## 3 Simulation Results and Analysis
### Effect of Temperature and Water Content Coupling on Methane Adsorption Performance
#### 3.3.2 Analysis of Extreme Variance of Test Results  
The polar analysis is shown in Table 5, where K is the sum of the experimental results corresponding to the influencing factors, k is the mean value of K, and R is the polar deviation of the factors. From the table, it can be seen that the effect of temperature on CH4 adsorption is more significant, and the best-optimized combination is a water content of 8.31% and a temperature of 363 K. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Numbering**} & \multicolumn{3}{c}{**Experiment Factor**} \\ \cline{2-3}  & **Factor 1 (Water Content)** & **Factor 2 (Temperature)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 4: Orthogonal table. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Numbering**} & \multicolumn{3}{c}{**Experiment Factor**} \\ \cline{2-3}  & **Temperature/K** & **Water Content/\%** \\ \hline
1 & 223 & 1.10 \\
2 & 243 & 4.27 \\
3 & 263 & 8.31 \\
4 & 313 & - \\
5 & 343 & - \\
6 & 363 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental factors and levels. To consider the effect of combined water and temperature on CH\({}_{4}\) adsorption, Equations (3) and (4) are synthesized to obtain the empirical Equation (5) for the coupled effect of water and temperature:  
\[X_{O}=X_{d}1.27e^{-0.009t}\frac{1}{(1.05+0.12w)} \tag{5}\]  
In the equation, \(Xo\) is the adsorption amount of coupling, mmol/g; \(X_{d}\) is the adsorption capacity of dry coal at room temperature, mmol/g; \(t\) is the temperature, \({}^{\circ}\)C; \(w\) is the water content of coal, %. To verify the accuracy of the empirical equation, the simulated data were fitted with Equation (5) and the Langmuir equation, and the fitting parameters are shown in Table 6. From the table, it can be seen that the difference between the empirical equation and the limit adsorption amount of CH\({}_{4}\) obtained by [PERSON] is no more than 2.9%, and the empirical equations with the \(R^{2}\) ranging from 0.989 to 0.996 have a good fitting degree, detailed information is shown in Table 7.  
The isothermal adsorption curve of CH\({}_{4}\) under coupling is shown in Figure 9, from which it can be seen that the adsorption amount of CH\({}_{4}\) increases gradually with the increase in pressure under the condition of a specific temperature and water content, indicating that the coupling will not change the overall trend of CH\({}_{4}\) adsorption. When one of the variables of water content and temperature is fixed, the CH\({}_{4}\) adsorption gradually decreases with the increase in the other variable. According to the fitted data, compared with the limiting CH\({}_{4}\) adsorption amount at room temperature without water, the limiting CH\({}_{4}\) adsorption amount of the optimal combination of single conditions decreased by 23.2% and 40.46%, respectively, while it decreased by 67.61% under the coupling effect, which indicates that the coupling of temperature and water content inhibits the adsorption of CH\({}_{4}\) from the coal body more significantly.