## 5 Discussion  
For a stress regime described by uniaxial strain and mean stress, the predicted coal permeability ratios were determined from Equations (9) and (10). Assuming uniaxial strain with horizontal stress across the cleats, we determined the predicted coal permeability ratios from Equations (11) and (12). The obtained permeability depth dependencies are shown in Figures 10 and 11. Additionally, the permeability of the industrially significant coal seams of the Nikitinsky and Tambovsky fields were predicted (Tables 4 and 5). The coking coal seam name and depth data were taken from [PERSON] et al. 2003 [22]. Figure 10: Permeability of the coking coals perpendicular to the butt cleat direction: permeability-depth dependence for stress regimes, described by uniaxial strain and mean stress (gray line) and horizontal stress across cleats (black line). For the Nikitinsky field, we determined that as the depth increased from 730 to 1400 m, the coal permeability decreased by 4 times (from 16.9 to 4.2 mD perpendicular to the butt cleat direction; from 11.2 to 2.8 mD perpendicular to the face cleat direction) for the case considering the uniaxial strain and mean stress and by 2.6 times (from 26.5 to 10.2 mD perpendicular to the butt cleat direction; from 17.9 to 6.9 mD perpendicular to the face cleat direction) for the case considering the uniaxial strain with horizontal stress across the cleats. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Coal Seam Name**} & \multirow{2}{*}{**Depth, m**} & \multicolumn{2}{c}{**The Predicted Permeability of the Coking Goals of the Coking Goals**} \\  & & **Perpendicular to the Butt** & \multicolumn{2}{c}{**Perpendicular to the Face**} \\  & & **Cleat Direction, mD** & **Cleat Direction, mD** \\ \hline \hline \multicolumn{4}{c}{Nikitinsky field} \\ \hline
18 & 815 & 13.9 & 9.4 \\
19 & 850 & 12.9 & 8.7 \\
22 & 1050 & 8.6 & 5.8 \\
26 & 1175 & 6.6 & 4.5 \\
30 & 1245 & 5.7 & 3.9 \\
32 & 1315 & 5 & 3.4 \\
33 & 1350 & 4.6 & 3.1 \\ \hline \multicolumn{4}{c}{Tambovsky field} \\ \hline
18 & 1090 & 7.9 & 5.3 \\
22 & 1330 & 4.8 & 3.2 \\ n/a & 1460 & 3.7 & 2.5 \\
30 & 1550 & 3.1 & 2.1 \\
32 & 1675 & 2.4 & 1.6 \\
33 & 1760 & 2 & 1.3 \\
45 & 1915 & 1.4 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The predicted coking coal permeabilities for stress regime, described by uniaxial strain and mean stress. Figure 11: Permeability of the coking coals perpendicular to the face cleat direction: permeability depth dependence for stress regimes, described by uniaxial strain and mean stress (gray line) and horizontal stress across cleats (black line). Similarly, for the Tambovsky field, as the depth increased from 1000 to 1960 m, the coal permeability decreased by 7.3 times (from 9.5 to 1.3 mD perpendicular to the butt cleat direction; from 6.4 to 0.9 mD perpendicular to the face cleat direction) for the case of the uniaxial strain and mean stress and by 3.9 times (from 18.0 to 4.6 mD perpendicular to the butt cleat direction; from 12.2 to 3.1 mD perpendicular to the face cleat direction) for the case considering the uniaxial strain with horizontal stress across the cleats. For the Tarsminsky field, as the depth increased from 640 to 1470 m, the coal permeability decreased by 5.5 times (from 20 to 3.6 mD perpendicular to the butt cleat direction; from 13.5 to 2.4 mD perpendicular to the face cleat direction) for the case considering the uniaxial strain and mean stress and by 3.2 times (from 30.1 to 9.3 mD perpendicular to the butt cleat direction; from 20.3 to 6.3 mD perpendicular to the face cleat direction) for the case considering the uniaxial strain with horizontal stress across the cleats. The coal permeability obtained under the assumption of uniaxial strain and horizontal stress across the cleats was larger than the permeability obtained under the assumption of uniaxial strain with the mean stress model.