SA AHMAD FPE 220 (2004) 189-198

Fluid Phase Equilibria 220 (2004) 189–198

Interaction parameters for multi-component aromaticextraction with sulfolane

S.A. Ahmad, R.S. Tanwar, R.K. Gupta, A. Khanna∗

Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

Received 11 May 2002; accepted 4 February 2004

Available online 4 June 2004

Abstract

Aromatic extraction is an important operation in petrochemical processing. Design of an aromatic extractor requires the knowledge ofmulti-component liquid–liquid equilibrium (LLE) data. Such experimental LLE data are usually not available and therefore can be predictedusing various activity coefficient models. These models require proper binary interaction parameters, which are not yet available for allaromatic extraction systems. Furthermore, the parameters available for most of the ternary systems are specific to that system only and cannotbe used for other ternary or multi-component systems. An attempt has been made to obtain these parameters that areglobally applicable. Forthis purpose, the parameter estimation procedure has been modified to estimate the parameterssimultaneously for different systems involvingcommon pairs. UINQUAC and UNIFAC models have been used for parameter estimation. The regressed parameters are shown to be applicablefor the ternary as well as for the multi-component systems. It is observed that UNIQUAC parameters provide a better fit for ternary LLE data,whereas, as one moves towards the higher component systems (quaternary and quinary) the UNIFAC parameters, which are a measure of thegroup contributions, predict the LLE better. Effect of temperature on UNIQUAC binary interaction parameters has been studied and a lineardependence has been observed.© 2003 Published by Elsevier B.V.

Keywords: Multi-component; Maximum likelihood; Liquid–liquid equilibria; Binary interaction parameters; IVEM

1. Introduction

Aromatics such as benzene, toluene, and xylene are con-sidered essential in the chemical industry because they arethe source of many organic chemicals. These aromatics arepresent in the naphtha feed. High purity aromatics are dif-ficult to be separated using ordinary distillation operation,since they form several binary azeotropes with aliphatics.Extraction is therefore a better choice to separate the aromat-ics from the naphtha feed, as they are preferentially solublein a variety of solvents.

To predict the separation, it is necessary to know the LLEdata for a particular system. Various thermodynamic mod-els such as UNIQUAC, UNIFAC and NRTL can be used topredict the LLE. These models use the activity coefficients,which require properbinary interaction parameters that can

∗ Corresponding author. Tel.:+91-512-2597117;fax: +91-512-2590104.

E-mail address: [email protected] (A. Khanna).

represent LLE for highly non-ideal liquid mixtures usuallyencountered in aromatic extraction. These parameters areyet not entirely available for the multi-component systemsencountered in aromatic extraction. These are generally es-timated using experimental LLE data. In case no experimen-tal liquid–liquid equilibrium data for the systems of interestare available, theinfinite dilution activity coefficients can beused for parameter estimation but at the cost of accuracy[1].

A least square minimization or a maximum likelihood ap-proach can be used for the estimation of binary interactionparameters. It has been observed that the binary interactionparameters for the same pairs are found to be different fordifferent ternary systems[2]. For example, the binary inter-action parameters between the pair hexane–benzene in thesystem hexane–benzene–sulfolane are different from thosein hexane–benzene–triethylene glycol system[3]. Interac-tion parameters are therefore specific for the system fromwhich they have been estimated and hence cannot be used topredict LLE for the other systems or for the multi-componentextraction. It has also been reported that the different sets of

0378-3812/$ – see front matter © 2003 Published by Elsevier B.V.doi:10.1016/j.fluid.2004.02.008

190 S.A. Ahmad et al. / Fluid Phase Equilibria 220 (2004) 189–198

initial guesses result in different estimates of the parametersdue to existence of several local minima[4].

To overcome these problems, the parameter estimationapproach is modified in which the binary interaction pa-rameters for different ternary systems involvingcommonpairs are estimated simultaneously using a modified objec-tive function. A brief description of the method used for theparameter estimation is given in the next section. Results ofparameter estimation and multi-component LLE predictionare presented and discussed in the later section. The effectof temperature on UNIQUAC binary interaction parametersis also presented and discussed in the same section. Theconclusions drawn are reported in the final section.

2. Estimation of interaction parameter

Two approaches are widely used for parameter estima-tion [4]. Least square minimization approach and maxi-mum likelihood approach. The least square minimizationapproach requires less computational effort but it does nottake into account the possible random errors in the exper-iments. The maximum likelihood approach maximizes thelikelihood function and also takes into account the possiblerandom errors in the experiments[4]. This is therefore thepreferred method. Theobjective function that is to be mini-mized takes the following form

F(θ) = −ln L = mn

2ln 2π + m

2ln

(n∏

i=1

vii

)

+ 1

2

m∑k=1

eTk V−1

k ek (1)

whereL is the likelihood function,m is the number of ex-perimental data or tie lines,n is the number of measuredvariables,ek is the vector of errors forkth experimental data,V k is the variance-covariance matrix forkth experimentaldata, andνii is the variance ofith measured variable. Thismethod has been discussed in detail by Esposito et al.[5].

Table 1Ternary systems at different temperatures used for parameter estimation

S. no. System name Temperature (◦C) Reference

1 Hexane–benzene–sulfolane 25, 50, 75, 100 [7,8]2 Hexane–toluene–sulfolane 25 [7]3 Hexane–xylene–sulfolane 25 [7]4 Heptane–benzene–sulfolane 25 [9]5 Heptane–toluene–sulfolane 25, 50, 75, 100 [8–11]6 Heptane–xylene–sulfolane 17, 25, 50 [10,11]7 Octane–benzene–sulfolane 25, 35, 45, 70.2, 99.2, 129.2 [7,12,13]8 Octane–toluene–sulfolane 25, 35, 45, 70.2, 99.2, 129.2 [7,12,13]9 Octane–xylene–sulfolane 25, 30, 35, 45, 70.2, 99.2, 129.2 [7,12,13]

10 Pentane–benzene–sulfolane 17, 25, 50 [14]11 Pentane–toluene–sulfolane 17, 25, 50 [14]12 Cyclohexane–benzene–sulfolane 25, 50, 75, 100 [8]13 Cyclohexane–toluene–sulfolane 25 [10]

In the maximum likelihood approach a priori estimate ofvariances is made based on the experimental errors, but thismethod is internally inconsistent. This is because the apri-ori estimate of variance-covariance matrix is not, in general,equal to the final values obtained from the residuals at theconclusion of the regression procedure[4]. To avoid thisinconsistency in maximum likelihood approach, an Insidevariance estimation method (IVEM) recently implementedby Vasquez et al.[4] has been adopted in which the ob-jective function ofEq. (1) is used, butV k is re-estimatedat each iteration of the optimization procedure. At the end,the residuals are consistent withV k guaranteeing the mostlikely values for the parameter vectorθ.

2.1. Choice of initial guess

The Objective function defined byEq. (1) is highly non-linear and non convex in nature. Different initial guesses maylead to different minima. A proper choice of initial guess is,therefore, important in parameter estimation. Any one of thefollowing strategies may be used to obtain the initial guess.

1. By running “property estimation” program of Aspen Plussimulator using UNIF–LL method to estimate UNIQUACbinary interaction parameters.

2. By minimizing the activity difference objective function

F(θ) =m∑

k=1

n∑i=1

[aIik(x

Iik, θ) − aII

ik(xIIik, θ)]

2 (2)

using any initial guess. InEq. (2) aik represents the ac-tivity of the componenti for thekth tie line and I and IIrepresent the coexisting phases.

The objective function defined byEq. (2)does not yielda good agreement between experimental and predictedLLE. However it has a very good convergence propertyand therefore is better suited for initial guess for mini-mization of any other objective function[6].

3. By using reported values in the literatures. Both systemspecific or common parameters can be used.

S.A. Ahmad et al. / Fluid Phase Equilibria 220 (2004) 189–198 191

Table 2Quaternary and quinary systems used for validation

S. no. System name Temperature (◦C) Reference

1 Hexane–benzene–xylene–sulfolane 25 [7]2 Hexane–octane–benzene–sulfolane 25 [7]3 Octane–toluene–xylene–sulfolane 25 [7]4 Hexane–heptane–toluene–sulfolane 25 [15]5 Heptane–octane–xylene–sulfolane 25 [15]6 Heptane–benzene–toluene–sulfolane 25 [15]7 Hexane–octane–benzene–toluene–sulfolane 25 [7]8 Hexane–heptane–toluene–xylene–sulfolane 25 [15]9 Heptane–octane–benzene–xylene–sulfolane 25 [15]

The predicted LLE using binary interaction parametersobtained by minimization of the objective function ofEq. (1)are compared with the experimental ones using either thevalue of the objective function at optimality or the value ofroot mean square deviation (RMSD) which forc componentsystem is defined as

RMSD = 100

m∑

k=1

c∑i=1

2∑j=1

(xj

ik − x̂j

ik)2

2mc

1/2

(3)

wherexj

ik and x̂j

ik are the experimental and predicted molefraction of the componenti in the phasej for the tie linekrespectively.

3. Results and discussions

The naphtha feed from which the aromatics are extractedcontains large number of components belonging to differentfamilies (paraffin, iso-parrafin, olefin, naphthene, and aro-matics). It is very difficult to model the aromatic extractionsystem exactly because of the presence of components cov-ering a large range of molecular weights and also due todifferent compositions of aromatic and non-aromatic com-pounds in the naphtha feed obtained from different sources.

Table 3Specific UNIQUAC binary interaction parameters at 298.15 K for hexane–benzene–sulfolane for different initial guesses[7]

Binary pair i–j Initial guess,aij Regressed parameters,aij Objective function,−ln L RMSD RMSD DECHEMA[17]

Initial guess 1Hexane–benzene −116.105 −117.626 −154.822 0.6045 n.a.Hexane–sulfolane 561.401 609.336Benzene–hexane 157.958 156.310Benzene–sulfolane 21.908 19.931Sulfolane–hexane 67.843 69.250Sulfolane–benzene 59.084 60.264

Initial guess 2Hexane–benzene −288.367 −263.377 −143.962 0.7753 n.a.Hexane–sulfolane 501.863 459.073Benzene–hexane −25.304 −29.183Benzene–sulfolane 54.486 60.821Sulfolane–hexane 99.005 80.761Sulfolane–benzene −239.095 −260.902

n.a.: not available.

Therefore, the feed is generally assumed to be composed ofonly key components. The number of such key componentsis also tentative and depends largely on the availability of ex-perimental data. Therefore for simplicity, the feed has beenmodeled as having only one aromatic and one non-aromatickey component. More components can be added based onthe availability of experimental LLE data. Binary interac-tion parameters for different ternary systems are estimatedseparately, they are specific for a particular system. To over-come this specificity, parameters for different ternary sys-tems involvingcommon pairs are estimated simultaneously.The parameters obtained fromsimultaneous estimation havebeen used for the prediction of multi-component LLE andthey are compared with experimental data. The systems con-sidered in this work for parameter estimation are listed inTable 1and those for validation inTable 2. The correspond-ing temperatures and source of experimental LLE data arealso shown in these tables.

3.1. Separate estimation of parameters

Varhegyi and Eon[16] have shown that the binary in-teraction parameters for a particular ternary system mustbe evaluated from the same ternary data. This significantlyreduces the RMSD. Consequently this approach has been


Table 4Specific UNIQUAC binary interaction parameters for at 298.15 K Hexane–toluene–sulfolane for different initial guesses[7]


Initial guess 1Hexane–toluene 167.205 139.977 −161.705 0.6851 n.a.Hexane–sulfolane 561.401 658.218Toluene–hexane −137.162 −105.237Toluene–sulfolane 47.058 60.637Sulfolane–hexane 67.843 66.196Sulfolane–toluene 79.687 69.181

Initial guess 2Hexane–toluene −53.247 −53.808 −98.785 0.8528 n.a.Hexane–sulfolane 392.861 366.612Toluene–hexane −312.903 −296.944Toluene–sulfolane 246.093 255.279Sulfolane–hexane 132.275 121.639Sulfolane–Toluene −194.270 −221.172


implemented in DECHEMA Chemistry Data Series[2]for the ternary systems reported. Similar approach hasbeen adopted to confirm the specificity of the regressedparameters. Two systems, hexane–benzene–sulfolane andhexane–toluene–sulfolane at 298.15 K have been consid-ered. UNIQUAC binary interaction parameters for thesesystems have been estimated using two sets of initialguesses. Initial guess 1 is obtained by running the param-eter estimation program of Aspen Plus simulator usingUNIF–LL method and initial guess 2 is obtained by min-imizing the activity difference objective function definedby Eq. (2). The binary interaction parameters thus ob-tained are shown inTables 3 and 4respectively with thecommon pair parameters underlined. The correspondingvalues of objective function and RMSD are also shown. Itcan be seen that the binary interaction parameter for thecommon pair hexane–sulfolane are different for both thesystems. For the first set of initial guesses, the value of in-teraction parameter of hexane–sulfolane pair in the systemhexane–benzene–sulfolane is 609.336 whereas that in the

Table 5Specific UNIQUAC binary interaction parameters at 298.15 K for Hexane–benzene–sulfolane


Data Set 1[7]Hexane–benzene −116.105 −117.626 −154.822 0.6045 n.a.Hexane–sulfolane 561.401 609.336Benzene–hexane 157.958 156.310Benzene–sulfolane 21.908 19.931Sulfolane–hexane 67.843 69.250Sulfolane–benzene 59.084 60.264

Data Set 2[8]Hexane–benzene −116.105 −114.532 −184.434 0.5090 0.52Hexane–sulfolane 561.401 606.890Benzene–hexane 157.958 151.923Benzene–sulfolane 21.908 21.759Sulfolane–hexane 67.843 70.830Sulfolane–benzene 59.084 59.254


system hexane–toluene–sulfolane is 658.218. The same istrue for the reverse pair sulfolane–hexane. Similar resultsare obtained with the second set of initial guesses. It is alsoevident that the different sets of initial guesses result indifferent estimates of the binary interaction parameters. Aproper choice of initial guess is therefore important. An ac-ceptable choice would be that which gives the better RMSDand/or the objective function value. The parameters reportedin this work are those which exhibit less RMSD values.

Further the parameters estimated from different sets ofLLE data for the same systems are found to be different.For example, UNIQUAC binary interaction parameters re-gressed from LLE data reported by Chen et al.[7] aredifferent from those regressed from LLE data reported byDeFré and Verhoeye[8]. The regressed parameters for thesetwo data sets along with the corresponding objective func-tion and RMSD values are shown inTable 5. To avoid thisdiscrepancy such data sets are taken simultaneously in theregression procedure. Also both the objective function andRMSD values indicate that DeFré’s data[8] is slightly bet-


Table 6Simultaneous UNIQUAC binary interaction parameters at 298.15 K for Hexane–benzene/toluene/xylene–sulfolane

Binary pair i–j No. of datasets [Ref.]

Initial guess,aij Regressed parameters,aij Objective function,−ln L RMSD RMSDDECHEMA [17]

Hexane–benzene −116.105 −126.003 −329.271 0.6167 5.15Hexane–sulfolane 561.401 681.179Benzene–hexane 2 157.958 165.755Benzene–sulfolane [7,8] 21.908 21.598Sulfolane–hexane 67.843 65.573Sulfolane–benzene 59.084 59.180

Hexane–toluene 167.205 180.432 −157.126 0.9302 n.a.Hexane–sulfolane 561.401 681.179Toluene–hexane 1 −137.162 −128.705Toluene–sulfolane [7] 47.058 50.487Sulfolane–hexane 67.843 65.573Sulfolane–toluene 79.687 79.309

Hexane–xylene 272.415 262.852 −138.991 0.9120 n.a.Hexane–sulfolane 561.401 681.179Xylene–hexane 1 −212.109 −199.216Xylene–sulfolane [7] 98.425 97.216Sulfolane–hexane 67.843 65.573Sulfolane–xylene 65.007 48.879

Overall objective function value= −625.388

Overall RMSD= 0.8321


ter than Chen’s data[7]. Also for DeFré’s data[8] RMSDvalue is compared with those reported in DECHEMA[17] for the specific UNIQUAC parameters. The RMSDvalue obtained in this work is better than those reportedin DECHEMA, which confirms the authenticity of the es-timated parameters using IVEM. Chen’s data[7] have notbeen processed for UNIQUAC parameters and hence theirRMSD values could not be compared with those of presentwork.

3.2. Simultaneous estimation of parameters involvingcommon pair

In simultaneous estimation of parameters the objectivefunction is calculated for each ternary system keeping theparameters between thecommon pair same in all the sys-tems. The modified objective function is taken as the sumof objective functions of individual system.

Using the above scheme the UNIQUAC binary interactionparameters have been estimated simultaneously taking thesystems that involve only onecommon pair. Table 6showsthe results of simultaneous parameter estimation for the sys-tem hexane–benzene–sulfolane, hexane–toluene–sulfolane,and hexane–xylene–sulfolane, at 298.15 K. Thecommonpair involved in this system is hexane–sulfolane whoseparameters are kept same in all the three systems. Ini-tial guesses of the parameters have been obtained fromrunning the property estimation program of Aspen Plussimulator, as the results with these initial guesses exhibitbetter RMSD values. The parameters for thecommon pairhexane–sulfolane and sulfolane–hexane are shown under-

lined. The number of data sets available for each systemwith their sources is indicated. The objective function val-ues and the corresponding RMSD values are also shown.The RMSD values calculated from using the available com-mon UNIQUAC parameters reported in DECHEMA[17]for these systems are also given in the table.

Table 7Simultaneous UNIQUAC binary interaction parameters at 298.15 K forsystems inTable 1

Binary pair i–j Binary interaction parameters (K)

aij aji

Pentane–benzene −124.530 154.243Pentane–toluene 140.138 −105.381Pentane–sulfolane 849.121 82.770Hexane–benzene −126.003 165.755Hexane–Toluene 180.432 −128.705Hexane–xylene 262.852 −199.216Hexane–sulfolane 681.179 65.573Heptane–benzene −125.230 166.246Heptane–toluene 181.432 −129.505Heptane–xylene 264.201 −200.150Heptane–sulfolane 683.994 65.776Octane–benzene −120.367 165.083Octane–toluene 181.706 −126.341Octane–xylene 257.508 −198.570Octane–sulfolane 747.083 67.323CycloHexane–benzene −131.926 176.370Cyclohexane–toluene 161.663 −152.302CycloHexane–sulfolane 554.680 67.652Benzene–sulfolane 21.598 59.180Toluene–sulfolane 50.487 79.309Xylene–sulfolane 97.845 48.879


Table 8UNIFAC group interaction parameters at 298.15 K for sulfolane with othermain groups

i–j Binary group interaction parameters,aij

CH3 CH2 ACHa ACCH3a Sulfolane

CH3 0 0 −114.80 −115.70 665.45CH2 0 0 −114.80 −115.70 665.45ACHa 156.50 156.50 0 167.00 36.30ACCH3

a 104.40 104.40 −146.80 0 236.58Sulfolane 52.39 52.39 54.33 9.93 0

a AC stands for aromatic carbon.

Similar approach has been adopted to estimate the UNI-QUAC binary interaction parameters for the other ternarysystems (System 4 to 13 inTable 1) at 298.15 K by changingonly the nonaromatic component. The binary parameters re-ported inTable 6have been supplied as initial guesses. Whileestimating the parameters for these systems, the parame-ters of the aromatic-solvent pairs that is benzene–sulfolane,toluene–sulfolane, and xylene–sulfolane have been keptfixed at those obtained from earlier regression and as shownin Table 6. The comprehensive results of such parameterestimations are given inTable 7. The parameters that arekept fixed at previously obtained values are shown in italics.

UNIFAC group interaction parameters have also beenestimated in our previous work[18] with the same ap-proach taking the three systems hexane–benzene–sulfolane,hexane–toluene–sulfolane, and hexane–xylene–sulfolane, at298.15 K simultaneously. Sulfolane is considered as a singlegroup and its interaction parameter with the groups CH3,CH2, ACH and ACCH3 have been estimated. Mutual inter-action parameters between the groups CH3, CH2, ACH andACCH3 are directly taken from those given by Magnussenet al.[19] and are kept fixed because these are universally ac-cepted parameters tested by several investigators. The results

Table 9Comparative RMSD values for the ternary systems

S. no. System name UNIFAC UNIQUAC

This work This work DECHEMA[17]

Estimation1 Hexane–benzene–sulfolane 0.6249 0.6167 5.152 Hexane–toluene–sulfolane 0.4852 0.9302 n.a.3 Hexane–xylene–sulfolane 0.9236 0.9120 n.a.

Prediction4 Heptane–benzene–sulfolane 0.7233 0.5378 3.855 Heptane–toluene–sulfolane 0.7810 0.5799 2.186 Heptane–xylene–sulfolane 0.9166 0.5749 n.a.7 Octane–benzene–sulfolane 1.0542 0.9062 n.a.8 Octane–toluene–sulfolane 0.8164 0.5339 n.a.9 Octane–xylene–sulfolane 1.1409 1.0370 n.a.10 Pentane–benzene–sulfolane 0.8100 0.7193 n.a.11 Pentane–toluene–sulfolane 0.9515 0.6985 n.a.12 Cyclohexane–benzene–sulfolane 0.8494 0.6955 2.9113 Cyclohexane–toluene–sulfolane 0.8338 0.7716 8.60


are presented inTable 8. The fixed parameters are shown initalics and the estimated parameters are shown bold faced.

The RMSD values obtained using the UNIQUAC binaryinteraction parameters inTable 7and UNIFAC binary groupinteraction parameters given inTable 8are shown inTable 9.The calculated RMSD values using available common UNI-QUAC parameters reported in DECHEMA[17] are alsogiven for comparison. It is to be noted that the RMSD valuesobtained using UNIQUAC parameters are better than thoseobtained using UNIFAC parameters for all the ternary sys-tems studied. Additionally the RMSD values for simultane-ous parameter estimation are at least five times better thanthose calculated from using common parameters reported inDECHEMA [17].

3.3. Validation of simultaneous estimation of parameters

The UNIQUAC and UNIFAC parameters estimated in theprevious section and reported inTables 7 and 8have beentested for their validity for the multi-component systemslisted inTable 2. Table 10shows the experimental and pre-dicted equilibrium composition for the quaternary systemhexane–benzene–xylene–sulfolane at 298.15 K using the ex-perimental LLE data reported by Chen et al.[7]. Interactionparameters between the components of same homologousseries (e.g. benzene–xylene) are taken as zero as suggestedby Salem et al.[20]. Prediction of Chen et al.[7] usingtheir NRTL parameters are also shown. The correspondingRMSD values are also given in the table. The UNIFAC pa-rameters show a better agreement between the experimentaland predicted compositions than those for UNIQUAC andNRTL parameters as evident from their respective RMSDvalues.

LLE for the other multi-component systems listed inTable 2have been predicted similarly. The RMSD valuesusing UNIQUAC and UNIFAC parameters as well as those


Table 10Comparison of experimental and predicted LLE using estimated binary interaction parameters for the system hexane (1), benzene (2), xylene (3), Sulfolane(4) at 298.15 K

Tie line Raffinate phase Extract Phase

x1 x2 x3 x4 x1 x2 x3 x4

1 Experimental 0.857 0.076 0.051 0.017 0.016 0.052 0.010 0.921UNIQUAC 0.863 0.081 0.054 0.002 0.016 0.047 0.008 0.929UNIFAC [18] 0.869 0.079 0.049 0.002 0.020 0.049 0.012 0.919NRTL [7] 0.876 0.074 0.049 0.001 0.014 0.054 0.013 0.919





RMSD using UNIQUAC parameters= 0.6633 [This work]

RMSD using UNIFAC parameters= 0.4156 Ref.[18]

RMSD using NRTL parameters= 0.6900 Ref.[7]

reported by Chen et al.[7,15] are given inTable 11. It isseen that RMSD values for UNIFAC parameters are betterin most of the cases. Further, it is even better for the quinarysystems than those for quaternary systems. Thus it can besaid that UNIFAC parameters are more suitable for predic-tion of multi-component LLE as the number of componentsincrease.

3.4. Effect of temperature on UNIQUAC binary interactionparameters

Temperature dependence of UNIQUAC binary interac-tion parameters have been investigated for the systems,

Table 11Root mean square deviation (RMSD) between experimental and predicted LLE for quaternary and quinary systems at 298.15 K

S. no. System name UNIQUAC (this work) UNIFAC[18] NRTL [7,15]

1 Hexane–benzene–xylene–sulfolane 0.6633 0.4156 0.69002 Hexane–octane–benzene–sulfolane 0.8806 1.0566 0.99003 Octane–toluene–xylene–sulfolane 0.8332 0.6200 0.66004 Hexane–heptane–toluene–sulfolane 0.5933 0.4566 0.48005 Heptane–octane–xylene–sulfolane 0.5506 0.5644 0.69006 Heptane–benzene–toluene–sulfolane 0.9412 0.3541 0.59007 Hexane–octane–benzene–toluene–sulfolane 0.6416 0.3700 0.42008 Hexane–heptane–toluene–xylene–sulfolane 0.8091 0.6302 0.86009 Heptane–octane–benzene–xylene–sulfolane 0.9933 0.5211 0.9800

given in Table 1for which LLE data are available at morethan one temperature. The results are shown inTables12–16. To establish the temperature effect the binary inter-action parameters for the aromatic–sulfolane pairs (such asbenzene–sulfolane, etc.) which are involved in all the sys-tems are plotted against the temperature and are shown inFig. 1. A best-fit straight line is also drawn along with theestimated points. For other pairs the goodness of linear fitcan also be gauged from the coefficient of correlation whichlies in the range 0.6–0.98. The values of the coefficientof correlation,r, for the different pairs are also reportedin the respective tables. This establishes a linear depen-dence of binary interaction parameters on temperature,


Table 12UNIQUAC binary interaction parameters at different temperature for Hexane–benzene–sulfolane

Binary pair i–j Temperature (K) r

298.15 323.15 348.15 373.15

Hexane–benzene −126.003 −128.299 −139.180 −143.562 0.9705Hexane–sulfolane 681.179 570.130 565.053 447.108 0.9551Benzene–hexane 165.755 164.399 147.655 162.628 0.6015Benzene–sulfolane 21.598 22.580 23.626 24.275 0.8137Sulfolane–hexane 65.573 65.560 64.276 64.843 0.7167Sulfolane–benzene 59.180 65.100 67.873 68.527 0.9435

RMSD 0.6167 0.3602 0.8158 0.3325

Table 13UNIQUAC binary interaction parameters at different temperatures for Pentane–benzene/toluene–sulfolane


290.15 298.15 323.15

Pentane–benzene −125.791 −124.530 −127.329 0.7642Pentane–sulfolane 852.671 849.121 838.204 1.0000Benzene–pentane 157.850 154.243 154.910 0.6029Benzene–sulfolane 21.844 21.598 22.580 0.8137Sulfolane–pentane 80.249 82.770 81.722 0.6255Sulfolane–benzene 60.048 59.180 65.10 0.9435Pentane–toluene 150.199 140.138 147.187 0.6069Toluene–pentane −104.923 −105.381 −105.349 0.6448Toluene–sulfolane 45.811 50.487 52.018 0.6384Sulfolane–toluene 77.576 79.309 83.389 0.8327

RMSD 0.7358 0.7090 0.6042

Table 14UNIQUAC binary interaction parameters at different temperatures for heptane–toluene/xylene–sulfolane


290.15 298.15 323.15 348.15 373.15

Heptane–toluene – 181.432 178.809 173.809 177.601 0.6719Heptane–sulfolane 734.982 683.994 677.464 681.344 701.836 0.6266Toluene–heptane – −129.505 −130.562 −135.701 −135.836 0.9329Toluene–sulfolane 45.811 50.487 52.018 52.076 52.456 0.6384Sulfolane–heptane 63.961 65.776 65.260 64.483 64.122 0.6474Sulfolane–toluene 77.576 79.309 83.389 84.880 85.295 0.8327Heptane–xylene 272.322 264.201 273.643 – – 0.6065Xylene–heptane −177.500 −200.150 −194.354 – – 0.6875Xylene–sulfolane 99.815 97.845 96.625 – – 0.7819Sulfolane–xylene 46.059 48.879 51.467 – – 0.9072

RMSD 0.8562 0.5799 0.7813 0.8472 0.8191

Table 15UNIQUAC binary interaction parameters at different temperatures for Octane–benzene/toluene/xylene–sulfolane


298.15 308.15 318.15 343.35 372.35 402.35

Octane–benzene −120.367 −131.472 −144.329 −145.753 −149.229 −160.722 0.9094Octane-Sulfolane 747.083 777.310 747.070 742.058 701.039 646.127 0.9275Benzene–octane 165.114 165.491 163.086 161.158 158.327 150.997 0.9713Benzene–sulfolane 21.598 23.161 23.511 23.802 24.828 23.847 0.8137Sulfolane–octane 67.323 77.160 77.518 79.949 79.961 79.813 0.6777Sulfolane–benzene 59.180 62.660 64.613 67.210 66.985 72.028 0.9435Octane–toluene 181.706 182.684 156.195 154.468 155.577 154.141 0.7352Toluene–octane −126.341 −130.990 −141.442 −136.695 −139.776 −141.355 0.7214Toluene–sulfolane 50.487 49.116 49.416 51.418 51.069 51.157 0.6384Sulfolane–toluene 79.309 82.012 84.005 84.701 85.115 85.426 0.8327Octane–xylene 257.508 279.014 269.609 239.457 225.751 206.011 0.9320Xylene–octane −198.570 −171.034 −156.062 −164.696 −168.305 −188.333 0.6421Xylene–sulfolane 97.845 97.501 95.823 98.816 101.192 106.052 0.7819Sulfolane–xylene 48.879 49.631 47.944 50.780 52.006 55.393 0.9072

RMSD 0.9062 0.6655 0.9430 0.7553 0.9383 0.6190


Table 16UNIQUAC binary interaction parameters at different temperature for CycloHexane–Benzene–sulfolane

Binary Pair i–j Temperature (K) r

298.15 323.15 348.15 373.15

CycloHexane–benzene −131.926 −143.454 −150.836 −168.332 0.9863CycloHexane–sulfolane 554.680 456.733 405.443 390.101 0.9469Benzene–cyclohexane 176.370 185.511 198.411 201.515 0.9773Benzene–sulfolane 21.598 22.580 23.626 24.275 0.8137Sulfolane–cyclohexane 67.632 72.469 73.098 70.081 0.6133Sulfolane–benzene 59.180 65.100 67.873 68.527 0.9435

RMSD 0.6955 0.8680 0.9291 0.6376

Table 17Coefficients of the linear temperature dependent UNIQUAC binary interaction parameters

I j a0ij a1

ij a0ji a1

ji

Pentane Benzene −107.2440 −0.0624 174.7540 −0.0615Pentane Toluene 146.8190 −0.0021 −102.5710 −0.0095Pentane Sulfolane 982.1280 −0.4388 74.4837 0.0239Hexane Benzene −49.0543 −0.2547 158.7020 −0.0990Hexane Sulfolane 1519.4000 −2.8345 69.9034 −0.0129Heptane Toluene 200.5190 −0.0661 −100.7270 −0.0966Heptane Xylene 233.8820 0.1212 −89.6206 −0.3324Heptane Sulfolane 770.0360 −0.2219 67.4096 −0.0018Octane Benzene −33.7946 −0.3184 205.6910 −0.1307Octane Toluene −251.4260 −0.2551 −98.7479 −0.1105Octane Xylene 464.4700 −0.6382 −169.3070 −0.0165Octane Sulfolane 1061.4800 −1.0674 49.1646 0.0820Cyclohexane Benzene 7.9271 −0.4686 72.0021 0.3393Cyclohexane Sulfolane 1185.9800 −2.1830 60.2334 0.0320Benzene Sulfolane 15.6213 −0.0230 31.0430 0.1022Toluene Sulfolane 38.9405 0.0345 62.3736 0.0621Xylene Sulfolane 70.3958 0.0660 28.1608 0.0665

hence

aij = a0ij + a1

ijT (4)

whereT is in Kelvin.The coefficients of theEq. (4), a0

ij anda1ij, have been esti-

mated using simultaneous parameter estimation scheme. All

Temperature, K

280 300 320 340 360 380 400 420

Inte

ract

ion

para

met

ers,

K

0

20

40

60

80

100

120

140Benzene-Sulfolane Sulfolane-BenzeneToluene-Sulfolane Sulfolane-TolueneXylene-Sulfolane Sulfolane-Xylene

Fig. 1. UNIQUAC binary interaction parameters for aromatic–sulfolanepairs.

systems at all available temperatures have been taken simul-taneously, leading to the estimation of a total of sixty-eightcoefficients (four coefficientsa0

ij, a1ij, a0

ij, a0ji, anda1

ij corre-sponding to each seventeeni-j pairs). Initial guess for thesecoefficients are obtained by fitting a straight line through thepoints by linear regression. The estimated parameter valuesare given inTable 17. The overall RMSD value for each sys-tem is given inTable 18. The RMSD values are in the rangeof 0.6–0.95, which can be considered satisfactory. Addition-ally, the parameters obtained are applicable over a widerrange of temperatures and systems.

Table 18Overall RMSD values for the ternary systems for estimation of coefficientsin temperature dependent equation

S. no. System name RMSD

1 Pentane–benzene–sulfolane 0.76982 Pentane–toluene–sulfolane 0.77563 Hexane–benzene–sulfolane 0.74634 Heptane–toluene–sulfolane 0.87175 Heptane–xylene–sulfolane 0.91886 CycloHexane–benzene–sulfolane 0.79807 Octane-benzene–sulfolane 0.83248 Octane–toluene–sulfolane 0.75039 Octane-xylene-Sulfolane 0.6761


4. Conclusions

An Inside variance estimation method based on maxi-mum likelihood function has been used to estimate the bi-nary interaction parameters using ternary systems. Resultsof separate estimation show that the binary interaction pa-rameters for the same pair are different for different systems.To overcome this problem, the objective function has beenmodified to estimate the binary interaction parameters us-ing three systems withcommon pairs simultaneously. Theparameters thus obtained have been found applicable forthe other ternary systems. Results of simultaneous param-eter estimation have been used successfully to predict themulti-component (quaternary and quinary) LLE. The pre-dicted LLE have been found in good agreement with thereported experimental LLE. Both UNIQUAC and UNIFACmodels have been used. The UNIQUAC model gives betterprediction for ternary systems whereas UNIFAC is foundto be more suitable for multi-component systems. Temper-ature dependence of UNIQUAC binary interaction parame-ters has been investigated and a linear dependence has beenobserved. Coefficients in the linear model have been ob-tained by linear regression, which are further modified usingsimultaneous estimation scheme taking all the data sets forall systems at different temperature simultaneously.

List of symbolsa activity, binary interaction parametersc total number of componentse vector of errorsL likelihood functionm number of tie lines or experimental datan number of measured variablesr coefficient of correlation for linear regression

reported inTables 12–16V variance-covariance matrixx experimental mole fractionx̂ predicted mole fraction

Greek lettersθ vector of parametersν variance

Subscriptsi component, measured variablej componentk tie line

Superscriptsj phaseI, II coexisting liquid phases

Acknowledgements

Financial support from BPCL project entitled “extractionof aromatics from petroleum naphtha” is gratefully acknowl-edged.

References

[1] M. Mukhopadhyaya, A.S. Pathak, Ind. Eng. Chem. Process Des.Dev. 25 (1986) 733–736.

[2] J.M. Sorensen, W. Arlt, Liquid–liquid equilibrium data collection,Ternary Systems, DECHEMA, Chemistry Data Series V., Part 2,Frankfurt am Main, 1980.

[3] J.M. Sorensen, W. Arlt, Liquid–liquid equilibrium data collection,Binary Systems, DECHEMA, Chemistry Data Series V., Part 1,Frankfurt am Main, 1979.

[4] V.R. Vasquez, W.B. Whitting, Fluid Phase Equilibria 170 (2000)235–253.

[5] W.R. Esposito, C.A. Floudas, Ind. Eng. Chem. Res. 37 (1998) 1841–1858.

[6] T.F. Anderson, D.S. Abrams, E.A. Grens, AICHEJ 24 (1978) 20–29.[7] J. Chen, L. Duan, J. Mi, W. Fei, Z. Li, Fluid Phase Equilibria 173

(2000) 109–119.[8] R.M. DeFré, L.A. Verhoeye, J. Appl. Chem. Biotechnol. 26 (1976)

469–487.[9] B.S. Rawat, I.B. Gulati, K.L. Malik, J. Appl. Chem. Biotechnol. 26

(1976) 247–252.[10] J. Chen, Z. Li, L. Duan, J. Chem. Eng. Data 45 (2000) 689–692.[11] G.W. Cassel, M.M. Hasan, A.L. Hines, J. Chem. Eng. Data 34 (1989)

434–438.[12] S. Lee, H. Kim, J. Chem. Eng. Data 40 (1995) 499–503.[13] S. Lee, H. Kim, J. Chem. Eng. Data 43 (1998) 358–361.[14] G.W. Cassel, N. Dural, A.L. Hines, Ind. Eng. Chem. Res. 28 (1989)

1369–1374.[15] J. Chen, J. Mi, W. Fei, Z. Li, J. Chem. Eng. Data 46 (2001) 169–171.[16] G. Varhegyi, C.H. Eon, Ind. Eng. Chem. Fundam. 28 (1989) 182–

185.[17] J.M. Sorensen, W. Arlt, Liquid–liquid equilibrium data collection,

Ternary and Quaternary Systems, DECHEMA, Chemistry Data SeriesV., Part 3, Frankfurt am Main, 1980.

[18] R.S. Tanwar, Computation of LLE and evaluation of solvents foraromatic extraction, M.Tech. thesis, Indian Institute of TechnologyKanpur, 2001.

[19] T. Magnussen, P. Rasmussen, A. Fredenslund, Ind. Eng. Chem.Process Des. Dev. 20 (1981) 331–339.

[20] A.B.S.H. Salem, E.Z. Hamad, M.A. Al-Naafa, Ind. Eng. Chem. Res.33 (1994) 689–692.

Documents

SA AHMAD FPE 220 (2004) 189-198