# Influences of Different Factors and Sensitivity Analysis of Permeability of Gassy Coal
## 4 Influences of Gas Pressure on the Permeability of Gassy Coal
### Test Results and Discussion  
Two groups of seepage tests were performed on gassy coal under different gas pressures following the test schemes in Figure 8. In this way, the gas pressure-permeability curves under different axial pressures and confining pressures were plotted, as shown in Figure 9. The fitting formulas for gas pressure and permeability are shown in Table 4.  
As shown in Figure 9, with the same axial and confining pressures (identical stress conditions), the permeability of gassy coal reduces at first and then increases in a V-shaped trend with growing gas pressure. In addition, the value and change trend of permeability decline with the growing stress. The quadratic polynomial function was adopted to model the relationship between permeability and gas pressure in Figure 9, with the fitting results presented in Table 4.  
It can be seen from Table 4 that the quadratic polynomial function can fit changes of permeability with gas pressure under the same stress well, and the correlation coefficients are all higher than 0.8. Because the permeability declines at first and then increases with increasing gas pressure, there is a turning point in the seepage test process, that is, the critical gas pressure. The values of critical gas pressure of gassy coal in each stress state calculated using the fitting formulas for permeability and gas pressure are listed in Table 4. The table shows that the critical gas pressure of coal samples grows with the increment of the stress of coal samples.  
Factors that influence the permeability of gassy coal during variations of gas pressure include changes in the effective stress, adsorption of coal, and the Klinkenberg effect (slippage effect) under low atmospheric pressure [39]. Under the same stress, the effective stress of gassy coal samples declines with the increasing gas pressure, and the permeability should enlarge. Whereas, the gas adsorption of coal samples also increases as the gas pressure augments, so the coal matrix expands and internal pore space shrinks, thus leading to the decreased permeability of coal samples, which is the slippage effect. The  
Figure 8: Seepage test schemes for the influence of gas pressure on the permeability of gassy coal.  
slippage effect is generally more obvious under low gas pressure and low stress, as evident in Figure 9, which is consistent with the findings of reference [40]. Therefore, the critical gas pressure of gassy coal functions as a boundary between the slippage effect and effective stress. When the gas pressure is lower than the critical value, the slippage effect and the adsorption and expansion of the substrate dominate, with lower gas and annular pressures amplifying the influence of these factors on permeability. However, when the gas pressure exceeds the critical value, the reduction in effective stress leads to the expansion of pore spaces, which becomes the primary mechanism driving changes in permeability.  
Figure 9: Permeability–gas pressure curves of gassy coal in different stress states. (**a**) W1 coal samples; (**b**) W2 coal samples.  
To further study the influence of the slippage effect on the permeability of gassy coal, seepage tests with different gas pressures under constant effective stress were conducted. The test results are displayed in Figure 10.  
It can be seen from Figure 10 that the permeability of gassy coal decreases with growing gas pressure under the same effective stress and does not increase. This indicates that the reduction of permeability of gassy coal with increasing gas pressure before reaching the critical gas pressure is not determined by the effective stress but by the slippage effect instead. Moreover, this also suggests that after reaching the critical gas pressure, the permeability is determined by effective stress.  
Sensitivity Analysis of Permeability of Gassy Coal to Axial Pressure, Confining Pressure, and Gas Pressure