## 4 Simulation and Analysis of Coal's Adsorption of Gas  
### Distribution of Interaction Energy  
In the pore structures of coal with different pore diameters, energy changes occur when CH\({}_{4}\) comes into contact with the inner walls of the coal pores. To reveal the energy changes in the adsorption behavior of CH\({}_{4}\) under different pressures due to the change in pore diameter, the change in the energy peak of CH\({}_{4}\) adsorption was analyzed from the perspective of energy distribution. Fixed-pressure adsorption was carried out through the Sorption module in Materials Studio to obtain the distribution of the interaction energy between coal and methane. The peak represents the position where the energy is more concentrated [18], as shown in Figure 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample Elements** & **C** & **H** & **O** & **N** \\ \hline Mass fraction/\% & 85.81 & 5.64 & 6.63 & 1.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Percentage of each element in anthracite coal from a mine in Yang Blocs. Figure 2: Pore structure model of coal with different pore sizes. With the increase in pore diameter or porosity, the energies at the interaction energy peaks of the pore diameters ranging from 10 A to 60 A are \(-\)10.15 kJ/mol, \(-\)9.85 kJ/mol, \(-\)9.65 kJ/mol, \(-\)9.35 kJ/mol, \(-\)8.55 kJ/mol, and \(-\)7.90 kJ/mol, respectively. The results indicate that the distribution of the interaction energy between coal and CH\({}_{4}\) molecules gradually shifts to the right, suggesting that the interaction between coal and CH\({}_{4}\) gradually weakens. This is caused by the reduction in van der Waals forces in the pore models with higher porosity, and the number of CH\({}_{4}\) molecules that can interact between coal and CH\({}_{4}\) decreases, resulting in a gradual decrease in the interaction energy [19]. According to the analysis in Figure 3, the energy distribution diagram of CH\({}_{4}\) shows a single-peak state, indicating that there is only one adsorption site. CH\({}_{4}\) molecules are randomly and evenly adsorbed in the pores, and the adsorption states are the same, without two or more adsorption sites with significant differences in adsorption. It can be seen from Figure 3a,b that the relative interaction energy distribution hardly changes in the pore models with pore diameters of 10 A and 20 A. The main reason is that the distance between the inner walls of the relatively opposite pore channels within the micropores is small, and the van der Waals force potential generated by the inner walls overlaps, exerting a stronger force on CH\({}_{4}\) molecules than that in mesopores and macropores, resulting in relatively insignificant changes in the adsorption energy of CH\({}_{4}\) in micropores under pressure compared to other larger pore diameters. From the analysis of Figure 3b-e, it can be obtained that at 1 MPa, the interaction energy distribution decreases at the peak with the increase in pore size, and the decline is relatively slow when the distribution reaches the peak. It can be seen from Figure 3d,f that as the pore diameter increases, there is a trend of a gradual decrease in the peak of the energy distribution within the range from 1 MPa to 3 MPa. Based on the above analysis, it can be concluded that the larger the pore diameter of coal is, the weaker the van der Waals forces between the inner walls of the pores will be, and the smaller the interaction energy between CH\({}_{4}\) and the surface of the pores will be; so, CH\({}_{4}\) will not be adsorbed more strongly. When the pore diameter decreases, CH\({}_{4}\) molecules tend to gather at the pore entrances. Affected by the interaction forces at the narrow interface,  
Figure 3: Interaction energy distribution of coal with CH4 for different pore sizes. the interaction energy becomes stronger, and the adsorption becomes more significant.