50 A new model for calculating the viscosity of pure liquids at high pressures

3824Ind.Eng.Chem.Res.2003,42,3824-3830

ANewModelforCalculatingtheViscosityofPureLiquidsatHighPressures

RosanaJ.Martins, , Ma´rcioJ.E.deM.Cardoso,*, andOswaldoE.Barcia

Laborato´riodeF ´sico-Qu ´micadeL ´quidoseEletroqu ´mica,DepartamentodeF ´sico-Qu ´mica,InstitutodeQu ´mica,UniversidadeFederaldoRiodeJaneiro,CentrodeTecnologia,BlocoA,sala408,CidadeUniversita´ria,cep.21949-900,RiodeJaneiro,RJ,Brazil,andDepartamentodeF ´sico-Qu ´mica,InstitutodeQu ´mica,UniversidadeFederalFluminense,OuteirodeSa oJoa oBatistas/n,cep.24020-150,Nitero´i,RJ,Brazil

InthispaperwepresentanewmodelforcorrelatingthedynamicviscosityofNewtonianliquidsathighpressures.TheproposedmodelisbasedonEyring’sabsoluteratetheoryforliquidviscosityandconsiderstheactivationenergyforviscousflowasbeingathermodynamicfreeenergy.Theviscosityofthesystemisdescribedbyacombinationofareferenceterm,givenbytheChapman-Enskogtheory,andadeviationcontribution.Avirial-typeexpansioninpressureandatermcomprisinganexpressionfortheresidualHelmholtzfreeenergyofthesystemaccountforthedeviationfromthenonattractingrigidspheremodelviscositybehavior.Threecubicequationsofstate,Peng-Robinson,Soave-Redlich-Kwong,andPeng-Robinson-Stryjek-Vera,havebeentestedforevaluatingtheresidualHelmholtzfreeenergy.Themodelrequiresonlytwoadjustableparametersforeachpureliquid,ateachtemperature.Theparametershavebeendeterminedbyfittingliteratureviscositydataof49differentpureliquidcompoundsfrompressuresof0.1-250MPawithinthereducedtemperatureintervalof0.4-0.7.Theperformanceofthemodelhasbeenfoundtobeinsensitivetothechoiceoftheequationofstate,exceptatpressuresabove100MPaforwhichonlytheSoave-Redlich-Kwongequationofstatehasbeenabletodescribethevolumetricbehavioroftheliquids.Thestudiedliquidsaren-alkanes,substitutedalkanes,n-alkenes,cyclicalkanes,aromatics,alcohols,esters,1-butylamine,argon,nitrogen,oxygen,ammonia,andwater.Thecalculatedvaluesareingoodagreementwiththeexperimentalones.Thevalueoftheoverallaverageabsolutedeviation,forthe4380datapointscorrelatedwiththepresentmodel,is1.22%.

1.Introduction

Thetransportpropertiesoffluidsareoffundamentalimportanceforthedevelopmentandoptimizationofindustrialprocesses.Agreatamountofmodelsforestimatingpurefluidsandmixtureviscositieshaveappearedintheliterature.ThoroughdiscussionsaboutviscositycalculationmaybefoundintheworksofPolingetal.1andMonneryetal.2

Mostofthemethodsavailableforestimationoftheviscosityofpureliquidsandliquidmixturesarebasedontheprincipleofcorrespondingstates,3-5ontheabsoluteratetheoryofEyringandco-workers,6and,morerecently,onmoleculardynamiccalculations.7Nevertheless,fewofthemareappropriatetodescribetheviscosityoffluidsunderhigh-pressureconditionsand,frequently,thosethataresuitableforpurefluidcalculationscannotbereadilyextendedtomixtures.Themostreliablemixtureviscositymodelsrequiretheviscosityofthepurecomponentsasaninputparam-eter.2Therefore,thereisanincreasingdemandofaccuratemodelsforpureliquidviscosities,particularlyunderhigh-pressureconditions.

OnthebasisofthesimilaritybetweentheP-V-TandT-η-Pdiagrams,Guoetal.8developedmodelsfor

*Towhomcorrespondenceshouldbeaddressed.Tel.:(55)(21)25627172.Fax:(55)(21)25627265.E-mail:marcio@iq.ufrj.br.

UniversidadeFederaldoRiodeJaneiro.

UniversidadeFederalFluminense.Tel.:(55)(21)26207769.

thepressuredependenceoftheviscosityofpurefluidsandmixtures.TheviscosityequationsareobtainedbymeansofPatel-Teja9andPeng-Robinson10cubicequa-tionsofstate,insuchawaythatPandTareinter-changedintheexpressions,theviscosityreplacesthemolarvolume,andthegasconstantissubstitutedbyamodelparameter.ThemodelderivedfromthePeng-Robinsonequationdoesnotrequireanyadjustableparameterandisapplicabletohydrocarbonsandre-spectivemixtures.Itisalsosuitableforhigh-aswellaslow-pressureviscositycalculations.Forpuren-alkanes,anoverallaverageabsolutedeviation(AAD)of6.18%wasobtainedwiththePRviscosityequation.Usingclassicalandfluidmechanicconcepts,Qui-n ones-Cisnerosetal.11presentedanewmethodforviscositymodeling,calledftheory.Inftheory,viscosityistreatedasamechanicalpropertycomposedofadilutegascontributionandafrictionterm.RepulsiveandattractivepressuretermsfromcubicequationsofstateofthevanderWaalsfamily,likeSoave-Redlich-Kwong12andPeng-Robinson-Stryjek-Vera,13areusedinthedescriptionofthefrictioncontribution.Fiveadjustableparametersarenecessaryforeachpurefluid.Thismodelwastestedwithhydrocarbonsandrespectivemixturesoverwidetemperatureandpressureranges.Inthecaseofpurefluids,theoverallAADobtainedwas2.33%.Subsequently,thismodelwasgeneralized14bymeansofcorrespondingstatesconcepts.Besidesoneadjustableparameterforeachpurefluid,thegeneral-izedversionproposedbytheauthors14contains16

10.1021/ie021017oCCC:$25.00©2003AmericanChemicalSociety

PublishedonWeb07/02/2003

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