The simulation system is composed of a periodic slit-shaped calcite nanopore with a width of 2 nm. The simulation box with dimensions of 48.57 × 39.92 × 68.58 Å consists of two calcite blocks with each block composed of 6 calcite layers (Figure 1). The calcite surfaces were obtained by cutting calcite along the (104) crystallographic surface based on calcite unit cell. The calcite surfaces were immobilized in the simulation. Table 1 below describes the interatomic parameters used in this study.

Four systems were constructed to investigate the effect of hydration on the structure and diffusivity of CO₂ and CH₄. First, 100 molecules of pure CO₂ and CH₄ were randomly distributed in the pore space to investigate the structure and dynamics of gases in the absence of pore water as shown in Figure 1A. In the second case, a single layer of water composed of 150 water molecules was added at the calcite interface (Figure 1B). The thickness of water layer was chosen based on experimental observations reported by Fenter et al. (2000). In the third configuration, the nanopore was solvated with 500 number of water molecules (Figure 1C). The fourth scenario, the density of confined water was set to mimic that of bulk water i.e., density of 1 g/cm³ of water (1,296 molecules) for potential comparison with previous studies (Figure 1D) (Mutisya et al., 2017).

Canonical ensemble (NVT) simulation was performed on the product of energy minimization for 10 ns using Nose-Hoover (Nosé, 1984; Hoover, 1985) thermostat with time constant of 1 ps to control the temperature of both surface and the fluids. The energy of the initial configurations was minimized using steepest descent method for 50,000 steps to ensure that the energy is <100 kJ mol⁻¹ nm⁻¹. The simulations were performed at standard temperature and the pressure was calculated based on Ping Robinson equation of state (EOS) (Peng and Robinson, 1976) by inserting specific number of gas molecules to satisfy the required density. One hundred molecules of CH₄ were inserted in the system free of water to match a pressure of about 125 bar which was studied experimentally to represent the shale pressure (Zhong et al., 2016; Xing et al., 2018). Number of CO₂ molecules was chosen as an equimolar of methane for comparison purposes. Since we are interested in the effect of water on the properties of confined gases, number of CH₄ and CO₂ molecules were kept constant in all four configurations and various amount of water were added into each system.

Statistics were evaluated by dividing each simulation into three 1.5 ns blocks. Each block was treated as an independent replicate. The SHAKE algorithm was used to keep the water molecules rigid (Ryckaert et al., 1977). Van der Waals (vdW) interactions were modeled by Lennard-Jones (LJ) 12-6 function, and electrostatic interactions, which modeled by Coulomb's function as shown in Equation 1. (1)Uij=∑i<j[4εij[(σijrij)12-(σijrij)6]+qiqjrij] In Equation (1), q_iand q_j are the charges of i and j, r_ij is the distance between i and j. LJ parameters (i.e., ε_ij and σ_ij) for unlike molecular interactions were calculated based on Lorentz-Berthelot rule as following: (2)σij=σii+σjj2 (3)εij=εiiεjj The intramolecular interactions accounted for bond stretching, angle bending and dihedrals. Electrostatic and dispersion interactions were computed in real space up to a distance of 14 Å. Long range electrostatic interactions were evaluated using particle mesh Ewald (PME) (Darden et al., 1993). Simulations were carried out using the GROMACS program. Simulation results were analyzed to determine the structure and diffusivity in the calcite nanopores. The structural changes in the gas molecules in confinement were evaluated using radial distribution functions (RDFs) extracted from the trajectory using VMD (Humphrey et al., 1996).

The self-diffusion coefficients were calculated for each gas (i.e., CO₂ and CH₄) in the calcite nanopore. The diffusion coefficients were calculated based on the mean square displacement (MSD) for the directions and the plane parallel to the pore dimensions (D_X, D_Y, and D_XY) according to the following equation: (4)D=12dlimt→∞ddt∑i=1N[ri(t)-ri(0)]2 Where d is the number of dimensions (1 for D_X and D_Y and 2 for D_XY). The diffusion coefficients in x and y directions (i.e., D_X and D_Y) were calculated to determine if diffusion is isotropic or anisotropic for the confined fluids. The diffusivity of the molecules is considered to be isotropic if the diffusion coefficients in X and Y directions are equal, otherwise the diffusion is anisotropic (Bui et al., 2017).

The calcite surface was modeled using forcefield developed by Xiao et al. (2011). CO₂, CH₄, and water were modeled using EPM2 (Harris and Yung, 1995), OPLS/AA (Jorgensen et al., 1996), and SPC/E (Berendsen et al., 1987) models respectively. Several forcefields were used in the literature to model confined gases. For example, OPLS-UA (Bui et al., 2017), OPLS-AA (Gadikota et al., 2017), CVFF (Yuan et al., 2015), COMPASS (Sun et al., 2016a,b), and TraPPE-UA (Simoes Santos et al., 2018) were used to represent CH₄ in confinement. To evaluate the appropriate forcefield, MD simulations were performed using several forcefields to reproduce the properties of the confined CH₄ in the calcite pore and compare the governed data from each forcefield with published data. The structure of the confined CH₄ in 4 nm calcite pore with density of 96 kg/m³ and 375 K was calculated and compared with the data reported by Simoes Santos et al. (2018). We employed both Trappe-UA and OPLS-AA forcefields to calculate CH₄ distribution. As shown in Figure 2, the distribution of CH₄ in calcite nanopores are in reasonable agreement. Both forcefields proved the ability to reproduce the required data, however, we used OPLS-AA since the interatomic potentials of C and H are specified independently (Gadikota et al., 2017). To validate the choice of OPLS-AA further, the density of methane was calculated at standard temperature and pressure by simulating 500 methane molecules using NPT ensemble for 10 ns. Nose-Hoover thermostat and Parrinello–Rahman barostat (Parrinello and Rahman, 1982) were used to control the temperature and pressure, respectively. The governed density is 0.648 ± 0.013 kg/m³ which is consistent with the experimental value which is about 0.656.

Similarly, various forcefields such as EPM2 (Headen and Boek, 2010; Liu L. et al., 2015; Fazelabdolabadi and Alizadeh-Mojarad, 2017; Mohammed and Mansoori, 2018a,b,c), TraPPE (Javanbakht et al., 2015; Simoes Santos et al., 2018), and COMPASS (Liu B. et al., 2015; Liu et al., 2016; Fang et al., 2017) were used to model CO₂ and its behavior under bulk and confinement conditions. Various studies validated simulated properties such as diffusivity (Moultos et al., 2014, 2016) and solubility (Vlcek et al., 2011) of CO₂ in water using the EMP2 forcefield. To validate the choice of EMP2 forcefield in this study, the diffusion coefficient of CO₂ in water was calculated by dissolving 5 CO₂ molecules in 2000 SPC/E water molecules in an initial cell of 4 × 4 × 4 nm³ to be consistent with previous studies (Moultos et al., 2014). The system was simulated for 5 ns under 1 bar and 323 K using NPT ensemble. The produced self-diffusion coefficient is in reasonable agreement with the experimental and simulated data (Versteeg and Van Swaaij, 1988; Moultos et al., 2014). The diffusion coefficient for CO₂ in water is 4.3 (±0.4) × 10⁻⁵ cm²/s compared with 4 × 10⁻⁵ cm²/s (Moultos et al., 2014) and 3.4 × 10⁻⁵ cm²/s (Versteeg and Van Swaaij, 1988) reported in previous studies.

Probing the structure of gases in varying confined water environments provides insights into changes in the affinity of gases for the solid interfaces. As shown in Figure 3, the density profiles of gases (CO₂, CH₄) differ when there is no water, one layer of interfacial water composed of 150 molecules, 500 molecules of confined water, and confined water mimicking the density of bulk water (with 1,296 water molecules) in the calcite nanopore. In the absence of water, both CO₂ and CH₄ show a layered structure on the calcite surface and the density profiles are symmetric with respect to the pore center (Figure 3A). These density profiles indicate that CO₂ and CH₄ are adsorbed to create a single layer on the calcite surface in the absence of water which is consistent with previous studies (Franco et al., 2016; Sun et al., 2017; Wang et al., 2017; Simoes Santos et al., 2018). The higher density of CO₂ at the interface compared to CH₄ is attributed to the higher energetic affinity of CO₂ on the calcite interface compared to CH₄ as reported by Wang S. et al. (2016b).

In the presence of a single layer of interfacial water, the peak density of CO₂ at the calcite interface decreases from 749 to 550 kg/m³. Similarly, the peak density of CH₄ decreases from 239 to 126 kg/m³. Further, a higher density of CO₂ and CH₄ is noted at the center of the pore in the presence of interfacial water. A reduction in the number of molecules in the adsorbed shells of CO₂ and CH₄ and the shift of these shells away from the calcite surface is noted. CO₂ and CH₄ adsorbed layers were shifted by ~1.5 Å compared to the case where there is no water (Figure 3B). The variation in the relative density of CO₂ and CH₄ due to the presence of water layer can be explained by two factors: the higher adsorption energy of water on the calcite surface compared to CO₂ and CH₄ (Wang S. et al., 2016b) and the difference in the interfacial tension of CO₂ and CH₄ with water. CO₂ has lower interfacial tension with water compared with CH₄ and is partially miscible with water (Bachu and Bennion, 2008; Sakamaki et al., 2011; Yasuda et al., 2016).

In the third scenario, 500 water molecules were randomly distributed in the pore space to represent the abundance of the confined water within the pore. The equilibrium density profiles are shown in Figure 3C. After equilibrating the cell for 5 ns, the water molecules were arranged into two layers on the calcite surface as noted by the peak positions at 0.35 and 0.38 nm in Figure 3C. This specific arrangement of water molecules at calcite interfaces was noted experimentally and computationally (Fenter and Sturchio, 2004; Geissbühler et al., 2004; Argyris et al., 2008; Heberling et al., 2011; Ou et al., 2014; Keller et al., 2015; Fazelabdolabadi and Alizadeh-Mojarad, 2017). A significant reduction in the relative densities of CO₂ and CH₄ at the calcite interface is noted and compared to the case where a single layer of interfacial water is present. A bi-layered arrangement of CO₂ molecules with one peak located near the water-CO₂ interface and another at the calcite-water interface was noted. The existence of the water film leads to a wider distribution of CO₂ molecules at the calcite interface.

In the presence of interfacial water mimicking the density of bulk water, the bi-layer arrangement of water molecules was noted (Figure 3D) which is consistent with the studies reported by Keller et al. (2015) and Mutisya et al. (2017). Higher concentrations of CO₂ and CH₄ were noted at the center of the calcite pore in the presence of this interfacial water. The density maps in Figures 4, 5 provide further insights into the distribution of gases in varying levels of confined water. In general, the presence of different amounts of water displaces more CH₄ molecules toward the pore center compared with CO₂. At a density of 1 g/cm³, a phase separation was noticed between water and CH₄ molecules which are concentrated at the pore center. In contrast, CO₂ molecules was displaced toward the center of the pore while being solvated in the water phase, as shown in Figures 4, 5d.

It was interesting to note that the structure of a single layer of interfacial water (Figure 1B) did not change in the presence of CO₂ or CH₄ (Figures 6A,B). In the presence of 500 and 1,296 water molecules with 100 molecules of CO₂ (Figure 6A), the Ca_calcite-O_water interface changed significantly unlike in the case with 100 molecules of CH₄ (Figure 6B). The water layer in the system bearing CO₂ is about 1.3 times wider than CH₄ and is shifted away from the calcite surface. One hypothesis is that the higher solubility of CO₂ in water compared to CH₄ influences the interfacial structure of water. For example, at 298 K, the solubility of CO₂ and CH₄ in water are 0.0286 and 0.0008 mol/kg_water, respectively (Wiesenburg and Guinasso, 1979; Duan and Sun, 2003). The hydration of CO₂ in water potentially results in less sharp water layer. In the presence of interfacial water with a density similar to bulk water, fewer number of oxygen atoms corresponding to the water molecules are present in the first shell of Ca²⁺ in calcite.

Higher confined water concentrations reduced the number of oxygen atoms corresponding to calcite in the first coordination shell of C_CH4 and C_CO2. In the absence of water, about 11 and 9 oxygen atoms corresponding to calcite in the first coordination shell of C_CO2 and C_CH4 are noted. These data are consistent with the higher adsorption affinity of CO₂ for the calcite interface compared to CH₄. In the presence of 300, 500, and 1,296 water molecules, the number of oxygen atoms corresponding to calcite in the first coordination shell of C_CO2 are about 4, 3, and 1. Similarly, in the presence of CH₄, 300, 500, and 1,296 water molecules, the number of oxygen atoms corresponding to calcite in the first coordination shell of C_CH4 are about 3, 2, and <1, respectively. These data suggest that increasing the number of water molecules reduces the affinity of the gas molecules for the calcite interface.

The number of oxygen atoms corresponding to water in the first coordination shell of C_CH4 were in the range of 4–6 in varying confined water concentrations. The number of oxygen atoms corresponding to water in the first coordination shell of C_CO2 were about 10, 5, and 4 in the presence of 300, 500, and 1,296 water molecules. These data suggested that the number of water molecules in the confinement had a much stronger influence on the coordination behavior of water molecules with CO₂, unlike CH₄.

The orientation of the CO₂ molecules is determined by comparing the coordination behavior of oxygen and carbon in CO₂ with calcite and water interfaces. In all the simulated systems, the number of oxygen atoms in CO₂ are about twice the number of carbon atoms in CO₂ in the first shell. This observation suggests that the CO₂ molecules orientated parallel to the calcite surface, which is consistent with previous reports of CO₂ orientation with Na-montmorillonite surface (Botan et al., 2010; Myshakin et al., 2013; Yang et al., 2015; Kadoura et al., 2016). Also, the number of oxygen atoms of CO₂ in the first shell of the oxygen atoms of water is twice the number of carbon atoms in the case where a single layer of interfacial water is present. This observation is consistent with the orientation of CO₂ parallel to the water interface (Zhao et al., 2011).

The diffusivity of CO₂ and CH₄ through calcite nanopores without water, one layer of interfacial water composed of 150 water molecules, 500 water molecules, and 1,296 water molecules to mimic the density of bulk water yielded interesting insights. In general, the diffusion coefficients of CO₂ and CH₄ in the absence of water are in reasonable agreement with Sun et al. (2017) after accounting for the differences in temperature. The temperature used in this study is 298 K compared with 323 K studied by Sun et al. (2017). The diffusion coefficient for CO₂ in the absence of water is 0.4 x 10⁻⁵ cm²/s at 298 K compared with 2 × 10⁻⁵ cm²/s at 323 K. The diffusion coefficient for CH₄ is ~20 × 10⁻⁵ cm²/s at 298 K compared with 35 × 10⁻⁵ cm²/s at 323 K. CO₂ and CH₄ diffusivities in the presence of interfacial water with a density similar to bulk water are in the range reported by Mutisya et al. (2017) and Bui et al. (2017) (Table 2).

The diffusivities are calculated in X, Y directions and in XY plane. The anisotropic variations in the diffusivity of gases in the X and Y directions are noted and shown in Table 2, which is consistent with the data reported by Franco et al. (2016). The diffusion coefficients of CH₄ in X and Y directions are not equal in systems without water and in the presence of single water layer which is consistent with previous studies (Wang S. et al., 2016a; Bui et al., 2017). CH₄ diffusivity in the X direction is higher than that in Y direction by about 4.36 × 10⁻⁵ and 12.58 × 10⁻⁵ cm²/s in the absence of water and the presence of one layer of interfacial water, respectively. However, this difference is much smaller in systems containing more water molecules (Table 2).

Further, an increase in the diffusivity of CO₂ and CH₄ in the presence of one layer of interfacial water was noted. The diffusivity of CO₂ increased from ~ 0.4 × 10⁻⁵ to ~ 13 × 10⁻⁵ cm²/s on introducing a single layer of interfacial water in the simulation system. To date, studies have not reported the diffusivity of CO₂ in calcite nanopores in the presence of one layer of interfacial water. In the absence of pore water, CO₂ has a strong preference for the calcite interface as shown in Figure 3A. In the presence of interfacial water, the density of CO₂ at the interface is reduced which potentially allows for greater mobility within the pore space. Similar diffusivities of CO₂ are noted in the presence of a single layer of interfacial water and in the presence of 500 water molecules.

Similarly, the diffusivity of CH₄ in calcite nanopore composed of a single water layer is about three times higher than the diffusivity in calcite nanopores without water. The reduced affinity of CH₄ for the calcite surface in aqueous environments may be one of the factors enhancing the diffusivity of CH₄ at these conditions. CH₄ diffusivity in the system without water is much higher compared with CO₂ due to the reduced adsorption affinity to the calcite surface. Another contributing factor to the variation in the diffusivity is the molecular weight. The molecular weight of CO₂ is higher than CH₄. Enhanced diffusivity of CH₄ in the calcite nanopore in the presence of a single layer of interfacial water and 500 water molecules is noted.

The in-plane diffusivity (D_xy) of both CO₂ and CH₄ interestingly increased in the systems contain a single water layers compared to the systems free of water due to the reduction in the concentration of the gases adsorbed layers onto the pore surfaces in the presence of water molecule. In the systems free of water, the predominant movement of the molecules is the surface diffusion onto the calcite surface, however, when a preconstructed water layer added to the system, it prevents some of the gases molecules to be adsorbed which are consequently could move faster in the pore space. When additional water added to the system, the diffusivities of CO₂ and CH₄ decreased compared to the scenario of single water layer due the increase in the overall systems density which leads to more intermolecular collisions and higher steric hindrance.

Diffusivities of CO₂ and CH₄ in interfacial water with a density similar to bulk water are 1.6 × 10⁻⁵ and 0.87 × 10⁻⁵ cm²/s, respectively. The diffusivities of CO₂ and CH₄ in Na-montmorillonite nanopore bearing two layers of interlayer water at similar conditions are 1.04 × 10⁻⁵ and 0.85 × 10⁻⁵ cm²/s (Gadikota et al., 2017) which are in reasonable agreement with this study. It is interesting to note that despite the differences in the solid interface i.e., calcite vs. Na-montmorillonite, similar diffusivities of CO₂ and CH₄ in interfacial water are predicted. These data suggest that the diffusivities of fully solvated CO₂ and CH₄ are much lower compared to gases in the absence of confined water.

One of the important outcomes of this study is the observed differences in the diffusivities of confined CO₂ and CH₄ in the x and y directions. These data are the first systematic observations of the influence of varying levels of confined water on the diffusivities of confined CH₄ and CO₂. These differences are attributed to the organization of the water molecules in confinement and the interfacial interactions between the gases, water, and solid interfaces. In the absence of water, one of the key factors influencing the transport of gases is their interactions with calcium and carbonate species on the calcite surface. Previous studies by Bui et al. (2017) showed that the anisotropy in the diffusivity of gas molecules such as CH₄ in calcite pores is significantly greater compared to other solid substrates such as silica, MgO, alumina, and muscovite using Principal Component Analyses. The anisotropic variation in the diffusivities of the confined gas molecules is attributed to the difference in the energy barriers as the gas molecules are transported along a specific direction. It is important to note that the x- and y-orientations are interchanged in the data in this study with respect to the studies performed by Bui and co-workers. Regardless the scientific insights are similar.

In this study, diffusivity of methane in the x-direction is greater than that of the diffusivity in the y-direction in the absence of water suggesting that the free energy barrier for the movement of methane molecules in the x-direction is lower compared to the energy barrier associated with diffusivity in the y-direction. It was also interesting to note that as the water content in calcite pores is increased to 500 molecules and then 1,296 molecules, the diffusivity of methane molecules in the x and y directions are roughly equal, and then diffusivity in the y-direction exceeds that in the x-direction. These data suggest that the solvation free energy distributions of confined methane within the calcite pores vary with the water content. Our observations noted in Figure 5d suggest that in the presence of 1,296 water molecules, methane molecules undergo phase separation, which allows the molecules to move freely in the y-direction relative to the x-direction.

However, the observed diffusion behaviors of CO₂ in varying levels of confined water differ significantly from that of CH₄. Previous studies also showed that the solvation free energies of CO₂ in confined water are much lower compared to CH₄ (Gadikota et al., 2017). Unlike methane, the phase separation of CO₂ molecules in environments composed of 1,296 water molecules is not observed (Figure 4d). This observation is consistent with the similar diffusivities of CO₂ in the x and y directions in 1,296 water molecules. In the absence of confined water, the diffusivity of CO₂ in the y-direction is greater compared to that in the x-direction. However, the trends in the observed diffusivities are switched in the presence of a single layer of water and 500 water molecules. These data suggest that the energy barriers associated with the movement of CO₂ vary significantly in the x and y directions in the presence of fewer water molecules.

The van der Waals and electrostatic energies associated with the interactions of CO₂ and CH₄ with calcite interfaces with varying levels of water hydration were determined. These calculations provide insights into the energetics driving the interactions of CO₂ and CH₄ in confined water environments. In the absence of confined pore water, the affinity of CH₄ for the calcite interface was driven by van der Waals interactions. In the case of CO₂, however, the electrostatic and van der Waals interactions enhance the affinity of the calcite surface (Table 3). The overall energetic affinity of CO₂ for the calcite interface is much higher compared to that of CH₄. These findings are consistent with previous studies that pointed to the higher adsorption affinity of CO₂ for the calcite surface compared to CH₄ at the same conditions (Sun et al., 2016b; Wang S. et al., 2016b; Simoes Santos et al., 2018). The quadruple moment of CO₂ gives rise to the enhanced electrostatic interactions leading to higher affinity of CO₂ for calcite interfaces compared to CH₄ (Lithoxoos et al., 2010; Saha et al., 2010; Skarmoutsos et al., 2013; Duan et al., 2016; Liu et al., 2016; Molyanyan et al., 2016).

In the presence of a single layer of interfacial water, the van der Waals affinity of CO₂ and CH₄ for the calcite interface is lower than the systems free of water (Table 3). These data are consistent with the reduced number of first shell oxygen atoms corresponding to calcite with respect to the carbon atoms in CO₂ and CH₄. The number of oxygen atoms in calcite in the first shell of CO₂ decrease from 9 to about 3. Similarly, the number of oxygen atoms in calcite in the first shell of CO₂ decrease from 11 to about 4. The van der Waals and electrostatic affinity of CO₂ for the single layer of interfacial water compared to CH₄ is noted (Table 3).

When the number of water molecules in the calcite nanopore is increased to 500, the solvation of CO₂ and CH₄ in the confined water close to the calcite surface is noted from the overlap in the density distributions of gases with that of confined water (Figure 3C). The van der Waals affinity of gases corresponding to the solvation behavior increases with the increase in the number of water molecules (Table 3). The increase in the electrostatic energetic interactions of CO₂ with the calcite surface from −801 kJ/mol in the presence of a single layer of interfacial water to −1,412 kJ/mol in the presence of 500 water molecules is attributed to CO₂ solvation close to the calcite interface. The electrostatic interactions of methane with calcite in the presence of 500 water molecules are negligible.

The interaction of gases with the calcite surfaces are significantly reduced when the density of the interfacial water is similar to that of bulk water. The progressive reduction in the van der Waals affinity associated with CO₂ and CH₄ interactions with calcite with increasing water levels is noted (Table 3). This observation is consistent with the reduced number of oxygen atoms of calcite in the first coordination shell corresponding to C_gas-O_calcite. The number of oxygen atoms in calcite in the first shell of CO₂ or CH₄ are less than one when the density of interfacial water is similar to that of bulk water. Previous studies reported high van der Waals affinity of solvated gases for the solid interface (i.e., Na and Ca-montmorillonite) (see Schaef et al., 2013, 2015; Lee et al., 2014, 2015, 2017) with a pore size smaller than 1 nm. In this study, a pore size of 2 nm is simulated. With smaller pore sizes i.e., when the solid interfaces are closer, the overall energetic contributions arising from interactions with the solid interface may differ. In case of CO₂, the van der Waals and electrostatic interactions arising from interactions with water contribute to CO₂ solvation. However, the van der Waals interactions are the primary contributors to CH₄ solvation in confined water.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer VG and handling editor declared their shared affiliation at the time of the review.