## 3 Results and Discussion
### Gas seepage Regularity in Different Structural Bituminous Coal Samples  
The gas seepage behavior of raw coal samples under varying experimental conditions is illustrated in Figure 6. As shown, the permeability of raw coal exhibited a consistent trend across different gas types, axial pressures, and confining pressures: it initially decreased with increasing gas pressure, followed by a rapid rise and eventual stabilization. Notably, a critical inflection point marked the transition from permeability reduction to enhancement, occurring within a gas pressure range of \(\,p=1\ \sim\ 2\)MPa. This phenomenon arises from the Klinkenberg effect [63; 64], which distinguishes gas seepage from liquid flow. Due to the high compressibility of gases, gas density and viscosity vary significantly with pressure. At low pressures, gas density and viscosity were insufficient to form adsorption layers on pore walls with minimal gas adsorption occurring, resulting in negligible velocity gradients between pore centers and walls. This microscale behavior manifested macroscopically as the Klinkenberg effect, enhancing relative permeability. As gas pressure increased, gas density and viscosity rise, diminishing the Klinkenberg effect and reducing permeability. Beyond a critical pressure threshold, the Klinkenberg effect became negligible, and gas flow transitioned to Darcy-type behavior. Further pressure intensification elevated the gas pressure gradient, driving permeability growth at a decelerating rate. Gas seepage regularity of raw coal samples under different axial stress and confining pressures were depicted in Figure 6a,b. The measured permeability range is consistent in order of magnitude with that in the existing studies [29; 31], which can demonstrate the correctness of the measured data. Elevated axial stress and confining pressures compress the coal matrix, reducing pore connectivity and increasing flow resistance, thereby lowering permeability. The inflection point of the Klinkenberg effect shifted to higher gas pressures under increased axial stress and confining pressures. This shift reflected  
Figure 6: Gas seepage characteristics of raw coal samples. (**a**) Gas seepage regularity of raw coal sample under different axial stress; (**b**) gas seepage regularity of raw coal sample under different confining pressures; (**c**) gas seepage regularity of raw coal sample with different gases. intensified compaction, which narrowed pore channels and heightened the gas pressure required to overcome the Klinkenberg effect and restore Darcy flow. Gas seepage regularity of raw coal sample with different gases are outlined in Figure 6c, highlighting gas-specific permeability trends, with CO2 exhibiting the highest permeability, followed by N2 and CH4. Thereby, the permeability of coal to different gases exhibits discernible variations, which correlate with differences in gas adsorption properties. However, the dominant factor governing these permeability disparities is the molecular kinetic diameter of the gas molecules (CO2: 330 pm, N2: 364 pm, CH4: 380 pm). Smaller CO2 molecules navigate pore channels more easily, requiring lower pressures to mitigate the Klinkenberg effect. Conversely, larger molecules (e.g., CH4) demand higher pressures to achieve Darcy flow, shifting the Klinkenberg inflection point to the right on the horizontal axis of coordinate. These findings underscore that the stress state of coal directly governs gas transport through its pore structure, primarily by modulating pore geometry and gas-matrix interactions. In the same way, the gas seepage behavior of briquette coal samples under various experimental conditions is illustrated in Figure 7. Compared to raw coal, briquette samples exhibited permeability values two orders of magnitude higher, with no significant Klinkenberg effect observed across pressure conditions. This absence is attributed to the homogeneous and loosely compacted structure of briquette coal, characterized by larger pore sizes than raw coal.