Carnegie Mellon UniversityResearch Showcase @ CMUDepartment of Chemical Engineering Carnegie Institute of Technology1979Shortcut methods for complex distillation columns: part 2-- number of stages and feed tray locationJ CerdaCarnegie Mellon UniversityArthur Wjt. auth. WesterbergCarnegie Mellon UniversityDesign Research CenterFollow this and additional works at: htp://repository.cmu.edu/chemeTis Technical Report is brought to you for free and open access by the Carnegie Institute of Technology at Research Showcase @ CMU. It has beenaccepted for inclusion in Department of Chemical Engineering by an authorized administrator of Research Showcase @ CMU. For more information,please contact research-showcase@andrew.cmu.edu.Published In.NOTICEWARNING CONCERNINGCOPYRIGHT RESTRICTIONS:The copyright law of the United States (title17, U.S.Code) governs the makingof photocopiesor other reproductionsof copyrighted material.Any copying of thisdocument without permission of its author may be prohibited by law.SHORTCUT METHODS FOR COMPLEX DISTILLATION COLUMNS:PART 2 -- NUMBER OF STAGES AND FEED TRAY LOCATIONbyJ. Cerda & A.W. WesterbergDRC-06-11-79September1979Department of Chemical EngineeringCarnegie-Mellon UniversityPittsburgh, PA15213Paper to be presented at 72nd AIChE Annual Meeting,San Francisco, CA, November 25-29, 1979.AbstractShortcut Methods for Complex Distillation Columns:Part 2 ~ Number of Stages and Feed Tray LocationThis paper is the second part of a two-part paper on shortcut methodsfor ordinary and complex columns.The shortcut method to estimate the num-ber of stages is based on Edmister's method.The method includes a newapproach which locates feed trays to minimize the total number of stageswithin the column.Several example problems demonstrate the method and show, where com-parisons are available, that it compares favorably with other approaches.U M i V E P S i T Y L 5 5 R A R S E 3: : : . : ; - ; . V i . v A T - - 8 A 1 5 2 1 3(I)Conventional distillation columns:By introducing the notion of an effective absorption factor A,Edmister(1957)developedthefollowing expression(see Figure 1),"R(A )-1which relates the amounts of jth-component contained in the vapor streamcoming up f^om the feed plate and in the top product,through variableslike the reflux ratio (R), the number of ideal stages in the rectifyingsection section (IL) and the effective absorption factor (A ) . .As stated in Part I,the rectifying section of a conventional distilla-tion column serves to remove the heavy key from the vapor stream so that thefraction of the amount of heavy key in the feed present in the top productis (l-r..^), where r__ is the fraction of the heavy key in the feed to beHis.HKrecovered in the bottom product B.Equation (1) can be used as the recti-fying section design equation when written for the heavy key.By rearrangingequation (1), one can write|.H-(Ae-l)(vBR/ d)1Using the rectifying section design specificationdHK=(1"rHK)fHKand the definition of R, the ratio (vM/ d)ul_, can be expressed asrlK(3)HK'T'HKReb.As the heavy key is the design component for the rectifying section,the light key is the design component for the exhausting section.Fromequation (5), one can writebutwhere (x )is the light key mole fraction in the liquid coming downfrom the feed plate.Replacing equation (8) in (7) givesXn"ruc> Ls (s - i ,_-4-For sharp separations between the keys, the recovery fractions randrare close to 1.In such cases, design equations (4) and (9) can beL uxsimplified to eliminate either C Y f / ^ ) ^ o r^ f^ ^ L K' w h o s eevaluation isdifficult.A simple order of magnitude analysis will help us to achieve thissimplification.Typical values for the variables present in equation (4) areshown in Table 1.From them it can be concluded thatfor sharp separations.Ignoring the term 'I1, equation (4) can be written-1< V m r,-n/5rJ tnd- r^)-J&nI_R-*^1+ Anl (R+l)3+n^-S-sa.t-ss-"RAnLK(LK(L1/V1)(L/V)(L2/V2) = 1.605;(S *)v^ - 1.524i^ = 5.81; r^ = 5.52; nt = 12.33King(1971)reported that Lewis-Matheson1s method leads in this caseto the following results:i^ - 4;i^ = 5;nt = 10(II)Example related to thermally coupled distillation schemes asproposed by Stupin and Lockhart(1971):ComponentsA(LK)B(MK)C(HK)Other data:' = l! rL K =0.0.0.fi.333.334.333rMK = rH K= 0.>av.931990.0.di329700165-000Fi.0033.3307.00330.0.bi-001653297Values for the operating parameters were chosen as 1.3 times theirlimiting values already determined in Part I.Results are shown in Table 4.Table 4Comparison among the number of Ideal stages required in conventionaland thermally coupled distillation schemes, for the Example A.II.lType ofdistillation unitNumber of ideal stages requiredin each fractionatorTotal number ofideal stagesDirect conventionalschemeFirst column:22.20 (+ reboiler)Second column: 24.51 (+ reboiler)46.71Reverse conventionalschemeFirst column:21.07 (+ reboiler)Second column: 23.40 (+ reboiler)44.47ito00IDistillation systemwith a side-streamexhausting sectionFractionator (3,4):19.79 (+ reboiler)Fractionator (1,2):20.86 (+ reboiler)40.65Petlyuk's distillationsystemFractionator (1,2):19.64Fractionator (3,4):14.34Fractionator (5,6):18.90 (+ reboiler)52.88-29-References1.Edmister, W.C., Trans. A.I.Ch.E., 42, 15 (1946).2.Edmister, W.C., Chem. Eng. Progr., 44, 615 (1948).3.Edmister, W.C., A.I.Ch.E. Journal, 3, 165 (1957).4.Horton, G. and W.B. Franklin, Ind. Eng. Chem., 32, 1384 (1940),5.King, C.I,, "Separation Processes", McGraw-Hill Co., (1971).6.Stupin, W.I. and F.I. Lockhard, 64th Annual AIChE Meeting,San Francisco(1971)7.Van Winkle, M., "Distillation", McGraw-Hill Co., (1967).- 3 0 -NomenclatureA:Absorption factor(L/KV),dimensionlessb:Molalflow-rateof acomponentinthe bottom product,mole/hB:Bottom product molalflow- rate,mole/hd:Molalflow-rateof acomponentin the topproduct,mole/hD:Top product molalflow- rate,mole/hf:Molalflow-rate of acomponentin thefeed,mole/hF:Feed molalflow- rate,mole/hF:Parameter defined by equation(21)G:Errorfunction defined byequation(43)K:Equilibrium constant,dimensionlessI:Molalflow-rateof acomponentin aninternalliquidstream,mole/hL:Molalflow-rate of aninternalliquidstream,mole/h.Also,theliquid molalflow-ratein aconventionalcolumnrectifyingsectionLf:Liquid molalflow- ratein aconventionalcolumn exhaustingsection,mole/hn:Number ofidealstagesp:Molalflow-rate of acomponentin the middle product,mole/hP:Middle product molalflow- rate,mole/hR:Liquidrefluxratioin arectifyingsection,dimensionlessRf:Vaporrefluxratioin an exhaustingsection,dimensionlessS:Strippingfactor(KV/L),dimensionlessv:Molalflow- rateof acomponentin an internalvaporstream,mole/hV:Molalflow-rateof an internal vaporstream,mole/h.Also,thevapor molalflow- ratein aconventionalcolumnrectifyingsectionVf:Vapor molalflow- ratein aconventionalcolumn exhaustingsection,mole/h-31-x:Liquid mole fraction, dimensionlessy:Vapor mole fraction, dimensionlessZ:Parameter defined by equation (50)Greek letters:Qf:Volatility of a component relative to that of the heavy key,dimensionlessParameters defined by equations (39) and (40), respectively.Subscripts:B:Refers to either the bottom tray of a column section or the bottomproductBR:Refers to the bottom tray of a conventional column rectifyingsectione:Denotes an effective valuef:Refers to the feed trayF:Refers to the feedHK:Refers to the heavy keyj:Refers to jth-componentLK:Refers to the light keym:Denotes limiting valueMK:Refers to the middle keyo:Denotes value defined at the reboiler of an exhausting sectionR:Refers to a rectifying sectiont:Denotes totalT:Refers to the top tray of a column sectionX:Refers to an exhausting section-32-Superscripts:(o):Denotes approximate value(R):Refers to the rectifying section of a conventional column(X):Refers to the exhausting section of a conventional column