Stoichio-kinetic modeling and optimization of chemical synthesis Application to aldolic condensation

Stoichio-kineticmodelingandoptimizationofchemicalsynthesis:Applicationtothealdoliccondensationoffurfuralonacetone

NadimFakhfakha,PatrickCogneta,∗,MichelCabassuda,

YolandeLucchesea,ManuelD´ıasdeLosR´ıosb

a

LaboratoiredeG´enieChimique,UMR5503CNRS,INPT(ENSIACET),UPS,5ruePaulinTalabot,BP1301,31106ToulouseCedex1,France

bCubanResearchInstituteforSugarCaneByproducts(ICIDCA),P.O.Box4026,HavanaCity,Cuba

Availableonline16January2007

Abstract

Thecondensationreactionoffurfural(F)onacetone(Ac)givesahighaddedvalueproduct,the4-(2-furyl)-3-buten-2-one(FAc),usedasaromainalcoholfreedrinks,ice,candies,gelatinesandotherproductsofcurrentlife.Thissynthesisvalorisestheresiduesofsugarcanetreatmentsincefurfuralisobtainedbyhydrolysisofsugarcanebagassefollowedbyvaportrainingextraction.Inthefaceofnumerousandcomplexreactionsinvolvedinthissynthesis,itisverycomplicatedtodefinethekineticlawsfromexactstoichiometry.Asolutionallowingtocopetheproblemconsistsinidentifyinganappropriatestoichiometricmodel.Itdoesnotattempttorepresentexactlyallthereactionmechanisms,butproposesamathematicalsupporttointegrateavailableknowledgeonthetransformation.Theaimofthisworkisthedeterminationofstoichiometricandkineticmodelsofthecondensationreactionoffurfuralonacetone.Concentrationsofreagentsandproductsaredeterminedbygasandliquidchromatography.Concentrationprofilesobtainedatdifferenttemperaturesareusedtoidentifykineticparameters.ThemodelisthenusedfortheoptimizationoftheproductionofFAc.Theinterestofsuchtoolisalsoshownforthescaleupoflaboratoryreactortoalargescale.Theanticipationofthereactionbehaviourinlargescaleiscrucialespeciallywhenthereactorpresentsimportantlimitationsofthermalexchangecapacity.©2007ElsevierB.V.Allrightsreserved.

Keywords:Furfural;Acetone;Chromatography;Aldoliccondensation;Batchreactor;Stoichio-kineticmodeling

1.Introduction

Chemicalindustriesofindustrializedcountriesturnincreas-inglytoproductswithhighaddedvalue,especiallyinthesectoroffinechemistry(pharmaceuticalproducts,cosmetics,etc.).Thistypeofindustry[1–3]isdifferentfromtraditionalchem-icalindustry.ThefinechemicalindustrylikeinFranceiswellknowntobeastrategicareawhichneedsalotofinvestmentsnotonlyfinancialbutinhighlevelscientificknowledgefortheR&D.Thesynthesesofsuchproductsaregenerallycomplexandinvolvesecondaryreactionswhicharetobeminimized.Inthisfield,thefasterdevelopmentofprocessesisessen-tialinordertoanswertherapidevolutionsofthemarket.Thedetailedstudiesofthemechanismsandkineticsofreactionsaregenerallynotcarriedoutforreasonsofdurationandcost.Nev-ertheless,foroptimizationandadvancedcontrolofprocesses

∗

Correspondingauthor.Tel.:+33534615260;fax:+33534615253.E-mailaddress:Patrick.Cognet@ensiacet.fr(P.Cognet).

offinechemistry,itisnecessarytoobtainareliablemodelofthesystem.Thisproblemisoftencircumventedbytheuseoflinearorquadraticpolynomialmodelswhichparameterscanquicklybeidentifiedbytheinstallationofexperimentalplan-ning[4].Nevertheless,thesemodelsrapidlyfindtheirlimitsinarestrictedfieldofvalidityandadifficultyofaccountingforthedynamicsofthesyntheses.

Sincefinechemicalreactionsareusuallycomplex,theirskineticsarepoorlyknown.Therealproblemisthefastdevel-opmentofrealisticandsafetystoichio-kineticmodelsofthesynthesis[5–8].However,duetohighpurityrequirements,environmentalregulationandcompetitivepressureonthenewproducts,thedevelopmentofdynamicmodelshasbecomeanimportantobjective.

Theapproachproposeddoesnotdependonadetailedandpredictivemodeloftheprocessandatthesametimeitdoesnotignorewhatwealreadyknowabouttheprocess,suchasmaterialbalances,heatandmasstransfercharacteristics,etc.Nevertheless,astoichiometricmodelshoulddescribethediffer-entstagesofthesynthesis,orthemostimportanttendencies.It

0255-2701/$–seefrontmatter©2007ElsevierB.V.Allrightsreserved.doi:10.1016/j.cep.2007.01.015

350N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362

canbeobtainedbycreatingpseudo-reaction(roundupofseveralreactions)orpseudo-compound(roundupofseveralcompoundsoradditionoflosses)[5].Theidentifiedmodelcanbeusedtocalculatethekineticofthedifferentreactionsdeterminingthustherateofthechemicaltransformation.Thistechniquehasbeenusedwithsuccessbyseveralresearchers[9–15]forthemodel-ingofchemicalsynthesesliketheepoxidationofoleicacid[14],orthepolymerizationofacrylonitrile-styrene[10]carriedoutinbatchreactors.

Inseveralcases,theoptimizationproblemsofdiscontinuousreactorareformulatedwithtwokindsofobjectives:maximumconversionproblem,theoperativetimeisfixedapriori,ormin-imumtimeproblem,theconversionrateofwishedproductisfixedapriori.

Garciaetal.[16]consideredthefirstcase.Theyconvertedtheproblemofoptimalcontrolintoanon-linearproblemsolvedbyareducedgradientalgorithm(GRG)coupledwiththegoldensearchmethod.Thistoolallowstooptimizesimultaneouslydifferentvariables(temperature,feedflowrateandamountofreactant,operationtime,etc.)andtotakeintoaccountboundsandlinearand/ornon-linearconstraintsonthevariables.Theuseofconstraintsallowstoreachasolutionwitchisnotonlyanumericalsolutionbutwitchisclosertotheexperimentalreality.

AzizandMujtaba[17]areinterestedtotheconsecutivereac-tionoptimizationinbatchreactors.Theoptimizationproblemsareformulatedwithenvironmentalandoperationalconstraintsandsolvedbythecontrolvectorparameterisation(CVP)tech-nique.Twodifferentmodelsarepresented:ashortcutmodel,consistingofonlymassbalanceandreactionkinetics,allowsdeterminationoftheoptimalreactortemperatureprofilestoachieveadesiredperformance.Theoptimaltemperatureprofilescanthenbeusedasabasisforthedetaileddesignofthereactor(i.e.reactorvolume,heating/coolingconfiguration,etc.).Thedetailedmodel,consistingofmassandenergybalances,reactionkineticsandcooling/heatingconfiguration,allowsdetermi-nationofthebestoperatingconditionsofalreadydesignedreactors.

Inthiswork,themethodologyisillustratedthroughitsapplicationtoacomplexchemicaltransformation:aldoliccon-densationoffurfural(F)onacetone(Ac),whichallowsmainlytwoproductsnoted(FAc)and(F2Ac)tobeobtained.Thissynthesisvalorisestheresiduesofsugarcanetreatmentsincefurfuralisobtainedbyhydrolysisofthesugarcanebagassethenextractedbyvaportraining.The(FAc)isusedasaromainsev-eraltypesoffoodindustries.ThestudyofthissynthesishasbeenmadewiththecollaborationofCubanResearchInstituteforSugarByproducts(ICIDCA).2.Theoreticalpart

2.1.Identificationofastoichiometricmodel

Thestoichiometryofchemicaltransformationdeterminestheproportionsaccordingtowhichthedifferentconstituentsreactorareformed.Ingeneral,theseproportionsareintegerorsemi-integer.

ThestoichiometryofareactionsysteminvolvingNCspeciesAj(j=1,NC)andNRreactionsRi(i=1,NR),canbewritten:

󰀇NCνijAj=0(1)

j=1

whereνijisthestoichiometriccoefficientofAjinthereactionRi.

•Ifνij>0thenAjisaproductinthereactioni;•Ifνij<0thenAIfνjisareactantinthereactioni;•ij=0thenAjisnotinvolvedinthereactioni.

ForabatchreactorandadatabaseofNEexperiments(k=1,NE),themolenumberofthecompoundAjinthechemicaltransformation,representedbyseveralreactionsRi,isgivenby

n󰀇NRjk=n0jk+n

0

νijXik(2)

i=1

wherenjkisthemolenumberofAjintheexperimentkattheinstantt,n0jktheinitialmolenumberofAjintheexperimentk,XiktheextentofthereactionRiintheexperimentk,andn0isthenormalizingfactorequaltothesumoftheinitialreactantsmolenumbers.n0

=

󰀇NCn0jk,

k=1,NE(3)

j=1

Forsimplificationreasonswenote:Yjk=

yjk−y0n0jk

=

njk−jk

n0(4)

Eq.(2)becomes:󰀇NRYjk=

νijXik(5)

i=1

Theequationsystemrepresentingthewholesetofequationscan

beputunderthefollowingmatrixform:[Yjk]=[νij]T[Xik](6)

Ormoresimply:Y=νTX

(7)Severaltechniqueshavebeendeveloped[5]allowingtheiden-tificationofthestoichiometryofchemicalsyntheses.Thefirstmethodproceedswithiterativewaybyconstructingreactionbyreactionamoreandmorecomplexsystemtoimprovetherepresentativenessofthestudiedsynthesis.Thesecondmethodtreatstheprobleminamoreglobalmanneranddeterminesastoichiometricmatrixinonlyonestage:itisthesingularval-uesdecomposition(SVD)method[18,19].Anapproachcalled“targetfactoranalysis”(TFA)[20]enablestoknowwhetherapostulatedstoichiometryfromaprioriinformationiscompatiblewiththeabstractfactors.

N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362351

2.2.Identificationofkineticmodel

Themolarbalanceforareactoroperatinginbatchorsemi-batchmodegives:dnj

dt

=Fej+RjVr(8)

withnjisthemolenumberofAjatinstantt,FejthefeedrateofthecompoundAj(j=1,NC),andVristhereactorvolumeand󰀇NRRj=

νijri(9)i=1

Rjistheproductionrateifitispositiveandconsumptionrateifitisnegativeandriistherateofreactioni.

Eq.(8)maybewrittenwithextentofreaction,weobtain:dXidt=Vr

n0ri(10)

Inthiswork,thetransformationissupposedtobeapseudo-homogeneousoneandthekineticlawiswrittenasaclassicalArrhenius’slaw.Itisimportanttoemphasizethattheformofthekineticlawanditsdegreeofcomplexitydependontheuserandthedesiredaccuracyofthetendencymodel.So,wehaver󰀈

NCi=

k0ie

−Eai/RTCajij

(11)

j=1wherek0iisthepre-exponentialfactorforreactioni,Eatheacti-vationenergyforreactioni,Ci

jtheconcentrationofconstituentj,andaijistheorderofconstituentjinthereactioni.Accordingto(11),Eq.(10)maybewritten:

dXi

VNC

0−Ea/RTdt

=󰀈an0kiei

Cjij(12)

j=1

Theordersareassumedtobepartofthedataoftheproblem

andarechosenaprioritobeequaltotheabsolutevalueofthestoichiometriccoefficientsofeveryreactant.Theidentifi-cationofkineticparameters(pre-exponentialfactor,activationenergy)isdeterminedbyminimizingthedifferencebetweentheexperimentalconcentrationsandthosecomputedwiththeiden-tifiedparametersforthedifferentconstituentsaccordingtothefollowingcriterion:J=󰀇NE󰀇NCC00

0(Cfjkid−Cf

jkexp)

2

(13)

k=1j=1C1k

with

C00

=

󰀇NEC0

1k

(14)

k=1

andC0istheconcentrationofakeyreactantinexperimentk.The1k

wholeprocedurehasbeenimplementedonsoftware,Batchmod[21].

Thecorrelationcoefficient(r)isusedtomeasurethe“good-nessoffit”.Itisdefinedas

󰀆N

r=󰀉󰀆i=1(xi−¯)(yi−y¯)Ni=1(xi−x¯)2󰀉x󰀆N(15)i=1(yi−y¯)2

whereximeansdatapointsandyimeansmodelpoints.

Theaverageofthedatapoints(¯x)andthemodelpoints(¯y)aresimplygivenby1󰀇N

N

x¯=Nxi

and

y¯=1󰀇

Nyi

(16)

i=1i=1

Asthemodelbetterdescribesthedata,thecorrelationcoef-ficientwillapproachunity.Foraperfectfit,thecorrelation

coefficientwillapproachr=1.2.3.Optimizationofchemicalsynthesis

Thegeneralprocedureofoptimizationisformulatedasthefollowing[22]:minf(x),

x∈󰀊n;

gi(x)=0,

i=1,me;gj(x)≤0,j=me+1,m;

xl≤x≤xu

(17)

wherefistheobjectivefunctiontominimize,githeequalitycon-straints,gjtheinequalityconstraints,methenumberofequality

constraints,mthetotalnumberofconstraints,xlthelowlimitofxvariable,andxuistheuplimitofxvariable.

Thegoaloftheproblemistominimizeafunctionfthatdependsonseveralvariables.Thesevariablesarelimitedandsubmittedtoequalityandinequalityconstraints.Ingeneral,thefunctionfisnotlinearandisnotgivenunderexplicitshapeofvariables.

Theoptimizationofachemicalsynthesisisthedetermina-tionoftheworkingconditions(temperature,feed-rate,operativetime),thatmaximizeasynthesiscriterion(output,concentration,etc.)undersomeconstraints.

Theresolutionoftheproblemrequiresthediscretisationoftemperatureprofilesandfeed-ratesintofiniteintervalsinsidetheintervalofoperation[t0,tf],wheret0representstheinitialtimeofoperationandtfthefinaltimeofoperation.Theinterval[t0,tf]isdiscretisedintoafinitenumber(nint)ofintervals.Afunctionisdefinedtorepresenttheevolutionofthecontrolvariablev(t)ineverytimeinterval:

v(t)=Φ(t,zj),t∈󰀁

tj−1,tj󰀂,j=0,nint

(18)wheretisthecommutationtimeandzjisthetemperatureand

feed-ratevaluesinboundsofeachinterval.

Inordertoavoidcomplextemperatureandfeedprofiles,Φfunctionisassimilatedtoasimplefunction:

•Alinearfunctionforthe󰀄

temperature:

v(t)=zj−1+(t−tj−1)

zj−zj−1

󰀅tj−tj−1

,j∈[1,nint](19)

352N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362

Thelasttemperatureofintervaljissupposedtobeequaltotheinitialtemperatureofintervalj+1.•Aconstantfunctionforthefeed-rate:v(t)=aj,

j∈[1,nint]

(20)

Theprogramdeterminesthemassflowineveryintervalandsupposesthatitremainsconstantinthisinterval.Thefeed-rateisthusasuccessionoflandings.Theresolutionoftheoptimizationproblemreturnstothedeterminationof(nint+1)temperaturesandnintvaluesoffeed-rate.

Thisoptimizationmethodallowstoscaleupachemicalreac-tioninbatchreactorwithsafetyconstraints[23,24].2.4.Energybalance—thermalfluxmodeling

AclassicalSemenov-typeanalysis[25]isusedtodescribetheexothermicreaction.Therateofheatproductionisproportionaltothereactionspeed,whichmeansitisanexponentialfunctionoftemperature.Itisgiven󰀄byEq.(21):

QVEreleased=r󰀄Hk0exp−a

󰀅

RTCinitial

(21)whereQreleasedistheheatfluxreleasedbythereaction,Vrthereactingvolume,󰀄Htheheatofreaction,k0thepre-exponentialfactorofreaction,Eatheactivationenergy,andCinitialistheinitialconcentration.

ThethermalfluxevacuatedoutofthereactorisexpressedbyEq.(22).Itisproportionaltoatemperaturedifferencebetweenreactingsolutionandcoolantfluid,exchangeareaandglobalheattransfercoefficient.Alittlevariationofcoolantfluidtem-peratureinducesalinearvariationofthermalfluxevacuatedfromthereactor:

Qevacuated=UA(Tcf−Treactor)

(22)

whereQevacuatedisthethermalfluxevacuatedwithjacketreac-tor,Utheglobalheattransfercoefficient,Atheexchangesurfacereactor,Tcfthecoolingfluidtemperature,andTreactoristhereactortemperature.3.Experimentalpart

3.1.Aldoliccondensationoffurfuralonacetone

Thealdoliccondensation[26–29]offurfural(F)onacetone(Ac)takesplaceinalkalinemedium.Itimpliesthegenerationofacarbanionobtainedfromabstractionofaprotoninalphaofacetonecarbonylfunctionandleadstothe4-(2-furyl)-3-buten-2-one(FAc).Becauseofthesymmetryoftheacetonemolecule,asecondattackofthefurfuralcanhappenwhichthenleadstothedi-addingproduct,the1,4-pentadien-3-one,1,5-di-2-furanyl(F2Ac).

Thedifferentstepsfortheformationof(FAc)moleculecanbewritten:

(a)Extractionofaprotononacetoneandformationofthe

carbanion:

(b)Condensationofthecarbaniononthecarbonoffurfural

carbonylfunction:

(c)FixationofH+ontheoxy-anion:

(d)Regenerationofhydroxideionbaseanddehydrationinbasic

medium:

Finally,thereactionsofformationof(FAc)and(F2Ac)are:

(23)

(24)

Thereversibilityofreactions(23)and(24)arenegligi-ble.Besidesthesetworeactions,othersmayhappen.Amongsttheknownreactions,furfuralcanreactwithitselfinanoxydo-reductionreaction(Cannizaroreaction)togiveahigher

N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362353

oxidationproduct,the2-furoicacid(Furo),andaloweroxida-tionproduct,thefurfurylalcohol(Furfu)[30].Thisreactioncantakeplaceinhighlyalkalinemedium.Ontheotherhand,acetonecanreactonitselftogivethe4-hydroxy-4-methylpentan-2-one(Ox1),whichafterdehydrationleadstothemesityloxide(Ox2)[30].

3.2.Conditionsofthereaction

Thereactionsareachievedindiscontinuousmodeinajack-etedglassreactorof250mLcapacity(Fig.1).Theacetoneandthefurfuralarechargedinthereactorwithequi-molarquantities.Thesolventusedisanequi-molarmixtureofwaterandethanol.ThepresenceofethanolinthemediumfavoursthedissolutionofFAcandF2Acwhicharenotsolubleenoughinwater.Anaque-oussolutionofsodiumhydroxide(0.03molL−1)isinjectedtotriggerthereaction.Thetemperatureofthemediumcanbemain-tainedconstantthankstoaheating-coolingsystem.Thereactionvolumeisconstantandequalto98mL.

Theinitialcompositionsarechosenaccordingtothesug-gestionsoftheCubanResearchInstituteforSugarByproducts(ICIDCA).Itwasnotvariedbecauseofindustrialrestrictions.3.3.Analyticalprocedure

(25)

(26)

Allusedchemicalshaveanalyticalgrade.The1,4-pentadien-3-one,1,5-di-2-furanylisnotcommercialized,therefore,ithasbeenpreparedandpurifiedinthelaboratory.

Theconcentrationsofreagentsandproductsaredeterminedbygasandliquidchromatography.Onlytheacetoneismeasuredbygaschromatography,theformedproducts(FAcandF2Ac)beingheat-sensitives.Forthetwotechniques,ethanolisusedasaninternalstandardinadditiontoitssolventrole.

Fig.1.Experimentalequipmentusedforthechemicalsynthesis.

3N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362

Table1

WavelengthscorrespondingtoamaximalUVabsorptionProducts

AcetoneFurfuralFAcF2Ac

2-FuroicacidFurfurylalcoholMesityloxide

4-Hydroxy-4-methylpentan-2-one

λmax(nm)265274322382228220232232

Forgaschromatography,theinjectionsarerealizedinsplitmode.Aflameionizationdetector(FID)isused.Apolarcolumn(FFAP,25m×0.32mmi.d.)withafilmthicknessof0.25␮mseparatesthesolventandthematrixofcomponents.Theinjectorismaintainedatatemperatureof250◦C.Theflameionizationdetectorisheateduntil300◦C.Theinitialtemperatureoftheovenis50◦C.After1.5min,thetemperatureincreasesquicklyattherateof50◦C/minuntil240◦Cthenitremainsconstantduring5min.Thetotaltimeofanalysisis10.3min.Heliumisusedasthecarrier-gas.

Theproducts(F),(FAc)and(F2Ac)aremeasuredbyhighperformanceliquidchromatography(HPLC)[31–36].Thesys-temisequippedwithUV–visdetectorandanautomaticinjectorof25␮Linfullloop.AnODSHypersylC185␮mcolumn(125mm×4mmi.d.)isusedfortheseparationoftheproducts.ChemicalcompoundshavedifferentmaximumUVabsorp-tionatdifferentwavelengths.Table1showsthewavelengthatwhichthemaximumUVabsorptionisobservedforthecom-poundsofthesynthesis.Theuseofthreedifferentwavelengths(265,322and382nm)allowstomeasurewithprecisionthequantityofdifferentcompounds.

Theeluentisamixtureofwaterandmethanol.Fig.2sum-marizestheprocedureofHPLCanalysisadoptedtofollowtheconcentrationsofthedifferentcompoundsinthealdoliccon-densationoffurfuralonacetone.4.Resultsanddiscussion

4.1.Identificationofastoichiometricmatrix

Severalreactionshavebeencarriedoutattemperatureof24,29,34and40◦Candatmosphericpressure.Thestudyhasnotexceeded40◦Cbecausetheacetoneebullitiontemperatureis56◦C.Themolenumbervariationofthecompoundsat24◦C(Fig.3)showsthedisappearanceofacetoneandfurfuraland

Fig.3.Molenumberevolutionofthecompoundsat24◦C.

theapparitionof(FAc)and(F2Ac).Theconversionoffurfuralapproaches95%whilethatofacetoneisnear62%.Thepro-ductionof(F2Ac),moreimportantthanthatof(FAc),explainsthebestconversionofthefurfural.Furthermore,theanalysishasnotrevealedthepresenceofeither2-furoicacidorfurfurylalco-hol.Alsoneither(Ox1)nor(Ox2)wasdetected(Eq.(26)).Thensuggestedreactionsforthesynthesisareonlyreactions(23)and(24).

Inordertoverifytheaccuracyofthesupposedstoichiometricmatrix,itisnecessarytoverifythatmolarandmassbalancesarecorrect.Assumingthatonlyreactions(23)and(24)occur,themolarbalancecanbewrittenasn0F=nF+nFAc+2nF2Acn0Ac=nAc+nFAc+nF2AcnH2O=nFAc+2nF2Ac

(27)(28)(29)

Itisnecessarytodeterminethenumberofmolesofwaterformedduringthesynthesistobeabletoestablishthemolarandmassbalances.Theformedwaterisnotdeterminedbychromatogra-phybutcalculatedaccordingtoEq.(29).However,waterpresentatthebeginninginthemediumdoesnotappearinthebalanceandwastakenintoaccountintheconcentrationofthesolvent.Themassbalanceshowsadeficitwhichincreaseswithtimeandthendecreasesattheendofthesynthesis(Fig.4).Thefur-furalandtheacetoneweremoreconsumedthanthepredictionwiththesupposedreactionscheme.Supplementaryreactionsmustthereforebeaddedtothestoichiometricmodel.TheCan-nizaroreactionbeingrejected,thepossibilityofpolymerizationreactionswasstudied.Themainreactionofpolymerizationmen-

Fig.2.ChangeofwavelengthandeluentcompositionfortheanalysisbyHPLC.

N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362355

Sinceproduct(P)appearsatthesametimeas(FAc),thenitcannotbeapolymerofthelater.Itisratherformeddirectlyfromthefurfuralandtheacetone(Eq.(30)).Thisequationisonlyarepresentationanddoesnotaccountforachemicalmechanism.Itwouldthenimplyafivereactantsencounter,whichisnotrealistic.Theproduct(P)disappearsduringthereaction,thisdisappearancecouldberepresentedbyEq.(31).HPLCandGCanalyseshasnotrevealthepresenceofotherproductsasidefurfural,acetoneFAc,F2AcandP,thatiswhythedecompositionofPtoFAcandF2Acisthemostprobableandnototherproducts.Finally,itwassuggestedthatthissynthesiscouldberepresentedbythefourreactions(23),(24),(30)and(31).

Fig.4.Massbalancefortheexperimentat24◦C(H2OcalculatedfromEq.(21)).

(30)

(31)

Themolarbalancesassociatedtothereactions(23),(24),(30)and(31)become:

Fig.5.ExampleofHPLCchromatogram(experimentat40◦C,reactiontime=10min).

n0F=nF+nFAc+2nF2Ac+3nPn0Ac=nAc+nFAc+nF2Ac+2nPnH2O=nFAc+2nF2Ac+3nP

(32)(33)(34)

tionedintheliterature[37]istheformationof(FAc)nfromthe

(FAc)inbasicmedium,nbeingsuperiororequalto2.

IntheHPLCchromatogramsobtained,anunidentifiedpeakcanbenoticed.Itispresentduringthefirstminutesofthesyn-thesisandthenitdisappears.Ithasaretentiontimenearthatof(FAc).Theproduct(P)whichcorrespondstothispeakissensitivetothewavelengthof322nm(Fig.5).

Toidentifytheproduct(P),weusedtheHPLCanalysiscou-pledwithmassspectroscopy(Fig.6).Thisanalysisrevealedthatthisproducthasanimportantmolarmassnear350gmol−1.Thedevelopedformulaof(P)showninFig.6isoneofpossibleformulasdeducedfromthefragmentsidentifiedonthespectrum.

Withthenewreactionssystemproposedforthesynthesis,theconcentrationsof(P)andwatercanbecalculatedbytwoways,fromthebalanceonacetone(Eqs.(33)and(34)),orfromthebalanceonfurfural(Eqs.(32)and(34)).Thetwomethodshavebeentestedandthevaluesobtainedwereveryclose.Contrarilytothepreviouscase(systemoftworeactions)therepresentationofthesynthesisbyfourreactionsallowstogetacorrectmassbalance.Themaximalerrorobservedis6.1%(Fig.7).

Theexperimentcarriedoutattemperaturesof24,29,34and◦40Callowtogeneratearangeofinput/outputconcentrations

Fig.6.Spectrumofmassspectroscopy(thepeakat240.3amuisvisibleonthespectraofallanalyzedsamples).

356N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362

Fig.7.Massbalancefortheexperimentat24◦C(H2OcalculatedfromEq.(26)).

forthesixcomponentsofthesynthesisandthereforetofeedthealgorithmofcalculation.TheSVDmethodprovidesthefollow-ingsingularvalues:

Knowingthatthemostimportantvaluesindicatethenumberofnecessaryreactionsforthedescriptionofthesynthesis,itcanbeassumedthatthechemicaltransformationcanbedescribedadequatelybyasystemoffourorfivereactions.

Accordingtotheavailableknowledgeaboutthetransforma-tion,itwaspostulatedastoichiometrywithfourreactions:•Thefirstreactionrepresentstheformationof(FAc)fromfur-furalandacetone.

•Thesecondreactionrepresentstheformationof(F2Ac)from(FAc)andfurfural.

•Thethirdreactionrepresentstheformationof(P)fromthreemolesoffurfuralandtwomolesofacetone.

•Thefourthreactionrepresentstheconsumptionof(P).Onemoleof(P)givesonemoleof(FAc)andonemoleof(F2Ac).Table2containsthepostulatedstoichiometryandTable3containsthecalculatedstoichiometry.Eq.(35)allowstheerrorbetweenthetargetmatrixandthecalculatedmatrixforeveryreactionto󰀌

becalculated:

󰀋󰀋error(i)=󰀋󰀆NC󰀃󰀃2󰀋󰀊j=1󰀃󰀃νtargetij

−νcalculatedij󰀃󰀃󰀆NC󰀃󰀃ν󰀃(35)j=1󰀃targetij

󰀃󰀃2Table2

Targetstoichiometricmatrix

F

AcFAcF2AcPH2OReaction1−1−11001Reaction2−10−1101Reaction3−3−20013Reaction4

0

0

1

1

−1

0

Table3

Calculatedstoichiometricmatrix

F

AcFAcF2AcPH2OReaction1−0.983−1.0120.9850.048−0.0170.980Reaction2−1.0370.043−0.9850.9940.0341.044Reaction3−2.988−2.022−0.0430.0741.0212.987Reaction4

−0.015

0.025

1.039

0.916

−1.034

0.016

Table4

Kineticparametervalues(reactionrateinmolL−1s−1)

Activationenergy,Ea(Jmol−1)

Pre-exponentialfactor,k0Reaction174581.5593.7979×108Reaction235959.7312.2094×102Reaction3514.4594.4197×104Reaction4

117919.191

9.20×1015

Anerrorof3.02%wasobtainedforthemainreaction,4.05%forthesecondreaction,1.93%forthethirdreactionand6.03%forthefourthreaction.Resultsshowthatthepostulatedstoi-chiometryiscompatiblewiththeabstractfactors.Themodelcanthereforebeadoptedfortheidentificationofkineticparameters.4.2.Determinationofthekineticparameters

Thedeterminationofthestoichiometryofthechemicaltrans-formationallowstofindtheproportionsaccordingtowhichthecomponentsreact.Thenextstepformodelingconsistsinidenti-fyingthekineticparametersforeachreaction.Inthiswork,thetransformationissupposedtobeapseudo-homogeneousoneandthekineticlawiswrittenasaclassicalArrhenius’slaw.Theordersofcompoundsaretakenequaltoabsolutevaluesofstoichiometriccoefficientsforthereactantsandzerofortheproducts.Table4givesthevaluesofactivationenergy(Ea)andpre-exponentialfactor(k0)identifiedaccordingtoEq.(11).Thefirstreactionissensitivetotemperature;theproductionof(FAc)increasesastemperaturerises.Thesecondreactionislesssensitivetotemperaturethanthefirst.Thethirdreactionwhichcorrespondstotheformationof(P)isfarlessactivatedbytemperaturethanthefourthreactionwhichcorrespondstotheconsumptionof(P).Thedisappearanceof(P)issomorerapidat40◦Cthanat24◦C.

Fromthekineticparameters,thetime-dependenceoftheoret-icalconcentrationscanbeillustrated.Thecomparisonbetweenthetime-dependenceconcentrationsobtainedfromtheexperi-mentandfromthemodelisgiveninFigs.8–11.Astatisticalanalysisisprovidedregardingthesignificanceofthefittedkineticparameters.Table5showsthecorrelationcoefficients

Table5

Correlationcoefficients

F

AcFAcF2AcPH2OReactionat24◦C0.99950.99840.150.99740.92670.9995Reactionat29◦C0.99730.99860.90690.99860.91560.9973Reactionat34◦C0.99530.99560.90410.99940.90510.9953Reactionat40◦C

0.9972

0.9991

0.9252

0.9970

0.9688

0.9972

N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362357

Fig.8.Evolutionofcompoundconcentrationsforthereactionat24◦C((—)model;(󰀁)experimentalpoints).

Fig.9.Evolutionofcompoundconcentrationsforthereactionat29◦C((—)model;(󰀁)experimentalpoints).

obtainedusingEq.(15).Agoodagreementwasobtainedbetweentheexperimentalandmodelrepresentationoffur-fural,acetone,(F2Ac)andwater.However,theevolutionofthecompounds(FAc)and(P)isnotasgood.Behaviouroftheseintermediatecomponentsisthemostdifficulttopredict

Fig.10.Evolutionofcompoundconcentrationsforthereactionat34◦C((—)model;(󰀁)experimentalpoints).

Fig.11.Evolutionofcompoundconcentrationsforthereactionat40◦C((—)model;(󰀁)experimentalpoints).

becausetheyplaytheroleofreagentsandproductsatthesametime.

4.3.Optimizationofthesynthesis

Inthepreviousparagraphs,astoichio-kineticmodelofaldoliccondensationoffurfuralonacetonehasbeendetermined.Thismodelgivesasatisfactoryrepresentationofthesynthesisbehaviourandcanbeusedthereforeforitsoptimization.ThestoichiometricmatrixadoptedisReaction1:F+Ac−k→1

FAc+H2O,r1=k1[F][Ac]Reaction2:

F+FAc−k→2

F2Ac+H2O,r2=k2[F][FAc]Reaction3:3F+2Ac−k→3P+3H2O,r3=k3[F]3[Ac]2

Reaction4:

P−k→4

FAc+F2Ac,

r4=k4[P]

4.3.1.Optimizationatlaboratoryscale

Inthissection,theamountsofreactantsarethesameasthereusedforexperiments,1correspondingtoaninitialconcen-trationof3molL−forfurfuralandacetoneinbatchmode.Theoperationtimeisequalto4h.

ThecriteriontomaximizeisthefinalFAcyield,definedastheratiobetweenthemolenumberofFAcpresentattheendofoperation,andthemolenumberofinitialacetoneloadedinthereactor(Eq.(36)):criterion=

molenumberof(FAc)attheendofoperation

molenumberofinitialacetone

(36)

Thetemperaturedomainusedis20◦C≤temperature≤40◦C

Theminimalandmaximaltemperaturechoicehasbeenguidedbytheexperimentaldomainthathasbeencoveredwiththeexperimentaltests.Inparticular,thehighesttemperaturehasbeenlimitedto40◦C.Takingalargerdomainwouldleadtosolutionsforwhichthevalidityofthemodelwouldbevery

358N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362

Fig.12.Resultsofthesimulationindiscontinuousmodeatlaboratoryscale.

uncertain.Moreover,atatmosphericpressure,thetemperatureislimitedby56◦Ctheacetoneboilingpoint.

•Workingindiscontinuousmode(Batch),thebestisothermis40◦C,themaximumthermalfluxgeneratedisequalto10W(Fig.12)andFAcyieldapproaches29.82%.Feedingacetonecouldleadtolargeamountoffurfuraltogetherwithlowcon-centrationofacetone.ItwouldthenfavourF2Acformation.Itwasthendecidedtofeedfurfural.

Bycomparingthealdoliccondensationoffurfuralonace-tonetoathermodynamicsystem,itisclearthatthissystemlosesenergysincethesynthesisisexothermic,whichexplainsthenegativevaluesofthethermalfluxesinthedifferentfig-ures.

•Whileapplyingafeed-rateof2.2916×10−4kgmin−1during2handlookingforthebestisotherm,theoptimaltemperatureis40◦C,thethermalfluxreachesamaximumof1.5Wandtheyieldliesaround28.5%(Figs.13and14).Whenreduc-ing◦thefeedingtimeto1h,theoptimaltemperatureisalways40C,thethermalfluxreaches2.8Wandthechemicalyieldisslightlyimprovedandbecomes28.87%(Figs.15and16).Bydecreasingthefeedingtimeto30mn,theoptimaltem-peraturedoesnotchange(40◦C),thethermalfluxincreasesto5.2W.Furthermore,theobtainedchemicalyieldisabout29.43%.Thisresultisthenearestonecomparedtothediscon-

Fig.13.Resultsofthesimulationinsemi-continuousmodeatlaboratoryscalewithafurfuralfeed-rateduring120min.

Fig.14.Evolutionofcompoundconcentrationsofthereactionat40◦Cinsemi-continuousmodewithafurfuralfeed-rateduring120min(calculatedpointswithsmoothing).

Fig.15.Resultsofthesimulationinsemi-continuousmodeatlaboratoryscalewithafurfuralfeed-rateduring60min.

tinuousmode(Figs.17and18).Table6summarizesoperativeconditionsobtainedforthedifferentproblemstreatedinsemi-continuousanddiscontinuousmodeatlaboratoryscale.Heatgeneratedinbatchmodecanbeeasilyremovedatlabo-ratoryscale.Intheopposite,itisdifficulttoevacuatethisheatatindustrialscale.Thecoolingcapacityofdiscontinuousreactors(typeagitatedtank)isgenerallylimited.Especially,theratiosur-

Fig.16.Evolutionofcompoundconcentrationsofthereactionat40◦Cinsemi-continuousmodewithafurfuralfeed-rateduring60min(calculatedpointswithsmoothing).

N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362359

Fig.17.Resultsofthesimulationinsemi-continuousmodeatlaboratoryscalewithafurfuralfeed-rateduring30min.

Fig.18.Evolutionofcompoundconcentrationsofthereactionat40◦Cinsemi-continuousmodewithafurfuralfeed-rateduring30min(calculatedpointswithsmoothing).

face/volumedecreaseswhenthereactorsizeincreasesandtheexchangecoefficientsdegradeespeciallyforglasslinedreactors.4.3.2.Extrapolationtoindustrialscale

A3m3industrialreactorischosen(cylindricalshape,diame-terof1.4m,heightof1.95mandareaof10m2).Theamountsofreagentsintroducedaremultipliedby3×104comparedtothoseusedatlaboratoryscale.Thereactingvolumeisabout2850l.

ReagentsandsolventsFurfural828kg(8.618kmol)Acetone501kg(8.626kmol)Ethanol1050L(17.990kmol)Water

450L(24.934kmol)Sodiumhydroxide

1.8kg(0.045kmol)

Theoptimaloperatingmodeisbatch,assuggestedbythecon-secutive/competitivereactionscheme.At40◦C,themaximumthermalenergyreleasedisabout300kW(10Watlaboratoryscale).Eq.(22)isusedtoestimatethemaximumthermalfluxevacuatedbythejacketofthereactorconsideringaglobalheattransfercoefficientequalto150Wm−2K−1[38],aminimalexchangesurfaceof10m2andadifferenceof10◦Cbetweenthecoolingfluidtemperatureandthereactiontemperature.Thereactorcanonlyevacuate15kW.Asafetyconstraintbecomesnecessary.

Table6

Operativeconditionsobtainedfordifferentproblemsinsemi-continuousanddiscontinuousmode(reactiontime240min)Feed-rate120

60

30

Batch

time(min)Feed-rate2.2916×10−44.5833×10−49.1667×10−4Batch(kgmin−1)Temperature40404040(◦C)

Thermalflux1.42.75.210(W)Output(%)

28.46

28.87

29.43

29.82

Byrespectingthislimit,thesynthesiscanbecarriedoutindiscontinuousmodeatatemperatureof−10.3◦C.Theresult-ingyieldis1.5%smallerthanatalaboratoryscale.Interestofdiscontinuousmodeattheindustrialscaleisratherpoor.

Theproblemtosolveconsists,firstly,tomaximizetheyieldofFAcbyworkingathightemperature,andsecondary,toimposeasafetyconstraintof15kWinordertorespectthelimitsofthereactorcoolingsystem,minimizingthusthethermalrun-awayrisks.Thesemi-continuousmodebecomesnecessary.

Theaimofthispartistodetermineafurfuralfeed-rateprofileat40◦C,underasecurityconstraintof15kW.Thecriteriontomaximizeisstillthesame(Eq.(36)).Researchisunderthefollowingconstraints:•Limitsofthefeed-rate:

0kgmin−1≤flow≤15kgmin−1•Gradientofthefeed-rate:󰀄󰀄D

󰀅󰀄t=±2kgmin−2

max

•Tointroduce828kgoffurfuralinthereactorin240min,thenecessaryfeed-rateis3.45kgmin−1.Withthisfeed-rateandthetemperatureof40◦C,thethermalfluxreaches21.7kW(Figs.19and20).Thisvalueissuperiortothelimitsupported

Fig.19.Resultsofthesimulationinsemi-continuousmodeatindustrialscalewithafurfuralfeed-rateduring240min.

360N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362

Fig.20.Evolutionofcompoundconcentrationsofthereactionat40◦Cinsemi-continuousmodewithafurfuralfeed-rateduring30min(calculatedpointswithsmoothing).

Fig.21.Resultsofthesimulationinsemi-continuousmodeatindustrialscale.

bythereactorcoolingsystem.Itisnecessarytoincreasetheoperativetimetobeabletolimitthethermalfluxto15kW.•Torespectthesafetyconstraint,themaximaltimeofthereac-tionis◦multipliedbytwo(480min).Optimalfeed-rateprofileat40Cgeneratingathermalfluxlowerthan15kWcanthenbedetermined.Thefirstintervaloftheoperatingtimeisalsointroducedasavariabletobeoptimizedbythecalculationalgorithm.

Fig.22.Evolutionofcompoundconcentrationsofthereactionat40◦Cinsemi-continuousmodewithafurfuralfeed-rateduring30min(calculatedpointswithsmoothing).

TheoptimizationresultispresentedFig.21.Thefurfuralfeed-rateisconstantduring338minandthegeneratedthermalfluxdoesnotexceed15kW.Therestofthefurfuralamountisfedinthefourthinterval.Thetotaltimeofthesynthesisis478.6minattheendofwhichtheoutputis27.73%.Fig.22representstheevolutionofproductandreagentconcentrationsasafunctionoftime.

5.Conclusion

Theresultsobtainedforthestoichiometricidentificationshowthatthealgorithmisabletofindoutagoodrepresen-tationofthetransformationfromsolelytheinitialandfinalconcentrations.

Theidentifiedkineticconstantsallowtosimulatethecurvesrepresentingtheevolutionofreagentsandproductsconcentra-tionstakingpartinthesynthesis.Forcompoundsthatareonlyproductsorreagents,theexperimentalpointsandthesimula-tionareingoodagreement.Ontheotherhand,forcompoundsthataresimultaneouslyreagentandproduct,themodeldoesnotperfectlyfittheexperiments,butthedescriptionofcompoundsevolutionremainscorrect.

Theoptimizationofaldoliccondensationoffurfuralonace-tonehasbeenrealizedbymaximizingthechemicalyieldofFAc.Asexpectedfromthereactionschemeandthevaluesofkineticconstants,thebestcriterionisobtainedforasynthesisindis-continuousmode(batch)realizedatthetemperatureof40◦C,whichrepresentsthemaximallimitimposedfortheresearchofoptimaloperatingconditions.

Althoughthissynthesisisnotveryexothermic,theextrapo-lationtoindustrialscalehasbeenrealizedbyintegratingsomethermallimitations(heating/coolingrate,thermalevacuationcapacity)thatremainacrucialproblemforbigcapacityjacketedreactors.

AppendixA.Nomenclature

aorderoftheconstituentinthereactionCconcentrationoftheconstituentEaactivationenergyofArrheniuslawFefeedrate

󰀄Hheatofreaction

Joptimizationcriterion

k0pre-exponentialfactorofArrheniuslawnmolenumberNnumberofpoints

NCnumberofconstituentsNEnumberofexperimentsNRnumberofreactionsrrateofreaction

Rgasconstant(8.314JK−1mol−1)Rjoverallrateofproductionofspeciesjttime

Ttemperature

UglobalheattransfercoefficientV(NC×NC)orthonormalmatrix

N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362361

Vrreactorvolumexdatapoint

Xextentofreactionymodelpoint

Y(NE×NR)datamatrix

Greeksymbolsλwavelengthνstoichiometriccoefficient

SubscriptsAcacetoneexpmeasuredFfurfuralFAc4-(2-furyl)-3-buten-2-one

F2Ac1,4-pentadien-3-one,1,5-di-2-furanylH2OwaterireferstoreactionsortopointnumberidcalculatedjreferstoconstituentskreferstoexperimentsP1,5,9-tri-2-furylnona-1,8-diene-3,7-dioneSuperscripts0initialffinalTtransposeReferences

[1]P.J.LeMeur,L’ing´enierieenchimiefine:d´efinitionsetfonction,Inf.Chim.

343(1992)95–101.

[2]P.Pollak,Lachimiefinerˆevesetr´ealit´es,Inf.Chim.288(1987)195–

203.

[3]E.Polastro,S.Tulcinsky,LaR&Denchimiefine,pourquoifaire?Inf.

Chim.383(1996)82–84.

[4]G.E.P.Box,W.G.Hunter,J.S.Hunter,StatisticsforExperimenters,Wiley,

1978.

[5]Garcia,V.,Exploitationdesmod`elesdetendancestœchiom´etriqueset

cin´etiquespourl’optimisationdesr´eacteursdiscontinusdechimiefine,Ph.D.Thesis,INPToulouse,France,1993.[6]Sedrati,Y.,Strat´egieexp´erimentalepourlad´eterminationdesmod`eles

stoechio-cin´etiques,Ph.D.Thesis,INPToulouse,France,1999.[7]Toulouse,C.,Conduiteoptimalesouscontraintesdes´ecurit´edesr´eacteurs

batchoualiment´esdechimiefine,Ph.D.Thesis,INPToulouse,France1999.

[8]J.Villermaux,C.Georgakis,Probl`emesactuelsdanslamiseenœuvredes

r´eactionsdiscontinues,Entropie23(137/138)(1987)45–51.

[9]O.Abel,A.Helbig,W.Marquardt,H.Zwick,T.Daszkowski,Productiv-ityoptimizationofanindustrialsemi-batchpolymerizationreactorundersafetyconstraints,J.Proc.Cont.10(2000)351–362.

[10]G.D.Cawthon,K.S.Knaebel,Optimizationofsemibatchpolymerization

reactions,Comp.Chem.Eng.13(1/2)(19)63–72.

[11]C.Filippi,J.L.Greffe,J.Bordet,J.Villermaux,Tendencymodellingof

semibatchreactorsforoptimizationandcontrol,Chem.Eng.Sci.41(4)(1986)913–920.

[12]C.Filippi-Bossy,J.Bordet,J.Villermaux,S.Marchal-Brassely,Batchreac-toroptimizationbyuseoftendencymodels,Comp.Chem.Eng.13(1/2)(19)35–47.

[13]S.Marchal-Brassely,J.Villermaux,J.-L.Houzelot,J.L.Barnay,Optimal

operationofasemi-batchreactorbyself-adaptivemodelsfortemper-atureandfeed-rateprofiles,Chem.Eng.Sci.47(9–11)(1992)2445–2450.

[14]A.Rastogi,A.Vega,C.Georgakis,H.G.StengerJr.,Optimizationofcat-alyzedepoxidationofunsaturedfattyacidsbyusingtendencymodels,Chem.Eng.Sci.45(8)(1990)2067–2074.

[15]A.Rastogi,J.Fotopoulos,C.Georgakis,H.G.StengerJr.,Theidentifica-tionofkineticexpressionsandtheevolutionaryoptimizationofspecialtychemicalbatchreactorsusingtendencymodels,Chem.Eng.Sci.47(9–11)(1992)2487–2492.

[16]V.Garcia,M.Cabassud,M.V.LeLann,L.Pibouleau,G.Casamatta,Con-strainedoptimizationforfinechemicalproductionsinbatchreactors,Chem.Eng.J.Biochem.Eng.J.59(3)(1995)229–241.

[17]N.Aziz,I.M.Mujtaba,Optimaloperationpoliciesinbatchreactors,Chem.

Eng.J.85(2002)313–325.

[18]D.Bonvin,D.W.T.Rippin,Targetfactoranalysisfortheidentifica-tionofstoichiometricmodels,Chem.Eng.Sci.45(12)(1990)3417–3426.

[19]P.Tsobanakis,S.H.Lee,J.A.Phillips,C.Georgakis,Adaptativestoichio-metricmodelingandstateestimationofbatchandfed-batchfermentationprocesses,in:Am.Inst.Chem.Engrs.,AnnualMeeting,SanFrancisco,California,November9,1997.

[20]J.W.Hamer,Stoichiometricinterpretationofmultireactiondata:appli-cationtofedbatchfermentationdata,Chem.Eng.Sci.44(10)(19)2363–2374.

[21]Batchmod:Stoichiometricidentificationsoftware,LicenseINPT,

1997.

[22]M.Cabassud,P.Cognet,V.Garcia,M.V.LeLann,L.Rigal,G.Casamatta,

Modellingandoptimisationofthelacticacidsynthesisbythealkalinedegradationoffructoseinabatchreactor,Chem.Eng.Commun.192(2005)758–786.

[23]C.Toulouse,J.Cezerac,M.Cabassud,M.V.LeLann,G.Casamatta,

Optimisationandscale-upofbatchchemicalreactors:impactofsafetyconstraints,Chem.Eng.Sci.51(10)(1996)2243–2252.

[24]C.Toulouse,M.Cabassud,M.V.LeLann,G.Casamatta,Op´erationsopti-malesdanslesr´eacteursdiscontinussouscontraintesdefonctionnement,

Entropie210(1998)29–34.

[25]N.N.Semenov,Z.Phys.48(1928)571–581.[26]T.Bottin-Strzalko,Effetdestructuresurlar´eversibilit´edelacondensation

aldolique:R´eactiondesphosphonoestersetdubenzald´ehyde,Tetrahedron29(24)(1973)4199–4204.

[27]J.E.Dubois,P.Fellmann,Influencedelag´eom´etriedel’´enolatesurla

st´er´eochimiedelacondensationaldolique,TetrahedronLett.16(14)(1975)1225–1228.

[28]P.Fellmann,J.E.Dubois,Condensationaldolique:effetsdesubstituants

alcoylessurlast´er´eochimiedelar´eactionentreun´enolateetunald´ehyde

ouunec´etone,Tetrahedron34(9)(1978)1343–1347.

[29]G.Kyriakakou,M.C.Roux-Schmitt,J.Seyden-Penne,St´er´eos´electivet´e

delacondensationaldolique.R´eactiondubenzald´ehydeetd’´enolatescarb´eniatesmagn´esiens␣-chlor´es,J.Organomet.Chem.47(2)(1973)315–320.

[30]N.L.Allinger,M.P.Cava,D.C.DeJongh,N.A.Lebel,C.L.Stevens,

Chimieorganique–volumeII:R´eactions,3`e

mee´dition,McGrawHill,1981.

[31]A.L.Bailey,G.Wortley,S.Southon,Measurementofaldehydesinlow

densitylipoproteinbyhighperformanceliquidchromatography,FreeRad.Biol.Med.23(7)(1997)1078–1085.

[32]P.Chambel,M.B.Oliveira,P.B.Andrade,J.O.Fernandes,R.M.Seabra,

M.A.Ferreira,Identificationof5,5󰀈-oxy-dimethylene-bis(2-furaldehyde)bythermaldecompositionof5-hydroxymethyl-2-furfuraldehyde,FoodChem.63(4)(1998)473–477.[33]E.Ferrer,A.Alegr´ıa,R.Farr´e,P.Abell´an,F.Romero,High-performance

liquidchromatographicdeterminationoffurfuralcompoundsininfantfor-mulas:changesduringheattreatmentandstorage,J.Chromatogr.A947(2002)85–95.

[34]P.Ho,T.A.Hogg,M.C.M.Silva,Applicationofaliquidchromatography

methodforthedeterminationofphenoliccompoundsandfuransinfortifiedwines,FoodChem.(1999)115–122.

[35]S.Kermasha,M.Goetghebeur,J.Dumont,R.Couture,Analysesofphe-nolicandfurfuralcompoundsinconcentratedandnon-concentratedapplejuices,FoodRes.Int.28(3)(1995)245–252.

362N.Fakhfakhetal./ChemicalEngineeringandProcessing47(2008)349–362

[38]S.Cramer,R.Gesthuisen,Simultaneousestimationoftheheatofreaction

andtheheattransfercoefficientbycalorimetry:estimationproblemsduetomodelsimplificationandhighjacketflowrates-theoreticaldevelopment,Chem.Eng.Sci.60(2005)4233–4248.

[36]F.LoCoco,C.Valentini,V.Novelli,L.Ceccon,High-performanceliquid

chromatographicdeterminationof2-furaldehydeand5-hydroxymethyl-2-furaldehydeinhoney,J.Chromatogr.A749(1996)95–102.

[37]A.A.Patel,S.R.Patel,Synthesisandcharacterizationoffurfural-acetone

polymers,Eur.Polym.J.19(3)(1983)231–234.