# Influences of Different Factors and Sensitivity Analysis of Permeability of Gassy Coal
## 3 Influences of Axial Pressure and Confining Pressure on the Permeability of Gassy Coal
### Test Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline
**Coal Sample Number** & **Confining Pressure/MPa** &
\begin{tabular}{c} **Permeability–Axial Pressure Fitting** \\ **Formula** \\ \end{tabular} & **Correlation Coefficient** \\ \hline \multirow{4}{*}{Z1} & 2 & \(K=0.0096{\sigma_{1}}^{2}-0.2549{\sigma_{1}}+2.3451\) & \(R^{2}=0.9882\) \\  & 4 & \(K=0.0015{\sigma_{1}}^{2}-0.0657{\sigma_{1}}+0.7028\) & \(R^{2}=0.9911\) \\  & 6 & \(K=0.0002{\sigma_{1}}^{2}-0.0257{\sigma_{1}}+0.3268\) & \(R^{2}=0.991\) \\  & 8 & \(K=0.0011{\sigma_{1}}^{2}-0.0267{\sigma_{1}}+0.2064\) & \(R^{2}=0.9868\) \\  & 10 & \(K=3\times 10^{-5}{\sigma_{1}}^{2}-0.0065{\sigma_{1}}+0.094\) & \(R^{2}=0.9959\) \\ \hline \multirow{4}{*}{Z2} & 2 & \(K=0.0214{\sigma_{1}}^{2}-0.4995{\sigma_{1}}+3.6111\) & \(R^{2}=0.9949\) \\  & 4 & \(K=0.0071{\sigma_{1}}^{2}-0.1608{\sigma_{1}}+1.0985\) & \(R^{2}=0.999\) \\ \cline{1-1}  & 6 & \(K=0.002{\sigma_{1}}^{2}-0.0586{\sigma_{1}}+0.4521\) & \(R^{2}=0.9963\) \\ \cline{1-1}  & 8 & \(K=0.0003{\sigma_{1}}^{2}-0.0142{\sigma_{1}}+0.1452\) & \(R^{2}=0.9952\) \\ \cline{1-1}  & 10 & \(K=0.0002{\sigma_{1}}^{2}-0.0083{\sigma_{1}}+0.086\) & \(R^{2}=0.9975\) \\ \hline \end{tabular}
\end{table} 
Table 1: Fitting formulas for permeability and axial pressure of gassy coal under different confining pressures. Figure 5: Confining pressure–permeability curves of gassy coal under different axial pressures. (**a**) Z1, coal samples; (**b**) Z2 coal samples. Tests on the quantitative relationship between sensitivities of permeability to the axial pressure and confining pressure were performed according to test schemes in Table 3, thus attaining permeability curves at different unloading rates of axial pressure and loading rates of confining pressure (Figure 6). It can be seen from Figure 6 that as the axial pressure is unloaded from 10 to 1.5 MPa and confining pressure is increased from 2 to 3 MPa, that is, when the ratio of the unloading rate of axial pressure to the loading rate of confining pressure is 8.5:1, the permeability of gassy coal remains unchanged and is basically identical (7.68 md). This suggests that, during axial seepage, the permeability of gassy coal is significantly more responsive to \begin{table}
\begin{tabular}{c c c c} \hline
**Coal Sample** & **Axial Pressure/MPa** & **Permeability-Confining Pressure Fitting** & **Correlation Coefficient** \\
**Number** & **Axi1** & \(K=8.0727\sigma_{2}{}^{-1.896}\) & \(R^{2}=0.9894\) \\  & 2 & \(K=7.7766\sigma_{2}{}^{-1.905}\) & \(R^{2}=0.9918\) \\  & 3 & \(K=6.975\sigma_{2}{}^{-1.891}\) & \(R^{2}=0.9903\) \\  & 4 & \(K=6.1974\sigma_{2}{}^{-1.915}\) & \(R^{2}=0.9925\) \\ Z1 & 5 & \(K=5.2467\sigma_{2}{}^{-1.893}\) & \(R^{2}=0.9935\) \\  & 6 & \(K=4.4602\sigma_{2}{}^{-1.878}\) & \(R^{2}=0.9957\) \\  & 7 & \(K=3.6655\sigma_{2}{}^{-1.84}\) & \(R^{2}=0.9945\) \\  & 8 & \(K=3.434\sigma_{2}{}^{-1.897}\) & \(R^{2}=0.9972\) \\  & 9 & \(K=3.3461\sigma_{2}{}^{-1.939}\) & \(R^{2}=0.9981\) \\  & 10 & \(K=3.0957\sigma_{2}{}^{-1.968}\) & \(R^{2}=0.9997\) \\ \hline  & 1 & \(K=18.31\sigma_{2}{}^{-2.312}\) & \(R^{2}=0.9754\) \\  & 2 & \(K=16.224\sigma_{2}{}^{-2.292}\) & \(R^{2}=0.98\) \\  & 3 & \(K=13.436\sigma_{2}{}^{-2.226}\) & \(R^{2}=0.9815\) \\  & 4 & \(K=10.582\sigma_{2}{}^{-2.217}\) & \(R^{2}=0.9833\) \\ Z2 & 5 & \(K=8.2168\sigma_{2}{}^{-2.163}\) & \(R^{2}=0.9875\) \\  & 6 & \(K=6.5522\sigma_{2}{}^{-2.138}\) & \(R^{2}=0.9905\) \\  & 7 & \(K=5.4545\sigma_{2}{}^{-2.134}\) & \(R^{2}=0.9928\) \\  & 8 & \(K=4.673\sigma_{2}{}^{-2.152}\) & \(R^{2}=0.9976\) \\  & 9 & \(K=4.0289\sigma_{2}{}^{-2.159}\) & \(R^{2}=0.9954\) \\  & 10 & \(K=3.6822\sigma_{2}{}^{-2.185}\) & \(R^{2}=0.9971\) \\ \hline \end{tabular}
\end{table} 
Table 2: Fitting formulas for permeability and confining pressure of gassy coal under different axial pressures. \begin{table}
\begin{tabular}{c c c c c} \hline
**Number** & **Gas Pressure/MPa** & **Initial Axial Pressure/MPa** & **Initial Confining Pressure/MPa** & **Ratio of Axial Unloading Rate to Confining Pressure Loading Rate** \\ \hline  
\\ \hline \end{tabular}
\end{table}