cvd whitson torp

5/23/2018 CVD Whitson Torp

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WEPE 10067Evaluating Constant Volume Depletion Databy Curti s Hays WhHson, Roga/and Dktrlct Co//ege and Stei n BarreTorp, NorwegianInstitute of Technology

@Co py ri gh t 1981, So ci et y o f Pet ro leu m En gl neere o f / IIMEThi s paper was pr esen ted at t he 56th An nual Fal l Tech ni cel Co nf er en ce an d Ex hl bl tl on o f t he So ci et y o f Petr ol eu m En gin eer s of Al ME, h el d i nSan An to ni o, Texas, Oct ober 5-7,1981. Th e mat er ial Is s ub jec t t o co rr ect ion by t he au tho r. Per miesl on t o co py i s r est ri ct ed t o en ab st ract o fn ot mo re t han 300 w ords . Wr it e 6200 N. Cen tral Ex pres sw ay , Dal las , Tex ae 75206.

ABSTRACT Few engineersare awareof potentially-usefulataThis paperpresentsreeultaof analyzingconstant which can be derivedfromCVD data, someof themostvolumedepletiondata obtainedfrom experimental importantbeing&q& composition(andtherefromanalysesof gas condensatesand volatileoils. K-values),density,molecularmass (andspecificallyTheoreticaland practicaldevelopmentsare supported C7+ molecularmass); WUpOit density(usingtwo indep-by analysesof experimentaldata from twoNorth Sea endentmethods);and &L72&4g4@n molecularmass.condensatereservoirs. No assumptionscirempiricalreIationsare used tocalculatethesedata - only experimentalCVD dataThe threemajorcontributionsof thiswork are: and simllleaterialbalanceequations.(1) presentationof materialbalanceequationsused A procedureoutliningthesecalculationswas firstto calculatefluid (particularlyliquid)properties presentedby Reudelhuberand Hinds? Theirdescrip-frommeasuredconetantvolumedepletiondata, tion,however,is somewhatdifficultto followand(2) a simplemethodfor calculatingblackoil not extensivelyknown or usedby the industry. Weformationvolumefactorsand solutiongas-oilratios thereforedecidedto presentthematerialbalancesfor volatilesystemsusingmaterialbalanceresults in equation-formusing currentSPE nomenclature.

and a separatorflashprogram,and (3) investigationof the Peng-Robinsonequationof stateas a tool for Using thematerialbalance-derivedproperties,matchingmeasuredPVT data and studyingvapor-liquid a methodis proposedfor calculatingblackoilequilibriaphenomenaduringconstantvolumedepletion. PVT properties- i.e.,formationvolumefactorsandsolutiongas-oilratiosused in two-phaseflowThe main examplepresentedis a rich ga~ equationsand reservoirmaterialbalances. Thecondensatewhosemeasured,calculatedand simulated methodis not new in principle,as itwas firstphasebehaviorare fullydocumentedin tablesand suggestedby Dodson,Goodwilland Mayer2in 1953 forfigures. Completedescriptionof the heptanes-plus solutiongas/crudeoil systems. Theirmethod,fractionis also includedao that otherengineerscan however,requiresexpensiveand time-consumingliquidcheck,modifyand hopefullyimprovefluidcharacter- sampleremovalsand experimentalflashseparations.izationusing the Peng-Robinson(or.any other) The proposedmethod followsthe sameprocedurebutequationof state. uses experimentally-determinedaporcompositionsand materialbalance-derivedliquidcompositionstogetherwith a routinemulti-stageseparatorflaeh

INTRODUCTION program(usinglow pressureK-valuesindependentofsystemcomposition).PVT propertiescalc~latedusingConstantvolumedepletion(CVD)experimentsare thismethodare comparedwith thosecalculatedusingperformedon gas condensateand volatileoil fluids the Peng-Robinson3equationof state.to simulatereservoirdepletionperformanceand comp-

ositionalvariation. Resultingdata can be used in Thoughmore complicated,empiricalequationsofa varietyof reservoirengineeringcalculation, statecan alsobe used to evaluateCVD data. Severalamongthemost usefulbeingmaterialbalancecalcula- investigators1shave used the Peng-RobinsonEOS totiOnsjgeneratingblackoilPVT propertiesand more simulatePVT studiesof lightgas condensatesandrecex,tly,he tuningof empiricalequationeof state.All of theseapplicationsare addreasedin the crudeoils,needleesto say avoidingsystemsoperat-ing near the criticalpoint. Resultshave rangedpresentwork. fromexcellentto poor,dependingon whichpropertieswere compared. Conradand Gravier16proposedamethod to improveliquiddensityestimationsbyadjuetingpropertiesof theheaviestplus fractionReferencesand illustrationsat end of paper (boilingpointand Cl interactioncoefficient).


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Firoozabadi,Hekimand Ketzs studiedanotherlean Mercuryis reinfectedinto the cellat constantgas condensateand foundthatby only adjuatingthe pressurewhile simultaneouslyithdrawingan equiv-methane-plusfractioninteractioncoefficient,the alentvolumeof vapor. When initialcellvolumeisPeng-RobinsonEOS overestimatedliquiddrop-outby reached,mercuryinjectionis ceased. Withdrawnnearly100%. [As discussedlaterin thiswork, vapor is analyzedusinggas chromatographyto deter-materialbalancecalculationsof CVD data for this mine composition,j. Moles of vaporproducedaresystemindicatethatmeasuredliquidvolumesare calculatedusing the real gas lawand are reportedasapproximately100% low - i.e.calculatedliquid a cumulativepercentof initialmoles,np. Compres-densitiesweremuch too high.] sibilityfactor,Z, is also calculatedby notingproducedvapor surfacevolumeand equivilantcellOver 30 constantvolumedepletionstudies volume (at pressureand temperature).Frommeasuredparformedby commercialand privatelaboratories vapor gravityand composition,heptanes-pluswere analyzedusing the materialbalanceapproach. wlecular mass is back-calculated.LiquidvolumeThreeof these(NorthSea fluids)were chosento is measuredvisuallyand reportedas a percentorbe analyzedusing thePeng-Robinsonequationof state. fractionof cellvolume,which in essenceis a typeTheir choicewas basedon (1) internalconsistency of hydrocarbonliquidsaturation,SL.of measuredCVD data,as indicatedby materialbalancecalculations,and (2) availabilityof The experimentalprocedureis repeatedseveralextendedcompositionaldata for the heptanes-plus times(6-7)untila low pressureis reached,sayfraction. All threefluidshave similarparaffin- 700 psig (4828kPa). The remainingliquidis removednephthene-aromsticontent,with Watsonkcharacter- separated(i.e.distilled)and analyzedusinggasizationfactorsrangingfrom 11.95to 12.05for the chromatography.MeasuredliquidcompositionshouldC7+ fraction. checkwith materialbalance-derivedcomposition.[Somemuj okkboti t i t i noo-t hand adj wt meauzed

The firstfluid (NS-1)is a rich gas condensate vapo~ compo. 6 on4 W &[email protected] Wanw chech.and was chosento illustrateproposedtechniquesfor lti pmoceduu. d tieouzagedingenti. I$h goodanalyzingconstantvolumedepletiondata. Extensive pz at i c et o Lnquhewht i t i a. t abomtom f i epot idata for thissampleand itsheptanes-plusfraction mtxw, tkedok ~moo.thd data, and to toha.t xtenthave been includedin tabularform so that other mat- bathtce-dtived da.t atwe tied .& @wJ CWQengineerscan duplicate,mdify and hopefullyimprove kepoti . 1our analyses.The secondfluid (NS-2)is a leangas condensate MATERIALBALANCEEQUATIONSsimilarto thesystemsanalyzedin References5 and 16.Our discussionof NS-2 is limitedto behavioror LiquidCompositionand K-valueCalculationsobservationswhichdifferfrom thosepresentedforthe rich gas condensate. The lastfluid (NS-3)is a Perhapsthe most usefulapplicationof constantvolatileoil operatingnear itscriticalpoint. We volumedepletiondata is for calculatingliquidhad not completedour analysisof NS-3 using the compositionswhich, togetherwith measuredvaporPeng-RobinsonEOS when thispaperwas written; compositions,yield high pressureK-valueshaving

convergenceproblemswere encounteredwhen tryingto many importantreservoirand processengineeringsimulatetheCVD process. NS-3 is thereforeonly applications.To arriveat the finalexpressionformentionedwith regardto materialbalancecalculations liquidcompositionin termsof measuredCVD data,weand K-valuebehavior. More informationon any or all firststate molal a~:dcomponentmaterialbalances,of thesefluidscan be obtainedfrom the authors respectively,

DESCRIPTIONOF THE CONSTANTVOLUNEDEPLETIONPROCESS & = Lb+ vk . . . . . . . . . . . . . . * . . . . (1)A constantvolumedepletionexperimentisconductedat reservoirtemperatureand beginsat & jk = Liz.jk+ vkgjk . ..*..***.*.. (2)saturation pressure. Cell volume,Vcell,or thevolumecontainedby the fluid,is initiallynotedand used as a referencevolume. whera nL = moles of liquidwith compositionjMercuryis thenwithdrawnfrom thebottomof the ~ = molesof vaporwith compositionyjand nt =totalmoles in thesystemwith compositionz, eachcell, therebyloweringthe pressureas fluid expands. quantitybeingdeterminedat pressurestagei.During thisprocess,a secondphasedevelops- Subscriptj designatescomponentnumbersmakingupeitherretrogradeliquid(forgas condensates)or eachphase.solutiongas (forvolatileoils). Mercurywithdrawlis ceasedwhen a predeterminedpressureis reached. Eq. 1 statesthat totalmoles of the two phaseSome laboratoriesmeasureliquidvolumesduringthe systemequalsthe sum of liquidand vapormoles,whilfirstpressurereduction,beforeany vapor has been Eq. 2 statesthat totalmoles of componentj in theremoved;thesevolumes,reportedrelativeto Vcell, two phase systemequalsmoles of j in the liquidplusrepresentconstantcompositiondepletion. They molesof j in the vapor. The only datameasuredcloselyapproximate,however,volumeswhich would directlyand appearingin eitherof the equationsishave been meesuredif the processhad been constant

volumedepletion. [Thiswas checkedusing thePeng- vapor composition.The remainingunknownscan bedeterminedfromreportedCVD dataandmodifiedformsRobinsonEOS simulatorfor leanand richcondensates. of thematerialbalancerelations.* RogalandDistrictCollege,Ullandhaug,4000Stavanger,Norway


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cmn 7 nnc7 t . H. WWTTSC)N AND S. B. TORP 3Jrla Avuufl - . . . . --------- ---- -- - ---?irstwe note thattotalmolesat stagek equals All unknownsinEq. 1 have now been definedininitialmolesminus cumulativemolesof vapor termsof measuredCVD data exceptliquidcomposition,?roduced. We assumea basis of one mole initial whichwhenwrittenin termsof the othervariables,Eluid,thatis n&l = 1, yielding becomes

k % jk - nvh.g.k(3)%k= 1 i:2&pi * ** ** ** *

(9)jk = (n~- nvk)

o . . . . .* . . . .

rhe samematerialbalancecan be appliedon acomponentbasis, resultingin Equilibriumconstantsor K-valuesare definedas thek ratiobf equilibriumvaporto liquidcomposition,or

%kzjk=zjl - ~~ttipkgjk b-4) jk = yjkf~jk . . , . . , . . .. . . . ., (10). = the incrementalmolesof vaporproducedwhereAnplfromthe cellduringstage i, and zjl = the initial An effectivemeansof correlatingand checkingthefluidcompositionat stage? (saturatedconditions). consistencyof calculatedK-values(i.e. liquidcompositions)is to plotlog Kp vs the componentMoles of vapor remainingin the cellcan be characterizationfactorF$ as suggestedby Hoffman,calculatedusinga volumetricbalanceand the real Crumpand Hocott It has been our experiencethatgas law (pV=nZRT).Recallingthe basisof one mole sucha plot,when exhibitinglineartrendsapproach-

initialfluid,cellvolumecan be calculatedfrom ing a commonconvergencepoint,indicateshighinitialfluidproperties,which for gas condensatesis qualityvapor compositiondata,and to a lesserZd*R.T extent,goodnessof liquidvolumemeasurements.A more completediscussionof thismethodis present-Vcau . . . ...0.... . . . . . . . . . . . ,...0.Pd ( Sa ) ed in a latersection,

and for volatileoils (existingas a liquidat bubble PhysicalPropertyCalculationspointpressure), Constantvolumedepletiondatn can alsobe usedVca M@b

to calculatephysicalpropertiesof equilibriumvapol...... . * .+ .....*. . (5b ] and liquid. A mass balanceis employedto carryoutthe necessarycalculations,where R = 8.3143J/mol-Kfor preferredS1 units,and IR = 10.732 sia-ft3/mol-oRfor field units. [T(K),f Xkp(kpa), V(m ) andT(R),p(psia),V(ft3),respective-

mLk+muk ** * * ** * 17]lyl *

At eachdepletionpressure,liquidvolumeis wheremt = totalmass of the system,w = liquidmas:and ~ = vapormass at stagek. Anotherway ofmeasuredvisuallyand reportedas a fractionof the statingthe mass balanceis that totalmass at stagecellvolume,SLk. ActualliquidV01UK02vLk Can then k equalsinitialmassminuscumulativevapormassbe calculatedfrom producedfrom the cell. Recallingthebasisof onemole initialfluid,and therebyequatinginitialmaswith initial(saturation)nmlecular~ss~ Ms> givesLk Lk vcUf3 . . . .* . . , ,* , . . . . (6) k

a% = h - & np.i i . . . * .* , . . (72)and froma volumebalance,vaporvolumeVvk isw~i~~e~~i is thevaporphasemolecularmass atVvk= (~ S~k)VC~ . .... . .** * * (7) stageI. BothMs and Mv can be easilycalculatedusingKays pseudocriticalmixingruleand approprialcomponentmolecularmasses.Using the real gas law, the correspondingmolesofvapornvk are calculatedfrom Vapor mass can now be calculatedby notingthatmass equalsmolecularmass timesmoles,or

PkVk (81vk ~ *******...*.*****.********* = vk*vk (131vk . . . . . * . . * $, . $. . . . . . . . wherepressurepk correspondsto vaporcompressibilityfactorZk. * F = b(l/Tb- l/T)where b=[lOg(pc/pa)]/(l/Tb-l/Tcand: Tb = boilingpointat atmosphericpressurePasfMb and pb are buble pointmolecularmass and Tc and PC are criticaltemperatureand pressure,density,respectively.Zd and pd are dew point respectively,and T is the systemtemperature.compressibilitynd pressure,respectively.


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4 EVALUATINGCONSTAWTVOLUMEDEPLETIONDATA SPE 10067

Liquidmass is calculatedas the differencebetween BLACKOL PVT PROPERTIEStotalmass and vapormass, Dodson,ti.d~ suggestedan experimentalprocadurefor determiningso-calledblackoil PVTlb = %2 - vk , . . . . . . . . . . .* . . + (14) propertiesused in two-phaseflowequationsandsolution-gasdrivematerialbalancerelations.Currentlaboratoryproceduresfor estimatingoil

Havingcalculatedmassesand volumesof equilibrium formationvolumefactorB. and solutiongas-oilraticliquidand vapor,respective densitiescan be Rso onlyapproximatethe Dodson,@d. method-calculateddirectlyfrom the ratioof m to V, i.e. withoutflashingthe liquidphaseat each stageofp = m/V (wherevolumescome fromEqs. 6 and 7). thedifferentialvaporizationprocess, For mediumto lowvolatilecrudesthisprocedureappearsvalidAn independentcheckof vapordensitycan be for most engineeringcalculations.The vaporused to checkthe consistencyof measuredZ factors. solutiongas-oilratioRsg is alsoassumedequal toThe relationis deriveddirectlyfrom the real gas infinity- i.e.liquidcondensationis neglected.law and can be statedas Highlyvolatileoils and gas condensatefluids

VkP~ cannot,however,be analyzedor describedby the samevk ~ .,**...........0.0....*..**.(15) differentialprocess, The basicproblemposedbythesemore volatilefluidsis thatduring two phaseflow thereexistboth two phasesand two components.That is, flowingoil containssolutiongas which,We can also calculatemolecularmass of the when undergoingpressurereduction,evolvesand mixefequilibriumliquid,and specificallyits heptanes- with the existingvapor phase. Likewise,flowinggas

plus fraction. Rewritingthe mass balanceas containsretrogradeliquidwhich also evolvesandmixeswith the existingliquidwhen pressuredeclinesThis complexthermodynamicphenomenonis, for all.tk MLknLk%knvk .0.. ..... * . . (~6) practicalpurposes,impossibleto simulatein thelaboratory.

we can solvefor liquidmolecularmass~k, An alternativemethod is suggestedwhich,bymakingcertainsimplifyingassumptions,approximatesZk - vk-nvk the truemodel describedabove. Basically,Lk = *.**. *.. **., ****...,. (17] individualphase compositionsdeterminedfromCVDLk analysis(measuredor calculated)are flashedthrougla multi-stageseparatorsimulatorrepresentingfield

UsingKsysmixingrule,the heptanes-plusmolecular conditions. Fig. 1 describesthe processdiagrsm-mass can be back-calculatedto yield atically.N-l Beforewe beginour discussionof the proposedMLk - ~~1 j jki method,let us definethe fourbasicPVT propertiesMLkC7+ = .*. *,*,**. (18) used in two-phaseflowand reservoirmaterialbalanceequations:kC?+

. Li . quLdo. tumeof fx. a. tkuwi vo4L contiotiwhereMj are molecularmassesof purecomponents. %0 = ~.todz.tunko.il volumefiuu&&g @om dttih od x

The averageCT+ molecularmass ofthe two phase :systemshouldbe calculatedusing the relation Ao.tdg~ volumektiting @om tie ~ltihod x,Lk*XkC7+~hLkC7+ R=m + vkykC7+MvkCT+( 7+ (?9) 40 htick &nk oi l vo nemw tAg @om & atJt od xLkxkC7+ + vk*ykCT+

vapok vo&me od y, & atiehvoh cotiti8=9 .totig~ vo&unewwWng &om tie ~tih od giXotiga4 vohmemuting d~om tie f@h od y,

hg= ~tiektinko~ volwemwl$ing ~kom i~h od Y.

wherex- are liquidcompositionsdeterminedfrom1sterla balanceequations. Yj are vapor compositionmeasuredexperimentally.


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SPE 10067 C. H. WHITSONAND S. B. TORP 5.First, liquidcompositionx is flashedusinga~asicvapor-liquid APPLICATIONOF THE PENG-ROBINSONEQUATIONOF STATEsetof appropriateK-valuesandequilibriaequations. [GlasOand Whitsonghave MeasuredCVD dataand materialbalance-derived 1 low pressureocumentedthat Standings blackoil propertieswere controlledusinga fluidpropertiesK-valuesare quiteaccuratefor flashcalculationsof packagebasedon thePeng-Robinsonequationof stateblackoils. We have sincefound thattheyare also and developedby RogalandResearchInstitute. Aaccuratefor flashcalculationsof mediumto highly completedescriptionof the computerprogramscan be

volatilegas condensates- i.e.systemswith gas-oil obtainedfrom the authors. The PVT packagenot onlyratioslessthan about50 000 SCF/STB(9000Sm3/Sm3).] includesgeneralvapor-liquidequilibriumoptions,The sum of surfacegas volumesdividedby stock but it also includestwooptionsfor characterizingtankoil volumeis definedas the liquidgas-oil the heptan>s-plusfraction- me~hodspresentedbyratioRso. Whitson or Robinsonand Peng.Oil formationvolumefactorB. is calculated The numericalsolutiontechniqueused includesfrom the relation a pre-iterativesucessivesubstitutionsmethod

btigti followedby Newtonsmethodusinganalyticalz.m . + m~To derivatives. Convergenceproblemswere encounteredg4 for the NS-1 fluidat temperaturesapproachingtheB* = L * . * * * , , (20) criticalpoint- i.e.below reservoirtemperature.vSTOL Severalalternativenumericalmethodswere tried(Powellsmethodand a newly-developedacceleratedwhereVSTO is stock tankoil volume(e.g.1 STB)and sucessivesubstitutionmethod) withoutsuccesswheremg and mSTO are massesof totalsurfacegases Similarproblemswere notedwith the volatileoiland stocktankoil, respectively.Liquiddensity,PL, system (NS-3)which,fromall indications,liesverycan be determinedfrom eithermaterialbalance near the criticalpoint at reservoirtemperature.calculations(~ from Eq. 14 and VL fromEq. 6), or The lean gas condensate(NS-2)was solvedproblem-fromone of severalcompositionaldensitycorrelations freeovera wide rangeof temperatures.available6Jusingmaterialbalance-derivedliquidcompositions.We cautionthe use of PL calculated Pure componentproperties(criticalpressure,frommaterialbalanceequationssinceonlya slight criticaltemperature,acentricfactorand molecularerrorin retrogradeliquidvolumecan resultin a mass) were used for non-hydrocarbonsnd hydrocarbonsubstantialerrorin liquiddensity- and therefore frommethane to n-pentane, Only n-hexanewasBo. The same errorwill.notaffectliquidcomposition consideredfor theCG fraction. Heptanesandto the samedegree. heavierpropertieswere estimatedusing the procedureand equationssuggestedby Whitson~lwith severalAt the samedepletionsta~ek, vapor phasewith modificationsgivenin AppendixB.compositionj is separatedthroughthe flashsimulatorusing identicalK-values. The resulting To manipulatethe retrogradeliquidvolumecurvesurfacegas volumesdividedby stocktankoil volume theWatsoncharacterizationactorof theheaviestdefinesthe vapor solutiongas-oilratioRs .%

componentwas adjusted,makingsure thatadjustedGas formationvolumefactor,on the otherhan , can propertieswere physicallyrealistic,be accuratelyestimatedfrom the CVD compressibilityfactorZ using the real gas law, Binaryinteractioncoefficientswere set equalto zeroexcept*3: Nz- Nz = -0.02,COZ - hydrocarbonspbe*Z*T s70 p =0.15, N2 - hydrocarbons= 0.12,and Cl - ~n,B9 =*(1- .*. *,**.. *,..** (21) nPTAe n@d = 6~7*...*whichware esti~ted using a llnearfit of the Katz and Firoozabadi13ata (theirTable 2)where nSTO= 33301eS of stocktankoil resultingfromthe flashof nfeedmoles of reservoirvapor. ~cl - cn = o*14*yn - 0.0668 .***,.....***. [22]

The me.jorassumptionimplicitin the proposedmethod,assumingmeasuredCVD data are good:is that Theinteractioncoefficientbetweenmethaneand theliquidand vaporcompositionsare solelydependent heaviestcomponentwas thenadjusteduntila matchon pressure. That is, the composition-pressure of themeasureddew pointpressurewas obtained.relationis uniqueand not alteredby physicalflow.Examplesof PVT propertiesfor the richgas FluidDescription:Rich Gas CondensateNS-1condensate(NS-1)are presentedin Figs.2-5.Herewe have comparedpropertiescalculatedusing NS-1 is a richgas condensatefirst testedat amaterialbalanceresultswith thosecalculatedusingPeng-RobinsonEOS simulateddata. Identicallow gas-oilratio of 5500 SCF/STB(980Sm3/Sm3)fromanpressureK-valueswere used forboth sets of data. initialreservoirpressureof 7300psia (50340kPa)and temperatureof 280 oF (138oC). Stock tankoilVaporsolutiongas-oilratio is nearlythe gravitywas 44 oAPI (0,8055gin/cc).Separatorsamplfwere takenwhile flowingthewell at 16.3MMSCF/Dsame for bothmethodsof calculation.Liquid (460*103Sm3)and a flowingbottomltoleressureofsolutiongas-oilratioand oil formationvolumefactorare both low formaterialbalance-derived 7260 psia (50070kPa).properties. The differenceis clearlya resultofthe lowerliquiddensitiesestimatedby thePeng-Robinsonequation.


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6 EVALUATINGCONSTANTVOLUMEDEPLETIONDATA SPE 10067Heptanes-PlusCharacterization MCN specificgravitiesand Eq. 22, as was the C1-CGcoefficient. Using thesedata in thePeng-RobinsonExtendedcompositionaldataof theC7+ fraction EOS yieldeda dew pointpressuremuch lowerthanwas not availablefor theNS-1 fluid,onlymolecular measured. The C1-CZS+interactioncoefficientwasmass and specificgravity. Completetrueboiling thenincreaseduntil dew point pressurematched.point (TBP)datawere, however,availablefromanoffsettingwell, NS-lb. Thesedatawere adaptedto The CVD simulatorwas run usingtheMCNthe NS-1 fluidusing the methodpresentedin Ref. 11, properties,as given in Table 3. The overallmatchslightlymodifiedas discussedin AppendixB, was good to excellent,exceptfor liquidvolumeswhich weremuch too high (32%simulatedmximum vsMolal distribution(molefractionvs molecular 22%measuredmaximum). To check if measuredvolumesmess) of the NS-lb fluidwas fit using the ganma were lowwe comparedmaterialbalanceliquiddensitiedistributionparameteralphaand variableupper with Alani-Kennedy7densities(usingmaterialbalanceboundrymolecularmasses. The optimalalphawas 0.712 compositionsand molecularmasses). Table 4 showsfor eta (minimummolecularmass in theC7+ fraction) resultsof the comparison,indicatingthatmeasuredof 92. Table 2 givesresultsof thematch, volumesare consistentexceptfor perhapssmellerrorsin the firsttwo volumemeasurements.Molal distributionof theNS-1C7+ fractionwasthen calculatedusinga = 0.712,q = 92 and l&7+ = Basedon theseresults,it was decidedto lower184 (as comparedto 177 for the NS-lb fluid). We also the Peng-Robinsonliquidvolumesby adjustingthechose to holdupperboundrymolecularmassesconstant characterizationactorof the CZ5+ fraction.(equivalentto paraffinvalues),givingthe rasults By loweringthe factorfrom 12.42 to 11.80 resultedpresentedin Table 3. in a decreaseof the liquidvolumes- 8% for themaximumdrop-out(from32% to 26%). The adjustment

Propertiesof the singlecarbonnumber(SCN) had littleor no effecton other estimateddata.Togroupswere estimeted*~by definingtheKuop factors have loweredthe%Qp factorrmre wouldhave createdfromNS-lb SCN molecularmassesand specificgravities a physicallyunrealisticsystem. Adjustedphysicalusing the relational propertiesfor the CZE.+fractionare found inTable 3, as is the methaneinteractioncoefficientK =4. S579.M0*]5J7g. g4573 ........ (23) used to adjustdew pointpressure. CompleteresultsUop of theCVD simulationare presentedin Table 5.Peng-Robinsonliquiddensitiesare comparedwithAlani-Kennedyestimatesin Table 4.Eq. 23 was then invertedand combinedwith NS-1 SCNmolecularmassesto yield SCN specificgravitiesand Over twentyother adjustmentsof theC7+ char-normalboilingpoints,Tb, for the NS-1 fluid, acterizationprocedurewere attemptedfor improvingliquidvolumepredictions.None of thesewere part-icularlyhelpful,thoughsome are worthmentioning:Y =6.010770K-11$24 017q47 . . . . . . . . . . . (24]Uop (1) extendingthe CT+ split to Cqo+ such that thelastcomponentwas veryheavy, (2) increasingthenumberof MCN groupsused to nine,CZ5+ inclusive,

where Tb = (y*~ )3, per definition. SCN data for (3) splittingtheC7+ fractioninto eightSCN groupsNS-1 calculated;~ingEq. 24 are given in Table 3, and a Cls+ fraction,(4)using TBP %3p factors**togetherwith criticalpropertiesestimatedusing the insteadof thoseestimatedfromEq.Riazi-Daubert15orrelations(exceptfor Tb > 850 oF, (5) usingthe Lee-Kesslerzpropertyco~r~~tions.~**when modifiedcorrelationswere usedll).

TuningthePeng-RobinsonEquationof State ** ActuallyKuoE is definedas T~13 /Y and could,therefore,have een calculateddirectlyusing normalSinglecarbonnumbergroupswere combinedinto boilingpointsdeterminedfromTBP analysis. Usingfivemultiplecarbonnumber(MCN)groups- CVC9, Kuop estimatedfrom Eq. 23 and measuredmolecularC10-C13,C14-C17,C18-C24and C2S+- as suggestedin massesand specificgravities,estimatednormalRef. 11. Group propertieswere calculatedusing boilingpointswere calculatedfrom Tb = (y*Kuo)3Kayspseudocriticalmixingrule,exceptfor specific and are presentedin Table 2. fome of theseva uesgravitieswhich used a volume-weightedixingrule. were higher thanupperboilingpointboundriesdefineMethane interactioncoefficientswere estimatedusing for the specificSCN group. mo possibleexplanatioare provided:(1)due to distillationundervacuum itwas not possibleto duplicateexactboilir.goint* The TBP analysiswas performedaccordingto the boundriesas definedin Ref. 14, or (2)measuredprocedureoutlinedinRef. 14 and discussedbyKatz, uolecularmassesof theheavierfractionswere inti.d.~s The laboratoryonly reported,however, error. It was found,however,thatusingestimatedsinglecarbonnumbermolecularmasses,mole fractions op factorsfromEq, 23- when used for criticaland specificgravities. Cumulativevolumepercents propertyestimationsin thePeng-RobinsonEOS - gavewere thencalculatedby notingthatincremental bettermatchof measuredconstantvolumedepletionvolume (permole) = mole fractionx molecularmess + data; the differencewas onlyminor.specificgravity. Littlecurvaturewas exhibitedbythe TBP curve and normalboilingpointswere, there- *** Info~tion on theseor other simulationruns canfore,merelyaveragesof the boilingpointrange for be obtainedfrom the authors. We would alsoapprec-a given SCN group. iate suggestionsas to how one might improvetheliquidvolumeprediction.


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SPE 10067 C. H. WHITSONAND S. B. TORP 7RESULTSANO DISCUSSION Temperatureeffectson the &g Kp vs F plotsofNS-1were investigatedby runningthe Peng-RobinsonMost resultspresentedin this paperare taken EOS airnulatort 340 F (171.1oc], some 60 F higherfrom the threeNorth Sea systemsNS-1,NS-2 and NS-3. thanreservoirtemperature.Fig. 10 presentstheIt has been our experience,however,thatsome results,indicatingthattemperatureinfluenceisfeaturesof CUD analysisare commonto all systems. (1) largestforheavy componentsat largepressures,We have triedto differentiatebetweenobsemations (2)negligibleat low pressures(aswas found inwhich are specificto a givensyetem,and thosewhich Ref. 10), (3)relativelysmallcomparedto theare more generalin nature. We note in particular influenceof pressure,and (4) not significantinthat theK-valuecorrelationdevelopedin AppendixA changingthe apparentconvergencepressureof thewas developedfromour analysisof many fluids, system. Theseobservationsare also illustratedinrangingfromvolatileoils to lightgas condensates, Fig. 11.

Fig. 6 comparesmeasuredor more correctly, For lightereyatemssuchaa NS-2, theredoesnotemoothed)vapor compositionswith thosesimulated alwaysappearsucha uniqueconvergencepointforusingthe Peng-RobinsonEOS. The match is excellent, @ Kp VS F plots. We thoughtthat thisperhapsshowingonly slightdeviationfor the C7+ and C6 resultedfrom a changein the totalcompositionofcomponents. Deviationof the hexanecomponentis the system,or from alterationin theheptanes-plusprobablydue to its incorrectcharacterizations properties. We investigatedthesepossibilitiesbyn-hexane. runninga constantcompositionsimulationof NS-1(at 280 and 340 oF) andNS-2 (at 241 F). ResultingFig. 7 presentsheptanes-plusmolecularmassesof K-valueswere comparedwith CUD K-valuesand areliquidand vaporphasesand the totalsystem.Simulatedand materialbalance-derivedvaluesmatch

presentedas bg Kvs &lg p plots in Figs. 12, 13 and14. All threesystemsclearlyindicatethat compsi-well. Our experiencehas ahownthata goodmatchof tionalchangeduringconstantvolumedepletionis ?zo.4C7+ molecularmaas usingthe Peng-RobinsonEOS is significantenoughto influenceK-valuesor conver-usuallydifficult,and very dependenton proper gencepressure,if in fact thereexistsa truecharacterizationf the plus fraction. convergenceof K-valuesto unity. As seen in Fig. 14the lean gas condensate(NS-2)doesnot appeartoCalculatedequilibriumconstantswere correlated havea convergencepressurefor componentsheavierusingthe Hoffman,[email protected]. Threemain reasons thanhexane.are givenfor thischoice:(1) the@ Kp vs T plotprovidesa simplemeansof definingthe approximatepressure-and temperature-dependencef K-values, CONCLUSIONS(2) materialbalance-derivedK-valuescanbe evaluatedfor consistencyby checkingthat~Og Kp vs F plotsare 1. Measuredconstantvolumedepletiondata for twolinearand converge,more or less to a singlepoint gas condensatesand a volatileoil were analyzedusinand (3)an approximateestimateof con~ergence simplematerialbalancesand the Peng-Robinsonpressurecan be determinedby extrapolatingthe slope(of~og Kp vs F plots)vs pressurecurve to zero, equationof state(EOS).which can in turnbe used to improveinitialK-value 2. A simplemethod is proposedfor calculatingestimatesfor the Peng-Robinson(orany other) tblackoilpw properties(formationvolume factorsequationof state.SeeAppendixA. and solutiongaa-oilratios)of gas condensatesandvolatileoils.Fig. 8 presentsNS-1 K-valuescalculatedusingmaterialbalancerelations. The hg Kp vs F plots 3. Materialbalance-derived-valuescan be correlateare linearand appearto approacha commn point. to yieldan estimateof the apparentconvergenceAs discussedin AppendixA, the convergencepointcan pressurewhich,when used in a newly-developed-valtgivean estimateof the apparentconvergencepressure. correlation,helps calculatehigh pressureK-valuesActually,the most accuratevalueis obtainedby used as initialeatimateain equationsof state.extrapolatingthe elopevs pressurecurveto zero,as done in Fig. 11. The resultingestimateof pK 4. Simulatedconstantcompositionand constantvolume8000 psia (55170IcPa). depletionstudiesof lean and rich gas condensatesusingthe Peng-RobinsonEOS indicatethatK-valuesFig. 9 presentsNS-1 K-valuescalculatedfrom are depf 2nde of thedepletionprocess.the Peng-RobinsonEOS. Once againlinearplotsof

tog Kp vs F convergeto a point. From the extrapola- 5. Temperatureeffectson theHoffman,&&c&.8 K-valutionof slopeto zero in Fig. 11,(51720kpa). ~*7500 psia correlatingtechnique(logKp vs F) were studiedExperiencewith the Peng-RobinsonEOS using the Peng-RobinsonEOS.and materialbalanceevaluationof CUD data has shownthatrich gas condensatesand volatileoils exhibit 6. The Peng-Robinsonequationof atateusuallyover-a morewell-definedconvergencepointthanleaner estimatedliquiddrop-outfor gas condensatesduringsystems. constantvolumedepletion. The problemwas normallycorrectedor improvedby reducingtheWatsonAnotherinterestingfeatureshownin Fig. 9 is characterizationactorof theheaviestcomponent.thatheavycomponentsare bettercorrelatedusingthelog Kp vs F methodat higherpressurea. This~~suggestthatmethaneinteractioncoefficientsof theplusfractionshavemost influenceon K-valuesatlow pressures.


8/21

NOMENCLATURE K = convergenceA or A(p) = slope of @ Kp vs F plot L = liquidphaseb = elopeof the strai~htline connectingthe n = carbonnumbercriticalpointand atmosphericboiling o = oilpoint on a @ vapor pressurevs l/Tplot,cycle-oR; cycle-K P = producedB = formationvolumefactor,Bbl/STB; m3/Sm3 R = reducedCT+ = heptanes-pluscomponent s = saturated(bubbleor dew point)CVD E constantvolumedepletion Sc = standardconditionexp(x) = ex ; e = 2.71828... STO = stock tankoilEOS = equationof state t = total (twophase]F or F(T) = componentcharacterizationactor,cycle v = vapor phaseK = equilibriumconstant(K-value)K = Wataon characterizationactor GreekLettersUop&t = naturallogarithmto base e a = parameterin gammadistributionlog = logarithmto base 10 @ = parameterin gammadistributionm = UISSS, lbm ; kg r = gamma :EunctionM = moleuclarmass,ibm/lb-mole; kg/kg-mole Y = specificgravityrelativeto air orE = molecularmass of the totalsystem water (60/60)n = (1)moles,ibm-mole; kg-mole A = incremental

(2) exponentin K-valuecorrelation (s = interactioncoefficientNS = North Sea sample n = parameterin ganmadistribution(minimummolecularmass)P = pressure,psia ; kpa P = density,lbm/ft3;kg/m3 (gin/cc)p(x) = probabilitydensityfunctionPr w = acentricfactor= cumulativeprobabilityfunctionR = universalgas constant,10.732psia-ft3/mole-oR; 8.3143J/mole-KR = vaporsolutiongas-oilratio,SCF/STB; ACKNOWLEDGMENTSSg Sm3/Sm3 The authorswish to thankH. Xorvik,H. Asheim,R = liquidsolutiongas-oilratio(same) D. Murphy,V. Dalen and G. Nielsenfor usefulcommentsos = saturation,fractionor percent concerni ng thiepaper. We also acknowledgecomputertimeand facilitiesdonatedby RogalandDistrictT = absolutetemperature,R;K College,NorwegianInstituteof Technology(NTH)and

v =volume, ft3;m3 ContinentalShelfInstitute(IKU). PhillipsPetro-leumNorwayand Statoilshouldbe thankedfor contri-X = liquidcomposition,fractionor percent butingwell-neededfluiddata to the petroleumliter-= vaporcomposition,fractionor percent ature. Economicalsupportfrom fryingpan publica-Y tions,Inc. is,as usual,appreciated.Y or Y(p) = interceptof . bg Kp vs F plot

z = totalsystemcompositionz = vapor compressibilityfactor REFERENCES

1. Reudelhuber,F.O. and Hinds,R.F.:A CompositionSubscripts al MaterialBalanceMethod for PredictionofRecoveryfromVolatileOil DepletionDriveReser-a = atmospheric voirs,TMW.,AIME(1957)2?0,19-26b = bubblepoint(pb)or boiling(Tb) 2. Dodson~C.R., Goodwill,D. and Mayer,E.H.:c = critical Applicationof LaboratoryPVT Data to ReservoirEngineeringProblems;T&zM.,AIMB(1953)198,cell = cell,pertainingto PVT cellvolume 287-298d = dew point 3. Peng,D.-Y. and Robinson,D.B.: A New ho-g = gas ConstantEquationof State,l nd. Eng, Ckm Fund.i = indexfor sumatian (1976)IS,N0.1,59-64j = componentidentifierk = depletionstage


9/21

SPE 10067 C. H. WHITSONAND S. B. TORP 94,

5.

6.

7,

8.

9*

10*

Watson,K.M.,Nelson,E.F. and Murphy,G.B.:Characterizationf PetroleumFractions,Znd.Eng.Chn.(1935)27,1460-1464Firoozabadi,A., Hekim,Y. and Katz,D.L.:ReservoirDepletionCalculationsfor Gas Conden-satesUsingExtendedAnalysesin thePeng-RobinsonEquationof State,Can.J . ChsmEng.(Oct.,1978)56,10-615Standing,M.B. and Katz,D.L.: Vapor-LiquidEquilibriaof NaturalGas-CrudeOil Systems,Th.uti.AIME(1944)55,232Alani,G.H. and Kennedy,H.T.:Volumesof LiquidHydrocarbonsat High Temperaturesand Pressures,Tkuti .,,AIME(1960)219,288-292Hoffman,A.E.,Crump,J.S.and Hocott,C.R.:EquilibriumConstantsfora Gas-CondensateSystem,Tfiati.,AIME(1953)198,1-10Glas@,0. and Whitson,C.H.:TheAccuracy of PVTParametersCalculatedfromComputerFlash Separa-tionat PressuresLess Than 1000 psia,SPE Paper8033 (1979)Standing,M.B.:A Set of EquationsforComputingEquilibriumRatiosof a CrudeOil/NaturalGasSystemat PressuresBelow1,000psia,J.Pti.Tech.(Sept.1979)1193-1195

110

12*

13*

14.

15,

16.

17.

180

19.

Whitson,C.H.:CharacterizingHydrocarbonPlusFractions,EUR Paper183 Presentedat theEUROPEMeetingheld in London,England,Oct. 21-24,1980Risnes,R,, Dalen,V. and Jensen,J.I.:PhaseEquilibriumCalculationsin theNear-CriticalRegion,PaperPresentedat the 1981EuropeanSymposiumon EnhancedOil Recovery,Sept.21-23,1981Katz,D.L. and Firoozabadi,A.: PredictingPhaseBehaviorof Condensate/Crude-OilystemsUsingMethane InteractionCoefficients,T~ti.,AIME(1978)f6~,1649-1655SelectedValuesof Propertiesof HydrocarbonsanRelatedCompounds,API Project44, TexasA&MUniv.,CollegeStation(1969)Riazi,M.R, and Daubert,T.E.:SimplifyPropertyPredictions,[email protected].(March,1980)l15-116Conrad,P.G. and Gravier,J.F.:Peng-RobinsonEquationof StateChecksValidityof PVT Exper-iments,0ti4GaAJ.(April21,1980)77-86Yarborough,L.: Applicationof a GeneralizedEquationof Stateto PetroleumReservoirFluids,from Eqtutt t otiO{ $&W by Chao and RobinsonWilson,G.M.:A ModifiedRedlich-KwongEquationof State,Applicationto GeneralPhysicalDataCalculations,paperpresentedat the 65thNationalAIChEMeeting,Cleveland$1969Brinkman,F.H.and Sickling,J.N.:EquilibriumRatiosfor ReservoirStudies,Tuw.,AIME(1960)219,313-319

20. Standing,M.B.: Vo&una.t&icnd Pt i e 8ehavi o o{O l F.i&d ffyhoumbon Sy&tem, 8th printing,Societyof PetroleumEngineersof AIME,Dallas(1977)21. Robinson,D.B. and Peng,D.-Y.:TheCharacteri-zationof theHeptanesand HeavierFractions,ResearchReport28,GPA Tulsa,Oklahoma(1978)22. Kessler,M.G. andLee, B.I.:ImprovePredictionof Enthalapyof Fractions,[email protected]. (March,1978)153-158

I APPENDIXA IMPROVEDK-VALUEESTIMATIONAT HIGH PRESSURESSolutionof the Peng-Robinson(orany other)cubicequationof staterequiresinitialestimatesof K-values. At higherpressures(> 500 psia)andparticularlynear phaseboundriesor the criticalpoint,theseestimatesare very importantfor deter-miningthecorrectsolItionto the equation.AccurateK-valueestimatescan also reducenumericaldivergencewhen searchingfor the solution.

WilsonDproposedthe followingthermodynamicrelationfor estimatingK-valueswhichshould,inpra~tice,only be used at low pressures,

c { }j =~xp 5*37(~+~j)(~-J/TRj) /pRj ..*** (A- f)where

Rj E T/T cj

pRj = plp~jTb ./Tc .j+~.=? 10g (pcj/pa)J 71- Tb/__fcjd 5. 3 7 =$.W1O)

T and p definethe systemstemperatureand pressure,Tb is the atmosphericboilingpoint at pa, and Tc andpc are criticaltemperatureand pressure,respectivelyActually,Eq. A-1 appearedin the petroleumliteraturesome 10 yearabeforeWilsonproposedhis relation.Hoffman,ti,ti.apreeentedEq. A-1 graphically(theirFig. 4) and suggestedthe followinggeneralization(albeitgraphically),

log KjP = A(~)* Fj(T) + y(p) . . . . . . . . . . . . . . (A-2)

where 1/Tb . - l /TFj(T) E l og (P~j/PU) . . . . . . . (A-3)7Tbj - 1lTcj


10/21

10 EVALUATINGCONSTANTVOLUMEDEPLETIONDATA SPE 10067

A(p) = ~a~ti e- dependeti htope I pK (P4ti]=60*MC7+ - 4200 ............. (A-6)

It is easilyshownthatEqs.A-l&A-2 are identicalforA(p=pa)= 1 and Y(p=pa)=.&?gpa - i.e.atatmosphericpressure.

Engineersfamiliarwith Eq.A-1 are awarethatits accuracyis usuallylimitedto low pressures.An investigationof the pressure-dependentlopeinEq. A-2 showed,however,thatEq. A-1 couldbereformulatedto yieldequally-accurateesultsathigherpressures.The quasi-thermodynamicalodelused to extendEq. A-1 is basedon the suggestionby BrinkmenandSicklinglghat plotsof tog Kp vs F(T) at severalpressuresintersectat a commonpointdefiningtheapparentconvergencepressureof the system. Theirrelation,afterdroppingpressure-and temperature-

dependentnotation,isPK A(Fj - FKK = 10Jp .,.* .,.*...... O. (A-3)

where ~ = convergencepressureand FK = the F-valuecorrespondingto pK at the comnonpointof intersec-tion. Eq. A-3 is es{]ilyderivedby notingthatKj=lat convergencepressurepK. We can also show fromEq. A-1 thatFK = ~og(pK/pa),or in termsof theinterceptin Eq. A-2,

and thatexponentn = 0.6 for all systems.We can now reformulateEq. 1 (theWilson-type

equation)to giveK-valuesat all pressuresandtemperatures,

Pc A-jKi. (d) { }


11/21

SPE 10067 C. H. WHITSONAND S. B. TORP 11(4) In theoriginalmethodpresentedinRef. 11,sin Ie carbonnumbermolecularmassescorrespondingRto z. withmolecularmassboundriesM: and M +l w~sierey thearithmeticaverage. Dale Embry (~hllllpsPetroleumCompany,Bartlesville)noted in apersonalcommunicationthat this approximationwasnot necessaryand that the exactanalyticalexpres-sion is givenby

where ** (%-3) %,+- Qi3= .**** o*@** .*e** *e***..* (B-4)aPk(X x, a ,b, c ) = e - g ; [gU+j / r(u+j+l ) 1 (B- 5)j =og= (x-c)/ b *+**** **** . * . * . ** , * , * , . , , (B- 6)

and, as previouslymentioned,q = 92. ConcerningEq, B-4, @ is the samewhethera or a+l is used inthe cumulative.probabilityunctionPr.


12/21

TABLE 1 - MEASURSDCONSTANTVOLUMSDEPLETXONDATAFOR THE NS-1 FLUID AT 280 %+Coolpos i tions

Equilibrium EquilibriumVauor LiauidPressure - Psia Exp , Calc .

CO~ponent 6764.7 5514.7 4314.7 3114.7 2114,7 1214.7 714.7 714.7 714.7 . .Carbon Dioxide 2.37 2.40 2,45 2.50 2.53 2.57Nitrogen 2,60 0.59 0.5350.31 0.32 0.33Methane 0.34 t3.34 0.34 0.33 0.0273.19 75.56 0.017Ethane

77.89 79.33 79.62 78.90 77.80 12.42 10.7047.80 7.s3 7.87 7.92 8.04 E.ho 8.70 3.36 3.220Propane 3.55 3.47 3.40 3.41 3.53 ~.,4iso-Butane 3,91 2.920.71 0.67 2.S960.65 0.64 0.66 0.72 0.78 0,91normel-Butane 1.45 0.9161.37 1.31 1.30 1.33 1.44 1.56 2.09 2.103iao-PentaOe 0.64 0.59 0.55 0.53 0,54 0.59 0.64 1,40 1.417normel-Pentana 0.68 0.62 0.58 0.56 0.57 0.61 0.66 1,60Hexenea 1.09 1,6240,97 0.S8 0.83 0,82 0.s5 0.90 3.68 3,755Heptanes-plus 8.21 6,20 4,09 2,64 2.02 1.84 2,12 71,01 72, S15 ,. .

Totala 100,00 100.00 100,00 100,00 100.00100.00100.00100,00100,000.%,+ 184,0 160,0 142.0 127,0 119.0 115,0 114.0 213,0 207.9%,+ 0.816 0.799 0.783 0.770 0,762 0.758 0,757 0,833 0,843z 1,238 1,089 0,972 0.913 0,914 0.937 0.960n -%P 0.000 9.024 21,744 3S.674 55.686 72.146 81.301-zL 0.0 14.1 19.7 21.6 21,3 20,2 19.3

TABLE 2 - COMPOSITIONALAND PROPERTIES DATAOF FLUID NS-lB SAYPLEDFROMA WSLL OFFSETTING NS-1 COMFARSDWITH CALCULATEDDATAGENERATEDUSING THE METHODPFU%SENTEDN RSF . 11Measured

SingleCarbon Mole Molal SpecificNumber Percent }Iaea Gravity .0.94 95 0,715s

: 0.s4 104 0.73659 0.74 118 0.775710 0,60 132 0,763911 0.41 14412 0.77230.34 154 0.7s1413 0.31 167 0.793914 0,26 180 0,805315 0.22 197 0.8096

Calculated

K Boiling UpperUop Point Mole Molel MolalFactor (%) Parcant Mass Maes. .

12,05 641.7 0.935 95.111.93 678.3 0.83S 105,411,90 727.3 0.739 11s . 911,99 768.4 0.600 134,212.04 S04 ,0 0.410 148,712.04 832,7 0,340 161,712.03 871,2 00310 175.012.02 907,0 0.260 188,712.13 947.1 0.220 202,112,30 1008,1 0.190 215,412.19 1019.0 0.170 228.912.20 1039.4 0.150 242.812.26 1069,4 0.130 256,812,28 1097.6 0.110 270,612,29 1130.8 0.080 283.012.32 1161,0 0.070 294,112.36 1191.4 0.060 304,812,38 1234,9 0.070 316,712.87 1465.6 0.508 439,112.25 6.190 177,0(12.02)*

99.6111.9126.8142.4155.5168,4182.2195.7209.1222.4236,1250.1264.1277.8289.0299,9310.3324.0.

16 0.1917 0,1718 0.1519 0.1320 0.1121 0.0822 0.0723 0.0624 0,0625+ 0.51

6,19

212 0,8152226 0.8255234 0.8303250 0,8341262 0.8400277 0,8477292 0,8531308 0,8577329 0,8666471 0.8826177 0,8061

* The higher average hop valua was calculated using a weisht-averagemixing rule, wharaas the lower value was estimated using the Whitsoncorrelation.* The gamma distribution (Raf. 11) was usad where an optimal alpha of0,712 wae found for eta (minimum molecular maas in the C7+ fraction)of 92. Upper molecular maaaea wera found by fittins the meaeuredcompositions,


13/21

TABLE 3- PHYSICAL PROPERTIES OF THE C?+ SINCLE ANDlNILTIPLE CARMN NUf4BSR~ .OUPSUSED ~ THE PENG-ROBINSONEQIJAT~N oF STATE ~ DEP,c21BEL6SERV01R FLUID SEHAVIOROF THE NS-1 FLUID

SingleCarbonNumber

;9111121314151617181920212223242s+

7- 910-1314-1718-2425+

Boiling Critical MetheneMole Molel Specific Point Temp. Prese, Acentr ic InteractionParcant Meae Gravity (OR) (OR) (peie) Factor Coefficient ..1,2136 95,3 0,7177 646.8 971.6 457,5 0.27421,1730 106.5 0.7409 690,6 1021.4 423,4 0,30560,8600 120.7 0.7599 739.4 1073,2 383,2 0,34540,6872 134,7 0.76S2 781,4 1112.9 345,9 0,38610.5681 14s.7 0.7781 822.2 1152,1 316,8 0,42510.4783 162.7 0.7908 863.1 1192.3 294,0 0,46220,4074 176.7 0.8034 902.8 1231,2 2:4,9 0.49840.349s 190.7 0.8153 941.2 1268,3 258,4 0,53420,3021 204.7 0,8168 972.6 1294,2 240.4 0,57400.2621 218.7 0.8210 1029.8 1321.5 225.7 0.61270.2282 232,7 0.8310 1039,5 1354.0 214,6 0.64860.1992 246.6 0.8389 1072,0 1383,6 204,3 0.68550s1744 260,6 0,8432 1104.7 1408,7 194.0 0,72460.1529 274.6 0.8486 1131.6 1434.4 185,1 0,76340.1343 288.6 0.8554 1161.9 1461,0 177,4 0.80160.1182 302,6 0,8602 1190.2 1484.9 170,0 0.84160.1041 316.5 0.8639 1217.4 1507,0 162,9 0,88300.0918 330.5 0.8690 1245,1 1530,2 156.8 0.92410.7054 462,3 0,9192 1.488.0 1734,6 91.4 1,0590 S,21OO 184.0 0.8160

MULTIPLE CARBONNUMBERPROPERTIES USED IN THE FINAL CVO SIMULATION3.2466 106.1 0.7385 688,3 1016.5 425.5 0.3044 0 .03659 ***2,1410 152.7 0.7837 835,0 1163.6 313.1 0.4348 0,04292***1.1421 209.2 0.8205 984,4 1304.5 237.4 0.5S56 0.04807***0.9749 281,5 0.8524 1146.9 1446.0 182.7 0,78320,7054 462.3 0.9192 0 .05254 ***1276.1* 1584,2* 168,8* 0.8819* 0.18400**. S,21OO 184.0 0.8160

* Adjusted valuea representing e Kuop factor of 11,80, The original velueecorrespond to a Kuop factor of 12,42 and ere given above (e.g. 1488 .0) ,** Adjuetad valua ueed to match the maaeured daw POint Preeeur@.*** Calculetcd ueing the Katz and Firoozabadi correlation, curve-fit tO yield

= o,14. y - 0.0668. Though not ehown in thie~~~l&l~~i ~t~~~~n~Cl~n interect on coefficient wae also calculated usingthie relat ion,

TABLE 4 - CALCULATEDLIQUID DENSITIES AS A FUNCTIONOF PRSSSURE FOR NS-lCalculated Liquid Deneitiee (gin/cc)

Measured CVD Data Simulated CVDDataAlani-l(ennedy Alani-KennedyMaterial Daneity Peng- DenaityPressure Balanca (M.B. Liquid Robinson (P-R Liquid(pela) Deneity PrOpertiee)* Dcne i ty** Properties)*

5514.7 0.670 60B 0,541 0.5704314.7 0,680 0,649 0.554 0,5963114,7 0.688 0.670 0,580 0.6322114.7 0.700 0,682 0.608 0,6641214.7 0.711 0.700 0,636 0,692714,7 0,722 0,711 0,653 0,707

* The Alani-Kanncdy density cmralat ion requires 1 iquid compoai t ions,total liquid molecular mane, hcptanea-plue molecular mass ttnd specificSravity (ae well as preasurc and tempcraturo), Thase data were availablefrom either material balance calculations or P-R elmulntion reeulte,** Tha Pcng-Robinson s im ul at io n u aad p ro per ti ed giVenn Table 3 with anad ju et cd K UOP il,8 for the C25+ fraction, Using the original KUO factorf 12.42 gava evan lower liquid dcnnitlcs than thaac &ivcn ahovc, w th alarser deviation from tho Alani -Kenady va luca ,


14/21

TABLE 5 - SIMULATEDCONSTANTVOLUMEDEPLETIONDATA FOR THE NS-1 FLUIDAT 280OF USINGTHE PENG-ROBINSONEQUATIONOF STATE Compositions

Equilibrium EquilibriumVapor L


15/21

IDENTICAL MULTI-STAGE SEPARATION

LufA\.Y-

ii3g

z0H1-


16/21

rnsoooo~~ 11111111111111PENG-ROBINSON RESUL TS+fIIATERIAL BALANCE RESULTSUSING MEASURED DATA NS-I280F

LSEPARATOR CONDITIONS*10000 - PRESSURE TEMPERATURE(psia) (F)

1014.7 155264.7 * 5TA NDING L OU PRESSURE14.7 (BLACK OIL K-VALUECORREL ATION USEDO. l I l l

1000 2000 3000 4000 5000 6000 7000PRESSURE, psia

Fig. 3- Vapor solution gas.oil ratio vs pressure for NS.1at 280 F.

G\ IPENG-ROBINSON RESULTS-A-MATERIAL BALANCE RESULTSg ~MATERIAL BALANCE RESULTSUSI NG P-R LI QUI D VOLUMES (SL)~ 1.8 /rn2. 0~, l , , , , , 1 I I I r , , I , 1 t 1 I , , I , I 1 I I t I I t 1

NS-I280F

1.6

,.Qo~AJ 4000 5000 6000 7000PRESSURE, psia

Fig. 4-011 formation volume faotor vs pressure for NS.1at 280 F.


17/21

+-A--a-

PENG-ROBINSON RESULTS -MATERIAL BALANCE RESULTSMATERIAL BALANCE RESULTS

-1 , 1 I I I I I I I I 1 I I I I I I i I I 1 I 1 I 1 I 1 1 tNS-I280 FUSING P-R LIQUID VOLUMES

SEPARATOR CONDI TI ONS*PRESSURE TEMPERATURE(psia) ( F)

( L) p

1014. 7 155 ) A264. 7 8014. 7 60

* STANDING L OW PRESSURE BLACK OIL K-VALUECORRELA TION USECI

J t 1 1 I 1 I 1 , I 1 , t 1 I I 1 I I I , 1 1 I I 1 , I I 1 1 I 11000 2000 3000 4000 5000 6000 7000PRESSURE, psia

Fig.- J1-lqulds ol ut io n g aa..o il ratio vs pressure for NS-I at 280 F,

K 240, 1 I I I I 1 , 1 I i 1 1 I I 1 1 , I I I 1 1 I I , 1 I I , I 1 IwtoW[

+PENG-ROBINSON MATCHe

kaMATERIAL BALANCE RESULTS= USING MEASURED DATALIQUID

~ +MEASURED (+)-i

280 Fl oo~ I , , 1 , t , I1000 2000 3000 4000 5000 6000 7000PRESSURE, psia

Fig. 6-Calculated and measursd vapor compositions vs preesure for NS.1at 280 F.


18/21

102

10

1

I I I I 1 I I I I , I n , 8 I , 1 1 ,c1o 4 PENG-ROBINSON MATCH

o MEASURED (ACTUALLY THE DATA HAVE BEEN SMOOTHED AND ADJUSTED ACCORDINGTO CORE LABORATORIES PROCEDURE)

C2

P=2 oNS-I280 F10- ) 1 1 1 , I t I t t I 1 , 1 I , I I 1 ,0 1000 2000 3000 4000 5000 6000 7000PRESSURE, psia

Fig. 7-Calculated heptanes.plus molecular masses w pressure for NS.1at 280 F.

w XTRPWNSFLPES IF d, APPARENT CONVERGENCEPRESSURE s 7500 psiaCO* II~ ICI-2kZ n lo~ ; 1 1 1 12.0 2.5 3.0 3.5 4.0 4.5:

iC25+ *ADJ USTED C7+F VI AL,UE,S10- 3 1 I- 4 -2 0 2 4 6COMPONENT CHARACTERI ZATI ON FACTOR, F=b(l / Tb - I / T>Fig. 8- NS.1K.vak es at 280 F calculated using the material balance approach.


19/21

I I , T I , , t I , * I , , , JPRESSURE O MATERIAL BALANCE RESULTS I NS-I(psia> USING MEASURED DATA1-5514.7 LEAST SQUARES LINEAR

/:

.2 280*F2-4314. 7 REGRESSI ON 43- 3114. 7 (N2ANDCF+ DATA EXCLUDED)4-2114. 7 . / ~- 5- 1214. 7 A6- 714.7

COMPONENT CHARACTERIZATION FACTOR, F=b(l/Tb - I/T)

105 I I I I I 1.1-In 280 F 1

Fig. 9- NS.1 K.values at 280 F calculated using ths PengRoblnson EOS,

PRESSUREX 7500 psia-

NS-I280 Fd 1 1 I 1 [ I-2 -1 0 1 2 3 4 5

COMPONENT CHARACTERIZATION FACTOR, F=b ( 1/ Tb - I / T)~lg. 10-Temperat ureffect onthe Hoffman, et al. K.value corralatlon for NS.1.


20/21

u)>& 2. 0

1.0

0.0

PENG-ROBI NSON MATCH (280F) - - PENG-ROBI NSON MATCH (340F)o MATERI AL BALANCE RESULTS

1-=j/ I NTERCEPT Y (p)

g~gw>z$:+W~g%$$:

. NS- I COSTANT CO l POSI TI ON NS-I- - - - CONSTANT VOLUME DEPLETI ON 280 FII .?= 10

+z$1zouemH~

10-3 r

10-4 r

u10-5 F C25 ?.

~PRESSUREl .?10-6 (psia) 714.7 I , , , 1 1 ,3X102 103 104

PRESSURE, psiaFig. 12- Peng-Robinson K-values for NS.1 at 280 F representing twodepletlon processee.


21/21

102

10

1

10-

1o-i

10-2

10-

.v I I , t * I , , , , ,- - - - CONSTANT VOLUME DEPLETI ON NS- ICONSTANT COMPOSI TI ON 340F 1

C14-C17

cI&cz4

10-53X102 103 104PRESSURE, psiaFig. 13- PengRoblnson K.values for NS-1 at 340 F representing twodepletion processes.

x lo2k 1 1 , , , t I 1 1 1 t 1 t 1 1 -i< E CONSTANT COMPOSITI ONr 1 NS-2x - - - - CONSTANT VOLUME DEPLETI ON z410F 1

10- 41 , I , 1 1 I3X102 103 104PRESSURE, psiaFig, 14-Peng.Robinson Kwalues for NS.2 at 241 F representing twodepletion processes.

cl,+..--

cvd whitson torp

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