Solubility, liquid–liquid equilibrium and critical states for the quaternary system acetic acid–ethanol–ethyl acetate–water at 303.15 K and 313.15 K

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Fluid Phase Equilibria

j o u r n a l ho me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / f l u i d

Solubility, liquid–liquid equilibrium and critical states for the quaternary system acetic acid–ethanol–ethyl acetate–water at 303.15 K and 313.15 K

Maria Toikka, Artemiy Samarov, Maya Troﬁmova, Alexandra Golikova, Nikita Tsvetov, Alexander Toikka

^∗

DepartmentofChemicalThermodynamicsandKinetics,Saint-PetersburgStateUniversity,UniversitetskiyProspect26,Peterhof,St.Petersburg198504, Russia

a r t i c l e i n f o

Articlehistory:

Received14December2013 Receivedinrevisedform8April2014 Accepted13April2014

Availableonline23April2014

Keywords:

Liquid–liquidequilibria Ethylacetate Esteriﬁcation

Quaternaryreactingsystems Criticalstates

a b s t r a c t

Solubility,critical statesand liquid–liquid equilibrium(LLE)data forthequaternarysystemacetic acid–ethanol–ethylacetate–waterandfortheternarysubsystemsaceticacid–ethylacetate–waterand ethanol–ethylacetate–waterwerestudiedat303.15Kand313.15Kandatmosphericpressure.Binodal surfaces,binodalcurves,tie-linesandcompositionsofcriticalpointsweredetermined.Inordertocon- structthebinodalsurfacesandcriticalcurvesofthequaternarysystem,ﬁvequaternarysectionalplanes withseveraldifferentratiosofconcentrationofaceticacidtoethanolwerestudied.ExperimentalLLE datawerecomparedwiththevaluescalculatedbyUNIFACandNRTLmodels,anditwasfoundthatthe experimentalandcalculateddataareingoodagreement.

1. Introduction

Duringthepastfewdecades,interestincoupledprocesses(e.g., phasetransitionsaccompaniedbychemicalreaction)hasgrown becauseoftheirsignificanceforthedevelopmentofenergy-and resource-savingchemicalengineeringprocesses.Sometimesitis necessarytoincludethestages ofseparation orrecyclingofthe componentsintheindustrialchemicalprocessesifthecompletion ofchemicalreactionislimitedbychemicalequilibriumbetween reactantsandproducts.Inaddition,therunofchemicalreaction dependsonthelimited miscibilityof thereactingmixture,and therefore,industrialprocessescanbesignificantlycomplicated.It shouldbenotedthattheoverwhelmingmajorityofexperimental andtheoreticalworksinthefieldofcoupledprocessesisdevoted totheinvestigationofesterificationreaction[1].Thisinterestin studyingesterificationstemsfromthefactthattheideasofgreen chemistry,environmentalmanagementandthedevelopmentof

∗Correspondingauthor.Tel.:+78124284052.

E-mailaddresses:alexander.toikka@chem.spbu.ru,toikka@yandex.ru (A.Toikka).

renewableenergysourcesnowdominateinbothfundamentalas wellasappliedchemistry.

With respect to environmental management in the field of organicsynthesisand separation processes,we shouldmention reactivedistillation(RD)[2].Thisprocessconjoins reactionand separation stages,providesasignificantincrease intheconver- sionof reactants,and decreases theenvironmentalrisks. Some recentpapers[3,4]presenttheexperimentalkineticdataofhet- erogeneousesterificationofaceticandglutaricacidwithmethanol andshowthatRDtechnologyisafeasiblemethodtoconvertcar- boxylicacidstoestersandtorecoverthemfromaqueoussolutions.

Article[5]byYagyuetal.isdevotedtotheecologicalproblemof ethylacetateproduction,theimprovementofesteriﬁcationyield andwastewatertreatment.Theauthorsstudiedtheesteriﬁcation ofacetic acidwithethanol inaqueousmediaat 313.15Kusing variouscatalyststointensifytherecovery.Huandcolleagues[6]

reportthedesignofRDprocessfortheproductionofethylacetate.

Dataonvapor–liquidequilibrium andvapor–liquid–liquidequi- libriumatthetemperaturerange343.15–393.15Karesimulated byNRTL model(including severalphase diagrams).Besidesthe papersmentionedabove,therearesomeotherworksonRDand vapor–liquidequilibriuminsystemswithanesteriﬁcationreaction [7–11].

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Furthermore,researchinthefieldofbiodieselproductionhas developedinrecentyears.Thedataofworks[12,13]canbeusedfor thedevelopmentofbiodieselproductionprocessesviafattyacids esterification(e.g.,lauricacidwithethanol).Suchworksaremainly relatedtothestudyofkineticsofcatalyzedesterification,especially inusingthosekindsofcatalystsasdifferenttypesofion-exchange resins[14–17].

Inadditiontothepracticalimportanceofinvestigatingphase equilibriainreactivesystems,theyarealsoofinterestinthedevel- opmentofbasicthermodynamictheory.Itgives,forexample,new dataonthestructureandfeaturesofphasediagrams,suchascritical states[18–25].

However, despite the potential applied and basic signiﬁ- cance of systems with coupled processes, experimental data on these systems are relatively rare in comparison with non- reactive systems. We presented experimental results for a systemwithn-propylacetatesynthesisreactioninrecentpapers [26–28].

The present work continues the investigation of the sys- temacetic acid–ethanol–ethyl acetate–water,which has before been intensively studied by many authors, including our sci- entiﬁc group. Previously, we presented experimental data on solubility,criticalstates,LLEandchemicalequilibriumofesteri- ﬁcationinthissystemat293.15Kandatmosphericpressure;LLE datacalculated byUNIFAC modelwere alsoreportedin papers [29,30]. Our researchconcernsmostly solubilityand LLE deter- mination becausethedatasets onthese propertiesare limited in comparison with VLE. VLE was experimentally studied by Calvar et al. [31]. Experimental results of [31] are in agree- ment with the data of other authors [32,33]. Some works are only devoted to investigation of ethyl acetate synthesis reaction:e.g.,Venkateswarluetal.[34]studiedthisreactioninvapor phaseat519–559Kandatmosphericpressure.Systemwithethyl acetate synthesis reactionwas consideredby Reichlet al. [35], but the paper’s experimental data sets include only data for binarysub-systemsethanol–aceticacid,ethylacetate–waterand ethanol–water (at 50kPa and atmospheric pressure). Theoreti- calconsiderationofthermodynamicpropertiesanddescriptionof thetopologicalstructure ofthequaternarysystemarereported inRef. [36].The descriptionof LLE inacetic acid–ethanol–ethyl acetate–water system (at 101.3and 200kPa) with the help of UNIFACmodel;calculatedLLE diagramsfor thesepressuresare presentedinRef.[37].Thechemicalequilibriumsurfaceofthesys- temaceticacid–ethanol–ethylacetate–waterispresentedinRef.

[7].

Usingvariousmodels,Kangetal.[38]proposednewalgorithms for calculating simultaneous chemical and phase equilibrium for reactive systems. The calculation results for the acetic acid–ethanol–ethyl acetate–water system were compared with calculationsmadebyPeres-Cisnerosetal.[39].Thethermodynamic coherenceofexperimentaldatafor thequaternarysystemwith ethylacetatesynthesisreactionisdiscussedinRef.[40].Paper[41]

considerstheresultsofmodelingequilibriainthissystemusing MargulesandWilsonequations.Simulationonthebaseofagroup model(ASOG,AnalyticalSolutionsofGroups)isdescribedinRef.

[42].

Analysisofliteraturedatashowsthattherearenumerouspapers ontheexperimentalstudyofVLEandmodelingofVLEandchemi- calequilibriuminaceticacid–ethanol–water–ethylacetatesystem.

Incontrast,thedatasetsonLLEarelimitedandmostlyrelatedto isobaricconditions(e.g.,atmosphericpressure).Accordingly,the aimofourworkwastheexperimentalstudyofsolubilityandLLEin thissystemunderisothermalconditions(303.15and313.15K).Our experimentaltaskincludedthedeterminationofcriticalstatesof LLEinthissystem.ThecalculationswerecarriedoutusingUNIFAC andNRTLmodels.

Table1

Thepuritiesofthechemicals.

Substance Purity(molefraction)^a

Aceticacid 0.998

Ethanol 0.995

Ethylacetate 0.998

Water 0.999

aUncertaintyisestimatedtobe±0.002molefraction.

2. Experimental 2.1. Materials

Ethanol (“reagent” grade, Vekton, Russia) and ethyl acetate (“puriﬁed” grade, Vekton, Russia) were puriﬁed by distillation.

Waterwasbidistilled.Aceticacid(“purified”grade,Vekton,Russia) waspurifiedbytwotimesrectification,withthepresenceof98%

sulphuricacid.Thepurityofchemicals(seeTable1)wasveriﬁed chromatographicallyandintermsofrefractionindexesandboil- ingpoints.Allphysico-chemicalconstantsofpuresubstanceswere foundtobeinagreementwithNISTStandardReferenceDatabase [43].

2.2. Methods

Cloud-pointtechniquewasusedtostudysolubilityandcriti- calphenomena.Theoperatingprocedurewasthesameasinour previouswork.Detailsofthemethodhadbeenpublishedinpaper [29].Titrationwasperformedinaliquidthermostat(303.15and 313.15K).Accuracyofthedeterminationofconcentrationwasesti- matedtobe0.001molefraction.Inconsiderationofotherpossible factorsaffectingaccuracy(suchaspurityofchemicals,thermostatic controluncertaintyandothers),maximumerrorofexperimental datawasappreciableto±0.002molefractionofthecomponent.

LLEwasstudiedusinggaschromatography(GC).Firstly,binary, ternary andquaternary mixtures ofknownoverall composition within the heterogeneous region were prepared in glass vessels(5ml)bygravimetricmethod.Heterogeneousmixtureswere stirred in sealed vessels. Then vessels were placed in the liq- uidthermostat(303.15K).Weconsideredthephaseequilibrium reachedwhentherewasafullseparationofthephasesandthey becamequitetransparent.Afterreachingphaseequilibrium,sam- ples were taken from both phases with 1␮l chromatographic syringe (“Hamilton”, USA) and analyzed by GC.We useda gas chromatograph “ChromatecCrystal 5000.2” (Russia) withther- malconductivitydetector (TCD)and packedcolumn Porapak R (1mlongand0.003mi.d.).Heliumwithaﬂowrateof60ml/min wasused as a carriergas. Theoperating temperature ofa col- umnwas468K,vaporizinginjectorwasmaintainedat503K,and TCD temperature was 513K. Method of internal standard and relativecalibrationwereusedtocalculatecompositionsofequi- libriumliquid phases.Ethanolwasusedasaninternalstandard andacceptedasalinkingcomponent.UncertaintyofGCanalysis averaged±0.005molefraction.

3. Resultsanddiscussion

Binary mixtures ethanol–ethyl acetate and acetic acid–ethyl acetate were chosen as initial solutions for the study of solubility in ternary subsystems ethanol–ethyl acetate–water and acetic acid–ethyl acetate–water,respectively, and weretitrated with bidistilled water. All thesebinary systems were homoge- neousbeforetitration.Atthemomentwhenthesolutionbecame cloudy,i.e.,whenthesecondphasebegan,compositionsbelong- ingtothesolubilitycurvewereﬁxed.Itshouldbenotedthatthe

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Table2

Theexperimentaldataonsolubility(molefractions,x)fortheternarysystemethanol (1)–ethylacetate(2)–water(3)at303.15K,313.15Kandatmosphericpressure.^a

X1 X2 X1 X2

303.15K 313.15K

0.102 0.053 0.132 0.130

0.117 0.073 0.144 0.163

0.132 0.103 0.155 0.204

0.135 0.112 0.165 0.258

0.138 0.123 0.164 0.259

0.143 0.134 0.166 0.279

0.147 0.146 0.168 0.312

0.150 0.156 0.166 0.339

0.166 0.217 0.158 0.402

0.176 0.322 0.124 0.541

0.176 0.369 0.134 0.515

0.175 0.411 0.109 0.588

– – 0.094 0.621

– – 0.079 0.662

– – 0.107 0.081

– – 0.130 0.116

– – 0.134 0.124

– – 0.138 0.137

– – 0.145 0.150

– – 0.147 0.161

– – 0.158 0.206

aStandarduncertaintiesu(x)=0.002andu(T)=0.05.

Table3

Theexperimentaldataonsolubility(molefractions,x)fortheternarysystemacetic acid(1)–ethylacetate(2)–water(3)at303.15K,313.15Kandatmosphericpressure.^a

X1 X2 X1 X2

303.15K 313.15K

0.077 0.050 0.121 0.163

0.093 0.074 0.130 0.215

0.105 0.100 0.139 0.321

0.108 0.110 0.129 0.413

0.111 0.119 0.121 0.448

0.117 0.136 0.095 0.544

0.121 0.148 0.074 0.615

0.125 0.162 0.054 0.683

0.128 0.173 0.092 0.097

0.141 0.240 0.107 0.118

0.144 0.294 0.110 0.127

0.144 0.337 0.114 0.139

0.140 0.377 0.119 0.155

0.131 0.447 0.123 0.166

0.126 0.184

0.138 0.259

possible run of ethyl acetate hydrolysis reaction in ternary subsystems ethanol–ethyl acetate–water and acetic acid–ethyl acetate–water did not affect the composition of solutions [29]. Experimental data on the solubility of ternary subsystems ethanol–ethyl acetate–water and acetic acid–ethyl acetate–water at 303.15K and 313.15K are presented in Tables2and3.

Fig. 1. The diagram of solubility and LLE in ternary system ethanol–ethyl acetate–waterat313.15K:()solubilitydata,(䊉-䊉)tie-lines.Compositionsare giveninmolarfractions.

Fig.2. Thediagramofsolubilityinternarysystemaceticacid–ethylacetate–water at313.15K:()solubilitydata,(䊉-䊉)tie-lines.Compositionsaregiveninmolar fractions.

Figs.1 and2present therunofbinodalcurves for313.15K.

In order to construct the binodal surface in the composition tetrahedron, the solubility for quaternary system acetic acid–ethanol–ethylacetate–waterwasstudiedfortheinitialsolu- tionsofconstantratiosconcentrationsofaceticacidandethanol (3:1,5:3,1:1,3:5and1:3).

Theinvestigationofsolubilitywascarriedoutforcompositions belongingtochosenratios, i.e.,forsectionsoftheconcentration tetrahedron(seeFig.3).

Thechoiceofsectionsgavetheopportunitytopresenttheform ofthebinodalsurfaceclearlyandasawhole.Experimentaldataon solubilityinthesystemaceticacid–ethanol–ethylacetate–water at303.15Kand313.15KarelistedinTables4and5,anddiagrams ofsolubilityconstructedinconcentrationtetrahedronforseveral sectionsat313.15KareshowninFig.4.

Thesolubilitycurvesandexperimentaltie-linesqualitatively presentthedispositionofthebinodalsurface(Fig.4).Theliquid splittingregionoccupiesasmallareaoftheconcentrationtetrahe- dron.Onthebinodalsurface,themaximumoverallconcentration ofaceticacidandethanolis0.2molefraction.Astobeexpected, theareaofimmiscibilityinbothternaryandquaternarysystems increasesinsizewithadecreaseintemperature.Thesedatacanbe comparedwithrecentdataon293.15K[29],whentheimmiscibil- itygapbecameevengreater.

Compositionsofinitialsolutionsfortheexperimentalstudyof LLEinternarysubsystemsethanol–ethylacetate–waterandacetic acid–ethyl acetate–water were chosen so that compositions of coexistingphases(tie-lines)couldbeordereduniformlyonabin- odalcurve.ExperimentaldataonLLEforthesesystemsarelistedin Tables6and7andtie-linesarepresentedinFigs.1and2.Thereisa smalldifferencebetweenLLEdata(tie-lines)andsolubilitycurves thatisexplainedbymethod’sfeatures.

Thechoiceofcompositionsofinitialsolutionsinthestudyof thebinodalsurfaceofquaternarysystemaceticacid–ethanol–ethyl acetate–waterwasperformedunderthesameguidelinesasinthe investigationofsolubility(constantratiosofethanolandaceticacid

Fig.3. Planesofcompositiontetrahedronstudied.

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Table4

Theexperimentaldataonsolubility(molefractions,x)forthequaternarysystem aceticacid(1)–ethanol(2)–ethylacetate(3)–water(4)at303.15Kandatmospheric pressure.^a

Theratioofaceticacidand ethanolmolarfractions

X1 X2 X3

3:1 0.081 0.027 0.092

0.089 0.029 0.115

0.093 0.031 0.136

0.097 0.032 0.145

0.101 0.034 0.162

0.104 0.034 0.175

0.108 0.036 0.194

0.110 0.036 0.208

0.116 0.039 0.275

0.117 0.038 0.331

0.115 0.038 0.377

5:3 0.063 0.037 0.071

0.071 0.042 0.097

0.078 0.045 0.117

0.082 0.048 0.136

0.085 0.051 0.154

0.088 0.053 0.169

0.091 0.055 0.185

0.094 0.056 0.203

0.096 0.057 0.218

0.101 0.060 0.289

0.100 0.059 0.342

0.098 0.058 0.385

0.095 0.056 0.417

1:1 0.052 0.051 0.069

0.060 0.060 0.102

0.062 0.062 0.114

0.065 0.063 0.122

0.067 0.067 0.137

0.070 0.069 0.150

0.072 0.072 0.163

0.081 0.077 0.219

0.083 0.084 0.283

0.083 0.084 0.329

0.082 0.081 0.367

0.080 0.079 0.404

3:5 0.035 0.058 0.053

0.041 0.068 0.074

0.047 0.079 0.107

0.049 0.081 0.118

0.051 0.085 0.136

0.053 0.086 0.141

0.054 0.091 0.156

0.057 0.093 0.172

0.063 0.104 0.237

0.064 0.107 0.291

0.064 0.106 0.337

0.063 0.103 0.378

1:3 0.029 0.087 0.079

0.033 0.098 0.110

0.034 0.103 0.124

0.035 0.106 0.137

0.037 0.110 0.150

0.038 0.113 0.161

0.039 0.117 0.176

0.044 0.125 0.236

0.044 0.131 0.295

0.045 0.129 0.341

0.043 0.126 0.382

0.041 0.123 0.419

inmixturewere3:1,5:3,1:1,3:5and1:3).Compositionsofini- tialsolutionsbelongedtotheregionofsplitting(heterogeneous region).ExperimentaldataonLLEforthequaternarysystemare listedinTables8and9.

Thedeterminationofcriticalcompositionsinternaryandqua- ternarysystemswascarriedoutwithcloud-pointtechniqueand

Table5

Theexperimentaldataonsolubility(molefractions,x)forthequaternarysystem aceticacid(1)–ethanol(2)–ethylacetate(3)–water(4)at313.15Kandatmospheric pressure.^a

Theratioofaceticacidand ethanolmolarfractions

X1 X2 X3

3:1 0.081 0.027 0.107

0.087 0.029 0.123

0.091 0.030 0.138

0.092 0.031 0.146

0.093 0.030 0.152

0.099 0.032 0.165

0.101 0.034 0.180

0.103 0.034 0.189

0.109 0.037 0.243

0.108 0.041 0.251

0.111 0.037 0.342

0.101 0.034 0.432

0.096 0.032 0.471

0.073 0.024 0.557

0.056 0.019 0.621

0.040 0.013 0.682

5:3 0.069 0.041 0.113

0.075 0.046 0.135

0.080 0.05 0.152

0.082 0.051 0.169

0.088 0.053 0.188

0.086 0.052 0.190

0.087 0.054 0.211

0.094 0.057 0.252

0.090 0.057 0.256

0.095 0.057 0.350

0.089 0.051 0.432

0.081 0.049 0.482

0.063 0.037 0.570

0.047 0.028 0.622

1:1 0.057 0.057 0.099

0.060 0.060 0.116

0.063 0.062 0.131

0.067 0.067 0.152

0.072 0.061 0.156

0.069 0.069 0.165

0.071 0.069 0.179

0.073 0.071 0.188

0.077 0.073 0.212

0.077 0.077 0.241

0.079 0.078 0.319

0.076 0.076 0.386

0.072 0.072 0.428

0.053 0.053 0.561

0.039 0.038 0.640

3:5 0.043 0.068 0.104

0.048 0.078 0.132

0.051 0.085 0.151

0.053 0.088 0.167

0.055 0.089 0.177

0.057 0.091 0.193

0.057 0.095 0.203

0.058 0.096 0.220

0.060 0.097 0.251

0.061 0.100 0.267

0.060 0.100 0.369

0.053 0.088 0.451

0.037 0.063 0.572

0.029 0.048 0.633

0.020 0.033 0.658

1:3 0.03 0.087 0.113

0.033 0.097 0.126

0.034 0.101 0.137

0.031 0.104 0.146

0.035 0.105 0.151

0.037 0.107 0.162

0.039 0.109 0.185

0.038 0.114 0.204

0.042 0.112 0.210

0.041 0.122 0.272

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Table5(Continued) Theratioofaceticacidand ethanolmolarfractions

X1 X2 X3

0.041 0.121 0.372

0.033 0.101 0.493

0.026 0.077 0.585

0.020 0.059 0.652

0.014 0.041 0.703

Fig. 4. Qualitative view of the binodal surface of acetic acid–ethanol–ethyl acetate–watersystemat313.15K.Tie-linesinternarysystems:aceticacid–ethyl acetate–water(–)andethanol–ethylacetate–water(䊉–䊉);(–)and(–) selectedtie-linesinquaternarysystem;solubilitycurvesinternarysystems:acetic acid–ethylacetate–water()andethanol–ethylacetate–water().Points(♦)and ()representselectedsolubilitydataforquaternarysolutionswithconstantratios ofconcentrationsofaceticacidandethanol:3:1(♦)and1:1().Compositionsare giveninmolarfractions.

visualcontrol: transfer to a critical state was accompanied by opalescence[25].Experimentaldataonthecriticalstatesofternary subsystemsandthequaternarysystemat303.15Kand313.15K arelistedinTable10.Thesetofcriticalpointsinthequaternary

Table6

Theexperimental LLEdata for the ternary system ethanol (1)–ethyl acetate (2)–water(3)formolefractionsxat303.15K,313.15Kandatmosphericpressure.^a

Waterphase Organicphase

X1 X2 X1 X2

303.15K

0.032 0.000 0.858 0.000

0.027 0.010 0.825 0.018

0.029 0.026 0.788 0.042

0.033 0.040 0.736 0.068

0.033 0.061 0.667 0.102

0.044 0.080 0.570 0.135

0.053 0.095 0.496 0.159

0.060 0.107 0.419 0.174

(NRTL)=5.4%,(UNIFAC)=2.8%

313.15K

0.017 0.000 0.838 0.000

0.026 0.036 0.606 0.084

0.021 0.042 0.564 0.106

0.026 0.051 0.512 0.123

0.032 0.063 0.410 0.149

0.037 0.078 0.294 0.153

0.074 0.111 0.209 0.160

Table7

TheexperimentalLLEdatafortheternarysystemaceticacid(1)–ethylacetate (2)–water(3)formolefractionsxat303.15K,313.15Kandatmosphericpressure.^a

X1 X2 X1 X2

303.15K

0.032 0.000 0.858 0.000

0.029 0.014 0.815 0.016

0.032 0.025 0.769 0.039

0.035 0.037 0.697 0.066

0.043 0.057 0.592 0.099

0.049 0.069 0.470 0.129

313.15K

0.017 0.000 0.838 0.000

0.020 0.022 0.631 0.063

0.022 0.020 0.572 0.075

0.023 0.027 0.504 0.087

0.031 0.036 0.454 0.103

0.032 0.043 0.381 0.115

0.038 0.052 0.319 0.123

0.086 0.082 0.170 0.105

Fig.5.Thecriticalcurvesofaceticacid–ethanol–ethylacetate–watersystemat polythermalconditions,where()is293.15K [29],(䊉)is 303.15K,and()is 313.15K.Compositionsaregiveninmolarfractions.

systemformsacriticalcurveinthecompositiontetrahedron.The ﬁnalpointsofthiscurvecorrespondtocriticalstatesofternarysys- tems.TherunofcriticalcurvesispresentedinFig.5for303.15K and313.15K.

4. ModelingofLLE

Theexperimentaldatasetsonbothternaryandquaternarysys- temshavebeencomparedwithdatacalculatedusingUNIFACand NRTLmodels.

4.1. UNIFACmodel

TheapproachdevelopedinRef.[44]wasusedforcalculation.

ModelingwasbasedonUNIFACparameterspresentedinRef.[45].

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Table8

TheexperimentalLLEdataforthequaternarysystemaceticacid(1)–ethanol(2)–ethylacetate(3)–water(4)formolefractionsxat303.15Kandatmosphericpressure.^a Ratioofaceticacidtoethanolmol.fractionsin

theinitialheterogeneousmixture

X1 X2 X3 X1 X2 X3

3:1 0.010 0.005 0.025 0.015 0.011 0.753

0.020 0.010 0.036 0.026 0.023 0.664

0.032 0.017 0.048 0.049 0.028 0.589

0.036 0.020 0.060 0.086 0.035 0.438

5:3 0.007 0.005 0.023 0.003 0.008 0.794

0.010 0.009 0.026 0.005 0.016 0.744

0.013 0.015 0.031 0.014 0.025 0.667

0.018 0.019 0.033 0.030 0.036 0.568

0.027 0.032 0.057 0.053 0.055 0.420

1:1 0.014 0.006 0.050 0.017 0.013 0.750

0.017 0.019 0.050 0.025 0.031 0.630

0.021 0.036 0.044 0.033 0.064 0.477

0.035 0.052 0.072 0.058 0.082 0.376

3:5 0.005 0.007 0.023 0.008 0.012 0.787

0.007 0.015 0.026 0.009 0.025 0.727

0.010 0.023 0.028 0.012 0.040 0.616

0.014 0.035 0.034 0.015 0.057 0.568

0.014 0.047 0.043 0.025 0.078 0.458

1:3 0.006 0.009 0.024 0.007 0.016 0.796

0.008 0.027 0.028 0.012 0.050 0.672

0.009 0.043 0.033 0.018 0.070 0.613

0.010 0.056 0.046 0.027 0.099 0.542

0.011 0.065 0.050 0.012 0.120 0.491

Table9

TheexperimentalLLEdataforthequaternarysystemaceticacid(1)–ethanol(2)–ethylacetate(3)–water(4)formolefractionsxat313.15Kandatmosphericpressure.^a Ratioofaceticacidtoethanolmol.fractionsin

theinitialheterogeneousmixture

X1 X2 X3 X1 X2 X3

3:1 0.018 0.003 0.017 0.049 0.020 0.618

0.020 0.007 0.027 0.065 0.024 0.544

0.024 0.010 0.027 0.077 0.026 0.501

0.045 0.016 0.033 0.090 0.039 0.403

0.055 0.022 0.049 0.093 0.041 0.295

5:3 0.016 0.009 0.019 0.037 0.030 0.678

0.028 0.017 0.024 0.067 0.046 0.539

0.032 0.020 0.030 0.073 0.052 0.514

0.038 0.025 0.037 0.082 0.057 0.440

0.045 0.029 0.047 0.086 0.058 0.326

1:1 0.015 0.018 0.025 0.043 0.052 0.565

0.018 0.024 0.024 0.053 0.059 0.453

0.030 0.034 0.035 0.060 0.079 0.370

0.034 0.039 0.046 0.053 0.077 0.253

3:5 0.009 0.017 0.019 0.023 0.044 0.632

0.016 0.021 0.021 0.034 0.053 0.560

0.019 0.027 0.026 0.039 0.076 0.509

0.030 0.034 0.030 0.037 0.078 0.447

0.031 0.041 0.034 0.063 0.082 0.396

0.028 0.056 0.044 0.039 0.104 0.264

1:3 0.011 0.027 0.023 0.022 0.079 0.568

0.008 0.033 0.028 0.023 0.087 0.511

0.013 0.042 0.030 0.017 0.103 0.449

0.017 0.066 0.043 0.018 0.145 0.343

0.020 0.079 0.057 0.025 0.135 0.262

Standarddeviation,wasdeterminedusingthefollowingequa- tion:

=100×

n

i=1

m

i=1

(xîk_exp−xîk_cal)ôr₂ +(xîk_exp−xîk_cal)âq₂

2×m×n (1)

wherenisanumberofdatasetsandmisanumberofcomponents.

GenerallyUNIFACmodelsimulationleadstoresultsthatarein goodagreementwithexperimentaldata.Forthequaternarysys- temsandbothternarysubsystems,thestandarddeviationdoesnot exceed3.0%at303.15Kand5.5%at313.15K.Thesestandarddevi- ationsareapproximatelythesameasinourpreviousworkonthis systemat293.15K(<3.1%)[29].

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Table10

Theexperimentaldataoncompositionsofcriticalstates(molefractions,x)forthesystemaceticacid(1)–ethanol(2)–ethylacetate(3)–water(4)at303.15Kand313.15K andatmosphericpressure.^a

Temperature(K) X1 X2 X3

303.15 – 0.147 0.146

0.035 0.106 0.137

0.051 0.085 0.136

0.067 0.067 0.137

0.082 0.048 0.136

0.093 0.031 0.136

0.117 – 0.136

313.15 – 0.145 0.150

0.035 0.105 0.151

0.051 0.085 0.151

0.067 0.067 0.152

0.080 0.050 0.152

0.093 0.030 0.152

0.119 – 0.155

Table11

BinaryparametersforNRTLsimulation.

Aceticacid–ethanol Aceticacid–water Aceticacid–ethylacetate Ethanol–water Ethanol–ethylacetate Water–ethylacetate gji 76 1949 1128 1724 186 1001

gij −719 −636 −371 −515 391 2321

˛ji 0.3 0.2 0.2 0.3 0.4 0.35

4.2. NRTLmodel

TheNRTLmodel,developedbyRenonandPrausnitz[46],was chosentocorrelatetheexperimentalresults.NRTLequationforthe activitycoefﬁcientsinthesolutionofncomponentsisthefollow- ing:

ln(_i)=

m j=1x_j_jiG_ji

m

i=1x_iG_ji +

m

j=1

xjGij

m i=1x_iG_ij

_ij−

m r=1xr_rjG_rj

m i=1x_iG_ij

,

_ji=gji−gii

RT =gji

RT , G_ji=exp(−˛_ji_ji), (˛_ji=˛_ij), whereg_jiisenergyparameteroftheinteractionofcomponentsj andi;parameter˛jicharacterizesnonrandomnessinthesystems.

The optimization tool for the calculation of NRTL parameters, whichminimizesthecompositionobjectivefunction(OF),is:

OF=

n

k=1

n

i=1

(xêxp_ik −x_ik^cal)ôr₂ +(xêxp_ik −x_ik^cal)âq₂

ParameterspresentedinTable11wereusedforthesimulations.

TheNRTLparameterswereadjustedtothedataforthequaternary mixtures.GenerallyNRTLmodelsimulationalsoleadstoresults thatareingoodagreementwithexperimentaldata.Standarddevi- ationforsystemaceticacid–ethanol–ethylacetate–waterdoesnot exceed3.7%at303.15Kand2.8%at313.15K.Bothmodelsshowa lowstandarddeviationthatindicatesthepossibilityofsimulation ofLLEinaceticacid–ethanol–ethylacetate–watersystemonthe baseofUNIFACandNRTLmodels.

5. Conclusions

ThenewdetailedexperimentaldataonthesolubilityandLLE for quaternary system acetic acid–ethanol–ethyl acetate–water andtwoternarysystemsethanol–ethylacetate–waterandacetic acid–ethylacetate–waterat303.15Kand313.15Kwereobtained.

TheexperimentalstudywascarriedoutwiththeuseofGCanal- ysisandcloud-pointtechnique.Therunofcriticalcurvesinthe compositiontetrahedronwasdeterminedatbothtemperatures.A comparisonofLLEdatawiththevaluescalculatedbyUNIFACand

NRTLmodelsindicatestheexperimentalandcalculateddataarein sufﬁcientagreement.

Acknowledgments

This work was supported by Russian Foundation for Basic Research(RFBRproject13-03-00985a).Theauthorsaregratefulto TDEgroup(NIST)forthedataonthepropertiesoftheconsidered system.AlexanderToikkaisalsothankfultoSaint-PetersburgState Universityforthesupportoftheproject12.38.257.2014.

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