Investigation of the factors influencing methane adsorption on illite

The molecular simulation method was used to investigate the adsorption behaviors of methane on illite. The effects of several factors on methane adsorption, free gas amounts, and the proportions of absorbed gas in the illite nanopores, including the pore size, temperature, and water content, are discussed. The results obtained show that methane adsorption in illite nanopores is due mainly to van der Waals adsorption. With an increase in the pressure or of the pore size, the free gas amounts of methane increase, whereas the free gas amounts decrease with increasing temperature or water content. With increasing pressures or decreasing pore sizes, the methane adsorption capacity of the illite pores increases. When the pressure or pore size increases, the proportion of the adsorbed gas in the pores decreases. As the temperature increases, the methane adsorption capacity of the illite pores decreases, and the proportion of adsorbed gas in the illite pores decreases slightly. The adsorbed phase density decreases with increasing pore size and temperature, whereas the adsorbed phase density increases with increasing pressure. The electrostatic forces and hydrogen bonds have a positive effect on water adsorption in the illite nanopores, while the van der Waals forces have the opposite effect, which causes the water molecules in the illite pores to exist in the form of aggregates. The water molecules occupy the areas near the pore walls in a directional manner and occupy the adsorption space and the adsorption sites of methane, resulting in a decrease in the methane adsorption capacity and a slight reduction in the proportion of adsorbed gas.


| INTRODUCTION
With increasing global energy demand and the improvement of advanced techniques, unconventional oil and gas reservoirs have gradually become the focus of exploration and development in the United States and in many other countries, including Canada, China, and Europe. 1 Shale gas, which represents one type of unconventional gas, is an important energy resource. The modes of occurrence of shale gas mainly include the free state, the adsorbed state, and the dissolved state. 2 Based on the investigations of reservoir characteristics of shale gas reservoirs in the United States, Curtis suggested that the proportion of adsorbed gas ranged from 20% to 85%, which means that a sizeable share of shale gas consists of adsorbed gas. 3 Therefore, for shale gas resource evaluation, it is important to investigate the methane adsorption capacity of organic-rich shales. In an effort to better understand the key factors controlling the CH 4 adsorption capacity, many researchers have made valuable contributions using isothermal adsorption experiments. It was determined that there are obvious relationships between organic matter (OM) and CH 4 adsorption capacity, including the total organic carbon (TOC) content, OM maturity, and kerogen type, indicating that OM was the major factor controlling the CH 4 adsorption capacity. [5][6][7][8][9][10][11][12] Additionally, some researchers have suggested that clay minerals could contribute to the CH 4 adsorption capacity because of their high internal surface areas. 6,7,[13][14][15][16][17][18][19] The relationships between TOC content and CH 4 adsorption capacity are shown in Figure 1. The experimental data shown in Figure 1 for different organic-rich shale samples were taken from the reports of Wang et al, 4 Yang et al, 5 Gasparik et al, 9 Hou et al, 10 and Tan et al. 11 The experimental data for different clay-rich samples were obtained from the literature. 13,14,16,17 Examination of Figure 1 shows that there is positive relationship between the TOC content and CH 4 adsorption capacity, indicating that larger TOC content corresponds to larger CH 4 adsorption capacities. Further, the methane adsorption capacity of clay minerals is comparable to or even greater than the capacity for shales with lower TOC content, especially for montmorillonite, indicating that clay minerals can contribute significantly to the methane adsorption capacity of shales, which is in agreement with previous work 6,7,18 and suggests that clay minerals contribute significantly to the CH 4 adsorption capacity of shales. Furthermore, some researchers have investigated the contribution of clay minerals and OM to the CH 4 adsorption capacity of organic-rich shales. Yang et al 5 reported that the average contributions of clay minerals and OM to CH 4 to the adsorption capacity of shales in the Longmaxi Formation were approximately 28.6% and 67.6%, respectively. Fan et al 13 reported the contributions of clay minerals and OM to CH 4 adsorption capacity for shales in Longmaxi Formation samples were 44.12% and 43.08%, respectively, while the contributions of the Niutitang Formation shales samples were 16.74% and 56.58%, respectively. Rexer et al 19 noted that the contributions of clay minerals and OM to CH 4 adsorption capacities for Posidonia shales were approximately 45%-60% and 60%-70%, respectively. These studies indicated that the contributions of clay minerals to the CH 4 adsorption capacities of shales can be larger. In addition, clay minerals are important parts of the mineralogical compositions of organic-rich shales and can occur at relatively high concentrations, according to previous studies, 4,5,13,[20][21][22] which have provided details of the mineralogical compositions of the organic-rich shales from the Yanchang Formation in the Ordos Basin and the Longmaxi and Wufeng Formations in the Sichuan Basin. Therefore, research on the methane adsorption capacity of clay minerals is a significant component in the evaluation of methane adsorption capacity for these shales, and the average illite content in the clay minerals of these organic-rich shales was over 60%. 4,5,13,[20][21][22] To summarize, illite has an important influence on the CH 4 adsorption capacity of shales. Therefore, it is advisable to study the methane adsorption capacity of illite.
Currently, investigations of methane adsorption capacity rely primarily upon isothermal adsorption experiments. A great deal of research has been carried out to study the methane adsorption capacity of illite. Ross  . We note that these experiments for the CH 4 adsorption of illite were conducted over a limited range of pressures and temperatures, each of which had its own limitations for understanding the supercritical adsorption behaviors. Additionally, all of the mentioned studies aimed to obtain adsorption amounts to evaluate the CH 4 adsorption capacities of illite based on isothermal adsorption experiments, which are regarded as describing macroscopic behaviors. However, the values obtained for the adsorption amounts did not obtain the proportions of the adsorbed gas in the total gas amounts in the illite nanopores and failed to deeply reflect the change law of free gas amounts and the adsorption essences of methane in the illite nanopores; thus, these studies were not able to elucidate the adsorption mechanism of CH 4 in illite nanopores at the molecular scale.
In previous studies, as a theoretical research approach applied to investigate the adsorption characteristics of the adsorbent, the molecular simulation method, which is able to investigate the adsorption mechanisms between porous materials and fluid molecules at the molecular level, has gained increasing attention. Several studies have been performed on the adsorption behaviors of methane and carbon dioxide for clay minerals. Several researchers have investigated the diffusion and adsorption behaviors of CH 4 in montmorillonite pores using the grand canonical Monte Carlo (GCMC) method and the molecular dynamics (MD) method and have discussed the influences of pore size, temperature, and water on adsorption behaviors. [24][25][26][27] Concurrently, some researchers have investigated the structural properties and adsorption behaviors of CH 4 , CO 2 , and their mixtures for montmorillonite pores using the GCMC and MD methods and have discussed some of the important factors influencing adsorption, including pore size, temperature, and water content. [28][29][30][31] At the same time, Xiong et al 32,33 investigated the adsorption behaviors of methane for kaolinite and chlorite using the GCMC method. These studies indicated that the GCMC method has been proven to be an effective method for investigating of the microcosmic adsorption mechanisms of adsorbents and have obtained some knowledge regarding methane adsorption by clay minerals. In addition, Zhang et al 34 and Chen et al 35 studied the adsorption behaviors of CH 4 , CO 2 , and their mixtures of illite using the GCMC and MD methods. In these studies, the total gas amounts and excess adsorption amounts of clay minerals were used to investigate the methane adsorption capacity. For supercritical adsorption, however, excess adsorption amounts cannot describe realistic adsorption amounts, and these values should be converted into absolute adsorption amounts. 27,36 Additionally, these studies did not investigate the proportion of the adsorbed gas in relation to the total amount of gas in the illite nanopores and did not discuss the different factors impacting the proportion of adsorbed gas in the illite nanopores.
In this work, we used the GCMC method to investigate the adsorption mechanisms of methane in slit-like illite nanopores at the molecular scale. We constructed the skeleton patterns of illite nanopores and investigated the adsorption mechanisms of methane in the illite nanopores at the molecular scale. Based on this, the factors that influence methane adsorption, free gas amounts, and the proportion of the adsorbed gas in the total gas amounts were also studied, including pore size, temperature, and water content. In addition, the effects of pore size, temperature, and water on the adsorption behaviors of methane adsorption as well as their interaction mechanism are discussed, and the influences of the pore size, temperature, and water content on the change law of the free gas amounts and the proportion of the adsorbed gas in the total gas amount are also discussed.

| Models
The parameters for an illite crystal cell can be found in the references 37 ; illite is a layer of 2:1 clay mineral, which consists of an octahedral sheet sandwiched between two opposing tetrahedral sheets. The parameters of an illite crystal cell are as follows: a = 0.5198 nm, b = 0.9014 nm, c = 0.999 nm, α = γ = 90°, and β = 100.95°. We obtain from the results of the N 2 adsorption-desorption isotherm that the morphology of the illite pore shape can be simplified as a slit shape and is described in Figure S1. Therefore, we build a slit-like illite pore. First, a unit cell is defined in a rectangular box with periodicity in the x and y directions based on the illite crystal cell, including an 8a × 4b supercell structure in the x × y direction; thus, the size is 4.158 nm × 3.606 nm and the surface area is 2 × 4.158 nm × 3.606 nm. Second, the slit-like illite pore is built by placing a vacuum between the inner planes of the two supercell structures, and the pore size H of the slit-like illite pore is determined by the amount of the vacuum. Thus, slit-like illite nanopores of different pore sizes are created. In our simulations, illite is considered to be a rigid molecule. A schematic representation of the slit-like illite nanopore is shown in Figure 2, and the parameters of the slit-like illite nanopores are presented in Table S1.

| Parameters
In this work, we obtain the L-J potential parameters and the charges of sites in the illite unit cell from the references, 28,29,38 which are shown in Table S2; the charges of the sites are presented in the literature, 28,29,38 and the L-J potential parameters for the sites are seen in Cygan et al. 38 The

F I G U R E 2
The schematic representation of a slit-like illite nanopore ( is an oxygen atom, is a hydrogen atom, is a silicon atom, is an aluminum atom, and is a potassium atom) potential model used for the CH 4 molecule is simulated using the TraPPE model, 39 and its schematic is shown in Figure  S2. The potential model used for the H 2 O molecule is simulated using the SPC-E model, 40 and its schematic is shown in Figure S2. The L-J potential parameters and the charges of each atom are presented in Table S2.
In the GCMC simulation, the chemical potential is not a function of pressure but instead is a function of fugacity. In our previous work, 32,33,36 the SRK state equation was used to calculate the fugacity. Therefore, the SRK state equation 41 is adopted in this simulation. The fugacity coefficients of CH 4 at different temperatures and pressures in the simulations are shown in Figure 3A. In our simulation, the maximum pressure is 40 MPa and the simulation is under a constant pressure, point by point, and is divided into 15 points. Meanwhile, the Dreiding force field is chosen as the force field type 42 which has been widely adopted in related studies. [27][28][29][30]32,33 Additionally, the total potential energy includes the valence energy and the nonbonding energy. The valence electron energy contains the bond stretching energy, bond angle-bending energy, torsion energy, and inverse energy, whereas the nonbonding energy contains the van der Waals energy (Equation 1), electrostatic energy (Equation 2), and the hydrogen bond energy. The Ewald and Group method is applied to calculate the Coulomb force interaction, and the atom-based method is used to calculate the van der Waals force and the L-J potential cutoff distance is set as 1.55 nm. The maximum load step in each simulation was 3 × 10 6 , in which the balance step was 1.5 × 10 6 and process step was 1.5 × 10 6 . The latter 1.5 × 10 6 configurations were used for the statistical analysis.
where E vdW is the van der Waals energy, kJ/mol; E C is the electrostatic energy, kJ/mol; q i and q j are the charges of the atoms in the system, C; r ij is the distance between atom i and atom j, nm; ε 0 is the dielectric constant, 8.854 × 10 −12 F/m; and σ ij and ε ij are the parameters. The L-J parameters are determined from the standard Lorentz-Berthelot combining rules:

FREE GAS AMOUNT
For supercritical adsorption, the excess adsorption amount cannot describe a realistic adsorption amount and should be converted into the absolute adsorption amount. 26,36 In this work, we assume that the total amount of gas in the illitemethane adsorption system is N, so the excess adsorption amount can be expressed as follows: where n ex is the excess adsorption amount, mol/m 2 ; N is the total amount of gas, mol/m 2 ; V p is the free volume, g/cm 3 ; V g is the gas phase volume, g/cm 3 ; M is the molar mass of the gas, g/mol; S is the surface area of the unit cell, m 2 ; and g is the density of the bulk gas, g/cm 3 . The methane densities obtained from the National Institute of Standards and Technology (NIST) databases are shown in Figure 4 and Table S3, and the calculation results of the methane densities using the SRK equation and the GCMC simulations are noted in Figure 4 and Table S3; the force fields in the GCMC simulations for calculating the methane densities included the Drieding, Compass, Compass II, Universal, Cvff, and Pvff force fields. From Figure 4 and Table S3, we can observe that there is little difference between the methane densities obtained from the NIST databases and those calculated from the SRK equation, indicating that the SRK equation is an effective method. During the GCMC simulations, the errors between the methane densities obtained from the NIST databases and those calculated from the GCMC simulation based on the Drieding force field are the lowest, whereas the errors between the methane densities obtained from the NIST databases and those calculated from the GCMC simulation based on the universal force field are the greatest. The differences between the methane densities calculated from the GCMC simulation based on the Drieding force field and the compass force field are small. Therefore, we adopted the SRK equation to determine the methane densities and the Drieding force field was chosen as the type of force field. The methane densities at the different temperatures and pressures in the simulations are shown in Figure 3B. Furthermore, in this work, how to measure the free volume in the pore? Based on the fact that helium is an inactive gas and the interaction force between helium and other atoms is low, Talu and Myers 44 used a helium probe method to calculate the free volume in the pore. And the method would be used to obtain the free volume in this paper.
Based on the simulated results, we can obtain the excess adsorption amount through Equation (4). According to Gibbs definition, 45 the absolute adsorption amount can be expressed as follows: where n ab is the absolute adsorption amount, mol/m 2 , and V a is the adsorbed phase volume, cm 3 . The adsorbed phase volume can be calculated according to the region of adsorbed phase. However, some researchers have suggested that the methane formed in an absorbed layer near the pore walls and the adsorbed layer was a monolayer or multilayer. [28][29][30]36 Therefore, it is difficult to determine the volume of the adsorbed phase. In this work, how to measure the adsorbed phase volume in the pore? Based on the simulation results, we put forward a simplified processing method to calculate the adsorbed phase volume, and we can obtain an approximate measure of the adsorbed phase volume. 28 In this way, we can obtain the amount of excess adsorption and the absolute adsorption amount of the gas using Equations (4) and (5), respectively. The absolute adsorption amount is approximately equal to the adsorbed gas amount in the simulation system and the free gas amount can then be calculated, which can be expressed as follows: where n g is the free gas amount, mol/m 2 .
Based on this, we can calculate the proportion of the adsorbed gas in the total gas amount in the simulation system, which can be expressed as follows: where A ab is the proportion of the adsorbed gas in the total gas amount, %.

| Influences of pore sizes
To study the influence of pore size on methane adsorption, we carried out ten simulation experiments and used ten pore sizes. Based on the simulation results, the total amount of methane in the illite-methane adsorption system was obtained, and the results are shown in Figure S3. The excess adsorption amount and the absolute adsorption amount of methane in the illite-methane adsorption system were determined by Equations (4) and (5), respectively, as shown in Figure S3. The free gas amount of methane in the illite-methane adsorption system was calculated by Equation (6), and the results are shown in Figure S3. From Figure S3, we observe that these four kinds of isotherms have clear differences and reflect the different variation laws.
The total amount isotherms, excess adsorption isotherms, absolute adsorption isotherms, and free gas amount isotherms of methane in the illite pores for different pore sizes are described in Figure 5 and Figure S5. The data presented in Figure S5 show that the total methane amount increased with increasing pore size, and the total amount of methane first increased rapidly and then increased slowly with increasing pressure. This conclusion is in agreement with previous research for chlorite, 32 kaolinite, 33 and quartz, 36 which were investigated by molecular simulation. The excess adsorption isotherms and absolute adsorption isotherms of methane in the illite pores are presented in Figure 5A and Figure 5B, The methane densities calculated from the SRK equation and from the GCMC simulation respectively. As shown in Figure 5A, the excess adsorption amount of methane in the micropores is significantly larger than in the mesopores. This finding is in agreement with previous studies of chlorite, 32 illite, 33 quartz, 36 and carbon. 46 At a low pressure stage, the excess adsorption amounts of the methane in 1 nm pores were greater than those in 2 nm pores. This may be because the excess adsorption amounts at low pressure were dominated by the interactions between methane and illite, and the interactions gradually weakened with decreasing pore size. With increasing pressure, the increased extent of the excess adsorption amount of methane in the 2 nm pores gradually increased and exceeded that in 1 nm pores. This may be because the volume of the 1 nm pores is a limitation. These findings are in disagreement with previous works on illite, 35 quartz, 36 and carbon. 46 This may be related to the chemical structure of illite, quartz, and carbon and the potential cutoff distance.
Meanwhile, from Figure 5A, we observe that as the pressure increased, the excess adsorption capacity of the methane first increased and then decreased. In other words, the excess adsorption isotherm of the methane shows a maximum for the excess adsorption capacity (n exc-max ) and a corresponding maximum pressure (p max ), which is in line with previous studies of organic-rich shales investigated by isothermal adsorption experiments, 5,9,11,19 and these results are also in agreement with the results of previous molecular simulations of simplified kerogen, 47 graphite with different O/C ratios, 43 quartz, 36 and chlorite. 32 The maximum value of the excess adsorption capacity and its corresponding pressures are described in Figure 6 and Table S4. We see from Figure 5A and Table S4 that the maximum excess adsorption pressure corresponding to the maximum excess adsorption capacity are different, and the range of the maximum pressure is between 14 MPa and 18 MPa. This conclusion is somewhat different when compared to the results of molecular simulations. This finding is in accord with previous studies of chlorite 32 and quartz, 36 suggesting that the maximum pressure ranged from 14 MPa to 18 MPa when the pore sizes were between 1 nm and 20 nm; for illite, 35 indicating that the maximum pressure ranged from 8 MPa to 20 MPa when the pore sizes were between 0.74 nm and 3 nm, whereas this finding is in disagreement with a previous study for carbon 46 that indicated that the maximum pressure ranged from 6 MPa to 14 MPa when the pore sizes were between 1 nm and 9 nm, and for a study of graphite with different O/C ratios, 43 that suggested that the maximum pressure ranged from 10 MPa to 16 MPa when the pore sizes were between 1 nm and 10 nm. Compared to the results of the experimental studies, however, our findings are in agreement with the previous studies of organicrich shales 5,9,11,19 and suggest that the maximum pressure ranged from 10 to 23 MPa. This means that the results obtained from the simulations were in agreement with those obtained from the experiments, to a certain extent.
At the same time, we observe from Figures 5A and 6 that, when the pore size was 2 nm, the maximum methane excess adsorption amount reached a peak value of 0.003442 mmol/ m 2 . When the pore size was 20 nm, the maximum methane excess adsorption amount was 0.002024 mmol/m 2 . This finding indicates that the adsorption capacity for methane in the micropores increased as the pore size increased, whereas it decreased with an increase in the pore sizes in the mesopores. These conclusions are in agreement with previous studies, 32,33,36,43 indicating that it may be related to the surface potential effects of the pore walls and the pore volume. In the micropores, methane molecules could be affected by the surface potential effects of the pore wall, and the methane adsorption amount can be limited by the pore volume. In the mesopores, however, some methane molecules could be affected by the surface potential effects of the pore walls while some methane molecules would not be affected, and the methane adsorption amount would decrease as the pore size increased. This conclusion is inconsistent with previous research on illite 35 and carbon, 46 which indicated that the excess adsorption capacity of methane decreased with increasing pore size. This may be because the cutoff distance in this work was greater.
In addition, we note from Figure 5B that the changing laws of the absolute adsorption isotherms were different with those of the excess adsorption isotherms, that is, the absolute adsorption amount of the methane increased with the increase in the pressure, and it increased fast at first and then slowly. These findings are in agreement with previous researches on organic-rich shales, 5,6,9,11,18 which were investigated by the experiment, and on graphite with different O/C ratios, 43 quartz, 36 and kaolinite, 33 which were investigated by the molecular simulation. It can be observed from Figure 5B that the absolute adsorption amount of methane in 1 nm pore was almost the smallest, which may be related to the pore volume. And the absolute adsorption amount of methane in 1.5 nm and 2 nm pores was larger than that in mesopores. However, the absolute adsorption amount of methane in mesopores decreased with increasing the pore size. As shown in Figure S4 (the density profiles of methane in the illite pore), it can be observed that the density of methane exhibited an obvious peak near the pore wall, which indicated that the methane molecules that were near the pore walls gathered to form an adsorption layer, which is known as the adsorbed phase. However, the density of methane in the center of the pore was equal to that of bulk phase, which indicated that the methane molecules were away from the pore walls dispersed inside the pore, which is known as the free phase. From Figure S4, we note that the adsorbed phase density first increased and then decreased with increasing distance from the pore wall, that is, the adsorbed phase density shown a peak value of density within a certain distance from the pore wall.
There are many classic models for calculating the densities of the adsorbed phase. In this paper, two methods for calculating the density of the adsorbed phase were adopted. Ozawa et al 48 considered that the density of the adsorbed phase was related to temperature and a calculation model was proposed: ρ a = ρ b exp(−0.0025 × (T − T b )), where ρ a is the adsorbed phase density, ρ b is the density of the liquid at the boiling point, T is the temperature, and T b is the boiling point temperature. Ambrose et al 49 suggested that the density of the adsorbed phase was a fixed value, and a calculation model was proposed: ρ a = (8Mp c )/(RT c ), M is the molar mass, p c is the critical pressure, T c is the critical temperature, and R is the gas constant. In this work, based on the simulation results, the equation that will be used to calculate the adsorbed phase density is: ρ a = (M × S × n ex + ρ g V a )/V a , M is the molar mass, S is the surface area of the unit cell, n ex is the excess adsorption amount, ρ g is the density of bulk gas, and V a is the adsorbed phase volume. According to the adsorbed phase density in the illite pores at different pore sizes (Figure 7), the adsorbed phase density was larger than the density of the bulk gas, which is in agreement with previous research. 48,49 This density first increased rapidly and then slowed down, and the adsorbed phase density decreased with increasing pore sizes. Larger pore sizes lead to smaller differences between the adsorbed phase density obtained from the GCMC simulation and the bulk gas density. The adsorbed phase density in 1 nm pores is the highest, whereas the absolute adsorption amount of methane in 1 nm pores was the smallest, indicating that this may be related to the pore volume. This finding also demonstrates that the absolute adsorption amounts of methane in 1 nm pores are affected by the pore volumes. Furthermore, Figure 7 shows that the adsorbed phase density increased with an increase in pressure, indicating that the adsorbed phase density is not a fixed value but is related to the pressure. Greater pressures lead to smaller differences between the adsorbed phase density obtained from the GCMC simulation and the bulk gas density. These findings are inconsistent with previous research. 48,49 The adsorbed phase density calculated from the literature 49 is larger than the adsorbed phase density obtained from the GCMC simulation. When the pressure is below 18 MPa, the adsorbed phase density calculated from the literature 48 is larger than the GCMC simulation results, whereas when the pressure is greater than 18 MPa, the adsorbed phase density calculated from the literature 48 is in agreement with the GCMC simulation results. Finally, as shown in Figure 5C, the free gas amount of methane increased with increases in the pore sizes or the pressures. This may be because the density of methane increases as the pressure increases, and the free volume increases as the pressure increases. Figure 8 reports the excess adsorption isotherms and absolute adsorption isotherms of methane from both simulation results and experimental results. Figure 8 shows the experimental results of methane adsorption on illite at 338.4 K, as represented by Ji et al, 15 and at 333 K, as represented by Liu et al, 16 as well as the simulation result of methane adsorption for the slit-like illite pore with a pore size of 2 nm at 333 K, as reported by Chen et al. 35 As shown in Figure 8, we observe that there is a difference between the simulation results and the experimental results. The pore sizes of illite in the experiments showed a continuous distribution ranging from 1 nm to 100 nm, and the excess adsorption amounts and absolute adsorption amounts of methane obtained from the experiments reflect the synthesis results of the continuous pores, which is a single value for the illite sample. However, the illite pores in the simulation consist of a single pore size, and the excess adsorption amounts and absolute adsorption amounts of methane obtained from the simulation reflect the results of a single pore, which varies with changes in the pore size. At the same time, it can be noted that the simulation results for methane adsorption in the illite pores and the experimental results of the methane adsorption of illite showed the same trend and were of the same order of magnitude, but they did not exactly match. This conclusion is in good agreement previous work, 27 indicating that the simulation results are reasonable, and this is because they may be related to the specific surface area, pore size distribution, and chemical structure of illite. Therefore, from this aspect, the models and parameters in this work are reasonable. In addition, we note that the excess adsorption amounts of methane in the illite pores obtained from this work showed a similar trend with that obtained by Chen et al, 35 and the amounts from former were greater than those from the latter. This may be because the L-J potential parameters in the simulations were different and that the cutoff distance in this work was larger.
The absolute adsorption isotherms of methane in illite pore with 2 nm and 20 nm based on the Compass force field can be seen in Figure 8B. From Figure 8B, we observe that the absolute adsorption amount obtained from the simulation results based on the Drieding force field was larger than the Compass force field. However, there are little differences between the simulation results based on the Drieding force field and the Compass force field. On this basis, the Drieding force field and Compass force field are reasonable force field type to be used in simulation research in this work. And the Dreiding force field shows advantages in addition, that is to say, the L-J potential parameters and the charges of each atom could be revised according the practical situation. Therefore, it is reasonable that the Dreiding force field in this work was chosen.
According to Equation (7), we obtain the proportion of adsorbed gas in total amount of gas in the illite-methane adsorption system. The relationships between the proportions of the adsorbed gas and pore pressures for different pore sizes are shown in Figure 9. From Figure 9, we observe that the proportion of adsorbed gas declines with increases in pore size or pressure. Furthermore, the proportions in illite pores of the same pore size decreased rapidly at first and then slowly as the pressure increased. At the same time, the proportions in the illite pores under the same pressure decreased as the pore size increased. From Figure 5B,C, the absolute adsorption amounts and free gas amounts of methane for the same pore size increased with increasing pressure, and it can be seen in Figure S5 (Total amount isotherms of methane on illite for different pore sizes) that the total amount of methane also increased as the pressure increased. The total amount of methane increased more quickly than the absolute adsorption amounts and free gas amounts of methane, resulting in a decrease in the proportion of adsorbed gas. Furthermore, the total amount of gas at the same pressure increased with increasing pore size, whereas the absolute adsorption amount of methane decreased with increasing pore size, resulting in a decrease in the proportion of adsorbed gas. In addition, Figure 9 shows that when the pore size is larger than 6 nm, the proportion in the illite pores at a pressure of 20 MPa was 25.43%, and the proportion in the illite pores at a pressure of 40 MPa was reduced to 19.45%. This finding indicates that the proportion of adsorbed gas of the total amount under higher pressures in illite pores was lower, suggesting that the methane in the pores was mainly in a free gas state. This conclusion helps us to understand the enrichment mechanisms of the adsorbed gas in organic-rich shale pores. If the illite pores of the organic-rich shales are larger than 6 nm, the methane in the illite pores exists mainly as free gas.
According to the simulation results, the changes in system energy after the adsorption of methane in the illite pores are presented in Figures 10 and 11. From Figures 10 and 11, the valence electron energy of the system before and after the adsorption of methane in the illite pores did not change. For the nonbonding energy, the electrostatic energy and hydrogen bond energy of the system did not change the following adsorption of methane in the illite pores, whereas the van der Waals energy of the system dramatically decreased, indicating that methane adsorption in the illite pores was due mainly to the van der Waals adsorption. This finding suggests that the methane adsorption for illite is of the physical adsorption type, which is in agreement with previous research for illite, 14,15 investigated by experiment, and for illite, 35 which was investigated by molecular simulation.

| Influences of temperature
To study the influence of temperature on methane adsorption, we carried out four simulation experiments that used four different temperatures. Based on the simulation results, the excess adsorption isotherms, absolute adsorption isotherms, and free gas amount isotherms of methane on illite for different temperatures are presented in Figure 12. Examination of Figure 12 shows that, for a given pressure, the excess adsorption amounts, absolute adsorption amounts, and free gas amounts of the methane were inversely proportional to the temperature. This is because the methane adsorption of illite is of the physical adsorption type. This conclusion is in accord with the results of the isothermal adsorption experiments performed by Ji et al 14,15 who found that high temperatures impeded methane adsorption by illite. This observation was also reported by Mosher et al, 46 Zhang et al, 26,34 and Xiong et al, 32,33,36,43 who found that the methane adsorption capacities of carbon and minerals decreased with increasing temperature. Furthermore, Figure 11A shows that the range of maximum pressure was between 16 MPa and 18 MPa when the temperatures were between 313 K and 373 K, which is in disagreement with previous reports. 32,36,46,47 Mosher et al 46 reported the methane adsorption on carbon and suggested that the range of the maximum pressure was between 10 MPa and 13 MPa when the temperatures were between 318 K and 332 K. Zhang et al 47 investigated methane adsorption on simplified kerogen and found that the range of the maximum pressure was from 4 MPa to 6 MPa when the temperatures ranged from 308 K to 370 K. Xiong et al 32 investigated the methane adsorption of chlorite and indicated that the range of the maximum pressure was between 14 MPa and 20 MPa when the temperatures ranged from 308 K to 370 K. Xiong et al 36 studied the methane adsorption of quartz and suggested that the range of the maximum pressure was between 18 MPa and 20 MPa when the temperatures ranged from 313 K to 373 K. However, this finding is in line with previous research on illite, to a certain extent. 35 Chen et al 35 studied the methane adsorption of illite and found that the range of the maximum pressure was from 17.5 MPa to 25.8 MPa when the temperatures ranged from 333 K to 393 K. These findings indicate that there are differences between carbon, kerogen, and minerals. This may be related to the chemical structure of carbon, kerogen, and minerals. In addition, the density profiles of methane in the illite pores at different temperatures are presented in Figure S6 and the adsorbed phase density in the illite pores at different temperatures are shown in Figure  13. From Figure S6 and Figure 13, the adsorbed phase density decreased with increasing temperature, which is in agreement with a previous report, 48 suggesting that the density of the adsorbed phase is related to temperature.
According to the simulation results, we can obtain the influences of temperature on the proportion of adsorbed gas in the total gas amount in the illite-methane adsorption system. The relationships between the proportions of the adsorbed gas and the pressures in the pores at different temperatures are described in Figure 14. From Figure 14, the proportion of adsorbed gas declined slightly as the temperature increased under a constant pressure. From Figure 12B,C, the absolute adsorption amounts and the free gas amounts of methane decreased when the temperature increased. Figure S7 shows (Total amount isotherms of the methane on illite for different temperatures) that the total amount of gas also decreased as the temperature increased. The absolute adsorption amount decreased more than the total gas amount, resulting in a reduction in the proportion of adsorbed gas. Therefore, with increases in temperature, the adsorption capacity of methane in the illite nanopores declined and the proportion of adsorbed gas in the total gas amount decreased slightly. In other words, when the temperature increased, the adsorption amounts and free gas amounts of methane decreased. That is, the methane molecules transferred from the adsorbed state to the free state, and the free gas amounts also decreased at the same time, which would result in improved production from gas wells. Therefore, if the temperatures of shale gas reservoirs are increased by using technological methods, the recovery from the shale gas reservoirs would be enhanced.

| Influence of water content
To study the influence of water content on methane adsorption, we conducted four simulation experiments that included four different water contents. Before the simulations, we first needed to determine the adsorption sites of water molecules in the illite nanopores. In this work, the annealing simulation was chosen. The distributions of the different water contents on the surfaces of the illite pore walls are described in Figure  15. Based on the mass, the water content (wt%) = water mass/illite mass × 100. Based on the pore volume, the water saturation (Sw%) = water volume/pore volume of illite × 100. Their transformational relationship is: Sw% = wt% × illite mass × methane molar mass/water density/pore volume. The corresponding relationship between wt% and Sw% is shown in Table S5.
Examination of Figure 15 shows that the water molecules occupied the area near the pore walls in a directional manner; that is, the oxygen atoms in the water molecules were close to or pointed to the pore walls or to the hydrogen atoms of the surrounding water molecules, whereas the hydrogen atoms in the water molecules pointed away from the pore walls, which is in good agreement with previous research for minerals. 32,33,36 However, this finding is in disagreement with previous work 43 that suggested that the water molecules were close to the oxygen-containing groups. This finding indicates that the water molecules occupied the adsorption sites of methane molecules. The relative density profiles of methane in illite pores for various water contents are shown in Figure S8. Figure S8 also shows that the relative density profiles near the pore walls exhibited only an obvious peak and decreased to zero around the pore centers, suggesting that the water molecules only aggregated in the areas near the pore walls and did not disperse into the pores. The changes in system energy after the adsorption of water in the illite pores are described in Table 1, indicating that the system energy F I G U R E 1 5 Distributions of the water molecules with different water contents in the illite nanopore (pore size of 4 nm and a temperature of 333 K) after the adsorption of water in the illite pores decreased. The valence electron energy of the system after the adsorption of water in the illite pores increased, whereas the nonbonding energy of the system decreased. Compared with the valence electron energy, the nonbonding energy contributed mainly to the changes in system energy. At the same time, as seen in Table 1, for the nonbonding energy, the electrostatic and hydrogen bond energies of the system decreased dramatically, especially for higher water contents, whereas the van der Waals energy of the system increased, indicating that water adsorption in the illite pores was due to electrostatic adsorption and hydrogen bond adsorption, whereas the van der Waals force was a factor adversely affecting water adsorption. This may be related to the positive charges of the aluminum and silicon atoms on the illite surface and to the negative charges of the oxygen atoms in the water molecules. Additionally, the stronger electrostatic force caused the oxygen atoms in the water molecules to be close to or point to the surface of the illite pore walls. Additionally, the stronger hydrogen bond effect caused the oxygen atoms in the water molecules to point to the hydrogen atoms in the surrounding water molecules. These considerations mean that the water molecules occupied the areas near the pore walls in the form of aggregates, resulting in a reduction in the methane adsorption space. The excess adsorption isotherms, absolute adsorption isotherms, and free gas amount isotherms of methane in the illite pores for different water contents are shown in Figure  16. Examination of Figure 16 shows that when the temperature and pressure were kept constant, the excess adsorption amounts, absolute adsorption amounts, and free gas amounts of methane decreased as the water content increased. This finding is in agreement with previous studies, 28,29,32,33,36 which demonstrated that water greatly reduced the methane adsorption capacity of the minerals. This conclusion is also in line with the results of previous work 43,47 that indicated that water greatly reduced the methane adsorption capacity in graphite with different O/C ratios or kerogen pores. At the same time, from Figure 16, we observe that the range of the maximum pressure was between 14 MPa and 16 MPa when the water content varied from 0% to 8%, which is inconsistent with previous studies. 32,36,47 Xiong et al 32,36 investigated the methane adsorption of chlorite and quartz and showed that the range of maximum pressure was between 14 MPa and 18 MPa when the water content varied from 0% to 8%. Zhang et al 47 reported the methane adsorption of simplified kerogen and found that the range of maximum pressure ranged from 4 MPa to 6 MPa when the water content ranged from 0% to 3%. These findings indicate that there are differences among kerogen and different minerals. These differences may be related to the chemical structures and the distributions of water molecules in the pores.

The changes in system energy
To study the effects of temperature on methane adsorption under varying water conditions, we conducted three simulation experiments. The absolute adsorption isotherms and the free gas amounts of methane in the illite pores for different temperatures are presented in Figure 17. From Figure 17, when the water content and pressure were kept constant, the absolute adsorption amounts and free gas amounts of methane decreased as the temperature increased. The changing trend is in accord with that shown in Figure 12, indicating that temperature has the same effect on methane adsorption in either the presence or absence of water.
According to the simulation results, we obtain the influences of water content on the proportions of adsorbed gas in the total gas amount in the illite-methane adsorption system. The relationships between the proportions of adsorbed gas and pore pressures for different water contents are presented in Figure 18. From Figure 18, the proportion of the adsorbed gas declined slightly as the water content increased for the same pressure. From Figure 16B,C, the absolute adsorption amounts and free gas amounts of methane decreased when the temperature increased. Additionally, Figure S9 shows (total amount isotherms of methane in illite for different water contents) that the total amount of gas also decreased as the temperature increased. The absolute adsorption amount decreased less than the total amount of gas, resulting in a reduction in the proportion of adsorbed gas. Therefore, with increases in water content, the adsorption capacities of methane in the illite nanopores declined and the proportion of the adsorbed gas in the total gas amount decreased slightly. In F I G U R E 1 6 Excess adsorption isotherms (A), absolute adsorption isotherms (B), and free gas amounts (C) of methane in the illite pores for different water contents (pore size of 4 nm and a temperature of 333 K) other words, when the water content increased, the adsorption amounts and free gas amounts of methane decreased, that is, the methane molecules transferred from the adsorbed state to the free state, and free gas amount also decreased at the same time. According to our previous work, 17,20 water-based fluids can enter shale formations due to spontaneous inhibition by capillary effects. Therefore, during the hydraulic fracturing process in shale formations, water molecules can enter the illite pores in the shale formations and then occupy the adsorption spaces of the methane molecules, resulting in a reduction in methane adsorption capacity and resulting in accelerating desorption velocities of methane. At the same time, the water molecules also lead to a decrease in the amount of free gas, resulting in improved production from a gas well. In other words, water-based fracturing fluids can be used to stimulate shale gas reservoirs, and they enhance the recovery of shale gas reservoirs to a certain extent.

| CONCLUSIONS
The GCMC method was used to investigate the methane adsorption in the illite nanopores, and the influences of pore sizes, temperatures, and water contents on the methane adsorption capacity, free gas amount and the proportion of the adsorbed gas were discussed.
1. As the pressure or the pore size increases, the amount of free gas in methane increases, whereas the amount of free gas decreases with increased temperature or water content. 2. As the pressure decreases or the pore size increases, the methane adsorption capacity in the illite pores decreases. Additionally, when the pressure or the pore size increases, the proportion of the adsorbed gas in pores decreases. 3. As the temperature decreases, the methane adsorption capacity in the illite nanopores increases, and the proportion of the adsorbed gas in pores increases slightly. 4. Water adsorption in the illite nanopores is due to electrostatic adsorption and hydrogen bond adsorption, whereas the van der Waals force was a factor that adversely affected water adsorption. Additionally, water molecules occupy the area near the pore walls in a directional manner and occupy the adsorption spaces and adsorption sites of methane, resulting in a decrease in methane adsorption capacity and a slight reduction in the proportion of adsorbed gas.