Accurate Modeling of CO2

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Accurate Modeling of CO2 Solubility in Ionic Liquids Using a Cubic EoS⊥ Ricardo Macías-Salinas,†,* José Adrián Chávez-Velasco,† Marco A. Aquino-Olivos,‡ José Luis Mendoza de la Cruz,‡ and Jesus C. Sánchez-Ochoa† †

ESIQIE, Departamento de Ingeniería Química, Instituto Politécnico Nacional, Zacatenco, México, D.F. 07738 Programa de Aseguramiento de la Producción de Hidrocarburos, Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, México, D.F., 07730

‡

ABSTRACT: During the past decade, various experimental studies have shown that ionic liquids exhibit interesting and attractive thermo-physical properties such as extremely low volatilities, a high thermal stability, and ionic conductivity as well as high gas solubilities. It is in the latter where the use of an ionic liquid as gas separation media seems to be very promising particularly for the capture/sequestration of carbon dioxide (CO2) which has been shown to be highly soluble in ionic liquids as compared with other gases. Recently, a significant amount of experimental work has appeared in the literature dealing with the solubility of CO2 in several ionic liquids at different temperature and pressure conditions. A detailed analysis of these works reveals that the highest solubilities of CO2 have been exhibited in ionic liquids having cations of the imidazolium type together with anions of the [TF2N] type. The purpose of this work is to present a formal modeling approach of the CO2 solubility in the aforementioned ionic liquids by the use of a cubic equation of state (Soave or Peng−Robinson) coupled with modern mixing rules of the Wong−Sandler type. The resulting modeling approach proves to be able to correlate and/or predict the CO2 solubility in ionic liquids over diverse conditions of temperature, pressure, and solute composition.

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INTRODUCTION Ionic liquids (ILs) belong to a particular class of organic salts that behave as liquids below 100 °C. They usually comprise a large organic cation in combination with an organic or inorganic anion of smaller size. The various combinations of cations and anions conveniently allow tunable IL properties for the purpose of designing better IL-based solvents for reactions and separations. Recently, during the last 10 years, a huge amount of experimental studies have appeared in the literature dealing with the determination of thermo-physical properties of ILs either as a pure state or in solution. These studies have demonstrated that certain thermo-physical properties exhibited by ILs set them apart from other common or traditional liquids, thus making them (ILs) particularly attractive for different applications.1−4 In general, ILs exhibit key properties such as extremely low volatilities (namely, almost immeasurably vapor pressures), a high thermal stability, and ionic conductivity as well as a high gas solubility on a molar basis (mol of gas per mol of IL). Because of these properties (mainly the first and the last one), ILs have recently become promising solvent alternatives as a gas separating agent typically used in physical absorption processes; for example, as in desulfurization processes which nowadays are a main concern.5,6 To find the most suitable IL as an absorption solvent, a precise knowledge of the gas solubility in the IL is thus required. For the particular case of carbon dioxide (CO2), a gas pollutant mainly responsible for the socalled green-house effect, the use of an IL as gas separation media appears to be promising for the capture/sequestration of this gas which has shown to be highly soluble in ILs as compared with other gases.7 This finding is supported by a vast © XXXX American Chemical Society

number of experimental works that have appeared in the literature dealing with the CO2 solubility in different ILs.9−21 Although experimental CO2 solubilities in ILs have been extensively measured, there is still a lack of industrial applications using ILs as an absorption media to capture CO2 from a gas stream, probably because if a mol-CO2 per mass-IL basis is considered, a significant amount of IL would be required to treat a gas stream; besides, CO2 solubilities in ILs may be high on a mol-gas per mol-IL basis but they are not that high on a mol-gas per mass-IL basis. In fact, Carvalho and Coutinho22 demonstrated that the CO2 solubility in ILs of dissimilar sizes is almost identical if a molality basis is considered, that is mol-CO2 per kg-IL. Further, Bara et al.23 also showed that CO2 solubilities in ILs are comparable to nonpolar solvents such as n-hexane provided that a per-volume basis is used. Regardless, the rational design of the corresponding absorption system suitable for industrial scaleup purposes will require a precise knowledge of the physical equilibrium between CO2 and the IL. Since experimental measurements of phase equilibrium of ILs and their mixtures may often become expensive and time-consuming, it is highly desirable to have mathematical models for estimating CO2 solubilities in ILs that are valid within the operating conditions of the aforementioned absorption system. As a matter of fact, various modeling efforts have been reported in the literature regarding the gas solubility in ILs. Recently, Vega et al.24 published a comprehensive review on the state-of-the-art Received: January 9, 2013 Revised: April 29, 2013 Accepted: May 1, 2013

A

dx.doi.org/10.1021/ie400106g | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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approaches for modeling the thermo-physical properties of ILs including their gas solubilities. In general, these modeling efforts, for the particular case of CO2 solubilities in ILs, fall into four main approaches: (1) irregular ionic lattice models,25 (2) regular solution theory,26 (3) cubic equations of state,13,20,27,28 and more recently (4) statistical associating fluid theory29−31 (SAFT). Although the application of the above approaches usually yields satisfactory results, they still present some drawbacks. For the case of irregular ionic lattice models, the irregular ionic structure collapses in the limiting case of pure CO2. On the other hand, in the regular solution theory, a melting point is required but many ILs lack this quantity. In the solubility models based on cubic equations of state (CEoS), critical properties are required; however, they may not be readily available for the IL of interest. Further, use of classical mixing rules in the CEoS is sometimes insufficient for an accurate modeling of CO2 solubilities in ILs. The addition of an association term to a CEoS (CPA model), though, has very recently yielded promising results for VLE calculations of IL− CO2 mixtures.28 Recently, the SAFT approach, originally proposed by Chapman et al.,32 and Huang and Radosz,33 has been extended to model the gas solubility in ILs.29−31 For example, Ji and Adidharma31 used the so-called heterosegmented SAFT to estimate the CO2 solubility in ILs in which the cation of the IL was modeled as a chain molecule, whereas the anion was visualized as a spherical segment. Despite the success of the SAFT approach in representing well gas solubilities in ILs, it is still cumbersome to use in the sense that proper characterization of the mixture within the SAFT framework may lead to a considerable amount of adjustable parameters. On the basis of the above, in this work, we revisited the use of CEoS to accurately calculate the CO2 solubility in ILs over wide ranges of pressure, temperature, and gas composition. We rather favor the use of CEoS since they continue to be the simplest approach for modeling the phase behavior of mixtures; additionally, they are always available from any process simulator. To increase their estimation accuracy for gas solubilities in ILs, one must consider modern mixing rules rather than classical or augmented mixing rules of the van der Waals type. In this context, the present modeling approach makes use of the Wong−Sandler mixing rules in the CEoS to properly determine the nonideal phase behavior between CO2 and the IL. To best of our knowledge, Carvalho et al.19 is the only work so far published that uses a similar modeling approach to that proposed here. The authors used the Peng− Robinson CEoS with the Wong−Sandler mixing rules in combination with the UNIQUAC expression as the excess freeenergy model; however, rather than presenting a formal modeling attempt, the authors made use of this approach to perform a thermodynamic consistency test on their own experimental data, namely, CO2 solubilities in imidazoliumbased ILs at high pressures.

P=

am RT − Vm − bm (Vm + δ1b)(Vm + δ2bm)

(1)

where δ1 = 1, δ2 = 0 for SRK, and δ1 = 1 + √2, δ2 = 1 − √2 for PR. The application of the above equation to nonideal mixtures can be done by incorporating a suitable compositional dependence of the am and bm parameters into the CEoS. The mixing rules proposed by Wong and Sandler36 that combine excess free-energy models with a CEoS were used for this purpose:

am = RT ·Q bm =

D 1−D

(2)

Q 1−D

(3)

with Q=

⎛

∑ ∑ xixj⎜⎝b − i

D=

j

∑ xi

a ⎞⎟ RT ⎠i , j

ai GEX + biRT CRT

(4)

(5)

and the combining rule: aj ⎞⎤ a ⎞ ⎛ ⎛ 1 ⎡⎛ a ⎞⎟ ⎜b − ⎟ (1 − k ) = ⎢⎜bi − i ⎟ + ⎜bj − ⎥ i,j ⎝ 2 ⎣⎝ RT ⎠⎦ RT ⎠i , j RT ⎠ ⎝ (6)

The above mixing rules satisfy the low-density boundary condition: quadratic composition dependence of the second virial coefficient (eq 4) and the high-density condition: AEX EoS = GEX at infinite pressure (eq 5). Further, C appearing in eq 5 is a CEoS-specific constant: C = ln(1/2) for SRK, and C = ln(√2 − 1)/√2 for PR. The Wong−Sandler approach thus produces the desired equation of state behavior at both low and high densities without being density dependent and allows extrapolation over wide ranges of temperature and pressure. The UNIQUAC equation37 served as the excess Gibbs free energy model needed in the Wong−Sandler mixing rules through eq 5. For a binary mixture comprising CO2 (1) and the IL (2), the UNIQUAC GEX model is GEX GEX,combinatorial GEX,residual = + RT RT RT

(7)

where the combinatorial part describes the dominant entropic contribution as follows: φ φ GEX,combinatorial = x1 ln 1 + x 2 ln 2 RT x1 x2 ⎛ θ θ ⎞ z + ⎜⎜x1q1 ln 1 + x 2q2 ln 2 ⎟⎟ φ1 φ2 ⎠ 2⎝

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(8)

whereas the residual part primarily describes the intermolecular forces that are responsible for the enthalpy of mixing and is given by

MODELING FRAMEWORK In the present study, the gas−liquid phase behavior between CO2 and the IL was determined by the use of two relatively simple CEoS: Soave−Redlich−Kwong34 (SRK) and Peng− Robinson35 (PR). The general form of these equations for mixtures is given by

GEX,residual = −q1x1 ln(θ1 + θ2τ2,1) − q2x 2 ln(θ2 + θ1τ1,2) RT (9) B



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The coordination number z appearing in eq 8 is set equal to 10. Segment fraction φ, and area fraction θ are expressed as follows: xiqi xiri φi = θi = i , j = 1, 2 xiri + xjrj xiqi + xjqj

ranges, the maximum CO2 solubility measured, and the source of the experimental solubility data. As seen in this table, experimental data cover, overall speaking, a moderate temperature range (6.8−180 °C), a wide pressure range (0.0003−971 bar), and a maximum CO2 solubility of 0.792 in mole fraction for [omim][TF2N]. The present modeling approach was first applied to the correlation of experimental CO2 solubilities in selected ILs at 25 °C. Critical properties (Tc and Pc) and acentric factors needed in the two CEoS as well as UNIQUAC parameters (r and q) for CO2 and the five ILs are listed in Table 2. All properties for CO2 were obtained from the Pure-Component Databank of Aspen One, ver. 2006.1 thus leaving the possibility of further incorporating the results of the present modeling effort into the Aspen Plus Process Simulator. On the other hand, the critical properties and acentric factors of the five ILs were taken from Valderrama and Robles41 who estimated these properties using an extended group contribution method. Regarding the UNIQUAC structural parameters of the ionic species, these were obtained from Santiago et al.42,43 who performed quantum chemistry calculations to estimate them. A least-squares fit based on the Levenberg−Marquadt method was then performed to obtain the model parameters (ΔU1,2, ΔU2,1, and k1,2) at 25 °C. The minimization of the following objective function served for this purpose:

(10)

Parameters r and q are pure-component molecular-structure constants depending on molecular size and external surface areas. The binary interaction parameters τi,j appearing only in the residual part are given in terms of characteristic energies ΔUi,j by ln τi , j = −

ΔUi , j RT

i , j = 1, 2

(11)

For many cases, the above equation introduces the primary effect of temperature on τi,j. Within the present modeling framework, the two UNIQUAC interaction parameters (ΔU1,2 and ΔU2,1) were adjusted to fit experimental CO2 solubilities in ILs. Also, note that the interaction parameter for the second virial coefficient k1,2 = k2,1 was also treated as an adjustable parameter in eq 6. All gas− liquid equilibrium calculations were performed using the phi− phi method. Accordingly, the required expressions for the fugacity coefficients based on the Wong−Sandler approach have been already given elsewhere.36,38

N

■

min f =

j=1

RESULTS AND DISCUSSION Experimental evidence indicates that one of the highest solubilities of CO2 have been exhibited in ILS having cations of the imidazolium type together with anions of the [Tf2N] type;11,12,14−16,18,19 as a matter of fact, to best of our knowledge, an imidazolium-based IL with the tetracyanoborate anion [B(CN)4] is the one that exhibits the largest CO2 solubilities so far measured.39,40 For modeling purposes only, we considered here experimental CO2 solubilities in some representative imidazolium-based ILs having mainly [Tf2N] anions. Accordingly, Table 1 gives the ILs considered in this study along with their corresponding temperature and pressure

[bmim][PF6]

[emim][PF6] [bmim][Tf2N]

[emim][Tf2N]

[omim][Tf2N]

T [°C]

P [bar]

x-CO2 max

13.3−53.7 0.03−13

0.567 0.262

Aki et al.8 Cadena et al.9

0.0003− 13 10.9−971

0.262

Anthony et al.11

0.619

10, 25, 50 6.8−66.8

0.2−13

0.372

Shariati and Peters10 Anthony et al.11

2.9−48

0.512

25, 40, 60 40−180

11.7− 132.4 6.4−133.7

0.752 0.593

10, 25, 50 25 25, 40, 60

0.027−13

0.271

Schilderman et al.18 Cadena et al.9

2.1−9 13.3− 114.7

0.209 0.792

Kim et al.16 Aki et al.8

25 10, 25, 50 10, 25, 50 40−80

+

cal ]2 ∑ [1 − yCO ,j j=1

2

(12) exp

where N is the number of experimental points, P and Pcal stand for the observed and calculated total pressures, and ycal CO2 is the equilibrium composition of CO2 in the gas. The correlating results obtained at 25 °C are summarized in Table 3 for the ILs considered here except for [emim][PF6] for which no CO2 solubility data was available at 25 °C. Table 3 includes, for each CO2−IL pair, the three adjusted parameters (ΔU1,2, ΔU2,1, and k1,2) using the PR CEoS, and the resulting percent of absolute average deviations (AAD) between calculated and experimental total pressures. For comparison, Table 3 also lists the AAD values obtained using the SRK CEoS. It can be seen from Table 3 that the ability of the present approach in representing the experimental CO2 solubility data is quite good with overall AAD values of 2.33% using the PR CEoS and 2.36% using the SRK CEoS. As a matter of fact, both CEoS give comparable results for the four CO2−IL mixtures. Figure 1 graphically depicts the comparison between experimental and calculated total pressures (using the PR CEoS) for four imidazolium-based ILs over a wide range of CO2 compositions in the liquid. As shown by this figure, the present approach provides a very good fit to experimental CO2 solubilities in the four ILs under study. For the particular case of [bmim][PF6], its CO2 solubilities measured by different authors (Aki et al.,8 Cadena et al.,9 and Anthony et al.11) are well represented by the PR CEoS. Similarly, Figure 2 shows the correlating capabilities of the SRK CEoS in representing the same experimental solubility data. As evidenced by Figures 1 and 2, both CEoS coupled with Wong−Sandler mixing rules yield very similar results for the four ILs except for [bmim][PF6] for which the SRK CEoS gives slightly better estimations as the maximum solubility is approached. It is important to note that, as shown by Figures 1 and 2, the largest experimental CO2 solubilities are exhibited by those ILs having the [Tf2N] anion. This behavior might be attributed to

Table 1. Experimental CO2 Solubilities in Some Imidazolium-Based ILs ionic liquid

N

∑ [Pjexp − Pjcal]2

source

Lee and Outcalt15 Aki et al.8

C



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Table 2. Pure-Component Properties Needed as Model Inputs

a

component

Tc [K]

Pc [bar]

ω

r

q

CO2 [bmim][PF6] [emim][PF6] [bmim][Tf2N] [emim][Tf2N] [omim][Tf2N]

304.21 708.9 663.5 1265.0 1244.9 1311.9

73.83 17.3 19.5 27.6 32.6 21.0

0.223621 0.7553 0.6708 0.2656 0.1818 0.4453

1.29862 8.4606 20.1303 32.671a 10.1066 14.1544

1.292 6.808 8.1306 20.6844a 8.059 11.227

ΔU2,1 cal/mol

Taken from Carvalho et al.19

Table 3. Regressed Model Parameters and % AAD Values at 25 °C ionic liquid

N

k1,2

[bmim][PF6] [emim][PF6] [bmim][Tf2N] [emim][Tf2N] [omim][Tf2N] overall

107

0.814

34 25 6 172

0.793 0.811 0.797

ΔU1,2 cal/mol 1.43E8 443.31 3070 8056

AAD, P PR-CEoS

AAD, P SRK-CEoS

39.56

2.14

2.19

325.5 −262.5 −77.76

2.15 3.46 1.90 2.33

2.16 3.46 1.85 2.36

Figure 1. Representation of CO2 solubilities in some ILs at 25 °C using the PR CEoS.

Figure 2. Representation of CO2 solubilities in some ILs at 25 °C using the SRK CEoS.

the interaction between the −CF3 groups present in the [Tf2N] anion and the partial positive charge on the carbon of the CO2 molecule; however, it is not yet well understood.19 According to Kazarian et al.,44 who used ATR-IR spectroscopy, the increase in solubility in imidazolium-based ILs is not related to any specific interactions between the CO2 and the cation. Furthermore, Muldoon et al.45 suggest that the large free volume of the IL is the main factor responsible for the high CO2 solubilities; however, there are no values for free volumes provided by the authors that serve to confirm their idea. Just recently, Shannon et al.46 using dynamic molecular simulations via COSMOtherm computed free volumes for 165 imidazolium-based ILs and thus confirmed a link between free volume and gas solubility in ILs. As stated by the authors:46 “The overall implication is that large, highly delocalized anions paired with imidazolium cations that have minimally sized alkyl chains may hold the key to achieving greater CO2 solubility”. For such ILs having large free volumes, the entropic effects rather than the enthalpic effects should become more predominant. In this context, the UNIQUAC equation used

in the present modeling approach can give us a rough insight of the CO2−IL molecular interactions that in turn may allow us to confirm the findings and reasoning of Kazarian et al.,44 Muldoon et al.,45 and Shannon et al.46 about the large CO2 solubilities in some ILs. For such a purpose, two ILs were chosen having the same cation ([bmim]) and different anions ([PF6] and [Tf2N]). Figure 3 shows the variation of entropic and enthalpic contributions with liquid composition obtained from the UNIQUAC model for [bmim][PF6] (solid line) and [bmim][Tf2N] (dashed line) at 25 °C. It can be seen from this figure, that the enthalpic contributions for the two ILs look pretty similar; however, the entropic contribution for [bmim][Tf2N] is much larger with negative values, that is, the entropic effects for this particular IL are more dominant thus yielding increased CO2 solubilities. This supports the idea of Shannon et al.46 about the free volume concept; furthermore, the large molar mass of [bmim][Tf2N] appears to cause an increase in CO2 solubility (on a molar basis) simply because there are more solvent molecules per CO2 molecule than in [bmim][PF6]. D



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Figure 5. CO2 solubilities in some ILs at 25 °C using the SRK CEoS near the dilute region.

Figure 3. UNIQUAC G-excess contributions at 25 °C for two [bmim]-based ILs.

The present modeling approach also gives an accurate representation of CO2 solubilities near the dilute region. Accordingly, Figures 4 and 5 shows the performance of both

Figure 6. Predicted CO2 solubilities in [bmim][PF6] at T 25 °C with the SRK CEoS.

10, 27, 40, 50, 60, and 67 °C using the PR CEoS, respectively. As shown by these figures, the agreement between experimental and predicted solubility data is remarkably good except for [bmim][PF6] at 50 °C where the SRK CEoS somewhat underpredicts the experimental data of Anthony et al.11 For [emim][Tf2N] and [omim][Tf2N]; however, the present modeling approach failed to properly predict their experimental CO2 solubilities, as evidenced by Figures 8 and 9, respectively. For the case of [emim][Tf2N], although the SRK CEoS yields pretty good predictions at 10 and 50 °C, it gradually overpredicts the experimental CO2 solubilities at much higher temperatures (70, 100, 140, and 180 °C). This result apparently suggests that the temperature dependency of the UNIQUAC interaction parameters (eq 11) is not adequate at elevated temperatures or within a wide temperature range. Nevertheless, as shown by Figure 9, the present modeling approach largely overpredicts the experimental solubilities of [omim][Tf2N] even at temperatures that are not that high (40 and 60 °C).

Figure 4. CO2 solubilities in some ILs at 25 °C using the PR CEoS near the dilute region.

CEoS (PR and SRK, respectively) over this region with mole fractions of CO2 as low as 1 × 10−5. As evidenced by Figure 4, the PR CEoS captures more accurately the CO2 solubility of [bmim][PF6] at very low liquid compositions. An attractive feature of the Wong−Sandler approach is that it allows performing extrapolations of gas−liquid phase behavior to higher (or lower) temperatures and pressures with good accuracy. In an attempt to verify the predictive capabilities of the Wong−Sandler approach within the present modeling framework, CO2 solubilities were computed at temperatures other than 25 °C using the same UNIQUAC interaction parameters and k1,2 values previously obtained at 25 °C. Figures 6 and 7 depict the predicted CO2 solubilities for [bmim][PF6] at 10 and 50 °C using the SRK CEoS, and for [bmim][Tf2N] at E



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Figure 9. Predicted CO2 solubilities in [omim][Tf2N] at T 25 °C with the PR CEoS.

Figure 7. Predicted CO2 solubilities in [bmim][Tf2N] at T 25 °C with the PR CEoS.

Figure 10. Variation of k1,2 with temperature for two ILs.

Figure 8. Predicted CO2 solubilities in [emim][Tf2N] at T 25 °C with the SRK CEoS.

Finally, what remains is to verify the capability of the present approach in representing the experimental CO2 solubilities in [emim][PF6] measured by Shariati and Peters10 at elevated pressures (up to 971 bar). This particular CO2−IL system was not considered during the initial correlating process since no experimental data was available at 25 °C. Instead, model parameters were adjusted to fit experimental solubilities measured by the authors at the lowest temperature (40 °C). Figure 13 shows the correlation results at this temperature (via the use of the PR CEoS) along with model predictions at higher temperatures (60 and 80 °C) using the same model parameters obtained at 40 °C. As revealed by this figure, the present approach does a pretty good job in capturing the CO2 solubility behavior over a large range of pressures, particularly, the sharp increase in total pressure that starts at about 0.45 in CO2 mole fraction for the three isotherms. As a matter of fact, there was no need to make k1,2 temperature dependent for this particular system.

To obtain improved representations of experimental CO2 solubilities in certain ILs over a wide temperature range we need to introduce proper temperature dependences into the model parameters. To keep the number of model parameters to a minimum, only the interaction parameter for the second virial coefficient k1,2 was assumed to be temperature dependent. Accordingly, for the particular cases of [emim][Tf2N] and [omim][Tf2N], the value of k1,2 was adjusted to improve the fit at temperatures higher than 25 °C; the UNIQUAC interaction parameters remained unchanged during this process (those obtained at 25 °C). As depicted in Figure 10, we found that the k1,2 value varies linearly with temperature for the two aforementioned ILs. Making k1,2 temperature dependent greatly improves the estimations of CO2 solubilities in [emim][Tf2N] and in [omim][Tf2N] over a wide temperature range, as revealed by Figures 11 and 12, respectively. F



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Figure 11. Improved CO2 solubilities in [emim][Tf2N] making k1,2 temperature dependent.

Figure 13. Representation of high-pressure CO2 solubilities in [emim][PF6] using the PR CEoS.

(iii) High-pressure CO2 solubilities in [emim][PF6] (up to almost 1000 bar) were adequately represented by the present approach within a temperature range of 40−80 °C.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. ⊥ Paper presented at the 18th NIST Symposium on Thermophysical Properties, June 24−29, 2012, Boulder, CO.

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ACKNOWLEDGMENTS R. M.-S. and J.A.C.-V. gratefully acknowledge the Instituto Politécnico Nacional and CONACyT for providing financial support for this work.

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Figure 12. Improved CO2 solubilities in [omim][Tf2N] making k1,2 temperature dependent.

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CONCLUSIONS A formal modeling approach to represent the CO2 solubility in selected ILS is presented here. It makes use of a cubic equation of state (Soave or Peng−Robinson) coupled with modern mixing rules of the Wong−Sandler type. The following conclusions can be drawn from this work: (i) The present modeling approach (either using the SRK or PR CEoS) correlated quite well the experimental CO2 solubilities in four imidazolium-based ILs at 25 °C and over a pressure range of 0.0003−60 bar using three adjustable parameters: UNIQUAC interaction parameters (ΔU1,2 and ΔU2,1), and the interaction parameter for the second virial coefficient (k1,2). (ii) Model predictions at temperatures other than 25 °C were also satisfactory; however, some ILs required the use of temperature-dependent k1,2 values for improved CO2-solubility estimations. G

LIST OF SYMBOLS a = attractive parameter in the CEoS A = Helmholtz free energy b = Co-volume parameter in the CEoS C = CEoS-specific constant D = as defined in eq 5 f = objective function G = Gibbs free energy k = interaction parameter in the CEoS N = number of data points P = pressure q = surface area parameter in UNIQUAC Q = as defined in eq 4 r = volume parameter in UNIQUAC R = universal gas constant T = temperature V = molar volume x = liquid mole fraction y = gas mole fraction z = coordination number dx.doi.org/10.1021/ie400106g | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX


Correlation

Greek Letters

(16) Kim, Y. S.; Jang, J. H.; Lim, B. D.; Kang, J. W.; Lee, C. S. Solubility of Mixed Gases Containing Carbon Dioxide in Ionic Liquids: Measurements and Predictions. Fluid Phase Equilib. 2007, 256, 70. (17) Jacquemin, J.; Husson, P.; Majer, V.; Costa-Gomes, M. F. Influence of Cation on the Solubility of CO2 and H2 in Ionic Liquids Based on Bis(trifluoromethylsulfonyl)imide Anion. J. Solution Chem. 2007, 36, 967. (18) Schilderman, A. M.; Raeissi, S.; Peters, C. J. Solubility of Carbon Dioxide in the Ionic Liquid 1-Ethyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide. Fluid Phase Equilib. 2007, 260, 19. (19) Carvalho, P. J.; Á lvarez, V. H.; Machado, J. J. B.; Pauly, J.; Daridon, J. L.; Marrucho, I. M.; Aznar, M.; Coutinho, J. A. P. HighPressure Phase Behavior of Carbon Dioxide in 1-Alkyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide Ionic Liquid. J. Supercrit. Fluids 2009, 48, 99. (20) Ren, W.; Sensenich, B.; Scurto, A. M. High-Pressure Phase Equilibria of {Carbon Dioxide + n-Alkyl-imidazolium Bis(trifluoromethylsulfonyl)imide} Ionic Liquids. J. Chem. Thermodyn. 2010, 42, 305. (21) Revelli, A. L.; Mutelet, F.; Jaubert, J. N. High Carbon Dioxide Solubilities in Imidazolium-Based Ionic Liquids and in Poly(ethylene glycol) Dimethyl Ether. J. Phys. Chem. B 2010, 114, 12908. (22) Carvalho, P. J.; Coutinho, A. P. On the Nonideality of CO2 Solutions in Ionic Liquids and Other Low Volatile Solvents. J. Phys. Chem. Lett. 2010, 1, 774. (23) Bara, J. E.; Carlisle, T. K.; Gabriel, C. J.; Camper, D.; Finotello, A.; Gin, D. L.; Noble, R. D. Guide to CO2 Separations in ImidazoliumBased Room-Temperature Ionic Liquids. Ind. Eng. Chem. Res. 2009, 48, 2739. (24) Vega, L. F.; Vilaseca, O.; Llovell, F.; Andreu, J. S. Modeling Ionic Liquids and the Solubilities of Gases in Them: Recent Advances and Perspectives. Fluid Phase Equilib. 2010, 294, 15. (25) Ally, M. R.; Braunstein, J.; Baltus, R. E.; Dai, S.; DePaoli, D. W.; Simonson, J. M. Irregular Ionic Lattice Model for Gas Solubilities in Ionic Liquids. Ind. Eng. Chem. Res. 2004, 43, 1296. (26) Scovazzo, P.; Camper, D.; Kieft, J.; Poshusta, J.; Koval, C.; Noble, R. Regular Solution Theory and CO2 Gas Solubility in RoomTemperature Ionic Liquids. Ind. Eng. Chem. Res. 2004, 43, 6855. (27) Shariati, A.; Peters, C. J. High-Pressure Phase Behavior of Systems with Ionic Liquids: Measurements and Modeling of the Binary System Fluoroform+1-Ethyl-3-Methylimidazolium Hexafluorophosphate. J. Supercrit. Fluids 2003, 25, 109. (28) Maia, F. M.; Tsivintzelis, I.; Rodriguez, O.; Macedo, E. A.; Kontogeorgis, G. M. Equation of State Modelling of Systems with Ionic Liquids: Literature Review and Application with the Cubic Plus Association (CPA) Model. Fluid Phase Equilib. 2012, 332, 128. (29) Karakatsani, E. K.; Economou, I. G.; Kroon, M. C.; Peters, C. J.; Witkamp, G. J. tPC-PSAFT Modeling of Gas Solubility in Imidazolium-Based Ionic Liquids. J. Phys. Chem. C 2007, 111, 15487. (30) Andreu, J. S.; Vega, L. F. Capturing the Solubility Behavior of CO2 in Ionic Liquids by a Simple Model. J. Phys. Chem. C 2007, 111, 16028. (31) Ji, X.; Adidharma, H. Thermodynamic Modeling of CO2 Solubility in Ionic Liquid with Heterosegmented Statistical Associating Fluid Theory. Fluid Phase Equilib. 2010, 293, 141. (32) Chapman, W. G.; Gubbins, K. E.; Jackson, G.; Radosz, M. New Reference Equation of State for Associating Liquids. Ind. Eng. Chem. Res. 1990, 29, 1709. (33) Huang, S. H.; Radosz, M. Equation of State for Small, Large, Polydisperse, and Associating Molecules. Ind. Eng. Chem. Res. 1990, 29, 2284. (34) Soave, G. Equilibrium Constants from a Modified Redlich− Kwong Equation of State. Chem. Eng. Sci. 1972, 27, 1197. (35) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59. (36) Wong, D. S. H.; Sandler, S. I. A Theoretically Correct Mixing Rule for Cubic Equations of State. AIChE J. 1992, 38, 671.

δ1,δ2 = CEoS-specific constants ΔU = energy interaction parameter in UNIQUAC τ = dimensionless energy parameter in UNIQUAC θ = area fraction ω = acentric factor φ = segment fraction Subscripts

c = critical property EoS = equation of state i, j = i−j pair interaction m = mixture property 1 = CO2 2 = ionic liquid Superscripts

cal = calculated value combinatorial = combinatorial contribution exp = experimental value EX = excess property residual = residual contribution

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REFERENCES

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Correlation

(37) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116. (38) Orbey, H.; Sandler, S. I. Modeling Vapor−Liquid Equilibria; Cambridge University Press: New York, 1998. (39) Mahurin, S. M.; Lee, J. S.; Baker, G. A.; Luo, H.; Dai, S. Performance of Nitrile-Containing Anions in Task-Specific Ionic Liquids for Improved CO2/N2 Separation. J. Membr. Sci. 2010, 353, 177. (40) Babarao, R.; Dai, S.; Jiang, D. Understanding the High Solubility of CO2 in an Ionic Liquid with the Tetracyanoborate Anion. J. Phys. Chem. B 2011, 115, 9789. (41) Valderrama, J. O.; Robles, P. A. Critical Properties, Normal Boiling Point Temperatures, and Acentric Factors of Fifty Ionic Liquids. Ind. Eng. Chem. Res. 2007, 46, 1338. (42) Santiago, R. S.; Santos, G. R.; Aznar, M. UNIQUAC Correlation of Liquid-Liquid Equilibrium in Systems Involving Ionic Liquids: The DFT-PCM Approach. Fluid Phase Equilib. 2009, 278, 54. (43) Santiago, R. S.; Santos, G. R.; Aznar, M. UNIQUAC Correlation of Liquid-Liquid Equilibrium in Systems Involving Ionic Liquids: The DFT-PCM Approach. Part II. Fluid Phase Equilib. 2010, 293, 66. (44) Kazarian, S. G.; Briscoe, B. J.; Welton, T. Combining Ionic Liquids and Supercritical Fluids: In Situ ATR-IR Study of CO2 Dissolved in Two Ionic Liquids at High Pressures. Chem. Commun. 2000, 20, 2047. (45) Muldoon, M.; Aki, S.; Anderson, J. L.; Dixon, J. F.; Brennecke, J. F. Improving Carbon Dioxide Solubility in Ionic Liquids. J. Phys. Chem. B 2007, 111, 9001. (46) Shannon, M. S.; Tedstone, J. M.; Danielsen, S. P. O.; Hindman, M. S.; Irvin, A. C.; Bara, J. E. Free Volume as the Basis of Gas Solubility and Selectivity in Imidazolium-Based Ionic Liquids. Ind. Eng. Chem. Res. 2012, 51, 5565.

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Accurate Modeling of CO2

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