## 5 Conclusions  
1. The size of the pore diameter in coal directly affects the interaction energy during the adsorption of CH\({}_{4}\). Due to the relatively stronger van der Waals force generated between the upper and lower layers of smaller pores, the force exerted on CH\({}_{4}\) is more significant than that in other larger pores. As the pore diameter increases, the van der Waals forces between the inner walls of the pores decrease, and the interaction energy between CH\({}_{4}\) and coal molecules gradually weakens.
2. The adsorption processes of anthracite with different pore diameters all conform to the Langmuir model. There is a positive correlation between the pore diameter size and the adsorption amount. Under the same temperature and pressure conditions, with every 10 A increase in pore diameter, the absolute adsorption amount of CH\({}_{4}\) increases by an average of 16.43%. After reaching the critical pressure of CH\({}_{4}\), the absolute adsorption amount increases slowly and tends to reach a saturated state.
3. The diffusion coefficient of CH\({}_{4}\) in the pores of anthracite increases linearly with the change in diffusion time. When the pore diameter is less than 50 A, the diffusion coefficient of CH\({}_{4}\) in the pores increases at a uniform rate of 32.25%. When the pore diameter reaches 50 A, the diffusion of CH\({}_{4}\) changes from being mainly in a free state to being mainly in an adsorbed state, and the diffusion coefficient increases rapidly at a rate of 126% at 50 A.
4. In this paper, the microscopic adsorption law of methane by coal with pore diameters ranging from 10 A to 60 A has been studied. However, there are still many factors that affect the adsorption of methane by coal, such as the influence of different specific  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Adsorbate**} & **Pore** & \multirow{2}{*}{**a/(mmol\(\cdot\)g\({}^{-1}\))**} & **b/(MPa\({}^{-1}\))** & **R\({}^{2}\)** \\ \cline{3-5}  & & 10 & 51.55 & 6.40 & 0.9542 \\  & 20 & 64.00 & 2.73 & 0.9943 \\ \multirow{2}{*}{CH\({}_{4}\)} & 30 & 78.97 & 1.50 & 0.9928 \\  & 40 & 92.87 & 1.29 & 0.9933 \\ \multirow{2}{*}{CH\({}_{4}\)} & 50 & 106.80 & 1.13 & 0.9906 \\  & 60 & 124.60 & 0.86 & 0.9961 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Adsorption constants of different pore size pore coal with CH\({}_{4}\) Langmuir.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Pore Spacing/Å**} & \multirow{2}{*}{**Curve Slope**} & \multirow{2}{*}{**Diffusion**} & \multirow{2}{*}{**R\({}^{2}\)**} \\  & & & **Coefficient/Å\(\cdot\)ps\({}^{-1}\)** \\ \hline
10 & 3.40 & 0.567 & 0.9996 \\
20 & 4.56 & 0.760 & 0.9906 \\
30 & 6.46 & 1.077 & 0.9976 \\
40 & 7.83 & 1.305 & 0.9980 \\
50 & 10.33 & 1.722 & 0.9951 \\
60 & 23.35 & 3.892 & 0.9977 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Diffusion coefficients of CH\({}_{4}\) molecules in different coal pore sizes.  
surface areas of pores and changes in air pressure. For such issues, further in-depth research should be continued.  
C.Z.: conceptualization, methodology, validation, resources, writing--review and editing, supervision, project administration, funding acquisition. Y.Z.: conceptualization, software, validation, formal analysis, investigation, data curation, writing--original draft preparation, visualization. All authors have read and agreed to the published version of the manuscript.  
Financial support for this work, provided by the National Natural Science Foundation of China (No. 52374204), is gratefully acknowledged.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.