Phase equilibrium of the CO2/glycerol system: Experimental data by in situ FT-IR spectroscopy and thermodynamic modeling

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Phase equilibrium of the CO2/glycerol system:

Experimental data by in situ FT-IR spectroscopy and

thermodynamic modeling

Yaocihuatl Medina-Gonzalez, Thierry Tassaing, Séverine Camy,

Jean-Stéphane Condoret

To cite this version:

Yaocihuatl Medina-Gonzalez, Thierry Tassaing, Séverine Camy, Jean-Stéphane Condoret. Phase

equilibrium of the CO2/glycerol system: Experimental data by in situ FT-IR spectroscopy and

thermodynamic modeling. Journal of Supercritical Fluids, Elsevier, 2013, vol. 73, pp. 97-107.

�10.1016/j.supflu.2012.11.012�. �hal-00877680�

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_{: Medina-Gonzalez, Yao and Tassaing, Thierry}

and Camy, Séverine and Condoret, Jean-Stéphane Phase equilibrium of

the CO2/glycerol system: Experimental data by in situ FT-IR

spectroscopy and thermodynamic modeling. (2013) The Journal of

Supercritical Fluids, vol. 73 . pp. 97-107. ISSN 0896-8446

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Phase

equilibrium

of

the

CO

2

/glycerol

system:

Experimental

data

by

in

situ

FT-IR

spectroscopy

and

thermodynamic

modeling

Y.

Medina-Gonzalez

a,b,c,1,2

_,

_T.

_Tassaing

c,∗

_,

_S.

_Camy

a,b,1

_,

_J.-S.

_Condoret

a,b,∗∗

a_{UniversitédeToulouse,INPT,UPS,LaboratoiredeGénieChimiqueUMRCNRS5503,4,AlléeEmileMonso,F-31030Toulouse,France} b_{CNRS,LaboratoiredeGénieChimique,F-31432Toulouse,France}

c_{InstitutdeSciencesMoléculaires,UMR5255CNRS,UniversitéBordeaux,351,coursdelaLibération,33405TalenceCedex,France}

Keywords: Glycerol SupercriticalCO2 Biphasicsystem Phaseequilibrium Infraredspectra Thermodynamicmodeling

a

b

s

t

r

a

c

t

PhaseequilibriumexperimentaldatafortheCO2/glycerolsystemarereportedinthispaper.The

mea-surementswereperformedusinganinsituFT-IRmethodfortemperaturesrangingfrom40◦_Cto200◦_C

andpressuresupto35.0MPa,allowingdeterminationofthemutualsolubilityofbothcompounds. Con-cerningtheCO2richphase,itwasobservedthattheglycerolsolubilityinCO2wasextremelylow(in

therangeof10−5_{inmolefraction)inthepressureandtemperaturedomainsinvestigatedhere.}

Con-versely,theglycerolrichphasedissolvedCO2 atmolefractionsupto0.13.Negligibleswellingofthe

glycerolrichphasehasbeenobserved.Modelingofthephaseequilibriumhasbeenperformedusing thePeng–Robinsonequationofstate(PREoS)withclassicalvanderWaalsonefluidandEoS/GE_based

mixingrules(PSRKandMHV2).Satisfactoryagreementwasobservedbetweenmodelingresultsand experimentalmeasurementswhenPSRKmixingrulesareusedincombinationwithUNIQUACmodel, althoughUNIFACpredictiveapproachgivesunsatisfactoryrepresentationofexperimentalbehavior.

1. Introduction

Recently,interestinbiphasicsystems,whichcouple supercrit-icalCO2andaconventionalliquidsolventhavebeenhighlighted

[1,2],astheycanprovideinnovativereactionmedia.Theinterest ofthesebiphasicsystemsismaximumwhenthepartnersolventis abiosourcedsolventbecausesuchsystemsbecomethen environ-mentallyfriendly.Suchbiphasicsystemsareusefultoovercome thelimitedsolvatingpowerofpurescCO2,especiallyinrespectto

homogeneouscatalysiswhereinthiscasecatalystscanbemore easilysolubilizedintheliquidsolvent.Theycanalsoalleviatethe drawbackoftheconventionaluseofbiosourcedsolventswhoselow volatilityusuallyhandicapseasyrecoveryofthereactionproducts. Indeed,supercriticalCO2canbeusedtorecoverthereaction

prod-uctsbyextractionfromtheliquidphase.Inaddition,thesebiphasic systemscanbeconsideredasintensifiedsystemsbecause,inthis case,reactionandseparationareoperatedinonesinglestep.

∗ Correspondingauthor.Tel.:+330540002892;fax:+330540008402. ∗∗ Correspondingauthorat:UniversitédeToulouse,INPT,UPS,Laboratoirede GénieChimiqueUMRCNRS5503,4,AlléeEmileMonso,F-31030Toulouse,France. Tel.:+330534323697;fax:+330534323707.

E-mailaddresses:t.tassaing@ism.u-bordeaux1.fr(T.Tassaing),

jeanstephane.condoret@ensiacet.fr(J.-S.Condoret).

1 _{Tel.:+330534323713;fax:+330534323707.} 2 _{Tel.:+330534323670;fax:+330534323697.}

Amongthebiosourcedsolvents,glycerolisofprimeinterestas itisabyproductinbiodieselfabricationanditisthereforevery eas-ilyavailable.Provideditspotentialownchemicalreactivityisnot problematic,glycerolcanbeproposedasanalternativereaction mediumforwater,whenwaterisnotsuitableduetoitshydrolytic powerorinthecaseofdehydrationreactionsforinstance.Glycerol hasbeenshowntobeaninterestingalternativefordifferentorganic synthesis [3,4] asfor instanceselective reduction of aldehydes, ketonesandb-ketoesterswithNaBH4[5].Severalotherexamples

havebeengatheredina reviewbyDiaz-Alvarez etal.[6]. Stud-iesbyJérômeandGu[7–9],haveshownthat,insomereactions, suchastheAza-Michaelreactionofp-anisidineandtheMichael reactionofindole,glycerolusedassolventiscapabletoachieve yieldsupto80%undercatalyst-freeconditions,theseyieldsbeing higherthanthoseobtainedwithusualsolvents.Thesameresearch grouphasdeveloped aseriesofcatalystscombinedwith sugar-based-surfactantsoforganicsubstrateswhichfavorsmasstransfer oforganicsubstratesandlimitstheundesiredreactivityof glyc-erol [10].However,drawbacksin theutilizationof non-volatile solvents,suchasglycerol,arestilltheuneasyrecoveryofproducts andrecyclingofcatalysts.Inthiscontext,biphasicsystemsusing supercriticalCO2(scCO2)asapartnerphasemakeitpossiblethe

solubilizationofthecatalystintheglycerolphasewhileproducts areextractedbyscCO2[9,11,12].

Inthiscontext,oneprerequisiteforeffectivedesignandcontrol ofsuchbiphasicsystemsistheknowledgeofthephaseequilibrium

ofthemixture.Also,understandingtheeffectsofdissolvedCO2on

thephysicochemicalpropertiesoftheglycerol-richphaseis impor-tantforreactiondesign[13,14].Indeed,CO2modifiesthepolarity

ofthesolventand,forinstance,fromthiseffect,initiallymiscible compoundsarelikelytobecomeimmisciblewhenthesolventis pressurizedwithCO2,evenatmoderatepressures(5.0MPa)[15].

So,CO2canthenactasaswitchtocontrolthepolarityand

solvat-ingpropertiesofthepartnersolvent,allowingrecoveryofcatalysts, products,byproducts,andsoon.Despitethisrecentgrowing inter-estforscCO2/glycerolsystem,phaseequilibriumexperimentaldata

arescarceandnotyetfullyvalidated.Onlytwostudiesupon exper-imentaldeterminationsofsolubilityofglycerolinpressurizedCO2

havebeenpublished[16,17]andtheirresultsarenotincoherence. Toperformaccuratemeasurementsofconcentrationsofthephases inequilibrium,thetechniqueofinsituFTIRspectroscopycanbe proposed.Thismethodhasbeenpreviouslysuccessfullyappliedin phaseequilibriumstudiesforthedeterminationoftheCO2sorption

andswellinginliquids[18,19]andinpolymers[20,21].In particu-lar,wewouldliketostressthatmolarabsorptioncoefficientsofCH– stretchingvibrationalmodesandcombinationbandsareexpected toexhibitlittlesensitivityupontemperatureandpressure condi-tions[20,22,23].Forexample,Bubacketal.[24]haveshownthat themolarabsorptioncoefficientofcombinationbandsofCO2were

almostindependentoftheCO2density.Therefore,IRspectroscopy

allowsdeterminingtheconcentrationofagivenspecieinamixture withastatisticalerrorlowerthan10%.

Also,modelingofscCO2–glycerolphaseequilibriumhasbeen

alreadyproposed[25]butthelackofexperimentalresultsdidnot allowvalidationofthemodel.Suchcalculationsareusefulbut accu-ratepredictionofCO2–glycerolphaseequilibriumhasnotbeenyet

fullydevelopedandcomparedwithexperimentalresults. Inthiscontext,thepurposeofthepresentworkisto experi-mentallydeterminethephasebehavioroftheCO2/glycerolsystem

usinginsituFTIRspectroscopyandtoproposeanadequate ther-modynamicmodelingofthephaseequilibriumdata.

2. Experimental 2.1. Materials

Dry glycerol with purity of ≥99.5% was purchased from Sigma–Aldrich;watercontentwasdeterminedbytitrationwith a Mettler-Toledo DL38 Karl–Fischer titrator and found to be 0.04%. CO2 N45 was obtained from Air Liquide. All chemicals

wereusedwithoutfurtherpurification.ABioRadFTS-60A inter-ferometer equippedwitha globar asinfrared source,a KBr/Ge beamsplitterandaDTGS(deuteratedtriglycinesulfate)detector hasbeenemployedto recordsinglebeam spectrainthe range of 400–6000cm−1_{. Single beam spectra recorded with 2cm}−1

resolutionwereobtainedfromtheFouriertransformationof 30 accumulatedinterferograms.

2.2. Apparatusandprocedure

Thehigh-pressurecellandtheinfraredsetupusedforphase behaviordetermination experiments havebeen described thor-oughly elsewhere [18]. Solubility of glycerol in CO2 has been

determinedusingacellwithanopticalpath lengthof25.3mm andequippedwithgermaniumwindows,employingthefollowing procedure:bottomofthecellwasfilledwithdryglyceroland a magneticbarwasplacedinside.Thecellwastightlyclosedthen placedinsidetheinterferometerandthermostatedatthedesired temperatureusingcartridgeheaters.CO2waspumpedinsidethe

celltothedesired pressure and thesystemwasagitatedusing a magneticstirrer. Afteran equilibrationperiod of at least3h,

Table1

MolarextinctioncoefficientsofglycerolandCO2fordifferentabsorptionbands.

Glycerol CO2

Groupfrequency C–H C–H 22+3

Wavenumber(cm−1_{) 2933 2883 3696}

ε(Lmol−1_cm−1_{) 49.78 47.61 10.978}

FT-IRspectra of theCO2 rich phase wereobtained. During the

stabilizationof the operating conditions (weak decreaseof the pressurebetween1 and10barthatwascompensatedwiththe manualpump),consecutivespectrawererecordedevery30min. Equilibriumhasbeenconsideredasreachedwhenatleastthree consecutivespectraspacedby30mindidnotshowanysignificant absorbancedifference.Indeed,asaconsequenceofthehigh vis-cosityofglycerol,ithasbeenobservedthatequilibrationperiod wastemperaturedependentanddecreasedsharplywith tempera-ture:atlowtemperatures(40◦_{C)equilibrationneededabout120h.}

Twoseriesofmeasurementshavebeenperformedforanumberof pointsinspecifiedconditionsoftemperatureandpressuretocheck forthereproducibilityofthemeasurements.

CO2solubilityinglycerolwasdeterminedusingthesame

sys-tembyfillingthecellwithdryglycerol.Theopticalpathlengthwas fixedto0.12mmandsapphirewindowswereusedforthis deter-mination.FT-IRspectraoftheglycerol-richphasehavethenbeen acquired.Solubilityexperimentswereperformedattemperatures rangingfrom40to200◦_{Candpressuresupto35MPa.}

2.3. Dataprocessingforthedeterminationofmutualsolubility andphaseequilibrium

Beer–Lambertlaw(A=ε·L·c,whereAisthesampleabsorbance, εthemolarextinctioncoefficient(Lmol−1_cm−1_{),Ltheopticalpath}

length(cm)andcthesampleconcentration(molL−1_))wasusedto

calculatetheconcentrationsofglycerolandCO2ineachphase.In

ordertodeterminetheconcentrationofglycerolintheCO2-rich

phase,theabsorbanceofthetwopeakscenteredatabout2933and 2883cm−1_{associatedtotheCHstretchingmodeofglycerolwas}

used.

Asbaselinecorrectioncaninducelargeerrorswhenpeak inte-gratedareais usedforquantification,peakheightwasusedfor thesedeterminationsinordertominimizethiserror.Inorderto determinetheconcentrationofglycerol(Cglycerol)intheCO2-rich

phase,molarextinctioncoefficients(ε)fortwoselectedbandsof glycerolweredetermined fromspectraof aqueoussolutions of glycerolatknownconcentrations(seeTable1).Weemphasizethat thesignaloftheFTIRspectrumofglycerolintheC–Hstretching regionwasthesameinwater andinCO2 whichshows, asitis

expected,thattheC–Hstretchingvibrationalmodesofglycerolare notsensitivetothenatureofthesolvent.Thus,theconcentrations werecalculatedfromtheaverageoftheconcentrationvalues esti-matedwiththetwoconsideredCHpeaksofglycerol(seeTable1). In order to determine the CO2 concentration (CCO2) in the

glycerol-richphase,thepeakheightof the22+3 bandofCO2

centeredat3696cm−1 _{wasused.Molarextinctioncoefficientof}

thisbandwasdeterminedbyrecordingtheinfraredspectraofneat CO2atdifferenttemperaturesandpressures,thedensity

(concen-tration)wasthenobtainedfromliterature[26].Table1showsthe obtainedεvalue.

MolefractionofglycerolintheCO2-richphasehasbeen

calcu-latedas:

xglycerol=

Cglycerol

Cglycerol+CCO₂

(1) whereCglycerolistheconcentrationofglycerolasdeterminedbyour

Table2

Densityofpureglycerolatatmosphericpressureasfunctionoftemperature.

T(◦_{C) Density(kg/m}3₎a _Density(kg/m3_{) Relativedifference}c

40 1272.3 1248b _0.019 60 1281.3 1235b _0.036 80 1259.2 1223b _0.029 100 1209.3 1209.27b _2.5E−5 120 1189.7 1194.46c _0.004 140 1163.6 1179.51c _0.013 160 1131.0 1164.4c _0.029 180 1116.0 1148.64c _0.028 200 1083.1 1131.78c _0.043

a_{Datafromthisstudy(precision±5%).} b_{DatafromRef.[27].}

c _{DatafromRef.[48].Calculatedas}|obtainedvalue−literaturevalue|

literaturevalue .

Indeed,asthesolubilityofglycerolintheCO2richphaseisverylow

(seebelow),ithasbeenconsideredthattheconcentrationofCO2in

theCO2richphasewasnotaffectedbythepresenceofglyceroland

equaltothatofneatCO2underthesametemperature–pressure

conditions.

MolefractionofCO2 intheglycerol-richphasewasobtained

from: xCO₂ =

CCO2

CCO2+Cglycerol

(2) whereCCO₂ istheconcentrationofabsorbedCO2intheglycerol

rich-phasedeterminedbyourFTIRmeasurementsandCglycerolis

theconcentrationofneatglycerolobtainedfromFTIR measure-mentperformedonneatglycerolasafunctionoftemperature(see below).Indeed,asitwillbeevidencedbelowinSection3.2, signifi-cantswellingoftheglycerolrichphasebyscCO2wasnotdetectedin

therangeoftemperatureandpressureinvestigatedhere.Therefore, itwasassumedthattheconcentrationofglycerolintheglycerol richphasewasequaltothatofneatglycerolunderthesame tem-peratureconditions.Glyceroldensityatatmosphericpressurehas beencalculatedasafunctionoftemperaturefrompureglycerol spectra,byusingthepeak centered atabout5700cm−1_,which

wasassignedto2C–H.Thus,usingtheBeer–Lambertlaw,the

con-centration(density)ofneatglycerolwascalculatedusingthepeak heightofthebandobservedat5700cm−1_{associatedwiththe2}

C–H

overtone.Todeterminethemolarextinctioncoefficientεforthis mode,thespectrummeasuredatT=100◦_{Cwasusedasareference}

andthecorrespondingconcentrationdatareportedintheliterature atthesametemperature[27].Theconcentration(density)valuesof neatglycerolcalculatedusingthismethodareshowninTable2and goodagreementwithvaluesreportedintheliterature[27]canbe observed,relativedifferencebetweenbothvaluesispresentedas well.Thepresentvaluesofdensityhavethenbeenusedtocalculate theconcentrationoftheglycerol-richphase.

Finally,takingintoaccountallthesourceoferrorsassociated withourmethodology(baselinecorrection,constantmolar extinc-tioncoefficient,spectrometerstability),amaximumrelativeerror ofabout±5%intheconcentrationvalueshasbeenestimated.We emphasize thatthereliability of suchmethodology hasalready beendemonstratedinpreviousinvestigationsonthemutual solu-bilityofepoxidewithCO2 [19]andwaterwithCO2[23]wherea

satisfactoryagreementwithliteraturedatawasshown. 2.4. Phaseequilibriummodeling

Thermodynamic modeling was performed using the well-knownPeng–Robinson equationofstate(PREoS)[28],i.e.,with adifferentexpressionofthemitermforcompoundswith

acen-tricfactorgreaterthattheoneofn-decane(0.491)[29],asitisthe caseforglycerol.Inafirstapproach,Peng–RobinsonEoShasbeen

Table3

CharacteristicparametersofpurecompoundsusedinPREoS.

Compound Tc(K) Pc(MPa) ω M(kgkmol−1)

CO2[49] 304.21 7.38 0.2236 44.01

Glycerol[50] 850 7.5 0.516 92.09

usedwiththeclassicalvanderWaalsone-fluidmixingrule(vdW1f) foraandbparameters.Classicalcombiningrules,i.e.,geometric meanrulewithkijbinaryinteractioncoefficientforaijparameter,

andarithmeticmeanrule,withoutanyinteractioncoefficient,for bijparameterhavebeenused.Finally,aandbparametersofthe

mixtureareobtainedfromthefollowingequations: a(T )= n

X

i=1 n

X

j=1 zizj

p

aiaj(1−kij) (3) b= n

X

i=1 zibi (4) with a_i=0.457235529· R2_T2 c,i Pc,i ·˛_i(T ) (5) b_i=0.0777960739·RTc,i Pc,i (6) Thecomputationprocedurefortheparameter˛i(T)dependson

thetemperatureandacentricfactorvaluesofthecompound.For compoundsabovetheircriticaltemperature,˛i(T)iscalculatedas

recommendedbyBostonandMathias[30]: ˛i(T )=[exp[ci(1−Tr,idi)]] 2 (7) with di=1+ mi 2 (8) ci=1− 1 di (9) if ω_i≤0.491 then m_i=0.37464+1.54226ω_i−0.26992ω2 i (10) if ωi>0.491 then mi=0.379642+1.48503ωi −0.164423ω2 i +0.016666ω 3 i (11)

Else, if T<Tc,i, the conventional expression of ˛i(T) for

Peng–Robinsonisused: ˛_i(T )=[1+(0.37464+1.54226ω_i−0.26992ω2 i)(1−

p

T_r,i)]2 if ωi≤0.491 (12) ˛i(T )=[1+(0.379642+1.48503ωi−0.164423ω2i+0.016666ω 3 i)(1−

p

Tr,i)] 2 if ωi>0.491 (13)

PurecomponentpropertiesofCO2andglycerolnecessaryforthese

calculationsarepresentedinTable3.

Carbondioxideandglycerolexhibitverydifferentpolarityand theso-calledEoS/GE_{approachisthenexpectedtobemore}

appro-priatetomodelhigh-pressurefluidphaseequilibriaofthissystem. Indeed,thiskindofmixingrulesenlargesthefieldofapplicationof

Table4

SummaryofthemodelsusedinthisworktorepresentCO2–glycerolphaseequilibrium.

Nameoftheglobalmodel Equationofstate Mixingrule Activitycoefficientmodel Binaryinteractioncoefficients

PR PR Conventional – kij=f(T)

PSRK-UNIFAC PR PSRK UNIFACPSRK –

PSRK-UNIQUAC PR PSRK UNIQUAC Aij=f(T)/Aji=f(T)

MHV2-UNIFAC PR MHV-2 UNIFACLyngby –

MHV2-UNIQUAC PR MHV-2 UNIQUAC Aij=f(T)/Aji=f(T)

cubicequationofstatetopolarcompoundsathighpressure.This isdoneviatheincorporationoftheexcessGibbsenergy(GE_)inthe

calculationoftheenergyparameter,a,oftheEoS.TheexcessGibbs energyiscalculatedusinganactivitycoefficientmodel.Huronand Vidal[31] werethe firstto proposethis approach, and several modelsbased onthis concept have then beendeveloped, such as Wong-Sandler, MHV1, MHV2, PSRK...and were successfully appliedtodescribehighpressurefluidphaseequilibriaofmixtures containingpolarcompounds ([32,33] asexamples). A complete reviewofEoS/GE_{mixingrulesandtheirrangeofapplicationcan}

befoundintherecentbookofKontogeorgisandFolas[34]. ForthepurposeofthisstudyPSRK[35]andMHV2[36,37]mixing ruleshavebeenchosen,inadditiontoclassicalvdWf1mixingrules. Theirability tomodeltheCO2–glycerolthermodynamic

behav-iorhasbeencompared.For bothPSRK andMHV2mixing rules, Peng–RobinsonhasbeenusedastheequationofstateandEqs. (4)–(13)havebeenusedtoevaluatepurecomponentparameters andtocalculatemixtureparameterbofthePREoS.

ForPSRKandMHV2,mixtureparametersareobtainedfrom:

q1 ˛−

X

i zi˛i

!

+q2 ˛2−

X

i zi˛2i

!

= g E 0 RT+

X

i ziln



_b bi



(14) ˛= a bRT (15) ˛i= ai biRT (16) withai,biandbobtainedfrom(5),(6)and(4)respectively.Inthe

caseofPeng–Robinsonequationofstate,q1=0.64663andq2=0

forPSRK model(explicit calculationof ˛)and q1=−0.4347 and

q2=−0.003654forMHV2model(implicitcalculationof˛).Then

anactivitycoefficientmodelhastobechosentodeterminethe valueoftheexcessGibbsenergyatzeropressure(reference pres-sure)gE

0.Attheirinitialdevelopment,authorsofPSRK,soasMHV

mixingrules, coupledtheSRK orPRequationofstatewiththe UNIFACpredictiveactivitycoefficientmodel,leadingtoa predic-tiveway touse cubic equations of state.In thepresent study, PSRKmixingrulehasbeenusedwiththePSRKversionofUNIFAC modelproposedbyFredenslundetal.[38]andmodifiedinsucha waythatbinaryinteractioncoefficientsbetweenfunctionalgroups dependontemperature[35,39]andwithUNIQUACactivity coeffi-cientmodel[40,41].Inasameway,MHV2mixingruleisusedwith theLingbyversionofUNIFAC[42].WhenUNIQUACmodelisused inthemixingrule,twobinaryinteractioncoefficients(AijandAji)

havetobefittedonexperimentaldata.Inthepresentstudy,because ofthelargerangeofinvestigatedtemperatures,binaryinteraction coefficientshavebeenshowntobelinearlytemperature depend-ent.Fluidphaseequilibriacalculationshavebeenperformedusing Excel(Microsoft)coupledwithSimulis®_{Thermodynamicssoftware}

(ProSimS.A,France).Simulis®_{Thermodynamicscontainsthe}

dif-ferentmodelssummarized inTable4.Relativeabsoluteaverage deviation(expressedinpercentage,%AAD)wascalculatedto eval-uateabilityofthemodeltorepresentexperimentaldataforCO2

molefractioninliquidphase(xCO2)andglycerolmolefractionin

thevaporphase(yglycerol).%AADforavariablezisdefinedas:

%AADz= 1 Np Np

X

i=1









z_iexp−zcalc i z_iexp









×100 (17)

whereNpisthenumberofexperimentalvalues.

3. Resultsanddiscussion

3.1. SolubilityofglycerolintheCO2-richphase

Fig.1ashowstheevolutionoftheinfraredspectrainthe spec-tralrange2800–3050cm−1_{ofglycerolsolubilizedintheCO}

2-rich

phase with an increase of pressure from 10.0 to 35.0MPa at 120◦_{C.aprogressiveincreaseofthepeakscenteredat2883cm}−1

and 2933cm−1 _{assigned to }

CH of glycerol can be observed,

resultingfrom theincrease of glycerolconcentration.Fromthe intensityofbothpeaks,theevolutionofthesolubilityofglycerol in the CO2-rich phase as a function of CO2 density at

differ-enttemperatures(seeFig.1b)hasbeencalculated.Asit canbe observed, the values of solubility are very low, and increment oftheCO2densityincreasesthesolubilityofglycerolatagiven

temperature.Infact,glycerolisbarelysolubleinCO2atlow

temper-aturesandatconstantdensity;aslightincrementintemperature inducesasignificantincreaseofsolubility.Ourresultsare interme-diatebetweentheexperimentalresultspreviouslypublishedby SovovaandKhachaturyan[17]andbyElssierandFriedrich[16], whichpresentedadifferenceoftwoordersofmagnitudebetween them.Theauthorshaveattributedthisdifferencetoa0.37wt% dif-ferenceintheglycerolwatercontent.However,itcanbepointed outthatthemethodsusedinbothstudiescaninducesystematic errors,principallywhensolutesolubilityissmall(asinthecaseof glycerol).Inbothpublications,severalpointsarenotprovidedin details,suchasanalysismethodsandequilibrationtime justifica-tion.

Table5shows thecalculatedmolefractionofglycerolinthe CO2-richphase(yglycerol)obtainedfromexperimentalresultsofthe

solubilitypresentedinFig.1b.

Ascanbeconcludedfromthesevalues,amajoradvantageofthe experimentalmethodusedinthisstudyliesinitsabilitytomeasure verylowvaluesofconcentrationwithanacceptableprecision. 3.2. SolubilityofCO2andswellingofglycerolintheglycerol-rich

phase

Asanexample,Fig.2showsthespectralchangesofthe glycerol-rich phase occurringwith an increase of temperature from 40 to200◦_{C at10.0MPaas aresult of thechangein CO}

2

concen-tration in that phase. The peak at 3696cm−1_{, assigned to the}

combinationmode22+3 oftheCO2,decreaseswith

tempera-ture,which resultsfromadecreaseofCO2 concentrationinthe

glycerol-richphasewhentemperatureincreasesfrom40to200◦_C.

Thepeakdetectedat4740cm−1_{,assignedtothecombinationofthe}

(OH)+ı(OH)modeoftheassociatedOHofglycerol,presentsashift towards4865cm−1 _{(dashed lines)when temperatureincreases,}

Figure1.(a)SpectralchangesoftheCO2-richphasewiththepressureat120◦C.(b)SolubilityofglycerolasafunctionofCO2molardensityattemperaturesbetween40◦C

and140◦_{C.Lineshavebeenaddedtoguidetheeye.Errorbarsrepresentthe5%ofrelativeerrorallowedbyourmethod.}

Table5

CO2-richphaseequilibriumexperimentaldata.S=solubilityofglycerolinCO2.

40◦_{C 60}◦_{C 80}◦_C

P(MPa) yglycerol S(kmol/m3) P(MPa) yglycerol S(kmol/m3) P(MPa) yglycerol S(kmol/m3)

10 4.95×10−5 _0.7×10−3 _{10 4.70×10}−5 _3.06×10−4 _{10 7.41×10}−5 _3.73×10−4 13 6.96×10−5 _1.17×10−3 _{13 4.70×10}−5 _5.4×10−4 _{13 6.80×10}−5 _5.22×10−4 15 7.84×10−5 _1.39×10−3 _{15 7.29×10}−5 _1.0×10−3 _{15 9.33×10}−5 _9.03×10−4 20 1.12×10−4 _2.14×10−3 _{20 1.22×10}−4 _2.0×10−3 _{20 1.63×10}−4 _2.2×10−3 25 1.36×10−4 _2.72×10−3 _{25 1.73×10}−4 _3.09×10−3 _{25 2.16×10}−4 _3.37×10−3 30 1.49×10−4 _3.07×10−3 _{30 2.19×10}−4 _4.12×10−3 _{30 2.64×10}−4 _4.47×10−3 35 1.80×10−4 _3.83×10−3 _{35 2.53×10}−4 _4.96×10−3 _{35 3.09×10}−4 _5.54×10−3 100◦_{C 120}◦_{C 140}◦_C

P(MPa) yglycerol S(kmol/m3) P(MPa) yglycerol S(kmol/m3) P(MPa) yglycerol S(kmol/m3)

10 2.41×10−5 _1.06×10−4 _{10 4.18×10}−5 _1.59×10−4 _{10 6.93×10}−5 _2.39×10−4 13 1.93×10−5 _1.2×10−4 _{13 5.25×10}−5 _2.78×10−4 _{13 1.05×10}−4 _4.97×10−4 15 1.58×10−5 _1.22×10−4 _{15 7.61×10}−5 _4.85×10−4 _{15 1.53×10}−4 _8.59×10−4 20 1.21×10−4 _1.33×10−3 _{20 2.20×10}−4 _2.0×10−3 _{20 3.44×10}−4 _2.71×10−3 25 2.37×10−4 _3.17×10−3 _{25 3.93×10}−4 _4.51×10−3 _{25 5.50×10}−4 _5.52×10−3 30 3.46×10−4 _5.21×10−3 _{30 5.31×10}−4 _7.07×10−3 _{30 7.83×10}−4 _9.26×10−3 35 4.44×10−4 _7.22×10−3 _{35 6.66×10}−4 _9.77×10−3 _{35 9.60×10}−4 _1.27×10−2 whichresultsfromaprogressivebreakingofthehydrogenbond

network ofglycerolmolecules,aspreviously reportedforother alcohols[22].Infact,glycerolisahighlyflexiblemolecule form-ingboth intra-and inter-molecularhydrogenbonds; molecular dynamics simulations on this molecule have shown that the numberofinter-molecularhydrogenbondsdecreaseswhen tem-peratureisincreased[43,44].Theintensityofthepeakat4350cm−1

associatedtoa combination mode(CH)+ı(CH) decreaseswith temperature, as a result of the glycerol density decrease. No

glycerolswelling,asaresultofCO2 solubilization,wasobserved

duringourexperimentswithinthe±5%accuracyofour method-ologyasitisshowninFig.3.Indeed,nochangesintheintensity of characteristic bands of glycerolare observed (bandsaround 4000cm−1_and4370cm−1_{)althoughanincreaseofthe}

character-isticbandofCO2(3696cm−1)withpressureisclearlypresent.

ThesolubilityofCO2 intheglycerol-richphaseisreportedin

kmol/m3 _{inFig.4asafunctionofthepressure.Table6presents}

theCO2 molefractionintheglycerolrichphase(xCO₂)deduced

Table6

Glycerol-richphaseequilibriumexperimentaldata.S=solubilityofCO2inglycerol.

40◦_{C 60}◦_{C 80}◦_C P(MPa) xCO2 S(kmol/m 3_{) P(MPa) x} CO2 S(kmol/m 3_{) P(MPa) x} CO2 S(kmol/m 3₎ 5 0.0834 1.25 5 0.0685 1.01 10 0.0807 1.2 7.8 0.1068 1.64 10 0.0981 1.49 15 0.0967 1.47 10 0.1170 1.82 15 0.1065 1.63 20 0.1015 1.55 15 0.1259 1.97 20 0.1114 1.72 30 0.1215 1.89 20 0.1280 2.01 24.9 0.1210 1.88 30 0.1335 2.11 30 0.1215 1.89 100◦_{C 120}◦_{C 140}◦_C P(MPa) xCO2 S(kmol/m 3_{) P(MPa) x} CO2 S(kmol/m 3_{) P(MPa) x} CO2 S(kmol/m 3₎ 10 0.0631 0.92 10.2 0.0538 0.78 10 0.0428 0.61 15 0.0753 1.11 15 0.0646 0.95 15 0.0539 0.78 20 0.0900 1.36 20 0.0816 1.22 20 0.0674 0.99 30 0.1183 1.84 24.8 0.0952 1.44 25 0.0922 1.39 30 0.1132 1.75 30 0.1055 1.61 160◦_{C 180}◦_{C 200}◦_C P(MPa) xCO2 S(kmol/m 3_{) P(MPa) x} CO2 S(kmol/m 3_{) P(MPa) x} CO2 S(kmol/m 3₎ 10 0.0334 0.47 10 0.0246 0.35 10.2 0.0203 0.28 15 0.0442 0.63 15 0.0369 0.52 15 0.0242 0.34 20 0.0577 0.84 20 0.0470 0.68 20.2 0.0383 0.55 25 0.0821 1.23 25 0.0677 0.99 30 0.087 30 0.0966 1.46 30 0.0875 1.31

fromexperimentaldataofsolubility.Inallcases,atagiven tem-perature,solubilityincreaseswithpressure.Nevertheless,atlow temperature(T=40◦_{C),thereisastrongincreaseofthesolubility}

whenpressureisincreased,upto10MPa.Forgreaterpressures,this effectisleveledoff.Astemperaturesincreases,amoreimportant effectofpressurehasbeenobserved,andatT=200◦_C,thiseffect

ismaximal.Inallcases,temperaturehasanegativeeffecton sol-ubilityofCO2inglycerolinthetemperatureandpressureranges

studied.ItcanbeobservedthattheshapeofthecurvesofCO2

sol-ubilityasafunctionofthepressureisdifferentabove140◦_C.This

behaviormaybetheconsequenceofasignificantweakeningofthe hydrogenbondedstructureofglycerolabovethistemperature. 3.3. PhasediagramofthescCO2/glycerolsystem

3.3.1. Experimentalresults

PhasediagramfortheCO2–glycerolsystemhasbeenobtained

fromsolubilitymeasurementsfortemperaturesrangingfrom40◦_C

to200◦_{Candpressuresupto35MPaandispresentedinFig.5a.As}

describedabove,quitelowmutualsolubilityisobservedbetween

Figure3.Spectralchangesoftheglycerol-richphasewithpressureat40◦_C.

CO2andglycerolinthepressureandtemperaturerangesstudied

here.Inthecaseoftheglycerol-richphase,lowquantitiesofCO2

canbedissolved.However,at30MPaand40◦_C,aCO

2molefraction

ofupto0.13(Fig.5b)canbeobtained.

ConcerningtheCO2-richphase,whateverthetemperature,the

quasi-verticallinerevealsthelowsolubilityofglycerolinCO2;a

closerlookonFig.5cindicatesanimportanteffectoftemperature onglycerolsolubility.Thisbehavioristypicalforbinarysystems withcompoundsof widelydifferent molarmass and/orcritical temperatures,suchasCO2/waterorCO2/glycolsystems.Such

sys-temsexhibitaliquid–liquidimmiscibilityzoneatlowtemperatures andbelongtotypeIIIoftheclassificationofScottandKonynenburg [45,46].ThelowsolubilityofglycerolintheCO2richphaseisan

importantcharacteristicinrespecttothedevelopmentofbiphasic reactivesystemsusingglycerolasthecatalyticphaseandscCO2as

thereactantsandproductscarrier[12].Indeed,thisinsuresthatlow amountsofglycerolareextractedbyscCO2duringtheseparation

step.

3.3.2. Phaseequilibriummodeling

Models of Table 4 have been used to describe fluid phase equilibriumoftheCO2/glycerolsystem.Aspreviouslymentioned,

Figure4. SolubilityofCO2inglycerolasafunctionofpressureatT=40–200◦C.

Lineshavebeenaddedtoguidetheeye.Errorbarsrepresentthe5%ofrelativeerror allowedbyourmethod.

Figure5. (a)PressureversusCO2molefractiondiagramforthescCO2/glycerolsystem.(b)Glycerol-richphaseand(c)CO2-richphase.Lineshavebeenaddedtoguidethe

eye.

PSRK-UNIFACandMHV2-UNIFACmodelsarepredictive,whilefor PSRK-UNIQUACand MHV2-UNIQUAC modelsbinaryinteraction parametershave tobefittedfromexperimentaldata.Valuesof globalabsoluteaveragedeviations,%AADxCO2and%AADyglycerol(Eq.

(17)),obtainedforeachmodel,togetherwithexpressionsoffitted binaryinteractionparametersaregiveninTable7.Thefittingof experimentaldatahasbeendoneminimizinganobjectivefunction (leastsquaremethod)andresultsarepresentedinTable7where itisfirstnoticeablethat,whateverthemodelused,the%AADon bothphasesarenotverygood,noneofthembeingbelow5%.This showsthat,onaglobalpointofview,PREoSfailstoaccurately representexperimentalbehaviorofthatsystem,evenwithEoS/GE

mixingrules.

ForthePREoSwithclassicalmixingrule,ithasnotbeenpossible touseanobjectivefunctionsimultaneouslyinvolvingcomposition ofliquidphaseandcompositionofthevaporphaseinthesame resolution,becauseinthatcase,itledtogloballypoordescription forbothphases.Especially,theverylowexperimentalmole frac-tionsofglycerolintheCO2richphaseweresystematicallylargely

overestimated.ThusforPRmodelwithclassicalmixingrule,the optimizationmethodwasdonefirstlywiththeleastsquaremethod applied to xCO2 values only (entry 1),that explains the rather

Fied on x kij = 0.0025T - 0.8827 Fied on x kij= 0.0009T - 0.2045 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 300 320 340 360 380 400 420 440 460 480 500 T /K P R b in a ry i n te ra c o n c o e ffi ci e n t kCO2-glycerol Fied on yk=0.0007T + 0.0008

Figure 6.Influence of the temperature on binary interaction coefficients of Peng–RobinsonequationofstatefittedonxCO2oryglycerol.

satisfactoryvalueof%AAD(7.7)fortheglycerolrichphaseinthat case;Thenthefittingwasdoneonyglycerolonly(entry2),giving

acceptable%AADforthevaporphase(61.1,stilloverestimatingthe

Table7

Valuesofbinaryinteractioncoefficientsandcorrespondingvaluesoftherelativeabsoluteaveragedeviations(%AAD)forCO2liquidmolefractionandglycerolvapormole

fractionforeachmodel.

Entry Globalmodel Binaryinteractionparameters %AADxCO2 %AADyglycerol

1 PRfittedonxCO2only kCO2–glycerol=0.009T /K−0.2075 for T≤413K 7.7 345

kCO2–glycerol=0.025T /K−0.8827 for T>413K

2 PRfittedonyglycerolonly kCO2–glycerol=0.0007T /K+0.0008 62.2 61.1

3 PSRK-UNIQUACfittedonbothxCO2andyglycerol ACO2–glycerol/calmol−1=−3.00T /K+1523.31 18.4 57.2

Aglycerol–CO2/calmol

−1

=3.84T /K−1056.75

4 PSRK-UNIFAC – 71.3 297.1

5 MHV2-UNIQUACfittedonbothxCO2andyglycerol ACO2–glycerol/calmol

−1

=75,698.7T /K+358.30 19.5 97.5 Aglycerol–CO2/calmol

−1

=−2.81T /K+2109.18

(a)

(b)

0 5 10 15 20 25 30 35 40 0 0.05 0.1 0.15 0.2 0.25 0.3 xCO2 P / M P a exp PR PSRK-UNIQUAC PSRK-UNIFAC MHV2-UNIQUAC 0 5 10 15 20 25 30 35 40 0.995 0.996 0.997 0.998 0.999 1 y CO2 P / M P a exp PR PSRK-UNIQUAC PSRK-UNIFAC MHV2-UNIQUAC 0 5 10 15 20 25 30 35 40 0 0.05 0.1 0.15 0.2 0.25 0.3 xCO2 P / M P a exp PR PSRK-UNIQUAC PSRK-UNIFAC MHV2-UNIQUAC 0 5 10 15 20 25 30 35 40 0.995 0.996 0.997 0.998 0.999 1 y CO2 P / M P a exp PR PSRK-UNIQUAC PSRK-UNIFAC MHV2-UNIQUAC

(c)

(d)

(e)

(f)

(g)

0 5 10 15 20 25 30 35 40 0 0.05 0.1 0.15 0.2 0.25 0.3 xCO2 P / M P a exp PR PSRK-UNIQUAC PSRK-UNIFAC MHV2-UNIQUAC 0 5 10 15 20 25 30 35 40 0.995 0.996 0.997 0.998 0.999 1 y CO2 P / M P a exp PR PSRK-UNIQUAC PSRK-UNIFAC MHV2-UNIQUAC 0 5 10 15 20 25 30 35 40 0 0.05 0.1 0.15 0.2 0.25 0.3 xCO2 P / M P a exp PR PSRK-UNIQUAC PSRK-UNIFAC MHV2-UNIQUAC

Figure7. P-x,ydatafortheCO2/glycerolsystem,experimentaldataandmodelingresults.(aandb)40◦C,(candd)80◦C,(eandf)120◦C,(g)200◦C(kijforPREoSisfrom

glycerolmolefraction),but,inthiscaseworsepredictionswere correlativelyfoundfortheliquidphase(62.2).InthecaseofPR EoS,adetailedstudyoftheinfluenceoftemperatureuponbinary interactioncoefficients hasbeendoneandresultsareplottedin Fig.6.WhenfittingwasrealizedonxCO2 only,twolinear

correla-tionshavebeenevidenced,dependingonthetemperaturerange. Whateverthetemperature,thekij valueofthePREoSispositive

forthissystem,asitisoftenthecasebecauseofoverestimation ofinteractionbetweenmoleculesissuedfromtheuseof geomet-ricmixingrule(Eq.(3)).Moreover,thevalueofkijincreaseswith

temperature,reflectingthedecreaseofthesolubilityofCO2intothe

glycerolrichphaseandtheincreaseofsolubilityofglycerolintoCO2

richphase,becauseself-associationofglycerolbyhydrogen bond-ingisweakerathightemperature,aspreviouslymentioned.Ascan beseeninFig.6,influenceoftemperatureonkijismoreimportant

above140◦_{Candthisispresumablyaconsequenceoftheobserved}

changeofthemixturebehaviorabove140◦_{C,asitisclearly}

observ-ableinFig.4,whereachangeofconcavityoccurswhensolubility ofCO2inglycerolrichphaseversuspressureisplotted.Thesimilar

analysisonkij fittedonyglycerol shows that,ata same

tempera-ture,kijvalueishigher,andthesametendencyisobservedasa

functionofthetemperature(Fig.6).Notethatexperimentalvapor phasecompositionshavebeendeterminedforT<140◦_Conly.For

thepurposeofthetargetedapplicationoftheCO2–glycerolsystem

asabiphasicmediumtoperformreactions,informationuponthe amountofCO2solubilizedinglycerolisofprimeinterestbecause

oftheconsequencesuponphysico-chemicalpropertiesor reactiv-ityintheglycerolrichphase.Inaccuratepredictionofthetraces ofglycerolintheCO2richphasewouldnothandicapthe

develop-mentofsuchbiphasicsystems.Thus,inthefollowing,theresults withPREoSandkij fittedonxCO2 onlyhave beenretained.The

approachwhichprivilegesthevaporphasedescriptioncouldbe proposedinthecontextofanapplicationwhereanaccurate calcu-lationofthevaporphasecompositionisneeded.However,ascan beseeninTable7,whenadescriptionforbothphases simulta-neouslyisneededthePSRK-UNIQUACshouldbepreferred(entry 3)becauseitgivesacceptable%AAD(18.4and57.2forxCO2 and

yglycerolrespectively)althoughthereisalossofaccuracyforthe

liq-uidphaseincomparisontoentry1.Visualassessmentofcalculated andexperimentalCO2molefractionsintheglycerolrichphasecan

bedoneinFig.7(a),(c),(e)and(g),andintheCO2 richphasein

Fig.7(b),(d)and(f),at40,80,120and200◦_{C.Amongmixingrules}

basedonEoS/GE_{approach,itappearsclearlythatPSRKmixingrule}

withUNIQUACactivitymodelprovidesthebestresultsinterms ofbothliquidandvaporcompositions,followedbyMHV2mixing rulewithUNIQUAC(entry5),thatgivesworseresults.Although thedeviationsobtainedwithPSRK-UNIQUACarestillratherhigh, thisresultconfirmsthatthesemixingrulesarethemostadequate topredict experimentalbehavior ofsuch complexmixtures, as comparedtoclassicalvdW1fmixingrules.Essentially,thehigh val-uesofdeviationsmaybeexplainedbythelargedifferenceofCO2

andglycerolcritical volumes(94cm3_mol−1 _{and 264cm}3_mol−1_,

respectively).Indeed,theCO2–glycerolmixturecouldbe

classi-fiedasa size-asymmetricsystem,for whichit hasbeenshown thatthiskindofmodelisactuallysomewhatunsuitable[47],due tothedifference betweenthecombinatorial termof the activ-itycoefficient modeland theoneof theequationofstate.This differenceincreasesasthedifferenceinmoleculesizeincreases [47].

To better investigatethe ability of the modelsto represent globalexperimentalbehavioroftheliquidphaseoftheCO2/glycerol

system on the wide range of temperature, it is interesting to considervariations of %AADxobtained withthe different mod-els with the temperature (Fig. 8) (Note: MHV2-UNIFAC is not consideredbecause%AADxisvery high,whatever the tempera-ture).

Figure8. Influenceofthetemperatureon%AADforxCO2obtainedwithdifferent

models.

SeveraltendenciescanbeobservedfromFigs.7and8.Firstly,as previouslypointedout,whateverthetemperature,non-predictive modelswithfittedbinaryinteractionparametersarethemost suit-able.Ofcourse,thisresultwasexpected,consideringthefactthat forthesemodelsfourcoefficientsarefittedtoexperimentaldatain ordertominimizeglobalaveragedeviation.ItisshowninFig.8that deviationsarehigherathightemperature,wheretheexperimental curvesshowachangeinconcavityandwhereexperimentalpoints arescarce.

Essentially,predictivemodels,i.e.,modelsusingUNIFACin mix-ing rules, yielded poor representation of experimental results, particularly MHV2-UNIFAC (Table 7, entry 6). PSRK-UNIFAC approachissatisfactoryatlowtemperature,butdeviationsharply increaseswithtemperaturetoreachabout200%at200◦_C(Fig.8).

Concerningthislastmodel,thisresultwasexpectedconsideringthe factthat,forthefunctionalgroupsofourdatabaseusedtodescribe theCO2/glycerolsystem(i.e.,CO2,OHandCH2functionalgroups),

binaryinteractionparameterswithinthesegroupsareprovidedas temperatureindependent.

PSRKmixingrulewasfoundheresuperiortoMHV2,whatever theactivitycoefficientmodel,UNIFACorUNIQUAC,choseninthe mixing rule.Thisresultis somewhatsurprising,becauseMHV2 mixing rule providesgenerally a better match of experimental results.

The thermodynamic behavior of CO2/glycerol system is

obviouslygovernedbyself-interactionofglycerol.Forsucha sys-tem, an improvement in phase equilibrium modeling could be achievedbyusingadvancedmodelsbasedonassociationtheories, suchasSAFT(StatisticalAssociatingFluidTheory)orCPA(Cubic PlusAssociation)models.Althoughgroundedonamorecomplex theoreticalbasis,thesemodelshavebeenprovedtobeparticularly suitableforassociatingcompounds[34].

4. Conclusions

Inthiswork,themutualsolubilityofCO2andglycerolhasbeen

studiedattemperaturesrangingfrom40◦_Cto200◦_{Candpressures}

upto35.0MPa.ThishasbeendoneusingtheFT-IRtechniquewhich provedtogiveaccesstoverylowvaluesofequilibrium concen-trationswithagoodaccuracy.ConcerningtheCO2richphase,it

wasobservedthat theglycerolsolubilityin CO2 wasextremely

low (intherange of10−5 _{in molefraction) inthepressureand}

temperaturedomainsinvestigatedhere.Conversely,theglycerol richphasedissolvedCO2atmolefractionsupto0.13.Negligible

swellingoftheglycerolrichphasehasbeenobserved,which indi-catesthatglycerolbehavesasaclassIGasExpandedLiquid(GXL)

accordingtothe classificationof Jessop etal. [1], i.e.,a system wheretheexpandinggashasaquitelowsolubilityintheliquid, whichconsequentlydoesnotexhibit largeexpansion.Although thesolubilityofCO2 inglycerolislargelyhigherthantheoneof

CO2inwater,thethermodynamicbehaviorofthissystemisrather

similarto that of CO2/water binarymixture, which is a class I

GXL.

ConcerningthemodelingoftheCO2/glycerolsystem,the

suit-ability of PR EoSwith PSRK mixing rule and UNIQUAC model, hasbeen highlighted.Evolution with pressure of the composi-tion of both phases in the 40–200◦_{C range of temperature is}

quitewelldescribedbythismodel,providedthatsuitablevalues ofbinaryinteractioncoefficientsareused.Conversely,predictive approachesprovedtobenonsatisfactory.Simplerapproachwith Peng–RobinsonequationofstatewithvdW1fmixingruledidnot allowcomputing accuratelyboth liquid and vapor phaseswith thesamevalueofbinaryinteractioncoefficient.Dependingonthe application,accuratedescriptionofonlyonespecificphasecouldbe needed.Inthiswork,anadaptedfittingprocedurethathas consid-eredonlythetargetedphase,haveprovidedthespecificinteraction coefficientsforeachcase.

This study has also shown that the system scCO2/glycerol

remained biphasic for all studied pressures and temperatures, allowingfurtherdevelopmentofbiphasicreactionsystems,which involveenvironmentallyfriendlysolventsonly.Thesesystemsalso makeitpossibletocouplereactionandseparationsteps,allowing thedevelopmentofintensifiedprocesses.

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