Correlation of liquid–liquid equilibrium for binary and ternary systems containing ionic liquids with the tetrafluoroborate anion using ASOG

Correlation of liquid–liquid equilibrium for binary and ternary systems containing ionic liquids with the tetrafluoroborate anion using ASOG

Fluid Phase Equilibria 404 (2015) 42–48 Contents lists available at ScienceDirect Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l...

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Fluid Phase Equilibria 404 (2015) 42–48

Contents lists available at ScienceDirect

Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

Correlation of liquid–liquid equilibrium for binary and ternary systems containing ionic liquids with the tetrafluoroborate anion using ASOG Pedro A. Robles* , Luis A. Cisternas Department of Mineral Process and Chemical Engineering, University of Antofagasta, Angamos 601, P.O. Box 170, Antofagasta, Chile

A R T I C L E I N F O

A B S T R A C T

Article history: Received 2 February 2015 Received in revised form 15 June 2015 Accepted 18 June 2015 Available online 29 June 2015

Ionic liquids are neoteric, environmentally friendly solvents (since they do not produce emissions) composed of large organic cations and relatively small inorganic anions. They have favorable physical properties, such as negligible volatility and wide range of liquid existence. Liquid–liquid equilibrium (LLE) data for systems including ionic liquids, although essential for the design, optimization and operation of separation processes, are still scarce. However, some recent studies have presented ternary LLE data involving several ionic liquids and organic compounds such as alkanes, alkenes, alkanols, water, ethers and aromatics. In this work, the ASOG model for the activity coefficient is used to predict LLE data for 15 binary and 09 ternary systems at 101.3 kPa and several temperatures; all the systems are formed by ionic liquids including the tetrafluoroborate anion plus alkanes, alkanols, water, ethers, esters and aromatics. New group interaction parameters were determined using a modified Simplex method, minimizing a composition-based objective function of experimental data obtained from literature. The results are satisfactory, with rms deviations of about 3%. ã 2015 Elsevier B.V. All rights reserved.

Keywords: Prediction Liquid–liquid equilibrium Ionic liquids ASOG Activity coefficient

1. Introduction Over the past few years, research about ionic liquids has increased greatly, mainly in two directions: as reaction media, especially in homogeneous catalysis, and as solvents for separation processes [1,2]. Particularly for this latter purpose, their physical and chemical properties make them especially suitable as solvents, potentially substituting the most common volatile organic solvents in the chemical industry. Ionic liquids have very low vapor pressures [3–5]; this special characteristic of almost null vapor pressure has transformed ionic liquids into good alternatives as green solvents of future potential and high commercial interest. Liquid–liquid or solvent extraction is a major industrial process in the chemical industry that depends on the physical and chemical properties of a solvent to effect the separation of complex liquid mixtures, such as in the recovery of valuable products and the removal of contaminants in effluent streams. The separation potential and feasibility of solvents for commercial applicability

Abbreviations: ASOG, analytical solutions of groups; LLE, liquid–liquid equilibrium; RMS, root mean square absolute deviations; UNIFAC, universal functional activity coefficient; UNIQUAC, universal quasichemical activity coefficient; Ref., reference. * Corresponding author. E-mail addresses: [email protected], [email protected] (P.A. Robles). http://dx.doi.org/10.1016/j.fluid.2015.06.025 0378-3812/ ã 2015 Elsevier B.V. All rights reserved.

are dependent on physical properties such as boiling point, thermal stability, viscosity, ease of recovery, toxicity and corrosive nature of the solvent. Liquid–liquid equilibrium data are essential for a proper understanding of extraction processes. The analysis of the composition of the two phases in equilibrium supplies considerable information about mass balance and mass transfer calculations in the design and optimization of separation processes. Liquid–liquid equilibrium (LLE) data for multicomponent systems including ionic liquids, although essential for the design and operation of separation processes, are still scarce. However, some recent studies [6–34] have presented binary and ternary LLE data involving several ionic liquids and organic compounds such as alkanes, alkanols, water, eter, esters and aromatics. Robles et al. [24–26] proposed in previous works the ASOG model for the activity coefficient in binary and ternary systems including ionic liquids with tetrafluoroborate (BF4), hexafluorophosphate (PF6) anions and imidazolium cation (Imid). In this work, LLE data for binary and ternary systems including ionic liquids with the tetrafluoroborate anion are correlated by a group-contribution model for the activity coefficient, the ASOG model [35–38]. New group interaction parameters were determined by using a modified Simplex method, minimizing a composition-based objective function. The results are satisfactory, with rms deviations of about 3%.

P.A. Robles, L.A. Cisternas / Fluid Phase Equilibria 404 (2015) 42–48

3. Analytical solution of groups (ASOG)

Nomenclature ak/l c D eqs f mk/l,nk/l N M NC NDP NG P S T x X

Group interaction parameters, temperature dependent Component Number of data sets Equations Fugacity Group interaction parameters, temperature independent Number of systems Number of tie lines Number of components Number of data points Number of groups in the mixture Pressure Objective function Absolute temperature Mole fraction in liquid phase Group mole fraction

Greek letters Γ Group activity coefficient g Activity coefficient y Number of groups Superscripts/subscripts C Combinatorial FH Size contribution G Group contribution (i) Standard state (pure component i) I, II Liquid phase R Residual 1, 2, i, j Molecule 1, 2, i, and j calc Calculated value exp Experimental value k, l, m Group k, l, and m k, i Group k in molecule i

II

FH i

yFG

(5) 1

yFG

AP i ¼ 1 þ [email protected] i NC FH FH j¼i xj yj j¼i xj yj

lng G i ¼

NG X

yk;i ðlnGk  lnGðiÞ k Þ

(6)

(7)

k¼1

is the measure of the size of molecule i, In these equations, yFH j defined as the number of atoms in the molecule (except for hydrogen atoms), while G k is the residual activity coefficient of ðiÞ

(1)

i ¼ 1; 2; 3; :::

(4)

In ASOG, the Flory–Huggins [44,45] equation was used for the combinatorial part of the activity coefficient and the Wilson equation [46] was used for the determination of group residual activity coefficients. The activity coefficient of component, i, can be calculated by the following equations, where the superscripts FH and G stand for “Flory–Huggins” (combinatorial part) and “groups” (residual part), respectively:

lng

is satisfied [39]. Introducing the activity coefficient definition into Eq. (1) yields: xIi g Ii ðT; P; xI Þ ¼ xIIi g IIi ðT; P; xII Þ

lng i ¼ lng Ci þ lng Ri

0

The thermodynamic requirement for any type of phase equilibrium is that the compositions of each species in each phase in which it appears be such that the equilibrium criterion: f i ðT; P; xI Þ ¼ f i ðT; P; xII Þ

A group-contribution method is more effective in predicting the activity coefficient of the components compared to other methods. The effectiveness of this kind of method depends on the division of the solution into a number of interacting groups. As the mutual behavior of interacting groups cannot be determined experimentally, group-contribution thermodynamic models can be used, where the interaction parameters determined from the behavior of one or several real systems [40]. The analytical solution of groups, ASOG [35–38] and UNIFAC [41–43] methods are mainly based on the assumption that the contribution to the activity coefficient of component i can be separated into two parts, namely, a combinatorial, entropic part (molecular size contribution) and a residual, enthalpic part (intermolecular forces):

G lng i ¼ lng FH i þ lng i

2. Liquid–liquid equilibrium

I

43

(2)

The compositions of the coexisting phases are the sets of mole fractions xI1 ; xI2 ; :::::; xIc ; xII1 ; xII2 ; :::::; xIIc that simultaneously satisfy Eq. (2) and the restrictions Xc Xc xI ¼ 1 and xII ¼ 1 (3) i¼1 i i¼1 i The activity coefficient g i can be determined with an appropriate thermodynamic model.

group k in the mixture, Gk is the residual activity coefficient of group k in pure compound i and yk;i is the number of atoms (other than hydrogen atoms) in group k in molecule i. Both the residual activity coefficients can be calculated by the Wilson [46] equation: ! " # NG NG X X X l al=k lnGk ¼ 1  ln X l ak=l  (8) PNC l¼1 l¼1 m X m al=m where Xl is the group fraction of group l in liquid solution, given by PNC xi yl;i X l ¼ PNC i¼1PNG (9) x i¼1 i k¼1 yk;i where yl;i is the number of atoms of the group l in molecule i, NC is the number of components and NG is the number of groups in the mixture. In Eq. (8), ak=l are the group interaction parameters, which depend on the temperature as   nk=l (10) ak=l 6¼ al=k ak=l ¼ exp mk=l þ T where mk/l and nk/l are the group interaction parameters, which depend only on the group pair and not on the temperature.

44

P.A. Robles, L.A. Cisternas / Fluid Phase Equilibria 404 (2015) 42–48

Table 1 Ionic liquids with BF4 anion used in this work. N

Name

Abbreviation

1

1-Butyl-3-methylimidazolium tetrafluoroborate

[bmim][BF4]

2

1-Hexyl-3-methylimidazolium tetrafluoroborate

[hmim][BF4]

3

1-Octyl-3-methylimidazolium tetrafluoroborate

[omim][BF4]

4

1,3-Dihexyloxymethylimidazolium tetrafluoroborate

[C6H13OCH2mim][BF4]

5

1-Butylpyridinium tetrafluoroborate

[bupy][BF4]

Formula

new group have been determined for 15 binary and 09 ternary systems using the Fortran code TML-LLE 2.0 [47]; the procedure is based on the Simplex method [48], and consists in the minimization of a concentration-based objective function, S [49].

In this work, new group interaction parameters for OH/pyrid, COO/pyrid, Imid/O and BF4/O have been determined from 15 binary and 09 ternary systems using the procedure below. 4. Parameter estimation



In this work, a new group, the tetrafluoroborate anion (BF4), is proposed. New ASOG group interaction parameters involving the

D X M N 1 X X ½ðxI;exp  xI;calc Þ2 þ ðxII;exp  xII;calc Þ2  ijk ijk ijk ijk j

k

(11)

i

Table 2 The values of yk;i and yFH i . N

Component

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

Water Hexane Methanol Ethanol 1-Butanol 1-Pentanol 1-Hexanol 1-Octanol Isobutanol DIPE MTBE TAME [bmim][BF4] [hmim][BF4] [omim][BF4] [C6H13OCH2mim][BF4] [bupy][BF4] rac-1-Phenylethyl propionate rac-1-Phenylethanol

19

yk;i

yFH i

CH2

ArCH

H2O

OH

COO

Imid

BF4

O

Na

Pyrid

0 6 1 2 4 5 6 8 4 6 5 6 5 7 9 8 4 4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6

1.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3

0 0 0 0 0 0 0 0 0 0 0 0 5 5 5 5 0 0

0 0 0 0 0 0 0 0 0 0 0 0 5 5 5 5 5 0

0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0

2 6 2 3 5 6 7 9 5 7 6 7 15 17 19 19 15 13

2

6

0

1

0

0

0

0

0

0

9

P.A. Robles, L.A. Cisternas / Fluid Phase Equilibria 404 (2015) 42–48

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Table 3 ASOG group interaction parameters mk=l and nk=l estimated. Group k

Group l

mk=l

ml=k

nk=l

nl=k

H2O OH COO Imid BF4

O Pyrid Pyrid O O

3.9650 0.2792 3.2114 0.3612 1.8696

2.5974 0.1719 0.5340 0.5720 0.9744

0.6117 2.6814 0.5266 1.6492 3.3431

3.7939 2.0987 0.4250 6.3965 0.7161

Table 4 ASOG group interaction parameters mk=l and nk=l used. Group k

Group l

mk=l

ml=k

nk=l

nl=k

CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 ArCH ArCH ArCH Imid BF4 H2O H2O H2O H2O H2O OH OH OH OH COO COO

Pyrid BF4 ArCH H2O OH COO Imid O BF4 COO Imid BF4 Pyrid OH COO Imid Pyrid BF4 COO Imid O BF4 Imid BF4

85.899 24.401 -0.7457 -0.2727 -41.250 -15.262 -2.3117 -0.0900 0.0671 0.5812 0.9517 38.807 0.7856 1.4318 2.4686 0.4019 0.6486 17.298 0.0583 5.4567 0.6710 0.1498 0.1201 11.331

3.8532 0.3227 0.7297 0.5045 4.7125 0.3699 3.6123 0.5097 0.0482 1.0000 3.4086 28.050 48.034 5.8346 1.0000 25.228 0.5628 29.676 0.0296 2.1066 0.9348 19.575 23.981 0.1722

78.688 98.128 146.00 277.30 7686.4 515.00 33.103 32.400 11.576 249.30 8.1351 21.676 26.699 280.20 565.70 19.978 5.4000 581.39 455.30 810.11 150.80 79.009 230.98 199.17

133.52 19.504 176.80 2382.3 3060.0 162.60 29.013 165.70 0.6054 1.0000 11.133 0.6384 29.423 1582.5 1.0000 60.269 3.0000 11.451 2.6000 16.823 152.20 0.0475 196.77 81.451

Here, D is the number of data sets, N and M are the number of components and tie lines in each data set and superscripts I and II refer to the two liquid phases in equilibrium, while superscripts ‘exp’ and ‘calc’ refer to the experimental and calculated values of the liquid phase concentration. With these parameters, LLE calculations can be made. Comparisons between experimental and calculated data can be made through root mean square (rms) absolute deviations between the experimental and the calculated composition of each component in both phases. These rms deviations are given by

Fig. 1. LLE of DIPE + [bmim][BF4]. Phase I: experimental [30]: ^, ASOG: ^ and Phase II: experimental [30]: ~, ASOG: D.

Fig. 2. LLE of DIPE + [bmim][BF4]. Phase II: experimental [30]: ^, ASOG: ^.

Fig. 3. LLE of [omim][BF4] + water. Phase I: experimental [32]: ^, ASOG: ^ and Phase II: experimental [32]: &, ASOG &.

rms ¼ 100

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PM PN1 I ðxexp  xIcalc Þ2 þ ðxIIexp  xIIcalc Þ2 n i 2MN

(12)

5. Results and discussion The ionic liquids involved in this work are listed in Table 1. The values of yk=l and yFH i of the 19 substances are shown in Table 2. The group interaction parameters H2O/O, OH/pyrid, COO/pyrid, Imid/O, and BF4/O, are shown in Table 3. In this table, the values were estimated by the procedure above, while values shown in Table 4 are taken from Kojima and Tochigi [35], Tochigi et al. [36], Robles et al. [24,25] and Robles [26]. Fig. 1 shows the comparison between the experimental and the predicted LLE for DIPE + [bmim][BF4] system at to 315 K. Experimental data is available up to 340 K, near the critical point, however, the results are not in agreement with experimental data. The reason for this behaviour can be attributed to the ASOG model cannot model the critical zone. From this figure, we can observe that ASOG can predict accurately the behavior of the ionic liquidrich phase, while the behavior of the DIPE-rich phase is predicted in a less accurate way at temperatures below the critical point. Fig. 2 shows the right hand side in Fig. 1 the comparison between the experimental and the predicted LLE of the phase II for the binary system DIPE + [omim][BF4]. Fig. 3 shows the comparison between the experimental and the predicted LLE for the binary system [omim][BF4] + water. The conclusion is similar, the ionic liquid-rich phase is well predicted and the prediction for the water-rich phase is poorer. Fig. 4 shows the comparison between the experimental and the predicted LLE

46

P.A. Robles, L.A. Cisternas / Fluid Phase Equilibria 404 (2015) 42–48

Fig. 4. LLE of [C6H13OCH2mim][BF4] + 1-butanol. Phase I: experimental [34]: ~, ASOG: D and Phase II: experimental [34]: ^, ASOG: ^.

Fig. 7. LLE of TAME + methanol + [bmim][BF4] at T = 298.15 K. Experimental [29]: &, ASOG: &.

Table 5 Root mean square (rms) deviations in binary and ternary systems.

Fig. 5. LLE of DIPE + water + [bmim][BF4] at T = 298.15 K. Experimental [30]: &, ASOG &.

N

System

Ref.

ND

rms (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

DIPE + [bmim][BF4] [hmim][BF4] + water [omim][BF4] + water [hmim][BF4] + 1-butanol [hmim][BF4] + 1-pentanol [hmim][BF4] + 1-hexanol [hmim][BF4] + isobutanol [omim][BF4] + 1-butanol [omim][BF4] + 1-pentanol [omim][BF4] + 1-hexanol [omim][BF4] + 1-octanol [omim][BF4] + 1-isobutanol [C6H13OCH2mim][BF4] + 1-butanol [C6H13OCH2mim][BF4] + 1-hexanol [C6H13OCH2mim][BF4] + 1-octanol DIPE + water + [bmim][BF4] at 298.15 K DIPE + water + [bmim][BF4] at 303.15 K DIPE + water + [bmim][BF4] at 313.15 K MTBE + methanol + [bmim][BF4] MTBE + ethanol + [bmim][BF4] TAME + methanol + [bmim][BF4] TAME + ethanol + [bmim][BF4] [bmim][BF4] + rac-1-phenylethyl propionate + hexane [bmim][BF4] + rac-1-phenylethanol + hexane

[30] [32] [32] [33] [33] [33] [33] [33] [33] [33] [33] [33] [34] [34] [34] [30] [30] [30] [28] [28] [29] [29] [36]

05 06 10 08 07 06 08 11 08 09 07 10 15 07 06 13 07 18 04 04 06 05 03

2.87 1.27 1.23 1.41 5.23 1.99 1.58 2.11 2.35 2.06 1.40 2.11 1.73 2.16 1.44 2.72 4.65 5.49 5.71 2.81 3.00 3.03 8.09

[36] 03

9.76

24

Global

Fig. 6. LLE of DIPE + water + [bmim][BF4] at T = 313.15 K. Experimental [30]: &, ASOG &.

for the binary system [C6H13OCH2mim][BF4] + 1-butanol with similar results. Figs. 5–7 show the same comparisons for four ternary systems. Depending of the system, the ASOG predictions can be considered

186 3.18

accurate. Fig. 5 shows the comparison between the experimental and the predicted LLE for the system DIPE + water + [bmim][BF4] at T = 298.15 K. Fig. 6 shows the comparison between the experimental and the predicted LLE for the system DIPE + water + [bmim][BF4] at T = 313.15 K. Fig. 7 shows the comparison between the experimental and the predicted LLE for the system TAME + methanol + [bmim][BF4] at T = 298.15 K. In these four cases, ASOG is able to represent accurately the behavior of both equilibrium phases. At last, Fig. 7 shows a system with a higher deviation, in order to provide a better insight on the model performance. For a more general view of the results, Table 5 shows the rms deviations between experimental and calculated compositions for all 24 systems, comprising 186 tie lines, according to Eq. (12), with the values always below 10% and generally below 5%. The global

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47

Table 6 Root mean square for different models. N

System

T (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

[hmim][BF4] + benzene + heptane [hmim][BF4] + benzene + dodecane [hmim][BF4] + benzene + hexadecane Benzene + n-hexane + [mebupy][BF4] Benzene + n-hexane + [mebupy][BF4] Ethylbenzene + n-octane + [mebupy][BF4] Ethylbenzene + n-octane + [mebupy][BF4] M-xylene + n-octane + [mebupy][BF4] M-xylene + n-octane + [mebupy][BF4] Toluene + n-heptane + [mebupy][BF4] Toluene + n-heptane + [mebupy][BF4] THF + water + [emim][BF4] THF + water + [bmim][BF4] [C2OHmim][BF4] + water + 1-butanol [C2OHdmim][BF4] + water + 1-butanol

298 298 298 313 333 313 348 313 348 313 348 337 337 293 293

value for rms was about 3%. From these deviations, we can conclude that ASOG was able to predict the phase behavior of the experimental data with a good precision. Table 6 compares the ASOG [26], UNIQUAC [50] and UNIFAC [51] models for 15 systems containing ionic liquids with BF4 anion, showing that the three models reported acceptable results [24]. The UNIQUAC model usually give better results than the ASOG and UNIFAC models, but the model use molecular interaction parameters, and thus, experimental data including these molecules are needed to be able to apply these model. On the other hand, the ASOG and UNIFAC models use group contribution interaction parameters, which makes it possible to apply these models to systems that can be represented by the groups available. Thus, the group contribution parameters calculated in this paper can be applied to other molecules or systems that can be represented by the new groups. 6. Conclusions LLE data for 24 systems and 186 tie lines including ionic liquids were predicted by the ASOG model for the activity coefficient. The group interaction parameters were estimated by minimization of a composition-based objective function using the Simplex method. The results of the prediction were satisfactory, with rms deviations between experimental and calculated equilibrium compositions with the values always below 10% and generally below 5%. The global value for rms was about 3%. From these deviations, we can conclude that ASOG was able to predict the phase behavior of the experimental data with a good precision. Acknowledgements P.A. Robles is grateful to the National Council for Scientific and Technological Research (CONICYT-Chile) for grant FONDECYT Posdoct Project 3140013/2014 and L. Cisternas is grateful to University of Antofagasta for the support of this research. References [1] K.R. Seddon, Ionic liquids for clean technology, J. Chem. Technol. Biotechnol. 68 (1997) 351–356. [2] T. Welton, Room-temperature ionic liquids. Solvents for synthesis and catalysis, Chem. Rev. 99 (1999) 2071–2083. [3] J.O. Valderrama, P.A. Robles, Ind. Eng. Chem. Res. 46 (2007) 1338–1344. [4] A. Heintz, J. Chem. Thermodyn. 37 (2005) 525–535. [5] L.P. Rebelo, J.N. Canongia Lopes, J.M. Esperanca, E. Filipe, J. Phys. Chem. B 109 (2005) 6040–6043. [6] M. Aznar, Braz. J. Chem. Eng. 24 (2007) 143–149. [7] A. Arce, O. Rodríguez, A. Soto, J. Chem. Eng. Data 49 (2004) 514–517.

rms (%) ASOG

UNIQUAC

UNIFAC

3.37 2.97 5.03 2.08 2.05 1.38 0.76 0.99 0.93 1.84 1.17 1.17 1.52 4.20 5.38

2.41 2.43 2.76 0.96 0.86 0.85 0.77 0.70 0.66 0.49 0.52 0.58 0.14 1.33 1.38

2.65 2.94 2.57 1.16 0.86 1.13 0.99 1.14 0.97 0.67 0.56 1.22 3.84 2.72 4.13

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