# Experimental Study on the Influence of Low Temperature on the Gas Permeability of Granite
## 2 Materials and Methods
### One-Dimensional Gas Permeability Test  
In this experiment, the steady-state flow rate method was employed at the outlet end to evaluate the 1D gas permeability of granite. The testing apparatus is a high-precision, hermetically sealed gas permeability system imported from France. The system primarily comprises a confining pressure chamber, a high-precision servo-controlled confining pressure loading unit, a gas transmission control module, and a data acquisition system. The high-precision servo confining pressure loading system has a maximum oil storage  
Figure 2: XRD pattern of granite. capacity of 100 mL, a loading rate range of 0 to 20 mL/min, and a confining pressure loading limit of 60 MPa. The enclosing pressure chamber is composed of a base, a press head, a barrel wall, a barrel lid, and other components. Once the enclosing pressure chamber is installed, the internal liquid is drained using the servo pump to remove excess gas, after which the sealing screws are tightened. The liquid is then discharged again, and the enclosure pressure increases until it reaches the target value and the system stops. A gas pipe is connected to one end of the base of the enclosing chamber and is linked to a gas transmission control module. The gas transmission module includes a gas tank, a pressure controller, a gas pressure sensor, an air inlet valve, a gas storage cylinder, and other parts. A simplified schematic of the test principle is shown in Figure 3. The permeation medium used in this test was argon, a colorless, odorless, and inert gas with a viscosity coefficient of 2.25 \(\times\) 10\({}^{-5}\) Pa-s. Argon is well-suited for permeation in low-permeability media due to its ease of flow. The apparatus is capable of measuring gas permeability as low as 10\({}^{-22}\) m\({}^{2}\). During testing, the data acquisition system continuously records variations in inlet and outlet pressures as well as the real-time volumetric gas flow at the outlet. The gas volumetric flow meter has an accuracy range of 0 to 20 mL/min. The granite specimen was placed within the pressure chamber of the gas permeation device, and a rubber sleeve was used to provide lateral confinement. This configuration effectively prevented penetration of the confining fluid and ensured unidirectional gas flow along the axial direction. During testing, three levels of confining pressure--5 MPa, 10 MPa, and 15 MPa--were applied using the servo-controlled confining pressure system. For each confining pressure, gas permeability tests were conducted under three different inlet pressures: 5 bar, 10 bar, and 15 bar. These measurements were used to calculate the apparent gas permeability, from which the intrinsic permeability was derived under varying confining conditions. The 1D gas permeability was determined based on the steady-state flow method, using [PERSON]'s law as the theoretical foundation [32; 33]. The 1D gas permeability was calculated using the following equation:  
\[K_{x}=\frac{\mu 2 hQ_{x}P_{0}}{A\left(P_{ini}^{2}-P_{0}^{2}\right)} \tag{1}\]  
Figure 3: Simplified schematic diagram of 1D gas permeability test device. where \(K_{x}\) is the gas permeability coefficient, \(Q_{x}\) is the volumetric gas flow rate at the outlet, \(\mu\) is the dynamic viscosity of the gas, \(A\) is the cross-sectional area of the specimen, \(h\) is the height of the specimen, \(P_{ini}\) is the inlet gas pressure, and \(P_{0}\) is the atmospheric pressure. According to classical fluid dynamics, the viscosity of a fluid near the pipe wall significantly influences flow behavior. Fluid velocity approaches zero at the pipe wall due to viscous shear, while it reaches a maximum at the center of the pipe. However, when the mean free path of gas molecules becomes comparable to or exceeds the characteristic pore size, the velocity distribution deviates from this classical profile. Unlike liquids, gas molecules do not form a thin adsorption layer along the pore walls, resulting in diminished velocity gradients across the flow field.