# 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  
Two groups of seepage tests were conducted on gassy coal under different axial pressures and confining pressures following test schemes in Figure 3, thus obtaining the axial pressure-permeability curves under different confining pressures, as illustrated in Figure 4. The fitting formulas for axial pressure and permeability are shown in Table 1. The confining pressure-permeability curves under different axial pressures are shown in Figure 5. The fitting formulas for confining pressure and permeability are listed in Table 2.  
Figure 4: Axial pressure–permeability curves of gassy coal under different confining pressures. (**a**) \(Z1\) coal samples; (**b**) Z2 coal samples. It can be seen from Figure 4 that under the same confining pressure, the permeability of gassy coal decreases with the growing axial pressure, and so does the decrease rate. Meanwhile, the overall decreased amplitude of permeability with increasing axial pressure is not large, particularly under high confining pressure, when the permeability basically remains unchanged with growing axial pressure. This indicates that the permeability is less sensitive to axial pressure during axial seepage. As shown in Table 1, the fitting formula for permeability and axial pressure of gassy coal under the same confining pressure is a quadratic polynomial function, and the correlation coefficients are always higher than 0.98. This suggests that under the same confining pressure, the relationship between permeability and axial pressure of gassy coal meets the quadratic polynomial function. As shown in Figure 5, the permeability of gassy coal decreases with the increment of confining pressure, and so does the decrease rate under the same axial pressure. The permeability reduces substantially with the increasing confining pressure on the whole, almost in an exponential manner. This indicates that the axial permeability is far more sensitive to confining pressure than to axial pressure; that is, the axial seepage is greatly affected by confining pressure, whose reason is as follows: In the seepage test, the gas seepage occurs parallel to the axial pressure and perpendicular to the confining pressure. Consequently, changes in the confining pressure have a more pronounced effect on the fissure opening in the direction of gas seepage, leading to a greater sensitivity of permeability to the confining pressure. It can be seen from Table 2 that under the same axial pressure, the fitting formula for permeability and confining pressure of gassy coal is a power function, and the correlation coefficients are always higher than 0.97. This shows that, at constant axial pressure, the permeability of gassy coal is governed by a power function with respect to confining pressure. In summary, the permeability of gassy coal during axial seepage is far more sensitive to confining pressure than to axial pressure. To further study the quantitative relationship between sensitivities of axial permeability of gassy coal to confining pressure and axial pressure, the quantitative relationship between the above sensitivities was explored by tests. In the tests, the gas pressure was 0.5 MPa. Prior to each test, the initial axial pressure and confining pressure were set at 10 MPa and 2 MPa, respectively. Seepage tests were conducted with varying unloading rates of axial pressure and loading rates of confining pressure, as detailed in Table 3.