10-7  
Rectifiedspirit |  29 |  0.96340 |  0.96333 |  4.900•10-9  
  
Thus, an adequate description of theinstallationworkis carried out fermentation-rectification =17andnp=epyuratsionnoy29 indistillationcolumns.

Figure 2.A plot ofthe squaredeviationsof calculated andexperimentalvalues ​​ofthe averagestrengthrectificationof ethanolon the number oftheoretical plates, and distillationcolumnsepyurational rectificationinstallation.

  


Figure 3.A plot ofthe squaredeviationsof the fortressof ethanolon the number oftheoretical platesepyurationcolumn with _n_ _p_ _= 29_

  


Figure 4.A plot ofthe squaredeviations ofthe calculatedandthe averageExperimentalvalues ​​of thestrengthofEAFnumber of theoretical plates, and distillationcolumnsepyurationrectificationinstallation.

  


Figure 5.-A plot ofthe squaredeviationsof the fortresson the number ofEAF theoretical platescolumn withthe 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\.