## 3 Simulation Results and Analysis
### Effect of Different Water Content on Methane Adsorption Performance  
The actual coal seam contains a large amount of water, and the water content in the coal seam is also an important factor affecting CH\({}_{4}\) adsorption [19,20]. In order to clarify the effect of different water contents on CH\({}_{4}\) adsorption, different water molecules were added to the dry coal model, and the coal models with water content of 1.1%, 4.27%, and 8.31% were constructed, respectively. The number of water molecules were 23, 64, and 110, respectively. The molecular models with different water contents are shown in Figure 4, where the green ball-and-stick models represent the water molecules. The isothermal adsorption data obtained from the simulation were fitted with the Langmuir equation. The fitting parameters of the Langmuir equation with different water content as shown in Table 2. Based on the adsorption constants a and b, with values under different water content conditions, the methane adsorption capacity X1-X10 at a pressure of 1-10 MPa was calculated, respectively. With the correction coefficient of 0% water content as 1, the curve of water content and 1/\(\eta_{w}\) under different water content conditions was obtained, as shown in Figure 5. From Figure 5, it can be seen that the temperature correction factor \(\eta_{w}\) and water content \(w\) satisfy Equation (4):  
\[\eta_{w}=\frac{1}{1.04+0.12w}, \tag{4}\]  
In the formula, \(\eta_{w}\) is the correction coefficient of water content; \(w\) is temperature, %. Figure 4: Molecular structure models with different water content (**a**) 0% H\({}_{2}\)O (**b**) 1.1% H\({}_{2}\)O (**c**) 4.27% H\({}_{2}\)O (**d**) 8.31% H\({}_{2}\)O.  
Figure 3: Methane adsorption capacity and heat adsorption heat at different temperatures: (**a**) Isothermal adsorption curves of CH\({}_{4}\) at different temperatures; (**b**) CH\({}_{4}\) adsorption heat at different temperatures. The isothermal adsorption curves and heat of adsorption of CH\({}_{4}\) after [PERSON]'s equation and consideration of water content correction are shown in Figure 6. From Figure 6a, it can be seen that the adsorption of CH\({}_{4}\) decreases with increasing water content when the temperature and pressure are certain. According to the fitted data, the limiting adsorption amount of CH\({}_{4}\) decreased by 15.2%, 28.09%, and 40.46% with the increase in water content relative to the water content of 0%, respectively, and the increase in water content had an inhibitory effect on the adsorption of CH\({}_{4}\). The magnitude of the heat of adsorption can be used to measure the strength of gas adsorption by the coal body [21]. From Figure 6b, it can be seen that the heat of adsorption of CH\({}_{4}\) by the coal body decreases gradually when the water content increases from 1.1% to 8.31%. The heat of adsorption decreases because the addition of H\({}_{2}\)O competes with CH\({}_{4}\) for adsorption and H\({}_{2}\)O is more readily adsorbed in the coal. Figure 7 shows the adsorption sites occupied by water molecules and methane molecules at 303 K under different water content conditions. The linear structure in the figure is a coal model, the red dot is the density distribution of CH\({}_{4}\), and the green \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Water Content** & **a/(mmol/g)** & **b/MPa\({}^{-1}\)** & \(\mathbf{R^{2}}\) \\ \hline
0\% & 3.88 & 0.10 & 0.995 \\
1.1\% & 3.29 & 0.23 & 0.991 \\
4.27\% & 2.79 & 0.22 & 0.994 \\
8.31\% & 2.31 & 0.26 & 0.992 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The fitting parameters of the Langmuir equation with different water content. Figure 5: \(1/\eta_{iw}\) with water content curve. Figure 6: Methane adsorption capacity and heat adsorption heat with different water content: (**a**) Isothermal adsorption curves of CH\({}_{4}\) with different water content; (**b**) adsorption heat of CH\({}_{4}\) with different water content. ball-and-stick structure is composed of H\({}_{2}\)O molecules.