Computation of liquid–liquid equilibrium of organic-ionic liquid systems using NRTL, UNIQUAC and NRTL-NRF models

Journal of Molecular Liquids 171 (2012) 43–49

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Computation of liquid–liquid equilibrium of organic-ionic liquid systems using NRTL, UNIQUAC and NRTL-NRF models Ali Haghtalab ⁎, Aliakbar Paraj Department of Chemical Engineering, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 3 February 2012 Received in revised form 17 April 2012 Accepted 18 April 2012 Available online 1 May 2012 Keywords: ionic liquid NRTL UNIQUAC NRTL-NRF liquid–liquid equilibrium

a b s t r a c t Ionic liquids (ILs) with their limitless combination of cations and anions can offer an optimal solvent for a specific purpose especially separation processes. Among ionic liquids, alkyl-sulfate derivatives are the most promising ILs to be applied in industrial processes. The present work investigates liquid–liquid equilibrium phase behavior of 12-ILs comprising sulfate-based anions. Computation of liquid–liquid equilibrium for 36 ternary systems is carried out using three local composition models, namely non-random two liquid (NRTL), non-random two liquid non-random factor (NRTL-NRF) and universal quasi chemical (UNIQUAC) activity coefficient models. All the interaction parameters of the three models are regressed using an optimization program based on Simplex method of Nelder and Mead. Comparison of the results is expressed by root mean square deviation (rmsd) between the experimental and calculated compositions. It is demonstrated that the NRTL-NRF model presents very good satisfactory results with rmsd values of about 1.05 so that this model is highly appropriate to calculate thermodynamic properties of ionic liquid solutions. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Ionic liquids (ILs) are a class of organic salts that are comprised entirely of ions and are liquid at conditions around room temperature in their pure state [1]. ILs have been considered a novel replacement for many traditional organic compounds; because these types of electrolyte present negligible volatility, low melting points, favorable solubility, and high polar character [2]. Due to their low volatility, they can be easily recycled through removing volatile solutes by simple distillation. Moreover, some ILs possess other interesting physical properties such as relatively good stability up to 300 °C or higher, low viscosity and are much less corrosive than conventional high melting salts. Thus, these unique characteristics have presented ILs as chemicals of high commercial interest [2]. Nowadays, these salts have attracted worldwide scientific interest in academia and industry. ILs are being investigated to have wide applications in chemical industry in which knowledge of phase equilibrium is essential; as entertainers in extractive distillation in order to separate closeboiling or azeotropic mixtures [3,4], a suitable solvent in separation and extraction processes such as extraction of aromatic hydrocarbons from mixtures of aromatic/aliphatic hydrocarbons and recovery of amino acids from aqueous media, membrane separation processes where ILs are used as in-between porous support membranes, as a solvent or a catalysis reagent for chemical reactions, etc. [5,6].

⁎ Corresponding author. Tel.: + 98 21 82883313; fax: + 98 21 82883381. E-mail address: [email protected] (A. Haghtalab). 0167-7322/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.molliq.2012.04.008

Comprehensive coverage of experimental works to investigate phase behavior of ternary organic IL systems is impossible, because the number of possible systems involving ILs is enormous. Therefore, thermodynamic modeling of such IL systems is necessary for computation of liquid–liquid equilibrium (LLE) that allows one to have a strong tool to design separation processes that are applicable in chemical industry and biotechnology. In spite of wide studies in calculation of LLE, however, macroscopic modeling of LLE involving ILs is still in its infancy [5]. In recent years, several authors have systematically studied LLE of ternary IL systems. Aznar [7] correlated the LLE data for ternary systems including ILs using the NRTL model [8] with an overall rmsd value of 1.4%. Santiago et al. [9,10] correlated LLE data for 50 and 41 ternary systems involving ILs using the UNIQUAC model [11] . In the two other works, Santiago et al. [12,13] used the UNIFAC [14] model to correlate 50 and 24 ternary LLE systems involving ILs. Also, Alevizou et al. [6] used the extended the UNIFAC model to predict phase equilibrium in mixture containing ILs. Using the COSMO-RS model, Banerjee et al. [15] predicted LLE for 32 ternary systems with the different ILs. Simoni et al. [5] employed three different excess Gibbs energy models for six different IL ternary LLE systems. Robles et al. [16,17] employed ASOG group contribution model of activity coefficient to predict ternary LLE for 17 and 32 IL systems. An excellent review of phase equilibria of ILs are given by Heintz [18] and Vega et al. [19]. Alkyl-sulfate derivatives can be easily synthesized in an halidefree way at a reasonable cost, are also chemically and thermally stable and have low melting points and relatively low viscosity [3]. Thus,

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A. Haghtalab, A. Paraj / Journal of Molecular Liquids 171 (2012) 43–49

It is important to notice that all the models tend to calculate very small quantities (less than 0.001 mole fractions) of ionic liquid in upper (or lower) phase for given ternary systems.

Table 1 The names and abbreviations for the ionic liquids used in the present work. Ionic liquid

Abbreviation

[1-ethyl-3-methylimidazolium][hydrogen sulfate] [1-buthyl-3-methylimidazolium][hydrogen sulfate] [1-hexyl-3-methylimidazolium][hydrogen sulfate] [1-ethyl-3-methylimidazolium][ethyl sulfate] [1-buthyl-3-methylimidazolium][methylsulfate] [1,3-dimethylimidazolium][methylsulfate] [1-ethyl-3-methylimidazolium][2-(2-methoxyethoxy) ethyl sulfate] [1-ethyl-3-methylimidazolium][octyl sulfate] [tris-(2-hydroxyethyl)-methylammonium][methyl sulfate] [1-methyl-3-octylimidazolium][diethyleneglycolmonomethyl ether sulfate] [1-ethyl-3-methylpyridinium][ethyl sulfate] [1-ethylpyridinium][ethyl sulfate]

[emim][HSO4] [bmim][HSO4] [hmim][HSO4 [emim][eSO4] [bmim][mSO4] [mmim][mSO4] [emim][meSO4] [emim][oSO4] [TEMA][mSO4] [moim] [MDEGSO4] [empy][eSO4] [epy][eSO4]

ionic liquids based on alkyl-sulfate are the most promising ILs to be applied in industrial processes. In this work, LLE calculations have been carried out for the correlation of the 36 ternary systems including 12-types ILs comprising sulfate-based anions. The names and abbreviations for the ionic liquids used in this work are presented in Table 1. Different excess Gibbs energy models, i.e., NRTL, UNIQUAC and NRTLNRF [20], are used and applied successfully for ternary IL solvent and co-solvent systems. It is the first time that the NRTL-NRF model is employed to correlate ternary LLE IL systems. As shown in Table 2, the experimental data of such ternary systems are given in the literature and most of them were published during 2010–2011.

2. Computation LLE including ionic liquid systems In this work, correlation of LLE containing ionic liquid is investigated, and as given in Appendix A, the NRTL, UNIQUAC and NRTLNRF models are used to calculate activity coefficient of species in liquid phases. Thus, liquid–liquid equilibrium equation can be written as I

II

ai ¼ ai ; ai ¼ xi γ i

ð1Þ

where ai and γi are activity and activity coefficient of component i, respectively. Also, I and II stand for two liquid equilibrium phases. Energy interaction parameters are optimized by LLE calculation of the ternary ionic liquid systems through the following objective function [35]: OF ¼

N X 3 h X

6 I  II i2 X 2 xij γij − xij γij þQ Pk

i¼1 j¼1

ð2Þ

k¼1

where x denotes the mole fraction composition, Pk stands for interaction parameter, and Q is used as a penalty function with a constant value. Subscripts i, j and k are referred to tie-lines (1, 2, …, N), components (1, 2, 3) and parameters (1, 2, 3, …, 6), respectively. All the interaction parameters (Δgij for NRTL and NRTL-NRF, Δaij for

Table 2 The rmsd (%) values of liquid–liquid equilibrium calculation for the different ternary systems using three local composition models. System no.

System

No. of tie-line

σx (%) NRTL

NRTL-NRF

UNIQUAC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Overall

Hexane (1) + benzene (2) + [bmim][mSO4] (3) Hexane (1) + thiophene (2) + [emim][eSO4] 3) Heptane (1) + thiophene (2) + [emim][eSO4] (3) Dodecane (1) + thiophene (2) + [emim][eSO4] (3) Hexadecane (1) + thiophene (2) + [emim][eSO4] (3) Hexane (1) + ethanol (2) + [emim][eSO4] (3) Heptane (1) + ethanol (2) + [emim][eSO4] (3) Hexane (1) + benzene (2) + [emim][eSO4] (3) Heptane (1) + benzene (2) + [emim][eSO4] (3) Octane (1) + benzene (2) + [emim][eSO4] (3) Heptane(1) + toluene(2) + [empy][eSO4](3) Octane(1) + toluene(2) + [empy][eSO4](3) Nonane(1) + toluene(2) + [empy][eSO4](3) Hexane(1) + o-xylene(2) + [empy][eSO4](3) Hexane(1) + m-xylene(2) + [empy][eSO4](3) Hexane(1) + p-xylene(2) + [empy][eSO4](3) Hexane(1) + toluene(2) + [empy][eSO4](3) Hexane(1) + ethylbenzene(2) + [empy][eSO4](3) Cyclohexane(1) + ethylbenzene(2) + [emim][eSO4](3) Cyclooctane(1) + ethylbenzene(2) + [emim][eSO4](3) Limonene(1) + linalool(2) + [emim][meSO4](3) Limonene(1) + linalool(2) + [emim][meSO4](3) Octane(1) + benzene(2) + [epy][eSO4](3) Nonane(1) + benzene(2) + [epy][eSO4](3) Thiophene(1) + heptane(2) + [TEMA][mSO4](3) Heptane(1) + benzene(2) + [emim][oSO4](3) Heptane(1) + hexadcane(2) + [emim][oSO4](3) Heptane(1) + benzene(2) + [moim][MDEGSO4](3) Heptane(1) + hexadcane(2) + [moim][MDEGSO4](3) Ethylacetate(1) + ethanol(2) + [hmim][HSO4](3) Ethylacetate(1) + aceticacid(2) + [hmim][HSO4](3) Ethylacetate(1) + ethanol(2) + [emim][HSO4](3) Ethylacetate(1) + aceticacid(2) + [emim][HSO4](3) Ethylacetate(1) + ethanol(2) + [bmim][HSO4](3) Ethylacetate(1) + aceticacid(2) + [bmim][HSO4](3) 2-Butanone(1) + ethanol(2) + [mmim][mSO4](3)

8 8 7 12 12 11 12 8 8 9 8 8 8 8 8 7 8 7 10 8 10 10 8 8 8 4 5 4 4 6 8 4 6 5 5 7 277

0.57 2.39 4.49 4.77 4.04 2.52 0.64 0.78 1.86 1.42 0.86 0.50 0.80 2.25 1.00 0.94 1.49 2.01 0.37 0.30 0.58 1.19 1.51 0.93 4.39 2.43 1.04 2.41 1.01 2.15 2.49 1.44 0.49 1.26 2.89 3.59 1.77

0.15 1.19 1.39 2.59 3.35 1.61 0.38 1.24 2.08 1.51 1.33 1.28 1.28 1.47 0.81 0.95 1.07 0.52 0.3 0.72 0.34 1.3 1.58 1.65 1.98 0.61 1.44 0.77 1.41 0.28 0.25 0.22 0.19 0.27 0.09 0.11 1.05

0.64 3.75 4.26 1.98 4.77 2.31 0.64 0.72 0.65 0.82 0.47 0.76 5.06 4.94 2.09 1.39 1.70 1.75 0.71 2.75 2.79 3.18 0.80 0.73 3.05 3.52 2.09 0.78 2.13 2.67 2.63 2.71 1.31 2.99 0.27 2.45 2.12

T (K)

References

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 308.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 313.15 313.15 313.15 313.15 313.15 313.15 298.15

[21] [22] [22] [22] [22] [23] [23] [24] [24] [24] [25] [25] [25] [26] [26] [26] [27] [27] [28] [28] [29] [29] [30] [30] [31] [32] [32] [32] [32] [33] [33] [33] [33] [33] [33] [34]

A. Haghtalab, A. Paraj / Journal of Molecular Liquids 171 (2012) 43–49

45

Input Exp. Mole Fraction

xl xu

xl xu

x l,cal x u,cal

x l,exp x u,exp

Initial Guess for Binary Parameters ( 0)

N

3

x ijI

OFa i

Minimization

I ij

x ijII

2

II ij

3

3

j

k

2 jk

Q

j

No OFa < Yes

No

Mole Fraction Calculation

x l,cal ; x u,cal

Print

Yes

OFx

OFx <

1 6N

N

3

2 cal x ijk

i

j

exp x ijk

2

k

Fig. 1. The flow chart of experimental data reduction in ternary liquid–liquid equilibria.

UNIQUAC) are obtained using an optimization program based on Simplex method of Nelder and Mead. The second term of Eq. (2) presents a penalty parameter that is designed to reduce the risks of multiple solutions associated with high parameter values. The algorithm for optimization of parameters and the LLE calculation is shown in Fig. 1. As one can see, the input to the optimization program is the experimental values of compositions of species in upper and lower phases. Following initialization of the parameters, activity of all species are calculated via the given activity coefficient model. Thus, following optimization of the parameters through minimization of Eq. (2), one can obtain the calculated compositions of the species in each phase. Finally, to get an idea of quality of the correlations and to choose the binary interaction parameters that lead

to a better agreement between experimental and calculated data, root-mean-square deviation (rmsd) of composition, σx, is calculated as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 u 0 u N 3 2 i u 1 @X X X h calc: exp: 2 A x −xijk σx ¼ 100t 6N i¼1 j¼1 k¼1 ijk

ð3Þ

In the NRTL and NRTL-NRF models, the non-randomness parameter, αij, was set to different values between 0.05 and 0.5 during parameter optimization so that the best results are presented in Table 2. The structural parameters, ri and qi, of UNIQUAC equation

Table 3 The volume and surface parameters of the different compounds. Component

r

q

q'

Reference

Component

r

q

q'

Reference

Acetic acid Benzene 2-Butanone Cyclohexane Cyclooctanea Dodecane Ethanol Ethylacetate Ethylbenzene Heptane Hexadecane Hexane Limonene Linalool m-Xylene Nonane Octane

2.20 3.19 3.25 4.05 3.95 8.55 4.74 3.48 4.60 5.17 11.24 4.50 6.28 7.04 4.66 6.52 5.85

2.07 2.40 2.88 3.24 3.16 7.10 2.12 3.12 3.51 4.40 9.26 3.86 5.21 6.06 3.54 5.48 4.94

2.07 2.40 2.88 3.24 3.16 7.10 0.92 3.12 3.51 4.40 9.26 3.86 5.21 6.06 3.54 5.48 4.94

[27] [27] [12] [9] [22] [36] [36] [9] [27] [27] [27] [37] [37] [9] [9] [11]

o-Xylene p-Xylene Thiophene Toluene [bmim][mSO4] [bmim][HSO4] [emim][eSO4] [emim][oSO4] [emim][HSO4] [emim][meSO4]a [empy][eSO4]a [epy][eSO4]a [hmim][HSO4] [mmim][mSO4] [moim][ MDEGSO4] [TEMA][mSO4]a

4.66 4.66 2.86 3.87 11.90 8.22 7.94 12.39 6.91 7.34 5.93 5.46 5.53 6.90 14.98 6.15

3.54 3.54 2.14 2.93 6.54 6.63 7.21 9.79 5.50 5.87 4.74 4.36 4.51 5.50 11.96 4.92

3.54 3.54 2.14 2.93 6.54 6.63 7.21 9.79 5.50 5.87 4.74 4.36 4.51 5.50 11.96 4.92

[9] [9] [22] [36] [18] [9] [10] [10] [9] [9] [9] [9] -

a

Calculated using Eq. (3).

46

A. Haghtalab, A. Paraj / Journal of Molecular Liquids 171 (2012) 43–49

Table 4 The binary interaction parameters of the NRTL, NRTL-NRF and UNIQUAC models. System no.

Model

1

NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

Δgij (for NRTL and NRTL-NRF) or Δuij (for UNIQUAC) (j/mol)

αij

1–2

1–3

2–1

2–3

3–1

3–2

8643.9 16239 − 7463.3 − 15065 7518.3 − 1072.8 − 10964 − 9213 − 1415.3 − 3261 − 4355.9 − 842.89 − 8903.2 − 294.44 − 204.5 8643.9 16239 − 7463.3 − 584.31 6908.1 − 2139.4 − 5241.6 − 2750.9 − 1543.9 − 2775.7 − 2710.3 − 670.68 − 5159.3 − 2429.4 − 815.55 − 3336.9 663.58 − 622.295 − 2264.5 131.8077 − 55.1417 − 2945.1 − 422.096 − 6033.63 − 503.4 − 4119.5 14039 − 5466.1 − 1810.6 − 1375.1 − 1365.3 − 2908.4 6070.2 − 96265 5827.2 − 1287.3 − 5842.6 − 4288.3 − 3089.3 − 357.39 1716.1 − 84.149 − 510.66 4386.3 − 855.11 − 6170.9 23122 − 7258.8 − 11819 28970 − 2173.1 − 3686.5 − 6313.2 − 244.63 − 3228.6 − 2277.1 12697 − 3345.1 − 13458

25797 − 14986 2763.8 4017.4 15246 − 59.859 7063.8 15319 214.0 21629 9983.7 1800.4 14783 − 0.05346 2335.6 25797 − 14986 2763.8 4590.3 21524 − 3614.8 20248.0 13438.0 2023.3 19169 13853 2143.5 18314 15429 2022.7 19987 15115 4101.623 18303 12341.37 4322.056 18069 − 15423.8 3958.621 21503 7746.8 6374.0 21283 7786.3 4132.6 18629 4435.6 − 3236.0 10453 20760 4097.6 18737 7832.3 3722.9 19326 13421 2330.1 19710 11507 1836.7 29628 13867 4004.1 5722.3 20411 4053.0 19556 14724 4721.7 18157 5959.9 − 4463.6 13515 − 23064

21122 0.85652 7523 15331 9124.7 1844.4 − 1979.7 − 3890.6 2619.1 18501 − 4460.2 2365.1 4468.4 − 0.57049 − 100.62 21122 0.85652 7523 5947.7 − 3288.6 4804.5 6228.1 − 3574.6 3949.4 1719.7 − 3934.5 1826.6 2344.7 − 4357.5 1145.8 3093.1 − 352.75 759.349 2147.8 177.8043 129.7379 5489.2 − 6035.65 2126.362 171.30 − 3418.3 − 3951.1 8057.3 − 6077.5 2119.5 2330.2 − 1106.1 23269 − 47946 − 6970.2 1523.8 − 205.0 52.462 891.72 944.19 − 1508.2 78.399 1847.5 − 4287.2 1401.6 − 15267 − 365.67 3097.3 − 14282 6948.8 − 5024.6 4306.5 − 9390.8 1153.8 8224.2 − 2932.4 760.76 − 11992 − 14428

23386 − 4829.1 7308.4 42594 − 3329.8 6163 47848 − 14.925 6608.5 19655 − 815.82 3868.3 33682 − 0.07219 4241.2 23386 − 4829.1 7308.4 − 20007 8625.6 − 2210.5 32988 1262 4315.5 31782 3264.6 4498.9 34752 1460.4 4591.1 30261 4426.2 6438.275 25066 4584.638 6555.408 22381 4830.484 4335.752 11510 5931.2 6578.8 28486 6812.3 5881.5 21344 3817.7 − 1231.4 108688 6108.6 6362.9 21426 − 8983.8 5247.8 20062 10730 3652.6 19763 9245.0 3374.0 − 11014 2295.0 5001.3 − 25565 9072.3 − 8875.7 31086 6075.2 6480.6 21548 − 2838.6 647.03 8540.5 23420

10215 − 3.3105 480.26 8975.1 20517 3329.7 60001 15023 2421.4 22659 9819.2 1870.1 15075 − 0.14571 915.73 10215 − 3.3105 480.26 22445 19053 14855 2845.1 18876 1584.1 4834 18056 1355.7 5893.8 20040 1519.4 3607.5 19261 851.6661 7267.3 15155.35 589.8909 10626 − 9897.93 866.9695 − 2283.8 − 15813 857.61 1661.0 − 25565 791.38 7736.2 − 14231 22629 8879.6 28423 818.54 6003.4 555.48 1223.3 7035.7 19284 1091.8 9855.8 15165 1966.9 − 6128.3 12305 − 139.16 4836.0 30123 − 1.7915 4407.0 − 29777 580.79 10120 − 6230.3 − 22481 − 2152.9 1262.4

9570.7 19571 − 5920.7 − 15138 9150 − 1871.9 − 15005 − 9239.2 − 1815.8 2078.9 − 8412.6 − 619.02 − 9680.9 13358 − 1029.1 9570.7 19571 − 5920.7 − 1087.2 951.42 − 4651.5 − 7883.7 − 11234 − 838.85 − 6796.7 − 10975 − 834.98 − 9254.5 − 14031 − 1112.4 − 6620.1 18308 − 1179.61 − 2748.4 14605.36 − 1155.27 − 706.26 8769.548 − 2834.97 − 4470.2 9814.4 − 1276.5 − 4764.0 12625 − 898.42 1113.6 − 6757.6 19556 − 84224 26949 − 1285.0 − 2297.1 1785.0 − 1753.0 3567.0 19195 − 523.63 5285.7 15118 − 312.47 − 8253.2 24217 − 6181.7 − 1731.6 31938 385.02 − 7231.8 18016 − 808.00 − 592.28 − 5881.2 33061 8994.2 15726

0.3 0.3 – 0.1 0.1 – 0.1 0.1 – 0.35 0.3 – 0.1 0.1 – 0.3 0.3 – 0.16 0.1 – 0.1 0.1 – 0.12 0.12 – 0.1 0.1 – 0.1 0.1 – 0.15 0.15 – 0.2 0.35 – 0.05 0.3 – 0.1 0.2 – 0.2 0.5 – 0.1 0.05 – 0.15 0.3 – 0.25 0.1 – 0.3 0.15 – 0.05 0.1 – 0.05 0.05 – 0.1 0.1 – 0.2 0.5 – 0.2 0.05

A. Haghtalab, A. Paraj / Journal of Molecular Liquids 171 (2012) 43–49

47

Table 4 (continued) System no.

26

27

28

29

30

31

32

33

34

35

36

Model

UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC NRTL NRTL-NRF UNIQUAC

Δgij (for NRTL and NRTL-NRF) or Δuij (for UNIQUAC) (j/mol) 1–3

2–1

2–3

3–1

3–2

− 2503.9 − 2776.9 − 12726 − 442.83 − 347.98 − 4476.5 − 2183.8 − 4405.6 − 4853.5 26477 − 3261.4 3444.0 14788 10855 − 3099.1 − 795.89 − 3997.5 − 6137.5 − 2921.0 1512.1 11090 − 317.57 − 1011.5 19938 3018.2 1226.6 25622 1774.6 − 2275.9 42582 1879.3 − 7872.9 5171.5 2090.6

− 1600.5 13892 − 2647.0 1814.0 12976 0.0000 1782.6 20203 7117.8 − 2311 − 53.937 5221.1 − 3393.3 15710 6937.1 1778.2 15468 14759 2074.7 18987 − 12798 2241.8 17490 4382.0 2348.5 15302 9634.0 1573.4 19326 6808.9 217.16 11527 − 8221.2 2803.6

6152.7 − 81.674 0.00058 − 441.30 8333.5 − 11144 − 2291.8 − 6395.3 9914.0 29875 − 9277.3 − 1476.6 18954 4351.0 − 9722.6 − 7371.6 4776.8 − 14280 − 2906.5 − 6856.6 5480.4 − 8952.2 − 2272.6 5179.0 − 4033.7 − 263.87 3510.3 − 6404.4 − 330.20 13060 9640.1 3180.0 11567 − 3694.2

− 8862.4 17041 6642.2 3422.0 13178 0.0000 − 535.96 19986 2800.5 − 1473.6 − 10199 191.03 177.28 11069 6499.4 − 200.50 9170.7 12503 − 236.49 4118.9 − 8213.6 − 5045.2 562.23 4593.1 1048.3 1968.1 6658.6 − 3757.1 − 2923.8 10821 9261.3 7233.3 − 14362 − 2738.8

50639 3717.9 − 0.00065 − 149.15 4934.7 24505 1181.0 1761.2 13311 8621.3 − 65.498 6703.4 20482 12682 − 19938 3212.5 11392 − 26639 2469.3 7617.3 10734 3456.5 6513.1 8556.6 2208.1 5529.4 8063.2 1371.4 3854.5 16865 1838.8 3987.0 15297 − 274.89

− 44570 − 1234.9 10297 − 1145.9 − 623.04 1057.2 − 1997.9 2064.0 5881.0 9860.5 549.46 4903.2 4909.3 9958.6 − 9864.2 − 2525.7 − 3286.1 12761 − 1608.8 − 5246.3 11425 261.86 − 1606.5 8266.6 − 1742.8 − 403.41 28952 − 2698.1 1880.8 12833 1452.7 − 10788 − 11634 − 2186.8

were taken from the literature as shown in Table 3. The values r and q for some compounds are not available in literature; hence, they are calculated using the following relations [38]: r i ¼ 0:029281vm ðz−2Þr i 2ð1−li Þ þ qi ¼ z z

αij

1–2

ð4Þ

where vm is molar volume of pure component i at 298.15 K. A value of 10 is used for coordination number z, and bulk factor, li, is set to 1 and also for cyclic molecules li = 1. The values of the interaction parameters for the three local composition models are represented in Table 4, and the values of the corresponding standard deviation are given in Table 2.

Benzene (2) + [emim][eSO4] (3)} and {Nonane (1) + Toluene(2) + [empy][eSO4]}. In each figure, the results of a more suitable model with less rmsd value from Table 4 are depicted. It is easy to see that there is a good agreement between the experimental and calculated liquid phase compositions especially for those results are obtained by the NRTL-NRF model. From the rmsd values and visual analysis of the figures, it can be concluded that all the models are able to correlate liquid–liquid equilibrium of the ternary systems including ionic liquids with good precision but the results of the NRTLNRF model is more satisfactory. In addition, these results indicate

A NRTLNRF-model Experimental

3. Results and discussion As one can see from Tables 2 and 4 and Figs. 2, 3 and 4, the results of correlation are very satisfactory and in very good agreement with the experiments. The rmsd values for each of the LLE ternary systems with the overall rmsd values for the three models, NRTL, UNIQUAC and NRTL-NRF, are shown in Table 2. While maximum rmsd value for the NRTL, UNIQUAC and NRTL-NRF models are 4.77, 5.06 and 3.35, respectively, the overall rmsd values for the three models are 1.85, 2.18 and 1.05, respectively. Among the 32 investigated systems, the UNIQUAC model results the minimum rmsd value for only the six systems while the NRTL model is more suitable for only the seven systems. For the remaining 23 systems, NRTL-NRF presents the best results. In this work using the NRTL-NRF model, the rmsd values are always below 1.65% and, in most cases, about 1% with an overall value of about 1.05%. As shown in Figs. 2, 3 and 4, comparisons among experimental and calculated tie-lines are presented for the systems {Hexane (1) + Benzene (2) + [bmim][mSO4] (3)}, {Hexane (1) +

– 0.3 0.2 – 0.4 0.05 – 0.4 0.5 – 0.5 0.5 – 0.4 0.3 – 0.4 0.1 – 0.2 0.3 – 0.2 0.4 – 0.3 0.4 – 0.2 0.1 – 0.5 0.1 –

0.2

0.8

0.4

0.6

0.6

0.4

0.8

B

0.2

0.2

0.4

0.6

0.8

C

Fig. 2. Experimental and calculated LLE for the hexane (A), benzene (B), [bmim][mSO4] (C) system at 298.15 K.

48

A. Haghtalab, A. Paraj / Journal of Molecular Liquids 171 (2012) 43–49

A

excess Gibbs energy [8] is written as: UNIQUAC-model Experimental

0.2

E ∑j xj τji Gji g ¼ ∑ xi RT i  ∑k xk G ki Gij ¼ exp −α ij τij g ij −g jj Δg ij ¼ τ ij ¼ RT RT

0.8

0.4

0.6

0.6

0.4

0.8

ðA  1Þ

where gij is a characterizing energy parameter that specifies interaction between species i and j and parameter αij = αji is related to non-randomness in a mixture so that it can be treated as an adjustable parameter.

0.2

A.2. The UNIQUAC model

B

0.8

0.6

0.4

0.2

C

Fig. 3. Experimental and calculated LLE for the hexane (A), benzene (B), [emim][eSO4] (C) system at 298.15 K.

that using the non-randomness state (NRF) for reference state in development of local composition models is a suitable assumption in applying for ionic liquid systems. 4. Conclusion Calculation of the ternary liquid–liquid equilibrium was performed for the 36 systems including 12 types of ionic liquids using the NRTL, UNIQUAC and NRTL-NRF activity coefficient models. Although the results of all the models are satisfactory but the overall rmsd value of the NRTLNRF model is significantly superior to the other known local composition models namely NRTL and UNIQUAC, with overall rmsd values of 1.05. Finally, it was demonstrated that the NRTL-NRF model is overally more appropriate for calculation of thermodynamic properties of ionic liquid solution, even in very small quantities of ionic liquid. Appendix A A.1. The NRTL model The NRTL model generally predicts large heat of mixing that is characteristic of electrolyte solutions [5]. The NRTL model for molar A

0.8

0.4

0.4

0.8

0.2

C 0.2

′

θj¼

q′ i xi ∑k q′ k xk ðA  2Þ

The parameters r, q and q' are molecular structure parameters of a pure component, representing volume and surface areas, respectively. For most of substances, q = q', except for water and some small alcohols. Coordination number, z, is fixed as 10. A.3. The NRTL-NRF model

0.6

0.6

B

! ! gE gE gE ¼ þ RT RT RT comb !  res  E g ϕ z θ ¼ ∑i xi ln i þ ∑ qi xi ln i 2 i RT xi ϕi !comb   gE ′ ′ ¼ − ∑i q i xi ln ∑j θ j τ ji RT res     uij −ujj Δuij ¼ exp − τ ij ¼ exp − RT RT ri xi qi xi ϕi ¼ θi ¼ ∑k r k xk ∑k qk xk

Haghtalab and Vera [40] proposed the NRTL-NRF model for mean activity coefficient of binary aqueous electrolyte systems. For this model, the random state of species is considered as a reference state and non-random factor, Г, is used to show deviation of local composition from bulk composition. The molar excess Gibbs free energy for a multicomponent mixture based on the NRTL-NRF model is given as [20]:

NRTL-model Experimental 0.2

The UNIQUAC model for the excess Gibbs energy, g E, consists of two parts: a combinatorial or entropic contribution, which accounts for molecular size and shape effects, and a residual or enthalpic contribution, that accounts for energy interaction effects [9]. Thus, the molar excess Gibbs equation has presented as [39]

0.4

0.6

0.8

Fig. 4. Experimental and calculated LLE for the nonane (A), toluene (B), [empy][eSO4] (C) system at 298.15 K.

  gE ¼ ∑ ∑ xi xj τji Γ ji −1 RT i j Gij Γ ij ¼ ∑k xk Gkj   Gij ¼ exp −α ij τ ij g ij −g jj Δg ij ¼ τ ij ¼ RT RT

ðA  3Þ

where gij, αij and Гij are Gibbs interaction energy, non-randomness and non-random factor, respectively, between species i and j. Parameter τij is a binary adjustable energy parameter of the NRTL-NRF model.

A. Haghtalab, A. Paraj / Journal of Molecular Liquids 171 (2012) 43–49

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