Prediction of CO2 solubility in ionic liquids using the PSRK model

Prediction of CO2 solubility in ionic liquids using the PSRK model

Accepted Manuscript Title: Prediction of CO2 Solubility in Ionic Liquids Using the PSRK Model Author: Hanee F. Hizaddin Mohamed K. Hadj-Kali Inas M. A...

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Accepted Manuscript Title: Prediction of CO2 Solubility in Ionic Liquids Using the PSRK Model Author: Hanee F. Hizaddin Mohamed K. Hadj-Kali Inas M. AlNashef Farouq S. Mjalli Mohd A. Hashim PII: DOI: Reference:

S0896-8446(15)00070-4 http://dx.doi.org/doi:10.1016/j.supflu.2015.02.009 SUPFLU 3239

To appear in:

J. of Supercritical Fluids

Received date: Revised date: Accepted date:

8-10-2014 6-2-2015 7-2-2015

Please cite this article as: H.F. Hizaddin, M.K. Hadj-Kali, I.M. AlNashef, F.S. Mjalli, M.A. Hashim, Prediction of CO2 Solubility in Ionic Liquids Using the PSRK Model, The Journal of Supercritical Fluids (2015), http://dx.doi.org/10.1016/j.supflu.2015.02.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Graphical abstract

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Highlights The PSRK model is successfully used to predict CO2 solubility in ILs

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The UNIFAC PSRK matrix is extended to include new ILs groups

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Experimental VLE data were subject to consistency test

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The model shows good predictability for ILs having longer alkyl chain

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Prediction of CO2 Solubility in Ionic Liquids Using the PSRK Model

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Hanee F. Hizaddina, Mohamed K. Hadj-Kalib*, Inas M. AlNashefb, Farouq S. Mjallic, Mohd A. Hashima a

Department of Chemical Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia.

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Petroleum and Chemical Engineering Department, Sultan Qaboos University, Muscat 123, Oman.

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*Corresponding author: Tel. +966-1-4676040, [email protected]

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Chemical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia.

Abstract

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The predictive Soave–Redlich–Kwong (PSRK) model was applied to predict CO2 solubility in

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imidazolium-based ionic liquids containing bis(trifluoromethylsulfonyl)imide [Tf2N], tetrafluoroborate [BF4], and hexafluorophosphate [PF6] anions. The UNIFAC PSRK matrix was extended to include these new groups. Binary

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interaction parameters were obtained by regressing experimental vapor-liquid equilibrium data available in the literature. Experimental data were subjected to a consistency test, and only consistent data were considered during the regression. The model predictions showed satisfactory agreement with the experimental data at pressures up to 5 MPa, with an overall root mean square deviation (RMSD) of 0.31. The prediction ability of the model was tested for ionic liquids containing long alkyl chains, exhibiting an overall RMSD of 0.40. The results indicated that the PSRK model provides a reasonable prediction of CO2 solubility in ionic liquids at pressures not in the vicinity of the critical pressures of CO2 and ionic liquids.

Keywords: PSRK model; ionic liquids; CO2 capture; solubility prediction.

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1 Introduction

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CO2 capture has received increasing interest in recent years as a method for addressing the challenge of climate change caused by rising CO2 emissions, mainly from power plants and fossil fuel processing plants (e.g.,

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coal, crude oil, and natural gas). Currently, the process applied for CO2 capture at a large scale is the amine-based solvent absorption process dating back to the 1940s [1]. Amines are used as solvents for CO2 absorption because of

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their high reactivity with CO2. However, despite being the most widely used process, amine scrubbing of CO2 has many disadvantages, including low CO2 capture capacity; corrosiveness of the amines; loss of the solvent because of

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the high volatility of amines, which damage the environment; low thermal stability; degradation of the solvent during regeneration, causing low solvent recovery; and high energy consumption in the regeneration process

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because of the large enthalpy of formation produced in reactions with CO2 [1,2]. Ionic liquids have emerged as promising alternatives and have gained increasing attention as potential candidates for replacing amine-based solvents. Ionic liquids are molten salts that exist in a liquid phase at room

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temperature. They consist of a combination of asymmetrical, large cations such as quaternary imidazolium (IMI),

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phosphonium, and pyridinium and smaller, more symmetric anions such as chloride, tetrafluoroborate (BF4), and

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hexafluorophosphate (PF6). The appealing properties of ionic liquids include the negligible vapor pressure, which leads to zero emissions of volatile organic compounds; high thermal and chemical stability; nonflammability; and tunability. The tunability of ionic liquids is the reason they are known as “designer solvents”; this name originates from the numerous ways in which cations and anions can be combined to suit a specific application. The way in which cations, anions, and substituents are combined affects the physical properties of ionic liquids, such as the viscosity, density, electrochemistry, and affinity to other compounds. Studies on CO2 solubility in ionic liquids began to flourish after Blanchard et al. discovered that CO2 is highly soluble in ionic liquids [3]. Studies on CO2 solubility at high pressures have reported solubility in ionic liquids up to 0.87 (mole fraction) [4,5]. To scale-up the potential of using ionic liquids for CO2 capture at a large scale, many crucial factors must be considered, one of which is the thermodynamic properties and behavior of systems containing CO2 and ionic liquids. However, because there are numerous possible combinations of ionic liquids [2], performing experiments to characterize each of their properties and behaviors with CO2 is impractical. 4

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Therefore, predictive methods for determining the thermodynamic behavior of systems with ionic liquids are necessary and would facilitate selecting appropriate ionic liquids, process design, and optimizing the CO2 capture process. Reports on the models proposed to represent the solubility of CO2 in ionic liquids are summarized in Table

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1. These models can be categorized into molecular models, quantum chemistry models, equations of state (EoSs), and other types of model. Shah and Maginn performed Monte Carlo simulation in 2005 by using two approaches

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(i.e., test particle insertion and expanded ensemble Monte Carlo methods) to model the solubility of CO2 and other

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gases (i.e., methane, ethane, oxygen and nitrogen) in 1-butyl-3-methylimidazolium hexafluorophosphate at room temperature and atmospheric pressure [6,7]. Urukova et al. [8] used Monte Carlo simulations in the Gibbs ensemble

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to model the solubility of CO2, carbon monoxide, and hydrogen in the same ionic liquid, but used a different source of experimental data. Ally et al. adopted the irregular ionic lattice model to predict vapor pressure and the solubility of gases, including CO2 in [C4mim][PF6] and [C8mim][BF4] ionic liquids at low and high pressures and at

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temperatures between 298 and 333 K [9].

The COSMO-RS and COSMO-SAC models are quantum chemistry models frequently used to represent

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CO2 solubility in ionic liquids. Manan et al. evaluated the use of COSMO-RS with COSMOtherm software in

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predicting the solubility of nine gases, including CO2 in 27 ionic liquids. COSMO-RS qualitatively predicted gas solubility in the ionic liquids at the correct order of magnitude according to experimental data, even when the

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calculated solubility did not match the experimentally measured solubility for each ionic liquid exactly [10]. Sumon et al. applied the COSMO-RS model to screen gas solubility in 2701 ionic liquids for CO2 capture [11]. COSMO-RS was shown to be suitable for rapidly screening suitable solvents, but was unable to reproduce several trends that appeared in the experimental solubility data. Shimoyama and Ito applied the COSMO-SAC model to predict the solubility of CO2, nitrogen, and methane in IMI-based ionic liquids and concluded that the predicted solubility of each gas was acceptable within a 20% deviation from the experimental data [12]. Maiti combined the COSMO-RS model and Soave–Redlich–Kwong (SRK) EoS to predict CO2 solubility in all-functionalized guanidinium- and BF4based ionic liquids [13]. Lastly, the most widely used approach in modeling CO2 solubility in ionic liquids is the use of an EoS. In 2005, Shiflett and Yokozeki claimed to be the first to use a cubic EoS to model CO2 solubility in ionic liquid [14]. They used a generic Redlich–Kwong-type EoS with an empirical function for the parameter a and modified the van

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der Waals-Berthelot mixing rule to model CO2 solubility in two IMI-based ionic liquids. The predictions were consistent with their experimental results and those of Anthony et al. [15] and Kamps et al. [16]. Valderrama et al. used the Peng–Robinson (PR) EoS with the Kwak–Mansoori mixing rule to model CO2 solubility in IMI-based ionic liquids, and the modeling results were compared with those obtained using various combinations of EoSs, mixing

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rules, and activity coefficient models [17]. Carvalho et al. [4,5], Ren et al. [18], and Yim et al. [19] reported CO2 solubility in ionic liquids at high pressures, namely 74 MPa, 25 MPa, and 48 MPa, respectively. Carvalho et al. used

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the PR EoS with the Wong–Sandler mixing rule and UNIQUAC activity coefficient model, whereas Yim et al. and

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Ren et al. used the PR EoS with the van der Waals mixing rule. Other EoSs were used for modeling the solubility of CO2 and other gases in ionic liquids, including (1) the square-well chain fluid (SWCF) EoS [20]; (2) the group

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contribution nonrandom lattice fluid EoS [21]; (3) the statistical-associating-fluid-theory (SAFT) EoS [22]; and (4) the Sanchez–Lacombe EoS [23]. Maia et al. [24] used the cubic-plus-association (CPA) EoS to model CO2 solubility in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (C2mim[Tf2N]) and 1-butyl-3-

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methylimidazolium bis(trifluoromethylsulfonyl)imide C4mim[Tf2N]. They also included a review of the EoSs used to describe gas solubility in ionic liquids.

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Approaches other than molecular modeling, quantum chemistry, and EoSs have been adopted; for example,

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Eslamimanesh et al. [25] used an artificial network model to predict CO2 solubility in 24 ionic liquids, and Kamps et al. [16] and Chen et al. [26] used an extended Henry’s law correlation to represent experimental CO2-IL VLE data.

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This paper proposes a new approach that combines the advantages of using cubic equations of state with the predictive capabilities offered by the UNIFAC group contribution method. The resulting predictive Soave– Redlich–Kwong (PSRK) model has all the advantages of an equation of state; it guarantees the continuity of the phase diagram in the vicinity of the critical point. It can be applied to systems with supercritical components and allows the calculation of densities, enthalpies and other properties even in systems with polar components. Another application of PSRK is the prediction of critical lines of mixtures. The PSRK model can be used for predictions of VLE over a temperature and pressure range much wider than that possible with UNIFAC. Moreover, there was no introduction of new parameters which would require a fitting procedure, only existing UNIFAC group-interaction parameters and pure component parameters are required. It gives better result with non-polar systems than the UNIFAC model does. The PSRK model is described in details in Section 2. Then, the thermodynamic consistency

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test adopted to screen the experimental data is explained in Section 3. These data are used in Section 4 to regress the binary interaction parameters among CO2, imidazolium cation, and various anion groups in the PSRK matrix.

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2 Thermodynamic modeling background At a constant temperature and pressure, vapor–liquid equilibrium is achieved when liquid and vapor

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refer to the liquid phase L and the vapor phase V composition, respectively.

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where

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fugacities of each component within the two phases are equal [27-29]:

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To express the fugacity, the homogeneous or the heterogeneous approach can be used. In the homogeneous approach (φ-φ approach), the liquid and vapor phases are described by the same cubic EoS, such as the SRK or PR EoS. However, in the heterogeneous approach (γ-φ approach), the vapor phase is described by an EoS, and the

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nonideality of the liquid phase is expressed by activity coefficients derived from a molar excess Gibbs energy (Gex) model, such as the NRTL, UNIQUAC, and UNIFAC models. The first approach ensures the continuity of the

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equilibrium curve near the critical region, and the saturation vapor pressure does not need to be approximated above

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the critical point; however, the second approach is appropriate for strongly non-ideal mixtures because it enables a

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superior description of the non-idealities in the liquid phase. When mixtures are considered, the advantages of both approaches can be combined using a complex mixing rule based on the homogeneous approach where the mixing rule parameters (a and b) are expressed in terms of the excess molar enthalpy directly related to the activity of coefficients. An example of the combination of a cubic EoS with a predictive activity coefficient model is the PSRK model [30-32], which was developed by Gmehling and based on the model proposed by Michelsen [33]. The PSRK model uses zero pressure as the reference state.

The parameters a and b are those which appear in the cubic EoS, such as the SRK EoS: 7

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The PSRK model provides realistic predictions of phase equilibria in systems containing supercritical

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components, such as the solubility of gases at low and high pressures. Accurate results are also achieved with polar

2.1 Mathias–Copeman α-function

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The UNIFAC consortium published the most recent version in 2011.

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and nonpolar systems over wide temperature and pressure ranges. The UNIFAC PSRK matrix is regularly updated.

When the PSRK mixing rule is used with either the SRK or PR EoS, replacing the original α-function with

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the Mathias–Copeman function is recommended [34]:

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The parameters are fitted to experimental vapor pressure data on pure components and provide a superior

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description of the vapor pressure than the original relation does. The form of the equation is chosen as it can be reduced to the original Soave form by setting the parameters C2 and C3 to zero.

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The parameter C1 can be obtained from the acentric factor () by using the following relation:

2.2 Modified UNIFAC (Dortmund) method Developing the PSRK model requires regressing the binary interaction parameters between the various groups that appear in the expression of the activity coefficient model. The modified UNIFAC Dortmund version [35] was used in this study. The activity coefficient is expressed as follows:

The relation between the excess Gibbs energy Gex which appears in Eq. (2) and the activity coefficient is given by the fundamental equation:

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The combinatorial term is given by the expression:

with:

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The pure component parameters ri and qi respectively represent molecular van der Waals volumes and molecular surface areas. They are calculated as the sum of the group volume and group area parameters Rk and Qk

where the quantity vk

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obtained from van der Waals group volumes and surface areas [36]:

is the number of subgroups of type (k) in the component (i).

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where

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Conversely, the residual term is expressed as

Subscript i identifies species, and j is a dummy index running over all species. Subscript k identifies

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subgroups, and m is a dummy index running over all subgroups. One major modification provided by the Dortmund version is the dependence of the binary interaction parameters mk on temperature:

Section 4 describes the determination of these parameters for the main ionic liquid groups.

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Application of UNIFAC model to ionic liquids Lei et al. extended the group parameters of the UNIFAC model to systems with ionic liquids. Twelve main

groups and 24 subgroups were added to the classical UNIFAC parameter matrix [37]. These showed that the new group parameters can be used to predict the vapor–liquid equilibria of systems with ionic liquids at finite concentrations and to screen suitable ionic liquids for separation processes.

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The van der Waals parameters ri and qi for some ionic liquids are available in the literature [38]. For other

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parameters, the authors used the following correlations:

where Vm is the molar volume of ionic liquids at 298.15 K, z is the coordination number, and li is the bulk factor.

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In 2011, Nebig and Gmehling [39] revised and extended the group interaction parameters of the modified

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UNIFAC model for ionic liquids. The current matrix contains the group interaction parameters for 37 group pairs. In this study, the group interaction parameters between several classical main groups and IMI cation with three anions

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3 Thermodynamic consistency test

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(bis(trifluoromethanesulfonyl)imide [Tf2N], BF4, and PF6) were fitted to experimental vapor–liquid equilibria data.

Before the regression was performed, the experimental data were tested for thermodynamic consistency.

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Only consistent data points were included in the regression of the PSRK parameters. A thermodynamic consistency

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test of vapor–liquid equilibrium data for mixtures containing ionic liquid developed by Valderrama et al. [40] was

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Valderrama et al. used the PR equation with the Wong–Sandler mixing rule and the van Laar activity coefficient model. While in this study, the PR EoS was combined with the Modified Huron-Vidal (MHV1) mixing rule and the Margules activity coefficient model. The proposed area test, which was based on the Gibbs–Duhem equation written in the integral form, can be represented as follows:

In this equation, P is the system pressure; x1 is the mole fraction of the dissolved gas (CO2) in the liquid mixture; φ1 and φ2 are the fugacity coefficients of the gas and ionic liquid in the liquid mixture, respectively; and Z is the compressibility factor of the liquid mixture. The flow diagram of the consistency test is provided as supplementary data (Figure S.1). In this flowchart Ap expresses the left-hand-side integral of Eq. (14), and A expresses the right-hand-side summation. The Ap integral values were calculated using the trapezoidal rule.

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The MHV1 mixing rule [33] is expressed similarly to the PSRK mixing rule, and the Margules activity coefficient [41] is expressed as follows:

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The consistency test was developed using Simulis® Thermodynamics package, a thermo-physical property calculation server provided by ProSim [42] and available as an MS Excel add-in. The parameters Aij and Aji from the

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Margules model were regressed using the experimental data. The GRG nonlinear optimization method from the

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Excel Solver was used to satisfy the following objective function:

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The binary interaction parameters of the Margules model for CO2+C2mim[Tf2N] and CO2+C4mim[Tf2N] were reported in the Supplementary Material (Tables S1 and S3).

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3.1 Consistency test results

Correlation with the PR/MHV1/Margules model revealed that pressure deviations for all systems were

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within 10%, indicating that the PR/MHV1/Margules model can be used in performing the area test to determine the

3.1.1

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were found to be fully consistent.

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consistency. The test was applied to the systems described in Sections 3.1.1 to 3.1.3, and the remaining systems

System: CO2 (1) + C2mim[Tf2N] (2) For the system CO2 (1) and C2mim[Tf2N] (2), experimental VLE data from three sources, namely Carvalho

et al. [4, 5], Schilderman et al. [43], and Kim et al. [21], were included in the regression. Carvalho et al. reported nine isotherms with temperatures ranging between 293 and 363 K; each isotherm had nine data points. The pressures ranged between 0.6 and 48 MPa, with the concentration of CO2 in ionic liquids ranging between 0.221 and 0.75. Carvalho et al. tested their data for consistency by using an approach developed by Alvarez and Aznar [44], which involves using PTy data, PR and Wong-Sandler mixing rules, and the UNIQUAC activity coefficient model. The results of the consistency test performed in this study and that of Carvalho et al. verified that none of the isotherms were fully consistent and that, for all isotherms, points for which xCO2 = 0.75 or higher were not consistent. However, in this study, on average, only five to six data points were considered

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consistent for each isotherm. After two to three data points for which %∆A > 20% were removed, the data in the isotherms were consistent. Schilderman et al. [43] reported the solubility of CO2 in C2mim[Tf2N] at moderate pressures ranging from 0.6 to 12 MPa in a total of nine isotherms at temperatures between 313 and 391 K. The concentrations of CO2 in

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ionic liquid were reported to be between 0.123 and 0.593. For this set of data, only data at isotherms 323 and 332 K were reported to be fully consistent; others were not fully consistent (NFC) or thermodynamically inconsistent (TI).

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On average, two NFC data points were removed at each isotherm.

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Kim et al. reported only one isotherm at a temperature of 298.15 K and a pressure range between 0.2 and 0.9 MPa and that the concentration of CO2 in ionic liquid was between 0.05 and 0.209 [21]. The data set from Kim

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et al. was found to be thermodynamically consistent (TC). System: CO2 (1) + C4mim[Tf2N] (2)

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For the system CO2 + C4mim[Tf2N], VLE data reported by Carvalho et al. [5], Oh et al. [45], and Aki et al. [46] were tested for consistency. Carvalho et al. [5] reported a total of eight isotherms with a pressure range between

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0.6 and 46 MPa, a temperature range between 293 and 363 K, and a concentration of CO2 in ionic liquid between 0.231 and 0.801. None of the isotherms were found to be fully consistent, and therefore inconsistent data were

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removed and tested again to verify that the remaining data points were fully consistent.

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In addition, Oh et al. [45] provided VLE data on CO2 and C4mim[Tf2N] at high pressures, reporting a total of seven isotherms with a pressure range between 0.6 and 32 MPa, a temperature range between 298 and 345 K, and a concentration of CO2 in ionic liquid between 0.212 and 0.754. Oh et al. reported that phase behavior other than vapor–liquid equilibrium was observed in this system (i.e., liquid–liquid equilibrium existed for some of the phase change). In this test, only the points that exhibited vapor–liquid equilibrium were considered. The consistency test results indicated that six of the isotherms were NFC and that one was TI. Similarly, inconsistent data were removed and subsequent tests resulted in fully consistent data for all isotherms. Aki et al. reported the solubility of CO2 in C4mim[Tf2N] at moderate pressures ranging from 1.4 to 13 MPa for two temperatures, 313 and 333 K, and concentrations of CO2 in ionic liquid between 0.250 and 0.824 [46]. Data at isotherm 333 K were determined to be fully consistent; however, data at isotherm 313 K were not fully consistent and were consistent only after the removal of inconsistent points.

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3.1.3

System: CO2 (1) + C6mim[Tf2N] (2) For the system CO2 + C6mim[Tf2N], data from Kim et al. [21] and Yokozeki et al. [47] were tested for

consistency. Each data set reported one isotherm at low pressure. Kim et al. reported solubility of CO2 in C6mim[Tf2N] at a temperature of 298.15 K, in a pressure range between 0.2 and 0.9 MPa, and at a concentration of

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CO2 in ionic liquid between 0.069 and 0.236. The data from Kim et al. were determined to be fully consistent. Yokozeki et al. reported VLE data at 297 K with a pressure range between 0.01 and 1.97 MPa and a concentration

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of CO2 in ionic liquid between 0.006 and 0.433. Data from Yokozeki et al. were not fully consistent, and after the

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removal of three points, the data became fully consistent.

3.2 Discussion of the results of the consistency tests

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At high pressures, phase behavior other than VLE may occur. This results in the data being reported as inconsistent because the test used here is specific to VLE data. This occurrence may be attributed to the estimated

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critical pressures of the used ionic liquids, which were approximately 30 bar (3 MPa), whereas the pressures involved in the experiments were much higher. For example, in Carvalho et al. [4,5], the system pressure reached 46

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MPa (approximately 460 bar), which is more than 10 times greater than the pseudo-critical pressures of the ionic

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liquid C2mim[Tf2N]. Therefore, at high pressures, there is a high possibility that the phase of the mixture of CO2 and the ionic liquid cannot be determined. To support this justification, Ren et al. [18], Shin et al. [48], and Oh et al. [45]

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reported the occurrence of liquid–liquid and vapor–liquid–liquid equilibria for the system CO2 + Cnmim[Tf2N] (n = 2, 4, 6, 8) at high pressures. Therefore, extra care should be taken in measuring the solubility of CO2 in ionic liquids at pressures greater than the pseudo-critical pressures of the ionic liquids.

4 Regression technique and prediction tests The model developed in this work assumes that ionic liquids are insoluble in the pure CO2 vapor phase. Then, as in other group contribution models, in the PSRK model, specifying the group segmentation of the compounds is essential for determining the group interaction parameters. In this study, segmentation approach used by Nebig and Gmehling [39] was adopted. For example, the ionic liquid C2mim[Tf2N] was broken down into two CH3 groups, one CH2 group, one IMI group, and one Tf2N group.

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The properties of CO2 and ionic liquids required for the PSRK model are listed in Table 2. Data for CO2 were obtained from the Design Institute of Physical Properties (DIPPR) database available in Simulis thermodynamics package [42], whereas the estimated pseudo-critical properties for ionic liquids were taken from the report by Valderrama et al. [49], who developed a group contribution method for obtaining these properties.

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Table 3 shows the van der Waals area and volumes Rk and Qk for each of the subgroups involved in this regression. Values for CO2, CH3, and CH2 were obtained from the original PSRK matrix available in Simulis

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thermodynamics package [42]. Values for IMI, Tf2N, and BF4 were obtained from the report by Nebig and

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Gmehling [39]; values for PF6 were obtained from the report by Alevizou et al. [50].

Regression was initially performed using all experimental data available in the literature. However, large

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deviations were obtained between calculated and experimental pressures near 10 MPa and above. This may be attributed to the system pressure being substantially greater than the pseudo-critical pressure of the ionic liquids, and even that of the CO2 (approximately 7.3 MPa). A second liquid phase may occur under these conditions, and

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analyzing the vapor phase may be necessary. Therefore, during the regression, only consistent experimental VLE data up to pressures of 5 MPa were included; data that exhibited LLE or VLLE were excluded. Details on the

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consistency of experimental VLE data are discussed in Section 3.

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Table S1 in the supplementary materials shows details on the experimental VLE data that were included in the regression. For the regression of CO2-IMI and CO2-Tf2N binary interaction parameters, data for the systems

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CO2+ C2mim[Tf2N] and CO2+ C4mim[Tf2N] were used, whereas for CO2-BF4 parameters, data for the system CO2+ C4mim[BF4] were used. For CH2-PF6, IMI-PF6, and CO2-PF6, data for the system CO2+ C4mim[PF6] were used; the maximum experimental pressure for this mixture was slightly above the critical pressure of CO2. A total of 410 data points from all sources at various temperature and pressure ranges were included. As for the consistency test, the regression was performed using Simulis® Thermodynamics capabilities coupled with the Excel Solver tool. The objective function used in the calculation is as follows:

where P is the total pressure of the system at equilibrium, and x1 is CO2 solubility.

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4.1 Discussion of the regression results Table 4 shows the group interaction parameters for the groups involved in this study and for the parameters obtained from the regression. The parameters for CO2-CH2 were obtained from the UNIFAC PSRK matrix

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published by the UNIFAC consortium and available via Simulis thermodynamics package [42]. The parameters for CH2-IMI, CH2-Tf2N, CH2-BF4, IMI-Tf2N, and IMI-BF4 were obtained from the report by Nebig and Gmehling [39].

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The rows in bold show the parameters obtained in this study. Figure 1 shows the extended PSRK matrix with new group interaction parameters.

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Graphical and statistical analyses were performed to evaluate the results of the regression. The root mean square deviation (RMSD) and average absolute relative deviation (AARD) were calculated. The formulas for the

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RMSD and AARD are as follows:

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Figures 2–5 show a comparison between the calculated bubble pressure (Pcal) and experimental bubble

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pressure (Pexp) for the systems CO2 + C2mim[Tf2N], CO2 + C4mim[Tf2N], CO2 + C4mim[BF4], and CO2 + C4mim[PF6]. A graphical comparison between the calculated and experimental CO2 solubility values is available as

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supplementary data (Figures S2–S5). Agreement was observed for all systems between Pcal and Pexp as well as between the calculated CO2 and experimental solubility values, with a slight deviation at elevated pressures. The RMSD and AARD for each data set are summarized in Table 5. We could have obtained a better correlation if we had regressed and fitted the parameters according to all groups involved; however, we used the reported parameters (i.e., from the original PSRK matrix and from Nebig and Gmehling for the groups of cations and anions), and we optimized only parameters for groups that needed to be paired with CO2 to demonstrate the prediction ability of the PSRK model.

4.2 Prediction tests This section describes the feasibility of using the PSRK parameters obtained in this study to predict the VLE for systems with CO2 and IMI-based ionic liquids with Tf2N, BF4, and PF6 anions and a comparison of the

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predicted values with experimental data that were not included in the regression. The results of the prediction test were evaluated graphically and statistically. To test the prediction ability of the binary interaction parameters between CO2-IMI and CO2-Tf2N, PSRK prediction was performed for the systems CO2 + C5mim[Tf2N] and CO2 + C6mim[Tf2N]. The results were compared

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with experimental data from Carvalho et al. for the system CO2 + C5mim[Tf2N], whereas for the system CO2 + C6mim[Tf2N], the results were compared with experimental data from Kim et al. [21] and Yokozeki et al. [47].

cr

For the system CO2 + C5mim[Tf2N], the comparison between Pcal and Pexp was initially performed for all

us

pressures in the data set (up to 60 MPa). However, because previously reported regression results showed marked deviations (up to 60% deviation) at high pressures, Figure 6 shows only a comparison between Pcal and Pexp for

an

pressures up to 14 MPa; at these pressures, deviations from the experimental data were within 20%. The RMSD and AARD for the prediction were 0.41 and 11.6%, respectively.

For the system CO2 + C6mim[Tf2N], the PSRK prediction exhibited a notable deviation from the

RMSD and AARD of 0.23 and 50.9%, respectively.

M

experimental VLE data (Figure 7). The predicted bubble pressures were marginally overestimated with an average

d

To test the CO2-BF4 parameters, the PSRK prediction was performed for the system CO2 + C4mim[BF4]

te

and compared with experimental data reported by Aki et al. [46], which was not included in the regression. Figure 8 shows a plot of Pcal versus Pexp. The prediction was in satisfactory agreement with the experimental data; the RMSD

Ac ce p

and AARD values were 0.72 and 15.5%, respectively. The CH2-PF6, IMI-PF6, and CO2-PF6 binary interaction parameters were tested using the systems CO2 + C4mim[PF6] and CO2 + C6mim[PF6]. The results were compared with experimental data provided by Aki et al. [46] and Kim et al. [21] for the systems CO2 + C4mim[PF6] and CO2 + C6mim[PF6], respectively. Figure 9 shows that the Pcal and Pexp values were in agreement, but that marked deviations occurred at pressures close to 10 MPa and above. The RMSD and AARD values were 0.75 and 13.3%, respectively. A similar comparison was made for the system CO2 + C6mim[PF6], in which agreement between Pcal and Pexp was observed, as shown in Figure 10. The RMSD and AARD for this prediction were 0.06 and 8.7%, respectively. The aforementioned trends regarding calculated and experimental pressures were observed between calculated and experimental CO2 solubility values. The corresponding graphs are included in the supplementary information (Figures S10–S14).

16

Page 16 of 33

5 Conclusion UNIFAC PSRK group contribution method was applied to predict the solubility of CO2 in imidazoliumbased ionic liquids with bis(trifluoromethylsulfonyl)imide (Tf2N), tetrafluoroborate (BF4) and hexafluorophosphate

ip t

(PF6) anions. New group interaction parameters were reported for the groups CO2-IMI, CO2-TF2N, CO2-BF4, CH2PF6, IMI-PF6, and CO2-PF6 obtained by regressing experimental VLE data on the systems CO2 + C2mim[Tf2N], CO2

cr

+ C4mim[Tf2N], CO2 + C4mim[BF4], and CO2 + C4mim[PF6]. The obtained parameters were used to predict the solubility of CO2 in ionic liquids with longer alkyl chains and were compared with experimental VLE data that were

us

not included in the regression. The PSRK model can be used to predict the solubility of CO2, demonstrating satisfactory agreement with the experimental VLE data for pressures up to 10 MPa. Regarding the parameter

an

regression, the overall average RMSD reported was 0.31, whereas the overall average AARD was 9.7%. Regarding the prediction test, the overall average RMSD reported was 0.40 and the overall average AARD was 25.2%.

M

Although various sets of experimental data with different methods of CO2 solubility measurement were used in the regression, graphical analyses showed that this did not affect the quality of the regression because the experimental

d

data obtained from various sources were determined to be coherent. However, consistency tests applied to a given data set showed that experimental VLE data at pressures higher than those of the critical pressure of CO2 and the

te

ionic liquids were inconsistent. This may be because it is difficult to distinguish between liquid and vapor phases at

Ac ce p

these supercritical conditions or because of the presence of two liquid phases as reported by other groups. Therefore, additional care must be taken when measuring CO2 solubility in ionic liquids at pressures and temperatures above their critical properties. Even when the experimental VLE data available are limited to the considered systems, the parameters obtained show a good correlative and predictive ability. Because databases on the solubility of CO2 in ionic liquids continue to grow, the PSRK matrix can be extended to include other anion and cation groups for predicting the solubility of CO2 and other gases in ionic liquids. Moreover, a similar approach can be adopted to extend the applicability of the PSRK model to the prediction of gas solubility in deep eutectic solvents considered as ionic liquid analogous systems and which have received a considerable amount of attention in recent years.

17

Page 17 of 33

6 Acknowledgement This research was funded by the Deanship of Scientific Research at King Saud University through the group project number RGP-VPP-108 in collaboration with the University of Malaya Center for Ionic Liquids

ip t

(UMCiL) through grant HIR-MOHE D000003-16001.

Bis(trifluoromethyl)sulfonylimide Tetrafluoroborate Hexafluorophosphate

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Anions Tf2N BF4 PF6

1-ethyl-3-methylimidazolium 1-butyl-3-methylimidazolium 1-pentyl-3-methylimidazolium 1-hexyl-3-methylimidazolium

an

Cations C2mim C4mim C5mim C6mim

cr

Nomenclature

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7 References

[1] M. Hasib-ur-Rahman, M. Siaj, F. Larachi, Ionic liquids for CO2 capture-Development and progress, Chemical Engineering and Processing 49 (2010) 313–322.

te

d

[2] M. Ramdin, T.W. de Loos, T.J.H. Vlugt, State-of-the-Art of CO2 Capture with Ionic Liquids, Industrial & Engineering Chemistry Research 51 (2012) 8149−8177.

Ac ce p

[3] L.A. Blanchard, D. Hancu, E.J. Beckman, J.F. Brennecke, Green processing using ionic liquids and CO2, Nature 399 (1999) 28-29. [4] P.J. Carvalho, V.H. Álvarez, I.M. Marrucho, M. Aznar, J.A.P. Coutinho, High pressure phase behavior of carbon dioxide in 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and 1-butyl-3-methylimidazolium dicyanamide ionic liquids, J. Supercritical Fluids 50 (2009) 105–111. [5] P.J. Carvalho, V.H. Álvarez, I.M. Marrucho, M. Aznar, J.A.P. Coutinho, High pressure phase behavior of carbon dioxide in 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids, J. Supercritical Fluids 48 (2009) , 99–107. [6] J.K. Shah, E.J. Maginn, A Monte Carlo simulation study of the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate: liquid structure, volumetric properties and infinite dilution solution thermodynamics of CO2, Fluid Phase Equilibria 222–223 (2004) 195–203. [7] J.K. Shah, E.J. Maginn, Monte Carlo Simulations of Gas Solubility in the Ionic Liquid 1-n-Butyl-3methylimidazolium Hexafluorophosphate, The J. of Physical Chemistry B 109 (2005) 10395-10405. [8] I. Urukova, J. Vorholz, G. Maurer, Solubility of CO2, CO, and H2 in the Ionic Liquid [bmim][PF6] from Monte Carlo Simulations, The J. Physical Chemistry B 109 (2005), 12154-12159. [9] M.R. Ally, J. Braunstein, R.E. Baltus, D. Dai, D.W. DePaoli, J.M. Simonson, Irregular Ionic Lattice Model for Gas Solubilities in Ionic Liquids, Industrial & Engineering Chemistry Research 43 (2004) 1296-1301.

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[10] N.A. Manan, C. Hardacre, J. Jacquemin, D.W. Rooney, T.G.A. Youngs, Evaluation of Gas Solubility Prediction in Ionic Liquids using COSMOthermX., J. of Chemical & Engineering Data 54 (2009) 2005–2022. [11] K.Z. Sumon, A. Henni, Ionic liquids for CO2 capture using COSMO-RS: Effect of structure, properties and molecular interactions on solubility and selectivity, Fluid Phase Equilibria 310 (2011) 39– 55.

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[12] Y. Shimoyama, A. Ito, Predictions of cation and anion effects on solubilities, selectivities and permeabilities for CO2 in ionic liquid using COSMO based activity coefficient model, Fluid Phase Equilibria 297 (2010) 178–182. [13] A. Maiti, Theoretical Screening of Ionic Liquid Solvents for Carbon Capture, ChemSusChem 2 (2009) 628 – 631.

cr

[14] M.A. Shiflett, A. Yokozeki, Solubilities and Diffusivities of Carbon Dioxide in Ionic Liquids: [bmim][PF6] and [bmim][BF4], Industrial & Engineering Chemistry Research 44 (2005) 4453-4464.

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[15] J.L. Anthony, E.J. Maginn, J.F. Brennecke, Solubilities and thermodynamic properties of gases in the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate, the J. of Physical Chemistry B (2002) 7315-7320.

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[16] A.P.S. Kamps, D. Tuma, J. Xia, G. Maurer, Solubility of CO2 in the ionic liquid [bmim][PF6], J. of Chemical & Engineering Data 48 (2003) 746-749. [17] J.O. Valderrama, F. Urbina, C.A. Faúndez, Gas–liquid equilibrium modeling of mixtures containing supercritical carbon dioxide and an ionic liquid, J. of Supercritical Fluids 64 (2012) 32– 38.

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[18] W. Ren, B. Sensenich, A.M. Scurto, High-pressure phase equilibria of {carbon dioxide (CO2) + n-alkylimidazoliumbis(trifluoromethylsulfonyl)amide} ionic liquids, J. of Chemical Thermodynamics 42 (2010) 305–311.

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[19] J-H. Yim, H.N. Song, B-C. Lee, J.S. Lim, High-pressure phase behavior of binary mixtures containing ionic liquid [HMP][Tf2N], [OMP][Tf2N] and carbon dioxide, Fluid Phase Equilibria 308 (2011) 147–152.

te

[20] T. Wang, C. Peng, H. Liu, Y. Hu, Description of the PVT behavior of ionic liquids and the solubility of gases in ionic liquids using an equation of state, Fluid Phase Equilibria 250 (2006) 150–157.

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[21] Y.S. Kim, W.Y. Choi, J.H. Jang, K.P. Yoo, C.S. Lee, Solubility measurement and prediction of carbon dioxide in ionic liquids, Fluid Phase Equilibria 228–229 (2005), 439–445. [22] M.C. Kroon, E.K. Karakatsani, I.G. Economou, G.J. Witkamp, C.J. Peters, Modeling of the Carbon Dioxide Solubility in Imidazolium-Based Ionic Liquids with the PC-SAFT Equation of State, the J. Physical Chemistry B 110 (2006) 9262-9269. [23] H. Machida, R. Taguchi, Y. Sato, L. J. Florusse, C. J. Peters, R. L. Smith Jr, Measurement and correlation of supercritical CO2 and ionic liquid systems for design of advanced unit operations, Frontiers of Chemical Engineering in China, 3 (2009) 12-19. [24] F.M. Maia, I. Tsivintzelis, O. Rodriguez, E.A. Macedo, G.M. Kontogeorgis, Equation of state modelling of systems with ionic liquids: Literature review and application with the Cubic Plus Association (CPA) model, Fluid Phase Equilibria 332 (2012) 128– 143. [25] A. Eslamimanesh, F. Gharagheizi, A.H. Mohammadi, D. Richon, Artificial Neural Network modeling of solubility of supercritical carbon dioxide in 24 commonly used ionic liquids, Chemical Engineering Science 66 (2011) 3039–3044. [26] Y. Chen, S. Zhang, X. Yuan, Y. Zhang, X. Zhang, W. Dai, R. Mori, Solubility of CO2 in imidazolium-based tetrafluoroborate ionic liquids, Thermochimca Acta 441 (2006) 42–44.

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[27] J.M. Prausnitz, R.N. Lichtenthaler, E.G. de Azevedo, Molecular Thermodynamics Of Fluid-Phase Equilibria, Third Ed., Prentice Hall PTR, New Jersey, 1999. [28] G.M. Kontogeorgis, G.K. Folas, Thermodynamic Models for Industrial Applications: From Classical and Advanced Mixing Rules to Association Theories, John Wiley and Sons Inc., 2010.

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[29] B.E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, Fifth Ed., McGraw Hill, 2004. [30] T. Holderbaum, J. Gmehling, PSRK: A group contribution equation of state based on UNIFAC, Fluid Phase Equilibria 70 (1991) 251-265.

cr

[31] J. Gmehling, From UNIFAC to modified UNIFAC to PSRK with the help of DDB, Fluid Phase Equilibria 107 (1995) 1-29.

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[32] K. Fischer, J. Gmehling, Further development, status and results of the PSRK method for the prediction of vapor – liquid equilibria and gas solubilities, Fluid Phase Equilibria 121 (1996) 185-206.

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[33] M.L. Michelsen, A Method for Incorporating Excess Gibbs Energy Models in Equation of State, Fluid Phase Equilibria 60 (1990) 42-58. [34] P.M. Mathias, T.W. Copeman, Extension of the Peng-Robinson Equation of State to Complex Mixtures: Evaluation of the Various Forms of the Local Composition Concept, Fluid Phase Equilibria 13 (1983) 91-108.

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[35] J. Gmehling, L. Jiding, M. Schiller, A modified unifac model. 2. Present parameter matrix and results for different thermodynamic properties, Industrial & Engineering Chemistry Research 32 (1993) 178-193. [36] A. Bondi, van der Waals Volumes and Radii, J. of Physical Chemistry 68 (1964) 441-451.

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[37] Z. Lei, J. Zhang, Q. Li, B. Chen, UNIFAC Model for Ionic Liquids, Industrial & Engineering Chemistry Research 48 (2009) 2697–2704.

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[38] T. Banerjee, M.K. Singh, R.K. Sahoo, A. Khanna, Volume, surface and UNIQUAC interaction parameters for imidazolium based ionic liquids via Polarizable Continuum Model, Fluid Phase Equilibria 234 (2005) 64-76.

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[39] S. Nebig, J. Gmehling, Prediction of phase equilibria and excess properties for systems with ionic liquids using modified UNIFAC: Typical results and present status of the modified UNIFAC matrix for ionic liquids, Fluid Phase Equilibria 302 (2011) 220–225. [40] J.O. Valderrama, A. Reategui, W.W. Sanga, Thermodynamic Consistency Test of Vapor-Liquid Equilibrium Data for Mixtures Containing Ionic Liquids, Industrial & Engineering Chemistry Research 47 (2008) 8416–8422. [41] S.B. Margules, Akad. Wiss. Wien Math. Naturviss 104 (1895) 1243-1278. [42] http://www.prosim.net/

[43] A.M. Schilderman, S. Raeissi, C.J. Peters, Solubility of carbon dioxide in the ionic liquid 1-ethyl-3methylimidazolium bis(trifluoromethylsulfonyl)imide, Fluid Phase Equilibria 260 (2007) 19–22. [44] V.H. Alvarez, M. Aznar, Application of a Thermodynamic Consistency Test to Binary Mixtures Containing an Ionic Liquid, The Open Thermodynamics J. 2 (2008), 25-38. [45] D.J. Oh, B.C. Lee, High-pressure phase behavior of carbon dioxide in ionic liquid 1-butyl-3methylimidazolium bis(trifluoromethylsulfonyl)imide, Korean J. of Chemical Engineering 23 (2006) 800-805. [46] S.K. Aki, B.R. Mellein, E.M. Saurer, J.F. Brennecke, High-Pressure Phase Behavior of Carbon Dioxide with Imidazolium-Based Ionic Liquids, J. of Physical Chemistry B 108 (2004) 20355-20365.

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[47] A. Yokozeki, M.B. Shiflett, C.P. Junk, L.M. Grieco, T. Foo, Physical and Chemical Absorptions of Carbon Dioxide in Room-Temperature Ionic Liquids, J. of Physical Chemistry B 112 (2008) 16654–16663. [48] E.K. Shin, B.L. Lee, J.S. Lim, High-pressure solubilities of carbon dioxide in ionic liquids: 1-Alkyl-3methylimidazolium bis(trifluoromethylsulfonyl)imide, J. of Supercritical Fluids 45 (2008) 282–292.

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[49] J.O. Valderrama, L.A. Forero, R.E. Rojas, Critical Properties and Normal Boiling Temperature of Ionic Liquids. Update and a New Consistency Test, Industrial & Engineering Chemistry Research 51 (2012) 7838–7844.

Ac ce p

te

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an

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[50] E.I. Alevizou, G.D. Pappa, E.C. Voustas, Prediction of phase equilibrium in mixtures containing ionic liquids using UNIFAC, Fluid Phase Equilibria 284 (2009) 99–105.

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Page 21 of 33

Table 1: Summary of the models proposed to represent solubility of CO2 in ionic liquids. Table 2: Pure component properties of CO2 and ionic liquids involved in this work.

ip t

List of tables

cr

Table 3: The van der Waals area and volume Rk and Qk for the subgroups involved in this work.

Ac ce p

te

d

M

an

Table 5: RMSD and AARD for the regression of each system.

us

Table 4: PSRK parameters for groups involved. Rows in bold show parameters obtained in this work.

22

Page 22 of 33

Table 1: Summary of the models proposed to represent solubility of CO2 in ionic liquids

Model used

System

References

Molecular Modeling

Monte Carlo simulation using: 1) Test particle insertion and 2) Expanded ensemble methods

H2O, C2H6, CO2, C2H4, CH4, O2, N2 in [C4mim][PF6]

Shah & Maginn [6,7]

Monte Carlo: Gibbs Ensemble MC simulation

CO2, CO and H2 in [C4mim][PF6]

Urukova et al. [8]

Irregular Ionic Lattice Model (IILM)

CO2+[C4mim][PF6]

Ally et al. [9]

us

cr

ip t

Approach

CO2+[ C4mim][BF4] CO2 in 27 ILs

COSMO-RS

Screened gas solubility in 2701 ILs for CO2 capture

Sumon et al. [11]

COSMO-SAC

CO2, N2, CH4 in [C2mim]; [C4mim]; [C6mim] with anions [BF4], [PF6], [OTf], [Tf2N]

Shimoyama & Ito [12]

CO2 in all-functionalizedguanidinium and BF4-based ILs

Maiti [13]

CO2 with either [C4mim][PF6], [C4mim][BF4]

Shiflett & Yokozeki [14]

PR-Kwok Mansoori

CO2 with either [C8mim][PF6], [C2mim][EtSO4], [C6mim][Tf2N], [C8mim][BF4], [C4mim][PF6], [C4mim][NO3]

Valderrama et al. [17]

PR/Wong-Sandler/UNIQUAC

CO2 with either [C2mim][Tf2N], [C5mim][Tf2N]

Carvalho et al. [5]

PR/Wong-Sandler/UNIQUAC

CO2 with either [C4mim][Tf2N], [C4mim][DCA]

Carvalho et al. [4]

PR + van der Waals mixing rule

CO2 + Cnmim[Tf2N]

Ren et al. [18]

PR + van der Waals mixing rule

CO2 with either [ C8mpyr][Tf2N], [C8mpyr][Tf2N]

Yim et al. [19]

Square-Well Chain Fluid (SWCF) EoS

CO2 with either [Cnmim]/[BF4], [PF6], [Tf2N]

Wang et al. [20]

an

COSMO-RS

M

Quantum Chemistry

COSMO-RS + SRK EoS

Equations of State

Generic RK EOS + empirical function for “a” + modified vdWBerthelot mixing rule

Ac ce p

te

d

Quantum Chemistry + EoS

Manan et al. [10]

23

Page 23 of 33

CO2 with either [C4mim][PF6], [C6mim][PF6], [C2mim][BF4], [C6mim][BF4], [C2mim][Tf2N], [C6mim][Tf2N]

Y.S. Kim et al. [21]

Statistical Associating Fluid Theory (SAFT)-type EoS

CO2 with either [C2mim][PF6], [C4mim][PF6], [C6mim][PF6], [C8mim][PF6], [C2mim][BF4], [C4mim][BF4], [C6mim][BF4], [C8mim][BF4]

Kroon et al. [22]

Sanchez-Lacombe EoS

CO2 with either [C2mim][PF6], [C4mim][PF6], [C2mim][BF4], [C4mim][BF4], [C4mim][Tf2N], [C6mim][Tf2N], [C8mim][Tf2N], [C4mim][OcSO4], [C4mim][NO3], [C4mim][Tfa], [tibmp][pTSO3]

Machida et al. [23]

Cubic Plus Association (CPA)

CO2 with [C2mim][Tf2N] and [C4mim][Tf2N]

Maia et al. [24]

Artificial Neural Network (ANN)

CO2 with 24 ILs

Eslamimanesh et al. [25]

Extended Henry’s Law correlation

CO2+[ C4mim][PF6]

Kamps et al. [16]

CO2+[ C4mim]/[ C6mim]/[ C8mim]-[BF4]

Chen et al. [26]

an

Ac ce p

te

d

Extended Henry’s Law correlation

M

Other approaches

us

cr

ip t

Group Contribution Non-random Lattice Fluid (GC NLF) EoS

24

Page 24 of 33

Table 2: Pure component properties of CO2 and ionic liquids involved in this work

CO2

C2mim[Tf2N]

C4mim[Tf2N]

C5mim[Tf2N]

C6mim[Tf2N]

C4mim[BF4]

C4mim[PF6]

Reference

[42]

[49]

[49]

[49]

[49]

[49]

[49]

Formula

CO2

C8H11N3F6S2O4

C10H15N3F6S2O4

C11H17N3F6S2O4

C12H19N3F6S2O4

C8H15N2BF4

C8H15N2PF6

MW (g/mol)

44.010

391.317

419.371

433.4

447.425

Tb (K)

194.7

816.7

862.4

885.3

908.2

Tc (K)

304.21

1249.3

1269.9

1281.1

1292.8

Pc (MPa)

7.286

3.265

2.765

2.564

2.389

Vc (cm3/mol)

94

875.9

990.1

1047.2

Zc

0.274

0.2753

0.2592

0.2521

Ω

0.2236

0.2157

0.3004

0.3444

ip t

Compound

284.184

495.2

554.6

643.2

719.4

2.038

1.728

1104.4

655.0

762.5

0.2454

0.2496

0.2203

0.3893

0.8877

0.7917

te

d

M

an

us

cr

226.025

Table 3: The van der Waals area and volume Rk and Qk for the subgroubs involved in this work Subgroup

Rk

Qk

Ref

CO2

CO2

1.3

0.982

[42]

CH2

CH3

0.9011

0.848

[42]

CH2

0.6744

0.54

[42]

IMI

C3H3N2+

2.411

2.409

[39]

Tf2N

Tf2N-

5.8504

5.7513

[39]

BF4

BF4-

4.6200

1.1707

[39]

PF6

PF6-

4.1271

7.2872

[50]

Ac ce p

Main group

25

Page 25 of 33

Table 4: PSRK binary interaction parameters. Rows in bold show parameters obtained in this work (*). Main Groups

cmn

CO2

CH2

anm

bnm

cnm

919.80

-3.91320

0.0046310

-38.67

0.86149

-0.0017910

[42]

IMI

64.20

0.10295

0.0004785

817.00

-0.02604

-0.0001946

[39]

CH2

Tf2N

1425.40

-5.19280

0.0075167

204.17

-1.09780

0.0030870

[39]

CH2

BF4

702.86

-2.91270

0.0095811

-189.34

1.80980

-0.0042777

[39]

CH2

PF6

400.00

3.14739

-0.0075700

IMI

Tf2N

-1525.40

0.13812

IMI

BF4

-2083.10

IMI

PF6

CO2

ip t

bmn

cr

CH2

amn

us

Group 'n'

Ref

-0.24306

0.4279270

*

0.0277250

-1374.00

3.05600

0.0123040

[39]

0.12213

-0.0105190

-3977.90

4.69090

0.0260130

[39]

-1200.00

-5.73470

-

-87.19

1.50170

-

*

IMI

-430.44

0.79478

-

-117.13

-1.16120

-

*

CO2

Tf2N

-91.86

4.34210

-

1300.30

-2.71840

-

*

CO2

BF4

-1258.01

-4.30570

-

3586.00

0.94047

-

*

CO2

PF6

1034.00

0.65918

-

1523.00

1.04892

-

*

Ac ce p

te

d

M

3624.98

an

Group 'm'

Group Interaction Parameters

26

Page 26 of 33

Table 5: RMSD and AARD for the regression of each system AARD (%)

Carvalho et al. [5]

0.17

6.83

Schilderman et al.[43]

0.26

6.12

Kim et al. [21]

0.04

8.28

Average

0.16

Carvalho et al. [4]

0.49

Oh et al. [45]

0.38

Aki et al. [46]

0.22

Average

21.83 16.14 5.73

15.56

0.08

5.58

0.35

5.81

0.21

5.70

Anthony et al. [15]

0.05

3.65

Shiflett&Yokozeki [14]

0.07

12.46

Kamps et al. [16]

1.30

14.67

Average

0.47

10.26

Shiflett&Yokozeki [14] Kroon et al. [22]

Ac ce p

te

d

M

Average CO2+ C4mim[PF6]

7.08

0.36

an

CO2+ C4mim[BF4]

ip t

CO2 + C4mim[Tf2N]

RMSD

cr

CO2 + C2mim[Tf2N]

Reference

us

System

27

Page 27 of 33

List of Figures Figure 1: Updated PSRK matrix to include parameters obtained from this work.

ip t

Figure 2: Comparison between calculated and experimental pressure of Carvalho et al. [5] (), Kim et al. [21] (▲) and Schilderman et al. [43] () for the system CO2 + C2mim[Tf2N].

cr

Figure 3: Comparison between calculated and experimental pressure of Carvalho et al. [5] (), Oh et al. [45] (▲) and Aki et al. [46] () for the system CO2 + C4mim[Tf2N].

us

Figure 4: Comparison between calculated and experimental pressure of Shiflett and Yokozeki [14] (▲) and Kroon et al. [22] () for the system CO2 + C4mim[BF4].

an

Figure 5: Comparison between calculated and experimental pressure of Shiflett and Yokozeki [14] (▲), Anthony et al. [15] () and Kamps et al. [16] () for the system CO2 + C4mim[PF6].

Figure 6: Comparison between predicted and experimental pressure (Carvalho et al.[5]) for the binary system CO2 +

M

C5mim[Tf2N].

Figure 7: Comparison between predicted and experimental pressure for the binary CO2 + C6mim[Tf2N] – experimental data from

d

Kim et al. [21] (▲) and Yokozeki et al. [47] ().

te

Figure 8: Comparison between predicted and experimental pressure (Aki et al. [46]) for the system CO2 + C4mim[BF4]. Figure 9: Comparison between predicted and experimental pressure from Aki et al. [46] for CO2 + C4mim[PF6].

Ac ce p

Figure 10: Comparison between predicted and experimental pressure (Kim et al. [21]) for the binary CO2 + C6mim[PF6].

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ip t cr us an M

Ac ce p

te

d

Figure 1: Updated PSRK matrix to include parameters obtained from this work

Figure 2: Comparison between calculated and experimental pressure of Carvalho et al. [5] (), Kim et al. [21] (▲) and Schilderman et al. [43] () for the system CO2 + C2mim[Tf2N].

29

Page 29 of 33

ip t cr us an M

Figure 3: Comparison between calculated and experimental pressure of Carvalho et al. [5] (), Oh et al. [45] (▲) and Aki

Ac ce p

te

d

et al. [46] () for the system CO2 + C4mim[Tf2N].

Figure 4: Comparison between calculated and experimental pressure of Shiflett and Yokozeki [14] (▲) and Kroon et al. [22] () for the system CO2 + C4mim[BF4].

30

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ip t cr us an

M

Figure 5: Comparison between calculated and experimental pressure of Shiflett and Yokozeki [14] (▲), Anthony et al.

Ac ce p

te

d

[15] () and Kamps et al. [16] () for the system CO2 + C4mim[PF6].

Figure 6: Comparison between predicted and experimental pressure (Carvalho et al.[5]) for the binary system CO2 + C5mim[Tf2N].

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ip t cr us an

M

Figure 7: Comparison between predicted and experimental pressure for the binary CO2 + C6mim[Tf2N] – experimental

Ac ce p

te

d

data from Kim et al. [21] (▲) & Yokozeki et al. [47] ()

Figure 8: Comparison between predicted and experimental pressure (Aki et al. [46]) for the system CO2 + C4mim[BF4].

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ip t cr us an

Ac ce p

te

d

M

Figure 9: Comparison between predicted and experimental pressure from Aki et al. [46] for CO2 + C4mim[PF6].

Figure 10: Comparison between predicted and experimental pressure (Kim et al. [21]) for the binary CO2 + C6mim[PF6].

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