Stoichio-kinetic modeling and optimization of chemical synthesis

14 Pages·2008·1.55 MB·English

Stoichio-kinetic modeling and optimization of chemical synthesis:
Application to the aldolic condensation of furfural on acetone
Nadim Fakhfakha, Patrick Cogneta,∗, Michel Cabassuda,
Yolande Lucchesea, Manuel D´ıas de Los R´ıosb
aLaboratoiredeGe´nieChimique,UMR5503CNRS,INPT(ENSIACET),UPS,5ruePaulinTalabot,BP1301,31106ToulouseCedex1,France
bCubanResearchInstituteforSugarCaneByproducts(ICIDCA),P.O.Box4026,HavanaCity,Cuba
Abstract
Thecondensationreactionoffurfural(F)onacetone(Ac)givesahighaddedvalueproduct,the4-(2-furyl)-3-buten-2-one(FAc),usedasaroma
inalcoholfreedrinks,ice,candies,gelatinesandotherproductsofcurrentlife.Thissynthesisvalorisestheresiduesofsugarcanetreatmentsince
furfuralisobtainedbyhydrolysisofsugarcanebagassefollowedbyvaportrainingextraction.Inthefaceofnumerousandcomplexreactions
involvedinthissynthesis,itisverycomplicatedtodefinethekineticlawsfromexactstoichiometry.Asolutionallowingtocopetheproblem
consistsinidentifyinganappropriatestoichiometricmodel.Itdoesnotattempttorepresentexactlyallthereactionmechanisms,butproposes
amathematicalsupporttointegrateavailableknowledgeonthetransformation.Theaimofthisworkisthedeterminationofstoichiometricand
kinetic models of the condensation reaction of furfural on acetone. Concentrations of reagents and products are determined by gas and liquid
chromatography.Concentrationprofilesobtainedatdifferenttemperaturesareusedtoidentifykineticparameters.Themodelisthenusedforthe
optimizationoftheproductionofFAc.Theinterestofsuchtoolisalsoshownforthescaleupoflaboratoryreactortoalargescale.Theanticipation
ofthereactionbehaviourinlargescaleiscrucialespeciallywhenthereactorpresentsimportantlimitationsofthermalexchangecapacity.
Keywords: Furfural;Acetone;Chromatography;Aldoliccondensation;Batchreactor;Stoichio-kineticmodeling
1. Introduction of fine chemistry, it is necessary to obtain a reliable model of
the system. This problem is often circumvented by the use of
Chemicalindustriesofindustrializedcountriesturnincreas- linear or quadratic polynomial models which parameters can
inglytoproductswithhighaddedvalue,especiallyinthesector quickly be identified by the installation of experimental plan-
of fine chemistry (pharmaceutical products, cosmetics, etc.). ning[4].Nevertheless,thesemodelsrapidlyfindtheirlimitsin
This type of industry [1–3] is different from traditional chem- arestrictedfieldofvalidityandadifficultyofaccountingforthe
icalindustry.ThefinechemicalindustrylikeinFranceiswell dynamicsofthesyntheses.
known to be a strategic area which needs a lot of investments Since fine chemical reactions are usually complex, theirs
notonlyfinancialbutinhighlevelscientificknowledgeforthe kinetics are poorly known. The real problem is the fast devel-
R&D. The syntheses of such products are generally complex opment of realistic and safety stoichio-kinetic models of the
andinvolvesecondaryreactionswhicharetobeminimized. synthesis [5–8]. However, due to high purity requirements,
In this field, the faster development of processes is essen- environmentalregulationandcompetitivepressureonthenew
tial in order to answer the rapid evolutions of the market. The products, the development of dynamic models has become an
detailedstudiesofthemechanismsandkineticsofreactionsare importantobjective.
generallynotcarriedoutforreasonsofdurationandcost.Nev- The approach proposed does not depend on a detailed and
ertheless, for optimization and advanced control of processes predictive model of the process and at the same time it does
not ignore what we already know about the process, such as
material balances, heat and mass transfer characteristics, etc.
∗ Correspondingauthor.Tel.:[phone];fax:[phone]. Nevertheless,astoichiometricmodelshoulddescribethediffer-
E-mailaddress:[email protected](P.Cognet). entstagesofthesynthesis,orthemostimportanttendencies.It
canbeobtainedbycreatingpseudo-reaction(roundupofseveral ThestoichiometryofareactionsysteminvolvingNCspecies
reactions)orpseudo-compound(roundupofseveralcompounds A (j=1,NC)andNRreactionsR (i=1,NR),canbewritten:
j i
or addition of losses) [5]. The identified model can be used to
(cid:2)NC
calculatethekineticofthedifferentreactionsdeterminingthus
ν A =0 (1)
therateofthechemicaltransformation.Thistechniquehasbeen ij j
j=1
usedwithsuccessbyseveralresearchers[9–15]forthemodel-
ingofchemicalsynthesesliketheepoxidationofoleicacid[14], where ν is the stoichiometric coefficient of A in the reaction
ij j
orthepolymerizationofacrylonitrile-styrene[10]carriedoutin R.
i
batchreactors.
Inseveralcases,theoptimizationproblemsofdiscontinuous • Ifν >0thenA isaproductinthereactioni;
ij j
reactorareformulatedwithtwokindsofobjectives:maximum • Ifν <0thenA isareactantinthereactioni;
ij j
conversionproblem,theoperativetimeisfixedapriori,ormin- • Ifν =0thenA isnotinvolvedinthereactioni.
ij j
imum time problem, the conversion rate of wished product is
fixedapriori. ForabatchreactorandadatabaseofNEexperiments(k=1,
Garciaetal.[16]consideredthefirstcase.Theyconvertedthe NE), the mole number of the compound A in the chemical
j
problemofoptimalcontrolintoanon-linearproblemsolvedby transformation,representedbyseveralreactionsR,isgivenby
i
a reduced gradient algorithm (GRG) coupled with the golden
search method. This tool allows to optimize simultaneously (cid:2)NR
n =n0 +n0 ν X (2)
different variables (temperature, feed flow rate and amount of jk jk ij ik
reactant, operation time, etc.) and to take into account bounds i=1
and linear and/or non-linear constraints on the variables. The where n is the mole number of A in the experiment k at the
jk j
use of constraints allows to reach a solution witch is not only instantt,n0 theinitialmolenumberofA intheexperimentk,
jk j
a numerical solution but witch is closer to the experimental X the extent of the reaction R in the experiment k, and n0 is
ik i
reality.
the normalizing factor equal to the sum of the initial reactants
AzizandMujtaba[17]areinterestedtotheconsecutivereac-
molenumbers.
tionoptimizationinbatchreactors.Theoptimizationproblems
areformulatedwithenvironmentalandoperationalconstraints (cid:2)NC
n0 = n0 , k =1,NE (3)
andsolvedbythecontrolvectorparameterisation(CVP)tech- jk
nique. Two different models are presented: a shortcut model, j=1
consisting of only mass balance and reaction kinetics, allows Forsimplificationreasonswenote:
determination of the optimal reactor temperature profiles to
achieveadesiredperformance.Theoptimaltemperatureprofiles Y =y −y0 = njk−n0jk (4)
canthenbeusedasabasisforthedetaileddesignofthereactor jk jk jk n0
(i.e. reactor volume, heating/cooling configuration, etc.). The
Eq.(2)becomes:
detailedmodel,consistingofmassandenergybalances,reaction
kinetics and cooling/heating configuration, allows determi- (cid:2)NR
nation of the best operating conditions of already designed Yjk = νijXik (5)
reactors. i=1
In this work, the methodology is illustrated through its
Theequationsystemrepresentingthewholesetofequationscan
applicationtoacomplexchemicaltransformation:aldoliccon-
beputunderthefollowingmatrixform:
densationoffurfural(F)onacetone(Ac),whichallowsmainly
two products noted (FAc) and (F2Ac) to be obtained. This [Yjk]=[νij]T[Xik] (6)
synthesis valorises the residues of sugar cane treatment since
Ormoresimply:
furfuralisobtainedbyhydrolysisofthesugarcanebagassethen
extractedbyvaportraining.The(FAc)isusedasaromainsev- Y =νTX (7)
eral types of food industries. The study of this synthesis has
been made with the collaboration of Cuban Research Institute Severaltechniqueshavebeendeveloped[5]allowingtheiden-
forSugarByproducts(ICIDCA). tification of the stoichiometry of chemical syntheses. The first
method proceeds with iterative way by constructing reaction
2. Theoreticalpart by reaction a more and more complex system to improve the
representativenessofthestudiedsynthesis.Thesecondmethod
2.1. Identificationofastoichiometricmodel treats the problem in a more global manner and determines a
stoichiometric matrix in only one stage: it is the singular val-
Thestoichiometryofchemicaltransformationdeterminesthe uesdecomposition(SVD)method[18,19].Anapproachcalled
proportionsaccordingtowhichthedifferentconstituentsreact “target factor analysis” (TFA)[20] enables to know whether a
orareformed.Ingeneral,theseproportionsareintegerorsemi- postulatedstoichiometryfromaprioriinformationiscompatible
integer. withtheabstractfactors.
2.2. Identificationofkineticmodel Thecorrelationcoefficient(r)isusedtomeasurethe“good-
nessoffit”.Itisdefinedas
Themolarbalanceforareactoroperatinginbatchorsemi- (cid:4)
N (x −x¯)(y −y¯)
batchmodegives: r = (cid:5)(cid:4) i=1 i (cid:5)(cid:4)i (15)
N (x −x¯)2 N (y −y¯)2
dnj =Fe +R V (8) i=1 i i=1 i
j j r
dt
wherex meansdatapointsandy meansmodelpoints.
i i
withnjisthemolenumberofAjatinstantt,Fejthefeedrateof Theaverageofthedatapoints(x¯)andthemodelpoints(y¯)
thecompoundAj(j=1,NC),andVristhereactorvolumeand aresimplygivenby
(cid:2)NR (cid:2)N (cid:2)N
1 1
Rj = νijri (9) x¯ = xi and y¯ = yi (16)
N N
i=1 i=1 i=1
Rjistheproductionrateifitispositiveandconsumptionrateif Asthemodelbetterdescribesthedata,thecorrelationcoef-
itisnegativeandriistherateofreactioni. ficient will approach unity. For a perfect fit, the correlation
Eq.(8)maybewrittenwithextentofreaction,weobtain: coefficientwillapproachr=1.
dX V
i = rr (10)
dt n0 i 2.3. Optimizationofchemicalsynthesis
In this work, the transformation is supposed to be a pseudo-
The general procedure of optimization is formulated as the
homogeneous one and the kinetic law is written as a classical
following[22]:
Arrhenius’s law. It is important to emphasize that the form of
thekineticlawanditsdegreeofcomplexitydependontheuser minf(x), x∈(cid:4)n; g(x)=0, i=1,m ;
i e
andthedesiredaccuracyofthetendencymodel.
g (x)≤0, j =m +1,m; x ≤x≤x (17)
So,wehave j e l u
(cid:3)NC wherefistheobjectivefunctiontominimize,githeequalitycon-
ri =ki0e−Eai/RT Cjaij (11) straints,gjtheinequalityconstraints,methenumberofequality
j=1 constraints,mthetotalnumberofconstraints,xlthelowlimitof
xvariable,andx istheuplimitofxvariable.
u
whereki0isthepre-exponentialfactorforreactioni,Eaitheacti- The goal of the problem is to minimize a function f that
vationenergyforreactioni,Cj theconcentrationofconstituent depends on several variables. These variables are limited and
j,andaijistheorderofconstituentjinthereactioni. submittedtoequalityandinequalityconstraints.Ingeneral,the
Accordingto(11),Eq.(10)maybewritten: functionfisnotlinearandisnotgivenunderexplicitshapeof
variables.
(cid:3)NC
dX V
dti = n0ki0e−Eai/RT Cjaij (12) tionTohfethoeptwimorikzaintigoncoonfdiaticohnesm(tiecmalpesyranttuhrees,ifseeisd-trhaeted,eotpeermraitnivae-
j=1
time),thatmaximizeasynthesiscriterion(output,concentration,
The orders are assumed to be part of the data of the problem etc.)undersomeconstraints.
and are chosen a priori to be equal to the absolute value of The resolution of the problem requires the discretisation of
the stoichiometric coefficients of every reactant. The identifi- temperatureprofilesandfeed-ratesintofiniteintervalsinsidethe
cationofkineticparameters(pre-exponentialfactor,activation intervalofoperation[t ,t ],wheret representstheinitialtime
0 f 0
energy)isdeterminedbyminimizingthedifferencebetweenthe ofoperationandt thefinaltimeofoperation.Theinterval[t ,t ]
f 0 f
experimentalconcentrationsandthosecomputedwiththeiden- isdiscretisedintoafinitenumber(n )ofintervals.Afunction
int
tifiedparametersforthedifferentconstituentsaccordingtothe isdefinedtorepresenttheevolutionofthecontrolvariablev(t)
followingcriterion: ineverytimeinterval:
(cid:6) (cid:7)
J =(cid:2)NE(cid:2)NC C00 (Cf −Cf )2 (13) v(t)=Φ(t,zj), t∈ tj−1,tj , j =0,nint (18)
C0 jkid jkexp
k=1j=1 1k where t is the commutation time and z is the temperature and
j
feed-ratevaluesinboundsofeachinterval.
with
Inordertoavoidcomplextemperatureandfeedprofiles, Φ
(cid:2)NE
functionisassimilatedtoasimplefunction:
C0 = C0 (14)
0 1k
k=1 • Alinearfunctionforthetemperature:
andC0 istheconcentrationofakeyreactantinexperimentk. (cid:8) (cid:9)
BatTchhem1kowdh[o2le1]p.rocedure has been implemented on software, v(t)=zj−1+(t−tj−1) ztjj −−ztjj−−11 , j∈[1,nint] (19)
Thelasttemperatureofintervaljissupposedtobeequalto
theinitialtemperatureofintervalj+1.
• Aconstantfunctionforthefeed-rate:
v(t)=a , j∈[1,n ] (20)
j int
Theprogramdeterminesthemassflowineveryintervaland
supposesthatitremainsconstantinthisinterval.Thefeed-rateis
thusasuccessionoflandings.Theresolutionoftheoptimization
problem returns to the determination of (n +1) temperatures
int
andn valuesoffeed-rate.
int (b) Condensation of the carbanion on the carbon of furfural
Thisoptimizationmethodallowstoscaleupachemicalreac-
carbonylfunction:
tioninbatchreactorwithsafetyconstraints[23,24].
2.4. Energybalance—thermalfluxmodeling
AclassicalSemenov-typeanalysis[25]isusedtodescribethe
exothermicreaction.Therateofheatproductionisproportional (c) FixationofH+ontheoxy-anion:
tothereactionspeed,whichmeansitisanexponentialfunction
oftemperature.ItisgivenbyEq.(21):
(cid:8) (cid:9)
E
Q =V (cid:4)Hk0exp − a C (21)
released r initial
RT
whereQ istheheatfluxreleasedbythereaction,V the
released r
reactingvolume,(cid:4)Htheheatofreaction,k0thepre-exponential (d) Regenerationofhydroxideionbaseanddehydrationinbasic
factor of reaction, E the activation energy, and C is the medium:
a initial
initialconcentration.
Thethermalfluxevacuatedoutofthereactorisexpressedby
Eq.(22).Itisproportionaltoatemperaturedifferencebetween
reacting solution and coolant fluid, exchange area and global
heattransfercoefficient.Alittlevariationofcoolantfluidtem-
perature induces a linear variation of thermal flux evacuated
fromthereactor:
Q =UA(T −T ) (22)
evacuated cf reactor
whereQ isthethermalfluxevacuatedwithjacketreac-
evacuated
tor,Utheglobalheattransfercoefficient,Atheexchangesurface
reactor, T the cooling fluid temperature, and T is the
cf reactor
Finally,thereactionsofformationof(FAc)and(F Ac)are:
reactortemperature. 2
3. Experimentalpart
3.1. Aldoliccondensationoffurfuralonacetone
(23)
Thealdoliccondensation[26–29]offurfural(F)onacetone
(Ac) takes place in alkaline medium. It implies the generation
ofacarbanionobtainedfromabstractionofaprotoninalphaof
acetonecarbonylfunctionandleadstothe4-(2-furyl)-3-buten-
2-one(FAc).Becauseofthesymmetryoftheacetonemolecule,
asecondattackofthefurfuralcanhappenwhichthenleadsto
thedi-addingproduct,the1,4-pentadien-3-one,1,5-di-2-furanyl
(F Ac).
2 (24)
Thedifferentstepsfortheformationof(FAc)moleculecan
bewritten: The reversibility of reactions (23) and (24) are negligi-
ble.Besidesthesetworeactions,othersmayhappen.Amongst
(a) Extraction of a proton on acetone and formation of the the known reactions, furfural can react with itself in an
carbanion: oxydo-reductionreaction(Cannizaroreaction)togiveahigher
oxidationproduct,the2-furoicacid(Furo),andaloweroxida- 3.2. Conditionsofthereaction
tionproduct,thefurfurylalcohol(Furfu)[30].Thisreactioncan
takeplaceinhighlyalkalinemedium.Ontheotherhand,acetone Thereactionsareachievedindiscontinuousmodeinajack-
canreactonitselftogivethe4-hydroxy-4-methylpentan-2-one etedglassreactorof250mLcapacity(Fig.1).Theacetoneand
(Ox ),whichafterdehydrationleadstothemesityloxide(Ox ) thefurfuralarechargedinthereactorwithequi-molarquantities.
1 2
[30]. Thesolventusedisanequi-molarmixtureofwaterandethanol.
Thepresenceofethanolinthemediumfavoursthedissolutionof
FAcandF Acwhicharenotsolubleenoughinwater.Anaque-
2
oussolutionofsodiumhydroxide(0.03molL−1)isinjectedto
triggerthereaction.Thetemperatureofthemediumcanbemain-
tainedconstantthankstoaheating-coolingsystem.Thereaction
volumeisconstantandequalto98mL.
(25)
The initial compositions are chosen according to the sug-
gestionsoftheCubanResearchInstituteforSugarByproducts
(ICIDCA).Itwasnotvariedbecauseofindustrialrestrictions.
3.3. Analyticalprocedure
(26) Theconcentrationsofreagentsandproductsaredetermined
bygasandliquidchromatography.Onlytheacetoneismeasured
Allusedchemicalshaveanalyticalgrade.The1,4-pentadien- by gas chromatography, the formed products (FAc and F Ac)
2
3-one,1,5-di-2-furanyl is not commercialized, therefore, it has beingheat-sensitives.Forthetwotechniques,ethanolisusedas
beenpreparedandpurifiedinthelaboratory. aninternalstandardinadditiontoitssolventrole.
Fig.1. Experimentalequipmentusedforthechemicalsynthesis.
Table1
WavelengthscorrespondingtoamaximalUVabsorption
Products λmax(nm)
Acetone 265
Furfural 274
FAc 322
F2Ac 382
2-Furoicacid 228
Furfurylalcohol 220
Mesityloxide 232
4-Hydroxy-4-methylpentan-2-one 232
For gas chromatography, the injections are realized in split
mode.Aflameionizationdetector(FID)isused.Apolarcolumn
(FFAP, 25m×0.32mm i.d.) with a film thickness of 0.25(cid:2)m
Fig.3. Molenumberevolutionofthecompoundsat24◦C.
separatesthesolventandthematrixofcomponents.Theinjector
◦
ismaintainedatatemperatureof250 C.Theflameionization
detector is heated until 300◦C. The initial temperature of the theapparitionof(FAc)and(F2Ac).Theconversionoffurfural
◦ approaches 95% while that of acetone is near 62%. The pro-
ovenis50 C.After1.5min,thetemperatureincreasesquickly
at the rate of 50◦C/min until 240◦C then it remains constant ductionof(F2Ac),moreimportantthanthatof(FAc),explains
thebestconversionofthefurfural.Furthermore,theanalysishas
during5min.Thetotaltimeofanalysisis10.3min.Heliumis
notrevealedthepresenceofeither2-furoicacidorfurfurylalco-
usedasthecarrier-gas.
hol.Alsoneither(Ox )nor(Ox )wasdetected(Eq.(26)).Then
The products (F), (FAc) and (F Ac) are measured by high 1 2
2 suggestedreactionsforthesynthesisareonlyreactions(23)and
performanceliquidchromatography(HPLC)[31–36].Thesys-
(24).
temisequippedwithUV–visdetectorandanautomaticinjector
Inordertoverifytheaccuracyofthesupposedstoichiometric
of 25(cid:2)L in full loop. An ODS Hypersyl C 5(cid:2)m column
18 matrix,itisnecessarytoverifythatmolarandmassbalancesare
(125mm×4mmi.d.)isusedfortheseparationoftheproducts.
correct. Assuming that only reactions (23) and (24) occur, the
ChemicalcompoundshavedifferentmaximumUVabsorp-
molarbalancecanbewrittenas
tionatdifferentwavelengths.Table1showsthewavelengthat
which the maximum UV absorption is observed for the com- n0 =n +n +2n (27)
F F FAc F2Ac
poundsofthesynthesis.Theuseofthreedifferentwavelengths
(265, 322 and 382nm) allows to measure with precision the n0Ac =nAc+nFAc+nF2Ac (28)
quantityofdifferentcompounds.
n =n +2n (29)
Theeluentisamixtureofwaterandmethanol.Fig.2sum- H2O FAc F2Ac
marizestheprocedureofHPLCanalysisadoptedtofollowthe Itisnecessarytodeterminethenumberofmolesofwaterformed
concentrations of the different compounds in the aldolic con- duringthesynthesistobeabletoestablishthemolarandmass
densationoffurfuralonacetone. balances.Theformedwaterisnotdeterminedbychromatogra-
phybutcalculatedaccordingtoEq.(29).However,waterpresent
4. Resultsanddiscussion atthebeginninginthemediumdoesnotappearinthebalance
andwastakenintoaccountintheconcentrationofthesolvent.
4.1. Identificationofastoichiometricmatrix Themassbalanceshowsadeficitwhichincreaseswithtime
andthendecreasesattheendofthesynthesis(Fig.4).Thefur-
Severalreactionshavebeencarriedoutattemperatureof24, furalandtheacetoneweremoreconsumedthantheprediction
◦
29,34and40 Candatmosphericpressure.Thestudyhasnot with the supposed reaction scheme. Supplementary reactions
◦
exceeded 40 C because the acetone ebullition temperature is mustthereforebeaddedtothestoichiometricmodel.TheCan-
◦ ◦
56 C. The mole number variation of the compounds at 24 C nizaroreactionbeingrejected,thepossibilityofpolymerization
(Fig. 3) shows the disappearance of acetone and furfural and reactionswasstudied.Themainreactionofpolymerizationmen-
Fig.2. ChangeofwavelengthandeluentcompositionfortheanalysisbyHPLC.
Sinceproduct(P)appearsatthesametimeas(FAc),thenit
cannotbeapolymerofthelater.Itisratherformeddirectlyfrom
thefurfuralandtheacetone(Eq.(30)).Thisequationisonlya
representationanddoesnotaccountforachemicalmechanism.
It would then imply a five reactants encounter, which is not
realistic. The product (P) disappears during the reaction, this
disappearancecouldberepresentedbyEq.(31).HPLCandGC
analyses has not reveal the presence of other products aside
furfural,acetoneFAc,F AcandP,thatiswhythedecomposition
2
ofPtoFAcandF Acisthemostprobableandnototherproducts.
2
Finally,itwassuggestedthatthissynthesiscouldberepresented
bythefourreactions(23),(24),(30)and(31).
Fig.4. Massbalancefortheexperimentat24◦C(H2OcalculatedfromEq.
(21)).
(30)
(31)
Themolarbalancesassociatedtothereactions(23),(24),(30)
and(31)become:
Fig. 5. Example of HPLC chromatogram (experiment at 40◦C, reaction n0 =n +n +2n +3n (32)
F F FAc F2Ac P
time=10min).
n0 =n +n +n +2n (33)
Ac Ac FAc F2Ac P
tionedintheliterature[37]istheformationof(FAc)n fromthe n =n +2n +3n (34)
(FAc)inbasicmedium,nbeingsuperiororequalto2. H2O FAc F2Ac P
IntheHPLCchromatogramsobtained,anunidentifiedpeak With the new reactions system proposed for the synthesis, the
canbenoticed.Itispresentduringthefirstminutesofthesyn- concentrationsof(P)andwatercanbecalculatedbytwoways,
thesis and then it disappears. It has a retention time near that from the balance on acetone (Eqs. (33) and (34)), or from the
of (FAc). The product (P) which corresponds to this peak is balanceonfurfural(Eqs.(32)and(34)).Thetwomethodshave
sensitivetothewavelengthof322nm(Fig.5). beentestedandthevaluesobtainedwereveryclose.Contrarily
Toidentifytheproduct(P),weusedtheHPLCanalysiscou- tothepreviouscase(systemoftworeactions)therepresentation
pled with mass spectroscopy (Fig. 6). This analysis revealed of the synthesis by four reactions allows to get a correct mass
thatthisproducthasanimportantmolarmassnear350gmol−1. balance.Themaximalerrorobservedis6.1%(Fig.7).
Thedevelopedformulaof(P)showninFig.6isoneofpossible Theexperimentcarriedoutattemperaturesof24,29,34and
◦
formulasdeducedfromthefragmentsidentifiedonthespectrum. 40 Callowtogeneratearangeofinput/outputconcentrations
Fig.6. Spectrumofmassspectroscopy(thepeakat240.3amuisvisibleonthespectraofallanalyzedsamples).
Table3
Calculatedstoichiometricmatrix
F Ac FAc F2Ac P H2O
Reaction1 −0.983 −1.012 0.985 0.048 −0.017 0.980
Reaction2 −1.037 0.043 −0.985 0.994 0.034 1.044
Reaction3 −2.988 −2.022 −0.043 0.074 1.021 2.987
Reaction4 −0.015 0.025 1.039 0.916 −1.034 0.016
Table4
Kineticparametervalues(reactionrateinmolL−1s−1)
Activationenergy,Ea(Jmol−1) Pre-exponentialfactor,k0
Reaction1 74581.559 3.7979×108
Reaction2 35959.731 2.2094×102
Fig.7. Massbalancefortheexperimentat24◦C(H2OcalculatedfromEq. Reaction3 58914.459 4.4197×104
(26)). Reaction4 117919.191 9.5420×1015
forthesixcomponentsofthesynthesisandthereforetofeedthe
algorithmofcalculation.TheSVDmethodprovidesthefollow- An error of 3.02% was obtained for the main reaction, 4.05%
ingsingularvalues: forthesecondreaction,1.93%forthethirdreactionand6.03%
for the fourth reaction. Results show that the postulated stoi-
chiometryiscompatiblewiththeabstractfactors.Themodelcan
thereforebeadoptedfortheidentificationofkineticparameters.
4.2. Determinationofthekineticparameters
Knowingthatthemostimportantvaluesindicatethenumber
ofnecessaryreactionsforthedescriptionofthesynthesis,itcan
Thedeterminationofthestoichiometryofthechemicaltrans-
be assumed that the chemical transformation can be described
formationallowstofindtheproportionsaccordingtowhichthe
adequatelybyasystemoffourorfivereactions.
componentsreact.Thenextstepformodelingconsistsinidenti-
Accordingtotheavailableknowledgeaboutthetransforma-
fyingthekineticparametersforeachreaction.Inthiswork,the
tion,itwaspostulatedastoichiometrywithfourreactions:
transformation is supposed to be a pseudo-homogeneous one
and the kinetic law is written as a classical Arrhenius’s law.
• Thefirstreactionrepresentstheformationof(FAc)fromfur-
The orders of compounds are taken equal to absolute values
furalandacetone.
ofstoichiometriccoefficientsforthereactantsandzeroforthe
• Thesecondreactionrepresentstheformationof(F Ac)from
2 products.Table4givesthevaluesofactivationenergy(E )and
a
(FAc)andfurfural. pre-exponentialfactor(k0)identifiedaccordingtoEq.(11).
• Thethirdreactionrepresentstheformationof(P)fromthree
Thefirstreactionissensitivetotemperature;theproduction
molesoffurfuralandtwomolesofacetone.
of(FAc)increasesastemperaturerises.Thesecondreactionis
• The fourth reaction represents the consumption of (P). One
less sensitive to temperature than the first. The third reaction
moleof(P)givesonemoleof(FAc)andonemoleof(F Ac).
2 which corresponds to the formation of (P) is far less activated
bytemperaturethanthefourthreactionwhichcorrespondstothe
Table 2 contains the postulated stoichiometry and Table 3
consumptionof(P).Thedisappearanceof(P)issomorerapid
containsthecalculatedstoichiometry.Eq.(35)allowstheerror ◦ ◦
at40 Cthanat24 C.
between the target matrix and the calculated matrix for every
Fromthekineticparameters,thetime-dependenceoftheoret-
reactiontobecalculated:
(cid:10) icalconcentrationscanbeillustrated.Thecomparisonbetween
(cid:11) (cid:13) (cid:13)
(cid:11)(cid:4) (cid:13) (cid:13)2 the time-dependence concentrations obtained from the experi-
(cid:11)(cid:11) Nj=C1(cid:13)νitjarget−νicjalculated(cid:13) ment and from the model is given in Figs. 8–11. A statistical
error(i)=(cid:12) (cid:4) (cid:13)(cid:13) (cid:13)(cid:13)2 (35) analysis is provided regarding the significance of the fitted
NC (cid:13)νtarget(cid:13)
j=1 ij kinetic parameters. Table 5 shows the correlation coefficients
Table2 Table5
Targetstoichiometricmatrix Correlationcoefficients
F Ac FAc F2Ac P H2O F Ac FAc F2Ac P H2O
Reaction1 −1 −1 1 0 0 1 Reactionat24◦C 0.9995 0.9984 0.8915 0.9974 0.9267 0.9995
Reaction2 −1 0 −1 1 0 1 Reactionat29◦C 0.9973 0.9986 0.9069 0.9986 0.9156 0.9973
Reaction3 −3 −2 0 0 1 3 Reactionat34◦C 0.9953 0.9956 0.9041 0.9994 0.9051 0.9953
Reaction4 0 0 1 1 −1 0 Reactionat40◦C 0.9972 0.9991 0.9252 0.9970 0.9688 0.9972
Fig.8. Evolutionofcompoundconcentrationsforthereactionat24◦C((—) Fig.11. Evolutionofcompoundconcentrationsforthereactionat40◦C((—)
model;((cid:2))experimentalpoints). model;((cid:2))experimentalpoints).
becausetheyplaytheroleofreagentsandproductsatthesame
time.
4.3. Optimizationofthesynthesis
In the previous paragraphs, a stoichio-kinetic model of
aldoliccondensationoffurfuralonacetonehasbeendetermined.
This model gives a satisfactory representation of the synthesis
behaviourandcanbeusedthereforeforitsoptimization.
Thestoichiometricmatrixadoptedis
Reaction1: F+Ac−k→1 FAc+H O, r =k [F][Ac]
2 1 1
Reaction2: F+FAc−k→2 F Ac+H O, r =k [F][FAc]
2 2 2 2
mFiogd.e9l.;(E(cid:2)v)oeluxtpioernimofenctoamlppooiunntsd).concentrationsforthereactionat29◦C((—) Reaction3: 3F+2Ac−k→3 P+3H2O, r3 =k3[F]3[Ac]2
obtained using Eq. (15). A good agreement was obtained Reaction4: P−k→4 FAc+F Ac, r =k [P]
2 4 4
between the experimental and model representation of fur-
fural, acetone, (F Ac) and water. However, the evolution of
2 4.3.1. Optimizationatlaboratoryscale
the compounds (FAc) and (P) is not as good. Behaviour of
In this section, the amounts of reactants are the same as
these intermediate components is the most difficult to predict
thereusedforexperiments,correspondingtoaninitialconcen-
trationof3molL−1forfurfuralandacetoneinbatchmode.The
operationtimeisequalto4h.
ThecriteriontomaximizeisthefinalFAcyield,definedas
theratiobetweenthemolenumberofFAcpresentattheendof
operation,andthemolenumberofinitialacetoneloadedinthe
reactor(Eq.(36)):
molenumberof(FAc)attheendofoperation
criterion= (36)
molenumberofinitialacetone
Thetemperaturedomainusedis
20◦C≤temperature≤40◦C
Theminimalandmaximaltemperaturechoicehasbeenguided
by the experimental domain that has been covered with the
experimental tests. In particular, the highest temperature has
◦
Fig.10. Evolutionofcompoundconcentrationsforthereactionat34◦C((—) been limited to 40 C. Taking a larger domain would lead to
model;((cid:2))experimentalpoints). solutions for which the validity of the model would be very
Fig.14. Evolutionofcompoundconcentrationsofthereactionat40◦Cinsemi-
Fig.12. Resultsofthesimulationindiscontinuousmodeatlaboratoryscale. continuous mode with a furfural feed-rate during 120min (calculated points
withsmoothing).
uncertain. Moreover, at atmospheric pressure, the temperature
◦
islimitedby56 Ctheacetoneboilingpoint.
• Workingindiscontinuousmode(Batch),thebestisothermis
◦
40 C,themaximumthermalfluxgeneratedisequalto10W
(Fig.12)andFAcyieldapproaches29.82%.Feedingacetone
couldleadtolargeamountoffurfuraltogetherwithlowcon-
centrationofacetone.ItwouldthenfavourF Acformation.
2
Itwasthendecidedtofeedfurfural.
Bycomparingthealdoliccondensationoffurfuralonace-
tone to a thermodynamic system, it is clear that this system
losesenergysincethesynthesisisexothermic,whichexplains
thenegativevaluesofthethermalfluxesinthedifferentfig-
ures.
• Whileapplyingafeed-rateof2.2916×10−4kgmin−1during Fig.15. Resultsofthesimulationinsemi-continuousmodeatlaboratoryscale
2handlookingforthebestisotherm,theoptimaltemperature withafurfuralfeed-rateduring60min.
◦
is 40 C, the thermal flux reaches a maximum of 1.5W and
theyieldliesaround28.5%(Figs.13and14).Whenreduc- tinuousmode(Figs.17and18).Table6summarizesoperative
ingthefeedingtimeto1h,theoptimaltemperatureisalways conditionsobtainedforthedifferentproblemstreatedinsemi-
40◦C,thethermalfluxreaches2.8Wandthechemicalyield continuousanddiscontinuousmodeatlaboratoryscale.
isslightlyimprovedandbecomes28.87%(Figs.15and16).
By decreasing the feeding time to 30mn, the optimal tem- Heatgeneratedinbatchmodecanbeeasilyremovedatlabo-
peraturedoesnotchange(40◦C),thethermalfluxincreases ratoryscale.Intheopposite,itisdifficulttoevacuatethisheatat
to 5.2W. Furthermore, the obtained chemical yield is about industrialscale.Thecoolingcapacityofdiscontinuousreactors
29.43%.Thisresultisthenearestonecomparedtothediscon- (typeagitatedtank)isgenerallylimited.Especially,theratiosur-
Fig.16. Evolutionofcompoundconcentrationsofthereactionat40◦Cinsemi-
Fig.13. Resultsofthesimulationinsemi-continuousmodeatlaboratoryscale continuousmodewithafurfuralfeed-rateduring60min(calculatedpointswith
withafurfuralfeed-rateduring120min. smoothing).