# Influences of Different Factors and Sensitivity Analysis of Permeability of Gassy Coal
## 4 Influences of Gas Pressure on the Permeability of Gassy Coal
### Experimental Schemes  
The above tests and analysis reveal that when the gassy coal is under the isobaric condition (axial pressure is equal to confining pressure), the permeability of gassy coal before reaching the critical gas pressure is determined by the slippage effect caused by the gas pressure, that is, determined by the gas pressure. Meanwhile, the permeability of gassy coal after reaching critical gas pressure is determined by effective stress. If the gassy coal is in the non-isobaric deviatoric stress state (axial pressure is unequal to confining pressure), the sensitivities of permeability of gassy coal to axial pressure, confining pressure, and gas pressure remain unclear. Hence, to carry out sensitivity analysis on the permeability of \begin{table}
\begin{tabular}{c c c c c c} \hline
**Coal Sample** & **Axial** & **Confining** & **Permeability–Gas** & **Correlation** & **Critical Gas** \\
**Number** & **Pressure/MPa** & **Pressure/MPa** & **Pressure Fitting Formula** & **Coefficient** & **Pressure/MPa** \\ \hline \multirow{4}{*}{W1} & 4 & 4 & \(K=0.0409P^{2}-0.1003P+0.1427\) & \(R^{2}=0.9247\) & 1.226 \\  & 5 & 5 & \(K=0.0141P^{2}-0.0440P+0.0828\) & \(R^{2}=0.9094\) & 1.560 \\  & 6 & 6 & \(K=0.0072P^{2}-0.0290P+0.0644\) & \(R^{2}=0.9188\) & 2.014 \\  & 7 & 7 & \(K=0.0043P^{2}-0.0231P+0.0544\) & \(R^{2}=0.8898\) & 2.686 \\ \hline \multirow{4}{*}{W2} & 4 & 4 & \(K=0.0193P^{2}-0.0532P+0.0609\) & \(R^{2}=0.8960\) & 1.378 \\  & 5 & 5 & \(K=0.0086P^{2}-0.0316P+0.0407\) & \(R^{2}=0.8933\) & 1.837 \\ \cline{1-1}  & 6 & 6 & \(K=0.0037P^{2}-0.0169P+0.0253\) & \(R^{2}=0.8298\) & 2.284 \\ \cline{1-1}  & 7 & 7 & \(K=0.0021P^{2}-0.0116P+0.0181\) & \(R^{2}=0.8382\) & 2.762 \\ \hline \end{tabular}
\end{table} 
Table 4: Fitting formulas for permeability and gas pressure of gassy coal under different stresses. Figure 10: Permeability–gas pressure curves of gassy coal under the same effective stress. (**a**) Y1 coal samples; (**b**) Y2 coal samples. gassy coal to axial pressure, confining pressure, and gas pressure in seepage tests in the non-isobaric deviatoric stress state, gassy coal should be selected to carry out seepage tests under different axial pressures, confining pressures, and gas pressures. Considering that this calls for multi-factor (axial pressure, confining pressure, and gas pressure) tests many times, which is tedious, orthogonal experiments were selected. The influences of three factors, namely, the axial pressure, confining pressure, and gas pressure, on the permeability of gassy coal need to be studied in the experiments, while their interactions are not considered. Therefore, three-factor and four-level L16(43) orthogonal experimental tables were used, which could meet the experimental requirements. In the meanwhile, the above analysis reveals that there is a critical point of gas pressure in terms of its influence on the permeability, so two orthogonal experimental tables were designed: one with low gas pressure (lower than the critical value) and the other with high gas pressure (higher than the critical value). The factors and levels  
It can be seen from Figure 11 that various factors are listed in descending order, such as the confining pressure, gas pressure, and axial pressure, according to their influences on