MethodtoCalculatetheSolubilitiesofLightGasesinPetroleumandCoalLiquidFractionsontheBasisofTheirP/N/AComposition
M.R.Riazi*,†andJ.H.Vera
DepartmentofChemicalEngineering,McGillUniversity,3610UniversityStreet,Montreal,Quebec,H3A2B2Canada
Inthispaper,aparaffinic/naphthenic/aromatic(P/N/A)compositionalmodelisproposedforcalculationofthesolubilitiesoflightgasessuchasmethane,ethane,carbondioxide,andhydrogeninvariouspetroleumandcoalliquidfractionsunderdifferentconditionsoftemperatureandpressure.TheproposedmodelusesScatchard-HildebrandtheorywithacorrectedvalueforthesolubilityparameterofthedissolvinggasandcharacterizestheliquidphasebyitsP/N/Acomposition.Theresultsshowthat,forthefractionsstudied,theP/N/Acompositionhasaneffectongassolubility.Themodelcorrelatedthesolubilitiesofgaseswithanaverageerrorof4.5%whenevaluatedwith11fractionsandmorethan180datapointsforapressurerangeof5-250bar.CorrectedsolubilityparametersforhydrocarbongasesarerecommendedfortheirusewithpetroleumfractionsandcoalliquidsofdifferentP/N/Acompositions.Themainadvantageoftheproposedapproachisthatnoexperimentaldataarerequiredtoadjustanybinaryparameter.Theapproachisofdirectusewiththevaluesofthesolubilityparametersreportedinthisworkandcharacterizationparametersofthefraction.
Introduction
Knowledgeofthesolubilitiesofgasesinhydrocarbonmixturesisimportantinpetroleumproductionandprocessing.Gasessuchasmethane,ethane,andcarbondioxideareinjectedintopetroleumreservoirstoincreaseoilmobilityandtoimproveoilproduction,especiallyinreservoirscontainingheavyoils.Itisawell-knownfactthat,whenalighthydrocarbonorCO2isaddedtoaheavyoil,theoil’sviscosityisreducedanditsflowbecomeseasier.Inpetroleumrefining,hydrogenisaddedtoheavypetroleumfractionstoincreasetheirhydrogen-to-carbon(H/C)ratiosandtoupgradetheirqualitythroughprocessessuchashydrocrackingorhydrovisbreaking.1Additionofhydrogentocoalliquidsisusedfordesulfurizationandotherupgradingpro-cesses.Inthedesignandoperationofequipmentrelatedtosuchprocesses,itisimportanttoknowthesolubilityofaddedgasintheliquidoil.Usually,suchcalculationsaremadethroughequationsofstate.Inthistypeofmodeling,specificbinaryinteractionparametersaredeterminedforeachgasandeachfraction.2,3Thereareanumberofdatasets,publishedmainlyinthepast25years,thatincludesolubilitydataformethane,ethane,CO2,andhydrogeninpetroleumfractions,coalliquids,andfractionsfromtarsands.2-4Thesedatasetscanbeusedtoevaluatevariousmodelsortodevelopanewmethodforpredictingthesolubilitiesofgasesinpetro-leumfractions.Themethodofpseudo-componentsforthecalculationofpropertiesofpetroleumfractionsisbasedontheassumptionthatafractionisamixtureofthreepseudo-componentsrepresentativeofthefamiliesofparaffins(P),naphthenes(N),andaromatics(A).Mixturepropertiesarecalculatedthroughtheproperties
*Towhomcorrespondenceshouldbeaddressed.Address:CollegeofEngineering&Petroleum,KuwaitUniversity,P.O.Box1084Surra,45711Kuwait.Tel.:(965)481-7662.Fax:(965)483-9498.E-mail:riazi@kuc01.kuniv.edu.kw.†
OnleavefromKuwaitUniversity.
ofthepseudo-componentsandtheP/N/Acompositionofthemixture.Thismethodhasbeensuccessfullyusedforthecalculationofvariousthermodynamicproper-ties.5-7Ithasbeenshownthat,forsomepropertiesandsomefractions,theP/N/Acompositionmighthaveaneffectontheaccuracyofthecalculatedproperty.ThepurposeofthisstudyistoinvestigatethiseffectonthecalculationofgassolubilitiesinpetroleumandcoalliquidfractionsandtoproposeaP/N/A-basedmodelforsuchcalculations.
ThermodynamicFrameworkfortheProposedMethod
Thesolubilityofagas(denotedascomponent1)inaliquidmixture,intermsofitsmolefractionx1,canbecalculatedfromthevapor-liquidequilibriumrelationas
x1)
φV1P1γ1fL1
(1)
whereP1isthepartialpressureofcomponent1,φV1is
itsfugacitycoefficientinthegasphase,γ1isitsactivitycoefficientinthesolventliquidphase,andfLiisitsfugacityasapureliquidattemperatureTandpressureP.
Forcalculatingthefugacityofagasintheliquidphase,therearedifferentoptions.Onepossibilityistousecubicequationsofstate.Onedisadvantageofthismethodisthatthenecessarypure-compoundparam-eters(i.e.,criticalpropertiesandacentricfactor)arenotavailablefortheheavyoil,norcantheybeaccuratelyestimated.Inaddition,theuseofcubicequationsofstaterequiresexperimentaldataforadjustingthebinaryparameterforeachpetroleumcutorliquidcoalatvarioustemperatures.2,3Inthiswork,Scatchard-Hildebrandtheory8,9waschosenforthecalculationofγ1becauseofitspredictivepotentialandtheavailability
10.1021/ie040056sCCC:$30.25©2005AmericanChemicalSociety
PublishedonWeb12/29/2004
Table1.ValuesofLiquidMolarVolumeandSolubilityParametersforSomeLightGasesat298KfromDifferentSources
DIPPR10
Prausnitzetal.8
ponentcom-a(K)
Tc(bar)Pc(cmVL3/mol)[(J/cmδi3)1/2](cmVLi3/mol)i
[(J/cmδi3)1/2]
CH4190.5645.9952.011.62[35.3]52.0[15.14]11.6C2H6305.3278.83(55.23)45.712.4[45.7]70.0[19.43]13.50CO2304.2178.8337.27(52)14.5655.0
12.3
H2
33.1913.13
28.568
6.648
ComponentsN2,CO,O2,CO2,CH4,andC2H6at298Kareinthegaseousphase(Tc<298K),andvaluesofVLgiveninsquare1andδiarehypotheticalliquidvalues.Valuesbracketsareat90Kforrealliquids.ValuesgiveninparenthesesaretakenfromAPI.9
ofinformationonpure-compoundparameters.Accordingtothistheory,thevalueofγ1isgivenby
VLδ2
lnγ1(δ1-mix)
1)
RT
(2)
whereVL1isthemolarvolumeofthesolute1asaliquid;δ1isitssolubilityparameter;andforapseudo-binarysystem,δmixisgivenby
δmix)Φ1δ1+(1-Φ1)δ2
(3)
with
LΦx1V1
1)
xL(1-xL
1V1+1)V(4)
2
BothδandVLneedtobeatthetemperatureofthesystem,consideredtobeat25°Cinthisstudy.ValuesofδandVLaregivenindifferentliteraturesources.8-10At25°C,lightcompoundssuchasmethane,ethane,andhydrogenareinthegaseousstate,andfictitiousvaluesfortheparametersforthesespecies,asrecommendedintheliterature,aregiveninTable1.Foracompoundsuchasethane,therearefourdifferentvaluesforVLat25°C,reportedbyDIPPR,10API,9andPrausnitzetal.8Thisdiscrepancyisduetothefactthatthesevaluesarenottrueliquidmolarvolumesbutaretheresultofextrapolations.Inthiswork,weusethevaluesforVLsuggestedbyDIPPR10thatarereproducedinTable1.Ontheotherhand,inthiswork,thevaluesofδareadjustedusingexperimentaldataonsolubility.
Onemajorprobleminusingeq1tocalculatesolubili-tiesofalightgas(CH4,C2H6,orHhigherthanthecriticaltemperature2)inanoil,attemperatures(Tc)ofthesecomponents,isthatthecalculationoffLpossiblebecausethecomponentisnotinliquid1isnotform.Inthiscase,fLirepresentsthefugacityofcomponentiinahypotheticalliquidstate,andthefollowingequation
isrecommendedtocalculatefLiwhenTr>1
8f
L
i
)f
oLrPexp
[VL1(P-1.013)c
RT
](5)
wherefoLristhereducedhypotheticalliquidfugacityat
pressureof1atm(foLr)foL/Pc)andTristhereduced
temperature.
Ind.Eng.Chem.Res.,Vol.44,No.1,2005187
CalculatedresultsforfoL8.Forcomputationalrarepresentedinafigureinrefconvenience,thefollowingequationwasobtainedfromthatfiguretocalculatefoLr
foLr)exp(7.902-
8.19643
T-3.08lnTr
r
)(6)
Dataintherange0.95 φV1)exp {Pr1 [(0.083-0.422T-1.6Tr1)+r1 ω4.21(0.139-0.122T-r1)] }(7) whereTr1isthereducedtemperature,Ppressure,andωofr1isthereduced 1istheacentricfactorthedissolvinggas.Forgasesathigherpressure,thevirialequation,truncatedafterthethirdvirialcoefficient,canbeused.12P/N/AApproachfortheSolubilitiesofGasesinPetroleumandCoalLiquids Inthiswork,forthepseudo-binaryapproach,weusethefollowingequationsfortheparametersoftheliquidsolvent δ2)ΦPδP+ΦNδN+ΦAδA (8) Foreq8,weuse ΦxLjVjj) V L forj)P,N,A(9) 2 with VLLLL 2)xPVP+xNVN+xAVA (10) wherexP,xN,andxAarethemolefractions;VLL P,VN,andVLAaretheliquidmolarvolumes;andδP,δN,andδAarethecorrespondingsolubilityparametersfortheparaffinic,naphthenic,andaromaticpseudocompounds,respectively.Inthiswork,thevaluesforVLallevaluatedat25°C. jandδjareOnthebasisofthedataavailableinDIPPR,10weproposethefollowingrelationsforestimatingtheliquidmolarvolumesofn-alkanes(P),n-alkylcyclohexanes(N), andn-alkylbenzenes(A)at25°C,VL 25j lnVL 25P )-0.51589+2.75092M0.15forn-alkanes(C1-C36)(11) 188Ind.Eng.Chem.Res.,Vol.44,No.1,2005 VL25N)10.969+1.1784M forn-alkylcyclohexanes(C6-C16)(12)lnVL 25A)-96.3437+96.54607M0.01 forn-alkylbenzenes(C6-C24)(13) whereVL3of25thejisincm/molandMisthemolecular weightpetroleumfraction,evaluatedasdiscussedbelow.Thesecorrelationsreproducethedatawithaveragedeviationsof0.9%,0.4%,and0.2%forn-alkanes,n-alkylcyclohexanes,andn-alkylbenzenes,re-spectively.Similarly,inthiswork,weproposethefollowingrelationsforestimatingthesolubilityparam-etersat25°C,δj δP)16.22609[1+exp(0.65263-0.02318M)]-0.4007 forn-alkanes(C1-C36)(14)δN)16.7538+7.2535×10-5M forn-alkylcyclohexanes(C6-C16)(15)δ-3 2 A)26.8557-0.18667M+1.36926×10M-4.3464×10-6M3+4.89667×10-9M4 forn-alkylbenzenes(C6-C24)(16) whereδiisin(J/cm3)1/2.Theuseofeqs8and10forthecalculationofδ2andV2requiresknowledgeoftheP/N/Acompositionofthepetroleumfraction.Thelinearrela-tionshipsforVNandδAversusMgiveahigherpowerofextrapolationforpredictingthesepropertiesforheaviern-alkylcyclohexanecompounds,asseeninFig-ures1and2.Forthishydrocarbonfamily,limiteddatafromC6toC16areavailable,10andforthisreason,itwasdecidedtousethesimplelinearrelationproposedineq15.Inthesefigures,SCNreferstosinglecarbonnumber(pseudo-mixtureofhydrocarbonsfromdifferentgroupshavingthesamecarbonnumber).Ifexperimen-taldataarenotavailable,methodsdevelopedbyRiaziandDaubert,13whicharealsoincludedintheAPITechnicalDataBook,9canbeusedtocalculatethecompositionfromcharacterizationdata.ThesemethodsaregiveninAppendixB. Forcomparisonpurposes,wealsoconsiderhereanalternativepseudo-componentmethodbasedontheassumptionthatthepetroleumorcoalliquidfraction Figure1.Solubilityparameters(δ)ofP,N,A,andSCNgroupsversuscarbonnumber[δisat25°Cin(J/cm3)1/2]. Figure2.Liquidmolarvolumes(VL 25j)ofP,N,A,andSCN groupsversuscarbonnumber(VL 25jisat25°Cincm3/mol). isasingle,molecularlyhomogeneouspseudocomponent.Theassumptionsusedinthismethodaredetailedbelow. SCNApproachfortheSolubilitiesofGasesinPetroleumandCoalLiquids Inthisapproach,theliquidphaseisagainconsideredtobeamixtureoftwocomponents:thesolute(dissolv-inggas)andthesolvent(petroleumorcoalliquidfraction),whicharedenotedascomponents1and2,respectively.However,inthiscase,thepetroleumorcoalliquidfractionisrepresentedbyasinglecarbonnumber(SCN)hydrocarbongroup.13Onthebasisofdatapre-sentedinref14,thefollowingrelationscanbeusedtocalculateδ2andV2fromthemolecularweightoftheliquidfraction δ2)17.5913-exp(3.0076-0.54907M0.3)(17) VL2) M 1.05-exp(3.80258-3.12287M0.1) forSCN(C6-C50)(18) whereδ2andVL2arebothat25°Candhaveunitsof (J/cm3)1/2andcm3/mol,respectively.Thesecorrelationscanbeusedforthemolecularweightrangeof80-700(∼C6-Can50).Theseequationscorrelatetheoriginaldatawithinaverageerrorof0.1%,andtheresultsarepresentedinFigures1and2.Thesevaluesofδ2andVL2arebasedonestimatedvaluesforpropertiesoflightSCNhydrocarbongroups.CalculationResultsandDiscussion Thecharacterizationdata,P/N/Acomposition,anddatasourcesforgassolubilitiesinvariouspetroleumfractionsderivedfromcrudeoil,coalliquids,andtarsandsarereportedinTable2.ThecompositionswerecalculatedaccordingtothemethodsdescribedinAp-pendixB.Morethan180datapointsonthesolubilitiesofmethane(C(H1),ethane(C2),carbondioxide(CO2),andhydrogenThe2)weretakenfromvarioussourcesaslistedinTable3.temperature,pressure,andsolubilityrangesarealsoincludedinTable3.Datatakenfromref2forthesolubilitiesofmethane,ethane,andcarbondioxideindifferentpetroleumfractionsandcrudeoilshaveexperimentalerrorsintemperatureof(0.2K,inpressureof(0.03bar,andinsolubilityof(5×10-6mol/gor(2%.Theworstuncertaintyinsolubilitywas Ind.Eng.Chem.Res.,Vol.44,No.1,2005189 Table2.CharacterizationParametersa,bforPetroleumFractionsUsedinThisStudyfractionc 1234567891011 ac oilmixtureExxonAcut1ExxonAcut5ExxonBcut1ExxonBcut4WCLPcut7WCLPcut8CLPPA5cut1CLPPA5cut2SRCno.5SRCno.9SRCno.12 oilsourcecrudeoilcrudeoilcrudeoilcrudeoilcoalliquidcoalliquidcoalliquidcoalliquidcoalliquidcoalliquidcoalliquid Tb(K)651.2707.0630.2714.0603.0630.5483.3558.9541.0598.0658.0 SGat60°C0.9331.0000.9441.0550.9841.0210.9320.9840.9831.0311.091 M310.7351.7282.3338.5232.3247.3145.5190.9176.5211247.2 CH7.0057.1907.3087.6908.3328.6149.1989.1669.5139.5529.529 m15.00431.19815.68141.80718.83625.6717.55615.75214.44923.37536.650 Ri1.05851.06531.06031.07251.06591.07001.06291.06721.06751.07221.0793 xP0.5950.5640.5470.4840.3850.340.0450.0000.0000.0000.000 xN0.2680.2750.2870.3040.3530.3690.2750.1900.2200.1100.000 xA0.1370.1600.1660.2120.2620.2910.6790.8100.7800.8901.000 AllparametersaredefinedintheNomenclaturesection.bCharacterizationparametersarecalculatedfrommethodsgiveninAppendixB.Dataforfractions1-6fromref2andforfractions7-11fromref4. Table3.EvaluationsofP/N/A(Eqs8-16)andSCN(Eqs17and18)ModelsforthePredictionofGasSolubilitiesinthePetroleumFractionsofTable2 P/N/A dataset123456789101112131415161718192021 solutegasmethanemethanemethanemethanemethanemethanemethanemethanemethaneethaneethaneethaneethaneethaneCO2CO2 hydrogenhydrogenhydrogenhydrogenhydrogen fractioninTable2 123467891012345647891011 Trange(K)473-573473-571375-423474-573474-549462-541462-544543543 473-574474-574375-424474-574375-425375-549472-571463-623463-543462-544464-544542 Prange(bar)6-218-217-218-219-2050-24950-25550-25152-2436-196-207-207-165.5-198-187-1850-10150-10150-10248-10051-101 xlrange(×100)1.5-51.9-5.21.4-4.92.0-4.81.6-3.89-44.48-369-398-372.4-11.52.9-94.3-16.42.9-10.63.5-13.81.5-7.72.3-7.13.3-9.54.4-8.33.5-9.33.2-8.13.9-7.1 datano.11101011131094420910111113673442 RPNA(eq19)0.9400.9400.9400.9400.8000.8900.8500.8500.8001.3001.3001.0201.2190.9720.6801.1001.2101.2101.2100.4700.400 AAD(%)5.54.51.45.92.82.45.76.40.95.37.32.52.93.56.211.05.912.15.33.84.2 SCNRSCN(eq20)0.9400.9400.9400.9400.8000.8300.8100.9300.8901.3321.3321.1021.2190.9400.6801.1001.3001.2001.2900.6100.610 AAD(%)5.57.52.44.93.94.46.16.13.25.37.33.33.13.66.811.26.18.25.04.84.9 avariationof11%.Datareportedbyotherresearchershavesimilaruncertainties.Forexample,Linetal.4reportexperimentaldataonsolubilityofhydrogenwithuncertaintiesof(3%.Generall,yexperimentalerrorscanbeintherangefrom(1%to(5%.Usually,experimentalerrorsarehigherathigherpressuresthanatlowpressures. Asmentionedabove,valuesofδ1andVL1reportedinTable1forlightgasesarenotthetruevaluesbecausethesegasesarenotintheliquidstateat298K.Forthisreason,differentvaluesforδ1andVL1canbefoundforthesamegasindifferentliteraturesources.Torepro-ducethedataonthesolubilitiesofthegaseswell,the 10andrepro-valuesofδ1andVL1reportedbyDIPPR, ducedinTable1,wereusedwithacorrectionfactorforparameterδ1.ThecorrectionfactorsRweredefinedforthePNAandSCNmodelsasfollows δ1,PNA)RPNAδ1(DIPPR)foruseineqs3and8(19)δ1,SCN)RSCNδ1(DIPPR)foruseineqs3and17 (20)RPNAandRSCNrefertoP/N/AandSCNmodels,respec-tively.Thevaluesoftheseparametersdependonthetypeofgasandsolvent(i.e.,apetroleumfractionoracoalliquid),butareindependentoftemperature.These factorsmustbeusedwithvaluesofδandVLfromtheDIPPRcompilation9reproducedinTable1.Nomodifi-cationwasintroducedforthevaluesofVL1oncethesecorrectedvaluesofδ1wereused.ValuesofRPNAandRSCNfordifferentgasesandasummaryoftheresultsforestimatinggassolubilitiesarepresentedinTable3.ValuesofRgiveninTable3arebasedontheuseofeq7forthecalculationofgasfugacitiesatallpressures.Itwasfoundthat,athigherpressures(e.g.,250bar),eq7isapplicable,andtheuseofthethirdvirialcoefficientforfugacitycalculationsdoesnotimprovesolubilitycalculations,aslongasvaluesofRarebasedoneq7. TheresultsreportedinTable3indicatethat,forsomecoalliquidsrichinaromatics,thedifferencebetweenthetwoapproachesismarginal;however,forsomelightpetroleumfractions,theP/N/AapproachgivesbetterresultsthantheSCNapproach.Thepredictedsolubili-tiesofmethaneinalightfraction(fraction7inTable2)attwodifferenttemperaturesarealsoshowninFigures3and4.Inthesefigures,theeffectoftheP/N/Acompositiononthesolubilitypredictionisalsodemon-strated.Overall,theP/N/Aapproachproducesbetterresultsforall21datasets(182datapoints),withanaverageerrorofabout4.5%.Itshouldbenotedthatthesecalculationsarebasedonestimatedcompositionsoftheliquidfraction.IfexperimentaldataonP/N/A 190Ind.Eng.Chem.Res.,Vol.44,No.1,2005 Figure3.Predictionofthesolubilityofmethaneinfraction7at462K. Figure4.Predictionofthesolubilityofmethaneinfraction7at541K. Table4.RecommendedValuesofSolubilityParametersforMethaneandEthaneforUsewithEqs2and8-16(P/N/AApproach)forVariousHydrocarbonFractionsRPNAVLδi gasfraction(eq19)(cm3/mol)i [(J/cm3)1/2]methanepetroleum/crudeoil0.945210.923methanecoalliquid 0.8529.296ethanepetroleum/crudeoil1.345.716.12ethane coalliquid 1.0 45.7 12.4 compositionsareavailable,moreaccuratesolubilitypredictionscanbeobtained. AnalysisofresultspresentedinTable3showsthat,whennoexperimentaldataonsolubilityareavailable,asinglevalueofRcanbeusedforeachgas.Forexample,avalueofR)0.94canbeusedforthesolubilityofmethaneinpetroleumfractions.Forethane,thisvalueis1.3,andforhydrogenincoalliquids,thisvalueis1.21.ForthesevaluesofRandthevaluesofRgiveninTable1,recommendedvaluesofthesolubilityparameterandmolarvolumeformethaneandethaneforsolubilitycalculationsaregiveninTable4.AcomparisonbetweenthesolubilitiespredictedusingtherecommendedvaluesofRorδ(asgiveninTable4)andtheoptimumvaluesofR(asgiveninTable3)ispresentedinTable5.Asseeninthistable,asinglevalueofδcanbeusedforthecalculationofthesolubilitiesofmethaneandethaneinvarioustypesofpetroleumfractionsderivedfromcrudeoils.Similarly,asinglevalueofδcanbeusedforthecalculationofthesolubilitiesofhydrocarbongasesindifferentcoalliquidfractions.ForthesystemsshowninTable5,theerrorincreasesfrom4.9%to5.5%whenafixedvalueofδisusedforallfractions.Suchsinglevaluesofδcannotbe Table5.ComparisonofResultsObtainedwiththeP/N/AModelUsingOptimumValuesofrPNA(Table3)andRecommendedFixedValuesofrPNA(Table4)withtheResultsObtainedwithanEOSModel AAD(%) solutefractioninno.ofdataoptimumfixedgasTable2 points RPNA RPNAEOSmethane1115.55.55.3methane2104.54.53.4methane3101.41.44.3methane4115.95.94.4methane6132.82.84.2methane7102.44.65.1ethane1205.35.35.6ethane296.26.26.4ethane3102.516.37.3ethane4112.93.84.2ethane5 113.15.06.7overall 126 3.9 5.5 5.2 usedfortheSCNmodel.ThisisthemajoradvantageofusingtheP/N/AmethodovertheSCNmethodforsolubilitycalculations. Tocomparethepredictionsofsolubilitybythepro-posedapproacheswiththeresultsobtainedwithequa-tionsofstate,weusedirectlytheresultsobtainedfromaperturbed-hard-chainEOSasreportedbySchwarzandPrausnitz.2Theyobtainedoptimumvaluesofthebinaryinteractionparametersforeachgasfractionandateachtemperature.TheoverallerrorproducedbytheaboveEOSforthesystemsconsideredinTable5is5.2%.Thisvaluecomparescloselywithanoverallerrorof5.5%obtainedwiththeproposedP/N/Aapproach.AgraphicalcomparisonbetweenthesolubilitypredictionsoftheEOSandtheproposedP/N/AmodelusingtheproposedvaluesofδisshowninFigures5and6fortwodifferentfractionsfromcrudeoilandcoalliquid.ResultsshowninTable5andFigures5and6indicatethattheproposedmodeliscomparabletotheEOSmodelwithouttheneedforparameteradjustment.Thefol-lowingexampleshowsindetailanapplicationofthemodelproposedinthiswork. Example1.Apetroleumfiractionderivedfromcrudeoilhasaboilingpointof630.5Kandaspecificgravityof0.944.Estimatethesolubilityofmethaneinthisfractionat375Kand14.26bar.Theexperimentalvalue(intermsofmolefraction)asreportedbySchwarzandPrausnitz2is0.035. Solution:Fromtheboilingpoint(TvalueofMandthePNAb)andspecificgravity(SG),thecompositionarecalculatedaccordingtomethodsgiveninAppendixB.CalculatedvaluesarereportedinTable2(fraction Figure5.Solubilityofmethaneincoalliquid(fraction6inTable2)at474K. Figure6.Solubilityofethaneinpetroleumcrude(fraction1inTable2)at474K. 3).FromDIPPR,10Tc)190.56K,Pc)45.99bar,andω)0.0115,andfromTable1,δ1)11.62(J/cm3)1/2and VL1)52.0cm3/mo1.Thetemperatureandpressureare givenasT)375KandP)14.26bar.Fordissolvingmethaneinafractionfromcrudeoil,RPNa)0.94,andeq19givesδ1)10.923(J/cm3)1/2.Fromeqs3and8,δmix)16.3976(J/cm3)1/2andTr)1.968,andfromeq7, φVoLL 1)0.9908.Fromeq6,fγr)5.47,andfromeq5,fbar.Fromeq2,1)245.2771)1.649,andfromeq1,x1)0.0349,whichdiffersby0.2%fromtheexperimentalvalueof0.035.Similarcalculationsthrougheqs17and18givex1)0.0339witherrorof-3.2%.Calculationsrequireatrial-and-errorapproach,andaninitialguessvalueofxl)0.0canbeusedforthestartofthecalculations.Conclusions AsimpleP/N/AapproachisproposedtocalculatesolubilitiesoflightgasesinpetroleumandcoalliquidfractionsusingScatchard-Hildebrandsolubilitypa-rametertheory.Asimplerapproachbasedonthesinglecarbonnumber(SCN)grouphasalsobeentested,anditisrecommendedforpetroleumandcoalliquidfrac-tionswithmolecularweightsfrom80to700.Theapproachesproposedinthisworkcancalculatethesolubilitiesofgasesinvariousfractionswithinadevia-tionof4-5%.Theresultsshowthat,forsomepetroleumfractions,theP/N/Acompositionproducesbetterresultsforthecalculationofthesolubility.Modifiedsolubilityparametersformethaneandethaneinpetroleumfrac-tionsandcoalliquidsaresuggested.Thesevaluescanbeusedintheabsenceofanyexperimentaldata.ThepredictionsobtainedwiththeproposedmodelsarecomparablewiththeresultsobtainedforsolubilitycorrelationsusinganEOSmodel.Insummary,whereastheuseofcubicequationsofstaterequiresexperimentaldatatoadjustthebinaryparameterforeachpetroleumcutorliquidcoalandthusisonlycorrelationalandnotpredictive,theapproachusingsolubilityparametersispredictive.Oncethevalueofthesolubilityparameterofthegasisknown,itcanbeusedformixturesofheavycompoundswithdifferentP/N/Acompositions.Noex-perimentaldataarerequiredfortheadjustmentofanybinaryparameter.Withthevaluesofthesolubilityparametersforthegasesreportedinthiswork,theapproachcanbeuseddirectlyforotherpetroleumcutsorcoalmixturesofinterest. Ind.Eng.Chem.Res.,Vol.44,No.1,2005191 Acknowledgment TheauthorsaregratefultoKuwaitUniversityforgrantingsabbaticalleavetoM.R.R.andtoNSERCCanadaforpartialfinancialsupport.Nomenclature AAD)averageabsolutedeviation,%CH)carbon-to-hydrogenat20weight°Candratio d20)liquiddensity1atm,g/cm3foL1)fugacityofpurehypotheticalliquid1attempera-tureT(T>Tc),barfoL r)reducedfugacityofpurehypotheticalliquidattemperatureT()foL/Pc) I)refractiveindexparameterM)Molecularweight,g/mol n)sodiumDlinerefractiveindexofliquidat20°Cand1atm P)pressure,bar Pc)criticalpressure,bar Pr)reducedpressure()P/Pc),dimensionless Pi)partialpressureofdissolvinggasinthevaporphase,bar R)gasconstant)8.314J/mol‚K SG)specificgravityofaliquidsubstanceat15.5°C(60°F) T)absolutenormalboilingtemperature,pointofK Tb)afraction,KTc)criticaltemperature,K Tr)reducedtemperature()T/Tc),dimensionlessV)molarvolume,cm3/molVL253)j)liquidmolarvolumeat25°C,cmmolefractionofcomponentiinamixture/mol xi(usuallyusedforliquids)GreekLetters R)parameterdefinedbyeqs19and20 δi)solubilityparameterforcomponenti,(J/cm3ofcomponentiinaliquidmixture)1/2 Φi)volumefractionφvi)fugacitycoefficientofcomponentiatTandPinthevaporphase ω)acentricfactor γ1)activitycoefficientofcomponent1(gas)inliquidsolutionSubscripts A)aromaticN)naphthenicP)paraffinici)componenti r)reducedproperty 1)dissolvinglightgas(CH4,C2H6,C3H8,CO2,orH2) AppendixA RelationbetweenTthan2.ThecompressibilityrandPrRequiredToHaveVrLargerfactorobtainedfromthevirialequation,truncatedafterthesecondvirialcoefficient,canbewrittenas Z)PV RT)1+ PrT(A.1) r whereisthereducedsecondvirialcoefficient,which, accordingtoref11,iswellapproximatedby )(0.083- 0.4221.6)+ω(0.172 T0.139-rT4.2 r)(A.2) 192Ind.Eng.Chem.Res.,Vol.44,No.1,2005 RearrangingeqA.1,wewrite V1r) (Tr Z+cPr )(A.3) whereZcisthevalueofthecompressibilityfactorofthecompoundatthecriticalpoint.Thus,fortheconditionVrg2,weobtain PTr re 2Z(A.4) c-AppendixB ToestimatetheP/N/Acomposition,assumingTapetroleumfractionareknown,M,n,dbandSGfor,andCHcanbecalculatedfromthefollowingrelations9,13,15 M)42.965[exp(2.097×10-4Tb-7.78712SG+ 2.08476×10-3T4.98308bSG)]T1.26007bSG(B.1) I20)0.3773T-0.02269bSG0.9182 (B.2)n) (1+2I1/21-I)(B.3)d0.00201620)0.983719TbSG1.0055 (B.4) CH)3.4707[exp(1.485×10-2Tb+16.94SG- 1.2492×10-2TbSG)](B.5) Thecompositioniscalculatedfromthemethodgiveninref13as m)M(n20-1.475)(B.6)Ri)n20-d20/2 (B.7) ForfractionswithMe250 xP)3.7387-4.0829SG+0.014772m (B.8) xN)-1.5027+2.10152SG-0.02388m(B.9)ForfractionswithM>250 xP)1.9842-0.27722Ri-0.15643CH(B.10)xN)0.5977-0.761745Ri-0.068048CH (B.11)xA)1-(xP+xN) (B.12) ForcoalliquidswithM<250 xMA)-62.8245+59.90816Ri-0.0248335m (B.13) xPA)11.88175-11.2213Ri+0.023745m (B.14)xA)xMA+xPA (B.15) wherexmonoaromaticMAandxandPArepresentthemolefractionsofpolyaromatichydrocarbons,respec-tively. 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ReceivedforreviewFebruary11,2004 RevisedmanuscriptreceivedOctober4,2004 AcceptedOctober26,2004 IE040056S 因篇幅问题不能全部显示，请点此查看更多更全内容