2/19/2015 PengRobinsonequation

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PengRobinsonequation

PureFluid

General

EquationwaspresentedinPengandRobinson(1976)withsomecorrectionsmadebythesameauthorsin(1978).Inwhatfollowswearetryingtosticktooriginalnotations,someofthemaredescribedhere.

PengRobinsonequationitselfisthespecialversionofthegeneralcubicequationofstatewith and :

where

and isadimensionlessparametersuchthat

Withnewvariables and itcouldberewrittenintermsofcompressibilityfactor

PlotExample

Cubicpolynomialexamplesformethane(CH4)forcriticalpressureatcriticaltemperatureandfornearlycriticalpressureat

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2/19/2015 PengRobinsonequation

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criticaltemperature: Itcouldbeseenthatatsubcriticalpressuretherearetwopossibilitiesforaroot.Itmeansthatthevalueofcompressibilityfactorhastwovalues:liquidandvapor.

Fugacity

Formulaforfugacitycoefficientofsimplefluid,calculatedviaPRequation,hasexpression

HeatCapacity

Departurefunctionofheatcapacity,calculatedviaPRequation,hasexpression

Differencebetweencapacities,calculatedviaPRequation,hasexpression

where

Inthecaseofsimplefluidfollowingformulasforderivativeofparameter couldbeapplied

SonicSpeed

Accordingtothesectionaboutsonicspeed,incaseofPRequation,sonicspeedcouldbeexpressedinanalyticformas

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2/19/2015 PengRobinsonequation

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where osthemolarweight.

Mixtures

MixingRules

ParametersofPRequationforthemixtureof simplefluidswheremolarpercentofthe thcomponentis aredefinedbymixingrules

Here isexpressedthroughempiricallydeterminedbinaryinteractioncoefficient characterizingthebinaryformedbycomponent andcomponent as

Some aretabulated(e.g.table4.2inPedersenandChristensen(2006)).ForthoseonewhicharenottabulatedformulaofChuehandPrausnitz(1967)couldbeused:

Fugacity

Formulaforfugacitycoefficientofthemixture,calculatedviaPRequationandstandardmixingrules,hasexpression(seePengandRobinson(1976)orequation4.65inPedersenandChristensen(2006)formoredetail)

HeatCapacity

Formulasforheatcapacitydeparturefunctionanddifferenceofcapacitiesforthemixtureofsimplefluidsarethesameasforthesimplefluid.Correspondingchangesfortheexpressionsofderivativesof shouldbedone.

Since isthelinearcombinationofparameters ,derivativesof areexpressedthroughderivativesof straightforward

Derivativesof inthecaseoftimeindependentinteractioncoefficientsaregivenbyformulas

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2/19/2015 PengRobinsonequation

http://kshmakov.org/fluid/note/3/ 4/4

1. WikionPengRobinsonEquation

2. Peng,D.Y.,andRobinson,D.B.(1976).ANewTwoConstantEquationofStateIndustrialandEngineeringChemistry:Fundamentals15:5964DOI:10.1021/i160057a011

3. Peng,D.Y.,andRobinson,D.B.(1978).TheCharacterizationoftheHeptanesandHeavierFractionsfortheGPAPeng&ndashRobinsonProgramsGasProcessorsAssociationDOI:no

4. MethoddocumentationforPVTsim16

5. Poling,B.E.,Prausnitz,J.M.andO'Conell,J.P.(2001).ThePropertiesofGasesandLiquids.McGrawHillProfMed/TechISBN:0070116822,9780070116825

6. Leland,Th.W.Jr.,andChapellear,P.S.(1968).TheCorrespondingStatesPrincipleAReviewofCurrentTheoryandPracticeIndustrialandEngineeringChemistry60(7):1543DOI:10.1021/ie50703a005

7. Pedersen,K.S.andChristensen,P.L.(2006).PhaseBehaviorofPetroleumReservoirFluids.CRCPressISBN:9780824706944

8. Chueh,P.L.,andPrausnitz,J.M.(1967).VaporLiquidEquilibriaatHighPressures.CalculationofPartialMolarVolumesinNonpolarLiquidMixtures.AIChEJournal13(6):10991107DOI:10.1002/aic.690130612

9. Huron,M.J.,andVidal,J.(1979).NewMixingRulesinSimpleEquationsofStateforRepresentingVaporliquidEquilibriaofStronglyNonIdealMixtures.FluidPhaseEquilibria3(4):255271DOI:10.1016/03783812(79)800011