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

))