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

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