Volume-translated Peng-Robinson equation of state

FluidPhaseEquilibria349(2013)37–55ContentslistsavailableatSciVerseScienceDirectFluidPhaseEquilibriajournalhomepage:∗SchoolofChemicalEngineering,OklahomaStateUniversity,Stillwater,OK74078,UnitedStatesarticleinfoArticlehistory:Received18January2013Receivedinrevisedform3April2013Accepted5April2013Availableonline15April2013Keywords:VolumetranslationPeng-RobinsonequationofstateSaturatedliquiddensitiesSingle-phasedensitiesBubblepointBinarymixturesAsymmetricmixturesVapor–liquidequilibriaabstractTwo-parametercubicequationsofstate(CEOS)arewidelyusedinprocessengineeringcalculations.However,inaccurateliquiddensitypredictionsremainasignificantdeficiencyintheseequations.Toremedythisproblem,avolumetranslationoftheCEOSisfrequentlyemployed.Inarecentwork,wepresentedavolume-translatedPeng-Robinsonequationofstate(VTPREOS)thatiscapableofprovidingaccuratedensitypredictionsforbothsaturated-andsingle-phaseregionsofpurefluidsathighpressures.Inthecurrentwork,wepresentanextensionofthatapproach,employingconventionalmixingrules,topredictdensitiesofliquidmixturesoverlargerangesofpressureandtemperature.Forthispurpose,twodatabaseswerecompiledforvapor–liquidequilibriumandliquiddensitymeasurementsof73binarysystemscomposedofdiversechemicalspecies.Themolecularspeciesinthedatabasesrangedwidelyintermsofmolecularsize,shape,asymmetryandpolarityand,thus,werewellsuitedtotesttheefficacyofourapproach.Overall,thedatabasescontainedmorethan5000datapointsforvapor–liquidequilibriummeasurementsandover13,000datapointsforliquiddensitymeasurementsofmixtures.ResultsindicatethatextensionoftheVTPREOStoliquidmixturesiscapableofprovidingreliabledensitypredictionsfordiversebinarymixturesoverlargerangesofpressure.TheVTPREOSpredictionsofmixtureliquiddensitiesyielderrorsthatarethreetofivetimeslowerthanthecorrespondingpredictionsfromtheuntranslatedPeng-Robinsonequationofstate(PREOS).Specifically,theoverallpercentageaverageabsolutedeviations(%AAD)fromtheVTPREOSvariedfrom1.5to3forbinarymixtures.ThisrepresentsasubstantialimprovementrelativetotheuntranslatedPREOS,forwhicherrorsrangedfrom2to15%AAD.©2013ElsevierB.V.Allrightsreserved.1.IntroductionReliable,accuratethermodynamicmodelsarenecessaryfordesignofchemicalprocessesandforreservoirsimulationsinthepetroleumandnaturalgasindustry.Duetotheirinherentsimplic-ityandcomputationalefficiency,cubicequationsofstate(CEOS)suchastheSoave-Redlich-Kwong(SRK)[1]andPeng-Robinson(PR)equationsofstate[2]arewidelyusedinprocessdesignandreservoirsimulations.However,awell-knowndeficiencyinthetwo-parametercubicequationsofstateistheirinaccurateliq-uiddensitypredictions.Toaddressthisproblem,atranslationinthecalculatedvolumeisfrequentlyemployed.BeginningwiththeworksofMartin[3]andPenelouxetal.[4],severalvolume-translationapproacheshavebeenproposedintheliterature.Theserangefromaconstantcorrectiontermtomorecomplexformsthatarebothtemperatureanddensity-dependent[3–16].Inarecentwork[17],wepresentedanewvolume-translationfunction∗Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](K.A.M.Gasem).basedonthedimensionless-distanceapproachofMathiasetal.[13]andChouandPrausnitz[7].Thenewvolume-translationfunctioncontainsonlyonefluid-specificparameter,andwehavegener-alizedthisparameterintermsofmolecularpropertiessuchascriticalcompressibilityfactor,acentricfactoranddipolemoment[17].Thenewvolume-translatedPeng-Robinsonequationofstate(VTPREOS)providesaccuratepredictionsofliquiddensitiesinboththesaturated-andsingle-phaseregionsforpurefluidsofdiverseclassesofmolecules.Inaddition,theVTPREOSdoesnotleadtother-modynamicinconsistencies,suchasisothermcross-oversinthecompressedliquidregionathighpressures,whichwereobservedinsomeofthetemperature-dependentmethodsintheliterature[18].Animportantaspectofvolume-translationmethodsistheirextensiontomixtures.ApartfromPeneloux’swork[4],onlyafewvolume-translationmethodsintheliteraturehavebeenextendedtomixtures.TsaiandChen[14]andLinandDuan[11]extendedtheirvolume-translationmethodstomixtures,butonlyforatmosphericpressureconditions.Sincemostvolume-translationmethodsavailableintheliteraturehavebeendevelopedandtestedonlyforpurefluids,aneedexistsforareliable0378-3812/$–seefrontmatter©2013ElsevierB.V.Allrightsreserved.fluid.2013.04.00238A.M.Abudouretal./FluidPhaseEquilibria349(2013)37–55volume-translationmethodthatcanprovideaccuratepredictionsofsaturated-andsingle-phaseliquiddensitiesformixtures.There-fore,inthiswork,weextendtheVTPREOSfromourpreviouswork[17]topredictdensitiesofdiversemixturesoverlargerangesofpressureandtemperature.Asisshownherein,theVTPREOSappearscapableofprovidingaccuratepredictionsofliquiddensi-tiesforbinarymixturescomprisedofdiversemolecularspecies.Asdiscussedelsewhere[7],asuccessfulapplicationofvol-umetranslationtomixturesrequiresasatisfactorydescriptionofphaseequilibriaofthemixtures.Thus,inthisw