P.Susial*,D.García R.SusialY.C.Clavijo A.Martín *

1 Escuela de Ingenierias Industriales y Civiles,Universidad de Las Palmas de Gran Canaria,35017 Las Palmas de Gran Canaria,Canary Islands,Spain

2 Dept.Ingeniería Química y Tecnología del Medio Ambiente,Universidad de Valladolid,47071 Valladolid,Spain

1.Introduction

The vapor-liquid equilibrium(VLE)of mixtures with associating or solvating components shows non-ideal behavior.This is due to the formation and rupture of hydrogen bonding between the different molecules in such systems.In the case of ester+alcohol systems,a cross-association interaction between ester and alcohol molecules is developed.These phenomena are caused by the activity of the alcohol as proton-donor and proton-acceptor as well as the capacity of the ester to act as proton-acceptor.

Different researchers[1,2]have studied the formation of hydrogen bonding between alcohol or ester molecules of the same type as well as between different types of molecules at room and low temperatures.For example,Blanco and Ortega[3]analyzed the measured values of GE,νEand HEof ester+alcohol mixtures.However,the experimental data at high temperature and its modeling are less common[4].Therefore,studies about the behavior of the complex interactions via hydrogen bonding requires phase equilibrium data at medium and high pressures and temperatures to facilitate the modeling of mixtures using equations of state(EOS).

For this reason,in a previous work[5,6]the VLE of binary mixtures of alkyl ester+alcohol was determined at moderate pressures.To complement these results,in this work experimental data was determined for binary mixtures(1)propyl acetate+(2)methanol(PAM),(1)butyl acetate+(2)methanol(BAM)and(1)isobutyl acetate+(2)methanol(IBAM),in all cases at 0.6 MPa.These systems have been previously studied by different authors at different operating conditions.The PAM system has been reported at a pressure of 141.3 kPa by Blanco[7]and at 0.15 MPa by Susial et al.[8],in addition to the data at 101.3 kPa reported by Grishunin et al.[9]and by Resa et al.[9].Furthermore,the BAM system has been studied isothermally[9]and also isobarically at P=101.3 kPa by Beregovikh et al.[10],Patlasov et al.[11]and by Resa et al.[12],while results at P=141.3 kPa have been reported by Blanco[7]and studied by Espiau etal.[13].Finally,the IBAM system has been studied at P=101.3 kPa by Resa et al.[12]and at P=0.15 MPa by Susial et al.[14].

In this work the obtained data were verified and modeled using the φ-φ approach.For this purpose,the measured data were correlated with the Peng-Robinson(PR)EOS[15]using the Wong-Sandler(WS)mixing rules[16].In addition,the statistical associating fluid theory for chain mixtures presented by Chapman et al.[17,18]combined with the theory for chain molecules,applying the perturbation theory of Barker and Henderson[19,20]in the EOS of perturbed-chain statistical associating fluid theory[21,22](PC-SAFT)was also employed for simulation and comparison purposes,as this molecular model can account for the size and shape effects of molecules.

2.Experimental

2.1.Chemicals

Methanol,propyl acetate,isobutyl acetate and butyl acetate were purchased from Panreac Química S.A.These products were used as received from the manufacturer,and further treatments for substance purification were not applied.

These solvents were characterized measuring their normal boiling point(Tbp),density(ρii)and refractive index(nD)determined at 298.15 K,employing a Kyoto Electronics DA-300 vibrating tube density meter with an uncertainty of±0.1 kg·m-3and a Zusi 315RS Abbe refractometer with an uncertainty of±0.0002 units.Results for methanol,propyl acetate and isobutyl acetate did not differ from the values previously published[6,14].Moreover,the physical properties for butyl acetate with 99.5%purity and their comparison with values from literature are shown in Table 1,also showing good agreement.

Table 1 Physical properties with literature values of pure substance at atmospheric pressure①

2.2.Equipment and procedure

For the experimental VLE data,an ebulliometer made of 2 mm-thick stainless steel was employed.The general description of the equilibrium ebulliometer and the disposition of the different elements in the installation can be found in previous papers[5,6].

The equilibrium still operates dynamically by using a vapor lift pump effect and with both phases recirculating.After 90 min of recirculation of both phases it was considered that steady state was reached,thus proceeding to take sample of the liquid and the vapor phases in airtight bottles.Subsequently,a disturbance is generated in the mixture by addition of one of the substances,working continuously and without stopping the operation of the ebulliometer.

To determine temperature,a digital recorder Dostmann Electronic GmbH p655 and two Pt100 probes with±0.03 K of uncertainty were employed.The calibration of the system was done by Dostmann Electronic GmbH.Proper operation of the probes installed in the equipment was verified by measuring the boiling point of distilled water.Pressure was controlled with a pressure regulating valve(Binks MFG Co.)included in the nitrogen supply line,and measured with a digital transducer 8311 from Burket Fluid Control Systems,with an operating range from 0.0 to 4.0 MPa(uncertainty±0.004 MPa).

The composition of the samples was determined by measuring their density.A calibration curve composition vs.density was previously obtained at298.15 K using the vibrating tube density meter previously described.The uncertainty for these systems by this composition analysis method was estimated to be better than 0.002 units in mole fraction.

3.Results and Discussion

3.1.Densities

Mixtures of(1)ester+(2)alcohol were prepared by mass and the densities(ρii)were measured at 298.15 K.Mole fraction(xi)vs.density(ρij)pairs(Table 2)were verified by the adequate correlation of the excess molar volumes(νE)(see Fig.1).Table 2 shows composition density pairs of this work and their comparison with values found in the bibliography[12,13].The small discrepancies on density values between these data sources reported in Table 2 may be due to different purities of the products used in each case.As shown in Table 2,excess molar volumes were calculated from our data,and from the data found in bibliography[12,13].The(νE)vs.(xi)pairs were correlated using a polynomial equation proposed in previous papers[8,14].The result obtained for BAM and IBAM systems are shown in Eqs.(1)and(2),respectively:

Good correlations were observed,being the standard deviations of fitting curves,SD(vE×109)=1.7 m3·mol-1for BAM and SD(vE×109)=2.1 m3·mol-1for IBAM.

Fig.1 plots the experimental excess volume points and the fitted curves of BAM and IBAM mixtures and compares the results with the literature data[12,13].The data of the BAM system determined in this work exhibited moderate differences with literature data[12,13]except at high composition of ester by considering the values of Resa et al.[12].However,in the IBAM system the data measured in this work show important differences with respect to literature data[12].

3.2.Treatment of VLE data

The VLE data T-x1-y1of PAM,BAM and IBAM at0.6 MPa are shown in Table 3.Figs.2-4 also show data and fitting curves obtained in a similar way as in previous works[5],together with isobaric data from the literature to verify the evolution of systems with pressure.The data up to the mole fraction of ester less than 0.3 have been plotted in inserts included in Figs.2-4 for better observation of the different data and the azeotrope in the PAM system.In Fig.3,corresponding to the BAM system,along with information measured in this work,data presented by Resa et al.[12]and reported at 141.3 kPa by Espiau et al.is also presented[13],which have proven to be in very good correspondence with data at 141.3 kPa informed by Blanco[7]in 1997.On the one side,considering the pressure effect on the system(see Figs.2-4),it is observed that there is a uniform evolution in all systems,except for the PAM system at low pressures,which has already been previously discussed[8].It seems evident that there is lesser volumetric compression in vapor phase respect of the liquid phase by increasing the ester chain.In addition,as shown in Fig.2,a decrease in the difference between yi-xiwith pressure increasing,produces a change from positive to negative values from 0 to 1 ester mole fraction,thus generating the disappearance at 0.6 MPa of the azeotrope of PAM as was mentioned in the literature[8].

3.3.Modeling of VLE data

Since the proper description of the VLE data is of great importance for the design and simulation of chemical processes,different EOS have been used by chemical engineers for applications at moderate or high pressures[25],including the PR-EOS.However,due to its simplicity,this EOS may be restricted in its application to complex systems.Therefore,models which account for molecular size and shape,or including association effects of the molecules by using different terms or contributions,such as PC-SAFT model,show improved predictive capabilities and good precision in correlating mixtures[21,22]of a wide range on industrially important systems[4]and therefore should be verified with mixtures of solvents at moderate pressures,such as those presented in this work.

Table 2 Densities and excess volumes for the binary systems EA1P and PA1P at 298.15 K①

3.3.1.PR equation

Mixtures of substances,such as those used in this work,containing and/or associating polar components as methanol,are of interest to chemical industries.Usually,traditional thermodynamic models such as cubic EOS perform well correlating VLE data.For this reason,a relative simple EOS model as PR[15]was used in this work.This EOS has the following form,

Fig.1.Excess molar volumes of BAM(■)and IBAM(●)for this work.[Literature data[12](?)and[13](?)for BAM,also[12](▲)for IBAM].

where p is the pressure,T is the temperature,R is the universal gas constant and v is the molar volume.Through parameters b and a free volume effects and intermolecular attractive interactions are taken into account.For a pure component the energy and size parameters are calculated,respectively,as follows,

where C is a numerical constant equal tothe kij=kjiis the binary interaction parameter for each system.Also,isan excess Helmholtz free energy model at infinite pressure that can be equated to a low-pressure excess Gibss energy model[16].In this study,we used the NRTL model[26]by,being(αji)=(αji)as well as(τij)and(τji)adjustable parameters,to obtain optimal agreement between theory and experiment for vaporliquid equilibria.

Table 3 Experimental VLE data for binary systems at 0.6 MPa①

Fig.2.Equilibrium diagram(★)and fitting curve for PAM at 0.6 MPa.[Literature data(?)[7]at 141.4 kPa,(?)[8]at 0.15 MPa and(▲)[9]at 101.3 kPa].

The MATLAB program of Martín et al.[25]that utilize the previous PR equations was employed to obtain the predictions of the systems of this work.The flash point routine of this program[25]was utilized to obtain the optimal fitting parameters of this PR-EOS.The statistical parameter utilized was the objective function(OF),by using the liquid and vapor phase composition for minimization properties,as follows:

Fig.3.Experimental data(■)and fitting curve for BAM at 0.6 MPa.[Literature data(▲)[12]at 101.3 kPa and(?)[13]at 141.3 kPa].

Fig.4.Plot of VLE points(●)and fitting curve for IBAM at 0.6 MPa.[Literature data(▲)[12]at 101.3 kPa and(?)[14]at 0.15 MPa].

Results obtained are shown in Table 4.It can be observed that the mean absolute deviation(MAD)in vapor phase ester mole fraction is higher than the deviation in the liquid phase ester mole fraction.This can be justified because in vapor phase the uncertainty in pressure should be included.Figs.5 and 6 represent the experimental data and the fitting curve of PR-EOS prediction.It is shown that the binary interaction parameter enables a good representation of the behavior of the real mixture.The adjustable parameters using the NRTL model produces a good agreement between experimental data and predictive data in IBAM system as shown in Figs.5 and 6.However the modeling of PAM and BAM systems shows small deviation in T vs.x1,y1diagram(seeFig.6)but higher deviations in y1-x1vs.x1plot(see Fig.5).Probably this uneven behavior is a consequence of the important influence of the mixing rules in the data prediction.

Table 4 Optimal parameters and binary interaction parameters with systems at 0.6 MPa

Fig.5.Plot of y1-x1 vs.x1 experimental data at 0.6 MPa and PR-WS-NRTL modelizations.[Respectively data and prediction:(★)and(-----)for PAM;(■)and(— —)for BAM;(●)and(——)for IBAM].

Fig.6.Representation of T vs.x1,y1 data at 0.6 MPa and PR-WS-NRTL predictions.[Respectively data and prediction:(☆,★)and(-----)for PAM;(□,■)and(— —)for BAM;(○,●)and(___)for IBAM].

3.3.2.PC-SAFT model

A molecular equation developing a theory for chain molecules,applying the perturbation theory of Barker and Henderson[19,20]has been presented by Gross-Sadowski[21,22].This EOS uses a new dispersion term and the same chain term and association term as in Wertheim thermodynamic perturbation theory of first order[27]applying and extending it to mixtures in the statistical associating fluid theory of Chapman[17,18].

The perturbed chain-statistical associating fluid theory(PC-SAFT)equation is usually written in terms of residual Helmholtz free energy(Ares/NkT).Each term in the equation represents different contributions to the total free energy of the fluid.The equation is written as:

whereis the mean segment number in the mixture,and for the i substance,miis the number of segments perchain,xiis the mole fraction,σiis the segment diameter,andis the Helmholtz free energy of the hard-sphere fluid.The temperature dependent segment diameter diis given by:

being A1the Helmholtz free energy of first-order perturbation term and A2the Helmholtz free energy of second-order perturbation term,and the(Aassoc/NkT)term in Eq.(12)represents the Helmholtz energy from associating contribution.The Helmholtz free energy due to association is defined by[17,18],

where XAiis the fraction of molecules i that are not bonded at the association site A,and Miis the number of association sites on molecule i.

For representing thermodynamic properties, five parameters of PC-SAFT are necessary.In addition to the three pure component parameters for simple fluid,the segment number,the segment energy parameter and the segment diameter,there are two more pure component parameters needed for the associating interaction description,the association energy(εAiBj)and the association volume(κAiBj).These parameters are required in describing the cross associating interactions between associating substances.The mixing rules of Wolbach and Sandler[28]were employed:

The previous equations were employed in a MATLAB program by Martín et al.[25].However,a simplified version in the subroutines of PC-SAFT from Martín et al.[25]has been developed.It was adapted to pure substances without association,or with association scheme number 2 and symmetric matrix.For pure substances some conditional statements and many nested loops with index range from one to one,can be substituted by simple sentences.In this way,we can eliminate redundant assignment sentences that usually,with mixture substances,are executed thousands of times.This redundant assignment sentences are only calculated one time and transferred to other functions by declaring a global variable.

On the other side,the association contribution to the residual Helmholtz energy,for pure substances with association scheme number 2 and symmetric matrix,can be calculated by a direct solve of the nonlinear system,instead of using iterative method in the inner loop of the program.Avoiding unnecessary loops,and eliminating redundant assignment sentences,the program has improved speed in execution(from days to a few hours for larger tests),and without losing precision.This is a significant advantage for a problem formulated in a so widely and complete manner.

On this way,the modified PC-SAFT program from Martin et al.[25]was employed with the literature data[8,29]of vapor pressures.Consequently,the parameters m,σiand εiof pure fluids were calculated.To obtain the parameters of methanolεAiBiandκAiBi,as indicated,a scheme 2B with 2 number association sites was applied.The standard deviation(SD)was used as minimization parameters.The mean percent deviations(MPD)were also calculated for comparison proposed.Results are shown in Table 5,always compared with the literature parameters.Parameters of isobutyl acetate for comparison were calculated following Tihic et al.[31]technique.It can be seen that the results are not very different except for the number of segments per chain in methanol.Furthermore,good agreement is observed between the vapor pressures calculated by PC-SAFT model and the experimental data.

After this the VLE data of PAM,BAM and IBAM systems were employed to obtain the binary interaction parameter of mixtures.The computer program of Martín et al.[25]was also used incorporating our pure component parameters.One association site was considered for all the esters and self-association was not permitted.Solvation was only considered through cross-association between the site of the ester and the sites of alcohol molecule.A flash algorithm was used to perform VLE predictions by PC-SAFT model.The interaction parameter was correlated by minimization of the OF presented in Eq.(11).Results are shown in Table 4.It can be seen that the MAD in vapor phase ester mole fraction is higher than the MADin liquid phase ester mole fraction.This can be due to the flash algorithm utilized and to the systematic error due to uncertainty in pressure.

The adjustable interaction parameters of PC-SAFT model produce a good agreement between experimental and calculated data in both systems as shown in Figs.7 and 8.The higher deviations are in y1-x1vs.x1plot and in the T vs.x1,y1diagram also for BAM system(see Figs.7 and 8).However the modeling of PAM and IBAM shows a very good prediction in T vs.x1,y1and in the y1-x1vs.x1diagrams as shown in Figs.7 and 8.Probably this uneven behavior is a consequence of considering that a given molecule is a homonuclear chain composed of identical spherical segments.

Table 5 PC-SAFT pure component parameters

Fig.7.Comparison of y1-x1 vs.x1 data at 0.6 MPa and prediction results with PC-SAFT.[Respectively data and prediction:(★)and(-----)for PAM;(■)and(— —)for BAM;(●)and(___)for IBAM].

4.Conclusions

Excess molar volumes for BAM and IBAM at 298.15 K and VLE data for binary systems PAM,BAM and IBAM at 0.6 MPa were measured and the results were compared with published data.It has been verified that the azeotropic point in PAM system was not found at a pressure of 0.6 MPa.

The PR-WS-NRTL EOS was utilized to model and verify the VLE data obtained in this work.Results show good predictions in the T vs.x1,y1diagram.However in the plot of y1-x1vs.x1,major deviations in modeling the PAM and BAM systems were observed,as presented through the higher values of MAD(x1)and MAD(y1).These results probably are a consequence of the algorithm used or indicate that the Wong-Sandler mixing rules used are not completely suitable for strongly associated systems.

Fig.8.T vs.x1,y1 experimental data at 0.6 MPa and PC-SAFT modeling.[Respectively data and prediction:(☆,★)and(-----)for PAM;(□,■)and(— —)for BAM;(○,●)and(___)for IBAM].

The binary systems of this paper were used to verify the PC-SAFT modeling capacity of mixtures of associating components at moderate pressure.The homonuclear chainlike molecules,association scheme number 2 with symmetric matrix and the binary interaction parameter adjustable was considered by applying a fl ash algorithm.Results obtained have shown good predictions of VLE data of this paper in both T vs.x1,y1and y1-x1vs.x1representations.

[1]A.Breitholz,J.S.Lim,J.W.Kang,K.P.Yoo,Nonrandom lattice fluid group contribution parameter for vapor-liquid equilibrium of esters and their mixtures,Korean J.Chem.Eng.26(2009)230-234.

[2]A.Aucejo,S.Loras,R.Mu?oz,J.Wisniak,H.Segura,Phase equilibria and multiple azeotropy in the associating system methanol+diethylamine,J.Chem.Eng.Data 42(1997)1201-1207.

[3]A.M.Blanco,J.Ortega,Densities and vapor-liquid equilibrium values for binary mixtures composed of methanol+an ethylester at 141.3 kPa with application of an extended correlation equation for isobaric VLE data,J.Chem.Eng.Data 43(1998)638-645.

[4]A.F.Cristino,S.Rosa,P.Morgado,A.Galindo,E.J.M.Filipe,A.M.F.Palvra,C.A.Nieto de Castro,High-temperature vapour-liquid equilibrium for the(water+alcohol)systems and modelling with SAFT-VR:2.water+1-propanol,J.Chem.Termodynamics 60(2013)15-18.

[5]P.Susial,A.Sosa-Rosario,J.J.Rodriguez-Henriquez,R.Rios-Santana,Vapor pressures and VLE data measurements.Ethyl acetate+ethanol at 0.1,0.5 and 0.7 MPa binary system,J.Chem.Eng.Jpn.44(2011)155-163.

[6]P.Susial,D.García-Vera,R.Susial,V.D.Castillo,E.J.Estupi?an,J.C.Apolinario,J.J.Rodriguez-Henriquez,Experimental determination of vapor-liquid equilibria.Binary systems of methyl acetate,ethyl acetate and propyl acetate with 1-propanol at 0.6 MPa,J.Chem.Eng.Data 58(2013)2861-2867.

[7]A.M.Blanco,Analysis of the vapor-liquid equilibrium at 141.3 kPa of binary mixtures containing methanol with n-alkanes(C5,C6)and alkyl esters(Doctoral thesis)University of La Laguna,Canary Islands,1997.

[8]P.Susial,J.J.Rodríguez-Henríquez,J.C.Apolinario,V.D.Castillo,E.J.Estupi?an,Vapor pressures and vapor-liquid equilibrium of propyl acetate+methanol or+1-propanol at 0.15 MPa.Binary systems,Rev.Mex.Ing.Quim.12(12)(2013)595-608.

[9]J.Gmehling,U.Onken,Vapor-liquid equilibrium data collection,vol.1,Dechema,Frankfurt,2005(Part g).

[10]J.Gmehling,U.Onken,W.Arlt,Vapor-liquid equilibrium data collection,vol.1,Dechema,Frankfurt,1982(Part 2c).

[11]J.Gmehling,U.Onken,J.R.Rarey-Nies,Vapor-liquid equilibrium data collection,vol.1,Dechema,Frankfurt,1988(Part 2e).

[12]J.M.Resa,C.González,B.Moradillo,J.Lanz,(Vapour-liquid)equilibria for(methanol+butyl acetate),(vinyl acetate+butyl acetate),(methanol+isobutyl acetate),and(vinyl acetate+isobutyl acetate),J.Chem.Thermodynamics 30(1998)1207-1219.

[13]F.Espiau,J.Ortega,E.Penco,J.Wisniak,Advances in the correlation of thermodynamic properties of binary systems applied to methanol mixtures with butyl esters,Ind.Eng.Chem.Res.49(2010)9548-9558.

[14]P.Susial,J.C.Apolinario,V.D.Castillo,E.J.Estupi?an,J.J.Rodríguez-Henríquez,Isobaric VLE for the binary systems isobutyl acetate+methanol or+1-propanol at 0.15 MPa,Afinidad 69(69)(2012)95-100.

[15]D.Y.Peng,D.B.Robinson,A new two-constant equation of state,Ind.Eng.Chem.Fundam.15(1976)59-64.

[16]D.S.H.Wong,S.I.Sandler,A theoretically correct mixing rule for cubic equations of state,AIChE J.38(1992)671-680.

[17]W.G.Chapman,G.Jackson,K.E.Gubbins,Phase equilibria of associating fluids.Chain molecules with multiple bonding sites,Mol.Phys.65(1988)1057-1079.

[18]W.G.Chapman,K.E.Gubbins,G.Jackson,M.Radosz,SAFT:Equation-of-state solution model for associating fluids,Fluid Phase Equilib.52(1989)31-38.

[19]J.A.Baker,D.Henderson,Perturbation theory and equation of state for fluids:The square-well potential,J.Chem.Phys.47(1967)2856-2861.

[20]J.A.Baker,D.Henderson,Perturbation theory and equation of state for fluids:II.A successful theory of liquids,J.Chem.Phys.47(1967)4714-4720.

[21]J.Gross,G.Sadowski,Perturbed-chain,SAFT an equation of state based on a perturbation theory for chain molecules,Ind.Eng.Chem.Res.40(2001)1244-1260.

[22]J.Gross,G.Sadowski,Application of the perturbed-chain SAFT equation of state to associating systems,Ind.Eng.Chem.Res.41(2002)5510-5515.

[23]TRC thermodynamic tables non-hydrocarbons and hydrocarbons,Thermodynamic Research Center,Texas A and M University System,College Station,Tx,1993.

[24]J.Acosta,A.Arce,E.Rodil,A.Soto,A thermodynamic study on binary and ternary mixtures of acetonitrile,water and butyl acetate,Fluid Phase Equilib.203(2002)83-98.

[25]A.Martín,M.D.Bermejo,F.A.Mato,M.J.Cocero,Teaching advanced equations of state in applied thermodynamics courses using open source programs,Educ.Chem.Eng.6(2011)e114-e121.

[26]H.Renon,J.M.Prausnitz,Local compositions in thermodynamic excess functions for liquid mixtures,AIChE J.14(1968)135-144.

[27]M.S.Wertheim,Fluids with highly directional attractive forces.I.Statistical thermodynamics,J.Stat.Phys.35(1984)19-34;II.Thermodynamic perturbation theory and integral equations,J.Stat.Phys.35(1984)35-47;III.Multiple attraction sites,J.Stat.Phys.42(1986)459-476;IV.Equilibrium polymerization,J.Stat.Phys.42(1986)477-492.

[28]J.P.Wolbach,S.I.Sandler,Using molecular orbital calculations to describe the phase behavior of cross-associating mixtures,Ind.Eng.Chem.Res.37(1998)2917-2928.

[29]P.Susial,J.J.Rodríguez-Henríquez,J.C.Apolinario,V.D.Castillo,E.J.Estupi?an,Vapour pressures and vapour-liquid equilibria of binary systems of n-propyl acetate and isobutyl acetate with ethanol or 2-propanol at 0.15 MPa,J.Serb.Chem.Soc.77(2012)1243-1257.

[30]M.Kleiner,G.Sadowski,Modeling of polar systems using PCP-SAFT:An approach to account for induced-association interactions,J.Phys.Chem.C 111(2007)15544-15553.

[31]A.Tihic,G.M.Kontogeorgis,N.von Solms,M.L.Michelsen,A predictive groupcontribution simplified PC-SAFT equation of state:Application to polymer systems,Ind.Eng.Chem.Res.47(2008)5092-5101.