Experimental data, correlation and prediction of isobaric VLE for the ternary mixture (2-butanol + n-hexane + 1-chlorobutane) at 101.3 kPa

Fluid Phase Equilibria 211 (2003) 179–188

Experimental data, correlation and prediction of isobaric VLE forthe ternary mixture (2-butanol+ n-hexane+ 1-chlorobutane)

at 101.3 kPa

Magdalena Domıngueza, Ana M. Mainarb, Juan Pardoc,Jesús Santaféb, José S. Urietab,∗

a Departamento de Qu´ımica Orgánica-Qu´ımica Fısica, Área de Qu´ımica Fısica, Universidad de Zaragoza,EUITIZ Marıa de Luna 3, 50018 Zaragoza, Spain

b Facultad de Ciencias, Sección de Qu´ımicas, Departamento de Qu´ımica Orgánica-Qu´ımica Fısica,Ciudad Universitaria, Plaza San Francisco s/n, 50009 Zaragoza, Spain

c Departamento de Qu´ımica Orgánica-Qu´ımica Fısica, Área de Qu´ımica Fısica,Universidad de Zaragoza, CPS Mar´ıa de Luna 3, 50018 Zaragoza, Spain

Received 4 October 2002; received in revised form 14 April 2003; accepted 15 April 2003

Abstract

Isobaric vapour–liquid equilibrium (VLE) has been experimentally studied for the ternary mixture 2-butanol(1) + n-hexane (2)+ 1-chlorobutane (3), at the pressure of 101.3 kPa. The activity coefficients were found tobe thermodynamically consistent and they were satisfactorily correlated with the Wilson, NRTL and UNIQUACequations. They have been also compared with the results obtained from the application of the ASOG and themodified UNIFAC group contribution methods. The boiling points of the solutions were correlated with compositionsby using the Wisniak–Tamir equations. The results obtained indicate that the ternary system deviates positively overthe whole compositions range. Azeotropic behaviour was not found for the ternary mixture.© 2003 Elsevier B.V. All rights reserved.

Keywords:Isobaric VLE; 2-Butanol;n-Hexane; 1-Chlorobutane; Ternary mixtures

1. Introduction

Vapour–liquid equilibrium (VLE) data are indispensable in the design of separation processes suchas distillation. These data can be obtained experimentally or by using generalized methods that allowthe calculation of the properties of the mixtures. The very ground of these generalized methods liesin the availability of good VLE data. For binary systems there is a huge amount of information and

∗ Corresponding author. Tel.:+34-976-76-1298; fax:+34-976-76-1202.E-mail address:[email protected] (J.S. Urieta).

0378-3812/03/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0378-3812(03)00182-1

180 M. Domınguez et al. / Fluid Phase Equilibria 211 (2003) 179–188

the performance of some of the methods is really excellent. However, experimental measurements ofvapour–liquid equilibria for ternary or higher mixtures are quite scarce because of the effort necessary toobtain a complete description of the system. Nevertheless, these measurements are fundamental for bothto test the existing generalized methods and to improve them.

This paper is a continuation of our work on the determination of isobaric VLE data of binary andternary mixtures[1–4]. We present here experimental data of isobaric vapour–liquid equilibrium for theternary mixture containing 2-butanol,n-hexane and 1-chlorobutane at a pressure of 101.3 kPa. In previousworks, we presented results on densities and speeds of sound[5], and viscosities[6], for the same ternarymixture and the related binary systems. No values of isobaric VLE are available for this ternary systemin the available literature, but several references have been found for isothermal and isobaric VLE of thebinary systems[7–10].

The experimental results are compared with those correlated and predicted with the equations of Wilson[11], NRTL [12], and UNIQUAC[13] and with those predicted by the ASOG[14] and modified UNIFAC[15] group contribution methods.

2. Experimental

2-Butanol (>99.0 mol%),n-hexane (>99.5 mol%) and 1-chlorobutane (>99 mol%) were provided byAldrich. The measured physical properties of the pure compounds (densities, refractive indices and normalboiling points) are presented inTable 1along with the corresponding ones found in literature. 2-Butanolwas dried over activated molecular sieve type 0.3 nm from Merck. Liquids were used without furtherpurification.

The vapour–liquid equilibrium experiments in this study were performed using an all-glass, dynamicrecirculating still, equipped with a Cottrell pump. It is a commercial unit (Labodest model) built byFischer and capable of handling pressures from 0.25 to 400 kPa and temperatures up to 523.15 K.

Temperatures were measured using a thermometer (model F25) from Automatic System Laboratories,with an uncertainty of±0.01 K. Pressures were measured with a pressure transducer Druck PDCR 110/Wand pressure indicator PDI201 with an uncertainty of±0.1 kPa.

The still had been previously tested with the system benzene+ cyclohexane at several pressures[19].For each experiment, the experimental pressure was fixed and the liquid mixture was heated and stirred

properly. The system was kept at the boiling point for 15 min in order to ensure that the equilibrium stateis reached. A set of electromagnetic valves permitted extraction of samples (approximately 2 ml) of liquidand condensed vapour phases. The composition of the liquid and vapour samples were determined by

Table 1Physical properties: densities (ρ), refractive indices (nD), and normal boiling points (Tb) of the pure components

Component ρ (298.15 K) (kg m−3) nD (298.15 K) Tb (101.3 kPa) (K)

Experimental Literature[16] Experimental Literature Experimental Literature[16]

2-Butanol 802.39 802.41 1.39488 1.3950[17] 372.75 372.66n-Hexane 654.93 654.84 1.37544a 1.3723[18]a 341.98 341.891-Chlorobutane 880.85 880.95 1.40015 1.4001[17] 351.71 351.58

a At 293.15 K.

M. Domınguez et al. / Fluid Phase Equilibria 211 (2003) 179–188 181

measuring their densities and speeds of sound at 298.15 K with an Anton Paar DMA-48 vibrating tubedensimeter and sound analyser. The composition dependence of density and speed of sound has beenpreviously reported[5]. The densimeter and sound analyser were calibrated at atmospheric pressure withdoubly distilled water and dry air. The maximum estimated uncertainties in the determination of the liquidand vapour phase mole fractions are±0.0002 and±0.002, respectively.

3. Experimental results and discussion

The isobaric vapour–liquid equilibrium data (T, x1, y1) and the activity coefficients for the binary mix-tures 2-butanol (1)+ n-hexane (2), 2-butanol (1)+ 1-chlorobutane (3) andn-hexane (2)+ 1-chlorobutane(3) are given in previous works[3,4,10]. For the ternary system 2-butanol (1)+ n-hexane (2)+ 1-chloro-butane (3) the experimental vapour–liquid equilibrium data (T, x1, x2, y1, y2) along with activity coeffi-cients at 101.3 kPa are shown inTable 2.

The activity coefficients,γi, were calculated taking into account the non-ideality of the vapour phase,through the equation:

γi = yiP

xiP0i

exp

((Bii − V 0

i )(P − P0i )

RT+ P

2RT

n∑1

n∑1

yjyk(2δji − δjk)

)(1)

where

δji = 2Bji − Bjj − Bii (2)

andxi andyi are the mole fractions of componenti in the liquid phase and in the vapour phase, respectively,P the total pressure,P0

i the vapour pressure of purei component that we have calculated from the Antoineequation taking the coefficientsA, B, andC from Riddick et al.[16], Bii the second virial coefficients ofcomponenti obtained from the expressions included in the TRC tables[17], whileBij are the cross-secondvirial coefficients estimated by means of the Amdur–Mason equation[20]. The molar volumes of thesaturated liquids,V 0

i , were determined using the Yen and Woods method[21].The boiling temperatures of the ternary system were correlated with the Tamir and Wisniak’s equation

[22]

T =3∑

i=1

xiT0i +

2∑i=1

3∑j>i

{xixj

∑k=0

Ck(xi − xj)k

}+ x1x2x3 {A + B(x1 − x2) + C(x1 − x3)} (3)

whereT 0i is the boiling temperature of the pure componenti in Kelvin, andm is the number of terms in

the series expansion of (xi −xj). Ck are the binary constants, andA, B, andC are ternary constants. Theseconstants along with the standard deviations and root mean square deviations are reported inTable 3.Fig. 1shows the three-dimensional surfaces of the vapour and liquid phases for the ternary system correlatedwith the Wilson model. The equilibrium composition diagram of the ternary system is shown inFig. 2.The isolines for the boiling temperature of the liquid phase calculated fromEq. (3)using the parametersreported inTable 3are shown inFig. 3.

In order to rigorously verify the non-existence of a ternary azeotrope in the mixture such as suggestFigs. 1 and 2, we have used the Wang et al. method[23] that employs a dual iterative technique.


Table 2Experimental vapour–liquid equilibrium data for the ternary mixture 2-butanol (1)+ n-hexane (2)+ 1-chlorobutane (3) at101.3 kPa

T (K) x1 x2 y1 y2 γ1 γ2 γ3

348.73 0.107 0.075 0.096 0.142 2.293 1.552 1.015348.62 0.137 0.089 0.107 0.148 2.005 1.367 1.052349.15 0.218 0.077 0.162 0.138 1.865 1.450 1.068350.31 0.367 0.059 0.215 0.128 1.399 1.697 1.189352.01 0.514 0.042 0.279 0.112 1.206 1.989 1.354354.81 0.652 0.028 0.361 0.096 1.095 2.367 1.544359.50 0.796 0.015 0.498 0.072 1.025 2.925 1.810364.50 0.896 0.007 0.669 0.046 1.008 3.523 2.037369.60 0.965 0.002 0.869 0.016 1.006 3.786 2.110345.74 0.174 0.224 0.131 0.335 2.192 1.334 1.059345.45 0.125 0.244 0.102 0.344 2.406 1.269 1.058346.34 0.269 0.201 0.173 0.326 1.823 1.421 1.108347.65 0.424 0.155 0.221 0.309 1.395 1.682 1.257349.65 0.548 0.118 0.271 0.285 1.214 1.924 1.409352.39 0.655 0.089 0.337 0.259 1.125 2.148 1.541355.89 0.765 0.057 0.426 0.218 1.054 2.566 1.764360.29 0.854 0.033 0.551 0.163 1.024 2.951 1.970364.18 0.910 0.020 0.675 0.116 1.013 3.137 2.088368.31 0.959 0.008 0.830 0.058 1.013 3.541 2.125343.45 0.160 0.432 0.121 0.521 2.438 1.150 1.125343.17 0.112 0.443 0.091 0.531 2.653 1.153 1.099343.28 0.209 0.387 0.139 0.507 2.160 1.256 1.130344.40 0.346 0.316 0.194 0.483 1.732 1.417 1.190346.13 0.488 0.243 0.230 0.463 1.348 1.680 1.346348.40 0.613 0.182 0.285 0.434 1.205 1.969 1.508352.72 0.747 0.114 0.373 0.375 1.077 2.408 1.753357.51 0.845 0.069 0.490 0.304 1.028 2.833 2.017363.32 0.919 0.034 0.667 0.192 1.025 3.124 2.148368.25 0.967 0.013 0.846 0.087 1.026 3.275 2.101342.07 0.188 0.600 0.133 0.684 2.427 1.133 1.156342.15 0.078 0.640 0.078 0.682 3.419 1.057 1.137341.80 0.183 0.568 0.134 0.652 2.543 1.150 1.161342.48 0.281 0.499 0.175 0.630 2.097 1.239 1.172344.12 0.456 0.372 0.222 0.602 1.522 1.513 1.285346.65 0.603 0.269 0.272 0.567 1.261 1.831 1.460351.00 0.741 0.173 0.352 0.505 1.101 2.243 1.692357.73 0.864 0.086 0.495 0.387 1.007 2.879 1.974362.40 0.927 0.045 0.654 0.263 1.032 3.312 2.177367.85 0.965 0.020 0.805 0.144 0.993 3.559 2.155341.11 0.164 0.754 0.133 0.804 2.907 1.091 1.061340.72 0.105 0.808 0.107 0.816 3.719 1.045 1.238341.07 0.248 0.691 0.156 0.792 2.259 1.174 1.179342.48 0.414 0.532 0.205 0.755 1.667 1.394 0.980344.57 0.567 0.390 0.233 0.721 1.259 1.708 1.325348.10 0.712 0.258 0.302 0.664 1.113 2.147 1.259354.45 0.845 0.138 0.441 0.527 1.048 2.671 1.731363.67 0.943 0.052 0.663 0.316 0.979 3.336 2.979


Table 3Coefficients in the correlation of boiling points with liquid phase composition, standard deviation (σ), and root mean squaredeviation (RMSD) in temperature

Binary system C0 C1 C2 C3 C4 σa RMSDb

2-Butanol (1)+ n-hexane (2)[4] −56.03 −34.84 −25.92 −13.62 −30.38 0.34 0.07242-Butanol (1)+ 1-chlorobutane (2)[18] −36.51 −13.61 −13.91 −1.53 −13.04 0.08 0.0181n-Hexane (1)+ 1-chlorobutane (2)[3] −11.83 2.67 −1.52 1.46 0.03 0.0062

Ternary system A B C σ RMSD

2-Butanol (1)+ n-hexane (2)+ 1-chlorobutane (3) 8.70 33.20 0.28 0.0395

a σ =√ ∑

(Texp tl − Tcalc)2

(m − number of parameters).

b RMSD = 1

m

√√√√( m∑i

(Texp tl − Tcalc)2

).

The thermodynamic consistency of the experimental ternary data has been checked by means of the pointto point test of Van Ness et al.[24] modified by Fredenslund et al.[25] and extended to multicomponentmixtures, employing the following equation proposed by Prausnitz et al.[26] in order to determine theactivity coefficient,γi, of the componenti:

ln γi = Q +(∂Q

∂xi

)T,P,xj �=i

−k−1∑j=1

xj

(∂Q

∂xj

)T,P,xi �=j

(4)

Fig. 1. Three-dimensional surfaces of the vapour and liquid phases obtained at 101.3 kPa according to the Wilson model.


Fig. 2. Tie lines: (�) liquid-phase mole fraction; (�) vapour-phase mole fraction.

Fig. 3. Boiling isotherms in liquid phase: (—) calculated from Tamir–WisniakEq. (3)and the parameters reported inTable 3;(– – –) predicted by UNIFAC model; (- - -) predicted by ASOG model.


wherek is the number of components in the mixture,xi is the mole fraction of componenti, andQ is thereduced excess Gibbs energy,Q = GE/RT. We used an equation of the Redlich–Kister type extendedto a multicomponent mixture in order to establish the relationship betweenQ and the liquid phasecomposition

Q =n∑

i=1

n∑j=i+1

xixj

p∑p=0

Ap(xi − xj)p + x1x2(1 − x1 − x2)(B1 + B2x1 + B3x2) (5)

According to this consistency test, the experimental data are considered thermodynamically consistentwhen the average deviation for the vapour phase composition (�y) is less than 0.01. The values of�ycalculated for our system satisfy that condition (�P = 2.1 kPa;�y = 0.007;�y1 = 0.006;�y2 = 0.009;�y3 = 0.006).

The activity coefficients,γi, have been fitted to Wilson, NRTL, and UNIQUAC equations[27]. Theadjustable parameters for these equations were obtained through a least squares method using the simplexmethod[28] to minimize an objective function (OF) which is expressed in terms of experimental andcalculatedγi values

OF =m∑i=1

n∑

j=1

(γ

exp tlj − γcalc

j

γexp tlj

)2

i

(6)

wherem is the number of experimental data andn the number of components in the mixture.The study of the ternary system has been carried out in two different ways. First, we fitted the experi-

mental activity coefficients with Wilson, NRTL and UNIQUAC equations extended to multicomponentmixtures[27] considering the correlation parameters as “ternary parameters” to minimize the objectivefunction (6). These parameters along with the deviations�T and�y are given inTable 4marked with theletter (A). Secondly, the VLE values for the ternary mixture were predicted by the same equations but with

Table 4Correlation parameters for the Ternary System 2-Butanol (1)+ n-Hexane (2)+ 1-Chlorobutane (3). Average deviation inT(�T) and average deviation iny (�y) at 101.3 kPa: (A) correlated; (B) predicted from binary coefficients

Equation i, j Aij Aji �T (K) �y �y1 �y2 �y3

Wilsona 1, 2 5337.08 761.201, 3 2771.40 588.74 (A) 0.40 0.005 0.005 0.006 0.0052, 3 3794.18 −1195.73 (B) 0.36 0.008 0.008 0.009 0.006

NRTLb 1, 2 1652.86 3342.641, 3 488.82 2729.60 (A) 0.36 0.005 0.005 0.006 0.0052, 3 679.47 284.18 (B) 0.37 0.007 0.008 0.009 0.006

UNIQUACc 1, 2 −546.09 2325.611, 3 −486.39 1671.01 (A) 0.34 0.006 0.006 0.007 0.0052, 3 −1130.04 1820.40 (B) 0.42 0.008 0.008 0.009 0.006

a Aij = (λij − λii ) (J mol−1).b Aij = (gij − gjj ) (J mol−1); αij = αji = 0.30.c Aij = (uij − ujj ) (J mol−1).


Table 5Parameters from UNIFAC[14] and ASOG[15] methods used in the prediction of VLE

Main group Subgroup Rk Qk

UNIFACCH2 CH3 0.6325 1.0608

CH2 0.6325 0.7081CH 0.6325 0.3554

OH OH (secondary) 1.0630 0.8663CCl CH2Cl 0.9919 1.3654

Component Group νFHi νk,i

ASOG2-Butanol CH2 4.8 3.8

OH 1

n-Hexane CH2 6 6

1-Chlorobutane CH2 5 4Cl 1

the “binary parameters” obtained from the fitting of the respective binary mixtures. The deviations fromthese predictions are also listed inTable 4marked with the letter (B). The deviations achieved throughthe direct correlation of the experimental values and those corresponding to the predictions from binarycoefficients are not very different each other.

ASOG[14] and modified UNIFAC[15] group contribution methods have been also employed to predictthe vapour–liquid equilibrium of the ternary system under study. Parameters used are presented inTable 5.The average deviations of both the temperature (�T) and the composition of the vapour phase (�y) aregiven inTable 6. In this table, we can see that the UNIFAC model gives smaller deviations.Fig. 3shows thepredictions by the UNIFAC (– – –) and ASOG (- - -) models and they are compared with the experimentalvalues.

According to the obtained results in the present paper the ternary mixture 2-butanol (1)+ n-hexane(2) + 1-chlorobutane (3) deviates positively from ideality over whole composition range. The molecularinteractions that govern the thermodynamic behaviour have been described in previous papers[5,6]. Themost important effects in the mixing process are the breaking of the self-association in the alkanol anddipole–dipole interactions in chlorinated derivative, and the formation of crossed OH–Cl interactions inthe mixture.

Table 6ASOG and UNIFAC predictions, average deviation inT (�T) and average deviation iny (�y) for the ternary mixture 2-butanol(1) + n-hexane (2)+ 1-chlorobutane (3) at 101.3 kPa

Model �T (K) �y �y1 �y2 �y3

UNIFAC 0.52 0.009 0.011 0.010 0.006ASOG 0.82 0.010 0.014 0.009 0.008


List of symbolsA, B, C ternary constants inEq. (3)Bii second virial coefficient of componenti (m3 mol−1)Bij cross-second virial coefficient (m3 mol−1)Ck binary constants inEq. (3)m number of experimental datan number of components in the mixtureOF objective function inEq. (6)p0i vapour pressure of purei component (Pa)

P total pressure (Pa)Q reduced excess Gibbs energyQk molar surface area of groupk (UNIFAC model)R molar gas constant (8.31441 J K−1 mol−1)Rk van der Waals volume of groupk (UNIFAC model)RMSD root mean square deviationT temperature (K)T 0i boiling point of pure componenti (K)

V 0i molar volume of saturated liquid (m3 mol−1)

xi mole fraction in the liquid phaseyi mole fraction in the vapour phase

Greek lettersαi non-randomness parameter in the NRTL equationδij defined byEq. (2)� average deviationγi activity coefficient of componentiνk,i total number of atoms (other than hydrogen atoms) in groupk of moleculei (ASOG model)νFHi number of atoms (other than hidrogen atoms) in moleculei (ASOG model)

ρ density (kg m−3)σ standard deviation

Acknowledgements

M. Domınguez gratefully acknowledges support by Departamento de Educación y Cultura delGobierno de Navarra. The authors are grateful for financial assistance from Project number PCB-0694from Diputación General de Aragón.

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Documents

Experimental data, correlation and prediction of isobaric VLE for the ternary mixture (2-butanol + n-hexane + 1-chlorobutane) at 101.3 kPa