Ioa

BD

ARRAA

KIVoNH

1

aatsvbA([Asminotrat

0h

Fluid Phase Equilibria 352 (2013) 86– 92

Contents lists available at SciVerse ScienceDirect

Fluid Phase Equilibria

j our na l ho me pa ge: www.elsev ier .com/ locate / f lu id

sobaric vapor–liquid equilibrium for binary systemsf toluene + o-xylene, benzene + o-xylene, nonane + benzenend nonane + heptane at 101.3 kPa

hupender S. Gupta, Ming-Jer Lee ∗

epartment of Chemical Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 106-07, Taiwan

a r t i c l e i n f o

rticle history:eceived 2 January 2013eceived in revised form 11 April 2013ccepted 15 May 2013vailable online 29 May 2013

a b s t r a c t

Isobaric vapor–liquid equilibrium (VLE) data for the binary systems of toluene + o-xylene, benzene + o-xylene, nonane + benzene and nonane + heptane were measured at 101.3 kPa by using a modified Othmerstill. The thermodynamic consistency of these new VLE data was checked by using the point to pointtest of Van Ness. No azeotrope was found in these binary systems investigated. While nonane + benzenewere found to have large positive deviation, toluene + o-xylene, benzene + o-xylene, and nonane + heptane

eywords:sobaricLE-Xyleneonane

exhibited large negative deviation from ideal behavior. The binary interaction parameters of the Wilson,the NRTL, the UNIQUAC models and the SRK equation of state for these four binary systems were deter-mined through the VLE data reduction. These new VLE data were compared with the predicted valuesfrom the UNIFAC and the COSMO-RS (conductor-like screening model for realistic solvents) models aswell. Generally, reasonable agreement was found between the predicted results and the experimental

+ ben

ydrocarbons values, except for nonane

. Introduction

Hydrocarbons are the main components in crude oils. The sep-ration of paraffins and aromatics, such as benzene (B), toluene (T)nd xylenes (X), from petroleum fractions, is commonly encoun-ered in refinery processes. Since distillation is the most populareparation method in the chemical and petroleum industries,apor–liquid equilibrium (VLE) data of the related mixtures areasically important for development of the separation processes.lthough a plenty of VLE data of the mixtures containing paraffins

from C6 to C9) and aromatics (BTX) are available from literature1–14], the VLE data for some specific systems are still insufficient.s a part of our continued studies on the isobaric VLE data mea-urements for the mixtures containing C6–C9 and BTX [3,9], weeasured the isobaric VLE data for four binary systems, includ-

ng toluene + o-xylene, benzene + o-xylene, nonane + benzene, andonane + heptane, at 101.3 kPa in this work. According to the resultsf literature survey, no isobaric VLE data of these four binary sys-

ems at 101.3 kPa has been reported in literature. Chen et al. [8]eported the density and the isothermal VLE data (P-T-x at 333.15 Knd 353.15 K) for nonane + benzene and toluene + o-xylene, buthey did not measure the vapor compositions (y) and thus

∗ Corresponding author. Tel.: +886 2 2737 6626; fax: +886 2 2737 6644.E-mail addresses: mjlee@mail.ntust.edu.tw, mjl6626@gmail.com (M.-J. Lee).

378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.fluid.2013.05.016

zene system.© 2013 Elsevier B.V. All rights reserved.

thermodynamic consistency test cannot be made for those VLEdata. In the present study, P-T-x-y data were measured and sub-sequently checked with the thermodynamic consistency test byusing the point to point test method of Van Ness [15] modified byFredunsland et al. [16].

In VLE data reduction, vapor phase was considered as non-ideal.The two-term virial equation and the Hayden and O’Connell (HOC)model [17] were used to estimate the fugacity coefficient and thesecond virial coefficient for each component in the vapor phase,respectively, and the non-ideality of each liquid component wererepresented by the Wilson [18], the non-random two-liquid (NRTL)[19], and the universal quasi-chemical (UNIQUAC) [20] activitycoefficient models. These new VLE data were also correlated withthe Soave–Redlich–Kwong (SRK) equation of state [21]. In addition,the predicated results from both the UNIFAC [16] and the COSMO-RS [22] models were also compared with these new experimentalVLE data.

2. Experimental

2.1. Materials

All the chemicals used in this study are listed in Table 1, includ-ing the suppliers and the purity levels. The purity level of eachsubstance has been confirmed by gas chromatography (GC) anal-ysis. In addition, the density (�) and the normal boiling point

B.S. Gupta, M.-J. Lee / Fluid Phase Equilibria 352 (2013) 86– 92 87

Table 1Materials description, densities (�) at 298.2 K and the normal boiling points (Tb) of the pure components.a

Compound Source Mass fraction purity �/(g cm−3) Tb/K

This work Literature This work Literature

Nonane Aldrich, USA 0.9998 0.71407 0.71402 [23] 423.8 423.8 [24]Benzene R.D. Germany 0.9997 0.87366 0.87360 [25] 353.3 353.20 [26]Heptane Acros, USA 0.9998 0.67952 0.67950 [7] 371.4 371.55 [7]

00

(s±wt[N

2

r

Fcav

Toluene Aldrich, USA 0.9996o-Xylene Alfa Aesaer, USA 0.9995

a u(�) = 0.00005 g cm−3; u(T) = 0.1 K.

Tb) of each compound were measured with a vibrating-tube den-imeter (DMA 4500, Anton Paar, Austria) to an uncertainty of0.00005 g cm−3 and a modified Othmer VLE apparatus facilitatedith a thermocouple calibrated to an uncertainty of ±0.1 K, respec-

ively. The results are also compared with the literature values7,23–26] in Table 1, which shows that the agreement is excellent.o further purification has been made for the chemicals before use.

.2. Apparatus and procedure

The VLE measurements were conducted by using an Othmer-ecirculation still [27] with some modification as reported by

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

370

380

390

400

410

420

430

440

450

T/K

x1, y

1

(a) Toluene (1) + o-xylene (2)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

340

350

360

370

380

390

400

410

420

430

440

450

T/K

x1, y

1

(c) Nonane (1) + benze ne (2)

ig. 1. (a–d) (T, x1 or y1) plot for the investigated binary systems at 101.3 kPa: (�), exalculated liquid and vapor phase compositions from the Wilson model; (–), calculated lnd vapor phase compositions from the UNIQUAC model; (-·-), calculated liquid and vapapor phase compositions from the UNIFAC model; (-··-), predicted liquid and vapor phas

.86218 0.86219 [25] 383.4 383.75 [25]

.87566 0.87557 [7] 417.5 417.55 [7]

Johnson et al. [28]. The schematic diagram and the operating tech-nique are similar to those reported in literature [29,30]. In eachexperimental run, about 100 cm3 of freshly prepared mixture wasinjected in the still and then heat was provided gradually by meansof external heater. The pressure was maintained at 101.3 ± 0.2 kPaduring the course of measurement by a pressure adjustment sys-tem, which has been described in our previous articles [3,9]. This

pressure controlling system is composed of a graduated burrete,directly connected with an elevation-adjustable water reservoir.By adjusting the required water level diffrence between the bur-rete and the water resiorvoir, the pressure difference between localatmospheric pressure and 101.3 kPa was compensated during each

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

340

350

360

370

380

390

400

410

420

430

440

450T/

K

x1, y

1

(b) Benzene (1) + o-xylene (2)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

360

370

380

390

400

410

420

430

440

450

T/K

x1, y

1

(d) Nonane (1) + hepta ne (2)

perimental liquid phase and (o); experimental vapor phase compositions; (- - -),iquid and vapor phase compositions from the NRTL model; (–·–), calculated liquidor phase compositions from the SRK equation of state; (····), predicted liquid ande compositions from the COSMO-RS model.

8 Phase Equilibria 352 (2013) 86– 92

eaI

ttccecu

2

beSwgtGMtm

3

xagTfi

om[ibca00xrt

el

�

ı

wrsvcc

Table 2Experimental VLE data for toluene (1) + o-xylene (2), benzene (1) + o-xylene (2),nonane (1) + benzene (2) and nonane (1) + heptane (2) systems at 101.3 kPa.a

T/K x1 y1 �1 �2

Toluene (1) + o-xylene (2)383.4 1.000 1.000 1.000 –385.0 0.937 0.981 1.014 0.750385.4 0.920 0.976 1.016 0.737386.3 0.880 0.961 1.021 0.776388.1 0.796 0.930 1.041 0.776390.5 0.693 0.886 1.070 0.781391.4 0.662 0.871 1.075 0.781393.9 0.579 0.825 1.092 0.790396.3 0.500 0.765 1.103 0.833399.0 0.426 0.693 1.097 0.877401.3 0.367 0.626 1.087 0.908404.4 0.291 0.526 1.069 0.943407.0 0.230 0.436 1.054 0.962411.4 0.132 0.269 1.024 0.984413.2 0.094 0.196 1.006 0.989414.3 0.069 0.147 1.003 0.993417.5 0.000 0.000 – 1.000

Benzene (1) + o-xylene (2)353.3 1.000 1.000 1.000 –353.8 0.980 0.998 1.003 0.734354.6 0.948 0.995 1.009 0.684355.7 0.909 0.991 1.015 0.675356.3 0.887 0.989 1.020 0.650357.9 0.826 0.981 1.037 0.686359.8 0.768 0.973 1.048 0.682363.9 0.657 0.950 1.067 0.736368.7 0.543 0.921 1.099 0.737375.2 0.428 0.855 1.093 0.866383.6 0.318 0.758 1.060 0.924384.7 0.305 0.743 1.055 0.930387.5 0.273 0.703 1.044 0.942393.2 0.216 0.612 1.008 0.961401.4 0.139 0.451 0.965 0.978406.7 0.093 0.326 0.934 0.984410.8 0.057 0.214 0.921 0.989413.9 0.030 0.120 0.923 0.993417.5 0.000 0.000 – 1.000

Nonane (1) + benzene (2)353.3 0.000 0.000 – 1.000354.3 0.048 0.005 0.956 1.014354.8 0.061 0.006 0.884 1.012355.2 0.089 0.008 0.795 1.029356.2 0.130 0.013 0.851 1.041357.2 0.182 0.018 0.809 1.070358.2 0.231 0.023 0.783 1.100363.4 0.359 0.049 0.880 1.110367.3 0.455 0.073 0.895 1.144374.2 0.574 0.118 0.896 1.162374.9 0.586 0.123 0.893 1.168383.6 0.694 0.207 0.946 1.153391.4 0.773 0.302 0.966 1.140392.5 0.783 0.318 0.970 1.137402.9 0.869 0.490 0.988 1.123411.1 0.925 0.657 0.989 1.117423.8 1.000 1.000 1.000 –

Nonane (1) + heptane (2)371.4 0.000 0.000 – 1.000373.3 0.071 0.010 0.628 1.015375.7 0.163 0.027 0.680 1.037378.7 0.249 0.050 0.744 1.041382.3 0.367 0.084 0.753 1.084385.1 0.420 0.117 0.837 1.062390.3 0.534 0.176 0.840 1.084396.2 0.641 0.274 0.909 1.076401.6 0.722 0.375 0.943 1.056407.5 0.802 0.506 0.969 1.029409.6 0.830 0.560 0.978 1.020413.9 0.883 0.675 0.986 1.000

8 B.S. Gupta, M.-J. Lee / Fluid

xperimental run. The local atmospheric pressure was measured by Fortin mercury barometer (model 453, stability = ± 0.1 kPa, Princonstruments, USA).

Equilibrium state was assumed to be attained when tempera-ure in the still reached a constant for at least 2 h. This constantemperature was recorded. Then, the liquid samples and theondensed vapor samples were collected (about 1 cm3 each) foromposition analysis. At least 3 replicated samples were taken forach phase. Temperature in the still was measured with a pre-isely calibrated digital thermometer (TES 1310 type-K) with anncertainty of ±0.1 K.

.3. Analysis

The compositions of the collected samples were determinedy GC (model 8700, China Chromatography, Taiwan). This GC wasquipped with a TCD detector and a stainless-steel column (modelE-30, Supelcoport, 80/100 mess, 14′ × 1/8′′, 20%, USA). Helium gasith purity of 0.9995 in mass fraction was employed as a carrier

as. Prior to the composition analysis, the calibration curves forhese binary systems should be obtained. The standard samples forC calibration were prepared by using an electronic balance (R&Dodel GR-200, USA) with an uncertainty of ±0.1 mg. The uncer-

ainty of compositions determination is estimated as ±0.005 inole fraction.

. Results and discussion

The isobaric VLE data of toluene + o-xylene and benzene + o-ylene, nonane + benzene, and nonane + heptane, were measuredt 101.3 kPa. Experimental data (T, x, y) for all systems investi-ated along with estimated activity coefficient (� i) are listed inable 2. The graphical presentation of the VLE data can be seenrom Fig. 1(a–d). These graphs clearly reveal that all the systemsnvestigated have no azeotrope formation.

For the sake of reliability, the thermodynamic consistencyf the new VLE data were tested with the point to point testethod of van Ness et al. [15] modified by Fredunslund et al.

16] The mean absolute deviations between calculated and exper-mental vapor-phase composition and saturated pressure shoulde less than 0.01 and 1.33 kPa, respectively, for passing theonsistency test. From the consistency test, it is found that the devi-tions of vapor-phase composition are 0.0021, 0.0019, 0.0016, and.0015, and those of saturated pressure are 0.0079 kPa, 0.0054 kPa,.0050 kPa, and 0.0056 kPa for toluene + o-xylene, benzene + o-ylene, nonane + benzene, and nonane + heptane, respectively. Theesults indicate that all the new VLE data are passed the consistencyest.

The reported values of activity coefficients � i in Table 2 werestimated by considering vapor phase as non-ideal, from the fol-owing equations:

i = yiP

xiPsi

exp

[(Bii − VL

i

) (P − Ps

i

)+ (1 − yi)

2Pıij

RT

](1)

ij = 2Bij − Bii − Bjj (2)

here xi and yi are the mole fractions of liquid and vapor phase,

espectively. P and Ps

iare the total pressure and the vapor pres-

ure of pure components i, respectively. Bii, and Bjj are the secondirial coefficients of pure gases and Bij is the cross second virialoefficient. The liquid molar volume of pure component i, VL

i , wasalculated from the modified Racket equation (Yamada and Gunn

415.5 0.902 0.720 0.987 0.995420.0 0.957 0.867 0.997 0.984420.7 0.965 0.891 0.998 0.977423.8 1.000 1.000 1.000 –

a u(T) = 0.1 K; u(x1) = 0.005; u(y1) = 0.005; u(�1) = 0·005.

B.S. Gupta, M.-J. Lee / Fluid Phase Equilibria 352 (2013) 86– 92 89

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.5

1.0

1.5

γ 1,γ2

x1

(a) Toluene (1) + o-xylene (2)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.5

1.0

1.5

2.0

x1

(c) Non ane (1) + benze ne (2)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.5

1.0

1.5

x1

(d) Non ane (1) + hepta ne (2)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.5

1.0

1.5

x1

(b) Benze ne( 1) + o-xylen e (2)

γ 1,γ2

γ 1,γ2

γ 1,γ2

F kPa: (e ated at ····), pc

[t

l

wpawi

B

tct

fipoUo

ig. 2. (a–d) (�1, �2 versus x1) plot for the investigated binary systems at 101.3

xperimental activity coefficient of component 2 in the binary mixture; (- - -), calculhe NRTL model; (–·–), calculated activity coefficients from the UNIQUAC model; (oefficients from the UNIFAC model.

31]). The vapor pressure of pure component i was calculated fromhe extended Antoine equation:

n(Psi ) = A1 + B2

T + C3+ D4T + E5 ln T + F6TG7 (3)

here Psi

is in kPa and T in K. The coefficients A1 to G7 for each com-onent were taken from Aspen Plus physical property databanksnd reported in Table 3. The self and cross second virial coefficientsere calculated by using Hayden and O’Connell model [17], which

nvolves the following terms:

= Bfree−nonpolar + Bfree−polar + BmetasTable + Bbound + Bchem (4)

Since no association effect was expected in these binary sys-ems investigated, Bchem term was vanished in the virial coefficient

alculation. The physical properties of each component required inhe calculation of the second virial coefficients given in Table 4.

The experimental VLE data are correlated with the activity coef-cient model, the Wilson, the NRTL, or the UNIQUAC, for liquidhase and the two-term virial equation for vapor phase. The valuef ˛ij in the NRTL model was fixed to 0.3 and the parameters of theNIQUAC model (r and q) are also given in Table 4. The followingbjective function (�), based on the maximum-likelihood principle,

o); experimental activity coefficient of component 1 in the binary mixture; (�),ctivity coefficients from the Wilson model; (–), calculated activity coefficients fromredicted activity coefficients from the COSMO-RS model; (–··–), predicted activity

was adopted for the data reduction.

� =np∑

k=1

⎧⎨⎩[(

Pcalck

− Pexp tk

)�p

]2

+[(

Tcalck

− Texp tk

)�T

]2

+[(

xcalc1,k

− xexp t1,k

)�x1

]2

+[(

ycalc1,k

− yexp t1,k

)�y1

]2⎫⎬⎭ (5)

where np is the number of data points. The superscripts of calc. andexpt. denote the calculated and the experimental values, respec-tively. The standard deviations of temperature (�T), pressure (�P),liquid composition (�x), and vapor composition (�y) are 0.1 K,0.2 kPa, 0.005, and 0.005, respectively. By using this objective func-tion, the uncertainties of all measured variables are consideredsimultaneously and the determined optimal values of the modelparameters are much more statistically sound.

The measured VLE data were also correlated with theSoave–Redlich–Kwong (SRK) equation of state. The results of cor-relation presented in Fig. 1(a–d). This equation is applicable tononpolar and slightly polar components. For calculating mixtureproperties, the SRK equation of state with the invariant asymmetric

90 B.S. Gupta, M.-J. Lee / Fluid Phase Equilibria 352 (2013) 86– 92

Table 3Parameters of the extended Antoine equationa,b for pure compounds.

Compound A1 B2 C3 D4 E5 F6 G7 T1/K T2/K

Nonane 102.44 −9030.40 0 0 −12.88 7.85 × 10−6 2.0 219.66 594.60Heptane 80.92 −6996.40 0 0 −9.88 7.21 × 10−6 2.0 182.57 540.20Benzene 76.19 −6486.20 0 0 −9.21 6.98 × 10−6 2.0 278.68 562.05Toluene 70.03 −6729.80 0 0 −8.17 5.30 × 10−6 2.0 178.18 591.75o-Xylene 83.49 −7955.20 0 0 −10.08 5.95 × 10−6 2.0 247.98 630.30

a Taken from Aspen Plus physical property databanks.b Extended Antoine equation: ln(PS) = A1 + B2

T+C3+ D4T + E5 ln T + F6TG7 for T1 < T < T2, where PS is in kPa and T in K.

Table 4Physical properties and parameters of the UNIQUAC model for pure components.

Compound Tca/K Pc

a/kPa Vca/(cm3 mol−1) �a/debye Zc

a ωa ra qa

Nonane 594.60 2290 551 0 0.255 0.4435 5.476 6.523Heptane 540.20 2740 428 0 0.268 0.3495 5.174 4.396Benzene 562.05 4895 256 0 0.261 0.2103 3.190 2.400

mi

P

w

b

a

w

a

a

t

k

twe

iSontimaawyoRp

model with the binary parameters as given in Table 5. The variationsof the experimental and the calculated excess Gibbs free energies(GE/R) with liquid composition for the systems investigated arepresented in Fig. 3. The binary system of nonane + benzene wasfound to have large positive deviations, while toluene + o-xylene,

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-20

-10

0

10

20

30

40

50

60

70

(GE/R

)/K

x1

Fig. 3. Plot of experimental excess Gibbs free energies at 101.3 kPa and the calcu-lated values from the NRTL model against mole fraction; (�), experimental excessGibbs free energy of toluene (1) + o-xylene (2); (�), experimental excess Gibbs free

Toluene 591.75 4108 316

o-Xylene 630.30 3732 370

a Taken from Aspen Plus physical properties databanks.

ixing rule of Mathias et al. [32] was used in this study. The models defined as

= RT

V − b− a

V(V + b)(6)

ith

m =c∑

i=1

xibi (7)

m = a(0) + a(1) (8)

here

(0) =c∑

i=1

c∑j=1

xixj

√aiaj(1 − kij); kij = kji (9)

(1) =c∑

i=1

xi

⎛⎝ c∑

j=1

xj((aiaj))1/2lji)

1/3

⎞⎠

3

; lij /= lji (10)

The binary interaction parameter kij was treated as aemperature-dependent function:

ij =k(01)

ij+ k(02)

ij

T(11)

For a binary system, there are four binary interaction parame-ers, k(01)

ij, k(02)

ij, lij, and lji. The optimal values of these parameters

ere determined by fitting the binary VLE data to the above definedquation of state.

The optimal values of binary interaction parameters of the activ-ty coefficient models (the Wilson, the NRTL, and the UNIQUAC), theRK equation of state and the root mean square deviations (RMSD)f the data correlation are reported in Table 5. In addition, theew VLE data are also compared with the predicted results fromwo predictive models: the UNIFAC and the COSMO-RS, as givenn Table 5. The comparisons of the calculated values with experi-

ental data are illustrated in Fig. 1(a–d). As seen from this graphnd the RMSD values tabulated in Table 5, we found that all threectivity coefficient models and the SRK equation of state correlated

ell for all binary systems investigated. In general, the NRTL model

ields the best results. We also found that reasonable results werebtained from two predictive models, the UNIFAC and the COSMO-S. However, the COSMO-RS fails to quantitatively predict the VLEroperties of nonane + benzene.

0.3597 0.264 0.2640 2.968 3.9230.6295 0.264 0.3101 4.658 3.536

The calculated activity coefficients (� i) from the correlativemodels (the Wilson, the NRTL, and the UNIQUAC) and the predic-tive models (the COSMO-RS and the UNIFAC) are compared withthe experimental values in Fig. 2(a–d). Again, the NRTL modelrepresents satisfactorily of the activity coefficients varying withcomposition for all systems investigated.

To assess the non-ideality of these investigated systems, wecalculated the excess Gibbs free energies GE from the followingequation:

GE = RT(x1 ln �1 + x2 ln �2) (12)

where the activity coefficients, � i, were calculated from the NRTL

energy of benzene (1) + o-xylene (2); (o), experimental excess Gibbs free energyof nonane (1) + benzene (2); (�), experimental excess Gibbs free energy of nonane(1) + heptane (2); (—), calculated excess Gibbs free energy of toluene (1) + o-xylene(2); (–·–), calculated excess Gibbs free energy of benzene (1) + o-xylene (2); (····), cal-culated excess Gibbs free energy of nonane (1) + benzene (2); and (–··–), calculatedexcess Gibbs free energy of nonane (1) + benzene (2).

B.S. Gupta, M.-J. Lee / Fluid Phase Equilibria 352 (2013) 86– 92 91

Table 5Optimal binary interaction parameters and root mean square deviation (RMSD) for variables (T, P, x1 and y1).

Model Parameters RMSD �Ta/K RMSD �Pa/kPa RMSD �x1a RMSD �y1

a

Toluene (1) + o-xylene (2)Wilsonb M12 = −0.43

M21 = −23.75N12/K = 596.01N21/K = 8196.45

0.17 0.019 0.009 0.010

NRTLc D12 = 24.48D21 = 6.96

E12/K = −8158.08E21/K = −3396.29

0.13 0.015 0.002 0.003

UNIQUACd P12 = −29.59P21 = 0.72

Q12/K = 10693.7Q21/K = 119.24

0.14 0.015 0.004 0.005

SRKe k(01)12 = −0.94

k(02)12 = 0.002

l12 = 0.05l21 = −0.12

0.26 0.029 0.003 0.002

UNIFACf 0.72 – – 0.034COSMO-RSf 0.51 – – 0.026

Benzene (1) + o-xylene (2)Wilsonb M12 = 2.44

M21 = −27.97N12/K = −534.41N21/K = 9304.69

0.06 0.007 0.004 0.009

NRTLc D12 = 25.57D21 = 3.31

E12/K = −7971.53E21/K = −1835.54

0.06 0.006 0.002 0.003

UNIQUACd P12 = −15.11P21 = 2.03

Q12/K = 4870.50Q21/K = −421.44

0.05 0.006 0.004 0.007

SRKe k(01)12 = −0.30

k(02)12 = 0.001

l12 = 0.07l21 = −0.07

0.10 0.011 0.003 0.004

UNIFACf 1.80 – – 0.023COSMO-RSf 1.11 – – 0.018

Nonane (1) + benzene (2)Wilsonb M12 = −18.42

M21 = 1.42N12/K = 5721.16N21/K = −202.62

0.08 0.008 0.004 0.007

NRTLc D12 = 2.71D21 = 15.75

E12/K = −1556.45E21/K = −4386.76

0.07 0.007 0.004 0.002

UNIQUACd P12 = 1.93P21 = −10.79

Q12/K = −442.95Q21/K = 3412.33

0.09 0.008 0.004 0.005

SRKe k(01)12 = −0.41

k(02)12 = 0.001

l12 = −0.10l21 = 0.05

0.11 0.011 0.004 0.003

UNIFACf 0.82 – – 0.012COSMO-RSf 3.35 – – 0.037

Nonane (1) + heptane (2)Wilsonb M12 = −28.80

M21 = 0.80N12/K = 9916.22N21/K = 106.49

0.08 0.008 0.006 0.010

NRTLc D12 = 4.45D21 = 20.83

E12/K = −6559.22E21/K = −2365.51

0.07 0.007 0.003 0.002

UNIQUACd P12 = 1.26P21 = −14.68

Q12/K = −121.46Q21/K = 4905.53

0.07 0.006 0.004 0.003

SRKe k(01)12 = −0.59

k(02)12 = 0.002

l12 = −0.08l21 = 0.08

0.09 0.010 0.003 0.002

UNIFACf 1.01 – – 0.022COSMO-RSf 0.63 – – 0.015

a RMSD �M =

(1

np

np∑k=1

(Mcalc

k− Mexp t

k

)2

)0.5

, where np is the number of data points and M represents T, P, x1 or y1.

b Wilson model: lnAij = [Mij + Nij/T].c NRTL model: ij = [Dij + Eij/T]. The value of ̨ was fixed to be 0.3 for each binary system.d UNIQUAC model: ij = [exp(Pij + Qij/T)].[

01 02]

btainc

bt

4

taitwtN

e SRK : kij = kij

+ kij

/T , kij = kji

lij /= 1jif The RMSDs from two predictive models, the UNIFAC and the COSMO-RS, were o

omposition are given and thus no RMSDs of �P and �x1 are reported.

enzene + o-xylene, and nonane + heptane systems exhibit nega-ive deviations from Raoult’s law.

. Conclusions

Isobaric VLE data have been measured for four binary sys-ems, toluene + o-xylene, benzene + o-xylene, nonane + benzene,nd nonane + heptane, at 101.3 kPa. No azeotrope was formed

n these four systems investigated. All the VLE data passed thehermodynamic consistency test. These experimental VLE dataere correlated well by using the Wilson-HOC, the NRTL-HOC,

he UNIQUAC-HOC models and the SRK equation of state. TheRTL model yields the best results. While nonane + benzene system

ed via the Bubble-T VLE calculation, in which the experimental pressure and liquid

exhibits large positive deviations, toluene + o-xylene, benzene + o-xylene, and nonane + heptane systems show negative deviationsfrom the Raoult’s law. This study also found that the UNIFAC andthe COSMO-RS predict the VLE properties of the systems investi-gated fairly well. However, the COSMOS-RS failed to quantitativelyestimate the VLE behavior of nonane + benzene system.

List of symbols

a b constants in the SRK equation.A1–G7 coefficients of the extended Antoine equationB second virial coefficient (cm3 mol−1)

9 Phase

cDGkMnPPqrRTuVxyZ

G˛�����ω

Sbciim

SceES

F

t2o

[

[[[[

[[

[

[[[[[[

[

[

[

[[28] A.I. Johnson, D.M. Ward, W.F. Furter, Can. J. Technol. 34 (1957) 413.[29] D. Meranda, W.F. Furter, AIChE J. 18 (1972) 111–116.[30] J.F. Morrison, J.C. Baker, H.C. Meredith, K.E. Newman, T.D. Walter, J.D. Massle,

R.L. Perry, P.T. Cummings, J. Chem. Eng. Data 35 (1990) 395–404.[31] T. Yamada, R.D. Gunn, J. Chem. Eng. Data 18 (1973) 234–236.[32] P.M. Mathias, H.C. Klotz, J.M. Prausnitz, Fluid Phase Equilib. 67 (1991) 31–44.

2 B.S. Gupta, M.-J. Lee / Fluid

number of componentsij, Eij parameters of the NRTL model

Gibbs free energy (J mol−1)ij, lij parameters of the SRK equationij, Nij parameters of the Wilson activity coefficient models

p number of data points pressure (kPa)ij, Qij parameters of the UNIQUAC model

surface area parameter of the UNIQUAC model volume parameter of the UNIQUAC model

gas constant (J mol−1 K−1) temperature (K)

uncertainty molar volume (cm3 mol−1)

mole fraction in liquid phase mole fraction in vapor phase

compressibility factor

reek letters non-randomness parameter of the NRTL model

activity coefficient dipole moment (debye)

objective function density (g cm−3)

standard deviation acentric factor

ubscripts normal boiling

critical property, j components i and jj i–j pair interaction

mixture

uperscriptsalc calculated valuexpt experimental value

excess property saturation

unding

The authors gratefully acknowledge the financial support fromhe National Science Council, Taiwan, through Grant No. NSC102-218-E002-006 and scholarship from National Taiwan Universityf Science & Technology.

Equilibria 352 (2013) 86– 92

Acknowledgement

The authors thank to Dr. Ho-mu Lin for valuable discussions.

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