On-line estimation of product properties for crude distillation units

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JournalofProcessControl14(2004)61–77

www.elsevier.com/locate/jprocont

On-lineestimationofproductpropertiesforcrudedistillationunits

TirthaChatterjee,DeokiN.Saraf*

ProcessControlLaboratory,DepartmentofChemicalEngineering,IndianInstituteofTechnology,Kanpur208016,India

Received12December2002;receivedinrevisedform23April2003;accepted22May2003

Abstract

Thestringentqualityrequirementofpetroleumproductsinahighlycompetitivemarketmakeson-linemonitoringandcontrolofproductpropertiesessential.Butunfortunatelyfewon-linehardwaresensorsareavailableandthesearealsodiﬃculttomaintain.Itis,therefore,necessarytodevelop‘softwaresensors’topredictthequalityusingothereasilymeasurablesecondaryvariables.Thisstudypresentsanalgorithmthatusesthecrudetrueboilingpoint(TBP)curveandotherroutinelymeasuredﬂowrates,tempera-turesandpressuresinthecrudedistillationunit(CDU)topredicttheproductproperties.Themeasuredtopplate,side-stripperdrawplatesandﬂashzonetemperaturesarecorrectedforhydrocarbonpartialpressurestoobtainequilibriumﬂashvaporization(EFV)temperatures.TheseproductEFVsareconvertedtoproductTBPsandaresuperimposedonthecrudeTBPcurve.Anassumption,thattheinitialboilingpoint(IBP)ofthenextheavierproductliesverticallybelowtheﬁnalboilingpoint(FBP)oftheproductunderconsiderationandthetwopointsareequidistantfromthecrudeTBPcurve,allowsestimationoftheIBPandFBPtemperaturesofallthedistillateproducts.AstraightlineapproximationoftheproductTBPcurveisusedtoobtainintermediatetemperatures.TheseTBPtemperaturesareconvertedtoproductASTM(AmericanSocietyforTestingMaterials)temperatureswhicharecorrelatedwiththedesiredproductproperties.Severalpropertieshavebeenpredictedusingtheaboveprocedure.TheseincludedensitiesofalltheCDUproducts,FlashPointsforalltheside-streamproducts,ReidVaporPressure(RVP)forthedis-tillate,FreezePointforkerosene,PourPointandtherecoveryforthegasoilsetc.ItispossibletopredictthesepropertiesrepeatedlyeveryminuteaslongassteadystateconditionsprevailintheCDU.Thealgorithmhasbeenappliedoﬀ-linewiththeavailableon-linedatafromtwodiﬀerentoperatingreﬁneries.Asatisfactorymatchbetweenthepredictedandthemeasuredpropertiesvalidatedthedevelopedsoftsensors.However,extensivetestingisrecommendedbeforetheimplementationofthesesoftsensorsontheactualprocess.#2003ElsevierLtd.Allrightsreserved.

Keywords:Softsensors;Productproperties;Propertiesprediction;Crudedistillation

1.Introduction

Acrudedistillationunit(CDU)isonethroughwhichtheentirecrudeenteringareﬁnerymustbeprocessed.Becauseofahighlycompetitivemarketandstringentenvironmentallaws,strictqualitycontrolofreﬁneryproductsisessential.Alltheseproductsarecomplexmixturesofhydrocarbonsanditisnotpossibletocharacterizethemintermsofindividualcomponents.Moreover,itisoftensuﬃcienttocharacterizetheseproductsintermsofcertaingrosspropertiessuchasReidVaporPressureforvolatileproducts,FlashPointforlightdistillates,PourPointforheavydistillatesetc.Thestringentproductqualityrequirementmakesit

*Correspondingauthor.Tel.:+91-512-2597-827;fax:+91-512-2590-104.

E-mailaddress:dnsaraf@iitk.ac.in(D.N.Saraf)0959-1524/03/$-seefrontmatter#2003ElsevierLtd.Allrightsreserved.doi:10.1016/S0959-1524(03)00036-2

necessarythatalltheproductpropertiesshouldbemonitoredandcloselycontrolledcontinuously.Thisrequiresthatthesepropertiesshouldbemeasuredon-linesothattheunitcanbeeﬀectivelycontrolledthroughafeedbackmechanism.

Unfortunatelynosuitablehardwaresensorsareavailableinthemarketwhichcouldbeusedtomeasurerequiredpropertiesofvariouspetroleumproductson-line.Thelaboratorymeasurementproce-duresaretediousandtimeconsuming,and,hence,itisseldompracticaltomeasurethesepropertiesmoreoftenthanonceinashiftorevenoncein24h.Forthecontrolofatmosphericcrudedistillationunit,itiscustomarytousecutpoints.Horn[1]suggestedtheuseofcut-pointtemperaturesasameasureofproductquality.Thisessentiallymeansthatafractionationpro-ducthavingacertainrangeofboilingpointsisassumedtorepresentthequalityofthatproduct.However,pro-

62T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–77

Nomenclaturefdlmassﬂowrateoftheliquiddistillateproduct(kg/h)Fdlmolarﬂowrateofliquiddistillateproduct(kmol/h)Fdvmolarﬂowrateofthevapordistillateproduct(kmol/h)FLmolarﬂowrateofthetotalliquidside-stripperproductsandoverﬂashthatareinvaporformintheﬂashzone(kmol/h)Fomolarﬂowrateoftheoverheadvaporleavingtopofthecolumn(kmol/h)Frefmolarﬂowrateofthetopplatereﬂux(kmol/h)Fss,kmolarﬂowrateofthekthside-stripperliquidproduct(k=1,2,3,4)(kmol/h)Kjvapor-liquiddistributioncoeﬃcientforjthpseudo-component.Lr,(i-1)molarﬂowrateofthehydrocarbonliquidtothekthside-stripperproductdrawtray(i.e.ithtray)fromthetrayabove(kmol/h)mnumberofpseudo-componentspresentinaproduct.Mjmolecularweightofthejthpseudo-component(kg/kmol)MWmolecularweight(kg/kmol)pfzpartialpressureofthehydrocarbonvaporattheﬂashzone(psia)pss,kpartialpressureofthehydrocarbonvaporatthekthside-stripperproductdrawtray(k=1,2,3,4)(psia)ptoppartialpressureofthehydrocarbonvaporatthetopofthecolumn(psia)ductqualitywillvarywiththetypeofhydrocarbonspresent—paraﬃnic,naphthenicetc.and,hence,cut-pointisnotasatisfactorymeasure.Alternatively,attemptshavebeenmadetoestimateproductpropertiesusingmathematicalmodels.Thesemodelsaresodesignedthattheyuseonlyeasilymeasurablesec-ondaryvariablesasinput.Thesemodelsarealsoreferredtoas‘SoftSensors’sincetheyservethesamepurposeashardwaresensors,namelyprovidethepropertieson-line.Pfztotalpressureattheﬂashzone(psia)Pss,ktotalpressureattheproductdrawtrayofthekthside-stripper(k=1,2,3,4)(psia)Ptoptotalpressureatthetopofthecolumn(psia)(SG)jspeciﬁcgravityofthejthpseudo-component.(SG)kspeciﬁcgravityofthekthproduct.Skmolarﬂowrateofthesteaminputtothekthside-stripper(k=1,2,3,4)(kmol/h)SRmolarﬂowrateofthesteaminputtothebottomofthemaincolumn(kmol/h)STmolarﬂowrateofthetotalsteaminputtothecolumn(ST=SR+ÆSk)(kmol/h)TASTMASTMtemperature(K)TBnormalboilingpoint(K)TFFlashPointtemperature(K)TFPFreezePointtemperature(K)TPPourPointtemperature(K)TTBPtrueboilingpointtemperature(K)xjmolefractionofthejthpseudo-componentxjkmolefractionofthejthpseudo-componentinthekthproduct.Vjvolumeofthejthcomponentinthemixture(m3)Vss,imolarﬂowrateofhydrocarbonvaporandsteamleavingtheithside-stripperdrawproducttray(kmol/h)Vmid-volumefractioncumulativemiddlevolumefractionGreekletters󰀁kinematicviscosity(cS)Asteadystate,multicomponentdistillationmodel,basedonequilibriumstagerelationsiscommonlyusedtosimulatethecrudedistillationunit(CDU).ForamixtureofCcomponents,analgorithmdevelopedbyBostonandSullivan[2]andlatermodiﬁedbyRussel[3],hasbeenfoundsuitableformodelingcrudefractiona-tionunitswherealargenumberofstagesaswellasalargenumberofcomponentsarepresentandmostofthecommercialsoftwarepackagesusethisalgorithm.Kumaretal.[4]developedamodelusing(C+3)itera-

T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–7763

tionvariablessimilartothatbyRusselbutanalter-nativechoiceofindependentvariablesmadetheirmodelmorerobustandeﬃcient.Thismodelwillbereferredtoasthe‘Simulator’inlattersections.

Inordertobeabletousethesteadystatemodelforon-lineapplicationitisnecessarytotunethemodelfrequentlyusingon-lineoperatingdata.Stageeﬃ-cienciesarecommonlyusedfortuningdistillationmodels.However,crudefractionatorsneedoneaddi-tionaltuningandthatisfeedcompositionwhichisexpressedintermsofatrueboilingpoint(TBP)vsweightorvolumepercentdistilledcurveorsimplyknownasTBPcurve.Daveetal.[5]recentlydescribedaprocedureforon-linetuningofbothstageeﬃcienciesandfeedTBPcurveusingroutinelymeasuredoperatingdata.Stageeﬃciencytuning,beinganonlinearopti-mizationprocedure,isatimeintensivestepandmaynotallowrepetitionfasterthanevery10min.Aftertuning,themodelequationsaresolvedtoprovideproductTBPtemperaturesanddensities.TheseTBP(orASTM)tem-peraturesanddensitiesareempiricallycorrelatedtovar-iousproductproperties.Thismeansproductpropertiesestimationcannotberepeatedfasterthanevery10–12minwhichissatisfactoryforprocessmonitoringbutunacceptablyslowforfeedbackcontrol.

Thepresentstudyaimstouseanapproximatemodeltopredictproductpropertieseveryminutewhichissui-tableevenforon-linecontroloftheunit.Inthepresentalgorithmanalternativemethodisdevelopedwhich,basedondrawplatetemperaturesofdiﬀerentproductsandotheroperatingconditions,calculatesseveralpro-ductequilibriumﬂashvaporization(EFV)temperatures(sixinthepresentcase).TheseEFVsarethenconvertedintoTBPtemperatures,whichwhenplacedonthecrudeTBPcurve,allowestimationofsixmoreproductTBPtemperatures.InthismethodtheproductTBPcurvesareapproximatedbystraightlinesforeaseofinter-polation.TheseproductTBPtemperaturesarerelatedtoproductpropertieseitherdirectlyorafterconversiontoASTMtemperatures.Thuswithoutmakingthesimulationoverthemaincolumn,productpropertiesaredeterminedinaneasyandinstantway.

Atypicalcrudedistillationunitconsistsofthemaincol-umn,side-strippercolumnsandpump-aroundsasshowninFig.1.Preheatedfeedenterstheﬂashzonenearthebottomofthemaincolumnandvariousfractionationproductsarewithdrawnasside-streamswhicharesteamstrippedinthestrippercolumnstoremovethevolatiles.Pump-aroundﬂowsareusedtoregulatethevaportraﬃcthroughthecolumnaswellasforheatrecovery.AtypicallistofproductsfromCDUincludesunstabilizednaphthatakenfromthecondenseratthetopofthecolumn(whichissenttoastabilizercolumnforrecoveryofliqueﬁedpet-roleumgas),specialcutnaphtha(orheavynaphtha),ker-osene,lightgasoil(LGO)andheavygasoil(HGO)assideproductsandlongresidue(LR)asthebottomproduct.

2.CrudeTBPreconciliation

Thetrueboilingpoint(TBP)curveisoneofthemostsigniﬁcantcharacteristicfeaturesofthefeedstock.Itdecidestheamountsofvariousfractionationproductsavailablefromthecrudeaswellasthecompositionandpropertiesoftheseproducts.TheaccuracyofpropertypredictionlargelydependsontheaccuracyoftheTBPcurveused.GenerallyTBPdataofpurecrudeisavail-ablefromthecrudeassaywhichmaynotrepresentthecrudebeingprocessedatalatertime.Thesedeviationsmayariseduetovariousreasonssuchasblendingofdif-ferentcrudes,contaminationofonecrudewithanotherinstoragetanksorthecrudebeingproducedfromadiﬀerentsectionofthereservoiratdiﬀerenttimes.

ItisnotpossibletomeasurethecrudeTBPtempera-turesfrequentlysinceittakesseveraldaystoestablishacompletecurveinthelaboratory.Noon-linesensorisavailableforthemeasurementoffeedTBPeither.Thisproblemcanbetackledintwoways.OneisTBPback-calculationwheretheinitialfeedTBPisrectiﬁedinrealtimeusingsomesecondaryoperatingdatameasuredon-line[5].Thesecondstrategyisusedinoﬀ-linemodeandiscalledTBPreconciliation.

ThefeedTBPreconciliationisausefulmethodtoupdatecrudeTBPfromtimetotime.ItisformulatedasanoptimizationproblemwhereonetriestoadjustthecrudeTBPsuchthatthesimulatorcalculatedproductASTMtemperaturesmatchcloselywiththosemeasuredinthelaboratory.ItisassumedherethatthecrudeTBPcurve,soreconciledusingalargenumberoflaboratorymeasuredASTMtemperaturesofdiﬀerentproducts,willbeclosertotherealfeedbeingprocessedatthattimeascomparedtotheinitialTBPcurveavailablefromthecrudeassay.Thesuccessofthepropertypre-dictiondependslargelyonthesuccessoftheTBPreconciliation.Therefore,itisanintegralpartofthepropertypredictionprocedure.2.1.Problemformulation

Inthelaboratory,usuallyproductASTMsaremea-suredwhichcanbeconvertedtoTBPtemperaturesusinganempiricalcorrelation.UnfortunatelyproductASTMsaremeasuredoccasionallyandtherefore,theTBPrecon-ciliationtechniquecanonlybeusedinoﬀ-linemodewhenevercompleteproductASTMdataareavailable.TheobjectivefunctionisformulatedasaleastsquaredminimizationproblemwherethediﬀerencebetweenthesimulatorcalculatedproductTBPsandthoseobtainedfromlaboratorymeasuredproductASTMtemperaturesisminimizedsubjecttomodelequationsasconstraints.AnadditionalconstraintarisesfromthefactthatthefeedTBPisamonotonicallyincreasingfunctionofthevolumepercentdistilled.i.e.TBPtemperatureofthe‘i’vol.%distilledisalways

T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–77

Fig.1.Schematicdiagramofacrudedistillationunit.

greaterthantheTBPtemperatureof‘j’vol.%distilledforalli>j.TheTBPreconciliationproblemcanbemathematicallyexpressedas:

MinimizeI¼

FeedTBP

ðProductTBPMeasuredÀProductTBPCalculatedÞ2i

theminimizationproblem.NPSOL(Version4.0,1986),

aFORTRANpackage(SoftwareDistributionCenter,StanfordUniversity,USA)wasusedinthepresentstudy.

2.2.Reconciliationstrategy

ThedetailedstrategyforfeedTBPreconciliationisgivenbelow.

Subjectto:modelequationsandTBPj

vol:%ofcrude

fori>j

ð1Þ

TheproductTBPsincludedintheobjectivefunctionarethoseoftopdistillate,specialcutnaphtha(SCN),kerosene,lightgasoil(LGO)andheavygasoil(HGO).Sequentialquadraticprogramming(SQP)wasusedfor

2.2.1.Selectionofmanipulatedvariables

ThemanipulatedvariablesaretrueboilingpointtemperaturesatdiﬀerentvolumepercentofthecrudedistilledthatessentiallyconstitutetheTBPcurve.Inthepresentwork,ﬁfteenTBPtemperaturesareconsideredasmanipulatedvariablestocoverthe0.5–70%(byvolume)range.ThreeTBPpoints,namelytemperaturesat80,90and100%(byvolume),aretakentobecon-

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stant(sameasthereportedoriginalTBPvalues)throughouttheoptimizationprocess.Thisisnecessarysincecumulativevol.%ofthetopdistillateandallside-stripperproductsisseldommorethanseventy.TheinitialguessisthefeedTBPdataavailablefromthecrudeassay.

2.2.2.Boundingstrategy

Theupperandthelowerboundsarespeciﬁedforallthemanipulatedvariables.Forunrealisticboundsandadistantinitialguess,theoptimizationprocessmayfailtoproducecorrectresults.Ontheotherhand,thediversityandtheﬂexibilityoftheoptimizationprocessmaybelostiftheboundsarenarrow.Theupperandthelowerboundsoftheﬁrstmanipulatedvariable(i.e.0.5%,byvolume,TBPtemperature)aretakenasÆ20󰀆Cfromtheinitialguess(initialTBPtemperaturefromcrudeassaydata).Forthelastmanipulatedvariable(i.e.70%,byvolume,TBPtemperature)thelowerboundisÀ20󰀆Cfromtheinitialguesswhereastheupperboundis+25󰀆CfromtheinitialTBPtemperature.Forremain-ingmanipulatedvariables,theupperandthelowerboundsaresetatÆ30󰀆CfromtheinitialTBPvalue.Thesenumbersarechosensomewhatarbitrarilybasedonexperience.

Iftheboundsarehitthentheyarerelaxedgradually.Fortheﬁrstvariable,lowerandupperboundsarerelaxedfurtherbyhalfofthetotalboundgap(i.e.thedistancebetweeninitiallowerandupperboundsoftheﬁrstvariable)ineitherdirectionwhenthecorrespondingboundishit.Forexample,thetotalboundgapfortheﬁrstmanipulatedvariableis40󰀆Cinitiallyandhencethelowerboundisreducedbyafurther20󰀆Cifitishit.Forthelastmanipulatedvariabletheupperboundisrelaxedinthesamefashion.Forthelowerboundrelaxation,halfofthegapbetweenthepresentlowerboundofthelastvariableandthecurrentvalueofthepenultimatevariableisconsidered.

Therelaxationofboundsofintermediatevariablesisabittrickysincechangingtheboundsofanyvariabledirectlyaﬀectstheboundsofitsadjacentvariables.Ifthelowerboundofthenthvariableishitthenitislow-eredfurtherbyhalfofthegapbetweenthepresentlowerboundofthenthvariableandthevalueof(nÀ1)thvariable.Ifinthisprocessthelowerboundofthenthvariablebecomeslowerthantheupperboundofthe(nÀ1)thvariablethentheupperboundofthe(nÀ1)thvariableissetequaltonewlyreducedlowerboundofthenthvariable.Fortheupperboundhitofthenthvariabletheboundisfurtherraisedbyhalfofthegapbetweenthe(n+1)thvariablevalueandthepresentupperboundofthenthvariable.Ifinthispro-cessupperboundofthenthvariablebecomesgreaterthanthelowerboundofthe(n+1)thvariablethenthelowerboundofthe(n+1)thvariableissetequaltothenewlyincreasedupperboundofthenthvariable.Hav-

ingresetthebounds,theoptimizerisrestarted.Thisboundingstrategyisinbuiltintothecodethatistestedsuccessfullyforagoodnumberofcrudes.Thusbound-ingstrategyensuresthatthereconciledTBPstaysmonotonicallyincreasingwiththevolume%distilledatalltimes.

2.2.3.SelectionofproductTBPpointsintheobjectivefunction

Thenumberofparametersincludedintheobjectivefunctionisalsoimportant.Foraﬁxednumberofmanipulatedvariables,thehigherthenumberofpara-metersintheobjectivefunction,thelargerthedegreesoffreedomandthebetteristheoptimizationresult.OntheotherhandthelaboratoryreportsproductASTMs(whichareconvertedtoTBPsusingcorrelation)onlyatsomespeciﬁcvolumepercentages.Thislimitsthenum-berofdatapointsavailableforuseintheobjectivefunction.Inanycasethisnumbershouldbegreaterthanthenumberofmanipulatedvariables.Forthepre-sentworkatwenty-onepointschemeisemployed.Forspecialcutnaphtha(SCN),keroseneandlightgasoil(LGO),ﬁvepoints(10–90%,byvolume,atanintervalof20vol.%)aretakenforeach.InthelaboratoryusuallyASTMsofstabilizednaphthaaremeasuredwhereasthesimulatorpredictsthesamefortheunsta-bilizednaphthaorthetopdistillate.Sincethelighterfractionofthetopdistillateisdrawnasthestabilizeroverheadproduct(liqueﬁedpetroleumgas,LPG),10and30%(byvolume)temperaturesofthesameareexcludedfromtheobjectivefunction.Generallytheheavygasoil(HGO)ASTMsaremeasuredupto50vol.%andhence,onlythreepointsareincludedforHGO.Longresidue(LR)isexcludedsinceitsASTMtemperaturesareseldommeasuredinthelab.

AtanyiterationusingcalculatedTBPtemperatures(manipulatedvariables)completefeedTBPcurveisformedbyﬁttingacubicsplineequationbetweeneverytwoconsecutiveTBPtemperatures.OnceanewfeedTBPcurveiscalculateditisdiscretizedintotwenty-ﬁvepseudo-componentsandbasedonthosepseudo-com-ponentstheCDUsimulatormodelisexecuted.ThemodelpredictedproductTBPsareagainusedtocalcu-latetheobjectivefunction.Iftheobjectivefunctionvalueisbelowtheterminationcriterion(providedbytheuser)andnovariableboundsarehitthentheoptimiza-tionprogramsuccessfullyterminates.

3.ProductASTMtemperaturecalculation

Theoperatingconditionsofthecrudedistillationunit(CDU)andthereconciledcrudeTBPcurve(asdetailedabove)areusedtopredicttheproductASTMtempera-tures.Thepresentmethodstartswithvaluesofsixoperatingtemperaturesinthemaincolumn.Thesetem-

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peraturesare(a)distillatedrawtray(or,toptray)tem-perature,(b)ﬂashzonetemperatureand(c)side-streamcolumndrawtemperatures(fourinnumberastherearefourside-strippers).Allthesetemperaturescorrespondtothehydrocarbonproductpartialpressuresinthecol-umnatappropriatelocations.Thetopdistillateiswith-drawninthevaporphasewhereasalltheside-streamproductsarewithdrawnintheliquidphase.Therefore,thetopplatetemperatureactuallydenotestheequili-briumﬂashvaporization(EFV)dewpointofthedis-tillateatthecorrespondinghydrocarbonpartialpressure.Similarlyalltheside-streamcolumndrawtemperaturesaswellastheﬂashzonetemperaturedenotetheEFVbubblepointsoftheun-strippedpro-ductsatthecorrespondinghydrocarbonpartialpres-sures.However,theEFVandtheTBPcurvesareavailableonlyatatmosphericpressure;hencethesetemperatureshavetobecorrectedforthepressuredif-ference.Thepartialpressureofthehydrocarbonvaporsiscalculatedfromthetotalpressureontheplateandthemolarﬂowrateofhydrocarbons.

Thepartialpressureofthehydrocarbonvaporsintheoverhead,ptop,isgivenbyWatkins[6]as:ptop¼Ptop½ðFrefþFdlÞ=ðFoþSTÞ󰀉

ð2Þ

whereFrefandFoarethemolarﬂowratesofthetopplatereﬂuxandtheoverheadvaporleavingthetopofthecolumnrespectively.STisthemolarﬂowrateofthetotalsteaminputtothecolumn.Itcomprisesofthesteaminputtothebottomofthemaincolumnaswellastothebottomofalltheside-strippers.Ptopisthetotalpressureatthetopofthecolumn.

Thepartialpressureofthehydrocarbonproductvaporsattheﬂashzone,pfz,isgivenby:pfz¼Pfz½ðFLþFdlÞ=ðFLþFdlþFdvþSRÞ󰀉

ð3Þ

whereFListhemolarﬂowrateofthetotalliquidside-stripperproductsalongwiththeoverﬂashwhichareinvaporphaseintheﬂashzone.Fdvisthemolarﬂowrateofthevapordistillateproduct.SRisthemolarﬂowrateofthesteaminputtothebottomofthemaincolumn.Pfzisthetotalpressureattheﬂashzone.

Thepartialpressureofthehydrocarbonvaporsabovetheithtray(fromwhichkthside-stripperstreamiswithdrawn)pss;k¼Pss;kÂpÀss,k,isgivenLr;ðiÀ1ÞÁ=Àby:

Lr;ðiÀ1ÞþVss;iÀFss;ðkÀ1ÞÁÃ

ð4ÞwhereLr,(i-1)isthehydrocarbonliquidreﬂuxﬂowtotheith(kthside-streamcolumndraw)trayi.e.liquidﬂowfromthetrayabovethedrawtray.Vss,iisthemolarﬂowrateofhydrocarbonvaporandsteamleavingtheithtray(side-streamdrawtray).Forexample,ifSCN,SK/ATF,LGOandHGOarefourside-stripperproductsdrawn(inthisorder,fromthetop)fromacolumnthenwhen2nd(i.e.k=2,SK/ATF)side-stripperiscon-sidered,SKdrawplateistheithplateandLr,(i-1)isthe

liquidreﬂuxfromtheplatejustabovetheSKdrawplate.Fss,(k-1)denotestheSCNﬂowrate,theproductdrawnfromthe1stside-stripper.Diﬀerentﬂows,con-sideredforpartialpressurecalculation,areshowninFig.2.Inthepresentmethodequimolaroverﬂowisassumedforliquidreﬂuxcalculationandnointernalvaporizationorcondensationisconsidered.Asimplemassbalanceequationisemployedtocalculatetheliquidreﬂux.Theliquidreﬂuxdependsonthetopplatereﬂuxﬂowrate,theside-stripperproductsdrawrates,thepump-aroundreﬂuxﬂowratesandonthedrawandthereturnpositionsofthepump-aroundreﬂuxes.

Theﬂowrateofthepreviousside-stripperproduct(Fss,(k-1))isnotincludedinthetotalhydrocarbonvaporsleavingthedrawtray.Thereasonbehindthisisthatproductvapor,Fss,(kÀ1),isnearitscriticaltem-peratureasitleavesthedrawtrayunderconsiderationandhence,itisassumedtohavenoeﬀectonthepartialpressure[6].Buttheproductvaporswhicharetobewithdrawnfromtheside-stripperabovethepreviousone,i.e.Fss,(kÀ2),arewellabovetheircriticaltempera-tureswhentheyareatthisdrawplatetemperature.Thesevapors,alongwiththesteam,behaveasnon-condensablesandlowertheboilingpointoftheproductinaccordancewiththeDalton’slawofpartialpressures.Tocalculatethehydrocarbonpartialpressureattheﬁrstside-stripperdrawtray,thetopdistillatemustbesub-tractedfromthetotalhydrocarbonvaporsleavingthedrawtray.ThetraytemperaturesmeasuredintheplantarecorrectedtoatmosphericpressureusingClasiusClayperonequation.dðlnPÞ=dð1=TÞ¼K

ð5Þ

whereKisaconstantforthehydrocarbonstreamunderconsideration.ThevaporpressureofthehydrocarbonstreamataparticulartemperatureiscalculatedusingananalyticalmodeldevelopedbyLeeandKesler[7].

Thepressure-correctedEFVtemperaturesarethenconvertedtoTBPtemperaturesusingthecorrelationdevelopedbyRiaziandDaubert[8].ThesixTBPtem-peraturescorrespondtodistillateﬁnalboilingpoint(FBP),SCNinitialboilingpoint(IBP),keroseneIBP,LGOIBP,HGOIBPandﬂashzonetemperature.Thesetemperatures,whensuperimposedonthefeedTBPcurveattheirrespectivecumulativevolumepercentdis-tilled,formthecutpointsofthediﬀerentproducts.FeedTBPtemperaturesatcumulativevolumepercentofdiﬀerentproductsareobtainedfromthecrudeTBPcurve.Thesetemperaturesaretermedas‘Midtempera-tures’(seeMinFig.3).ItisassumedthatatthecutpointsthefeedTBPtemperaturesequallydividetheTBPoverlaps.i.e.thediﬀerencebetweentheheavierproduct’sIBPandthemidtemperature(atthecumula-tivevolumepercentdistilledofthelighterproduct)isequaltothediﬀerencebetweenthemidtemperatureandthelighterproduct’sFBP.Forexample,thediﬀerence

T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–7767

Fig.2.Sectionofdistillationcolumn(alongwithaside-stripper)indicatingdiﬀerentﬂows.

betweenLGOIBPandthemidtemperaturecalculatedatthecumulativevolumepercentkerosenedistilledisequaltothediﬀerencebetweenthatsamemidtempera-tureandkeroseneFBP.

Usingtheabovemethodﬁnalboilingpointsofallthesidestripperproductsarecalculated.Thesetempera-turesarereferredtoasconvertedproductIBPorFBPinEq.(6)(CorC0inFig.3).TocalculatetheFBPofHGO,thediﬀerencebetweentheﬂashzonetemperatureandthemidtemperaturecalculatedatthecumulativevolumepercentofHGOisused.Around2%(byvolume)ofcrudeisusuallycollectedasliqueﬁedpetroleumgas(LPG)fromthetopofthestabilizer.Sincethelaboratorygenerallyreportsthepropertiesofthestabilizednaphtha,thefeedTBPtem-peratureat2%(byvolume)distilledistakenastheIBPofthisproduct.ThususingthefeedTBPcurveandthesixTBPtemperaturescalculatedfromtheoperatingconditions,sixotherTBPtemperaturesareobtained.Knowingboth,theIBPandtheFBPofaproduct,astraightlineapproximationismadetorepresenttheproductTBPcurve.But,sincetheproductTBPsaswell

Fig.3.Agraphicaldescriptionofthepresentmethod.

68T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–77

astheproductASTMshavean‘S’shapedcurve,thestraightlinejoiningofIBPandFBPgivesapoorapproximationoftheintermediatevolumepercentpro-ductTBPs.ThesetwopointsareshiftedverticallybytakingaparticularratiobetweentheproductTBP(i.e.IBPorFBP)andthecorrespondingmidtemperature.Tobeprecise,IBPsareshiftedupwardswhereasFBPsareshifteddownwards(bothtowardsthecrudeTBPcurve).ThisisperformedtoprovideabetterlinearapproximationoftheproductTBPs.ExperimentallymeasuredproductASTMtemperaturesareusedtodeterminethisratio(shiftingconstant).Astraightlineisﬁttedintheleastsquaredsensethrough10–90%(byvolume)ASTMtemperaturesafterconvertingthesetocorrespondingTBPtemperatures.Thisstraightlineisthenextrapolatedtocover0–100vol.%range.TheseextrapolatedIBPorFBPrepresenttheterminaltem-peraturesoftheproductTBPcurveifitwereastraightline(EE0inFig.3).Theshiftingconstant‘x’iscalcu-latedasfollows:

x¼ðExtrapolatedproductIBPorFBP-MidtemperatureÞðConvertedproductIBPorFBP-MidtemperatureÞ¼EMCMð6ÞTheseshiftingconstantsarecalculatedforalltheproductIBPsandFBPsandareusedtoestimateline-arizedproductTBPsfromoperatingdata.Thesecon-stantsareupdatedasandwhenlaboratorymeasuredproductASTMsareavailable.Fromthelinearrelation10,30,50,70and90%(byvolume)productTBPtem-peraturesareextractedandsubsequentlyconvertedintocorrespondingproductASTMtemperaturesusingDaubert’s[9]correlation.

4.Propertypredictionpackage

Themainaimofthepresentstudyistodevelopamethodologyformakingon-lineestimationofthepro-ductpropertiesrepetitivelyandatshorttimeintervalsoftheorderofaboutoneminute.ThisinformationcanbeusedinfeedbacklooptocontroltheoperationoftheCDUforbetterproductqualitycontrol.Themoreinstantaneousthepropertyprediction,thequickerandmoreeﬀectiveisthecontrolsystem.

Inthissection,wepresentcorrelationswhichareusedtoestimatesiximportantpropertiesofthepetroleumpro-ductsnamelyspeciﬁcgravity,ReidVaporPressure,FlashPoint,PourPoint,FreezePointandRecoveryat366󰀆C.4.1.Speciﬁcgravity

Onecommonlyusedmethodofproductspeciﬁcgravityestimationismodel-based.Knowingthepro-ductcompositionintermsofthepseudo-components,alinearmixingruleisusedtocalculateproductspeciﬁcgravityas:

ðSGÞX

k¼

xjkðSGÞj

j¼1;2;::::::::;mð7Þ

where(SG)kisthespeciﬁcgravityofthekthproduct,misthetotalnumberofpseudo-componentsandxjkisthemolefractionofthejthpseudo-componentinthekthproduct.(SG)jisthespeciﬁcgravityofthejthpseudo-component.

Thepresentmethoddeterminesspeciﬁcgravityofthekthproductusingamodiﬁcationofanempiricalcorre-lationreportedbyRiaziandDaubert[8].Theseauthorsexpressedspeciﬁcgravityasafunctionof10and50%(byvolume)distilledtemperatures.Itwasobservedthatthepredictionsofproductspeciﬁcgravitiesusingtheabovecorrelationweresatisfactoryforsomecrudesbutdeviatedsigniﬁcantlyfromthemeasuredvaluesforsomeothers.Thecrudespeciﬁcgravitywas,therefore,includedinthecorrelationasfollows:

ðSGÞk¼0:08571ðTTBP10%Þ0k:1255ðTTBP50%Þ0k

:20862

ðSGcrudeÞsð8Þ

where‘s’isaproductspeciﬁcconstantandboththeTBPtemperaturesarein󰀆R.Inthepresentstudythevalueof‘s’wascalculatedusingregressiontechniquewhichinvolveddataforsevendiﬀerenttypesofcrudes.4.2.Reidvaporpressure(RVP)

Reidvaporpressure(RVP)denotesthevapor-lockingtendencyofavolatilematerialandisdeﬁnedasthepressureamaterialdevelopswithinaclosedcontainerat37.8󰀆C(100󰀆F).Thispropertyisespeciallyimportantforlightpetroleumproducts,namelytopdistillateandSCN.Inthepresentstudy,asimplemethodproposedbyDutt[10]wasusedtoestimateRVPwhichisgivenby:logP¼6:8736À

967:27þ2:TB

Tþð244:53À0:2977TBÞ

ð9Þ

whereTBisthenormalboilingpoint(NBP)ofthepro-ductin󰀆C.InthepresentstudyTBP50%(byvolume)temperatureisusedasNBP.Eq.(9)atT=37.8󰀆Cpre-dictstheRVPoftheproductinmmHg.4.3.Flashpoint

FlashPointisthetemperatureatwhichthevaporcol-lectedoverapetroleumfractionwillmomentarilyﬂashorigniteinthepresenceofaﬂame.Itindicatestherelativeamountoflowboilingmaterialpresentintheoil.

Nelson[11]ﬁrstproposedthefollowingcorrelationfordistilledfractions:TF¼0:tÀ100

ð10Þ

whereTFistheFlashPointandtisthe0–10%boilingrangein󰀆F.

T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–7769

Butleretal.[12]proposedarelationshipbetweenFlashPointandnormalboilingpoint,TB,ofaproductwhichwaslatermodiﬁedbyLenoir[13]toincludevapor-liquiddistributioncoeﬃcientas:ÆxjMjKj¼1:03;

j¼1;2::::::::::::;m

ð11Þ

wherexjisthemolefraction,MjisthemolecularweightandKjisthevaporliquid-distributioncoeﬃcientofthejthcomponent.SinceKjisafunctionoftemperature,thetemperatureatwhichEq.(11)issatisﬁedistheFlashPointoftheproduct.

RiaziandDaubert[14]reportedacorrelationwhichrelatesFlashPointwith10%(byvolume)ASTMtem-peratureofthepetroleumproductsasfollows:1T¼À0:014568þ2:84947þ1:903FTASTM10%

Â10À3lnTASTM

10%

ð12Þ

wherebothTFandASTM10%temperaturearein󰀆R.ThiscorrelationpredictsFlashPointforSCNquitesatisfactorilybutfailsforheavierproductssuchasker-osene,LGOorHGO.FortheheavierproductsanothercorrelationproposedbyRiaziandDaubert[14]wasmodiﬁedandconstantswereregressedafreshtoyield:1

T¼0:076204F

4:17015

TÀ0:01043lnðTASTM10%

ASTM10%Þ

ð13Þ

þ0:000257lnðSGÞ

whereFlashPointand10%ASTMtemperaturebothareinK.Thisregressedcorrelationisusedintheprop-ertypackagetopredictFlashPointsoftheaboveproducts.4.4.PourPoint

PourPointisameasureoftherelativeamountofwaxinoil.ThetestdoesnotprovidetheactualamountofwaxpresentbutitindicatesthatwaxymaterialswhichmeltabovethePourPointtemperature,areabsentintheoil.RiaziandDaubertcorrelationforPourPointÀ[14]T0PÁdevelopedanempiricalwhichwasmodiﬁedbyChakrabarti[15]asfollows:

T0SGÞ

P¼7:3243ðSGÞ11:2982ðMWÞðÀ0:8587þ1:1670

T3:3549À3:1975ð14Þ

ASTM90%

TASTM

0:1046

10%

wherethepredictedPourPointaswellasinputASTMtemperaturesareinK.MWrepresentstheaveragemolecularweightoftheproduct.Theconstantswereevaluatedbyregressingtheexperimentaldata.

Gangulyetal.[16]reportedtheinclusionofinitial

andﬁnalcumulativevolumecutoftheproductintheirArtiﬁcialNeuralNetwork(ANN)-basedPourPointpredictionmethod.Thisinclusionaccountsfortheeﬀectofwaxdistributioninthecrude.Inthepresentstudyinsteadoftwocumulativevolumesonlyonevolumecut,mid-volumefractionoftheproduct,isused.KeepingtheformandallregressionconstantsofEq.(14)unchangedthenewparameterisintroducedasfollows;

TP¼ÀaþðVmid-volumefractionÞHÁ

T0P

ð15ÞwhereT0PisthePourPointcalculatedusingEq.(14).

RegressingEq.(15)separatelyforLGOandHGOusinglabmeasuredpourpointdatawegetthefollowingequations:

TP¼À0:09236þðVmid-volumefractionÞ0:140535ÁT0P;

forLGOð16Þ

TP¼À

0:03931þðVmid-volumefraction

Þ0:1747ÁT0

P;forHGOð17Þ

4.5.FreezePoint

FreezePointisthetemperatureatwhichaliquidgetssolidiﬁed.ItisoneofthemostimportantpropertiesforAviationTurbineFuel(ATF).TheRiazi-Daubertcorrelation[14]forthePourPointwasfoundtopredicttheFreezePointquitesatisfactorilyinthepresentstudy.Theequationisasfollows:

TFP¼234:85ðSGÞ2:970566ðMWÞð0:61235À0:473575

SGÞ

ð󰀁100Þð0:310331À0:32834

SGÞ

ð18Þ

wheretheFreezePointisexpressedin0Rand󰀁100isthe

kinematicviscosityat100󰀆FincS.Theabovecorre-lationisapplicableforproductswithmolecularweightsrangingfrom140to800.

ThekinematicviscosityterminEq.(18)iscalculatedusingamodelproposedbyDutt[17].Itisgivenby:ln󰀁¼À3:0171þ

442:78À1:52TBtþð239:0À0:19TBÞ

ð19Þ

whereTBisthenormalboilingpoint(NBP)andissub-stitutedby50%(byvolume)TBPtemperaturein󰀆C,tisthetemperaturein󰀆Catwhich󰀁isdetermined.4.6.Recoveryat366󰀆C

Recoveryisthevolumepercentofaproductevapo-ratedupto366󰀆CwhenitisdistilledinasimpleASTMdistillationstill.Recoveryisgenerallymeasuredforheavierfractions,namelyHGOandLR.Itrepresents

70T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–77

theamountofvolatilematerialpresentintheheavierfractions.

ThepresentpropertypackageusesanempiricalcorrelationforrecoveryestimationdevelopedbyChak-rabarti[15].Thecorrelationexpressesrecoveryasafunctionofproductspeciﬁcgravity,molecularweight,ASTM10%(byvolume)temperatureandkinematicviscosityat100󰀆F.Thecorrelationis:Recovery¼391:092ðSGÞ18:437ðMWÞð49:386À58:59

SGÞ

ðTASTM

10%Þ

ð47:925SGÀ40:059Þ

ð󰀁ð20Þ

100ÞÀ0:275

Tocalculatekinematicviscosity,useismadeofEq.(19).ASTM10%temperatureinKisused.Eq.(20)givesRecoveryinvolumepercent.

5.Resultsanddiscussion

Themethodologyofpropertypredictionusingrouti-nelymeasuredtemperatures,pressuresandﬂowrates;asdiscussedearlier,wastestedoﬀ-lineusingon-lineoper-atingdatafromtwodiﬀerentunitsforsevendiﬀerentcrudes.Forunit1dataforsixdiﬀerentcrudetypesweretestedandasinglecrudetypedatawastestedforunit2.ThepredictedproductASTMsusingthepresentmeth-odologyarepresentedalongwiththelaboratorymea-suredvaluesforcomparison.Acomparisonbetweenthemodelpredictedandlabreportedpetroleumproductpropertiesisalsopresented.5.1.Propertiesprediction

Proposedspeciﬁcgravitycorrelation[Eq.(8)]isline-arlyregressedforallthepetroleumproductsusingdif-ferenttypesofcrudes.Theproductspeciﬁcregressionconstant‘s’isreportedinTable1.Fig.4showsaparityplotbetweenpredictedandexperimentallymeasuredspeciﬁcgravities.Asseeninthisﬁgurethedataarescatteredaroundthe45󰀆line.Table2showsthatinclu-sionofcrudespeciﬁcgravityinEq.(8)hasledtoaﬁvefolddecreaseinaverageabsolutedeviationbetweenthepredictedandthemeasuredvalue,

AparityplotbetweenthepredictedvaluesoftheFlashPointsusingEq.(13)andtheexperimentaldataisshowninFig.5.AlthoughEq.(13)predictedtheFlash

Table1

RegressionconstantsforspeciﬁcgravitycorrelationProductsDistillate0.332983SCN0.171457Kerosene0.097985LGO0.047446HGO

0.120141

Pointsreasonablyaccuratelyandbetterthanotheravailablecorrelations(asshowninTable2),onlyafewexperimentaldatawereavailableforregression,parti-cularlyforHGO,whichmakesthiscorrelationlessreli-ablefortheheavierproduct.

ThoughtheproposedcorrelationforthePourPointsworksbetterthanotherreportedcorrelations(seeTable2)forthelimitedamountofdataavailableforregression,thereisaneedtogeneralizethecorrelationwithmorelaboratorydata.5.2.Casestudies

Thealgorithmisstudiedwithseveraldatasetsinvol-vingsevendiﬀerenttypesofcrudesforwhichplantoperatingdataaswellaslaboratorymeasuredproper-tieswereavailable.ThesecrudesarefromKuwait,Dubai,IranMix,ZeitBay,QuaIboe,MumbaiHighandPersianGulf.Amongtheseseventypesofcrudestheﬁrstsixweretestedwiththeoperatingdataavailablefromunit1andtheseventhwastestedforoperatingdatafromunit2.TheresultsforonlyKuwaitandPersianGulfcrudesarepresentedhere.

Thedatasetsareclassiﬁedintotwocategories.Oneis‘trainingset’andtheotheris‘testset’.TheTrainingsetsarethoseforwhichthedetailedproductpropertiesandtheproductASTMtemperatureproﬁles,measuredinthelaboratory,wereusedtodevelopthismethodology.ThesesetswereemployedtoreconcilethecrudeTBPaswellastogeneratetheproductIBPandFBPshiftingconstants.Foraparticulartypeofcrude,thereconciledcrudeTBPandtheshiftingconstants,generatedfromthetrainingsets,wereusedtopredicttheproductprop-ertiesforthetestsets.

Figs.6and7showthereconciledcrudeTBPcurvesalongwiththeinitiallyavailablecurvesforKuwaitandPersianGulfcrudesrespectively.Tables3and4showthatevenminorchangesinthecrudeTBP(asshowninFigs.6and7)leadtosigniﬁcantlyimprovedproductTBPprediction.ThenusingthereconciledfeedTBP,measuredproductASTMsandplantoperatingcondi-tions,theshiftingconstantsweregenerated.Usingtheseshiftingconstants,theproductASTMswerecalculatedwhichwereusedintheestimationofproductproperties.FortestsetsusingalreadyavailablereconciledfeedTBPandtheshiftingconstantsfromtrainingsets,pro-ductASTMswerecalculatedforgivenoperatingdata.Thentheproductpropertieswerepredictedusingprop-ertypredictionpackage.OperatingdataforKuwaitcrude,processedinunit1,aregiveninTable5whereasTable6containssimilarinformationforPersianGulfcrudeprocessedinunit2.Datasets1and4aretrainingsetsandtherestaretestsets.

Tables7–10showthecomputationresults.Thepre-dictedproductASTMtemperaturesforKuwaitandPersianGulfcrudesareshowninTables7and9

T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–7771

Fig.4.Comparisonofpredictedspeciﬁcgravitywiththeexperimentaldata.

Table2

EvaluatingproductpropertiespredictioncorrelationsProperties

Range

No.ofdatapointsusedCorrelations

Speciﬁcgravity

FlashPoint

PourPoint

À12.0–39.0󰀆C

Absolutedeviation(󰀆C)Average

Maximum

0.6826–0.2833.0–134.0󰀆C

6296

AbsolutedeviationAbsolutedeviation(󰀆C)Average

Maximum0.0373

0.0435––

Average1.575–9.155–

Maximum7.9–35.7–

Present

Riazi-Daubert[8]Riazi-Daubert[14]Chakrabarti[15]0.00320.0169––2.2068.8––

8.5224.114.8827.6

󰀆󰀆Absolutedeviation¼󰀆Predictedproperty-experimentalproperty󰀆.Averagedeviation¼ðSabsolutedeviationÞ=ðno:ofdatapointsÞ.

Fig.5.ComparisonofpredictedFlashPointswiththeexperimentaldata.

72T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–77

Fig.6.ReconciledandinitialfeedTBPsforKuwaitcrude.

Fig.7.ReconciledandinitialfeedTBPsforPersianGulfcrude.

respectively.ThelaboratorymeasuredproductASTMtemperatures,whereveravailable,arealsoincludedinthetablesforcomparison.ThecomputedproductpropertiesarecomparedwiththelaboratorymeasuredvaluesinTables8and10.Forboththecrudes,whilemostofthelaboratorymeasuredvaluesofpropertiesareavailablefortrainingsets,onlylimiteddataarereportedfortestsets.

Fortrainingsets,theproductASTMtemperaturematchwiththelaboratoryreporteddataisgoodwhichistobeexpectedinviewofthecrudeTBPcurvesbeingreconciledusinglaboratorymeasuredproductASTMtemperatures.InmostofthecasestheaveragedeviationbetweentheexperimentalandthepredicteddataisÆ1󰀆C.ButafewlargerdeviationsareencounteredforHGOASTMtemperatures.Thereasonbehindthismightbethatinmostofthecasesarelativelysmallamountofproduct(below10%,byvolume,oftotalfeed)isdrawnasHGO.Moreover,thepartofthecrudeTBPthatcorrespondstoHGOisquitesteepandasaresult,themiddleportionofthe‘S’shapedHGOASTMcurve(whichisassumedtobelinear)isofrela-tivelysmallwidth.ForthisreasonourapproximationoflinearizationoftheproductTBPcurvemayfailforHGOresultinginerroneousestimationofintermediateTBP(orASTM)temperatures.AschemewithmultiplestraightlinesinsteadofasinglestraightlinemayimprovethetemperatureproﬁlepredictionforHGO.Forthetestsets,theaveragedeviationbetweentheexperimentalandthepredictedASTMtemperaturesisintherangeofÆ5󰀆C.Higheraveragedeviationfortestsetscomparedtotrainingsetsmaybeexpectedsinceanymeasurementerrorsinthetrainingsetarelikelytoleadtohigherdeviationsinpredictions.AÆ5󰀆CdeviationcanberegardedassatisfactoryassomeexperimentalerrorsarepresentinthemeasurementofproductASTMtemperaturesforthetestsetstoo.

Thecrudecharacteristicsmaychangewithtimebecauseofcontaminationwithothercrudesinlargestoragetanksorforavarietyofotherreasons.Afre-

T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–7773

Table3

ProductTBPtemperaturesbeforeandafterfeedTBPreconciliationandtheircomparisonwiththemeasuredvaluesforKuwaitcrude(dataset1)Objectivefunctionparameters

ProductASTM(measured)(󰀆C)

ProductTBPa(measured)(K)

CalculatedproductTBP(K)BeforereconciliationofcrudeTBP

SCN10vol.%SCN30vol.%SCN50vol.%SCN70vol.%SCN90vol.%Kero10vol.%Kero30vol.%Kero50vol.%Kero70vol.%Kero90vol.%LGO10vol.%LGO30vol.%LGO50vol.%LGO70vol.%LGO90vol.%HGO10vol.%HGO30vol.%HGO50vol.%

Valueoftheobjectivefunction

aAfterreconciliationofcrudeTBP

119.00124.00127.00131.00136.00165.00175.00187.00203.00228.00236.002.00281.00297.00322.00310.00346.00365.00

373.48375.96382.26390.20388.97392.81400.68396.61400.28408.29404.25408.91417.40417.73418.30421.47411.92415.99442.58436.03438.87461.457.55459.62482.81480.23481.39512.39509.59508.97496.44497.21497.00534.57531.66531.38558.06555.46554.18580.48578.82577.18609.610.53608.83575.58576.20572.06619.92624.82619.814.25653.957.09

346.102205.72

PlantmeasuredproductASTMsareconvertedtoproductTBPsusingRiazi–Daubertcorrelation[8].

Table4

ProductTBPtemperaturesbeforeandafterfeedTBPreconciliationandtheircomparisonwiththemeasuredvaluesforPersianGulfcrude(dataset4)

Objectivefunctionparameters

ProductASTM(measured)(󰀆C)

ProductTBPa(measured)(K)

CalculatedproductTBP(K)BeforereconciliationofcrudeTBP

SCN10vol.%SCN30vol.%SCN50vol.%SCN70vol.%SCN90vol.%Kero10vol.%Kero30vol.%Kero50vol.%Kero70vol.%Kero90vol.%LGO10vol.%LGO30vol.%LGO50vol.%LGO70vol.%LGO90vol.%HGO10vol.%HGO30vol.%HGO50vol.%

Valueoftheobjectivefunction

aAfterreconciliationofcrudeTBP384.88402.28409.20417.34430.68420.12442.74462.41474.744.58484.02518.48552.05578.78624.20570.35616.467.97423.43

126.50132.50137.00141.50148.00165.00175.00184.50195.50215.00222.00253.00272.50294.00324.00315.50346.50362.00387.44402.41411.40419.21430.03422.75444.35460.70476.95501.75475.13523.70552.78580.93615.27574.36622.367.19

379.62396.305.73415.09430.13419.58440.31455.09470.31492.290.16522.14547.54574.78613.42556.56595.76619.782411.63

PlantmeasuredproductASTMsareconvertedtoproductTBPsusingDaubertcorrelation[9].

quentcrudeTBPreconciliationandtheshiftingcon-stantsgenerationcanhelpinimprovingthepredictionofproductASTMs.Thequestionthatarisesishowoftendoweneedtoundertakethisretrainingexercise?Thereisnodeﬁniteanswerbutthealgorithmhasbeentested(usingthereconciledTBPandtheshiftingcon-stantsascalculatedusingthetrainingset)withthedatacollectedoveraperiodofseveraldays.Forexample,thegapbetweenobservationtimeofset1(trainingset)andset2(testset)wasover15days.Similarlythegap

74T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–77

Table5

Operatingconditionsfordatasets1–3(Kuwaitcrude)Inputs

Feedﬂowrate(MT/day)Reﬂuxﬂowrate(MT/day)TOPPAﬂowrate(MT/day)KeroPAﬂowrate(MT/day)LGOPAﬂowrate(MT/day)HGOPAﬂowrate(MT/day)

Un-stabilizednaphthaﬂowrate(MT/day)SCNﬂowrate(MT/day)Keroﬂowrate(MT/day)LGOﬂowrate(MT/day)HGOﬂowrate(MT/day)Bottomsteam(MT/day)SCNSSsteam(MT/day)KeroSSsteam(MT/day)LGOSSsteam(MT/day)HGOSSsteam(MT/day)

Heateroutlettemperature(󰀆C)Flashzonetemperature(󰀆C)Reﬂuxtemperature(󰀆C)Steamtemperature(󰀆C)Topplatetemperature(󰀆C)SCNdrawtemperature(󰀆C)Kerodrawtemperature(󰀆C)LGOdrawtemperature(󰀆C)HGOdrawtemperature(󰀆C)

Columntoppressure(kg/cm2,gage)Flashzonepressure(kg/cm2,gage)

Set1(Training)9030.00865.001446.004725.001200.003800.001200.00206.001300.001285.00767.0052.007.0058.000.000.00374.00369.3036.70330.00106.00153.70195.80269.10337.902.482.70

Set2(Test)7976.901017.00984.004500.00901.003465.001005.00279.871225.00986.007.0050.006.0060.000.000.00375.60369.8043.70330.00106.00143.50197.80269.70337.602.232.78

Set3(Test)7869.501005.001001.004400.00925.003408.001105.00214.791201.001013.00701.0045.005.0060.000.000.00373.20366.5040.90330.00104.20146.70192.20265.20334.302.262.78

Table6

Operatingconditionsfordatasets4–6(PersianGulfcrude)Inputs

Feedﬂowrate(m3/h)Reﬂuxﬂowrate(m3/h)HNPAﬂowrate(m3/h)KeroPAﬂowrate(m3/h)LGOPAﬂowrate(m3/h)

Un-stabilizednaphthaﬂowrate(m3/h)HNﬂowrate(m3/h)Keroﬂowrate(m3/h)LGOﬂowrate(m3/h)HGOﬂowrate(m3/h)Bottomsteam(MT/h)HNSSsteam(MT/h)KeroSSsteam(MT/h)LGOSSsteam(MT/h)HGOSSsteam(MT/h)

Heateroutlettemperature(󰀆C)Reﬂuxtemperature(󰀆C)Topplatetemperature(󰀆C)SCNdrawtemperature(󰀆C)Kerodrawtemperature(󰀆C)LGOdrawtemperature(󰀆C)HGOdrawtemperature(󰀆C)

Columntoppressure(kg/cm2,gage)Flashzonepressure(kg/cm2,gage)

Set4(Training)1080.20242.70499.70424.30400.70199.2055.00128.00229.8032.406.501.102.000.550.60369.3043.40143.80154.40186.70270.90341.402.502.80

Set5(Test)1109.30246.10449.50424.40399.90203.5054.80135.00234.9041.606.501.102.240.550.61368.0043.60144.20154.40196.90272.90342.702.502.80

Set6(Test)1119.40253.40451.20424.90400.40199.1055.00134.80235.0035.006.501.102.100.550.61367.8042.00144.40153.40196.10272.00339.802.502.80

T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–77

Table7

ComparisonofmodelpredictedproductASTMswithmeasuredvaluesfordatasets1–3(Kuwaitcrude)

Set1(training)

ProductSRN/UN

Vol.%10305070901030507090103050709010305070901030507090

Lab63.072.085.098.0114.0119.0124.0127.0131.0136.0165.0175.0187.0203.0228.0236.02.0281.0297.0322.0310.0346.0365.0N.R.N.R.

Model62.97284.398.7113.5119.5122.2126.4131.4136.11.3175.11.5206.2223.7241.4256.8276.6299.3323.8314.1338.8369403.3441.6

Set2(test)LabN.R.N.R.N.R.N.R.N.R.114.0N.R.123.0N.R.132.0N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.

Model61.870.381.995.4109.3116.1119.5124.7130.8136.7165.4177.8194.1212.8232.6240.3255.4274.8297.1321316.3342.6374.10.9451.6

Set3(test)LabN.R.N.R.N.R.N.R.N.R.116.0N.R.120.0N.R.133.0N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.N.R.

Model.274.187.5102.9119.0122.3125.4130.2135.9141.4167.1180.0197.0216.5237.2241.4258.5280.3305.3332.4314.5344.3379.9420.2465.9

SCN/HN

ATF/SK

LGO

HGO

N.R.:Notreported.

Table8

Comparisonofmodelpredictedproductpropertieswithmeasuredvaluesfordatasets1–3(Kuwaitcrude)

Set1(training)

PropertiesSRN/UN

SpeciﬁcgravityRVP(psi)SCN/HN

SpeciﬁcgravityFlashPoint(󰀆C)ATF/SK

SpeciﬁcgravityFlashPoint(󰀆C)FreezePoint(󰀆C)LGO

SpeciﬁcgravityFlashPoint(󰀆C)PourPoint(󰀆C)HGO

SpeciﬁcgravityFlashPoint(󰀆C)PourPoint(󰀆C)%RecoveryN.R.:Notreported.

Lab

0.69046.50.7433N.R.0.782742.5À56.00.832763.0<00.88>10518.054.0

Model0.69936.5

Set2(test)LabN.R.N.R.

Model

Set3(test)Lab

Model0.70085.8

0.6982N.R.7.1N.R.0.74830.73859.2N.R.0.792940.8À54.10.844166.6À8.6

0.783141.5À54.0N.R.N.R.N.R.

0.75020.737711.9N.R.0.791240.7À55.10.844967.1À8.4

0.78540.5À53.5N.R.N.R.N.R.

0.752214.20.794341.2À53.40.84667.1À4.90.8834115.519.851.0

0.88020.8767115.3N.R.14.915.054.8N.R.0.88230.8753

117.1N.R.16.515.053.0N.R.

76T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–77

Table9

ComparisonofmodelpredictedproductASTMswithmeasuredvaluesfordatasets4–6(PersianGulfcrude)

Set4(training)

ProductSRN/UN

Vol.%10305070901030507090103050709010305070901030507090

Lab53.559.567.578.599.0126.5132.5137.0141.5148.0165.0175.0184.5195.5215.0222.0253.0272.5294.0324.0315.5346.5362.0374.0388.0

Model

Set5(test)Lab

Model

Set6(test)Lab

Model52.058.968.579.791.1122.1125.3130.2136.0141.5161.8170.0181.2194.2207.6224.9243.0265.7291.8320.1319.2331.6347.9366.6386.5

SCN/HN

FAT/SK

LGO

HGO

52.954.0

60.260.570.469.582.381.594.4104.5126.4125.0130.0133.0135.4138.0141.8143.5148.0148.0165.2165.5173.6176.0185.1185.0198.4196.5212.2217.0227.3224.0246.0255.5269.4275.0296.3296.5325.6328.0323.9317.5336.9350.0353.9369.5373.5376.0394.3391.052.754.5

60.060.570.168.081.879.093.8102.0125.1128.0128.4133.5133.4138.0139.4142.0145.1148.5165.2167.0173.6176.5185.1185.5198.4197.0212.2217.0228.0221.0246.4251.0269.7269.5296.2290.5325.3321.0325.5317.5339.6348.0357.93.5378.9376.5401.4392.5

Table10

Comparisonofmodelpredictedproductpropertieswithmeasuredvaluesfordatasets4–6(PersianGulfcrude)

Set4(training)

PropertiesSRN/UN

SpeciﬁcgravityRVP(KPa)SCN/HN

SpeciﬁcgravityFlashPoint(󰀆C)ATF/SK

SpeciﬁcgravityFlashPoint(󰀆C)FreezePoint(󰀆C)LGO

SpeciﬁcgravityFlashPoint(󰀆C)PourPoint(󰀆C)HGO

SpeciﬁcgravityFlashPoint(󰀆C)PourPoint(󰀆C)%RecoveryN.R.:Notreported.

Lab0.6859.00.7576N.R.0.791340.0À61.00.840560.0À6.00.8785114.0N.R.56.5

Model0.691960.50.755617.40.7900.9À60.3

Set5(test)Lab0.685465.70.757N.R.

Model

Set6(test)Lab

Model

0.69170.68340.67161.258.25.90.754616.4

0.7559N.R.0.7539.5À59.00.83N.R.<À18.0

0.752614.00.788440.3À61.40.837559.3À7.90.8761120.06.967.4

0.79120.790639.540.9À58.0À60.3

0.8395

60.7À6.0

0.83920.841360.462.0À5.9À6.00.8788124.08.865.7

0.8795121.0N.R.52.5

0.88020.8873125.4122.010.218.0.552.0

betweenset4(trainingset)andset6(testset)wasabout

3days.Thepredictioncapabilityofthealgorithmwastestedforatimeintervaloftwoweeksbutonlywithalimitednumberofdatasets.ItisdesirablethatthecrudeTBPshouldbereconciledandthenewshiftingcon-stantsbegeneratedasfrequentlyaspossible.

SuccessofthepropertypredictionpackagelargelydependsonthesuccessofproductASTMsprediction

T.Chatterjee,D.N.Saraf/JournalofProcessControl14(2004)61–7777

sinceallthepropertiesarecorrelatedwiththeproductASTMtemperatures.Theproductspeciﬁcgravitypre-dictionworkswellandcouldpredictuptotwodecimalplacessuccessfullyinmostofthecases.Reidvaporpressure(RVP)predictionmatchessatisfactorilywiththeexperimentaldataformostofthecases.Themar-ginaldeviationmaybeduetoexperimentalerrors.

ThemodelpredictedvaluesoftheFlashPointforkeroseneandLGOwerefoundtobewithinÆ2󰀆Coftheexperimentaldata.ForSCN,theFlashPointtem-peratureswereintherangecommonlyencounteredintheliteraturebutinabsenceofexperimentalvaluesitwasnotpossibletocompare.

ForthePourPoint,thepredictedvaluesdeviatefromthelaboratorydatawhicharereportedattheintervalsof3󰀆Cresultinginhighermeasurementuncertainty.AlsothePourPointequation[Eq.(15)]wasregressedusingonlylimiteddata.ThoughTable2showsthatthepresentPourPointcorrelationworksbetterthanotheravailablecorrelations,thereisscopeforimprovementbyusingthesameequationbutregressingconstantswithalargernumberofexperimentaldata.AsPourPointisameasureofwaxcontent,itmayhelptoincludewaxcontentanditsdistributioninthecrudeasinputs.ThepredictionoftheFreezePointisalwayswithinÆ2󰀆Cofthelaboratorymeasureddatawhichisquitesatisfactory.Itmay,however,bepossibletofur-therimprovetheFreezePointpredictionbyincludingwaxcontentintheproductorameasureofitinthecorrelation.

ThepredictionofRecoveryat366󰀆Cisalwayshigherthanthelaboratoryreportedvalue.Duetounavail-abilityofsuﬃcientreporteddataitwasnotpossibletoregresstheRecoverycorrelation[Eq.(20)]tocoverawiderange.Generationofregressioncoeﬃcientsusingmoredataisexpectedtoimprovetheprediction.

Thoughthemethodologyofpredictingproductprop-ertieshasworkedsatisfactorilyforallthecrudestested,theauthorsfeelthatstillmuchscopeisleftforintro-ductionofnatureofcrudeasaparameterinpredictionofvariousproperties.Asweknowthatthedistributionofsaturatedandunsaturatedhydrocarbonsdiﬀersfromcrudetocrude,usingthatinformationonemayimprovethepredictioncapability,especiallyforFlashPoint,PourPoint,FreezePointand%Recoveryat366󰀆C.Thisisbeinginvestigatedinthislaboratory.

6.Conclusions

AmethodologyhasbeendevelopedtopredictCDUproductpropertieson-lineusingonlyroutinelymea-suredoperatingdataandareconciledcrudeTBPcurve.Usingthepresentmethodthepropertiescanbepre-dictedeveryminutewithareasonablelevelofaccuracy.

Becauseoftherelativelyshortcomputationtime,itmaybepossibletousekeypropertiesforatrulyfeedbackcontroloftheCDUasopposedtothepresentpracticeofcutpointcontrolandthusallowingtightercontrolonproductquality.

Thismethodologycanalsobeusedforsupervisorylevelon-lineoptimizationwhereoneaimstomaximizelong-termproﬁtsubjecttotheproductpropertiesbeinginacceptablelimits.Anotherpotentialofthismetho-dologycanberecognizedbyusingitforpredictionofpropertiesofFCCmainfractionatorunitiftheTBPortheASTMcurveoftheﬂuidizedcatalyticcracking(FCC)reactoroutputisavailable.Insummary,suc-cessfulinstallationofthismethodologyinanexistingreﬁnerycanensurebetterproductqualitycontrolwithhigherproductivity.

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On-line estimation of product properties for crude distillation units