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Journal of Chromatography A, 1151 (2007) 60–64

Calculation for liquid–liquid equilibria of quaternaryalkane–ethyl acetate–methanol–water systems

used in counter-current chromatography

Jian Chen ∗, Mengqiang Zhao, Yanmei Yu, Zongcheng LiState Key Laboratory of Chemical Engineering, Department of Chemical Engineering,

Tsinghua University, Beijing 100084, China

Available online 3 February 2007

bstract

The calculation of liquid–liquid equilibrium compositions of solvent systems is very important for the work on counter-current chro-atography (CCC), especially the phase composition and volume ratio obtained from liquid–liquid equilibrium calculation. In this work,

iquid–liquid equilibria of quaternary Arizona solvent systems, alkane–ethyl acetate–methanol–water, and related ternary systems are corre-ated and predicted using the non-random two-liquid model (NRTL). Hexane, heptane and isooctane are the used alkanes. The parameters

n the model are regressed only with the special systems considered. Detailed comparison with experimental data shows that liquid–liquidquilibria of these systems can be predicted with greatly improved accuracy as compared to the group contribution method (UNI-AC).

2007 Elsevier B.V. All rights reserved.

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eywords: Counter-current chromatography; Arizona solvent system; Liquid–l

. Introduction

Since counter-current chromatography (CCC) was proposedn the late 1960s [1], it has been widely used in analytical chem-stry and product separation in many areas [2,3]. In our previousorks [4,5], we have elaborated a method for the calculation of

he properties of solvent systems in CCC. These properties arehase composition, volume ratio, phase polarity, density, viscos-ty, dielectric constant and interfacial tension. All the propertiesre very important for the work in CCC, especially the phaseomposition obtained from liquid–liquid equilibrium calcula-ion.

The liquid–liquid equilibrium calculation can be carriedut with two kinds of thermodynamic models: molecularodels and group contribution models [6–9]. Compared with

xperimental liquid–liquid equilibrium data, the results of

iquid–liquid equilibrium calculation with group contribution

ethods are always not so accurate. The reason is that theroup interaction parameters were regressed with almost all

∗ Corresponding author. Tel.: +86 10 62782748; fax: +86 10 62770304.E-mail address: cj-dce@tsinghua.edu.cn (J. Chen).

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021-9673/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2007.01.107

equilibrium; Calculation

xperimental data for systems with the same group pairs. Forxample, Arizona solvent systems, which have components oflkane–ethyl acetate–methanol–water of particular compositionith the same alkane/ethyl acetate and methanol/water ratio,

re commonly used solvent systems in CCC. But calculatediquid–liquid equilibrium results with group contribution

ethod (UNIFAC) do not coincide satisfactorily with thexperimental ones [10]. So, it is necessary to use thermody-amic models with the consideration of molecular interactionarameters.

In this work, liquid–liquid equilibrium data of typicalrizona solvent systems in CCC are correlated and pre-icted using a molecular thermodynamic model NRTL [6].he parameters in the models are regressed only with thepecial system considered. The selected solvent systemsre ethyl acetate–methanol–water [11]; hexane–methanol–ater [12]; hexane–ethyl acetate–methanol–water [10,13];eptane–methanol–water [14]; heptane–ethyl acetate–ethanol–water [10]; isooctane–methanol–water [15];

sooctane–ethyl acetate–methanol–water [10]. Detailed com-arison with experimental data shows that liquid–liquidquilibria of these systems can be predicted with greatlymproved accuracy.

J. Chen et al. / J. Chromatogr. A 1151 (2007) 60–64 61

F(d

2

t

x

ib

trcmaasp

Fig. 2. Liquid–liquid equilibrium calculation for the system hexane(d

b

l

w

G

Fd

ig. 1. Liquid–liquid equilibrium calculation for the system ethyl acetate1)–methanol (2)–water (3) at 293.15 K with the RMSD as 0.015. Experimentalata are from literature [11].

. Theory

For the calculation or prediction of liquid–liquid equilibrium,he following equation is used:

′iγ

′i = x′′

i γ′′i i = 1, · · ·, n (1)

n which activity coefficient γ i of a compound i can be calculatedy some models with only parameters.

Non-random two-liquid (NRTL) model has been widely usedo calculate phase equilibria, especially vapor–liquid equilib-ia and liquid–liquid equilibria [6]. In the equation, the localoncentration of compounds are considered according to theolecular interaction, so it is valid for systems including polar

nd associating compounds such as water and methanol. Waternd methanol are used in the Arizona solvent systems in CCC,o NRTL is the best thermodynamic equation for calculation andrediction of properties of Arizona solvent systems.

iast

ig. 3. Liquid–liquid equilibrium calculation for the system hexane (1)–ethyl acetateata are from literature [13].

1)–methanol (2)–water (3) at 298.15 K with the RMSD as 0.010. Experimentalata are from literature [12].

The activity coefficient γ i of a compound i in a mixture cane expressed with NRTL equation [6] as:

n γi =∑

jτjiGjixj∑kGkixk

+∑

j

xjGij∑kGkjxk

(τij −

∑kxkτkjGkj∑

kGkjxk

)

(2)

here xi is the mole fraction of a compound i, and:

ij = exp(−αijτij), αij = αji = 0.2 (3)

n which τ is the interaction parameter between compounds i

ij

nd j, and αij is the third non-randomness parameter which waset to 0.2 for all pairs in this work. For the pairs in CCC at theemperature around 298 K, the interaction parameters were set

(2)–methanol (3)–water (4) at 298.15 K with the RMSD as 0.013. Experimental

62 J. Chen et al. / J. Chromatogr. A 1151 (2007) 60–64

F etated

t

τ

3

titefpttof

R

x

ikt

sd

ugt

gaati

fvtrd(im

Fswthe results are shown in Fig. 6 for comparison with literaturedata [10].

For ternary system, isooctane–methanol–water [15], theresults are shown in Fig. 7 for the comparison with lit-

ig. 4. Liquid–liquid equilibrium calculation for the system hexane (1)–ethyl acata are from literature [10].

o be independent on temperature:

ij = aij + bij

T≈ aij (4)

. Results and discussion

The thermodynamic model NRTL was used to correlateernary and quaternary liquid–liquid equilibrium data. First, withnitial values of parameters in the NRTL equation, the calcula-ion of equilibria was carried out with the minimization of Gibbsnergy as the objective function [16], and the equality of activityor each component in two phases was checked as Eq. (1). Thisrocedure confirmed the correct calculation of tie-line concen-rations with the given parameters in the NRTL equation. Thenhe parameters in NRTL were regressed with the minimizationf total root-mean square deviation (RMSD) of mole fractionsor all components:

MSD =⎡⎣ 1

2nM

n∑i=1

2∑j=1

M∑k=1

(xcalijk − x

expijk )

2

⎤⎦

1/2

(5)

calijk is the calculated mole fraction. xexp

ijk is the experimental ones.is for the number of components. j is for the number of phases.is for the number of tie-lines. M is the total number of the

ie-lines.Correlation results are shown in Figs. 1–8 for four ternary

ystems and three quaternary systems, respectively. All standardeviations RMSD are less than 0.02 for mole fractions.

For ternary system, ethyl acetate–methanol–water, which issed in all quaternary systems, the result is shown in Fig. 1 andood agreement is achieved between calculated and experimen-al data.

For ternary system, hexane–methanol–water shown in Fig. 2,ood agreement is also obtained. With the parameters fitted in

bove two ternary systems, the quaternary system hexane–ethylcetate–methanol–water are calculated with only two parame-ers fitted for hexane–ethyl acetate, and the results are shownn Figs. 3 and 4 for comparison with two sets of literature data

F(d

(2)–methanol (3)–water (4) at 298.15 K with the RMSD as 0.018. Experimental

rom [13] and [10], respectively. One can see that the calculatedalues are in good agreement with experimental ones, except inhe range for mole fractions around and less than 0.01. In thisange, both accurate measurement and accurate calculation areifficult and need more research efforts. For various propertiese.g., phase polarity, density, viscosity, dielectric constant andnterfacial tension) important for CCC, their calculations will be

ainly based on the main part components.For ternary system, heptane–methanol–water [14] shown in

ig. 5, good agreement is also obtained. Again the quaternaryystem heptane–ethyl acetate–methanol–water is calculatedith only two parameters fitted for heptane–ethyl acetate, and

ig. 5. Liquid–liquid equilibrium calculation for the system heptane1)–methanol (2)–water (3) at 298.15 K with the RMSD as 0.015. Experimentalata are from literature [14].

J. Chen et al. / J. Chromatogr. A 1151 (2007) 60–64 63

Fig. 6. Liquid–liquid equilibrium calculation for the system heptane (1)–ethyl acetate (2)–methanol (3)–water (4) at 298.15 K with the RMSD as 0.015. Experimentaldata are from literature [10].

Fig. 7. Liquid–liquid equilibrium calculation for the system isooctane(1)–methanol (2)–water (3) at 298.15 K with the RMSD as 0.012. Experimentaldata are from literature [15].

Table 1The NRTL parameters correlated for ternay systems

τij j = 1 2 3 4

Hexane–ethyl acetate–methanol–water at 298.15 Ki = 1 0.0 0.22263 × 100 0.65003 × 103 0.94884 × 103

2 −0.47946 × 102 0.0 0.33491 × 10−1 0.12989 × 103

3 0.64797 × 103 −0.22894 × 103 0.0 0.68045 × 100

4 0.24248 × 104 0.12795 × 104 −0.14745 × 103 0.0

Heptane–ethyl acetate–methanol–water at 298.15 Ki = 1 0.0 −0.47951 × 10-1 0.38096 × 103 0.12271 × 104

2 −0.10961 × 102 0.0 0.33491 × 10−1 0.12989 × 103

3 0.65488 × 103 −0.22894 × 103 0.0 0.68045 × 100

4 0.16166 × 104 0.12795 × 104 −0.14745 × 103 0.0

Isooctane–ethyl acetate–methanol–water at 298.15 Ki = 1 0.0 −0.47878 × 10−1 0.53692 × 103 0.13070 × 104

2 −0.33441 × 101 0.0 0.33491 × 10-1 0.12989 × 103

3 0.92279 × 103 −0.22894 × 103 0.0 0.68045 × 100

4 0.21278 × 104 0.12795 × 104 −0.14745 × 103 0.0

Fig. 8. Liquid–liquid equilibrium calculation for the system isooctane (1)–ethyl acetate (2)–methanol (3)–water (4) at 298.15 K with the RMSD as 0.012. Experimentaldata are from literature [10].

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rature data. Again the quaternary system isooctane–ethylcetate–methanol–water is calculated with only two parameterstted for isooctane–ethyl acetate, and the results are shown inig. 8 for comparison with literature data [10].

Table 1 lists all parameters regressed and used in the cal-ulation. The results show that the NRTL equation with thearameters in this work could be used to predict phase splitomposition for solvent systems widely used in CCC.

. Conclusion

Liquid–liquid equilibrium data of quaternary Arizona sol-ent systems used in CCC are correlated and predicted usingmolecular thermodynamic model NRTL. The parameters in

he model are regressed mainly from relevant ternary sys-em. Detailed comparison with experimental data shows thatiquid–liquid equilibria of these systems can be predicted withreatly improved accuracy than group contribution methodUNIFAC).

omenclature

ij temperature independent interacion parameter betweeni and j

ij temperature dependent interacion parameter between i

and j

al supercript for calculated dataxp supercript for experimental dataij interaction energy between i and j

[

[

. A 1151 (2007) 60–64

temperature (K)i mole fraction of component iij non-random parameter between i and ji activity coefficient of component iij interaction parameters between i and j

eferences

[1] Y. Ito, W.D. Conway, High-speed Countercurrent Chromatography (Chem-ical Analysis Series), vol. 132, Wiley, New York, 1996.

[2] A.P. Foucault, L. Chevolot, J. Chromatogr. A 808 (1988) 3.[3] A. Berthod, Countercurrent Chromatography (Comprehensive Analytical

Chemistry), vol. 38, Elsevier, Amsterdam, 2002.[4] L. Zhang, Z.-C. Li, J. Chen, T.-Z. Bao, J. Tsinghua Univ. 37 (1997)

25.[5] Z.-C. Li, Y.-J. Zhou, F.-M. Chen, L. Zhang, Y. Yang, J. Liq. Chromatogr.

Rel. Technol. 26 (2003) 1397.[6] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135.[7] D.S. Abrams, J.M. Prausnitz, AIChE J. 21 (1975) 116.[8] T. Magnussen, Aa. Fredenslund, P. Rasmussen, Ind. Eng. Chem. Proc. Des.

Dev. 20 (1981) 331.[9] P.A. Gupte, R.P. Danner, Ind. Eng. Chem. Res. 26 (1987) 2036.10] A. Berthod, M. Hassoun, M.J. Ruiz-Angel, Anal. Bioanal. Chem. 383

(2005) 327.11] J.M. Sorensen, W. Arlt, Liquid–Liquid Equilibrium Data Collection—

Ternary systems, vol. 2, DECHEMA, Frankfurt/Main, 1980.12] J.-G. Liu, Z.-F. Qin, Z.-G. Wang, J. Chem. Eng. Data 47 (2002) 1243.13] F. Oka, H. Oka, Y. Ito, J. Chromatogr. 538 (1991) 99.14] T.M. Letcher, S. Wootton, B. Shuttleworth, C. Heyward, J. Chem. Ther-

modyn. 18 (1986) 1037.15] B.E. Garcı́a-Flores, M.G. de Doz, A. Trejo, Fluid Phase Equilib. 230 (2005)

121.16] J.M. Sorensen, W. Arlt, Liquid–Liquid Equilibrium Data Collection—

Binary systems, Vol.1, DECHEMA, Frankfurt/Main, 1980.