Modeling vapor liquid equilibrium of ionic liquids + gas binary systems at high pressure with cubic equations of state

THERMODYNAMICS

Modeling vapor liquid equilibrium of ionic liquids + gas binary systems at high pressure with cubic equations of state

A. C. D. Freitas; L. P. Cunico; M. Aznar; R. Guirardello^*

School of Chemical Engineering, State University of Campinas, (UNICAMP), Phone: + (55) (19) 3521 3955, Fax: + (55) (19) 3521 3910, Av. Albert Einstein 500, 13083-852, Campinas - SP, Brazil. E-mail: [e-mail]; [e-mail]; [e-mail]

ABSTRACT

Ionic liquids (IL) have been described as novel environmentally benign solvents because of their remarkable characteristics. Numerous applications of these solvents continue to grow at an exponential rate. In this work, high pressure vapor liquid equilibria for 17 different IL + gas binary systems were modeled at different temperatures with Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state, combined with the van der Waals mixing rule with two binary interaction parameters (vdW-2). The experimental data were taken from the literature. The optimum binary interaction parameters were estimated by minimization of an objective function based on the average absolute relative deviation of liquid and vapor phases, using the modified Simplex algorithm. The solubilities of all gases studied in this work decrease as the temperature increases and increase with increasing pressure. The correlated results were highly satisfactory, with average absolute relative deviations of 2.10% and 2.25% for PR-vdW-2 and SRK-vdW-2, respectively.

Keywords: Ionic liquids; Vapor-liquid equilibria; PR and SRK Eos.

INTRODUCTION

Ionic liquids are organic salts that are liquid at room temperature and consist of a small organic or inorganic anion and a large asymmetric organic cation. Ionic liquids have negligible vapor pressure and a stable and wide liquid range of over 300 K. These fluids have been proposed as attractive alternatives to volatile organic compounds for green processes (Blanchard and Brennecke, 2001).

Ionic liquids have been described as novel environmentally benign solvents because of their remarkable characteristics, such as non-volatility, high thermal stability, non-flammability and high polarity (Anthony et al., 2001; Fadeev et al., 2001). Numerous applications of these solvents continue to grow at an exponential rate; the most common applications found in the literature are in gas and liquid separation processes (Blanchard and Brennecke, 2001; Anthony et al., 2001; Fadeev et al., 2001;Visser et al., 2000); as solvents in various reactions systems, such as hydrogenation, hydroformylations, isomerizations, dimerizations, alkylations, among others (Welton, 1999; Hermann et al., 1999; Seddon, 1995; Blanchard et al., 2001); in electrolytes/fuel cells (Souza et al., 2003); as CO₂ selective separation media (Anthony et al., 2002; Zhang et al., 2006); in the capture or sequestration of various gases such as CO₂, H₂S and SO₂ (Anderson et al., 2007); and as lubricants in different systems (Bermudez et al., 2009).

The use of carbon dioxide (CO₂) as a green reaction media has gained more and more research interest due to its environmental and nontoxic properties. Carbon dioxide is nonflammable, nontoxic and inexpensive. The most important aspect of CO₂ is its tunable properties, which can change significantly with temperature and pressure. CO₂ has a relatively low critical temperature (31.1 °C) and moderate critical pressure (73.8 bar) (Jessop and Leitner, 1999). Wu and coworkers (Wu et al., 2005) and Zhou and coworkers (Zhou et al., 2006) investigated the use of compressed and supercritical CO₂ as an environmentally benign alternative in ionic liquid synthesis.

The phase behavior of ionic liquids with CO₂ is unique. CO₂ is very soluble in ionic liquids, but, in contrast, ionic liquids are insoluble in the pure CO₂ phase. Therefore, the ionic liquid + CO₂ mixture does not become miscible (critical) even at elevated pressures, which makes them advantageous as biphasic reaction media. Moreover, compressed CO₂ can increase the solubility of reactive gases (H₂ and O₂) in ionic liquids (Solinas et al., 2004; Hert et al., 2005), and dramatically decreases the melting point of many ionic solids, even inducing melting over 100 °C below the normal melting points of some ionic solids (Scurto and Leitner, 2006; Scurto et al., 2008).

Phase equilibria in systems composed of ionic liquids + CO₂ were studied by several authors (Blanchard et al., 2001; Ren et al., 2010; Nwosu et al., 2009; Carvalho et al., 2009a, 2009b; Kroon et al., 2005; Liu et al., 2003; Blanchard et al., 1999), but few of them have assessed the solubility in ionic liquids of other gases. The phase equilibria of different imidazolium ionic liquids with 1,1,1,2-tetrafluoroethane (R-134a) were studied by Ren and Scurto (2009a, 2009b); the authors emphasize the importance of understanding these systems for the separation of hydrofluorocarbon refrigerant gases and in other engineering applications.

In this work, isothermal vapor-liquid equilibrium data for 17 binary mixtures composed of ionic liquids and different gases (CO₂, C₂H₆, CHF₃ and R-134a) were analyzed, totalizing 390 experimental data points distributed in 50 isotherms. Pressure and temperature ranges vary between 1-620 bar and 298.15-363.15 K, respectively. The systems were modeled with the Peng-Robinson (Peng and Robinson, 1976) and Soave-Redlich-Kwong (Soave, 1972) equations of state using the van der Waals mixing rule with two adjustable parameters (and ). These thermodynamic models were implemented in the PE 2000 software (Pfohl et al., 2000).

THERMODYNAMIC MODELING

The Soave-Redlich-Kwong equation of state is (Soave, 1972):

Here, P is the pressure, V the molar volume, T the temperature, α(T) the temperature-dependent attractive parameter, b the co-volume and R the ideal gas constant. The co-volume is temperature independent and is calculated using the critical properties as follows:

The attractive parameter, α(T), is calculated by a Soave-type expression:

where:

Here, T_r is the reduced temperature. The parameter m is correlated to the acentric factor ω for light non-polar compounds, through the following expression:

The expression for the Peng-Robinson equation of state is (Peng and Robinson, 1976):

The variables are the same explained above. Again, the co-volume is temperature independent and is calculated using the critical properties, as follows:

The attractive parameter, α(T), is calculated by:

where:

Here, the parameter m is also correlated to the acentric factor, ω, for light non-polar compounds through:

The Peng-Robinson equation is widely used in modeling the solubility of substances in supercritical fluids. For mixtures, cubic EoS like PR and SRK are widely applied utilizing the van der Waals-2-parameter (vdW-2) mixing rules:

where the cross energy, α_ij, and cross co-volume b_ij are calculated by combining rules:

Here, k_ij and l_ij are adjustable parameters, determined by fitting binary phase equilibrium data. The combination of van der Waals mixing rules with the PR-EoS and SRK-EoS provides a good compromise between simplicity and accuracy of the modeling algorithm for representing a large variety of systems (Florusse et al., 2008). Modeling high pressure phase equilibria with this combination showed good correspondence with experimental data in previous work (Gamse and Marr, 2000, 2001).

The software Phase Equilibrium 2000 (PE2000), chosen here to calculate the phase equilibria, was developed by Brunner and coworkers (Pfohl et al, 2000). The software was used by several other researchers (Petkov et al., 2000; Schwarz and Nieuwoudt, 2003a, 2003b; Teodorescu et al., 2003) with excellent results to correlate and predict phase equilibria. PE2000 uses the modified Simplex algorithm (Nelder and Mead, 1965) for parameter regression of the binary interaction parameters, k_ij and l_ij, minimizing the objective function of the average absolute relative deviation () for liquid and vapor phase mole fractions:

Here, is the experimental liquid mole fraction data; is the predicted value; is the experimental vapor mole fraction data; is the predicted value and NP is the number of experimental data points. This objective function was used in similar works in the literature with good results (Nwosu et al., 2009; Ren and Scurto, 2009; Ren et al., 2010). Several initial guesses were utilized to avoid the local minima in the regression in order to obtain final values for k_ij and l_ij.

RESULTS AND DISCUSSION

The critical properties of ionic liquids were taken from Valderrama et al. (2007, 2008a, 2009), Ren et al. (2010) and Nwosu et al. (2009). For CO₂, C₂H₆ and CHF₃, the properties were taken from the DIPPR data base (DIADEM, 2000). For R-134a, the critical properties are given by Ren and Scurto (2009a). All critical properties used in this work are given in Table 1.

The solubility of CO₂, CHF₃ and R-134a in various ionic liquids was modeled with the PR-EoS and SRK-EoS with the vdW-2 mixing rule, at different temperatures for each case. The experimental data were taken from the literature (Blanchard and Brennecke, 2001; Ren et al., 2010; Nwosu et al., 2009; Carvalho et al., 2009a, 2009b; Kroon et al., 2005; Liu et al., 2003; Ren and Scurto, 2009a; Shariati and Peters, 2003; Florusse et al., 2008) and the characteristics of these systems are shown in Table 2.

The adjustable parameters, k_ij and l_ij, the %AARD and the range of experimental data utilized (expressed in pressure and liquid phase molar composition) are shown in Table 3 for all 17 binary systems analyzed here.

Figure 1 shows the comparison between calculated and experimental data for the mole fraction of liquid phase for all 17 systems at all temperatures, for both EoS analyzed. Analyzing Figure 1 and Table 3, it can be verified that a good correlation between experimental and calculated data was obtained for most of the systems analyzed, with low computing time for all cases. Larger deviations were observed for the SRK equation, as shown in Table 3.

We can see that the solubility of CO₂, CHF₃ and C₂H₆ increases when the pressure increases and the solubility decreases with the increase of the temperature of the system. This behavior was observed for the two thermodynamics models studied here and also in the experimental data for all systems studied. This behavior is common in VLE. Another important point is that all systems studied here are at elevated pressures, up to 100 bars. In this condition, we can note the upward curvature in the isotherms, i.e., the elevation of the pressure entails very little increase in the gas solubility.

This behavior was observed in others works in the literature (Shariati and Peters, 2003, 2004; Arce et al., 2010). The solubility of CO₂ in ionic liquids follows a linear relationship with the length of alkyl chain. This relationship directly influences the prediction of data across equations of state, since the greater the solubility, the lower the error displayed, as seen for the systems studied (Shariati et al., 2005).

Overall, both EoS tested provided a good correlation for the bubble point data in the pressure range of the experimental data utilized, but the correlation was poor in the high pressure region for most systems. This behavior can be seen in Figure 1 in the high gas concentration (x_experimental) region of the graph. The high concentration of the gas coincides with the high pressure conditions for all systems.

Larger deviations in the regions of high pressure were described in other works in the literature (Carvalho et al., 2009a; Nwosu et al., 2009; Ren et al., 2010) and, because of this behavior, the extrapolation of the model much beyond the data pressure region in which the interaction parameters were fit is not recommended.

For some systems, the combination of the vdW-2 mixing rule with the PR and SRK Eos did not provide a good correlation between experimental and calculated data, mainly to represent the liquid phase. This behavior was expected due to the high complexity of the systems reviewed here. A possible solution to this problem would be to use more elaborate mixing rules, such as the Wong-Sandler (WS) type mixing rules (Wong and Sandler, 1992).

Some papers present the modeling of systems composed of ionic liquid and gas, principally CO₂, using the combination of PR and WS mixing rules with good representation of the thermodynamic behavior, such as Alvarez et al. (2008) (PR+WS combined with NRTL model); Valderrama et al. (2008b) (PR+WS combined with the Van Laar model); Arce et al. (2010) (PRSV-Peng Robinson+ Stryjek-Vera EoS combined with the WS mixing rule and the Van Laar model) and Chilla et al. (2011) (PR+WS combined with the Van Laar model).

In Table 4, the deviations presented in different papers and the deviations observed in this paper for the liquid phase (%AARDL, given by Equation (14)) are compared. The deviations were presented only for the liquid phase because in these papers the calculations were performed only for the mole fraction of the liquid phase.

Most of the papers that used the combination of PR EoS combined with the WS mixing rule showed minor deviations when compared with those that used the PR EoS combined with the vdW-2 mixing rule (see Table 4). In papers that used the same combination used in this paper (PR-vdW2), similar deviations were observed. Works that used the SRK Eos for this type of system were not found in the literature and the comparison was not possible.

Effect of Gas on [C₆mim][Tf₂N] Phase Behavior at 323.15 K

The solubility of three different gases (R-134a, CO₂ and C₂H₆) was analyzed in [C₆mim][Tf₂N] ionic liquid. The solubility of R-134a is greater than that of the other gases at 323.15 K (lower pressure results in higher solubility when compared with the other gases). The results can be seen in Figure 2. This behavior can be explained by the similarity between the molecules of [C₆mim][Tf₂N] and R-134a in terms of polarity.

Effect of Anion Modification on CO₂ and R-134a Solubility

The anion effect on CO₂ and R-134a solubility can be seen in Figures 3 (a) and (b), respectively. For CO₂ solubility, the anion effect is analyzed at 333.15 K for the cation 1-butyl-3-methylimidazolium ([bmim]) with the following anions: hexafluorophosphate ([PF₆]), tetrafluoroborate ([BF₄]) and nitrate ([NO₃]).

As can be seen in Figure 3 (a), CO₂ is more soluble in [PF₆] than in [BF₄] and [NO₃], but the solubility in [NO₃] is approximately equal to the solubility in [BF₄] at pressures up to 80 bar.

For R-134a solubility, the anion effect is analyzed at 323.15 K for the cation 1-hexyl-3-methyl-imidazolium with the following anions: bis(trifluoromethylsulfonyl) imide ([Tf₂N]), [BF₄] and [PF₆].

As can be seen in Figure 3 (b), R-134a is more soluble in [Tf₂N] than in [BF₄] and [PF₆]. The anions [BF₄] and [PF₆] have a very similar solubility for this gas for the whole range of pressure studied here.

The solubility parameter depends on the energy of vaporization and molar volume. Generally, the energy of vaporization is high for all IL, so because the [Tf₂N] anion is larger than other anions, such as ([PF₆] or [BF₄]) its molar volume is significantly larger and therefore [Tf₂N] dissolves CO₂ to a greater degree.

Effect of Cation Modification on CO₂ Solubility

Figure 4 shows the effect of the cation modification on the CO₂ solubility for the following1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids: [dmim][Tf₂N], [C₆mim][Tf₂N], [C₂mim] [Tf₂N], [pmim][Tf₂N] and [bmim][Tf₂N].

Furthermore, the solubility of CO₂ is also strongly dependent on the alkyl chain length of the ionic liquid; similar results were observed in the works of Shariati and Peters (2005) and Shin et al. (2008). In general, the solubility in IL increases with the increase of the length of the alkyl chain of the IL.

Additionally, the dramatic difference in size between CO₂ and an IL emphasizes the influence of the entropic effect on the solubility. The large entropic effect led to a negative deviation from the ideal solubility that might explain why CO₂ is more soluble in the larger 1-decyl- than in the smaller 1-ethyl-3-methylimidazolium IL`s (Cadena et al., 2004; Anthony et al., 2005).

CONCLUSION

Pressure-composition diagrams for 17 different binary systems of ionic liquids + CHF₃, C₂H₆, CO₂ and R-134a at high pressure were modeled at different temperatures with the PR and SRK equations of state and the vdW-2 mixing rule. Solubilities of all gases studied in this work decrease with an increase in the temperature of the system, and increase with increasing pressure. Predicted results were highly satisfactory for both EoS analyzed, with AARD% between experimental and calculated data of 2.10% and 2.25% for PR-vdW-2 and SRK-vdW-2, respectively.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support from CAPES. M. Aznar and R. Guirardello are recipients of fellowships from CNPq.

(Submitted: February 1, 2012 ; Revised: July 7, 2012 ; Accepted: July 11, 2012)

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Publication Dates

• Publication in this collection
  01 Mar 2013
• Date of issue
  Mar 2013

History

• Received
  01 Feb 2012
• Accepted
  11 July 2012
• Reviewed
  07 July 2012