1 y data perfume all steps for different values of x. 1.1 DewP calculationDuring the calculation of the dew P, datarequired are: Vaporphase composition at a particular pressure, Temperature, CriticalProperties (TC, PC, ZC) of all component thatare present in the system, Valuesof acentric factors of all component that are present in the system, Antoineequation constants, Valueof Wilson parameters for the given system. Following are the steps for performing DewP calculation1 Listthe data required.2 FindP1sat and P2sat using T in equation (3.1),3 Take? = 1 and ? = 1 and use Roult’s law to find x1 and x2,4 Findvalve of fugacity coefficients by use of Tsai and Jan EOS. (The maximum value of fugacity coefficient isrelated to vapor phase non-ideality).
5 Findthe value of ? by using (3.2) and (3.3).6 Recalculatevalue of P using equation (3.
4).7 Recalculatesteps 2 to 7 till following condition is satisfied, ……… (3.12)8 Whenabove condition satisfied value of temperature obtain is Bubble T. To obtain T-x-y data perfume all steps for different values of x. 1.
2 FlashcalculationFlash calculation is used when any of thetwo values (From P, T, x,y) are given. In flash calculation K-value are used for calculation. It does serve as a measure of the “Lightness”of a constituent species, i.
e., its tendency to favor the vapor phase. When itsvalue is greater that one means species iexhibits a higher concentration in vapor phase and if less than higherconcentration in liquid phase. K-values can be found from the nomographs.
……… (3.13) ……… (3.14) ……… (3.
15) Above equations are use to for VLEcalculation. Equation (3.13) used when T& P or x & y values aregiven. Equation (3.14) use for bubble point calculation and (3.15) use for dewpoint calculation. Nomographs and Algorithms for all the calculationare provided in the Appendix. CHAPTER 4DESIGN IN EXCELIn this chapter, the procedure forperforming calculations for bubble P for generating P-x-y data in Excel isshown.
The work in this course project has been restricted to only bubble Pcalculation. Following are the steps to perform Bubble P calculation. Step 1. Generationof Proper Data Base System.Proper Data Base willmake work easy when we need to call values for particular systems. In this work,I include three different types of the Data Base systems for my calculation.
1. Forcritical properties of individual compounds,2. Forbinary systems and their Wilson parameters,3.
Forcomparison with experimental data.First Data Base containscritical properties, Antoine constants, acentric factor etc. for thecalculation purpose (Fig. 4.1). There are two columns containing no, first for calling the compounds andsecond for calling the values.
Figure 4.1 DataBase for critical properties of components Second Database (Fig 4.2)containWilson parameter constants and slope and intersects values to generate parityplot. First column is for giving unique identity for particular system. Andsecond and third columns are unique identities of first and second compound insystems respectively. Last two columns are slope and intercepts to generateparity plot.
Ex no is unique identity for the experimental data and use to callexperimental data from Third Data Base. Third Data Base contains P-x-y data ofexperiments. Figure 4.2 DataBase for Wilson parameter constants Step 2. Listingproperties and parameters,List all the Parametersand properties that are remain constant during the calculation. For thiscalculation following are the parameters and properties that are constantduring the calculation of particular system.
Table 4.1 ConstantParameters and Properties. To call the values of different propertiesand parameters vlookup function isuse.
Syntax for vlookup can be givenas follow,= vlookup (lookup_value, table_array, column_index_no,range_lookup) Step 3. DesignTools,In this work, the buttonand combo box from the developer tab were used. To use that one first need tomake visible the developer tab which is hide default in any MS word. To make itvisible follow step below for MS Office 2016 or Office 20131.
Goto File ? Options ? Customize Ribbon,check the box before the developer. Figure 4.3 Excel Option for developer tab2. Fromdeveloper select insert ? combo box, Figure 4.4 Combo box 3. Afterselecting combo box draw box of appropriate size, and then follow window willopen, Figure 4.5 Format control for combo boxIn input rangeselect the cells whose value one want to show in box, in cell link select any blank cell, it will show the number of asystem that is selected from the list i.
e. if u select fifth system from thelist (combo box) then it will show 5in the cell and that is helpful to call the values using vlookup. To create button, go to developer ? insert ? button, Figure 4.6 Button tool After selecting button draw a button of an appropriatesize and after that on window will open to ask for macro but we don’t make itone so just close the window. Step 4.
Usethe equations mention in chapter 3 for Tsai and Jan to calculate the ? values and Wilson equation to find ?. To calculate follow the step givenbellow, 1. Listthe values of x at uniform intervals, 2. Findthe values of the parameters required in the calculation of Tsai & Jan EOS(Calculate till A, B, C). 3.
FromA, B, C generate the equation for Z using equation (2.31). and compare itwith following equation, ………. (4.1)By doing so, ……… (4.2)To solve this 3rddegree polynomial equation following equations are use,f = ((3*c/a) – (b^2/a^2))/3g = ((2*b^3/a^3) – (9*b*c/a^2)+ (27*d/a))/27h = (g^2/4) + (f^3/27)i = SQRT ((g^2/4)-h)j = I ^ (1/3)k = ACOS(-(g/(2*i)))L = j*(-1)M = COS(k/3) N = SQRT (3) * SIN(k/3)P = (b/(3*a)) * (-1)R = -(g/2) + SQRT(h)S = R ^ (1/3)T = – (g/2) – SQRT(h)U = T ^ (1/3)For h > 0, one realroot and two imaginaryZ1 = (S+U) -(b/3a),Z2 = (-(S+U)/2-(b/3a)) + i (S-U) *SQRT(3)/2,Z3 = (-(S+U)/2-(b/3a)) – i (S-U) *SQRT (3)/2,For h ? 0, three uniqueand real rootsZ1 = 2*j*COS(k/3)- (b/(3*a)),Z2 = L*(M+N) +P,Z3 = L*(M-N) +P;For f, g, h = 0, only onereal rootZ = (d/a) ^ (1/3) * (-1);For the all possiblevalues of Z obtain highest real rootis consider to calculate ? for boththe component from the system and same method is used to find ?b for equation(2.26).
4. Useequation (3.2) and (3.3) to find ?. 5.
CalculateP1sat and P2sat from AntoineequationStep 5. BubbleP calculation,To calculate bubble P inexcel follow the bellow steps,1. Makea column for estimate P, which willbe found by equation (3.5),2.
Calculateyi using equation (3.6),3. Makea column for calculated P, which iscalculated by equation (3.4),4. Copycalculated value on estimate as paste asvalue only, 5. Makecolumn for ?P and ?y.
?Pis difference between estimate and calculated P and ?y is summation ofy values.6. Usesolver to make ?y = 1 and ?P = 0, Step 6. Makeuse of solver,Solve is not installed bydefault in Excel. So, to install and use solver use steps given bellow foroffice 2013 or above,1. Goto File ? options ? add-ins ? solver add-in, click on GO.2.
Touse solver, go to data ? solver,following window will open, Figure 4.7 Solver window 3. Makeset cell as ?P, to value 0 and bychanging cell as copied P cell whichis paste as value only. Add constrain that ?ycell becomes 1. Run the solver.Step 7. Macrofor solver,Repetitive use of solveris very tedious and time consuming work. So, to avoid that we have to create macro.
Before that one has to make sure that its macro is enable. For that go to developer ? macro security ? enable allmacro. After that follow steps given bellow,1. Goto developer and click on record macro,2.
Performon single solver process,3. Goto developer and click on stop recording,4. Goto developer and click on Visual Basic,5. Copythe code and paste it in the sheet where calculation is performed,6. Sheetcan be found from the list of all active sheet shown in top-left penal,7. Goto tools ? reference and tick mark solver,press OK,8.
Editthe code as follow,9. Aftercreating macro assign it to button mention in step 3. Sub Macr()” Macr Macro Range(“BK51:BK71”).SelectSelection.CopyRange(“BD51”).
SelectSelection.PasteSpecialPaste:=xlPasteValues, Operation:=xlNone, SkipBlanks _:=False,Transpose:=False solverResetSolverOkSetCell:=”$BN$51″, MaxMinVal:=3, ValueOf:=0,ByChange:=”$BD$51″, _Engine:=1,EngineDesc:=”GRG Nonlinear”SolverAddCellRef:=”$BO$51″, Relation:=2, FormulaText:=”1″SolverSolve True In above coding firstparagraph is add for copy the calculated value and paste as value only so thatsolver can be run. In second paragraph first and last line are added fist lineis for reset solver after every titration and last line is to avoid clicking OK everytime solver run. Coding between that is generated by recording macro. Copysecond paragraph and paste it for the number of time one would run it fordifferent rows or cells. Change the value of cell references with appropriatevalues (i.e. if one want to use for next row then $BN$51 becomes $BN$52 and soon…).
Save coding and save excel file as macro enable file. Step 8. Graphplot.
After generating P-x-y data draw a scatter graphs of1. P vs x,2. P vs y, 3. y vs x.Step 9. Comparisonplots,To create comparison plotwe have to generate P-x-y data for thesame value of x that is given in experimental data and compare the calculated y and P values with experimental one. After that, draw various comparisongraphs. (All graphs are mentions in appendix.
) CHAPTER 5RESULTS AND DISCUSSIONIn this excel filearound 25 random systems are included and the result obtained are compared withthe actual experimentally 4 generated data. For Ethanol – Benzenesystem at 298.15 K temperature following data are generated and comparison withactual data generate graphs shown in figure 5.1.Table 5.1 P-x-ydata for Ethanol – Benzene system x 0.00 0.
10 0.20 0.30 0.40 0.50 0.
60 0.70 0.80 0.90 1.00 y 0.00 0.
41 0.53 0.59 0.63 0.65 0.67 0.
69 0.70 0.74 1.00 P (mmHg) 59.1 90.9 107.5 116.4 121.
1 123.6 124.7 125.0 124.
4 121.3 95.2 Figure 5.1Comparison plots for Ethanol – Benzene system Just like thismore systems can be calculated in Excel. For around 25 azeotropic and non- azeotropic system calculation has beendone and results are compiled in table 5.2 and table 5.3 with error in pressure,y values, parity plot error etc. Figure 5.
2 P-x-y diagram and x-y diagram for ethanol –benzene system Table 5.2 Resultfor non azeotropic systems Table 5.3 Resultfor azeotropic systems In above tables values of?Y and ?P average error are found by using equation given bellow, The number in the finalcolumn are show how good the fitting of the curve is, and 1.
Excellent, 2.Good, 3. Moderate, 4. Poor, 5.
Very Poor. Rating is done on the bases of howmany points are deviating from the experimental values and how much is thedeviation. i.e.
, for benzene – toluene systems all the points are perfectlymatch except one so, there is possibility that the point is due to experimentalerror, thus it is considered as perfect match. CONCLUSION From the above result Ican conclude that,vsomeof the non azeotropic systems with few of the azeotropic systems shows the verygood match with experimental data, but most of the azeotropic systems areshowing deviation from the experimental values. v More over system with combination ofaliphatic and aromatic compounds are showing more deviation compare to samesystems.
More details about thisEOS can be obtain by including more compounds.