# Experimental Study on the Influence of Low Temperature on the Gas Permeability of Granite
## 3 Results and Discussion
### One-Dimensional Gas Permeability
#### 3.2.2 Effect of Freezing Temperature on Intrinsic Gas Permeability  
To facilitate the analysis of changes in intrinsic gas permeability before and after freeze-thaw cycles in granite, the magnitude of change in intrinsic gas permeability is defined as the rate of change in permeability, expressed as:  
\[N_{T}=\frac{K_{f}-K_{s}}{K_{s}} \tag{9}\]  
Figure 8: Variation in intrinsic gas permeability in granites. Figure 7: Relationship between inlet gas pressure and apparent permeability of granite (selected specimens). where \(N_{\text{T}}\) is the rate of change in intrinsic gas permeability (a positive value indicates an increase in intrinsic gas permeability); \(K_{\text{f}}\) is the intrinsic gas permeability of granite after freeze-thaw cycle, \(K_{\text{s}}\) is the initial intrinsic gas permeability of granite. The results of the rate of change in intrinsic gas permeability with temperature for two different grain sizes of granite are shown in Figure 9. For both coarse-grained and fine-grained granite, the intrinsic gas permeability increases after the freeze-thaw cycles. This is due to the rocks being in a saturated condition. During the periodic freeze-thaw cycles, the mineral particles in the rock continuously expand and contract, while the water in the pores undergoes a phase transition between ice and water. This phase transition causes a 9% volume expansion, leading to significant tensile and compressive stresses between the rock mineral particles and the ice (i.e., Frost heave force). As these Frost heave forces and contraction stresses repeatedly act on the pore walls, the pores enlarge, ultimately damaging the internal structure of the rock. This damage leads to the formation of new microcracks and micropores, which increases the gas permeable pathways. Consequently, this manifests macroscopically as an increase in the intrinsic gas permeability [39; 40; 41]. Freezing temperature is a critical factor influencing the extent of freeze-thaw damage in granite. Generally, the lower the freezing temperature, the greater the damage caused  
Figure 9: Rate of change in intrinsic permeability of granite versus temperature curve. by freeze-thaw cycles. This relationship is primarily attributed to two key mechanisms. First, during the freezing process, the rock undergoes contraction and deformation. Due to differences in thermal expansion among the various mineral components, internal freeze-thaw stresses develop within the rock. The lower the freezing temperature, the higher the internal freeze-thaw pressure, and thus, the more severe the resulting damage. Second, from the perspective of pore structure, the freezing point of pore water varies with pore size due to the constraints of ambient pressure and limited volumetric space. Lower freezing temperatures lead to a more complete transformation of water to ice within the granite, especially in smaller pores [38]. As the freezing temperature decreases from \(-20\)\({}^{\circ}\)C to \(-40\)\({}^{\circ}\)C, the rate of change in intrinsic gas permeability shows a clear upward trend. When the temperature falls further into the \(-60\)\({}^{\circ}\)C to \(-90\)\({}^{\circ}\)C range, the increase in intrinsic permeability slows significantly--particularly for coarse-grained granite, where permeability remains nearly unchanged. However, as the temperature continues to drop from \(-90\)\({}^{\circ}\)C to \(-120\)\({}^{\circ}\)C, the rate of permeability change increases sharply again. This is because water in macropores typically freezes near \(0\)\({}^{\circ}\)C, whereas water in nanopores requires cooling to approximately \(-90.91\)\({}^{\circ}\)C to undergo a phase transition [42; 43]. It is only when the temperature approaches this threshold that water in nanopores freezes, further intensifying the freeze-thaw damage in granite. When comparing the temperature-permeability change curves of the three granite groups, it is evident that the lower the initial intrinsic gas permeability of granite, the greater the rate of change in permeability after freeze-thaw cycling.