Prediction of liquid−liquid equilibria of (aromatic + aliphatic + ionic liquid) systems using the Cosmo-SAC model

J. Chem. Thermodynamics 49 (2012) 62–69

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Prediction of liquidliquid equilibria of (aromatic + aliphatic + ionic liquid) systems using the Cosmo-SAC model Mitesh R. Shah, Ganapati D. Yadav ⇑ Department of Chemical Engineering, Institute of Chemical Technology,1 Nathalal Parekh Marg, Matunga, Mumbai 400019, India

a r t i c l e

i n f o

Article history: Received 15 July 2011 Received in revised form 17 November 2011 Accepted 11 January 2012 Available online 24 January 2012 Keywords: Cosmo-SAC Ionic liquids liquidliquid equilibrium Aromatics Extraction

a b s t r a c t The extraction of aromatic hydrocarbons from aliphatic hydrocarbons is an important problem. This process can be used to enhance the capacity of ethylene crackers by prior removal of aromatics that cannot be cracked. Ionic liquids have been investigated extensively for liquid–liquid extraction of aromatics from aliphatics. The choice of a suitable ionic liquid may be made by measuring liquidliquid equilibria. However, the large number of ionic liquids, formed by the various cation and anion combinations, makes the experimental measurements expensive and time consuming. Hence, a predictive thermodynamic model called Cosmo-SAC that uses quantum chemical calculations for calculating liquidliquid equilibria has been evaluated. A priori predictions are accurate for some ionic liquids and inaccurate for some ionic liquids. However, it has been shown that even when a priori predictions are inaccurate, the data can be correlated using a single parameter that is characteristic of the ionic liquid and accurate predictions can be made for additional aromatic/aliphatic combinations for the same ionic liquid. A comparison with the NRTL and UNIQUAC models has also been carried out. In addition, a preliminary screening of ionic liquids for aromatic/aliphatic separations has been carried out using the Cosmo-SAC model. Finally, the ‘‘Cosmo’’ files for eight cations and sixteen anions corresponding to 128 potential ionic liquids have been provided for the use of the general scientific community to predict any thermodynamic equilibria involving ionic liquids without the use of any molecular modeling software. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction The separation of aliphatic and aromatic hydrocarbons is an important problem [1]. A potential application is the removal of aromatics from the feed of ethylene crackers. Ethylene cracker feeds normally contain 10% to 25% aromatics. These aromatics are not cracked and act as an additional load on the cracker. By removing these aromatics from the feed, the load on the cracker can be reduced and greater quantities of the aliphatics can be processed. Abbreviations: mmim, 1,3-Dimethylimidazolium; emim, 1-Ethyl-3-methylimidazolium; bmim, 1-Butyl-3-methylimidazolium; hmim, 1-Hexyl-3-methylimidazolium; 4-mebupy, 1-n-Butyl-4-methylpyridinium; 3-mebupy, 1-n-Butyl-3methylpyridinium; 2-mebupy, 1-n-Butyl-2-methylpyridinium; N-epy, 1-ethylpyridinium; EtSO4, ethylsulfate; DCA, dicyanamide; MeSO4, methylsulfate; Tf2N, bis(trifluoromethylsulfonyl)imide; PF6, hexafluorophosphate; BF4, tetrafluoroborate; SCN, thiocyanate; tosylate, p-Toluenesulfonate; OcSO4, octylsulfate; CF3SO3, trifluorosulfonate; FAP, tris(pentafluoroethyl)trifluorophosphate; CF3COO, trifluoroacetate; B(CN)4, tetracyanoborate; C(CN)3, tricyanomethane. ⇑ Corresponding author. Tel.: +91 22 3361 1001; fax: +91 22 3361 1002/1020. E-mail addresses: [email protected], [email protected] (G.D. Yadav). 1 Institute of Chemical Technology (ICT) was formerly the University of Mumbai Institute of Chemical Technology (UICT), now a separate university. 0021-9614/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2012.01.012

Several aliphatic and aromatic hydrocarbons have boiling temperatures in a close range and some combinations even form azeotropes. Hence, their separation is challenging. Conventionally, the separation is carried out by liquid–liquid extraction using a solvent like sulfolane [2–7], N-methylpyrrolidone [8], ethylene glycols [9,10], propylene carbonate [11], or N-formylmorpholine [7,12,13]. However, the use of these solvents necessitates additional distillation and purification steps for separation of the extracting solvents resulting in additional costs. Ionic liquids are an important class of compounds that can be used for the separation of aromatic hydrocarbons from aliphatic hydrocarbons by liquid–liquid extraction. These solvents have negligible vapor pressure and can be readily separated from the extracted aromatics. It has also been shown in the literature that this process can be economical at a reasonable price of the ionic liquid if the ionic liquid is produced in large quantities [14,15]. However, there are a large number of ionic liquids formed by various combinations of cations and anions. Further, the separation capacity and the selectivity depend upon the concentration of the aromatics in the feed and the amount of ionic liquid used. The separation capacity and the selectivity also depend upon the particular aromatic and aliphatic compounds being investigated. Investigation of liquidliquid equilibria (LLE) for the large number

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of ionic liquids for the various aliphatic/aromatic combinations over the entire concentration range is a formidable task. Significant work has been done in this direction [1,16–24]. However, there still remain several aromatic/aliphatic/ionic liquid combinations that have not been investigated. Experimental measurements are expensive and time consuming. An alternative is to use thermodynamic models to predict the liquidliquid equilibria of the (aromatic + aliphatic + ionic liquid) ternary systems. However, conventional group contribution methods like UNIFAC cannot be used for this purpose as the required parameters are not available for most ionic liquids. Recently a new method called Cosmo-SAC has been proposed that can predict thermodynamic equilibria without any group contribution parameters or experimental data [25,26]. The method is a variant of the more popular Cosmo-RS model [27,28] and only requires quantum chemical calculations followed by the application of a thermodynamic model. It can handle variation in concentration as well as temperature. The Cosmo-RS model has been applied to a wide range of vapor – liquid equilibria and liquidliquid equilibria involving ionic liquids [29–45]. Diedenhofen and Klamt [46] have also reviewed the prediction of phase equilibria involving ionic liquids using the Cosmo-RS. In comparison, there has been significantly less work on the evaluation of the Cosmo-SAC model for phase equilibria involving ionic liquids. The most notable references are the papers by Yang et al. [47], Shimoyama and Ito [48], Shah and Yadav [49] and Yang et al. [50]. However, unlike the Cosmo-RS model, whose equations are hidden in proprietary software, the equations of the CosmoSAC model are available in the open literature. Hence, the Cosmo-SAC model is considered in this work. The aim of this work is to evaluate the Cosmo-SAC model as a predictive model for the separation of aromatic and aliphatic hydrocarbons using ionic liquids. Further, the liquidliquid equilibria for additional systems have been predicted so as to screen additional ionic liquids. In addition to a priori predictions, the ability of the Cosmo-SAC model to correlate the experimental data has also been evaluated and the performance of the Cosmo-SAC model has been compared with the NRTL [51] and UNIQUAC [52] models. Further, the results of the quantum chemical calculations have been provided in the form of ‘‘Cosmo’’ files in the supplementary data for eight cations and sixteen anions corresponding to 128 potential ionic liquids for the use of the general scientific community to predict any thermodynamic equilibria involving ionic liquids without the use of any molecular modeling software. 2. The Cosmo-SAC model

ps ðrÞ ¼

,

X

xi Ai pi ðrÞ

ð1Þ

X

i

xi A i ;

ð2Þ

i

where xi is the mole fraction of component i in the mixture. In the Cosmo-SAC model, the interactions between segments are based on segments of the same area. But the Cosmo quantum chemical calculations result in segments of different surface areas. Hence the screening charge densities from the Cosmo file r⁄ need to be averaged. The resulting ‘‘apparent’’ surface charge density r over a segment of standard size has to be used in the sigma profile calculation. The ‘‘apparent’’ surface charge density rm of a segment m is given by,

P



r 2 r2

n eff  n rm r 2 þr 2 exp f decay n

rm ¼ P



d2mn r 2n þr 2 eff

eff

r 2n r2eff

n r 2n þr 2 eff



   ; 2 mn exp f decay r2dþr 2 n

ð3Þ

eff

where rn is the radius of segment n (rn ¼ fAi ðrn Þ=pg1=2 ), dmn is the distance between segments m and n, reff is the effective radius (r eff ¼ faeff =pg1=2 ), aeff is the surface area of standard segment (empirical parameter) (aeff = 0.075 nm2) and fdecay is a parameter introduced to balance atomic and metric units (fdecay = 3.57). Finally, the sigma profiles of the various components are used in a thermodynamic model to calculate the activity coefficients of the components in a given solution which can in turn be used to calculate phase equilibria. The thermodynamic model is given by the following equations,

lnðci Þ ¼ ni

X

pi ðrm Þ½lnðCS ðrm ÞÞ  lnðCi ðrm ÞÞ þ lnðcSG i Þ;

ð4Þ

rm

" lnðCS ðrm ÞÞ ¼  ln

X

# pS ðrn ÞCS ðrn Þ expðDWðrm ; rn Þ=RTÞ ;

ð5Þ

rn

lnðCi ðrm ÞÞ ¼  ln

Both Cosmo-RS and Cosmo-SAC models are based on the Cosmo model [53]. The Cosmo model belongs to a class of dielectric continuum models. According to this approach, the solute is placed in a dielectric continuum of the solvent. As a result of the charge distribution on the solute, the adjacent solvent also gets polarized. This leads to the development of screening charges in the solvent corresponding to the charges on the solute. In the Cosmo model, the surface of the molecule is divided into segments and the screening charge density corresponding to each segment is calculated. This screening charge density and the area of each segment are provided in the ‘‘Cosmo file’’. In the Cosmo-RS and the CosmoSAC models, this three dimensional charge distribution is projected to a two dimensional histogram. This is done by calculating the probability of finding a segment having a screening charge density r. This probability distribution is known as the sigma profile and it is unique for a particular molecule. Thus we have,

pi ðrÞ ¼ Ai ðrÞ=Ai ;

where the subscript i refers to a pure component i, and pi(r) is the probability of finding a segment having a surface charge density r. Ai(r) is the total surface area with a surface charge density r and Ai is total surface area of the cavity formed by the solute. For most compounds the screening charge density falls between (2.5 and 2.5) e/nm2. In order to calculate the sigma profile, this interval is partitioned into 50 parts and the histogram of the averaged charge density is computed at each 0.1 e/ nm2 increment. The above equation gives the sigma profile for a single solute. The sigma profile of a mixture is given by a weighted average of the sigma profiles of the individual components. Thus we have,

" X

# pi ðrn ÞCi ðrn Þ expðDWðrm ; rn Þ=RTÞ ;

ð6Þ

rn

0 1 3 0:3a2eff @ Aðrm þ rn Þ2 DWðrm ; rn Þ ¼ f pol 2o þ C hb max½0; racc  rhb  min½0; rdon þ rhb ;

ð7Þ

where racc and rdon are the larger and smaller values of rm and rn

lnðcSG i Þ ¼ ln

hi ¼ xi qi

    /i z hi / X þ ln þ li  i xj l j ; 2 xi /i xi j

, X

, xj qj ;

/i ¼ xi r i

j

ri ¼ V i =r;

qi ¼ Ai =q;

X

xj r j ;

ð8Þ

ð9Þ

j

ð10Þ

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li ¼

z ðr i  qi Þ  ðri  1Þ; 2

ð11Þ

where ni is the total number of segments in component i (ni = Ai/aeff), aeff is the standard surface segment area (empirical parameter) (aeff = 0.075 nm2), R is the universal gas constant, T is the temperature, fpol is an empirical parameter (fpol = 0.64), e0 is the permittivity of vacuum (e0 = 2.395  103 (e2  mol)/(kcal  nm)), Chb is an empirical parameter (Chb = 8.558 (kcal/mol)  (nm 4/e2)), rhb is the cutoff value for hydrogen bonding interactions (rhb = 0.84 e/ nm2), Vi is the total volume of the cavity formed by a molecule of component i (obtained from the Cosmo file), r is the standard volume parameter (r = 0.06669 nm3), q is the standard area parameter (q = 0.7953 nm2) and z is the coordination number (z = 10). Equations (1), (2), (4) to (11) are solved to obtain the activity coefficient of a particular component in a liquid mixture. Equations (5) and (6) are solved iteratively. The rest of the equations can be solved by simple substitution. The above model is the version of Cosmo-SAC originally proposed in 2002 [25] and is henceforth referred to as the CosmoSAC 2002 model. A modified version of this model was proposed in 2007 with a different expression for hydrogen bonding [26]. This modified model is henceforth referred to as the Cosmo-SAC 2007 model. In the Cosmo-SAC 2007 model, two sigma profiles are constructed for each molecule, a hydrogen bonding sigma profile and a non-hydrogen bonding sigma profile, on the basis of the atoms involved in hydrogen bonding. The hydrogen bonding and the nonhydrogen bonding sigma profiles are then used in the modified version of the above equations as given below,

lnðci Þ ¼ ni

nhb;hb X

X

s

rm

pi ðrsm Þ½lnðCsS ðrsm ÞÞ  lnðCsi ðrsm ÞÞ þ lnðcSG i Þ; "

lnðC

t Sð

r

t m ÞÞ

¼  ln

nhb;hb X

X

s

rn

# s nÞ

ps ðr C

s Sð

s n Þ expðDWð

r

t m;

r r

s n Þ=RTÞ

t ¼ nhb; hb;

lnðC

r

t m ÞÞ

¼  ln

nhb;hb X

X

s

rn

# s nÞ

pi ðr C

s ið

r

s n Þ expðDWð

t m;

r r

s n Þ=RTÞ

t ¼ nhb; hb;

t m;

DWðr

;

ð13Þ "

t ið

ð12Þ

;

ð14Þ

s nÞ

r ¼ f pol

3 ! 0:3a2eff ðrtm þ rsn Þ2  Chb ðrtm ; rsn Þ2 ðrtm ; rsn Þ2 220

ð15Þ C hb ðrtm ; rsn Þ ¼

lnðcSG i Þ ¼ ln , hi ¼ xi qi



C hb ; if s ¼ t ¼ hb; rtm  rsn < 0; 0;

otherwise;

    /i z hi / X þ ln þ li  i xj lj ; 2 xi /i xi j

X

, xj q j ;

/i ¼ xi r i

j

r i ¼ V i =r; li ¼

qi ¼ Ai =q;

z ðr i  qi Þ  ðri  1Þ; 2

X

xj r j ;

ð16Þ

ð17Þ

ð18Þ

j

ð19Þ ð20Þ

where the superscripts hb and nhb refer to quantities pertaining to the hydrogen bonding and non-hydrogen bonding components respectively. The values of aeff and Chb are taken as 0.0725 nm2 and 0.348442 (kcal/mol)  (nm4/e2) respectively. The values of the

other parameters remain the same as in the Cosmo-SAC 2002 model. The above description is a brief overview of the Cosmo-SAC models. For more details, the reader is directed to the original papers pertaining to the Cosmo-RS and the Cosmo-SAC models [25,26,28] and the paper by Mullins et al. [54].

3. Computational details In order to carry out the quantum chemical calculations, we have used the Dmol3 module in Accelrys Materials Studio [55]. The first step in the quantum chemical calculations involves the geometry optimization of the molecule to its lowest energy configuration using density functional theory. In order to carry out the optimization, the GGA/VWN-BP functional setting and the DNP v4.0.0 basis set are used as proposed by Mullins et al. [54]. Here, GGA represents the generalized gradient approximation, and VWN-BP represents the Becke–Perdew version of the Volsko– Wilk–Nusair functional. The convergence criteria for energy, maximum force and maximum displacement are set to 1.0exp6 Ha, 0.02 Ha/nm and 0.0005 nm respectively. After the geometry optimization, an energy calculation is carried out using the same parameters as the geometry optimization. A ‘‘Cosmo’’ file is simultaneously generated by inserting the corresponding keywords and providing the necessary parameters in the input file for the energy calculation. An example of such an input file is provided in the supplementary data. Detailed step-by-step instructions for the quantum chemical calculations using Dmol3 can also be found in the paper by Mullins et al. [54] and the website maintained by the Liu research group [56]. The website of the Liu research group also provides the ‘‘Cosmo’’ files for several common compounds. The ‘‘Cosmo’’ files for the aromatic and aliphatic hydrocarbons used in this work are obtained from this database. The ‘‘Cosmo’’ files for the ionic liquid cations and anions have been generated by us and have been provided in the supplementary data. After the generation of the ‘‘Cosmo’’ files, the sigma profiles for the molecules have been obtained from equations (1) and (3). In the case of the Cosmo 2007 model, two sigma profiles have been created corresponding to the hydrogen bonding and non-hydrogen bonding components. In order to generate these sigma profiles, suitable atoms of the cations and anions have been considered as part of the hydrogen bonding and non-hydrogen bonding component. The selection of these atoms and the corresponding atom numbers of these atoms, as reported in the ‘‘Cosmo’’ file, have been provided in the supplementary data. In the case of ionic liquids, the quantum chemical calculation for the entire molecule comprising of the cation and the anion is computationally intensive. It also results in erroneous results as reported by Yang et al. [47]. An alternative approach called the metafile approach has been suggested by Banerjee et al. [36]. In this approach, quantum chemical calculations are carried out separately for the cation and the anion. The composite sigma profile of the ionic liquid is then computed by simply adding the sigma profiles of the corresponding cation and anion. An additional advantage of this method is that a small number of quantum chemical calculations can be carried out to compute the sigma profiles of a large number of ionic liquids. For example, the generation of ‘‘Cosmo’’ files of 10 cations and 10 anions would enable calculations for 100 ionic liquids. The same calculations by assuming a single ionic liquid molecule would require the generation of 100 ‘‘Cosmo’’ files. Once the sigma profiles have been generated, the activity coefficients are calculated from the sigma profiles using the equations in Section 2. Finally, the Rachford–Rice algorithm [57] is used to compute the tie lines of the ternary liquidliquid equilibria.

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fails for very high concentration of aromatics. However, such high concentrations are seldom encountered in practice. These shortcomings are evident from figure 1b.

4. Results and discussion 4.1. Evaluation of the Cosmo-SAC model for a priori prediction Predictions have been carried out using the Cosmo-SAC 2002 model for twelve different ionic liquids for which ternary liquidliquid equilibrium data is available in the literature. These systems cover a wide range of cations and anions. The list of the (ionic liquid + aromatic + aliphatic) systems that have been studied along with the temperature range of the data have been provided in table 1. The root mean square deviation in the predicted mole fractions from the experimental data (DxRMSD) has also been provided in table 1. DxRMSD is given by the following equation,

DxRMSD ¼

( XX X

)1=2 ðxpred  xexpt Þ2 =ndat  nph  ncomp

;

ndat nph ncomp

ð21Þ where xpred is the predicted mole fraction, xexpt is the experimental value of the mole fraction, ndat is the number of data points, nph is the number of phases (nph = 2) and ncomp is the number of components (ncomp = 3). The tie-line data for two systems along with the predictions has also been shown as a ternary diagram in figure 1. It can be seen that there is good agreement between the experimental and predicted data for these systems. Further, the variation of the aromatic partition coefficient and selectivity for the {[bmim][Tf2N] + benzene + n-hexane} system has been shown in table 2. It can be seen that the Cosmo-SAC model can accurately predict the effect of variation in concentration on the partition coefficient and selectivity for this system. The experimental and predicted liquidliquid equilibrium data for the remaining systems have been provided in the supplementary data in the form of ternary diagrams. On the basis of visual observation of the ternary diagrams, a value of DxRMSD < 0.04 was set as the criterion for successful prediction. It should be noted that this criterion for successful prediction is somewhat arbitrary and the reader is referred to the actual ternary diagrams in the supplementary data for a clearer picture of the accuracy of the model for the various systems. From the values of DxRMSD in table 1, it is evident that the predictions of the Cosmo-SAC 2002 model are reasonably good for the first eight ionic liquids but the model is inaccurate for the remaining four ionic liquids. This indicates that, though this model is accurate in several cases and can be used to provide pointers for the selection of the ionic liquid, it is not completely reliable for predicting ternary liquidliquid equilibrium data. It should be noted, however, that even when the model is successful, it sometimes slightly overpredicts the solubility of the aliphatic hydrocarbon and hence underpredicts the selectivity. Sometimes the model also predicts a lower plait point and hence

4.2. Correlation of data using Cosmo-SAC and subsequent predictions Since the Cosmo-SAC model is not always accurate in a priori predictions of the ternary LLE data, we tried to correlate the data using a minimum number of parameters and predict the behavior of additional systems on the basis of the derived parameters. The first step is the choice of the adjustable parameters. In the Cosmo-SAC model, Chb is an empirical parameter and a measure of the strength of the hydrogen bonds. While this parameter was treated as a constant in the earlier versions of the Cosmo-SAC model, it has been recently proposed that this parameter depends on the nature of the interacting functional groups [58]. In our case, hydrogen bonding occurs only between the cation and anion of the ionic liquid as the aromatic and aliphatic hydrocarbons do not participate in hydrogen bonding. Hence Chb can be treated as a characteristic of the ionic liquid. We first tried to correlate the experimental data by varying Chb in the Cosmo-SAC 2002 model. But our efforts were unsuccessful. We therefore decided to apply the Cosmo-SAC 2007 model which has a more fundamentally sound expression for hydrogen bonding. In the case of the Cosmo-SAC 2007 model, the empirical parameter Chb is a measure of the contribution of the hydrogen bonding sigma profile. In order to investigate the effect of Chb, the value of Chb has been varied and the corresponding changes in the ternary diagram have been observed. In figure 2 we have shown the variation in the predicted tie lines with the value of Chb for the {[4-mebupy][BF4] + benzene + n-hexane} system. As the value of Chb increases, the hydrogen bonding contribution increases, bonding between cations and anions is stronger as compared to bonding between the ions and the aromatic component. As a result, the solubility of the aromatic hydrocarbons in the ionic liquid decreases. This is in agreement with our predictions as shown in figure 2. Similar results have also been obtained for the {[bmim][MeSO4] + benzene + n-hexane} and {[hmim][BF4] + benzene + n-heptane} systems. The experimental data for several aromatic/aliphatic/ionic liquid combinations have been investigated using the Cosmo-SAC 2007 model. It has been found that the experimental data can be fitted very well using this model by using Chb as the fitting parameter. Figure 3 shows the correlation of the data for {[4-mebupy][BF4] + benzene + n-hexane} system using a single parameter Chb. Since the value of Chb is expected to be a characteristic of the ionic liquid, the derived value of Chb should not change with the aromatic/aliphatic combination. Hence the LLE for the {[4-mebupy][BF4] + toluene + n-heptane} and {[4-mebupy][BF4] + ethylbenzene + n-octane} systems have been predicted using the value

TABLE 1 Comparison of Cosmo-SAC 2002 predictions with experimental data.

a

Sr. No.

Ternary system

T/K

1 2 3 4 5 6 7 8 9 10 11 12

{[emim][EtSO4] + toluene + n-heptane} {[3-mebupy][DCA] + toluene + n-heptane} {[bmim][DCA] + toluene + n-heptane} {[mmim][MeSO4] + toluene + n-heptane} {[emim][Tf2N] + benzene + n-hexane} {[bmim][Tf2N] + benzene + n-hexane} {[N-epy][Tf2N] + benzene + n-hexane} {[bmim][PF6] + benzene + cyclohexane} {[4-mebupy][BF4] + benzene + n-hexane} {[bmim][MeSO4] + benzene + n-hexane} {[hmim][BF4] + benzene + n-heptane} {[bmim][SCN] + toluene + n-heptane}

313.15 303.15 303.15 313.15 298.15 298.15 313.15 298.15 313.15 298.15 298.15 303.15

Reference containing the experimental data.

to to to to to

348.15 328.15 328.15 348.15 313.15

to 318.15

DxRMSD

Referencea

0.032 0.011 0.017 0.020 0.035 0.018 0.040 0.022 0.054 0.061 0.089 0.045

[16] [17] [17] [16] [18] [19] [20] [21] [22] [23] [24] [17]

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M.R. Shah, G.D. Yadav / J. Chem. Thermodynamics 49 (2012) 62–69

FIGURE 1. Comparison of experimental data and Cosmo-SAC 2002 predictions for the {[3-mebupy][DCA] + toluene + n-heptane} system at 303.15 K and {[emim][Tf2N] + benzene + n-hexane} system at 298.15 K. Filled squares and solid lines, experiments; filled triangles and dashed lines, model predictions.

TABLE 2 Prediction of the variation of aromatic partition coefficient (Darom) and selectivity with concentration for benzene(1)/n-hexane(2)/[bmim][Tf2N](3) Overall compositiona

a

T/K

z1

z2

0.055 0.13 0.2 0.28 0.36 0.47 0.55 0.63

0.5 0.5 0.4 0.4 0.4 0.3 0.25 0.2

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15

Darom (molar)

Selectivity

Experimental

Predicted

Experimental

Predicted

1.79 1.66 1.51 1.43 1.26 1.09 1.02 0.95

1.70 1.57 1.47 1.34 1.23 1.12 1.05 0.99

17.39 15.89 14.65 12.92 10.31 8.95 7.20 5.42

14.86 13.00 11.52 9.66 7.89 5.96 4.65 3.48

Molar composition of the overall ternary mixture before phase splitting.

FIGURE 2. Effect of the parameter Chb on the ternary LLE predictions of Cosmo-SAC 2007 for the {[4-mebupy][BF4] + benzene + n-hexane} system at 313.15 K. Filled squares and solid lines, Chb = 320; filled triangles and dashed lines, Chb = 150; filled diamonds and dotted lines, Chb = 450.

FIGURE 3. Correlation of ternary LLE data for the {[4-mebupy][BF4] + benzene + nhexane} system using the Cosmo-SAC 2007 model. Filled squares and solid lines, experiments; filled triangles and dashed lines, model predictions.

of Chb derived from the {[4-mebupy][BF4] + benzene + n-hexane} system. Figure 4 shows the predicted and experimental tie lines for these systems. It can be seen that there is very good agreement between the experimental and predicted data for the {[4-mebupy][BF4] + toluene + n-heptane} system even though the data is at a different temperature from that of the {[4-mebupy][BF4] + benzene + n-hexane} system. The agreement for the {[4-mebupy][BF4] + ethylbenzene + n-octane} system is, however, only moderately good. Similarly, the data for {[bmim][MeSO4] + benzene + n-hexane} has been correlated and used for prediction of the data for {[bmim][MeSO4] + toluene + n-heptane}. Good agreement has been obtained between the experimental and

predicted data. The data for {[hmim][BF4] + benzene + n-heptane} and {[bmim][SCN] + toluene + n-heptane} have also been correlated successfully. The values of DxRMSD for all of these systems have been provided in table 3. It can be seen that, except in the case of {[4-mebupy][BF4] + ethylbenzene + n-octane}, the experimental data for various aliphatic/aromatic combinations can be successfully correlated using a single parameter that is characteristic of the ionic liquid. Predictions for additional systems involving a given ionic liquid can also be made using the derived parameter. To put this into perspective, the NRTL and UNIQUAC models require 14 and 8 adjustable parameters respectively to correlate the experimental data at different temperatures for a single

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M.R. Shah, G.D. Yadav / J. Chem. Thermodynamics 49 (2012) 62–69

FIGURE 4. Comparison of experimental data and Cosmo-SAC 2007 predictions for the {[4-mebupy][BF4] + toluene + n-heptane} and the {[4-mebupy][BF4] + ethylbenzene + n-octane} systems. Filled squares and solid lines, experiments; filled triangles and dashed lines, model predictions.

TABLE 3 Correlation of experimental data using the Cosmo-SAC 2007, UNIQUAC and NRTL models. Sr. No.

1 2 3 4 5 6 7 a b c

Ternary system

T/K

a

{[4-mebupy][BF4] + benzene + n-hexane} [22] {[4-mebupy][BF4] + toluene + n-heptane}a [16] {[4-mebupy][BF4] + ethylbenzene + n-octane}a [22] {[bmim][MeSO4] + benzene + n-hexane}a [23] {[bmim][MeSO4] + toluene + n-heptane}a [16] {[hmim][BF4] + benzene + n-heptane}a [24] {[bmim][SCN] + toluene + n-heptane}a [17]

313.15 313.15 to 348.15 313.15 298.15 313.15 to 348.15 298.15 303.15

DxRMSD Cosmo-SAC

UNIQUAC

NRTL

0.027 0.021b 0.04b 0.034 0.028c 0.013 0.031

0.020 0.012 0.011 0.008 0.087 0.028 0.013

0.0025 0.0100 0.0044 0.0049 0.0160 0.018 0.005

Numbers in brackets indicate the reference from which the experimental data has been taken. DxRMSD is based on the results predicted using parameter value from {[4-mebupy][BF4] + benzene + n-hexane} and not correlation. DxRMSD is based on the results predicted using parameter value from {[bmim][MeSO4] + benzene + n-hexane} and not correlation.

aromatic/aliphatic/ionic liquid combination and no predictions can be made for additional systems. Even in the case of correlation of experimental data at a single temperature, the NRTL and UNIQUAC models require 8 and 4 adjustable parameters respectively.

4.3. Comparison with UNIQUAC and NRTL In order to evaluate the ability of the Cosmo-SAC model to correlate the experimental data, the model has been compared with the UNIQUAC and NRTL models. The equations for the UNIQUAC and NRTL models have been provided in the supplementary data for reference. In the case of the UNIQUAC model, the Aspen Properties module of the AspenOne V7.0 software has been used for the regression of the experimental data. The pure component parameters ri and qi and the interaction parameters for the aromatic and aliphatic hydrocarbons are already available in Aspen Properties. The pure component parameters for the ionic liquids have been obtained from the literature. Santiago et al. [59] have calculated the values of ri and qi for [4-mebupy][BF4] and [hmim][BF4] using molecular simulations. These values have been used by us. Lei et al. [60] have calculated group contribution parameters for the calculation of ri and qi for ionic liquids using empirical correlations. The pure component parameters for the remaining ionic liquids have been calculated using their results. The aromatic/ionic liquid and the aliphatic/ ionic liquid interaction parameters have been treated as fitting parameters. Regression has been carried out using Aspen Properties. The root mean square errors (DxRMSD) have also been calculated using the model results and they have been provided in table 3. In the case of the NRTL model, the regression has already been carried out in the literature [16,17,22–24] and the corresponding

root mean square errors have been reported in table 3. It can be seen that, in general, the NRTL model performs better than the UNIQUAC model, and the UNIQUAC model, in turn, performs better than the Cosmo-SAC model. The only exceptions are the {[bmim][MeSO4] + toluene + n-heptane} system, where the Cosmo-SAC model performs better than the UNIQUAC model, and the {[hmim][BF4] + benzene + n-heptane} system, where the Cosmo-SAC model performs better than both the UNIQUAC and NRTL models. It should be noted, however, that the UNIQUAC and NRTL models use a large number of parameters and cannot be used for predictions for additional systems.

4.4. Prediction for additional systems and preliminary screening of ionic liquids Though the Cosmo-SAC model is not always accurate in predicting ternary LLE data, it can still be useful for preliminary screening of ionic liquids in cases where experimental data is not available. Therefore, the Cosmo-SAC 2002 model has been used for prediction of the partition coefficients and selectivities for 19 ionic liquids for the {toluene + n-heptane} system at 40 °C. A 15 mole percent mixture of toluene in n-heptane has been considered as this is representative of the feed of an ethylene cracker. Also, an equal number of moles of ionic liquid and the {aromatic + aliphatic} mixture have been considered. We have taken care to consider only those ionic liquids that are known to be liquid at the given temperature. The corresponding melting temperatures along with the sources have been provided in table 4. In the case of [bmim][tosylate], the melting temperature is higher than 40 °C [63]. Hence a higher temperature has been used for predictions. Unfortunately, a priori prediction of the melting temperatures of ionic liquids is

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M.R. Shah, G.D. Yadav / J. Chem. Thermodynamics 49 (2012) 62–69

TABLE 4 Predictions of aromatic partition coefficients (Darom) and selectivities for screening of ionic liquids.

a b c d e

Sr. No.

Cation

Anion

Melting temperaturea/°C

Model

T/K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

bmim bmim bmim bmim bmim bmim bmim emim emim emim emim emim emim emim emim emim N-epy N-epy 4-mebupy bmim 3-mebupy 3-mebupy

Tf2N SCN DCA MeSO4 PF6 tosylate OcSO4 Tf2N EtSO4 PF6 CF3SO3 FAP CF3COO B(CN)4 OcSO4 acetate Tf2N EtSO4 BF4 C(CN)3 C(CN)3 B(CN)4

2 Liquidc [17] Liquidc [17] 13 12 56 32 15 20 34 12 1 Liquidc [64] 13 9 20 Liquidc [20] Liquidc [65] Liquidc [16] Liquidc [1] Liquidc [1] Liquidc [1]

Cosmo-SAC 2002 Cosmo-SAC 2007 Cosmo-SAC 2002 Cosmo-SAC 2007 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2002 Cosmo-SAC 2007 Experimentd Experimentd Experimentd

313.15 313.15 313.15 313.15 313.15 353.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 303.15 303.15 303.15

Overall Compositionb z1

z2

0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.042e 0.043e 0.046e

0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.425 0.380e 0.391e 0.413e

Darom molar

Darom mass based

Selectivity

1.025 0.432 0.516 0.473 1.661 0.446 0.992 0.887 0.136 0.411 0.120 2.251 0.113 0.335 1.269 0.039 0.924 0.124 0.495 0.850 1.120 1.480

0.28 0.22 0.26 0.20 0.65 0.15 0.35 0.25 0.06 0.16 0.05 0.60 0.05 0.15 0.52 0.02 0.26 0.05 0.22 0.39 0.51 0.64

11.367 41.955 44.718 7.749 23.282 8.457 4.985 14.296 27.315 56.400 45.280 7.438 41.371 27.054 4.397 67.833 15.470 25.154 13.030 49.300 34.800 38.500

Melting temperature data was obtained from references [61–63]. Molar composition of the overall ternary mixture before phase splitting; components 1 and 2 refer to the aromatic and aliphatic components respectively. Compound is known to be a liquid on the basis of the data provided in the reference mentioned in the brackets. Experimental data from Meindersma et al. [1] Composition was reported by Meindersma et al. [1] in terms of ml. Density of ionic liquid is assumed to be 1.1 g/cm3 during conversion from ml to mole fraction.

not yet possible. Hence it is not possible to predict whether new combinations of cations and anions will form a liquid at a given temperature. The partition coefficients on mole basis and the selectivities for the various ionic liquids have been provided in table 4. The partition coefficients on mass basis have also been provided in table 4 as these are more representative of the costs associated with the ionic liquid. For the sake of comparison, the experimental values of the partition coefficients and selectivities for the three best ionic liquids from the review by Meindersma et al. [1] have also been provided. On the basis of the results in table 4, it can be seen that [bmim][PF6], [emim][FAP], [emim][OcSO4], [3-mebupy][C(CN)3], and [3-mebupy][B(CN)4] show high values of the mass based partition coefficient. However, [emim][FAP] and [emim][OcSO4] show very low selectivities and hence may not be very useful. Hence, [bmim][PF6], [3-mebupy][C(CN)3], and [3-mebupy][B(CN)4] may be considered as potentially useful ionic liquids. Of these, [bmim][PF6] is a readily available and common ionic liquid. However, it does have the drawback that it forms HF in the presence of traces of water at the moderately high temperature required for stripping of the ionic liquid.

matic/aliphatic combinations and the same ionic liquid. In comparison, it has been found that conventional models like UNIQUAC and NRTL are more accurate for correlation of the experimental data, but they cannot predict data for additional systems. The conventional models also require a large number of parameters for correlation of the data. Finally, although a priori predictions using Cosmo-SAC are not always accurate, they can be used to provide approximate pointers for the selection of the ionic liquid in the absence of experimental data. Hence, predictions have been made for several additional ionic liquids. On the basis of these predictions and experimental data from the literature, it has been concluded that [bmim][PF6], [3-mebupy][C(CN)3], and [3-mebupy][B(CN)4] are potentially useful ionic liquids for the extraction of aromatic hydrocarbons from aliphatic hydrocarbons. Acknowledgement M.R. Shah acknowledges the support from University Grants Commission, India in the form of the Dr. D.S. Kothari postdoctoral fellowship. G.D. Yadav acknowledges support from R.T. Mody Distinguished Professor Endowment and J.C. Bose National Fellowship, Department of Science and Technology, Govt. of India.

5. Conclusions Appendix A. Supplementary data The Cosmo-SAC model is an important predictive thermodynamic model, especially for systems involving ionic liquids. In this work, we have evaluated the ability of the Cosmo-SAC model for the prediction and correlation of ternary liquidliquid equilibrium data involving aromatic hydrocarbons, aliphatic hydrocarbons, and ionic liquids. It has been found that model is successful at a priori predictions only for some ionic liquids whereas it provides only qualitative agreement for others. However, even in the cases where the model is inaccurate at a priori predictions, the experimental data can be successfully correlated using a single parameter that is characteristic of ionic liquid. Further, the derived parameter can be used to make accurate predictions for additional aro-

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