Experimental data and modeling of the CO2 solubility in 2-methylimidazole aqueous solution

CO 2 capture plays a critical role in reducing carbon emissions. Novel chemical absorption media, such as imidazole aqueous solutions, have been extensively studied as potential candidates. In this work, new experimental data of CO 2 solubility in 5 – 30 wt% 2-methylimidazole (2-MeIm) aqueous solutions at 293.15 – 313.15 K were measured. The Cubic-Plus-Association equation of state (CPA EoS) with the pseudo chemical reaction approach has been proposed to model the CO 2 solubility in the 2-MeIm aqueous solutions. The CPA model can describe well the saturated vapor pressure (1.1%), liquid density (0.5%) and vapor – liquid equilibrium data (14%) of 2-MeIm aqueous solutions. Temperature dependent binary interaction parameters between 2-MeIm and CO 2 are needed in order to satisfactorily represent the phase equilibrium data of the 2-MeIm-H 2 O-CO 2 ternary systems (11%) in the temperature range of 293.15 – 393.15 K, which covers all the decarbonization process operation conditions. With the pseudo chemical reaction approach within CPA EoS, it is possible to distinguish the physical and chemical effects of CO 2 solubility in chemical absorbents. This work provides the experimental and model basis for further research and application of the novel imidazole-based separation media for CO 2 capture.


Introduction
The increasingly severe problem of global warming has become one of the main factors threatening the sustainable development of mankind, and the reduction of greenhouse gas emissions to mitigate climate change has attracted the attention of the international community [1,2]. Governments around the world have been committed to intensify scientific research and technological development to enhance the ability to deal with climate change [3][4][5][6]. CO 2 is the most important anthropogenic greenhouse gas, and increasing its level in the atmosphere will have a serious impact on the natural environment and human health [7,8]. Carbon capture, utilization and storage (CCUS) [9][10][11] is recognized as one of the most promising technologies to reduce CO 2 emissions. CCUS is the capture and separation of CO 2 generated in the chemical plants, such as power, steel, and ammonia plants, oil refineries [12,13], to realize the resource utilization or storage of CO 2 [14]. Numerous methods have been proposed to capture CO 2 , including physical absorption [15], chemical absorption [16,17], membrane separation [18,19], and adsorption [20]. Compared with other separation media, chemical absorbents [21] have the advantages of high solubility and low viscosity, which also makes it a relatively mature CO 2 capture technology currently used in industry [22]. The gas-liquid contact between the absorbent aqueous solution and CO 2 produces a reversible chemical reaction to capture CO 2 . Due to the strong bond energy between the absorbent and CO 2 , the absorption process can be carried out at ambient temperature and pressure. The CO 2 rich solution is desorbed through a temperature swing absorption process [23]. The high temperature (373-393 K) breaks the bond between CO 2 and the absorbent, which desorbs CO 2 from the solution and releases high concentrations of CO 2 . Alkanolamine solutions commonly used in industry include monoethanolamine (MEA) [24], diethanolamine (DEA) [25], N-methyldiethanolamine (MDEA) [26]. Alkanolamine solutions used for CO 2 removal have some drawbacks, such as corrosivity and high regeneration energy consumption. The mixed solvent [27][28][29] based on alkanolamine solution can improve the performance. Very recently, Liu et al. [30,31] have made extensive studies on the physical properties and reaction kinetics of the CO 2 -H 2 O-1-dimethylamino-2propanol solutions, and they have shown how to correlate the physical properties using artificial intelligence models and proposed a methodology to screen solvents effectively for CO 2 absorption.
Recently, imidazoles have been proposed as potential alternatives for CO 2 capture because of their excellent performance. Imidazoles are often used as the precursors for imidazolium ionic liquids, and the organic ligand for Zeolitic Imidazolate Frameworks (ZIFs) [32]. The weak alkalinity of imidazole and the pore structure, ZIFs have also been widely studied in the separation and purification of CO 2 [33]. In addition, imidazoles are used as co-solvents to strengthen the performance of the separation media, such as increasing the solubility of CO 2 in traditional physical absorbents [34], and improving the mass-transfer rates of CO 2 in amine solvents [35]. Imidazoles aqueous solutions are also used for CO 2 capture applications [36]. They have high thermal stability and low volatility compared with amine solutions [37], because the reaction mechanism of imidazole and CO 2 in water is the same as that of tertiary amines [38] and will not generate carbamates [39]. 2-methylimidazole (2-MeIm) is a methyl substituent on the imidazole ring, and its acid dissociation constant pK a is 7.87. The 2-MeIm aqueous solutions have CO 2 absorption solubility comparable to MDEA solution, which is widely used in industry, as shown in Table 1. However, the solubility of CO 2 in 2-MeIm aqueous solutions is more sensitive to temperature, and the greater CO 2 cyclic capacity can be achieved by changing temperature, then the CO 2 desorption gas of high pressure can be obtained, which reduces the cost of pressurization for transportation. Therefore, the 2-MeIm aqueous solution is suitable for processing high-pressure CO 2 mixtures, like the integrated gasification combine cycle syngas, and the high-pressure CO 2 desorption is convenient for the subsequent transportation and storage [40,41].
Many experimental works of imidazole aqueous solutions to capture CO 2 have been reported in literature, including information about the basic properties of imidazole aqueous solutions [37,43], reaction mechanism of CO 2 [39], CO 2 solubility and enthalpy [42,44,45], kinetics of absorption rate [35,46]. On one hand, however, these are still not enough for designing the corresponding processes and explore optimal operating conditions. On the other hand, a thermodynamic model that can accurately describe physical properties and CO 2 solubility over wide ranges of temperature, pressure and solution composition, will make process design no longer limited by experimental data and also help to explore optimal operating conditions. The absorption of CO 2 in the alkaline solution not only has a physical effect but also introduces a chemical reaction. This means that new species are formed in the alkaline substances-water-CO 2 ternary system, so in principle both phase equilibria and chemical equilibria should be considered. There have been several thermodynamic models used to model the vapor--liquid equilibria (VLE) of CO 2 in alkaline aqueous solutions. Electrolyte thermodynamic models are commonly applied to describe the phase equilibria and chemical equilibria of CO 2 capture process with consideration of interactions among the molecular and ionic species in an aqueous electrolyte system. Mondal et al. [47] predicted the liquid phase speciation, solvent capacity, pH of the solution and absorption heat of CO 2 in aqueous hexamethylenediamine (HMDA) solutions with the electrolyte Non-Random Two Liquid (e-NRTL) model. Faramarzi et al. [48][49][50] applied the extended Universal Quasi-Chemical Correlation Activity Coefficient (extended-UNIQUAC) model to calculate the CO 2 solubility and various thermodynamic properties of alkanolamine solutions. Uyan et al. [51] predicted the CO 2 solubility in aqueous MDEA solutions with electrolyte Perturbed-Chain Statistical Associating Fluid Theory (ePC-SAFT) model. For the electrolyte thermodynamic models, there are 3 pure components and 5 ions in the CO 2alkaline solution systems, and each species has 3-5 model parameters. In addition, ion pairs or ion-molecule pairs introduce more parameters, which require multiple and numerous experimental data and cause complicated calculations. It may be difficult to apply such electrolyte models to novel CO 2 capture media when there are not much data available. Another simplified approach to build a suitable thermodynamic model for such applications is to treat the chemical reaction as a strong cross-association, usually called pseudo chemical reaction approach. Rodriguez et al. [52] proposed this approach and successfully used it with the Statistical Associating Fluid Theory for potentials of variable attractive range (SAFT-VR model) to satisfactorily describe the solubility of CO 2 in alkanolamines solutions without the consideration of ionic species. Subsequently, Wang et al. [53] used a similar approach with the Peng-Robinson -Cubic-Plus-Association Equation of State (PR-CPA EoS) to model the solubility of H 2 S and CO 2 in MEA and MDEA aqueous mixtures, and the model can also accurately predict the speciation of acid gas reacting with aqueous alkanolamine solutions. Leontiadis et al. [54] also used the pseudo chemical reaction approach with the CPA EoS to model the CO 2 -MPA-H 2 O and CO 2 -MDEA-H 2 O systems.
In this work, new experimental data of CO 2 solubilities in 5-30 wt% 2-MeIm aqueous solutions at 293.15-313.15 K are reported. The CPA EoS combined with the pseudo chemical reaction approach is developed to model the thermodynamic properties of the 2-MeIm-H 2 O-CO 2 system. For the first time, the physical and chemical effects of CO 2 solubility in a chemical absorbent are distinguished using thermodynamic model calculations. The thermodynamic model presented in this study has the potential of being used in process design/simulation for reducing the experimental costs.

Experimental section
The experimental equipment, procedures, and data processing have been explained in detail in the previous studies [55][56][57]. In brief, the gas-liquid phase equilibrium experiments were conducted in the sapphire cell, which receives a specific mole of feed gas from a blind cell. The experimental temperature is controlled by an air bath. The solubility of CO 2 is expressed in terms of the mole fraction of CO 2 in 2-MeIm aqueous solution: where n CO2 , n 2-MeIm , n H2O represent the moles of CO 2 , 2-MeIm and H 2 O in solution, respectively. The standard uncertainty in temperature u(T) = 0.1 K, in pressure u (P blind cell ) = 10 kPa and u(P sapphire cell ) = 4 kPa, in height u(h) = 0.1 cm, in weight u(m) = 0.01 g, and in CO 2 solubility u(x CO2 ) are then calculated.

CPA EoS
The Cubic-Plus-Association EoS (CPA EoS) [58], in terms of pressure P, can be expressed as:

⏟̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅⏞⏞̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅⏟
Association term (2) where, V m is the molar volume, b is the temperature independent covolume parameter, and α(T) is the temperature dependent energy where k ij is the binary interaction parameter, which could be temperature-dependent [59]. α i (T) reads:   Table 3 Parameters of pure compounds.
Compound  where the parameter a 0,i can also be expressed as: In Eq. (2), ρ is the molar density, g is the radial distribution function, and X A i is the fraction of sites A on molecule i that do not form bonds with other hydrogen bonding sites. X A i is dependent on the association strength Δ A i B j between association sites belonging to the different molecules. For example, the association between the A site of the i molecule and the B site of the j molecule can be expressed as: where the association strength Δ AiBj can be expressed as: where, ε AiBi and β AiBi are the association energy and the association volume, respectively. CPA has, for pure components, 5 parameters, 3 (Γ, b, c 1 ) in the cubic term and 2 (ε AiBi , β AiBi ) in the association term. These 5 parameters can be obtained by fitting the saturated vapor pressure and liquid density of the pure components. For non-associative components, such as CO 2 , hydrocarbons, only the 3 parameters of the cubic term are required, and they can also be calculated from the critical properties and the acentric factor (although they too are typically fitted to vapor pressure and liquid densities together with the other parameters).
For self-associating components, the cross associative energy and cross associative volume using the CR-1 combining rule are expressed as: and A modified CR-1 combining rule can be used to account for the association (solvation effect or chemical reaction) between an associative component and a non-associative component: ε Ai Bj = ε cross = adjustable parameter and β AiBj = β cross = adjustable parameter

Pseudo chemical reaction approach
In this work, the CPA EoS and a pseudo chemical reaction approach are applied to the 2-MeIm-H 2 O-CO 2 system, using pseudo chemical association sites to describe the chemical reaction between 2-MeIm and CO 2 . Combined with the characteristics of 2-MeIm and the reaction mechanism with CO 2 , molecular models and association schemes suitable for 2-MeIm-H 2 O-CO 2 system are proposed, as shown in Fig. 1.
The pure component CO 2 is treated as a non-self-associating molecule. In order to represent its interaction with an associating component and the chemical reaction with 2-MeIm, solvation (a) site and active chemical reaction (ch) site are added, and both of them are negative association sites. The a site can associate with the d site of H 2 O and 2-MeIm molecules, indicating solvation effect, while the ch site only associates with d site of 2-MeIm molecule, simulating thus a chemical reaction.
For the H 2 O molecule, the 4C scheme used in previous work [59] is adopted. There are two proton donor (d) and two proton acceptor (a) sites. There is no difference in association behavior between d and a sites. There is a cross association between the a and d sites of the H 2 O and 2-MeIm molecules.
For the 2-MeIm molecule, a typical secondary amine molecular mode [60], the 2B scheme, is used according to its molecular structure. A 2-MeIm molecule has 2 sites, a proton donor (d) site and a proton acceptor (a) site. The d site of 2-MeIm molecule can associate with the a site of CO 2 and the ch site of CO 2 , respectively, indicating the physical absorption and chemical absorption of CO 2 in the 2-MeIm aqueous solution. Because CO 2 has only one ch site and 2-MeIm also has only d site, one CO 2 molecule can interact with one 2-MeIm molecule, and simultaneously associate with one H 2 O molecule, which conforms to the stoichiometry: 2-MeIm:CO 2 :H 2 O = 1:1:1 [42]. The chemical reaction of the 2-MeIm-H 2 O-CO 2 ternary system is:

Parameters of the model
Critical properties and acentric factors of pure components are listed in Table 2. The parameters of pure compounds of H 2 O and CO 2 are taken from literature [59]. Since 2-MeIm is a solid at room temperature and pressure, there are no saturated vapor pressure and liquid density data. Therefore, the pure compound parameters of 2-MeIm are obtained by fitting the saturated vapor pressure, liquid density and VLE data of the 2-MeIm aqueous solution [43].
The objective function of the 2-MeIm-H 2 O binary system is: The binary systems considered in this work are CO 2 -H 2 O, 2-MeIm-H 2 O and 2-MeIm-CO 2 . Each binary system has the interaction parameter k ij and the interaction association parameters ε AiBj and β AiBj . The binary parameters of CO 2 -H 2 O are taken from literature [59]. The interaction association parameters of 2-MeIm-H 2 O are based on CR-1 combining rule Eqs. (10) and (11). Due to the lack of experimental data for the 2-MeIm-CO 2 binary system, the parameters of 2-MeIm-CO 2 , which are based on modified CR-1 combining rule Eqs. (12) and (13), were fitted to the VLE data of 2-MeIm-H 2 O-CO 2 ternary system.
The objective function of the 2-MeIm-H 2 O-CO 2 ternary system is: where P exp i is the experimental value of the equilibrium pressure, P cal i is the calculated values using CPA model, and N P is the number of experimental data points.
AADP is defined as:

The 2-MeIm-H 2 O binary system
The pure compound parameters are listed in Table 3 and the binary parameters of 2-MeIm-H 2 O are presented in Table 4. Compared with the association parameters of pure water which indicates the strength of hydrogen bonds between water molecules, the association volume of 2-MeIm is smaller and the association energy is larger. The self-association strength calculated by Eq. (9), with g(ρ) ignored, is plotted in Fig. 2. It can be seen that the association strength gradually decreases with increasing temperature, and that of 2-MeIm molecules is always greater than that of water molecules. In fact, 2-MeIm molecule has two N atoms, one as imine N atom and the other as amine NH group, as shown in Fig. 1  (d), to accept or donate of proton, so 2-MeIm can both undergo protonated and deprotonation reactions [62]. Therefore, the interaction between 2-MeIm molecules is a strong chemical interaction. The cross associative parameters are calculated by CR-1 combining rule (Eqs. (10) and (11)), that is, no extra new parameters are introduced.
The density and vapor pressure of the separation medium are both important parameters for simulating and designing the absorption-desorption process, where the former affects energy consumption and the latter determines its loss during the absorption-desorption cycle process. The ranges of experimental data of the liquid density (ρ), saturated vapor pressure (P s ) and vapor phase composition of the 2-MeIm aqueous solution in the literature and the AADs are presented in Table 5. The comparison between the calculated results of the CPA model and the experimental data is shown in Fig. 3. The AADs of liquid density and saturated vapor pressure are 0.45% and 1.14%, respectively, which indicates that the model results are in excellent agreement with the experimental data. Because 2-MeIm is a non-volatile compound, the mole fraction of 2-MeIm (y 2-MeIm ) in the gas phase is at the magnitude of 10 -4 , and the slight difference between experimental and calculated results will lead to a large relative deviation. The calculated results are of the same order of magnitude as the experimental values, and the AAD is 14.1%, which can be considered satisfactory.

The 2-MeIm-H 2 O-CO 2 ternary system
The solubility data of CO 2 in the 2-MeIm aqueous solution from the literature are summarized in Table 6. There are 105 data points in total, with a solution concentration range 5-30 wt%, temperature range 293.15-393.15 K, and pressure range 0-4.2 MPa. These data will be used to fit the model parameters and verify the accuracy of the model.
The binary parameters are shown in Table 6. Using the CO 2 solubility data in 24.5 wt% and 30 wt% 2-MeIm aqueous solution at 293.15 ~ 393.15 K (Figs. 4 and 5), two sets of 2-MeIm-CO 2 binary parameters are fitted: one set is the temperature independent k ij , and the other set is temperature dependent k ij (T), with 4 cross-association parameters, 2 for the physical effect, and 2 for the chemical reaction. It is found out that it is reasonable to fix the chemical association volume of 2-MeIm-CO 2 to be the same as for 2-MeIm molecules, possibly because they represent a strong chemical interaction. This simplification reduces the number of parameters while ensuring the accuracy of the model. The chemical reaction between 2-MeIm and CO 2 is stronger than the solvent effect, so the association energy of the chemical reaction is larger (ε ch > ε cross ), and the association volume is smaller (β ch < β cross ), similar to the discussion with regard to Fig. 2. The AAD with temperature independent k ij is 29%, while with temperature dependent k ij (T) it drops to 11%, greatly improving the model accuracy. Different forms of k ij (T) have been investigated. The simple linear relationship shows the best correlation capability, so the results using this set of parameters are shown in this  Tables 7 and  8. Fig. 4 compares the experimental data with the published data, and the good consistency verifies the reliability of the new measurements. The temperature independent k ij is valid in the range of 293. 15-313.15 K, while the model deviation increases rapidly with increasing temperature. In contrast, temperature dependent k ij (T) provides good accuracy in the temperature range 293.15-393.15 K, which covers the operating temperature range of the CO 2 absorption-desorption process, so the CPA model can be used for the design and optimization of process for CO 2 capture in 2-MeIm aqueous solution. The performance of the model at high temperature has not been fully validated due to the limited experimental data. More accurate model parameters could be possibly obtained when more experimental data become available. Fig. 6 shows the comparison of CO 2 solubilities in the 5-30 wt% 2-MeIm aqueous solution at 303.15 K. For different concentration solutions, the CPA model can describe the overall trend of CO 2 solubility, but the model's performance becomes worse with decreasing concentration. This is probably because the CO 2 solubility in pure water is underestimated using the CO 2 -H 2 O parameters from the literature [59], in low concentration 2-MeIm aqueous solution we also see an underestimation. The CPA model is more suitable for high concentration (>20 wt%) 2-MeIm solution absorbing CO 2 at 293.15-313.15 K with the currently available CO 2 -H 2 O parameters.

Physical and chemical absorption
The physical solubility of CO 2 in alkaline solution is one of the useful parameters for calculating properties such as diffusion coefficient, reaction rate, and mass transfer coefficient [63]. Previously, the N 2 O analogy method [64,65] was used to measure the physical solubility of CO 2 in solution, and it was fitted by empirical equations [66], semiempirical equations [67,68], and the Redlich-Klister equations [69]. Defining physical absorption helps to analyze enthalpy from a thermodynamic viewpoint, thereby optimizing the operating conditions in the process. Tomizaki et al. [39] studied the dissolution mechanism of CO 2 in alkanolamine and imidazole solution by 13 C NMR, and provided the contribution ratio of physical and chemical effects. The experimental results showed that when the equilibrium pressure is 1 MPa, the physical absorption of CO 2 in 2-MeIm aqueous solution accounts for 12% of total absorption, while that in MDEA solution is about 5%.
A calculation approach for estimating physical and chemical solubility of CO 2 in chemical absorbents separately using the CPA model was    [54]. The calculation method of physical solubility is to retain the interaction parameters k ij of MDEA-CO 2 , and the association parameters of MDEA-CO 2 adopt the CR-1 rule instead of values from the literature, while other parameters and association rules remain unchanged. Correspondingly, the chemical solubility can be calculated by subtracting the physical solubility from the total solubility. Using this calculation approach, the physical and total solubility of CO 2 in 24.5 wt% for the 2-MeIm aqueous solution and 35 wt% for the MDEA aqueous solution at 313.15 K were calculated and these are presented and compared with experimental data in Fig. 7. It can be seen that the total absorption first increases rapidly with pressure, then increases slowly until saturation is reached, while the physical absorption increases almost linearly with pressure. The CPA model describes the total solubility and physical solubility very reasonable for both the 2-MeIm and MDEA solutions, indicating that the CPA model can distinguish physical and chemical absorption with corresponding calculation approaches for different CO 2 -chemical absorbent systems. It is interesting to note that the predicted physical solubility increases almost linearly as the pressure increases, which implies that the Henry's law may be able to successfully correlate the physical solubility, especially when the pressure is below 2.5 MPa.

Enthalpy
In the CO 2 capture process, another important characteristic is the absorption enthalpy, which determines the energy consumption of the separation process. Evjen et al. [36] measured the CO 2 absorption enthalpy in 30 wt% 2-MeIm and MDEA aqueous solution using heat-flow reaction calorimeter. We have used the CPA model to calculate the absorption enthalpy under the same conditions with the Clausius-Clapeyron equation (21).
where d(ln P)/d(1/T) can be obtained by differentiating the absorption isotherms at different temperatures, so the absorption enthalpy corresponding to CO 2 solubility can be calculated. A comparison between the CPA model results and experimental data is shown in Fig. 8. The estimated results are rather close with the experimental data at low temperatures, but not at high temperatures. Overall, the CPA model estimates the trend and range of enthalpy at a typical operating temperature of 313.15 K for the CO 2 absorption column, while the model underestimates the absorption enthalpy at high CO 2 solubility. At a typical desorption temperature of 353.15 K, the CO 2 enthalpy in 2-MeIm aqueous solution is smaller than that of MDEA solution, which indicates that the separation process using 2-MeIm aqueous solution has low energy consumption. However, the enthalpy estimated by the CPA model and the experimental data show a different trend with increasing CO 2 solubility at this temperature. It can also be seen in Fig. 8, there is a larger deviation between the experimental data and calculation results of the CO 2 absorption enthalpy in MDEA aqueous  solution at 353.15 K. It is surprising to see this large deviation, as it is clearly shown in Fig. 4 that the model can correlate the saturation pressure very well. More experimental data are needed for a more indepth and systematic evaluation. Moreover, an analysis of the impact of temperature and composition on the CO 2 absorption mechanism at the molecular level, for instance through molecular simulation, will be helpful in improving our understanding and the predictive capability of the model.

Conclusions
CO 2 capture is a favorable way to mitigate global climate change. In this work, the experimental and thermodynamic modeling study of the CO 2 solubility in 2-MeIm aqueous solutions have been investigated. The solubilities of CO 2 in 5-30 wt% 2-MeIm aqueous solution at 293.15-353.15 K were measured, and a thermodynamic model for the 2-MeIm-CO 2 -H 2 O system was developed by combining CPA EoS and a pseudo chemical reaction approach. The properties of the 2-MeIm aqueous solution such as density, vapor pressure and gas composition can be accurately represented by CPA with average deviations of 0.45%, 1.1%, and 14%, respectively. The absorption of CO 2 in 2-MeIm aqueous solution is greatly influenced by temperature, and thus using a temperature dependent k ij (T) of 2-MeIm-CO 2 represents better the VLE data of 2-MeIm-H 2 O-CO 2 system. A method to distinguish the physical and chemical solubility of CO 2 in chemical absorbents has been proposed, and the calculated physical solubilities of CO 2 in 2-MeIm and MDEA aqueous solutions show an excellent agreement with the experimental data. However, it is surprising to see that the predicted CO 2 absorption enthalpy does not match the experimental values satisfactorily, not even at qualitative level, especially since the vapor pressure can be correlated satisfactorily. More detailed experimental and molecular simulation studies will be useful in classifying the problems and resolving the modeling challenges. In general, the proposed modeling approach shows promising results, especially for relatively high concentration of 2-MeIm aqueous solutions at temperatures of 293.15-393.15 K, which covers the operating conditions of CO 2 capture process design and simulations.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Data will be made available on request.