Simulation Study on Molecular Adsorption of Coal in Chicheng Coal Mine

To study the importance of the adsorption mechanism of methane (CH4) and carbon dioxide (CO2) in coal for coalbed methane development, we aimed to reveal the influence mechanism of adsorption pressure, temperature, gas properties, water content, and other factors on gas molecular adsorption behavior from the molecular level. In this study, we selected the nonsticky coal in Chicheng Coal Mine as the research object. Based on the coal macromolecular model, we used the molecular dynamics (MD) and Monte Carlo (GCMC) methods to simulate and analyze the conditions of different pressure, temperature, and water content. The change rule and microscopic mechanism of the adsorption amount, equal adsorption heat, and interaction energy of CO2 and CH4 gas molecules in the coal macromolecular structure model establish a theoretical foundation for revealing the adsorption characteristics of coalbed methane in coal and provide technical support for further improving coalbed methane extraction.


Introduction
Coalbed methane (CBM) is a valuable energy source with many advantages such as richness, safety, and environmental protection [1]. China is a large coal-mining country, and coal seam gas resources in storage are very rich. According to relevant statistics in the literature, the depth of more than 2000 m of coal seam gas reserves is about 30.05 × 1012 m 3 . In the coal seam with a depth greater than 2000 m, the reserves of coalbed methane are about 40.71 × 1012 m 3 [2]. Therefore, efficient and reasonable CBM development is an important way to ensure the security and sustainable development of the national energy strategy. Because CBM usually exists on the surface of the coal body in the form of adsorption state, research on the adsorption characteristics of methane (CH 4 ), carbon dioxide (CO 2 ), and other gases in the coal seam is the key to solve the CBM development "bottleneck" problem.
In recent years, many researchers have conducted a lot of research on the adsorption characteristics of CH 4 , water (H 2 O), and CO 2 in coal. Lu et al. [3] conducted adsorption and strain experiments on coal samples at 30 • C, 40 • C, and 50 • C and at a pressure of 15 MPa, which showed that the shapes of swelling strain curves of different grades of coal were similar. Shen et al. [4] used the volumetric method to carry out the high-pressure adsorption experiment, which showed that the adsorption isotherm was consistent with the Langmuir model in the range of pressure and temperature. Wang et al. [5] studied the influence of water, pH value, and coal rank on the adsorption of CO 2 by coal and showed that water inhibited the adsorption of CO 2 by coal, and the change of pH value promoted the adsorption of CO 2 by coal. Qiu et al. [6] conducted an isothermal adsorption experiment on coals with different coal grades, water content, and grain size and showed that the Langmuir volume (V-L) of coal was unrelated to grain size but was inversely proportional to water content. It first decreased and then increased with the increase in

Selection of Force Field
In this study, we used MD and GCMC methods to simulate the adsorption mechanism of CO2 and CH4 gas molecules in coal macromolecular models under different conditions. We selected the COMPASS force field for model optimization and adsorption simulation, which fully considered the interactions between molecules. The parameters were derived from ab initio parameterization and empirical optimization [13].

Selection of Force Field
In this study, we used MD and GCMC methods to simulate the adsorption mechanism of CO 2 and CH 4 gas molecules in coal macromolecular models under different conditions. We selected the COMPASS force field for model optimization and adsorption simulation, which fully considered the interactions between molecules. The parameters were derived from ab initio parameterization and empirical optimization [13].

Transformation of Pressure and Fugacity
For nonideal gas, fugacity and pressure are different at different temperatures. The higher the pressure, the greater the difference between fugacity and pressure. In this study, we adopted the Peng-Robinson equation of state to calculate fugacity and pressure conversion of nonideal gas, with specific steps as follows [14]: Then, Equation (1) can be rewritten as follows: where Z is the gas compression factor, and A and B are the equation coefficients, which can be expressed as follows [13]: where P is the gas pressure, MPa; R is the mole constant of gas; and V is the molar volume of the gas, 22.4 L/mol. Next, Equation (1) is Equations (6) and (7) [13] at the critical point and Equations (8) and (9) at the noncritical point [13]: a(T) = a(T c ) · a(T r , ω) where T r is the comparison temperature, K, and T r = T/T c ; T c is the critical temperature, K; p c is the critical pressure, MPa; and ω is the eccentricity factor. By substituting Equation (10) into Equation (1), the fugacity (f) of a single component gas can be derived as follows: Molecules 2023, 28, 3302 4 of 22 (11) According to these principles, the conversion between fugacity and pressure of different gases at different temperatures can be performed using Perl script in Materials Studio 2017 (MS) [15].

Molecular Simulation of Gas Adsorption Characteristics of Coal
Based on the macromolecular structure model of noncohesive coal in the Chicheng Coal Mine, we studied the adsorption microscopic properties of CH 4 and CO 2 molecules in the macromolecular model by using GCMC and MD in molecular simulation [16].

Coal Model Construction and Optimization
We imported the two-dimensional plane model of coal macromolecules constructed in Figure 1 into MS (Materials Studio 2017, Accelrys, San Diego, CA, USA) molecular simulation software and constructed the initial three-dimensional structure, as shown in Figure 2a. We used the Forcite module for geometric optimization of the model and selected the COMPASS force field for geometric optimization. We set charges as assigned by Forcefield, calculation accuracy as Fine, and iteration steps as 5000. Then, we annealed the model and selected the NVT family. For Nose, the temperature was 300-600 K, and the number of cycles was five. The aerodynamic parameters were set as specified. The model structure after dynamic optimization is shown in Figure 2b.  To establish the periodic boundary condition, we used the Amorphous Cell module to put 10 optimized coal molecular models into the periodic cell. First, we conducted the geometric optimization, and then, we subjected the model to the 300-600 K NPT system annealing treatment. A total of five cycles were set up. We used the COMPASS force The energy changes of the macromolecular structure model of coal before and after optimization are shown in Table 1. As shown in Table 1, after optimization of the initial model, the valence electron energy and nonbond energy of the coal molecules both decreased somewhat. In the final model, the valence electron energy of coal molecules was higher than the nonbond energy, which was the main part of the total energy and contributed more to the stability of the model, and the bond torsion energy played a major role in valence electron energy. The chemical bond torsion of coal molecules was the basis for the model to bend and twist into a stereoscopic configuration. In the nonbonding energy, van der Waals energy was dominant. To establish the periodic boundary condition, we used the Amorphous Cell module to put 10 optimized coal molecular models into the periodic cell. First, we conducted the geometric optimization, and then, we subjected the model to the 300-600 K NPT system annealing treatment. A total of five cycles were set up. We used the COMPASS force field, the atom-based method for the van der Waals term, and the Ewald method for the electrostatic action term. After annealing and kinetic treatment for 1000 ps, the total energy of the coal cell model was reduced to the lowest level and then stabilized at 22,985.040 kcal/mol. The density of the coal cell structure was stabilized at 1.138 g/cm 3 , which was close to the real density of coal, as shown in Figure 3.  To establish the periodic boundary condition, we used the Amorphous Cell mo to put 10 optimized coal molecular models into the periodic cell. First, we conducted geometric optimization, and then, we subjected the model to the 300-600 K NPT sy annealing treatment. A total of five cycles were set up. We used the COMPASS field, the atom-based method for the van der Waals term, and the Ewald method fo electrostatic action term. After annealing and kinetic treatment for 1000 ps, the tota ergy of the coal cell model was reduced to the lowest level and then stabilize 22,985.040 kcal/mol. The density of the coal cell structure was stabilized at 1.138 g which was close to the real density of coal, as shown in Figure 3.   The optimized coal macromolecular structure model is shown in Figure 4a, w molecular formula is C2070H1810N30O320S10. By using Atom Volumes and Surfaces with MD radii of helium (He) (0.13 nm), CO2 (0.165 nm), and CH4 (0.19 nm) as the Conn The optimized coal macromolecular structure model is shown in Figure 4a, whose molecular formula is C 2070 H 1810 N 30 O 320 S 10 . By using Atom Volumes and Surfaces with the MD radii of helium (He) (0.13 nm), CO 2 (0.165 nm), and CH 4 (0.19 nm) as the Connolly probe radii, we calculated the pore profiles of different gases in the coal molecular surfaces. As shown in Figure 4a-c, the accessible hole of the He gas in the model was 3071.15 Å 3 , the accessible hole of CO 2 was 2295.89 Å 3 , and the accessible hole of CH 4 was 1550.92 Å 3 . The pore space on the coal surface was the main place for gas adsorption. The CO 2 was absorbed more easily by the coal surface than CH 4 in terms of the adsorption space provided by the coal surface for gas.

Construction and Optimization of Adsorbent Model
We used MS software to visualize and optimize the gas molecules, H 2 O, CO 2 , and CH 4 . The energy changes of the three optimized gas molecules and the final models are shown in Table 2 and Figure 5.
probe radii, we calculated the pore profiles of different gases in the coal molecular surfaces. As shown in Figure 4a-c, the accessible hole of the He gas in the model was 3071.15 Å 3 , the accessible hole of CO2 was 2295.89 Å 3 , and the accessible hole of CH4 was 1550.92 Å 3 . The pore space on the coal surface was the main place for gas adsorption. The CO2 was absorbed more easily by the coal surface than CH4 in terms of the adsorption space provided by the coal surface for gas.

Construction and Optimization of Adsorbent Model
We used MS software to visualize and optimize the gas molecules, H2O, CO2, and CH4. The energy changes of the three optimized gas molecules and the final models are shown in Table 2 and Figure 5.    probe radii, we calculated the pore profiles of different gases in the coal molecular surfaces. As shown in Figure 4a-c, the accessible hole of the He gas in the model was 3071.15 Å 3 , the accessible hole of CO2 was 2295.89 Å 3 , and the accessible hole of CH4 was 1550.92 Å 3 . The pore space on the coal surface was the main place for gas adsorption. The CO2 was absorbed more easily by the coal surface than CH4 in terms of the adsorption space provided by the coal surface for gas.

Construction and Optimization of Adsorbent Model
We used MS software to visualize and optimize the gas molecules, H2O, CO2, and CH4. The energy changes of the three optimized gas molecules and the final models are shown in Table 2 and Figure 5.

Simulation Methods and Parameter Settings
We used the Sorption module in the MS software to study the coal adsorption characteristics. We analyzed the adsorption behavior of CO 2 and CH 4 gas molecules in dry and water-containing coal macromolecular structure models according to the GCMC method. We performed adsorption simulation using fixed pressure in the Sorption module. The calculation accuracy was customized with equilibration steps and production steps of 1,000,000. We selected the COMPASS force field. We set the charges as assigned by Forcefield, the electrostatic action term as determined by the Ewald method, and the van der Waals energy according to an atom-based method. The adsorption equilibrium condition prevailed when the C/D ratio in the result file was close to one.
The unit of adsorption capacity in the simulation is molecules/u.c., and the unit of adsorption capacity in engineering is mL/g, which needs to be converted as follows: where Q is the gas adsorption capacity, mol/g; N is the number of adsorbed gases, molecules/u.c.; and M is the molar mass of coal molecular cell, g/mol. The gas adsorption capacity calculated in the software was the absolute adsorption capacity of gas. In engineering applications, however, capacity usually is the excess adsorption capacity of gas. A previous study [12] noted that the gas molecular adsorption quantity of the excess adsorption capacity was equivalent to the absolute adsorption capacity of coal minus the gas adsorption quantity contained in the pore volume of the coal macromolecular structure under simulated pressure and temperature, which can be expressed as follows [12]: where N ex is the amount of excess adsorption capacity of gas molecules in the coal macromolecular structure, molecules/u.c.; N ad is the number of absolute adsorption capacity of gas molecules in the coal macromolecular structure, molecules/u.c.; N A is Avogadro's constant, which is 6.02 × 10 23 ; and V v is the accessible pore capacity in the macromolecular structure of coal, mL. The excess adsorption capacity of gas molecules adsorbed by the coal macromolecular structure model was converted to the adsorption capacity, mL/g, under the following standard conditions: where Q ex is the excess adsorption capacity of coal macromolecular structure model (mL/g).

Correctness Verification of the Model
In this study, we verified the experimental and simulated adsorption isotherms of CH 4 , as shown in Figure 6, under the following conditions: temperature = 25 • C and pressure = 0-8 MPa. (Note that the experimental data came from the Akagi Coal Mine.) As shown in Figure 6, although our simulation results were slightly higher than the experimental results, they were in good agreement, which may have been because the coal macromolecule model considered only the organic part and ignored the inorganic part. A comparative analysis can prove that the relevant parameters established in this study are reasonable. pressure = 0-8 MPa. (Note that the experimental data came from the Akagi Coa As shown in Figure 6, although our simulation results were slightly higher than perimental results, they were in good agreement, which may have been because macromolecule model considered only the organic part and ignored the inorga A comparative analysis can prove that the relevant parameters established in th are reasonable.

Influence of Temperature on Adsorption Capacity
The isothermal adsorption curve of coal can be used to predict the reco amount of CBM. We evaluated the sealing capacity and saturation state of CB Figure 7 shows the adsorption isotherm of CO2 and CH4 in the coal macrom model at temperatures of 293.15 K, 298.15 K, 303.15 K, 308.15 K, and 313.15 K a sures of 100-10 MPa. We used the Langmuir model to fit the adsorption structur and CH4 gas in coal. The expression is shown in Equation (15), and the fitting re shown in Table 3.
where a is the saturated adsorption capacity of gas, mL/g, and b is the recip Langmuir pressure, MPa −1 .

Influence of Temperature on Adsorption Capacity
The isothermal adsorption curve of coal can be used to predict the recoverable amount of CBM. We evaluated the sealing capacity and saturation state of CBM [17]. Figure 7 shows the adsorption isotherm of CO 2 and CH 4 in the coal macromolecule model at temperatures of 293.15 K, 298.15 K, 303.15 K, 308.15 K, and 313.15 K and pressures of 100-10 MPa. We used the Langmuir model to fit the adsorption structure of CO 2 and CH 4 gas in coal. The expression is shown in Equation (15), and the fitting results are shown in Table 3.
where a is the saturated adsorption capacity of gas, mL/g, and b is the reciprocal of Langmuir pressure, MPa −1 .
A comparative analysis can prove that the relevant parameters established in this study are reasonable.

Influence of Temperature on Adsorption Capacity
The isothermal adsorption curve of coal can be used to predict the recoverable amount of CBM. We evaluated the sealing capacity and saturation state of CBM [17]. Figure 7 shows the adsorption isotherm of CO2 and CH4 in the coal macromolecule model at temperatures of 293.15 K, 298.15 K, 303.15 K, 308.15 K, and 313.15 K and pressures of 100-10 MPa. We used the Langmuir model to fit the adsorption structure of CO2 and CH4 gas in coal. The expression is shown in Equation (15), and the fitting results are shown in Table 3.
where a is the saturated adsorption capacity of gas, mL/g, and b is the reciprocal of Langmuir pressure, MPa −1 .    The simulation results showed the following: When the adsorption temperature was the same, the adsorption capacity of CO 2 and CH 4 increased with an increase in pressure. When the pressure was low, the adsorption capacity of coal to gas increased rapidly. When the pressure was greater than 5 MPa, the adsorption isotherm of coal gas tended to be gentle. This trend of CO 2 adsorption isotherm was more obvious than that of CH 4 , indicating that the CO 2 adsorption capacity of coal tended to saturate faster under the same pressure. Within the simulated temperature and pressure range, the saturated adsorption capacity of CO 2 was 1.24-1.31 times that of CH 4 , which was mainly due to the difference in the MD diameter, critical pressure, boiling point, and polarizability of the two gases. When the adsorption pressure was the same, the adsorption capacity of the two gas molecules decreased with the increase in temperature, indicating that the increase in temperature was not conducive to the adsorption of gas molecules by the coal macromolecule model. The increase in temperature promoted the increase in energy, activity, and kinetic energy of gas molecules, which was not conducive to the "capture" of gas molecules by the coal molecular surface during the adsorption process. Moreover, high temperature inhibited the transformation of gas molecules from the free state to the adsorption state, and some stable adsorbed gases also experienced desorption into active free-state gases because of this high temperature. Therefore, the adsorption capacity of coal to gas would decrease with the increase in temperature. This result showed that the adsorption of CH 4 /CO 2 by coal samples was an exothermic reaction.
As shown in Figure 8, the absolute value of slope k of CO 2 gas was greater than that of CH 4 , indicating that the influence of temperature change on the adsorption amount of CO 2 was greater than that of CH 4 , and the inhibition degree of the adsorption amount of CO 2 was stronger at high temperature. This result was related mainly to the interaction between the two gases and the functional groups on the coal surface. Figures 9 and 10 show the gas density distribution characteristics of CO 2 and CH 4 adsorbed by the coal macromolecular structure model under an adsorption pressure of 5 MPa and at different temperatures. With the increase in temperature, the adsorption sites of the two gases were almost the same, and we did not observe any particularly significant differences. The density of the adsorbed gas, however, decreased with the increase in temperature, which was more obvious from the comparison of the adsorption simulation results of the two gases at 293.15 K and 313.15 K. The simulation results of these two temperatures also showed that the space size and quantity of gas at the adsorption sites in the coal molecular structure at low temperature slightly increased compared with that at high temperature, and the density of gas adsorbed at the adsorption sites was also higher, which resulted in a larger amount of gas adsorption. At the same temperature, most of the adsorption sites of the two gases remained the same, but the space and density of the adsorption sites of CO 2 were greater than that of CH 4 . Figures 9 and 10 show the gas density distribution characteristics of CO2 a adsorbed by the coal macromolecular structure model under an adsorption press MPa and at different temperatures. With the increase in temperature, the ad sites of the two gases were almost the same, and we did not observe any par significant differences. The density of the adsorbed gas, however, decreased wit crease in temperature, which was more obvious from the comparison of the ad simulation results of the two gases at 293.15 K and 313.15 K. The simulation re these two temperatures also showed that the space size and quantity of gas at sorption sites in the coal molecular structure at low temperature slightly increas pared with that at high temperature, and the density of gas adsorbed at the ad sites was also higher, which resulted in a larger amount of gas adsorption. At t temperature, most of the adsorption sites of the two gases remained the same, space and density of the adsorption sites of CO2 were greater than that of CH4.  Figures 9 and 10 show the gas density distribution characteristics of CO2 and CH4 adsorbed by the coal macromolecular structure model under an adsorption pressure of 5 MPa and at different temperatures. With the increase in temperature, the adsorption sites of the two gases were almost the same, and we did not observe any particularly significant differences. The density of the adsorbed gas, however, decreased with the increase in temperature, which was more obvious from the comparison of the adsorption simulation results of the two gases at 293.15 K and 313.15 K. The simulation results of these two temperatures also showed that the space size and quantity of gas at the adsorption sites in the coal molecular structure at low temperature slightly increased compared with that at high temperature, and the density of gas adsorbed at the adsorption sites was also higher, which resulted in a larger amount of gas adsorption. At the same temperature, most of the adsorption sites of the two gases remained the same, but the space and density of the adsorption sites of CO2 were greater than that of CH4.

Influence of Temperature on Adsorption Heat
In the study of the gas adsorption behavior law of coal, adsorption heat is often used to judge the physical and chemical nature of CBM adsorption by coal rocks, which holds great significance to explain the adsorption law and adsorption mechanism [18]. Based on the energy particle fluctuation calculation in the great canonical ensemble [19], the equivalent adsorption heat Qst in the adsorption process of coal and gas can be obtained as follows: where Utotal is the total interaction energy in the system, kJ/mol, and Uintrl is the internal energy of the gas molecule, kJ/mol. Figure 11 shows the variation law of equal adsorption heat of CO2 and CH4 in coal within the range of simulated temperature and pressure. The simulation results showed that under the same pressure condition, the equivalent adsorption heat of CO2 gradually decreased with the increase in temperature, whereas the equivalent adsorption heat of CH4 changed in a small range [20]. This result indicated that the change in temperature had a small impact on the equivalent adsorption heat of the coal-CH4 system. Under the same temperature condition, the equivalent adsorption heat of CO2 gradually decreased with the increase in pressure, and the equivalent adsorption heat of CH4 increased with the increase in pressure at 0-2 MPa and then decreased with the increase in pressure. The equal adsorption heat was jointly affected by two factors: the interaction between gas and coal, and the interaction between gas fractions [14]. Obviously, the CO2-coal interaction was dominant in the process of adsorption pressure change. For CH4, the interaction between gas fractions was dominant at a low pressure, whereas the interaction between gas and coal was dominant at a high pressure. In the adsorption process, the

Influence of Temperature on Adsorption Heat
In the study of the gas adsorption behavior law of coal, adsorption heat is often used to judge the physical and chemical nature of CBM adsorption by coal rocks, which holds great significance to explain the adsorption law and adsorption mechanism [18]. Based on the energy particle fluctuation calculation in the great canonical ensemble [19], the equivalent adsorption heat Q st in the adsorption process of coal and gas can be obtained as follows: where U total is the total interaction energy in the system, kJ/mol, and U intrl is the internal energy of the gas molecule, kJ/mol. Figure 11 shows the variation law of equal adsorption heat of CO 2 and CH 4 in coal within the range of simulated temperature and pressure. The simulation results showed that under the same pressure condition, the equivalent adsorption heat of CO 2 gradually decreased with the increase in temperature, whereas the equivalent adsorption heat of CH 4 changed in a small range [20]. This result indicated that the change in temperature had a small impact on the equivalent adsorption heat of the coal-CH 4 system. Under the same temperature condition, the equivalent adsorption heat of CO 2 gradually decreased with the increase in pressure, and the equivalent adsorption heat of CH 4 increased with the increase in pressure at 0-2 MPa and then decreased with the increase in pressure. The equal adsorption heat was jointly affected by two factors: the interaction between gas and coal, and the interaction between gas fractions [14]. Obviously, the CO 2 -coal interaction was dominant in the process of adsorption pressure change. For CH 4 , the interaction between gas fractions was dominant at a low pressure, whereas the interaction between gas and coal was dominant at a high pressure. In the adsorption process, the equivalent adsorption heat ranges for CO 2 and CH 4 were 31.93-34.91 kJ/mol and 20.60-20.88 kJ/mol, respectively. The equivalent adsorption heat of CO 2 was greater than that of CH 4 because CO 2 had the highest polarizability. Moreover, it had the highest quadrupole moment and the smallest MD diameter. Compared with CH 4 , there was a stronger interaction between CO 2 and the coal surface, which resulted in the maximum heat release from the coal-adsorbed CO 2 . The equivalent heat of adsorption of the system reflected the adsorption capacity of coal to gas to some extent, but the variation trend of the equivalent heat of adsorption and the adsorption amount was not completely the same. For example, the equivalent heat of adsorption of CH 4 at 298.15 K was greater than that of CH 4 at 293.15 K, but the adsorption amount followed the opposite trend. Since the equivalent adsorption heat of the two gases in coal was less than 42 kJ/mol, the adsorption of CO 2 and CH 4 in coal was physical adsorption [13].
FOR PEER REVIEW 12 of 21 interaction between CO2 and the coal surface, which resulted in the maximum heat release from the coal-adsorbed CO2. The equivalent heat of adsorption of the system reflected the adsorption capacity of coal to gas to some extent, but the variation trend of the equivalent heat of adsorption and the adsorption amount was not completely the same. For example, the equivalent heat of adsorption of CH4 at 298.15 K was greater than that of CH4 at 293.15 K, but the adsorption amount followed the opposite trend. Since the equivalent adsorption heat of the two gases in coal was less than 42 kJ/mol, the adsorption of CO2 and CH4 in coal was physical adsorption [13].

Influence of Temperature on Interaction Energy
By calculating the interaction energy between gas and coal in the system, we evaluated the interaction strength between coal and gas [21]. The lower the calculated energy, the greater the absolute value of the interaction energy-that is, the more stable the adsorption between the two. The interaction energy can be calculated as follows: where EA/B is the total energy of the system, kJ/mol; EA is the energy of coal model, kJ/mol; and EB is the energy of the gas molecule, kJ/mol. We further studied the influence of temperature on the interaction energy between coal and gas. Figure 12 shows the variation curve of interaction energy between CH4/CO2 gas molecules and coal macromolecular structure model at temperatures of 293. 15

Influence of Temperature on Interaction Energy
By calculating the interaction energy between gas and coal in the system, we evaluated the interaction strength between coal and gas [21]. The lower the calculated energy, the greater the absolute value of the interaction energy-that is, the more stable the adsorption between the two. The interaction energy can be calculated as follows: where E A/B is the total energy of the system, kJ/mol; E A is the energy of coal model, kJ/mol; and E B is the energy of the gas molecule, kJ/mol. We further studied the influence of temperature on the interaction energy between coal and gas. Figure 12 shows the variation curve of interaction energy between CH 4 /CO 2 gas molecules and coal macromolecular structure model at temperatures of 293.15 K, 298.15 K, 303.15 K, 308.15 K, and 313.15 K and pressures of 100 kPa-10 MPa.
The simulation results showed that, under the same temperature condition, the interaction energy between coal, CH 4 , and CO 2 increased with an increase in adsorption pressure, which was consistent with the trend of adsorption capacity changing with pressure. Under the same adsorption pressure, the interaction energy between coal and CH 4 and CO 2 decreased with the increase in temperature, which was consistent with the trend of adsorption capacity changing with temperature. These results indicated that the interaction energy between coal and gas in the system is the essential factor determining the adsorption capacity.
where EA/B is the total energy of the system, kJ/mol; EA is the energy of coal model, kJ/mol; and EB is the energy of the gas molecule, kJ/mol. We further studied the influence of temperature on the interaction energy between coal and gas. Figure 12 shows the variation curve of interaction energy between CH4/CO2 gas molecules and coal macromolecular structure model at temperatures of 293. 15   In the simulated temperature and pressure range, the interaction energy between coal and CO 2 ranged from −759.51 kJ/mol to −1367.25 kJ/mol, the interaction energy between coal and CH 4 ranged from −328.01 kJ/mol to −819.15 kJ/mol, and the interaction energy between coal and CO 2 was greater than that of CH 4 . It was about 1.67-2.31 times that of CH 4 . These research results revealed the influence mechanism of temperature, pressure, and gas properties on gas adsorption on coal surface from the perspective of energy-that is, a stronger interaction energy led to a larger adsorption capacity.
The interaction energy was composed of van der Waals energy and electrostatic energy [22]. Figures 13 and 14 show the characteristics of the van der Waals interaction energy and electrostatic energy between coal and CH 4 /CO 2 as a function of temperature and pressure. The simulation results showed that with the increase in pressure, the van der Waals energy and electrostatic energy of coal and CH 4 /CO 2 gradually increased. With the increase of temperature, the two forms of energy in the system gradually weakened. In the adsorption process, the van der Waals energy of coal and CO 2 accounted for about 51%, and the electrostatic energy accounted for about 49%. In contrast, the van der Waals energy of coal and CH 4 accounted for about 99%, and the electrostatic energy accounted for about 1%. This result showed that the van der Waals interaction energy played a dominant role in the adsorption, in particular for CH 4 , because the electrostatic interaction is a long-range interaction with an action range of only a few nanometers. Although the simulation model satisfied the distance condition, the number of atoms with different charges in the coal and gas molecules was small, and therefore, the charge difference between them was also small [22].

Influence of Moisture on Adsorption Characteristics
In the development process of CBM mining, the influence of water content in coal on gas adsorption cannot be ignored. The relevant literature has indicated that the content of water in coal can generally reach about 8 wt.% [21][22][23][24]. We used the molecular simulation method to study the influence of water in coal on the adsorption of gas in coal and its mechanism. ergy accounted for about 1%. This result showed that the van der Waals interaction energy played a dominant role in the adsorption, in particular for CH4, because the electrostatic interaction is a long-range interaction with an action range of only a few nanometers. Although the simulation model satisfied the distance condition, the number of atoms with different charges in the coal and gas molecules was small, and therefore, the charge difference between them was also small [22].

Influence of Moisture on Adsorption Characteristics
In the development process of CBM mining, the influence of water content in coal on gas adsorption cannot be ignored. The relevant literature has indicated that the content of water in coal can generally reach about 8 wt.% [21][22][23][24]. We used the molecular simulation method to study the influence of water in coal on the adsorption of gas in coal and its mechanism.

Water-Bearing Coal Model Construction and Pore Analysis
According to the actual situation of water cut in Chicheng Coal Mine's coalbed, we established the macromolecular structure models of nonsticky coal with water cuts of 1%, 2%, 3%, and 5%. According to the calculation, the number of water molecules in the different models with moisture content of 1%, 2%, 3%, and 5% was 31, 63, 94, and 156, respectively. The macromolecular models of coal with different water cuts are shown in Figure 15.

Water-Bearing Coal Model Construction and Pore Analysis
According to the actual situation of water cut in Chicheng Coal Mine's coalbed, we established the macromolecular structure models of nonsticky coal with water cuts of 1%, 2%, 3%, and 5%. According to the calculation, the number of water molecules in the different models with moisture content of 1%, 2%, 3%, and 5% was 31, 63, 94, and 156, respectively. The macromolecular models of coal with different water cuts are shown in Figure 15.
According to the actual situation of water cut in Chicheng Coal Mine's coalbed, we established the macromolecular structure models of nonsticky coal with water cuts of 1%, 2%, 3%, and 5%. According to the calculation, the number of water molecules in the different models with moisture content of 1%, 2%, 3%, and 5% was 31, 63, 94, and 156, respectively. The macromolecular models of coal with different water cuts are shown in Figure 15. The presence of water in coal samples had a significant influence on the pore distribution of coal. To further study the influence of water content in coal on the adsorption and diffusion effect of CO 2 and CH 4 gas, we used MS software to simulate the pore characteristics of CO 2 and CH 4 in wet coal with water content of 1%, 2%, 3%, and 5%. The simulation results showed that if the MD radius of CO 2 was taken as the probe radius, the accessible pore volumes of wet coal with 1%, 2%, 3%, and 5% moisture content were 1719.29 Å 3 , 973.92 Å 3 , 693.69 Å 3 , and 337.96 Å 3 , respectively. Compared with the accessible pore volumes of the dry coal sample (2295.89 Å 3 ), the volume decreased by 25.11%, 57.58%, 69.78%, and 85.27%, respectively. Taking the MD radius of CH 4 as the probe radius, the pore volume of wet coal with 1%, 2%, 3%, and 5% moisture content was 1044.98 Å 3 , 460.71 Å 3 , 321.41 Å 3 , and 127.96 Å 3 , respectively. Compared with the pore volume of the dry coal sample (1550.92 Å 3 ), the effect of the increase in water content on CH 4 gas with a large MD radius was greater than that of CO 2 gas. Figures 16 and 17 show the pore characteristics of CO 2 and CH 4 accessible pores in coal samples with water content of 1%, 2%, and 3%. The simulation results showed that the presence of water in coal greatly reduced the accessible pore volume of the two gases in coal. The higher the water content of coal, the smaller the accessible pore volume of the two gases-that is, the stronger the inhibition on gas adsorption capacity. the dry coal sample (1550.92 Å 3 ), the effect of the increase in water content on CH4 gas with a large MD radius was greater than that of CO2 gas. Figures 16 and 17 show the pore characteristics of CO2 and CH4 accessible pores in coal samples with water content of 1%, 2%, and 3%. The simulation results showed that the presence of water in coal greatly reduced the accessible pore volume of the two gases in coal. The higher the water content of coal, the smaller the accessible pore volume of the two gases-that is, the stronger the inhibition on gas adsorption capacity.  the dry coal sample (1550.92 Å 3 ), the effect of the increase in water content on CH4 gas with a large MD radius was greater than that of CO2 gas. Figures 16 and 17 show the pore characteristics of CO2 and CH4 accessible pores in coal samples with water content of 1%, 2%, and 3%. The simulation results showed that the presence of water in coal greatly reduced the accessible pore volume of the two gases in coal. The higher the water content of coal, the smaller the accessible pore volume of the two gases-that is, the stronger the inhibition on gas adsorption capacity.

Influence of Moisture Content on Adsorption Capacity
At a temperature of 298.15 K and a pressure of 100 kPa-10 MPa, the adsorption isotherms of CO 2 and CH 4 gas molecules in the coal macromolecular structure model with water content of 1%, 2%, 3%, and 5% are as shown in Figure 18. At a temperature of 298.15 K and a pressure of 100 kPa-10 MPa, the adsorption isotherms of CO2 and CH4 gas molecules in the coal macromolecular structure model with water content of 1%, 2%, 3%, and 5% are as shown in Figure 18. The simulation results showed that the adsorption capacity of the two gases in the water-bearing coal sample increased with the increase of pressure. The adsorption capacity increased rapidly at low pressure and slowly at high pressure, indicating that the moisture in the coal did not change the trend of the adsorption capacity changing with The simulation results showed that the adsorption capacity of the two gases in the water-bearing coal sample increased with the increase of pressure. The adsorption capacity increased rapidly at low pressure and slowly at high pressure, indicating that the moisture in the coal did not change the trend of the adsorption capacity changing with the pressure. The adsorption isotherm of CO 2 and CH 4 in water-bearing coal samples satisfied the Langmuir equation. The fitting parameters are shown in Table 4, and the fitting accuracy is above 0.97. Compared with dry coal samples, the adsorption capacity of CO 2 and CH 4 gas decreased significantly with an increase in water content. In the adsorption system of coal and CO 2 , the saturated adsorption capacity of coal samples containing 1%, 2%, 3%, and 5% water was 21.43%, 35.73%, 50.18%, and 76.14% lower, respectively. In the adsorption system of coal and CH 4 , the saturated adsorption capacity of coal samples containing 1%, 2%, 3%, and 5% water was 24.43%, 40.36%, 50.08%, and 73.07% lower, respectively, indicating that water in coal was not conducive to the adsorption of CO 2 and CH 4 in coal because the existence of water shrank the pore space inside coal. In addition, water had stronger adsorption on the coal surface than CO 2 and CH 4 , occupying the original adsorption sites of the two gases through competitive adsorption. In addition, water not only had a strong dipole moment but also generated a Coulomb force between water molecules. Therefore, the presence of water reduced the interaction force between coal and gas to a certain extent [21], resulting in a decrease in the adsorption capacity of coal for the two gases. As shown in the fitting curve of saturation adsorption capacity of the two gases changing with temperature in Figure 19, the absolute value of slope k of CO 2 was greater than that of slope k of CH 4 , which indicated that the change of water content had a greater impact on the adsorption capacity of CO 2 than on that of CH 4 , and the inhibitory effect of water content on the adsorption capacity of CO 2 was stronger. According to this analysis, in actual engineering, the coal seam gas extraction effect can be improved through coal seam water injection, such as hydraulic fracturing and other technologies in drilling holes.

Influence of Moisture Content on Adsorption Heat
To further reveal the influence of water on the gas adsorbed by coal, we calculated the equivalent adsorption heat of CO 2 and CH 4 in coal samples with different water content when the temperature was 298.15 K and the simulated pressure was 100 kPa-10 MPa, as shown in Figure 20. The simulation results showed that the equivalent adsorption heat of CO 2 and CH 4 was 33.38-37.05 kJ/mol and 20.60-20.88 kJ/mol, respectively. The equivalent adsorption heat of CO 2 was still greater than that of CH 4 in the water-bearing coal sample. With the increase of pressure, the equivalent adsorption heat of CO 2 and CH 4 in the water-bearing coal sample decreased, which indicated that the interaction between CO 2 /CH 4 and coal was dominant in this process. The equal adsorption heat of the two gases decreased in the water-bearing coal sample because H 2 O molecules occupied part of the adsorption sites of CO 2 and CH 4 on the coal surface. Thus, there were fewer adsorption molecules of CO 2 and CH 4 at the strong energy position. Under the same pressure condition, the equivalent adsorption heat of CO 2 and CH 4 gradually increased with the increase in water content. Compared with the average equivalent adsorption heat of the dry coal sample in the pressure range (CO 2 :33.88 kJ/mol, CH 4 : 20.72 kJ/mol), the mean isothermal adsorption heat of CO 2 and coal samples containing 1%, 2%, 3%, and 5% water increased by 0.94%, 2.12%, 3.77%, and 7.02%, respectively. The average equivalent adsorption heat of CH 4 and coal samples containing 1%, 2%, 3%, and 5% water increased by 2.31%, 3.76%, 5.45%, and 7.67%, respectively. The equivalent adsorption heat of the two gases adsorbed by water-bearing coal samples increased because CO 2 and water combined to form carbonic acid on the surface of coal, thus releasing heat. As the increase of water in coal continued to promote the reaction of CO 2 and water, increasingly more heat was released. Although CH 4 did not react with water chemically, CH 4 molecules and water molecules formed hydration molecules [21], resulting in the reduction of energy in the system. Therefore, the higher the water content, the more the heat would be released. In addition, the adsorption heat of the two gases on the water-bearing coal sample was less than 42 kJ/mol. Thus, the adsorption of the two gases on the water-bearing coal sample also was physical adsorption.
Molecules 2023, 28, x FOR PEER REVIEW 1 As shown in the fitting curve of saturation adsorption capacity of the two gases ch ing with temperature in Figure 19, the absolute value of slope k of CO2 was greater than of slope k of CH4, which indicated that the change of water content had a greater impa the adsorption capacity of CO2 than on that of CH4, and the inhibitory effect of water co on the adsorption capacity of CO2 was stronger. According to this analysis, in actual neering, the coal seam gas extraction effect can be improved through coal seam water tion, such as hydraulic fracturing and other technologies in drilling holes.

Influence of Moisture Content on Adsorption Heat
To further reveal the influence of water on the gas adsorbed by coal, we calculate equivalent adsorption heat of CO2 and CH4 in coal samples with different water co when the temperature was 298.15 K and the simulated pressure was 100 kPa-10 MP shown in Figure 20. The simulation results showed that the equivalent adsorption he CO2 and CH4 was 33.38-37.05 kJ/mol and 20.60-20.88 kJ/mol, respectively. The equiv adsorption heat of CO2 was still greater than that of CH4 in the water-bearing coal sam With the increase of pressure, the equivalent adsorption heat of CO2 and CH4 in the w bearing coal sample decreased, which indicated that the interaction between CO2/CH coal was dominant in this process. The equal adsorption heat of the two gases decreas the water-bearing coal sample because H2O molecules occupied part of the adsorption of CO2 and CH4 on the coal surface. Thus, there were fewer adsorption molecules of CO CH4 at the strong energy position. Under the same pressure condition, the equivalen sorption heat of CO2 and CH4 gradually increased with the increase in water content. C pared with the average equivalent adsorption heat of the dry coal sample in the pre range (CO2:33.88 kJ/mol, CH4: 20.72 kJ/mol), the mean isothermal adsorption heat of CO coal samples containing 1%, 2%, 3%, and 5% water increased by 0.94%, 2.12%, 3.77% 7.02%, respectively. The average equivalent adsorption heat of CH4 and coal samples taining 1%, 2%, 3%, and 5% water increased by 2.31%, 3.76%, 5.45%, and 7.67%, respect The equivalent adsorption heat of the two gases adsorbed by water-bearing coal sampl creased because CO2 and water combined to form carbonic acid on the surface of coal, releasing heat. As the increase of water in coal continued to promote the reaction of CO

Influence of Water Content on Interaction Energy
We further studied the influence of temperature on the interaction energy between coal and gas. Figure 21 shows the interaction energy change curves of CO2 and CH4 gas molecules in the coal macromolecular structure model with water content of 1%, 2%, 3%, and 5% at a temperature of 298.15 K and a pressure of 100 kPa-10 MPa.

Influence of Water Content on Interaction Energy
We further studied the influence of temperature on the interaction energy between coal and gas. Figure 21 shows the interaction energy change curves of CO 2 and CH 4 gas molecules in the coal macromolecular structure model with water content of 1%, 2%, 3%, and 5% at a temperature of 298.15 K and a pressure of 100 kPa-10 MPa.

Influence of Water Content on Interaction Energy
We further studied the influence of temperature on the interaction energy between coal and gas. Figure 21 shows the interaction energy change curves of CO2 and CH4 gas molecules in the coal macromolecular structure model with water content of 1%, 2%, 3%, and 5% at a temperature of 298.15 K and a pressure of 100 kPa-10 MPa.  According to the simulation results, under the same water content condition, the interaction between the two gases, wet coal, and CH4/CO2 increased with the increase of pressure, which was the same as the change trend of dry coal samples with pressure. In the range of simulated pressure, the interaction decreased with the increase in water content, indicating that water could reduce the interaction between gas molecules and coal. The interaction energy of the water-bearing coal sample for CO2 adsorption was −538.481 kJ/mol to −1222.61 kJ/mol, and the interaction energy for CH4 adsorption was −216.931 kJ/mol to −737.48 kJ/mol. Under the same conditions, the interaction energy of CO2 in the system was greater than that of CH4, and the interaction energy of watercontaining coal samples decreases compared with dry coal samples. Figures 22 and 23 show the variation characteristics of van der Waals energy and electrostatic energy of CH4/CO2 on the coal surface at different pressures and with different water content during the adsorption process. According to the simulation results, the van der Waals energy and electrostatic energy of the two gases increased with the in- According to the simulation results, under the same water content condition, the interaction between the two gases, wet coal, and CH 4 /CO 2 increased with the increase of pressure, which was the same as the change trend of dry coal samples with pressure. In the range of simulated pressure, the interaction decreased with the increase in water content, indicating that water could reduce the interaction between gas molecules and coal. The interaction energy of the water-bearing coal sample for CO 2 adsorption was −538.481 kJ/mol to −1222.61 kJ/mol, and the interaction energy for CH 4 adsorption was −216.931 kJ/mol to −737.48 kJ/mol. Under the same conditions, the interaction energy of CO 2 in the system was greater than that of CH 4 , and the interaction energy of watercontaining coal samples decreases compared with dry coal samples. Figures 22 and 23 show the variation characteristics of van der Waals energy and electrostatic energy of CH 4 /CO 2 on the coal surface at different pressures and with different water content during the adsorption process. According to the simulation results, the van der Waals energy and electrostatic energy of the two gases increased with the increase in pressure and decreased with the increase in water content. When CO 2 was absorbed by coal, van der Waals interaction accounted for about 36-48%, and electrostatic interaction accounted for about 52-64%, indicating that electrostatic interaction played a dominant role-that is, the higher the water content, the greater the proportion of electrostatic interaction. This interaction was different from the dry coal sample when CO 2 was absorbed. When water-containing coal adsorbed CH 4 , van der Waals interaction energy accounted for about 99.5%, and electrostatic interaction accounted for about 0.5%. This result indicated that van der Waals interaction energy played a dominant role in adsorption, which was almost the same as that when dry coal samples adsorbed CH 4 . dominant role-that is, the higher the water content, the greater the proportion of electrostatic interaction. This interaction was different from the dry coal sample when CO2 was absorbed. When water-containing coal adsorbed CH4, van der Waals interaction energy accounted for about 99.5%, and electrostatic interaction accounted for about 0.5%. This result indicated that van der Waals interaction energy played a dominant role in adsorption, which was almost the same as that when dry coal samples adsorbed CH4.

Conclusions
By means of molecular simulation, we studied the pore structure characteristics of different gases and the influence rule and microscopic mechanism of different temperature, pressure, and water content on the adsorption performance of CO2 and CH4 gas by coal in the macromolecular structure model of noncohesive coal in the Chicheng Coal Mine. The main conclusions of this study are as follows: (1) A three-dimensional macromolecular structure model of nonsticky coal in the Chicheng Coal Mine was constructed using molecular simulation software. dominant role-that is, the higher the water content, the greater the proportion of electrostatic interaction. This interaction was different from the dry coal sample when CO2 was absorbed. When water-containing coal adsorbed CH4, van der Waals interaction energy accounted for about 99.5%, and electrostatic interaction accounted for about 0.5%. This result indicated that van der Waals interaction energy played a dominant role in adsorption, which was almost the same as that when dry coal samples adsorbed CH4.

Conclusions
By means of molecular simulation, we studied the pore structure characteristics of different gases and the influence rule and microscopic mechanism of different temperature, pressure, and water content on the adsorption performance of CO2 and CH4 gas by coal in the macromolecular structure model of noncohesive coal in the Chicheng Coal Mine. The main conclusions of this study are as follows: (1) A three-dimensional macromolecular structure model of nonsticky coal in the Chicheng Coal Mine was constructed using molecular simulation software.

Conclusions
By means of molecular simulation, we studied the pore structure characteristics of different gases and the influence rule and microscopic mechanism of different temperature, pressure, and water content on the adsorption performance of CO 2 and CH 4 gas by coal in the macromolecular structure model of noncohesive coal in the Chicheng Coal Mine. The main conclusions of this study are as follows: (1) A three-dimensional macromolecular structure model of nonsticky coal in the Chicheng Coal Mine was constructed using molecular simulation software. Through geometric and dynamic optimization of the model, the final density of the model stabilized at 1.138 g/cm 3 , which was close to the actual coal density. The rationality of the constructed model was proved by comparing the adsorption results of CH 4 between the model and the experiment. Based on this model, the accessible pore of CO 2 and CH 4 in dry coal samples was 2295.89 Å 3 and 1550.92 Å 3 , respectively, by probe analysis.
(2) In the macromolecular structure model of dry coal, the higher the temperature was, the stronger the inhibition of gas adsorption capacity and interaction could be. The equivalent adsorption heat of CO 2 decreased with the increase in temperature, the equivalent adsorption heat of CH 4 changed little with the increase in temperature, the equivalent adsorption heat of CO 2 decreased with the increase in pressure, and the equivalent adsorption heat of CH 4 first increased and then decreased with the increase in pressure. Under the same conditions, the adsorption capacity, interaction energy, and adsorption heat of CO 2 were all greater than that of CH 4 , and CO 2 was more sensitive to temperature changes. The adsorption of the two gases in the coal molecular model was physical adsorption. (3) The macromolecular structure model of water-bearing coal was established. In the macromolecular structure model of water-bearing coal, the higher the water content was, the smaller the adsorption capacity and interaction energy of the two gases were. The equivalent adsorption heat of CO 2 and CH 4 adsorbed in wet coal with different water content decreased with the increase in pressure and increased with the increase in water content.