A-New-Equation-of-State-for-Carbon-Dioxide-Coverin

ANewEquationofStateforCarbonDioxideCoveringtheFluidRegionfromtheTriple-PointTemperatureto1100KatPressuresupto800MPaR.SpanandW.WagnerLehrstuhlfurThermodynamik,Ruhr-UniversitatBochum,D-44780Bochum,GermanyReceived25May1994ThisworkreviewstheavailabledataonthermodynamicpropertiesofcarbondioxideandpresentsanewequationofstateintheformofafundamentalequationexplicitintheHelmholtzfreeenergy.ThefunctionfortheresidualpartoftheHelmholtzfreeenergywasfittedtoselecteddataofthefollowingproperties:(a)thermalpropertiesofthesingle-phaseregion(ppT)and(b)oftheliquid-vaporsaturationcurve(Psp',p)includingtheMaxwellcriterion,(c)speedofsoundwand(d)specificisobaricheatcapacitycpofthesinglephaseregionandofthesaturationcurve,(e)specificisochoricheatcapacitycv'(f)specificenthalpyh,(g)specificinternalenergyu,and(h)Joule­Thomsoncoefficient/-t.Byapplyingmodernstrategiesfortheoptimizationofthemath­ematicalformoftheequationofstateandforthesimultaneousnonlinearfittothedataofalltheseproperties,theresultingformulationisabletorepresenteventhemostaccuratedatatowithintheirexperimentaluncertainty.Inthetechnicallymostimportantregionuptopressuresof30MPaanduptotemperaturesof523K,theestimateduncertaintyoftheequationrangesfrom±0.03%to±0.05%inthedensity,±0.03%to±1%inthespeedofsound,and±0.15%to±1.5%intheisobaricheatcapacity.Specialinteresthasbeenfocusedonthedescriptionofthecriticalregionandtheextrapolationbehavioroftheformulation.Withoutacomplexcouplingtoascaledequationofstate,thenewformu­lationyieldsareasonabledescriptionevenofthecaloricpropertiesintheimmediatevicinityofthecriticalpoint.Atleastforthebasicpropertiessuchaspressure,fugacity,andenthalpy,theequationcanbeextrapolateduptothelimitsofthechemicalstabilityofcarbondioxide.Independentequationsforthevaporpressureandforthepressureonthesublimationandmeltingcurve,forthesaturatedliquidandvapordensities,andfortheisobaricidealgasheatcapacityarealsoincluded.Propertytablescalculatedfromtheequationofstatearegivenintheappendix.©1996AmericanInstituteofPhysicsandAmericanChemicalSociety.Keywords:carbondioxide;correlation;criticalregion;dataevaluation;equationofstate;extrapolation;fundamentalequation;meltingline;propertytables;sublimationline;thermalandcaloricproperties;andvapor-liquidcoexistencecurve.ContentsNomenclature..............................1513PhysicalConstantsforCarbonDioxide.........15131.Introduction................................15141.1Background............................15141.2PriorCorrelationsofCarbonDioxidePropertiesandDemandsontheNewCorrelation.............................15141.3OrganizationoftheArticle................15162.BasicElementsoftheDevelopmentofEquationsofStateinFormofaFundamentalEquation.....15162.1HelmholtzFunction......................15162.2HelmholtzEnergyoftheIdealGas.........15162.3ResidualPartoftheHelmholtzEnergy......15172.3.1FittinganEmpiricalEquationfor¢rtoData.........................15172.3.2OptimizingtheMathematicalForm....15182.3.3TheProcedureofWeighting.........15183.PhaseEquilibriaofCarbonDioxide............15193.1TriplePoint............................15193.2CriticalPoint...........................15193.3MeltingPressure........................15203.4SublimationPressure.....................15213.5VaporPressure.......................15213.6SaturatedLiquidDensity.................15243.7SaturatedVaporDensity..................15253.8CaloricDataontheLiquid-VaporPhaseBoundary..............................15264.ExperimentalBasisoftheNewEquationofState.....................................15264.1ThermalProperties....................15274.2SpecificIsobaricHeatCapacity............15284.2.1ExperimentalResultsfortheSpecificIsobaricHeatCapacity..............15284.2.2ResultsfortheSpecificIsobaricHeat0047-2689/96/25(6)/1509/88/$20.001509J.Phys.Chern.Ref.Data,Vol.25,No.6,19961510R.SPANANDW.WAGNERCapacityintheIdeal-GasState.......15294.3SpecificIsochoricHeatCapacity...........15304.4SpeedofSound.........................15324.5Enthalpy...............................15324.6InternalEnergy.........................15324.7Joule-ThomsonCoefficient..............,15324.8VirialCoefficients.......................15334.9Liquid-VaporEquilibrium................15334.10AdjustmentofData.....................15344.10.1AdjustmentofDataSetsDescribingtheCriticalRegion...............15344.10.2AdjustmentofppTData...........15344.10.3CorrectionofIsobaricHeatCapacities......................15355.DescriptionofThermodynamicPropert.iesintheCriticalRegion.............................15355.1LimitationsofAnalyticalEquationsofState.15365.2UseofNonanalyticTermsasanIntegralComponentinanEmpiricalWide-RangeEquationofState........................15376.NewEquationofState.......................15416.1Ideal-GasPartoftheHelmholtzEnergy.....15416.2ResidualPartoftheHelmholtzEnergy......15437.ComparisonsoftheNewEquationofStatewithExperimentalDataandOtherEquationsofState_]54()7.1Liquid-VaporBoundary..................15467.1.1ThermalPropertiesontheCoexistenceCurve............................15467.1.2CaloricPropertIesontheCoeXIste