Introduction

Natural gas contains large amounts of methane (CH4), but also all kinds of impurities such as sour gases (e.g., H2S and CO2). The acid gases in the natural gas should be removed to comply with environmental regulations and to avoid technological problems during gas transportation.1–3 For instance, dry ice or CO2 hydrate products can clog the system during liquefaction of the natural gas.2 Hence it would be beneficial to find an efficient and economical method for CO2 capture from natural gas. Amine-based natural gas “sweetening” (removal of sour gases) process is a widely used and mature technology. However, this process requires high energy for solvent regeneration and amines are corrosive and volatile which causes environmental pollution.1
In the past decade, ionic liquids (ILs) have emerged as a promising alternative to the amines due to their remarkable properties.4–6 Anderson et al.7 measured the solubility of various gases in the 1-hexyl-3-methylpyrolidium bis(trifluoromethylsulfonyl)amide [hmpy][Tf2N]. The solubility of the gases in [hmpy][Tf2N] at 298 K follows the trend: SO2>CO2>C2H4>C2H6>CH4>O2>N2. Similar gas solubility trends were observed in 1-hexyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl)amide ([hmim][Tf2N]), 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]), and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ([bmim][Tf2N]).8,9 Simple gases often interact weakly with the IL ions, hence the polarizability of the gases is reflected in the solubility behavior. Molecules that possess an electric quadrupole moment (such as CO2 and C2H4) show higher solubilities in ILs.10

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From an application point of view, solubility data only is not enough to judge the separation performance of a solvent, instead selectivity data is essential. One of the first mixed gas solubilities was reported by Hert et al.11 The authors surprisingly found that an enhancement of CH4 solubility when both CH4 and CO2 were dissolved in [hmim][Tf2N] liquid. It was speculated that the enhancement in CH4 solubility was due to favorable dispersion interactions between dissolved CO2 and CH4, while the drop in CO2 solubility was due to a reduction in free volume caused by the absorption of CH4. Carvalho and Coutinho12 measured CO2/CH4 and H2S/CH4 solubilities in three ILs and proposed that the ionic liquid polarity is an essential parameter in the design of ILs with high CO2 selectivities.
To design and optimize natural gas sweetening processes using ILs, mastering the important factors that dictate CO2/CH4 solubility as well as selectivity is essential. Shi and Maginn13 computed the mixed gas isotherms for the mixtures CO2/O2, SO2/N2, and CO2/SO2 dissolve in [hmim][Tf2N] and interpreted these mixed gas solubilities by energetic analysis. CO2 and SO2 interact more strongly with the anion than the cation due to stronger electrostatic interactions between the solute and the anion. N2 and O2 interact weakly with the ionic liquid and show little difference in interaction energy between the cation and anion. Thus CO2 and SO2 compete with each other in dissolution, while CO2 and O2 dissolve independently.13
However, there has no simulation motivated to address the unusual solubility behavior of CO2/CH4 mixtures in ILs. In this proposed research, molecular dynamics simulations will be utilized to investigate the enhanced solubility of CH4 in [hmim][Tf2N] in the presence of CO2.11 Also, with the aim of improving CO2/CH4 selectivity in ionic liquids, several other ILs described in the work done by Carvalho and Coutinho12 will be examined. These simulations could enable one to probe local structure of gases in ILs and energetics between different solutes and solvents, thereby give physical insight into the observed selectivity trends. The final goal is to find optimum structures of ILs that have satisfying performance in natural gas sweetening process.

Research Question

In this study, the solubilities of CO2/CH4 mixtures in four ILs will be investigated in order to understand the peculiar phenomenon of enhanced solubility of CH4 in the presence of CO2 in [hmim][Tf2N] and to understand the higher selectivity of CO2/CH4 in [bmim][Tf2N] as compare to that in 1-butyl-3-methylimidazolium methanesulfonate ([bmim][CH3SO3]) at molecular level. This work will be accomplished by classical molecular dynamics of systems consist of mixture gases with different molar ratios dissolve into four ionic liquids, [hmim][Tf2N], [bmim][Tf2N], [bmim][PF6] and [bmim][CH3SO3] respectively. The selectivities for different cases will be calculated and compare with experimental results at room temperature and at a pressure of 10 bar, which is a common operating pressure for natural gas sweetening process. Local electrostatic potential and radial distribution function of ILs will be computed to analyze the interactions between gas molecules and IL constituents and favorable absorption sites. Test particle insertion method will be utilized to calculate the excess chemical potential of CO2 and CH4 in different ILs. With this systematic information, a solid conclusion about the physical reasons lead to high CO2/CH4 selectivity could be achieved. The cation effect and anion effect to the selectivity could be drawn from the results in cases of these four ILs. In addition, more extensive work could be conducted to predict the relationship between the IL structure and the trend of selectivity of CO2/CH4 mixtures in ILs.

Significance of the Proposed Research

The global natural gas demand is expected to increase 1.4% per year in the next 20~30 years.2 Of great industrial relevance, carbon dioxide capture is very important in the natural gas sweetening process. Ionic liquids, due to their outstanding properties, such as negligible vapor pressure, high thermal stability, nonflammability and high solvation capacity, are believed to be promising alternatives for conventional CO2 capture solvents. Especially, the large differences in pure gas solubility reported in the literature suggest that selectivity for gas mixtures could be high, making ILs a strong candidate for effective separation processes.
It is possible to design many potential ILs by enormous combination of cations and anions and their functionalized ions. Therefore, the systematic study of different cation/anion combinations will provide us key parameters in the structure of ILs with high CO2/CH4 selectivity. However, measuring solubilities of gas mixtures is significantly more difficult than measuring pure gas solubilites.14 Therefore, molecular modeling is an efficient way to help understand solubility trends in ILs.
Through this proposed study, we can gain physical understanding in the selectivity of mixture gases in ILs at a molecular level. An additional advantage is that the simulations enable one to probe micro structure and energetics, thereby giving useful insight into the source of selectivity trends observed. The proposed research will inspire experimentalists to design ILs with higher CO2/CH4 selectivity, thus apply it into industrial natural gas sweetening process.

Proposed Studies

Simulation Details:
In this proposed research, I will perform systematic classical molecular dynamics simulations for systems representing CO2 and CH4 dissolve in [hmim][Tf2N], [bmim][Tf2N], [bmim][PF6] and [bmim][CH3SO3] ILs respectively. All simulations will be performed using the GROMACS15 program. Nose-Hoover temperature coupling will be used to set the temperature at 298 K and Parrinello-Rahman pressure coupling will be used to keep the pressure at 10 bar. Periodic boundary conditions will be applied in all directions. The cations and anions involved in this work are listed in scheme 1 with their molecular structures.

Scheme 1. Molecular structures of the cations and anions used in this study.

Force Field. In all simulations described in this study, ILs and CH4 will use the Canongia Lopes-Pádua16 and OPLS-AA17 force fields. Lennard-Jones parameters and the partial charges for CO2 will take from the TraPPE18 force field. The experimental C-O bond length (1.16 Å) and O-C-O bond angle (180Ëš) are fixed during simulations. The TraPPE model has been effectively used for predicting CO2 absorption in various ILs.13,19–22 Thus, all the force field parameters are available.
Pure Gas Absorption. The pure gas absorption for CO2 and CH4 will be computed following the method published by Huang et al.23 The initial configuration of the IL/CO2 or IL/CH4 binary system will be prepared from two independent bulk phase subsystems. The IL phase consists of 256 ionic pairs, and the gas (CO2 or CH4) phase initially has 216 molecules. Both IL phase and gas phase will first be equilibrated by a 1 ns NPT simulation at 298 K and 10 bar. Then the two subsystems will be concatenated along the Z direction to form a sandwich like simulation box with the gas phase in the middle. Some gas molecules are going to be removed in order to fit the cross section between the gas phase and IL phase. An energy minimization process is necessary to prevent steric hindrances in the combined system. The generated system then undergoes a 20 ns NPT equilibration run to allow gas molecules to diffuse into the IL phase. In order to improve sampling, five uncorrelated phase points will be collected from a successive 500 ps NPT run. Figure 1 shows a typical configuration of the equilibrium simulation box. These five configurations are used as initial coordinates for five 300 ps production runs in microcanonical (NVE) ensemble. The last 200 ps trajectories of each NVE simulation are used to collect data.

Figure 1. A snapshot of the equilibrium state of the simulation box.23

Mixed Gas Absorption and Selectivities. As described above, the only thing different for mixed gas absorption from the pure gas absorption is the gas phase contains two kinds of gas molecules, CO2 and CH4. In order to test the feed ratio effect, the molecular numbers of CO2 and CH4 are set to two distinct ratios, 1:9 and 1:1, which are the gas mixture compositions in ref. 11. As observed by ref. 11, only tiny amount of CO2 could enhance CH4 solubility.

The numbers of gas molecules can be easily obtained from the five final trajectories. Thus the mole fractions of CO2 or CH4 to ILs can be computed. Simply, the solubility is computed in terms of molar fraction by or , where x means the molecule number in IL phase. With the mole fractions of CO2 and CH4 in gas mixture/IL system, the selectivity for CO2 over CH4 can be computed as ,13 where x means the molecule number in IL phase and y means the molecule number in the initial gas phase.
This is the first goal of this research that aiming to confirm and predict the solubilities and selectivities of CO2 and CH4 gas molecules in different ILs. These data can also be used to validate the simulation method. It should be reasonable to expect that the above mentioned modeling procedure is capable of yielding good estimations of mixed gas absorption.

Radial Distribution Functions. The RDFs for pure liquid structures, gas/IL binary structures and mixed-gas/IL ternary structures can be calculated from the production simulations in NVE ensemble. Previous results23 showed that even though considerable amounts of CO2 diffused into the IL phase, the structure changes of the IL were small. However, the cases of CH4 gas diffuses into the IL phase have to be examined as well as the cases for CO2/CH4 gas mixtures dissolve in ILs. Therefore, the RDFs could tell us whether the structure will change significantly or not during the co-solvation process of CO2 and CH4 molecules.

Previous studies concluded that CO2 preferentially interacts with anions in ILs.5,8,13,23,24 However, little knowledge is known about the structure correlation for CH4 with cations and anions in ILs. Especially, the locations of CH4 molecules in ILs in the presence of CO2 would be very interesting.
From the NVE simulations, the Coulomb and Lennard-Jones potentials between different energy groups could be obtained. The energetic analyses could help explain the spatial distribution of CH4 and CO2 molecules in ILs. In addition, by comparing the relative interaction energies between solutes and the cations, anions and other dissolved solutes, one can understand which interaction makes CH4 more dissolvable in [hmim][Tf2N] when in the presence of CO2.

Local Electrostatic Potentials. Although the liquid is neutral in total charge, the local electrostatic environment within the first solvation shell of CO2 or CH4 molecule may have important effect on the solubility and selectivity performance.21 At any given time during the production runs, the position of each absorbed gas molecule can be determined. Also the surrounding atoms within , 1.5 nm, can be identified. Therefore, the local electrostatic potential U for a given absorbed gas molecule (x, y, z) can be calculated by:

where na is the number of surrounding atoms, qn,i is the partial charge on each surrounding atom, rn,i is the distance from each atom to the center carbon atom of absorbed gas molecule. Analyzing the distribution of local electrostatic potentials for CO2 and CH4 together with the selectivities, the relation between local electrostatic potentials can selectivities can be built.
Based on the fact that CO2 has a large quadrupole moment, CO2 molecule should be affected strongly by the local electrostatic potential. The more negative the local electrostatic potential is the higher preference for CO2 selectivity.21 I expect that the highest selectivity IL [bmim][CH3SO3] will give more negative distribution of local electrostatic potential as compare to other ILs.

Solvation Free Energy. In order to have more evidences for energetic analysis of the interactions between CO2/CH4 and ILs, Widom particle insertion method25 is utilized to determine the excess chemical potential of the solutes under study. The key quantity characterizing a solute in the solvation process is its solvation free energy, that is, the free energy necessary to insert the solute from pure ideal gas phase into solution. The solvation free energy per solute is equal to the excess chemical potential of the solute. In the case of an NPT ensemble the excess chemical potential can be written as26

where is the potential energy between the solute and the solvent, V is the volume of the system, =1/, and the angle brackets denote an isobaric-isothermal average over trajectory of the system without solute.
For each IL, the equilibration trajectory of pure IL in NPT ensemble is needed. Because test particle insertion method in GROMACS is currently limited to inserting a single charge group, the excess chemical potential of CO2 and CH4 can only calculated one at a time. At least, we can get information about the relative affinity of CO2 to ILs and CH4 to ILs. Thus the CO2/CH4 selectivities in different ILs could be compared using all the aforementioned methods.
In summary, the solubilities and selectivities of CO2 and CH4 pure gas and gas mixtures in four ILs will be calculated. The deep reasons that determine the CO2/CH4 selectivity will be investigated. Although only four ILs, [hmim][Tf2N], [bmim][Tf2N], [bmim][PF6] and [bmim][CH3SO3], are under this proposed research, we can expect to find out the anion effect to CO2/CH4 selectivity. By studying the spatial structure, interaction energy, local electrostatic potential and excess chemical potential, this work will contribute to the IL society with the first molecular dynamics simulation of CH4 dissolves in ILs and CO2/CH4 gas mixture dissolves in ILs.