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SUBSCRIBERACCESSPROVIDEDBYUICLIBRARYINDUSTRIALPROPANE,74986LITERATURECITEDALATIQI,IMLUYBEN,WLCONTROLOFACOMPLEXSIDESTREAMCOLUMN/STRIPPERDISTILLATIONCONFIGURATIONINDENGCHEMPROCESSDESDEV1986,25,762767BUCKLEY,PSCONTROLSFORSIDESTREAMDRAWOFFCOLUMNSCHEMENGPROG1969,655,4551DOUKAS,NLUYBEN,WLCONTROLOFANENERGYCONSERVINGPREFRACTIONATOR/SIDESTREAMCOLUMNDISTILLATIONSYSTEMINDENGCHEMPROCESSDESDEV1980,20,147153FINCO,MVLUYBEN,WLPOLLECK,RECONTROLOFDISTILLATIONCOLUMNSWITHLOWRELATIVEVOLATILITIESINDENGCHEMRES1989,28,7583LUYBEN,WLTENSCHEMESTOCONTROLDISTILLATIONCOLUMNSWITHSIDESTREAMDRAWOFFISAJ1966,137,3742LUYBEN,WLSIMPLEMETHODFORTUNINGSISOCONTROLLERSINMULTIVARIABLESYSTEMSINDENGCHEMPROCESSDESDEV1986,25,654660LUYBEN,WLDERIVATIONOFTRANSFERFUNCTIONSFORHIGHLYNONLINEARDISTILLATIONCOLUMNSINDENGCHEMRES1987,26,24902495MIJARES,GCOLE,JDNAUGLE,NWPREISIG,HAHOLLAND,CDANEWCRITERIONFORTHEPAIRINGOFCONTROLANDMANIPULATEDVARIABLESAICHEJ1986,32,14391449TAMPA,FL,1974OGUNNAIKE,BA,LEMAIRE,JPMORARI,MRAY,WHADVANCEDMULTIVARIABLECONTROLOFAPILOTPLANTDISTILLATIONCOLUMNAICHEJ1983,29,632640PAPASTATHOPOULOU,HSCONTROLOFBINARYSIDESTREAMDISTILLATIONCOLUMNSWITHVARYINGCONTROLOBJECTIVESANDCONSTRAINTAPHDTHESIS,LEHIGHUNIVERSITY,QETHLEHEM,PA,1990PAPASTATHOPOULOU,HSLUYHN,WLANEWMETHODFORTHEDERIVATIONOFSTEADYSTATEGAINSFORMULTIVARIABLEPROCESSESIDENGCHEMRES1990A,29,366369PAPASTATHOPOULOU,HSLUYBEN,WLPOTENTIALPITFALLSINRATIOCONTROLSCHEMESINDENGCHEMRES199OB,29,20442053PAPASTATHOPOULOU,HSLUYBEN,WLTUNINGCONTROLLERSONDISTILLATIONCOLUMNSWITHTHEDISTILLATEBOTTOMSSTRUCTUREINDENGCHEMRES199OC,29,18591868SKOGESTAD,SJACOBSEN,EWMORARI,MINADEQUACYOFSTEADYSTATEANALYSISFORFEEDBACKCONTROLDISTILLATEBOTTOMCONTROLOFDISTILLATIONCOLUMNSINDENGCHEMRES1990,29,TYREUS,BLUYBEN,WLCONTROLOFABINARYDISTILLATIONCOLUMNWITHSIDESTREAMDRAWOFFINDENGCHEMPROCESSDESDEV233923461975,14,391398RECEIVEDFORREVIEWJUNE27,1990REVISEDMANLLSCRIPTRECEIVEDSEPTEMBER19,1990ACCEPTEDOCTOBER9,1990SEPARATIONSMULTICOMPONENTBATCHDISTILLATIONCOLUMNDESIGNURMILAMDIWEKARSANDKPMADHAVANCADCENTRE,IITPOWAI,BOMBAY400076,INDIABATCHDISTILLATIONISCHARACTERIZEDASASYSTEMTHATISDIFFICULTTODESIGNBECAUSECOMPOSITIONSARECHANGINGCONTINUOUSLYWITHTIMETHEMODELSREPORTEDINTHELITERATUREANDUSEDINTHESIMULATORSLIKEPROCESSANDBATCHFRAC,ETC,ARETOOCOMPLEXTOUSEFOROBTAININGOPTIMALDESIGNBECAUSEOFHIGHCOMPUTATIONALTIMEANDLARGEMEMORYREQUIREMENTINTHISWORKWEAREPRESENTINGASHORTCUTMETHODFORDESIGNOFMULTICOMPONENTBATCHDISTILLATIONCOLUMNS,OPERATINGUNDERVARIABLEREFLUXANDCONSTANTREFLUXCONDITIONSTHEMETHODISESSENTIALLYAMODIFICATIONOFTHESHORTCUTMETHODWIDELYUSEDINTHEDESIGNOFCONTINUOUSMULTICOMPONENTCOLUMNSTHETECHNIQUEHASBEENTESTEDFORBOTHBINARYANDMULTICOMPONENTSYSTEMS,ANDTHERESULTSCOMPAREFAVORABLYWITHTHERIGOROUSMETHODSOFDESIGNTHEMETHODISVERYEFFICIENTANDCANBEUSEDFORPRELIMINARYDESIGNANDANALYSISOFBATCHCOLUMNSTHEMODELUSEDINTHISMETHODHASANUMBEROFTUNINGPARAMETERSTHATCANBEUSEDFORMODELADAPTATIONTHEMAINFEATURESOFTHESHORTCUTMETHODINCLUDELOWERCOMPUTATIONALTIMEWHICHISINDEPENDENTOFTHENUMBEROFPLATESINTHECOLUMN,LOWERMEMORYREQUIREMENTS,ANDITSADAPTABILITYTODESIGN1INTRODUCTIONTHEDESIGNOFABATCHDISTILLATIONCOLUMNISMUCHMORECOMPLEXINCOMPARISONWITHTHATOFACONTINUOUSDISTILLATIONCOLUMNASITREQUIRESCONSIDERATIONOFUNSTEADYSTATEBEHAVIORTHECOMPLEXITYOFTHEPROBLEMINCREASESWITHTHENUMBEROFCOMPONENTSINMULTICOMPONENTSYSTEMSTHEBATCHDISTILLATIONCOLUMNCANBEDESIGNEDBYTAKINGINTOACCOUNTTWOPOSSIBLEMODESOFOPERATION1VARIABLECURRENTADDRESSDEPARTMENTOFENGINEERINGANDPUBLICPOLICY,CARNEGIEMELLONUNIVERSITY,PITTSBURGH,PA1521308885885/91/263007130250/0REFLUXANDCONSTANTPRODUCTCOMPOSITIONOFAALLCOMPONENTSANDBONECOMPONENT2CONSTANTREFLUXANDVARIABLEPRODUCTCOMPOSITIONTHEDESIGNMETHODSDEVELOPEDTODATEHAVESOMEDISADVANTAGESMOSTOFTHEAPPROACHESAREDERIVEDFROMTHECLASSICALMCCABETHIELESMETHOD,WHICH,FORTHEBATCHDISTILLATIONCASE,CALLSFORANITERATIVESOLUTIONPROCEDURECHAO1954PROPOSEDASHORTCUTMETHODBASEDONTHEABSORPTIONSEPARATIONFACTORMETHODROSEETAL1950ANDHOUTMANANDHUSSAIN1956HAVEUSEDTHEPOLEHEIGHTCONCEPTFORDESIGN,WHICHDEPENDSONTHEWIDTHOFTHEINTERMEDIATEFRACTIONANDISAPPLICABLEONLYTOSHARPSEPARATIONS01991AMERICANCHEMICALSOCIETY714INDENGCHEMRES,VOL30,NO4,1991C7FIND“INEQUATION3,RMINEQUATION5,6ANDFROMRFINDNUSINGGILLILANDSCORRELATIONDECREASE4BYASMALLSTEP4CFINDSUSINGEQUATION2FIND“INEQUATION3,RMINEQUATION5,6ANDR,USINGTHEGILLILAUDSCORRELATIONCFIGURE1DESIGNPROCEDUREFORVARIABLEREFLUXCONDITIONSECTION211THEABOVEMETHODSAREAPPLICABLEONLYFORBINARIESTHEPOLEHEIGHTCONCEPTCANBEEXTENDEDTOAMULTICOMPONENTSYSTEMBYASSUMINGPSEUDOBINARIESALLOFTHEABOVEWORKPERTAINTOTHECONSTANTREFLUXCASEROSE1979HASPRESENTEDAMODELFORTHEVARIABLEREFLUXCASE,CONSIDERINGANONIDEALSYSTEM,WHICHTAKESLARGECOMPUTATIONALTIMEANDMEMORYHOWEVER,THISDOESNOTTAKEINTOCONSIDERATIONTHEHOLDUPEFFECTARIGOROUSAPPROACHTOSIMULATIONOFABATCHCOLUMNTHATTAKESINTOACCOUNTTHEPLATEHOLDUPREQUIRESTHEUSETABLEIINPUTCONDITIONSANDMAXIMUMPERCENTDEVIATIONINKEYCOMPONENTSTILLCOMPOSITIONVARIABLEREFLUXCASEINOAINX,WDEV1170116150910022015200910053171168098211041711611095201051711610098571062490958110107245095137OFDYNAMICMODELSMEADOWS,1963DISTEFANO,1968SOMEOFTHECOMMERCIALSIMULATORSBOSTONETAL,1981HAVETHISPROVISIONFORSIMULATIONOFBATCHCOLUMNSTHEUSEOFADYNAMICMODELREQUIRESACONSIDERABLEAMOUNTOFDATAANDEXTENSIVECOMPUTATIONTIMERECENTLYGALINDEZANDFREDENSLUND1988PROPOSEDAMETHODFORRIGOROUSSIMULATIONOFBATCHCOLUMNS,WHICHASSUMESQUASISTEADYSTATEAPPROXIMATIONATEACHTIMESTEPATTHEMETHODISMOREEFFICIENT,BUTTHEACCURACYOFTHERESULTSDOESDEPENDUPONTHEPROPERCHOICEOFATITISCLEAR,THEREFORETHATTHEREISAPRESSINGNEEDFORTHEDEVELOPMENTOFANEFFICIENTSHORTCUTALGORITHMFORMULTICOMPONENTBATCHDISTILLATIONTHATCANBEAPPLIEDTOBOTHVARIABLEANDCONSTANTREFLUXCASES2THEALGORITHMTHISMETHODISBASEDONTHEREASONABLEAPPROXIMATIONTHATTHEBATCHDISTILLATIONCOLUMNCANBECONSIDEREDASACONTINUOUSDISTILLATIONCOLUMNWITHCHANGINGFEEDIN00010203040506A1002D1000Q11XMXM1XXFORXM513XMASXMA,XBX,ANDASXMA,XB116THEFLOWCHARTFORTHEDESIGNPROCEDUREISGIVENINFORXM1,BOTHEQUATIONSGIVETHESAMESOLUTIONFIGURE53ALGORITHMVERIFICATIONTHEVALIDITYOFTHEPROPOSEDPROCEDUREHASBEENTESTEDEXTENSIVELYFORTHEPROBLEMSINTABLEIFORVARIABLEREFLUXANDTHEPROBLEMSINTABLE11FORCONSTANTREFLUXCONDITIONS31VARIABLEREFLUXCASEFOREACHOFTHETESTCASES,THERPROFILECALCULATEDBYTHESHORTCUTMETHODISUSEDINTHEPLATETOPLATEMETHODTOESTIMATETHESTILLCOMPOSITIONSTABLEIGIVESTHEINPUTCONDITIONSFORTHESAMPLEPROBLEMS,ANDITALSOSHOWSTHECOMPARISONOFTHERESULTSUSINGTHEPROPOSEDSHORTRCUTMETHODANDTHEPLATETOPLATECALCULATIONSINTERMSOFTHEMAXIMUMPERCENTDEVIATION718INDENGCHEMRES,VOL30,NO4,1991TABLE11INPUTCONDITIONSANDMAXIMUMPERCENTDEVIATIONINCOMPOSITIONOFKEYCOMPONENTSANDNUMBEROFPLATERCONSTANTREFLUXCASEMAXDEVDEVNOAIRXBXBXAN117,116,103220,15,10,0510320,15,10,0520417,116,103517,116,1020617,116,105717,116,103817,116,101009412074000740008962094820918309349092001I22511322938145117411111111181130FORTHEKEYCOMPONENTSTILLCOMPOSITIONITCANBESEENTHATTHEDEVIATIONISWITHINTHEACCEPTABLELIMITSFORASPECIFICCASEOFATERNARYSYSTEMCASE1,TABLEIDETAILEDRESULTSARESHOWNINFIGURE6THEPROFILESPREDICTEDBYTHESHORTCUTMETHODCORRESPONDCLOSELYTOTHEPROFILESOBTAINEDFROMTHEPLATETOPLATECALCULATION32CONSTANTREFLUXCASEFOREACHOFTHETESTCASES,THECOMPOSITIONPROFILESANDTHENUMBEROFPLATESNOBTAINEDBYTHEPLATETOPLATEMETHODROBINSON,1975ARECOMPAREDWITHTHECOMPOSITIONPROFILESANDVALUEOFNOBTAINEDBYTHESHORTCUTMETHOD,USINGTHESAMEVALUEOFREFLUXRATIORANDTHEINITIALXBTABLEI1GIVESTHEINPUTCONDITIONSFORTHESAMPLEPROBLEMS,ANDITALSOSHOWSTHECOMPARISONOFTHERESULTSINTERMSOFTHEMAXIMUMPERCENTDEVIATIONINTHEKEYCOMPONENTCOMPOSITIONSANDPERCENTDEVIATIONINNITCANBESEENTHATTHEDEVIATIONSARESMALLTABLEI11SHOWSTHECOMPARISONOFTHERESULTSOFTHESHORTCUTMETHOD,WITHBATCHFRACBOSTONETAL,1981RESULTS,FORTHEQUATERNARYSYSTEMCONSISTINGOFPROPANE,BUTANE,PENTANE,ANDHEXANETHECPUTIMEREQUIREDTOSOLVETHISPROBLEMFORTHEFIVEFRACTIONSIS5SONANND560SUPERMINI,EQUIVALENTTOVAX11/785SYSTEM,COMPAREDTOTHETIMEOF19MINONIBM370OFBATCHFRACINBOTHCASESTHETIMECONSTANTTOFTHESTAGE7HOLDUP/REFLUXRATIOXDISTILLATERATEISNOTLARGE,SOTHERESULTSAGREEWELL4MODIFICATIONOFTHESHORTCUTMETHODTHESHORTCUTMETHODHASBEENTESTEDEXTENSIVELYONANUMBEROFBINARYANDMULTICOMPONENTCASESWITHTHEASSUMPTIONOFCONSTANTAANDNOTFORNONIDEALSYSTEMSANDCOLUMNSWITHDOMINANTHOLDUPEFFECTSITWILLBEOFINTERESTTOASSESSTHECAPABILITYOFTHEMETHODTOHANDLENONIDEALSYSTEMSANDALSOSITUATIONSWHERETHEHOLDUPCANBESUBSTANTIAL41NONIDEALSYSTEMSTOANALYZETHECAPABILITYOFTHESHORTCUTMETHODUSEDINTHISSTUDYTOSIMULATENONIDEALSYATEMS,PROBLEMSONTWOSYSTEMSHAVEBEENSTUDIED,NAMELY,ETHANOLWATERANDMETHANOLWATERWITHTHEASSUMPTIONOFTHENEGLIGIBLEHOLDUPFURTHEREXPERIMENTALRESULTAREPORTEDBYDOMENCHANDENJALBERT1974FORTHENONIDEALSYSTEMCONSISTINGOFCYCLOHEXANEANDTOLUENEWITHHOLDUPARECOMPAREDWITHTHESHORTCUTMETHODINSTEADOFCONSTANTABEINGUSEDTHROUGHOUTTHECOURSEOFTHEDISTILLATION,THEVALUEOFAISUPDATEDATEACHSTEPBYUSINGAPPROPRIATECORRELATIONS,TOESTIMATETHECYVALUESATTHETOPANDBOTTOMOFTHECOLUMNSHEREFORTHEETHANOLWATERANDTHEMETHANOLWATERSYSTEMS,THEVALUESOFAATTHETOPANDBOTTOMAREESTIMATEDATEACHSTEPBYTHEUNIQUACEQUATIONANDAVERAGEDBYAATOPABOTTOML21OJ1NONOESHORTCUTMETHODANOCTANENDECANEIFIGURE9EXPERIMENTALANDTHEORETICALDISTILLATIONCURVES,TERNARYSYSTEMCONSTANTREFLUXAA006087MNHEXANESHORTCUTMETHODANHEPTANEXNOCTANE0NDECANEJFIGURE10EXPERIMENTALANDTHEORETICALDISTILLATIONCURVES,FIVECOMPONENTSYSTEMCONSTANTREFLUXACOMPARISONOFTHERESULTSOBTAINEDBYTHESHORTCUTMETHODANDTHERIGOROUSMETHODARESHOWNINFIGURE7FORTHESPECIFICCASEOFTHEETHANOLWATERSYSTEMINTHECASEOFCYCLOHEXANEANDTOLUENE,THEUNIFACMETHODISUSED,ANDTHERESULTSOBTAINEDARESHOWNINFIGURE8INDENGCHEMRES,VOL30,NO4,1991719TABLE111COMPDMNOFRERULTROFBATCHFRACBOSTONETAL,1981WITHTHESHORTCUTMETHODPENTANEREMOVALBUTANEREMOVALFRACTION1FRACTION2FRACTION3FRACTION4FRACTION5PROPANEREMOVALBATCHFRACSHORTCUTBATCHFRACSHORTCUTBATCHFRACSHORTCUTBATCHFRACSHORTCUTBATCHFRACSHORTCUTREFLUXRATIODISTILLATERATAVAPORRATETIMEPROPANEBUTANEPENTANEHEXANEPROPANEBUTANEPENTANEHEXANEPROPANEBUTANEPENTANEHEXANE521240708OOO0200009888001128132100206032540109005450917350520202525151522222221242425252323240718118118271820431431DISTILLATECOMPOSITIONMOLEFRACTION0817300150001900181709850097420164401593000630835607521080000763800005008860200002362AVERAGEDISTILLATECOMPOSITION,ATTHEENDOFEACHFRACTIONMOLEFRACTION09853052300522000002001450477004750099000991500058000500002600098000770984509840OOOO4000080009700110812203613036000365433638886020860150021700001032520319103193OOOO6OOOO60108801135011340133501335001730017405442056740567208658086580982709826918780881240881360716000717360629980629985POTCOMPOSITIONMOLEFRACTION25252178001610983902994070063600000002099985938902525217800168098320304406956353900000209998594580I/TOTALHOLDUP0570104NNOSHORTCUTMETHODIONOCTANE0NOECANEFIGURE11THEORETICALDISTILLATIONCURVES,TERNARYSYSTEMCONSTANTREFLUXTHOUGHTHEPROFILESOBTAINEDBYTHETWOMETHODSDONOTAGREEONANABSOLUTESCALE,ITCANBESEENTHATTHETRENDOFPROFILESOBTAINEDBYTHESHORTCUTMETHODISVERYCLOSETOTHATOBTAINEDBYTHERIGOROUSMETHODINORDERTOFORCEAGREEMENTBETWEENTHESHORTCUTANDTHERIGOROUSCASES,ITMAYBENECESSARYTOLOOKFORTUNINGPARAMETERSINTHESHORTCUTMODELANYDISCREPANCIESIN4TOCERTAINEXTENTACCOMMODATEDINUPDATINGTHEVALUEOFC1ATEACHSTEPEQ12ANOTHERPARAMETERTHATCOULDBEEXPLOREDASATUNINGPARAMETERISTHEVALUEOF4,WHICHOCCURSINTHEUNDERWOODEQUATION17WHERE4TU714TISCALCULATEDFROMEQ6USINGTHEESTIMATEDVALUEOFAIWITHUSEOFTHESIMULATIONRESULTSOBTAINEDFROMTHERIGOROUSMETHOD,PARAMETERRLCANBEOBTAINEDBYUSINGEITHERANINITIALESTIMATEOFAIORANESTIMATEOFAIOVERSOMEPARTOFTHECURVESOTHATTHEDEVIATIONISMINIMUMCONDENSERPLATE1TOTALCOLUMNPLATEREBOILERIII1IIIII1IIIIIITISHORTCUTMETHODEQUALIONSAPPLIEDTON1PLATESIIFIGURE12BATCHDISTILLATIONCOLUMN,MODIFIEDSHORTCUTMETHODMODELACOMPARISONOFTHERESULTSOFTHETUNEDSHORTCUTMETHODWITHTHOSEOFTHERIGOROUSCASEISSHOWNINFIGURE7FORTHENONIDEALETHANOLWATERSYSTEMTHEPROPOSEDTUNINGPROCEDUREAPPEARSTOBEEFFECTIVEINHANDLINGTHENONIDEALITIES42INCORPORATIONOFTHEHOLDUPTOESTIMATETHEEFFECTOFHOLDUPONTHEPERFORMANCEOFTHEMETHOD,THERESULTSOBTAINEDBYSTEWARTETAI1973ARECOMPAREDWITHTHERESULTSOBTAINEDBYOURSHORTCUTMETHODFIGURES911HERETHEINITIALTOTALREFLUXCONDITIONISSIMULATEDBYUSINGNNMI,ITCANBESEENTHATTHESHORTCUTMETHODRESULTSAGREEWELLWITHTHERESULTSOBTAINEDFORSMALLHOLDUPCONDITIONSFORLARGEHOLDUPVALUESANDLOWREFLUXRATIO,THEINITIALPARTOFTHECOMPOSITIONPROFILEFORTHEMOREVOLATILECOMPONENTSHOWSAGRADUALCHANGEFORTHERIGOROUSMODELS,WHILETHESHORTCUTMETHODPREDICTSASHARPDROPINTHECOMPOSITIONFIGURE11THISISDUETOTHELARGETIMECONSTANT7ASSOCIATEDWITHLARGEHOLDUPANDLOWREFLUXRATIO7HOLDUP/REFLUXRATIOXDISTILLATERATETHESHORTCUTMETHODNEEDSTOBEMODIFIEDFORSUCHDYNAMICSITUATIONSWHERETHESTATEVARIABLESASSOCIATEDWITHTHEPLATESHAVEADOMINANTDYNAMICCHARACTERINABATCHDISTILLATION,THEINPUTVARIABLETHATCHANGESSIGNIFICANTLYISTHEREFLUXRATIOIFONEEXAMINESTHETRANSITIONFROMTOTALREFLUXTOAFINITEREFLUXCONDITION,THEI720INDENGCHEMRES,VOL30,NO4,1991ACKNOWLEDGMENTWETHANKPROFRESWANEY,DEPARTMENTOFCHEMICALENGINEERING,UNIVERSITYOFWISCONSIN,MADISON,WI,FORTHENUMEROUSUSEFULDISCUSSIONSTHEASSISTANCEOFMRNDEVANATHAN,DEPARTMENTOFCHEMICALENGINEERING,WASHINGTONUNIVERSITY,STLOUIS,MO,INTHEPREPARATIONOFTHEMANUSCRIPTISGRATEFULLYACKNOWLEDGEDMODIFIED20HOLDUP1SHARTCUTXNOCTONEENNONANEONDECANEJRIGOROUSFIGURE13THEORETICALDISTILLATIONCURVES,TERNARYSYSTEMSHORTCUTMETHOD,WHICHNEGLECTSHOLDUPEFFECT,PREDICTSASHARPDROPINTHEPRODUCTCOMPOSITIONFIGURELL,WHILEINTHEACTUALCASETHETOPPRODUCTCOMPOSITIONVARIESINAGRADUALMANNERTOACCOUNTFORTHISDYNAMICEFFECT,ALUMPEDDYNAMICELEMENTISASSUMEDTOBELOCATEDATTHETOPOFTHECOLUMNAQUASISTEADYSTATEAPPROXIMATIONISASSUMEDFORTHEREMAININGPARTOFTHECOLUMNFROMTHEREBOILERTOTHEFIRSTPLATE,ASTHECOMPOSITIONCHANGESARESLOWERINTHISPARTOFTHECOLUMNTHESHORTCUTMETHODISUSEDFORTHATSECTIONOFTHECOLUMNFIGURE12THEMODIFIEDFORMOFTHESHORTCUTMETHODINVOLVESTHEFOLLOWING1DYNAMICMODELFORTHETOPPLATE1ANDTHECONDENSER2SHORTCUTMETHODEQUATIONSFORN1PLATESANDREBOILERTHESHORTCUTMETHODEQUATIONSUSETHECOMPOSITIONSPREDICTEDBYTHEDYNAMICMODELATTHETOP,ATEACHTIMESTEPTHERESULTSOBTAINEDBYTHEMODIFIEDSHORTCUTMETHODARECOMPAREDWITHTHOSEOBTAINEDBYUSINGTHERIGOROUSDYNAMICMODELFIGURE13ASCANBESEENINTHEFIGURE,THEINCLUSIONOFDYNAMICEFFECTINTHESHORTCUTMODELPERMITSCLOSERCORRESPONDENCEWITHTHOSEPREDICTEDBYTHERIGOROUSMODELTHEHOLDUPVALUEOFTHELUMPEDELEMENTATTHETOPCANBEADJUSTEDTOFORGEACLOSERMATCHWITHTHERESULTSOFTHERIGOROUSMODELHERE,INTHISEXAMPLETHEHOLDUPISTAKENEQUALTOTHEPLATEHOLDUPONLYFORCOLUMNSWITHALARGENUMBEROFPLATES,ASINGLELUMPEDELEMENTMAYNOTBEADEQUATETOREPRESENTTHEHOLDUPEFFECT,ANAPPROPRIATEMODELORDERMAYHAVETOBECHOSENTOREPRESENTTHERESULTINGDYNAMICEFFECT5CONCLUSIONSANDSIGNIFICANCETHESHORTCUTMETHODPROPOSEDHASBEENTEATEDASATOOLFORBOTH,PRELIMINARYDESIGNANDOPTIMIZATIONOFBATCHDISTILLATIONCOLUMNSANADVANTAGEOFTHISMETHODISTHATTHEINCREASEINTHENUMBEROFPLATESDOESNOTAFFECTTHECOMPUTATIONTIMEANDMEMORYREQUIREMENTSTHEPRESENCEOFTUNINGPARAMETERSINTHEMODELPERMITSTHEINCLUSIONOFNONIDEALBEHAVIORTHEDYNAMICEFFECTOFHOLDUPCANBEACCOMMODATEDBYINCLUSIONOFLOWERORDERMODELSNEARTHETOPOFTHECOLUMNFORTHECASESWHERETHEREFLUXRATEISTHEMAJORMANIPULATEDVARIABLETHEMODIFIEDSHORTCUTMETHOD,WHICHINCORPORATESTHETUNINGPARAMETERSANDTHEHOLDUPEFFECTS,CANBEUSEDFORONLINEAPPLICATIONWITHADAPTATIONFEATURESNOMENCLATUREBAMOUNTOFMATERIALREMAININGINTHESTILLC1HENGATEBECKGEDDESCONSTANTFAMOUNTOFFEEDHPLATEHOLDUPHDCONDENSERHOLDUPHKHEAVYKEYCOMPONENTLKLIGHTKEYCOMPONENTNNUMBEROFCOMPONENTSNNUMBEROFPLATESNMINMINIMUMNUMBEROFPLATESQFEEDCONDITION,THEUNDERWOODEQUATIONRR/RMMINITIALRREFLUXRATIORDNMINIMUMREFLUXRATIORMINAMINIMUMREFLUXRATIOUSINGTHEGILLILKDCORRELATIONRMUMINIMUMREFLUXRATIOUSINGTHEUNDERWOODEQUATIONRTREFLUXRATIOATTIMETTTIMEVVAPORBOILUPRATEOFREBOILERXIILIQUIDCOMPOSITIONOFCOMPONENTI,LEAVINGPLATEJXBSTILLCOMPOSITIONOFCOMPONENTIXKFINALSTILLCOMPOSITIONOFCOMPONENTIXDAVAVERAGEDISTILLATECOMPOSITIONOFCOMPONENTIXP,SPECIFIEDAVERAGECOMPOSITIONOFCOMPONENT1XBDISTILLATECOMPOSITIONOFCOMPONENTIXPFEEDCOMPOSITIONOFCOMPONENTIYYVAPORCOMPOSITIONOFCOMPONENTI,LEAVINGPLATEJYBVAPORCOMPOSITIONOFCOMPONENTI,LEAVINGTHESTILLGREEKSYMBOLSAIRELATIVEVOLATILITYOFCOMPONENTI4UNDERWOODEQUATIONCONSTANT3FRACTIONDISTILLEDAPPENDIXISENSITIVITYANALYSISFORVARIABLEREFLUXCASETHESENSITIYITYFUNCTIONSIDEFINEDBYEQ7CANBEOBTAINEDBYTHEPROCEDUREGIVENBELOWFROMEQ8AI“INAILXB42D1I2,3,NAL1“1“1XBFROMEQ10INDENGCHEMRES,VOL30,NO4,1991721WHERE1IANDMIFORTHEFIRSTTERMAND12ANDMNFORTHESECONDTERMSINCEYK/YL11BEINGTHEMOSTVOLATILECOMPONENTASXBDECREASES,WDECREASESA13ANDSUBSTITUTINGINEQA12GIVESI/1IA14FORCOMPONENTSHAVINGACLOSERRELATIVEVOLATILITY,AIALLE,FORTHELIMITAIAL,SI0ITCANBESEENFROMEQA14THATFORLARGEVALUESOFC1C,INCREASESASXKDECREASES,AK/ALCLISSMALL,SOISIL01/1IA15FORASXHDECREASESISIDECREASESFIGURE2ATHEINITIALVALUEOFISILISSUFFICIENTTOGETTHEIDEAOFWHETHERORNOTCOMPOSITIONCHANGESSHOULDBECONSIDEREDFORSMALLVALUESOFC1FIGURE2A,THETRENDCANNOTBEPREDICTEDINITIALLYHOWEVER,THEMAXIMUMVALUEAMONGALLTHEINITIALISILI2,3,NCANSTILLGIVEAGOODESTIMATETHISISGENERALLYTRUEBECAUSEINEQA14,SINCEBOTHTHETERMSINSQUAREBRACKETSAR