Kinetics and Mass Transfer of Free Fatty Acids Esterificatio(4)

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