Kinetics and Mass Transfer of Free Fatty Acids Esterification with Methanol in a

Ind.Eng.Chem.Res.2007,46,5113-51215113

KINETICS,CATALYSIS,ANDREACTIONENGINEERING

KineticsandMassTransferofFreeFattyAcidsEsterificationwithMethanolinaTubularPackedBedReactor:AKeyPretreatmentinBiodieselProduction

E.Santacesaria,*, R.Tesser, M.DiSerio, M.Guida, D.Gaetano, andA.GarciaAgreda DipartimentodiChimica,UniVersita`diNapoliFedericoII,ViaCintia80126Napoli,Italy,andASERS.r.L.,S.S.11PadanaSuperiore2/b,20063CernuscoS.N.,Milano,Italy

Biodieselcanbeeasilyobtainedstartingfromhigh-qualityorrefinedvegetableoilsandperformingonthesefeedstocksatransesterificationreactionusuallypromotedbyalkalinecatalystsinthehomogeneousphase.Inthisproductionschemetheemploymentoflow-qualityorwasterawmaterials,ascheapaspossible,mustbecarefullyconsideredtostronglyimprovetheeconomiccompetitivenessofthisbiofuelwithrespecttothepetroleum-deriveddiesel.Inthecaseofrawmaterialscharacterizedbyahighcontentoffreefattyacids(FFAs),apreliminaryesterificationtreatmentwithmethanolorethanolisnecessaryfortheabatementoftheFFAconcentrationbelowthethresholdlimitvalueof0.5-1.0%byweightthatistolerablebythesubsequentprocessstepofalkalinetransesterification.Inthepresentworktheesterificationreactionintubularpackedbedreactors,operatingunderpressureandusingasulfonicacidresinascatalyst,hasbeenextensivelystudied.Asitiswell-known,sulfonicexchangeresinsaresubjectedtoanimpressiveswellingphenomenon,anditisdifficulttoobtain,inthiscase,adimensionallystablepackedbedreactor.Aparticularsolutiontothisproblemhasbeenproposedbytheauthorsusingspringsofsuitablesizeandshapeascatalystdiluent.Theinfluenceofoperativeconditionslikeoverallfeedflowrate,reactantsfeedmolarratio,reactoraspectratioL/DR,andmixtureviscosityinthedescribedreactorshasbeeninvestigated.Thecollectedexperimentaldatahavebeeninterpretedbymeansofamono-dimensionalpackedbedreactormodelinwhichtheexternalmass-transferlimitation(fluid-to-particle)hasbeenaccountedfor.

Introduction

Biodieselproductionrepresentsoneofthemostattractivealternativestothetraditionaldieselfuelderivedfromapetroleumrefinery,especiallybyconsideringtherecentsteepincreaseinthepetroleumcost.

Thestandardbiodieselproductionprocessisbasedonatransesterificationreaction,normallycatalyzedbyalkalinehomogeneouscatalyst(suchNaOH,KOH,andrelatedalkox-ides),performedonhighqualityrefinedvegetableoilsfromwhichamixtureoffattyacidmethylesters(FAME)canbeobtained.1

Thenecessitytoimprovetheeconomiccompetitivenessofthisprocesswithrespecttopetroleum-deriveddieselfuelandtheincreasingglobalmarketdemandofbiodieselresultsinagrowinginteresttowardtheutilizationofwasterawmaterialsofbothvegetalandanimalorigin.Themainprobleminvolvedintheutilizationoftheselow-costrawmaterialsisrepresentedbythehighcontentoffreeacidity(freefattyacids,FFAs)thatmustbereducedbelowthethresholdlimitvalueof0.5-1.0%byweighttoensurethefeasibilityofthesubsequenttranses-terificationstep.AninterestingwayfortheabatementofFFAconcentrationisrepresentedbyanesterificationreactionusingmethanolorethanolforconvertingtheorganicacidstothecorrespondingmethylorethylesters.Theadvantageofusing

*Towhomthecorrespondenceshouldbeaddressed.E-mail:santacesaria@chemistry.unina.it. Universita`diNapoliFedericoII. ASERS.r.L..

theseshort-chainalcohols,besidestheirlowcostandeaseofrecovery,residesinthefactthattheyareusedalsoforthetransesterificationandarealreadyavailableintheplantsites.Inourpreviouswork2wehaveinvestigatedtheesterificationreactionofoleicacidwithmethanolonanacidionicexchangesulfonicresinascatalyst.WehaveconsideredoleicacidasamodelmoleculeassumedasrepresentativeofFFAmixtureactuallypresentinlow-costrawmaterials.Thereactionwasstudiedinawellmixedbatchreactoroperatedunderpressurewithcatalystdispersedintheliquidphase.

Oppositetotherelativelyhighavailabilityintheliteratureofbatchexperimentaldata,noinformationhasbeenreportedconcerningthepossibilitytoperformtheesterificationreactionoflongchainfattyacidswithmethanolinatubularpacked-bedreactorusingacidresinsascatalyst.

Acidresincatalystscanbeadvantageouslyusedinfixedbedreactorsforequilibriumreactionslike,forexample,theesteri-ficationofaceticacidandamylalcoholasreportedbyLeeetal.3Manyotherauthorshaveemployedapackedbedofresinparticlesaschromatographicoradsorptivereactorslike,asexamples,inthepaperofSilvaandRodriguez4forthesynthesisofdiethylacetalandofGelosaetal.5fortheesterificationofglycerolwithaceticacid.Themaindifficultyinusingresinpackedbedsascatalystarisesfromthehighswellingratiocommonlypresentedbyionicexchangeresinsthat,inatubularreactorconfiguration,givesplacetoreactorpluggingortoaveryhighpressuredrop.Thecontactoftheresinwithsolventslikemethanolandwatercanresultinavolumeincreaseofafactorof2-3,ifafreeexpansionisallowed.Inarecentpaper

10.1021/ie061642jCCC:$37.00©2007AmericanChemicalSociety

PublishedonWeb06/23/2007

5114Ind.Eng.Chem.Res.,Vol.46,No.15,2007

Figure1.Schemeoftheexperimentalapparatus.1,Tubularpackedbedreactor(TR1,TR2,orTR3);2,3,feedtemperaturemeasurements;4,outlettemperaturemeasurement;5,pressuremeasurement;6,liquid-phasetemperaturemeasurement;7,accumulationtank;8,bottomvalve;9,samplingvalve;10,nitrogenreservoir;P1,oilfeedpump;P2,methanolfeedpump;T1,T2,recirculationthermostaticbaths.

ofSteinigewegandGmehling6areactivedistillationapproachwasproposedforthesynthesisofdodecanoicacidmethylestersstartingfromdodecanoicacidandmethanol.ThecolumnwaspackedwithastructuredpackingKatapak-SPinwhichthecatalystwasAmberlyst15.Thehighvoidagedegreeofthereactivesectionallowsalow-pressuredropoperation,butarelativelyhighunitisnecessary(4mofreactivesectionplus2mforseparation),andamaximumconversionofdodecanoicacidof56%hasbeenobtained.

Veryrecentlywehaveproposedaninnovativesystemformitigatingtheswellingeffectoftheresin,7consistingintheuseofmetallicspringsofaparticularshapeandsizeascatalystdilutingtheinertmedium.Thespringsusedinthepresentworkweremadeofstainlesssteelhavingadistancebetweenthecoilwiressmallerthanthecatalyticresinparticlesdiameter.Byincreasingtheparticlediameter,asaconsequenceofswelling,thespringsarecompressed.Therefore,byopportunelychoosingthecatalyst/diluentratiowewereabletoobtainadimensionallystablecatalyticbedthatcanbeusedforalongtime-on-streamwithoutraisingtheproblemsofpressuredropincreasingorofreactorplugging.Theweightratiobetweenspringsusedasdiluentsandcatalystshouldbeintherange0.5-5ormore.Inourworktheadoptedweightratioofspring/catalystwas1.8.Inthepresentpaperthesameresincatalystusedinourpreviousworkonabatchreactor2(ReliteCFS)hasbeenusedforinvestigatingadifferentreactorconfiguration,tubularpackedbed,moresuitableforcontinuousindustrialoperation.Thefeasibilityoftheoperationinthetubularreactorshasbeenmadepossiblebytheuseoftheabove-mentionedcatalystdilutionapproach.Anextensiveexperimentalactivityhasbeencarriedoutwiththeaimofevaluatingtheinfluenceofdifferentoperativeconditions(totalfeedflowrate,methanol/oleicacidmolarratio)onthesystemperformancesintermsoffreeacidityreduction.Thecollectedexperimentaldatahavebeeninterpreted

bymeansofaplug-flowreactormodelinwhichapreviouslydeterminedkineticexpressionandtherelatedparameters2havebeenintroduced.Thekineticmodelconsistsinapseudo-homogeneoussecond-orderreversiblerateequationinwhichthecatalystconcentrationhasbeenexplicitlyconsidered.Coupledwithkinetics,alsotheexternalmass-transferlimita-tionhasbeenfoundrelevantforthisparticularsystemandhasbeenaccountedforinthemodel,8allowingasatisfactorysimulationoftheexperimentsperformedonthreedifferenttubularreactorsintheexploredrangeofoperativeconditions.Theexperimentallyevaluatedliquid-solidmass-transfercoefficientshavebeencomparedwiththevaluesobtainedfromliteraturecorrelations,andasatisfactoryagreementhasbeenfoundbyusinganeffectivediffusivityapproachbasedonbedporosityandtortuosity.Anattempttocorrelatetheexternalmass-transfercoefficientwiththeotheroperativeparameters,likebedinterstitialvelocity,mixtureviscosity,andreactoraspectratio,willconcludethepaper.ExperimentalSection

Apparatus,Reagents,andMethods.Aschematicrepre-sentationoftheexperimentalapparatusisreportedinFigure1.Continuousexperimentalrunshavebeenperformedattwodifferentreactorscales:(i)laboratorypackedbedmicroreactorindicatedwiththeacronymTR1and(ii)mini-pilotscalepackedbedtubularreactorswithtwodifferentL/DRgeometricratiosnamedTR2andTR3.ThegeometriccharacteristicsofthethreedifferentemployedreactorsarereportedinTable1.Inallthethreecasesavalueof1.8wasadoptedforthediluent/catalystweightratio.Moredetailsaboutthesizeandgeometryofthediluentcanbefoundelsewhere.7

Tubularfixedbedreactorswithdifferentsizeandaspectratio(L/DR)caneasilybeinterchanged,intheschemeofFigure

1,

Table1.GeometricCharacteristicsofCatalyticPackedBedsabedlengthbeddiameterL/DRcatalystinertdiluentreactorL(cm)D(cm)

ratioload(g)weight(g)

TR118.01.018.059TR270.02.528.0196356TR3

6.0

8.4

0.71

196

356

a

Note:forallthereactorsthebedporosityhasbeenestimatedas B)0.21.

Table2.PropertiesoftheCatalyst

commercialnameandproducerReliteCFSbyResindionmatrix

porouscopolymerstyrene-DVBfunctionalgroupssulfonicsacidity

3.6mequiv/gparticlesmeandiameter0.7mm

particlessizerange0.3-1.18mmtotalexchangecapacity

2.0equiv/Lmaximumoperatingtemperature140°C

bulkdensity0.840g/cm3pelletporosity

0.4

leavingpracticallyunalteredtherestoftheexperimentalapparatus.Allthereactorsusedhavebeenoperatedcontinuouslybyfeedingamixtureofacidifiedsoybeanoil(witholeicacid)andmethanolindifferentproportionsandwithadifferentoverallflowrate.OleicacidandmethanolarefurnishedbyCarloErba,bothatapuritylevelof99.9%byweight,whilesoybeanoilisacommerciallyavailableacidity-freeproduct.

Thetemperatureofthereactorhasbeenkeptconstantatapredefinedvaluebymeansofacirculationthermostat(HaakeS/F3,precision(0.1°C),andathermaloilflowedintothereactorjacket.Twothermocouples,placedatthereactorinletandoutlet,respectively,allowtheverificationofthesystemisothermalcondition.Theobservedtemperaturedifferencebetweentheinletandtheoutletwasofabout2°Cforalltherunsperformed.

Thereactoroutletstreamwascollectedinareservoirtank(totalvolume1liter)keptatthesametemperatureofthereactor.Thesystempressurehasalsobeenkeptconstantataprefixedvalue(usually6atmfortherunsat100°C)byusingasupplementarynitrogenstreamforadjustingmethanolvaporpressure.Thisarrangementensurethatmethanolismaintainedintheliquidstateavoidingflashphenomenathatcouldseriouslyaltertheflowpatternontocatalyticparticles(gas-liquidmixedflow,bypass,etc.).

Twopumpsareusedforfeedingseparatelyacidifiedsoybeanoilandmethanol.Anelectricalresistanceisusedforpre-heatingtheoilyphasetoavaluenearthereactiontemperaturewhilethemethanolphaseisfedatroomtemperature.Abedofglassspheres(bedheight10cm,spheresdiameter4mm)islocatedatthebottomofthetubularreactor,immediatelyabovethefeedingpoint,withthescopeofhomogenizingthetwoenteringphasesandheatingthematthereactiontemperature.Boththehotoilyphaseandthepre-heatingbedaresufficienttoheattheenteringmixturemethanol/oilatthedesiredtemperature.ThecatalyticbedislocatedjustabovethelayerofglassspheresandismadeofReliteCFSion-exchangeresin,forwhichthepropertiesarereportedinTable2,andbymetallicstainlesssteelspringsinaweightratioofabout1.8(diluent/catalyst).Forthebedvoidfraction B,avalueof0.21hasbeenestimatedbythefollowingprocedure:knownamountsofdiluentandcatalyst(inaratioof1.8byweight)havebeenmixedtogetherandintroducedinagraduatedcylinder,equippedwithastopperonthebottom.Methanolwasthenaddeduntilthebedwascompletelyfilled.Successively,methanolwasdrainedbythebottomofthecylinderandmeasured.Thevolumeof

Ind.Eng.Chem.Res.,Vol.46,No.15,20075115

collectedmethanolwasusedasanestimationofthebedbulkvoidfractionforthebedsofthethreereactorsTR1,TR2,andTR3,becausethethreereactorsarepackedinthesameway:aweighedamountofthemixturecatalyst/diluent,wettedwithasmallamountofneutralsoybeanoil,wasintroducedfromthetopofthereactor.Thepackingproceduresbeingthesame,weassumedthesamevalueofthebulkvoidfraction,0.21,foralltheusedreactors.Theobtainedestimationofthevoidfractionresultedasthemeanbyrepeatingthreetimesthepreviouslydescribedprocedurewithagoodreproducibility:0.20,0.21,and0.21.

Asamplelineequippedwithastoppingvalveislocatedattheexitofthereactorwiththepurposeofsampleswithdrawing.Theinstantaneousconversionofthesystemcanbeevaluatedbymeasuringtheacidityoftheoutletstreambyconventionalacid-basetitrationanalysis.2Foradirectevaluationoftheresidualacidity,incomparisontothatoftheinletoil,theunreactedmethanolisfirstevaporatedfromthecollectedsampleinawaythatthesuccessivetitrationfurnishesanacidityvaluereferencedtotheoilyphaseonly.Thefractionalconversionofoleicacidisthencalculatedas

X)

Ain-Aout

OAAin

(1)

Incorrespondencetoeachexperimentalrun,differentsamplesarecollectedandanalyzedattimeintervalsofabout0.5h.Thestationaryconditionforthereactorisassumedtobereachedwhentherelativedifferenceinaciditybetweenthreeconsecutivewithdrawnsamplesiswithin(2%.Theaverageacidityofthesethreelastsamples,collectedwhenthereactorhasreachedthesteady-stateconditions,representstheresultoftheexperimentalrun.Eachsetofexperimentalrunshasbeenperformedwiththesamecatalyst,andtheoperationofreactorpackinghasbeenmadeonlyonetimeatthestartoftheseriesofexperiments.Table3summarizestheoperativeconditionsadoptedforthetubularfixedbedmicroreactorTR1andtherelatedexperimentalresultsintermsofoleicacidconversion.ThesamekindofinformationisreportedinTable4forwhatconcernstherunsrelatedtopilot-scalereactorsTR2andTR3.ResultsandDiscussion

InternalDiffusion.Inourpreviouswork2wehaveproventhattheinternaldiffusionresistanceofresinparticles,intheconditionsadoptedforbatchruns,canbeneglected.Acom-parisonbetweenrunswithgranularandpowderedcatalystfurnishedavalueoftheeffectivenessfactorofmorethan0.96thatcanbeassumedsufficientlyclosetounitytoneglectthecontributionofinternaldiffusiontothereactionrate.Forthisreasonwehaveassumedavalueoftheeffectivenessfactorequalto1.

Ontheotherhand,relatedtothesameresinbutforadifferentreactivesystem,XuandChuang9havereportedaverydetailedanalysisontheevaluationoftheeffectivenessfactorandinternaldiffusionforapolymericresin(Amberlyst15)verysimilartothatusedinthepresentworkbutusedforaceticacidesterifi-cation.Thecitedauthors9havefoundthatforparticleswithanaveragesizebelow0.6mmtheeffectivenessfactorηisabove0.92.

Asafurtherconfirmationthatinourexperimentstheinternaldiffusiondoesnotrepresentalimitationonthereactionrate,theWeiszcriterion10hasbeencalculatedforsomerepresentativeexperimentalruns.Thiscriterionconsistsofthefollowingexpressionvalidforthesphericalisothermalcatalyticparticle:

5116Ind.Eng.Chem.Res.,Vol.46,No.15,2007

Table3.SummaryoftheExperimentalRunsPerformedwiththeLaboratoryPackedBedMicroreactor(TR1)ano.ofQtotWoilTPXOAksexptlruns(cm3/min)(g/min)(°C)(atm)(%)(cm/min)ReR12.71.48100628.20.004850.356R23.21.75100623.40.00460.422R33.82.08100619.30.004370.501R44.92.68100613.30.003750.646R58.14.44100610.50.00481.068R610.85.9210069.70.00591.424R713.57.4010067.70.00581.780R82.71.4885221.50.00360.004R93.21.7585221.90.00430.278R103.82.0885220.70.00480.331R114.92.6885216.90.00490.426R128.14.448528.90.00410.705R1310.85.928525.80.00350.940R1413.57.408522.20.00161.174R152.71.4865114.50.002350.124R163.21.7565111.70.00220.147R173.82.08651100.00220.175R184.92.686516.50.00180.225R198.14.446517.20.00340.373R2010.85.926514.30.00270.497R2113.57.406514.30.00330.621R222.71.485019.90.00160.071R233.21.755018.90.00170.084R243.82.085018.80.0020.100R254.92.685017.20.00210.129R268.14.445017.50.00280.213R2710.85.925014.90.00310.284R28

13.5

7.40

50

1

6

0.0031

0.355

a

TR1:beddiameter)1cm;bedheight)18cm;catalystweight)5g.Roil/MeOHIN)1.7(byvolume).Feedmixtureacidity)51%byweightofoleicacid.

Table4.SummaryoftheExperimentalRunsPerformedwithMini-PilotScalePackedBedTubularReactors(TR2andTR3)aQtotinitialWoilno.of(cm3/acidity(g/Roil/MeOHINXOAksexptlrunsmin)(%bywt)min)(byvol)(%)(cm/min)ReR29b43.841.023.71.6463.40.00560.895R30b21.441.011.71.6875.20.003890.437R31b43.847.023.71.6472.50.007420.895R32b71.147.039.41.7549.50.006171.453R33b21.441.511.71.6873.00.003640.437R34b21.414.911.71.6890.20.006250.437R35b6.448.63.51.6783.30.00160.131R36b2.748.61.51.791.00.001050.055R37b2.748.61.51.791.00.001050.055R38b14.448.611.713.423.40.000780.294R39b21.448.611.61.6770.50.003430.437R40b16.446.411.74.46750.40.001680.335R41b16.442.811.74.4750.20.001640.335R42b18.442.811.72.6854.70.001930.376R43b14.146.17.71.7183.70.003560.288R44b16.842.99.21.7176.70.003230.343R45b14.148.87.71.7180.20.003130.288R46b16.848.89.21.780.80.003810.343R47b18.349.1101.6978.30.00380.374R48b21.148.211.61.7175.90.004020.431R49b1844.07.70.9683.30.00410.920R50b1842.6101.7774.60.003250.736R51b1840.811.62.8366.50.002690.613R52b1839.014.61419.10.000690.368R53c1838.810.01.7756.80.001920.067R54c1838.413.1533.30.001020.041R55c

18

38.5

14.6

14

7.8

0.00026

0.034

a

Temperature)100°C,pressure)6bar.bTR2:beddiameter)2.54

cm;bedheight)70cm;catalystweight)196g.cTR3:beddiameter)8.4cm;bedheight)6cm;catalystweight)196g.

r*R2

pCD<0.6(2)

0eff

Table5.ResultsoftheApplicationofWeiszCriterionforthePresenceofInternalDiffusionaresultofWeiszresultofWeiszrunnumbercriterion

runnumber

criterion

R290.642R410.190R300.372R420.233R310.734R430.273R320.814R440.298R330.361R450.261R340.446R460.314R350.123R470.331R360.057R480.370R370.057R490.347R380.078R500.310R390.349R510.277R40

0.191

R52

0.079

a

Otherparametersforthecalculation:D)3.19×10-4cm2/min; p)0.4;σ)0.8;τP)3;Deff)3.4×10-5cm2/min;andRp)0.045cm.

wherer*istheobservedreactionrateperunitofparticlesvolume,Rpistheaverageparticleradius,C0isthereactantsurfaceconcentration,andDeffistheeffectivediffusivity.ThemainprobleminapplyingthiscriteriontoourspecificsystemistheevaluationofDefffromthefollowingexpression:8

DD pσeff)

τ(3)

P

whereDisthemoleculardiffusioncoefficient, pispelletporosity,σisthepelletconstrictionfactor,andτPistheintraparticletortuosityofthecatalyticparticle.Whiletheparameters p,σ,andτPcanbetakenfromliteratureasapproximatedvalues,8therigorousestimationofDinamulticomponentmixtureisratherdifficultandtheresultcanbeaffectedbyarelevantuncertainty.Asanexample,ageneralizedWilke-Changcorrelationcanbeemployedfortheevaluationofliquid-phasediffusioncoefficientofsoluteAinamixture:4

NC

0.5DjφjMwj)TA,M)7.4×10-8

∑(x(4)

j)1

j*A

µ(VA)

0.6

Inthisexpression,xjaretheliquid-phasemolefractions,φjaretheassociationfactors,Mwjarethemolecularweights,Tistheabsolutetemperature,µisthemixtureviscosity,andVAisthemolarvolumeofthesolute.Thediffusioncoefficientofoleicacid,inamixturewithanaveragecomposition,hasbeenestimatedbyusingrelation4andhasbeenconsideredconstantalongthecatalyticbed.

TheresultsobtainedarereportedinTable5andarereferencedtothesetofrunsperformedinthepilot-scalereactorTR2.Thecalculationsarerelatedtoabedofparticleswithauniformsizeof0.9mmofdiameter.Thisassumptionisconservativeforwhatconcernsparticlesize,therealsizesdistributionbeingmoreshiftedtowardsmallerparticlesforwhomthediffusionlimitationisoflessimportance.Theapproximatedvalueof3fortheparticletortuosityhasbeenassumedinagreementwiththevaluereportedbyFogler.8Practicallyinalltheexaminedcases,despitetheintroducedapproximations,thecriterionisfulfilled(valuesarelessthan0.6)orisattheborderlineforafewruns,andthis,consideringtheapproximationsintroduced,confirmsthenegligibilityofparticlesinternaldiffusionaspreviouslyevi-denced.2

StandardTubularReactorModel.Afirstapproachinmodelingtheexperimentalresultscollectedforvariousreactors

Table6.KineticEquationandParametersfromReference2a

KineticEquation

reaction:oleicacid+methanolTmethyloleate+waterr)kcxAxM{1-(1/ke)[(xExW)/(xAxM)]}Ccat

activationpre-exponentialenergyheatofreactionparameter

factor(k0)(Ea;kcal/mol)( Hr;kcal/mol)

kc12.93(2.8714.00(0.99

ke

4.17(0.04

2.68(0.05a

Subscripts:A,oleicacid;M,methanol;E,methyloleate;andW,water.Units:kc(moldm3)/(gcat2min);Ccat(gcat/dm3);r(mol/(gcatmin)).

hasbeenmadebyusingasimplifiedreactormodelinwhichthekineticspreviouslydetermined2hasbeenintroduced.InTables3and4arereportedtheaverageReynoldsnumberscalculatedforeachexperimentalrun.Asitcanbeobservedthesevaluesareverylow,andintheseconditionstheflowthroughtheporousmediumisveryprobablyinthecreepingflowregime.12Inthisconditiontheplugflowmodelisnotrigorous;onthecontrary,anaxialdispersionmodelcouldbemoresuitable.Nevertheless,theroughapproximationoftheplugflowreactorhasbeenadoptedforafirsttestingofthepreviouslydeterminedkineticsinthedescriptionofthepresentexperimentaldatacollectedfortubularreactors.Ontheotherhand,Seguinetal.12haveshownamaximumrelativedeviationof10%betweenthepurelyplugflowandtheaxialdispersionmodelsincreepingflowconditions.Theuseofasimplerapproachis,therefore,justifiedasapreliminaryone,consideringboththescatteringofexperimentaldataandtheintroducedapproxima-tions.Moreover,thefluiddynamicbehaviorofacomplexsystemliketheoneusedinthisworkcontainingamixtureofspheresandspringsinthepackedbedisneverdescribedintheliterature.

Referringtoanisothermalplug-flowreactor,thedifferentialmaterialbalanceequationforeachcomponentinthesystem(excludingtriglyceridethatisaninertmedium)canbewrittenas

dFi

dW)Viri)A,M,E,W

(5)

cat

whereFiisthemolarfeedflowrateoftheithcomponent(lettersmeaningA,oleicacid;M,methanol;E,estermethyloleate;W,water),Wcatisthetotalweightofcatalystloadedinthereactor,Viisthestoichiometriccoefficientreferencedtotheithcomponent,andristhereactionrate(seeTable6forparameters,units,andotherdetails).Thenumericalintegrationofthedifferentialequationssystem5,inwhichtheexpressionforrtakenfromourpreviousworkhasbeenintroduced,2resultsincalculatedperformancesthataremuchhigherthanthoseexperimentallyobservedforthethreetubularreactors.Thismeans,inotherwords,thatthepackedbedreactorconfigurationfurnishesalowerconversionwithrespecttothatpredictedonthebasisofthekineticsexperimentallyevaluatedinabatchwellstirredslurryreactor(batchWSSR).ThisparticularbehaviorisreportedinFigure2whereacomparisonisshownbetweentheexperimentalconversionofoleicacidobtainedintherunswiththereactorTR2(squaressymbols)andtheconversionpredictedbythemodelrepresentedbyrelation5(opencirclesymbols).Theconversion,inbothcases,isreportedasafunctionoftheoverallvolumetricfeedflowrate,anditisevidentfromthediagraminFigure2thatthekinetic-basedmodelpredictsahighconversionthatispracticallyinsensitivetotheincreaseinfeedflowratetowhichcorrespondsadecrease

Ind.Eng.Chem.Res.,Vol.46,No.15,20075117

parisonbetweentheexperimentalconversionintubularreactorTR2andthepredictionofthetubularreactormodelbasedonapreviouslydevelopedkineticsfrombatchexperiments.2

inresidencetime.Theexperimentaldatareportedarerelativelyscattered,thevaluesreportedintheplotbeingtheonesobtainedinsteady-stateconditionsafteralongtimeoperation(somehours).Scatteringisduetothefluctuationoftheoperativeconditionssuchasflowrates,temperature,andanalyses.Theflowrateatwhichthemodelstartstopredictadecreaseoftheconversionofoleicacidwasestimatedatabout5000cm3/min.Inthekineticmodelthereactorperformancesarehighenoughthatthesystemreachestheequilibriumcompositionnearlyinalltherunssimulated.Excludinginthissystemtheinfluenceoftheinternaldiffusion,wehavefocusedourattentiontotheinterventionofexternalfluid-to-particlemass-transferlimita-tions.Thefollowingsectionsofthepaperarethendevotedtothefurtherdeepeningofthisaspect.

ExternalDiffusion.Withthepurelykineticmodel(eqs5)unabletocorrectlydescribetheexperimentallyobservedbehaviorofthetubularreactors,anevaluationoftheexternalliquid-soliddiffusionalresistancehasbeenmadebyadoptingthegeneralizedcriterionofMears.11Thiscriterion,referencedtoanisothermalcatalyticpelletandtoann-orderreactionrateequation,isexpressedbythefollowingrelation:

r*RpC<0.15

(6)

0ksn

whereksisthefluid-to-particlemass-transfercoefficient.This

lastparameterhasbeenestimatedinanapproximatedwaybymeansoftheCoeuretcorrelation12,13expressedbythefollowingrelation:

Sh)5.4Re1/3Sc1/4

0.04<Re<30(7)

Thisexpressionhasbeenchosen,amongthewidecorrelationsavailableintheliteratureasreportedinref12,becauseitismoresuitableintermsoflinearvelocity(seethevaluesofReynoldsnumbersreportedinthelastcolumnsofTables3and4)andparticlesizerangesofapplicability.12Thiscorrelationisveryprobablynotfullysuitableforthepackedbedsusedinourexperimentsbecauseitwasoriginallydevelopedforpackedbedsofspheres,while,asmentioned,ourpackinghasamorecomplicatedstructurebeingcomposedofbothparticlesofvarioussizeandofmetallicsprings.However,wehavedevelopedourcalculationalsowithothersimilarcorrelations

5118Ind.Eng.Chem.Res.,Vol.46,No.15,2007

Table7.ResultsoftheApplicationoftheMearsCriterionforthePresenceofExternalDiffusiona

runnumber

ksfromcorrelation

resultofMearscriterion

R290.003601.263R300.003610.730R310.003571.457R320.003601.602R330.003610.709R340.003750.842R350.003570.245R360.003580.112R370.003580.112R380.004900.113R390.003560.694R400.004150.326R410.004180.322R420.003850.428R430.003590.538R440.003610.585R450.003580.518R460.003580.621R470.003570.657R480.003580.732R490.003380.727R500.003630.606R510.003890.503R52

0.00512

0.210

a

Otherparametersforthecalculation: B)0.21;σ)0.8;τB)3;andRp)0.045cm.

reportedinthereviewofSeguinetal.12withoutsignificantdifferencesintheresults.

Intheexpression7anaveragediffusioncoefficientforthemixture(embeddedintotheSherwood’snumber)hasbeenevaluatedbymeansoftherelation4.Byvaryingtheconversionfromzerototheoutletexperimentalvalueacompositionprofilealongthereactorhasbeengeneratedand,incorrespondencewitheachcomposition,adiffusioncoefficientofoleicacidDA,Mixhasbeenevaluatedandaveraged.Thediffusioncoef-ficientinthemixturehasthenbeencorrectedbytakingintoaccounttheporosity,tortuosity,andconstrictionfactorrelatedtothewholebedasmadepreviouslyforthesingleparticle(seeeq3):

Deff,B)

DA,Mix Bσ

τ(8)

B

Thisapproximationcanbejustifiedbyconsideringthereductionindiffusivityoccasionedbythenondirectflowpathcharacteristicofthefixedbed,10particularlyinthecaseoflow-porositybeds(inourcaseexperimentallyevaluatedandresultingin B)0.21),probablyoriginatedfromaratherwideparticlesizedistributionandatverylowReynoldsnumbers12inconditionsofcreepingflowregimeofviscousfluid.Theunusuallylowbedporositymeasuredcanprobablybeduetothespatialcollocationofsmallresinparticlesinsidethespringsusedascatalystdiluentresultinginalow-voidagebedstructure.Despitethisbedcharacteristic,thefluidflowwasnothinderedandthereactorhasbeenoperatedforseveralweeks,includingstart-upandshut-down,withoutpressuredropincrease.

Theeffectivediffusivityapproach,relatedtothewholebed,canbefurtherjustifiedbyconsideringtheverythinchannelsspacingavailabletofluidflowacrossthebedandtotherelativelyhighviscosityandlowlinearvelocities.Intheseconditionsthethicknessofstagnantfilmsurroundingtheparticles,throughwhichdiffusionalresistancesareoperative,isprobablyofthesameorderofmagnitudeofthechannelsinwhichthecreepingflowregimeisestablished.InTable7arereportedtheresultsoftheapplicationoftheMearscriterion,forwhichalimitvalueforneglectingtheinterventionoffluid-solidmass-transferlimitationis0.15,togetherwiththevaluesofthekscoefficientasobtainedfromCoeuretcorrelation(eq7).Aswecanobservefromthementionedtable,theinfluenceofthistypeofresistancecannotbeexcludedandmustbeproperlytakenintoaccountinthereactorsimulationmodelforthedescriptionofourexperimentaldata.

ModelConsideringtheExternalDiffusionLimitation.Withtheaimofintroducingthefluid-solidmass-transferresistance,eq5mustbemodifiedasfollows:8

-U

dCi

dz

+JS,iaS)0i)A,M,E,W(9)

whereUisthefluidlinearvelocity,zistheaxialreactorcoordinate,Ciisthebulkconcentrationofcomponenti,aSisthespecificsurfaceareaofcatalystperunitofbedvolume,andJS,iisthemass-transferrate.Thislastvariablerepresentstherateatwhicheachcomponentistransferredfrombulkliquidtothesolidsurfaceor,reversely,fromthecatalystsurfacetothebulkofliquid.AsuitableexpressionforJS,iisthefollowing:

-JS,i)ksi(Ci-CSi)

(10)

Inthisexpressionksiisthemass-transfercoefficientreferencedtoliquid-soliddiffusionaltransportresistanceandCiSistheconcentrationofcomponentievaluatedattheliquid-solidinterface.Accordingtotheseassumptionsrelation10canbesubstitutedintoeq9toyieldanordinarydifferentialequation(ODE)system:

-U

dCi

dz

)ksiaS(Ci-CSi)i)A,M,E,W(11)

Byassumingthatthepseudo-steady-stateconditionisfulfilledatthecatalyst-fluidinterface,theamountofeachcomponenttransferredbydiffusionmustbeequaltotheamountconsumedorformedbychemicalreaction.Inotherwords,thesurfaceaccumulationtermforeachcomponentisassumedasnegligibleandthefollowingexpressionsetcanbewritten:

ksiaS(Ci-CSi)-rFcat)0

i)A,M,E,W(12)

whereFcatisthecatalystconcentrationinthebed,expressedascatalystweightperunitofbedvolume.Theequationsinrelation12mustbesolvedsimultaneouslyateachintegrationstepintimeofODEsystem11togivethevaluesofsurfaceconcentra-tions,forallthecomponents.ThereactionrateexpressionisalsoreportedinTable6but,inthiscase,theconcentrationsaretakenatthecatalyst-liquidinterface.Moreover,fromageneralpointofview,eachcomponentischaracterizedbyitsownmass-transfercoefficientksi.

Themass-transfer-limitedreactormodel,representedbythedifferential-algebraicsystem(eqs11and12),hasbeenappliedtothedescriptionofthethreeexperimentaldatasetsrelatedtotheusedtubularreactors.Themodelhasbeensolvediteratively,andtheexternalmass-transfercoefficienthasbeenconsideredasanadjustableparameterthathasbeenvaried,ineachrun,toreproduceexactlytheexperimentalconversion.Inthisapproachtheksivaluescanbeconsideredasexperimentalvaluesforthemass-transfercoefficientwiththemainassumptionthattheentireeffectoflowerperformances,withrespecttoapurelykineticmodel,isattributedtotheexternalmass-transferresistance.Intherealsituationothereffectsareoperativeandsuperimposed

Figure3.ExperimentalksvaluesobtainedforthetubularreactorTR1asafunctionoftheoverallvolumetricfeedflowrate.(Valuesobtainedatafixedvolumetricflowrateratioofoil/methanolof1.7;T)100°

C.)totheconsideredexternalmass-transferphenomena,likeaxialandradialdispersion,flownonidealityandmaldistribution,bypass,andsoforth,butareconsideredasnegligible(alsobyconsideringtheuseofmetallicspringsasdiluent)andlumpedintotheonlykeyparameterks.Afurthercomplexityofourparticularsystemisrepresentedbythevariationinphysicalpropertiesofamixtureoccurringfromtheinletofthereactor,wheretheenteringmixtureisanemulsionoil/methanol,totheoutlet,wherethepresenceofahomogeneousphasewasobservedasaresultofoleicacidconversiontoitsmethylesterresultinginabettercompatibilitybetweenmethanolandtriglyceride.Aratherremarkabledecreaseofmixtureviscosityalongthereactorshouldalsobeexpectedbecause,foroleicacidandthecorrespondingmethylester,aratioofabout3hasbeenestimatedfortheirviscosityat100°C.Thementionedpeculiaritiesofthesystemunderinvestigationandthelackofliteraturedataonthemethanol/trigliceridesmixtureshinderarigorousmodelingapproachforwhichmanynewexperimentaldatashouldbenecessary.

Numerouscorrelationshavebeenproposedintheliteraturefortheevaluationofksforpackedbedreactorsandcolumnsoperatedinawiderangeofconditions.12-15Theapplicationofthesecorrelationsrequirestheknowledge,asseenbefore,ofmixturepropertieslikeviscosityanddiffusivitywhoseevalu-ationisfrequentlyaffectedbyasignificantuncertainty,espe-ciallyforacomplexmixtureofcomponentsforwhichphysicaldataarescarce.Inourparticularsystemthemixturechangesincompositionandphysicalpropertiesfrominlettooutletofthereactor,andarigorousmodelshouldaccountforthisvariation.Inthemodelrepresentedbyeqs11and12,aconstantvalueofksalongthereactoraxishasbeenintroducedwithafurtherroughapproximationthatthesamevalueisusedforthefourcomponents(oleicacid,methanol,water,andmethyloleate);thatis,ksi)ks.InTables3and4,inthelastcolumn,theseevaluatedvaluesofksarereported.InFigures3and4theexperimentalvaluesofksarereported,forthetwotubularreactorsofdifferentsizeTR1andTR2,asafunctionoftheoverallfeedflowrate.InthecaseofthesmalltubularreactorTR1thedataaremorescatteredprobablybecauseofthefluctuationsinmaintainingtheverylowflowrateadoptedforthissetofruns.Nevertheless,fromtheseplotsitisevidentthatageneralincreaseofmass-transfercoefficientisfound,andthismeansthatthesystembecomeslesslimitedfromtheexternaldiffusionastheflowrateisincreasedandthevelocitiesacrossthebedincreasedtoo.Thistrendisvalidatafixedvolumetric

Ind.Eng.Chem.Res.,Vol.46,No.15,20075119

Figure4.ExperimentalksvaluesobtainedforthetubularreactorTR2asafunctionoftheoverallvolumetricfeedflowrate.(Valuesobtainedatafixedvolumetricflowrateratioofoil/methanolof1.7;T)100°

C.)

Figure5.ExperimentalksvaluesobtainedforthetubularreactorsTR2andTR3asafunctionoftheoil/methanolvolumetricflow-rateratiointhefeed.(Valuesobtainedatafixedoverallflowrateof18cm3/min;T)100°C.)

ratioofacidicoil/methanol;otherwise,bychangingthisratioandmaintainingaconstantoverallflowrate,themixtureviscosityisaltered,andadifferenttrendforksisexpected.AnexampleofthisbehaviorisreportedinFigure5forthetworeactorsofcontainingthesameamountofcatalystTR2andTR3butdifferingonlyintheaspectratioL/DR.Thesetwodevicesshowsubstantiallythesametrendinwhichadecreaseofmass-transfercoefficientisfoundincorrespondencetoanincreaseintheacidicoil/methanolfeedflowrateatafixedoverallflowrate.Inthiscase,theincreaseofthementionedratiocorrespondstoanincreaseinthemixtureviscosityand,consequently,inalowerandmorelimitingvalueofks.Moreover,itisinterestingtoobservethebehaviorofthetworeactorsTR2andTR3incomparison.Inparticular,thereactorTR3ischaracterizedbyarelativelyhighcross-sectionalareaand,forthesamefeed,bylowerlinearflowvelocities.Thevaluesfoundforfluid-solidmass-transfercoefficientsarethenrelativelylower(seeFigure5),andlowerisconsequentlytheconversionobservedforthereactorTR3comparedtothatofreactorTR2operatinginthesameconditionsoftemperature,feedflowrate,andfeedcomposition.

InFigure6acomparisonisreportedbetweentheexperimentalconversiondata,forreactorTR1,andthemodel(eqs11and12)inwhichamass-transfercoefficientderivedfroma

literature

5120Ind.Eng.Chem.Res.,Vol.46,No.15,2007

parisonbetweenexperimentalandcalculatedconversionintubularreactorTR1at65and100°

C.

parisonbetweenexperimentalandcalculatedconversionintubularreactorTR2at100°C(runs:1,4,8,11,15,16,22).

correlationofCoeuret12,13isintroduced.Thecalculationofcoefficientksisbasedonamoleculardiffusivityevaluationthrougheq4andaglobalorbed-basedeffectivediffusivitywitheq9.Despitethelargeapproximationsintroduced,theagreementbetweentheexperimentalconversionandthemathematicalmodelseemssatisfactoryandasimilaragreementhasbeenfoundalsoforthereactorTR2,asreportedinFigure7.

InFigures6and7isreportedalsotheoleicacidconversioncalculatedwithamodifiedcorrelationbasedontheCoeuretexpressioninwhichthenumericalvaluesoftheconstantsandexponentshavebeenre-evaluatedbymathematicalregressiononalltheexperimentsperformedatT)100°Cforthethreedifferentreactors.Theobtainedexpressionisthefollowing:

Sh)0.256Re0.54Sc0.46

0.004<Re<1.78(13)

Thisexpression,obviously,hasonlyalimitedvaliditybeingdevelopedonlyforourparticularpackingstructure.Withinthisperspective,theexponentsappearingineq13cannotbeattributedtoaprecisefluid-dynamicsignificanceforthecomplexityofthesystemexaminedinwhichthesphericalparticlesaresurroundedbyspringcoils.Therangeofvalidity,intermsofReynoldnumber(0.004<Re<1.78),hasbeenevaluatedbytakingtheminimumandthemaximumofthecalculatedReasreportedinTables3and4.

Equation13forevaluatingtheexternalmass-transfercoef-ficienthasbeenusedforsimulatingtheexperimentsforthereactorsTR1andTR2,andthecorrespondingperformancesarereported,respectively,inFigures6and7asdashedlines.ForwhatconcernsthetubularreactorTR1,thediscrepancybetweenthemodifiedcorrelationandtheexperimentaldataintherangeofverylowflowratecanbeattributedtothedifficultyinmaintainingaconstantfeedinthisrangeofflowrates.However,ageneralimprovementinthedescriptionofourexperimentaldata,withrespecttotheoriginalcorrelationofCoeuret,hasbeenobtained,andthisrepresentsanencouragingfinding,mainlyintheperspectiveofusingthismass-transfercorrelationinafuturescale-uptowardapilotorindustrial-sizeoperationforthedescribedtubularreactorhavingspringsascatalystdiluent.Conclusions

Thefeasibilityofacontinuousesterificationpretreatmentwithmethanolofhigh-aciditywasteoils,usefulinthebiodieselproductionscheme,hasbeeninvestigatedbyusingthreedifferenttubularpackedbedreactorsoperatingunderpressureformaintainingtheoil/methanolmixtureintheliquidstate.Asubstantialimprovementinpackedbedstabilityanddurabilityhasbeenobtainedbyadoptingasuitablecatalystdiluentasrecentlyclaimedinaworldpatentbytheauthors.

Reactionrateparametersandkineticexpressions,previouslyevaluatedfrombatchexperiments,havebeenintroducedinatubularreactormodelinwhichtheexternalmass-transferresistancehasbeentakenintoaccount.Thevaluesofthefluid-to-particlemass-transfercoefficient,determinedfromexperi-mentalruns,havebeenfoundingoodagreementwiththevaluesobtainedfromaliteratureempiricalcorrelationinwhichanoverallreactoreffectivediffusivityhasbeenadopted.

Theeffectofoperativeconditionsliketemperature,overallvolumetricfeedflowrate,andreactantsfeedratiohasbeenstudied.Thetemperaturehastheobviouseffectofimprovingthereactionrate,butthiseffectiscoupledwiththatofloweringthemixtureviscositywiththeconsequentbenefitofloweringthemass-transferresistance.Forwhatconcernsfeedflowrateandcomposition,thefirstaffectstheconversionintwoways:anincreaseinfeedflowratelowerstheresidencetimeandthecorrespondingconversion,butinopposite,anincreaseofthisflowrateimprovesthefluid-particlemass-transfercharacter-isticsofthesystem.Thereactantratiointhefeedcanstronglyaffectthereactorperformances,notonlyforthemethanolmolarexcessbutalsomainlyforthestronglydecreasingviscosityofthemixture.

Asafinalremark,inalltheperformedexperimentalrunsandparticularlyforthereactorTR3,theadoptedlinearvelocitiesacrossthecatalyticbedareverylow,andacreepingflowregimeislikelyestablished.Intheseconditionsthethicknessofthestagnantlimitinglayer,throughwhichmass-transferoccurs,resultsincreased,andthecorrespondentlimitationwasmorepronounced.Byconsideringtheseaspectscharacterizingoursystem,are-parametrizationofaliteraturecorrelationfortheliquid-solidmass-transfercoefficienthasbeenmadewiththeaimtoprovidebasictools,evenoflimitedvalidity,forafuturereliablescale-upoperationofourparticularpackedbedtoanindustrialsize.Nomenclature

Fi)molarfeedflowratefortheithcomponent(mol/min)r)reactionrate(mol/(mingcat

))

r*)observedreactionrateperunitofparticlesvolume(mol/(mincm3))

Wcat)catalystweight(g)

XOA)fractionalconversionofoleicacid

Ain,Aout)acidity(%bywt)oftheinletandoutletstreams(wt%)

Qtot)overallvolumetricfeedflowrate(cm3/min)L)bedlength(cm)DR)beddiameter(cm)Rp)particleradius(cm)

xi)liquidphasemolefractionofcomponentiφi)associationfactorforcomponentiT)absolutetemperature(K)µ)viscosity(g/(cmmin))

Vi)molarvolumeofcomponenti(cm3/mol)W)weightofcatalystloadedinthereactor(g)η)catalysteffectivenessfactor

Vi)stoichiometriccoefficientofcomponentiMw)i)molecularweightofcomponenti(g/mol)C0concentrationattheparticlesurface(mol/cm3)

CiS)concentrationofcomponentiattheparticlesurface(mol/cm3)

Ci)concentrationofcomponenti(mol/cm3)z)reactoraxialcoordinate(cm)as)specificsurfacearea(cm2/cm3)JS,i)mass-transferrate(mol/(mincm2))U)linearvelocity(cm/min)

Deff)effectivediffusivity(cm2/min)Deff,B)effectivediffusivity(cm2/min)

D,DA,Mix)moleculardiffusivityofcomponentAinmixture(cm2/min)

p)particleporosity B)bedporosity

Fcat)catalystdensity(g/cm3)

σ)constrictionfactor(particleorbed)τP)intraparticletortuosityfactorτB)bedtortuosityfactor

ks,ksi)externalmass-transfercoefficient(cm/min)Sh)SherwooddimensionlessnumberSc)SchmidtdimensionlessnumberRe)Reynoldsdimensionlessnumber

Roil/MeOHIN)volumetricratioofacidicoiltomethanolinthefeed

xA)molefractionofoleicacidinthereactionmixturexM)molefractionofmethanolinthereactionmixturexE)molefractionofmethyloleateinthereactionmixturexW)molefractionofwaterinthereactionmixture

Ind.Eng.Chem.Res.,Vol.46,No.15,20075121

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ReceiVedforreViewDecember20,2006ReVisedmanuscriptreceiVedMay7,2007

AcceptedMay15,2007

IE061642J

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