## 3 Results
### Results of the Orthogonal Test of Sandstone with Different Pore Structures  
The results of the orthogonal test of subcategory \(\mathrm{I_{2}}\) and \(\mathrm{II_{2}}\) sandstones are shown in Table 6, Figure 12, Table 7 and Figure 13. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Sandstone**} & \multicolumn{3}{c}{**Fitting Curves of Permeability Varying with Water Pressures**} \\ \cline{2-4}
**Subcategories** & **Confining Pressure (20 MPa)** & **Confining Pressure (30 MPa)** & **Confining Pressure (40 MPa)** \\ \hline \(\mathrm{I_{1}}\) & \(\mathrm{y=25.774+4.281x~{}R^{2}=0.998}\) & \(\mathrm{y=24.108+3.590x~{}R^{2}=0.999}\) & \(\mathrm{y=22.168+3.176x~{}R^{2}=0.986}\) \\ \hline \(\mathrm{I_{2}}\) & \(\mathrm{y=0.080+0.028x~{}R^{2}=0.998}\) & \(\mathrm{y=0.087+0.021x~{}R^{2}=0.993}\) & \(\mathrm{y=0.069+0.019x~{}R^{2}=0.998}\) \\ \hline \(\mathrm{II_{1}}\) & \(\mathrm{y=0.130+0.004x~{}R^{2}=0.996}\) & \(\mathrm{y=0.123+0.003x~{}R^{2}=0.996}\) & \(\mathrm{y=0.118+0.002x~{}R^{2}=0.996}\) \\ \hline \multirow{3}{*}{\(\mathrm{II_{2}}\)} & \(\mathrm{y=0.004+0.001x}\) & \(\mathrm{y=0.001+0.001x}\) \\  & \(\mathrm{y=0.035x^{-0.522}}\) & \(-9.54\times 10^{-5}~{}\mathrm{x^{2}}\) & \(\mathrm{y=0.001+0.001x}\) \\ \cline{1-1}  & \(\mathrm{R^{2}=0.98}\) & \(+\) \(4.588\times 10^{-6}~{}\mathrm{x^{3}}\) & \(+\) \(9.29\times 10^{-6}~{}\mathrm{x^{3}}\) \\ \cline{1-1}  & & \(\mathrm{R^{2}=0.969}\) & \(\mathrm{R^{2}=0.992}\) \\ \hline \hline \end{tabular} The independent variable \(\mathrm{x}\) is water pressure, and the dependent variable \(\mathrm{y}\) is permeability in the above table.  
\end{table} 
Table 5: Functional relationships between permeability and water pressure under different confining pressures. Figure 12: Permeability variation of the four subcategories of sandstone with different temperature: (**a**) subcategory I\({}_{1}\) sandstone; (**b**) subcategory I\({}_{2}\) sandstone; (**c**) subcategory II\({}_{1}\) sandstone; (**d**) subcategory II\({}_{2}\) sandstone. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Numbers**} & \multicolumn{2}{c}{**Confining**} & **Water Pressures** & **Temperature** & **K** \\  & **Pressures (MPa)** & **(MPa)** & (\({}^{\circ}\)C) & **(mD)** \\ \hline
1 & 7 & 2 & 25 & 0.078035 \\
2 & 10 & 6 & 25 & 0.091888 \\
3 & 20 & 4 & 25 & 0.062407 \\
4 & 7 & 4 & 35 & 0.143773 \\
5 & 10 & 2 & 35 & 0.042103 \\
6 & 20 & 6 & 35 & 0.020217 \\
7 & 20 & 2 & 45 & 0.055881 \\
8 & 10 & 4 & 45 & 0.076364 \\
9 & 7 & 6 & 45 & 0.067883 \\ I & 0.289691403 & 0.176019915 & 0.232330126 \\ II & 0.210354872 & 0.282543283 & 0.206092635 & 0.63855 \\ III & 0.138504721 & 0.179987797 & 0.200128234 & (Sum) \\ Range value (R) & 0.151186682 & 0.106523368 & 0.032201892 & \\ Range ranking & Maximum & Minimum & Median & \\ \hline \hline \end{tabular}  
* sum of the permeability values of three tests for level 1; II—sum of the permeability values of three tests for level 2; III—sum of the permeability values of three tests for level 3; R—difference between the maximum and minimum values in I–III.  
\end{table} 
Table 6: Analysis of orthogonal test results for subcategory I\({}_{2}\) sandstone. The range ranking in Table 6 shows that the R value of the confining pressure was the largest and that the R value of the temperature was the smallest, indicating that the confining pressure had the largest impact on the seepage of subcategory I\({}_{2}\) sandstone, followed by the water pressure and the temperature. Figure 13 shows the comparison of the sums of the resulting permeabilities of three levels of confining pressure, water pressure and temperature. Figure 13 shows that the permeability of subcategory I\({}_{2}\) sandstone decreased with increasing confining pressure, slowly decreased with increasing temperature, and first increased and then decreased with increasing water pressure difference.