Experimental Study on the Influence of Low Temperature on the Gas Permeability of Granite

Abstract

Granite is widely regarded as an ideal material for the construction of underground liquefied natural gas (LNG) storage reservoirs due to its high mechanical strength and broad geological availability. However, the ultra-low storage temperature of LNG (−162 °C) poses potential risks in altering the permeability of granite, which may compromise the long-term safety and integrity of the reservoir. To investigate the permeability characteristics and microstructural degradation of granite under low-temperature conditions, both coarse-grained and fine-grained granite samples were subjected to a series of experiments, including one-dimensional (1D) gas permeability tests (conducted before and after freeze–thaw cycles ranging from −20 °C to −120 °C), nuclear magnetic resonance (NMR) tests, and two-dimensional (2D) gas permeability tests performed under real-time low-temperature conditions. Experimental results indicated that the gas permeability of granite under real-time low-temperature conditions exhibited a linear increase as the temperature decreased. In contrast, the gas permeability after freeze–thaw cycling followed a nonlinear trend: it increased initially, plateaued, and then increased again as the freezing temperature continued to drop. A further analysis of pore structure evolution and permeability changes revealed distinct degradation mechanisms depending on grain size. In coarse-grained granite, freeze–thaw damage was primarily characterized by the initiation and propagation of new microcracks, which originated as micropores and expanded into mesopores. In fine-grained granite, the damage primarily resulted from the progressive widening of existing fissures, with micropores gradually evolving into mesopores over successive cycles. The study’s findings provide a useful theoretical foundation for the secure subterranean storage of LNG.

1. Introduction

Amid the escalating impacts of climate change, the global community has increasingly prioritized reduction in greenhouse gas emissions and the pursuit of carbon neutrality to promote sustainable development and the continued advancement of human civilization [1]. As a relatively cleaner fossil fuel, natural gas plays a critical role as a transitional energy source in the optimization of global energy structures [2,3]. Compared to conventional above-ground liquefied natural gas (LNG) storage tanks, underground LNG storage systems have garnered significant attention and widespread application in the industry due to several distinct advantages, including a smaller surface footprint, larger storage capacity, enhanced safety, and improved environmental compatibility [4].

The operating temperature of liquefied natural gas (LNG) storage tanks is approximately −162 °C, making it essential to ensure the thermal stability and structural integrity of foundation materials and surrounding geological formations under cryogenic conditions when designing and operating underground LNG storage systems. In recent years, extensive experimental research has been conducted to investigate the physical, mechanical, and microstructural properties of rocks subjected to low temperatures and freeze–thaw cycles. These studies have primarily focused on various lithologies, including granite [5,6,7], marble [8,9], shale [10] and sandstone [11,12], and have explored the influence of factors such as rock type [13], water content [14], freezing temperature [15,16,17], and the number of freeze–thaw cycles [18] on rock deterioration and strength degradation under cryogenic conditions. While these investigations have provided valuable insights into macroscopic strength changes, such analyses alone are insufficient to fully elucidate the mechanisms of low-temperature damage in rocks. A more comprehensive understanding requires precise identification and quantification of internal pore damage, which forms the foundation for evaluating cryogenic degradation and developing predictive models of rock behavior in low-temperature environments.

At present, a range of advanced techniques are employed to investigate changes in the internal pore structure of rocks under low-temperature conditions, including acoustic emission (AE) [6], nuclear magnetic resonance (NMR) [19,20], scanning electron microscopy (SEM) [21] and computed tomography (CT) [22]. These methods provide multi-scale insights into pore evolution and damage mechanisms. For example, using CT and SEM imaging, Park et al. [23] observed grain disaggregation, crack initiation and propagation, and increased porosity in igneous rocks resulting from internal water volume expansion during freeze–thaw cycling. Liu et al. [24] employed NMR to analyze the pore size distribution characteristics of sandstone samples with initial damage. The results indicated that, during the first 20 freeze–thaw cycles, the number of micropores and mesopores increased. However, once the number of freeze–thaw cycles exceeded 20, subsequent changes in the pore size distribution were primarily dominated by the evolution of micropores. Sun et al. [25] conducted a comparative study using NMR and three-dimensional X-ray micrography (3D-XRM) on granite, limestone, and sandstone samples before and after freeze–thaw exposure. The results revealed material-specific trends: mesopore content in granite, micropore content in limestone, and the emergence of macroporous structures all increased with repeated cycling. In sandstone, both micropores and mesopores showed an overall increase, highlighting the cumulative deterioration of internal pore structures.

However, the operating temperature of underground LNG storage caverns—approximately −162 °C—imposes more extreme cryogenic conditions than those typically considered in conventional low-temperature studies. This ultra-low-temperature environment is expected to have a more severe impact on the internal microstructure and mechanical integrity of surrounding rock masses. Most existing studies on rock degradation under cryogenic conditions have focused on moderate low-temperature ranges, creating a knowledge gap regarding the behavior of rocks under LNG-relevant temperatures.

To address this, Inada and Yokota [26] conducted uniaxial compression and tensile strength tests on granite and andesite across a wide temperature range (−160 °C to 20 °C), under both saturated and dry conditions. Their results revealed that the compressive and tensile strengths of both rock types increased as the temperature decreased, regardless of moisture content. Li et al. [7] investigated the fracture characteristics of saturated and dry granite within a temperature range of −165 °C to 25 °C. Their study also introduced statistical models to describe the correlation between fracture energy and surface roughness at different temperatures.

To date, most investigations into cryogenic damage in rocks have primarily focused on mechanical properties, while the gas permeability behavior of rocks under low-temperature conditions has received comparatively limited attention. However, rock permeability is a critical parameter that directly influences the stability and sealing performance of geological formations, particularly in the context of subsurface energy storage. It governs the ability of rocks to transmit fluids and, therefore, plays a decisive role in ensuring the safety and containment integrity of underground LNG storage systems. At the operating temperature of LNG storage caverns (approximately −162 °C), significant alterations in the rock’s internal microstructure may occur, potentially leading to complex changes in permeability. Given that permeability is strongly influenced by factors such as porosity, pore size distribution, and fracture connectivity, understanding its evolution under cryogenic conditions is essential. Investigating the permeability behavior of rocks at ultra-low temperatures is thus crucial for optimizing the design and ensuring the long-term safety and operational reliability of LNG storage caverns.

It has been demonstrated that in underground coal gasification, a temperature of 1000 °C significantly influences the area within 0.5 m of the reactor chamber [27]. Similarly, the extreme low-temperature characteristics of liquefied natural gas (LNG), at approximately −162 °C, exert a considerable influence on the surrounding reservoir rock, resulting in the formation of ice rings around the storage area [28]. As the distance from the storage decreases, the temperature gradually decreases from the original formation temperature to approximately −162 °C. In accordance with earlier research [17,29,30], saturated coarse and fine-grained granite specimens with distinct particle sizes were subjected to freeze–thaw cycling at target temperatures of −20 °C, −40 °C, −60 °C, −90 °C, and −120 °C. One-dimensional gas permeability tests were conducted following the freeze–thaw cycles to assess changes in permeability performance. To further investigate the influence of cryogenic damage on pore structure evolution, nuclear magnetic resonance (NMR) analysis was employed to characterize microstructural variations in both granite types under different freezing conditions. The permeability test results were then analyzed alongside the NMR data to elucidate the freeze–thaw damage mechanisms and their effects on permeability evolution across varying particle sizes. Additionally, a custom-designed 2D real-time low-temperature gas permeability testing apparatus was developed to evaluate the gas permeability of granite under actual cryogenic conditions. This enabled a direct comparison between the permeability characteristics observed during real-time low-temperature evaluations and those measured after freeze–thaw cycling. The findings of this work are expected to provide theoretical insights and technical guidance for ensuring structural integrity and sealing performance of underground LNG storage systems operating in ultra-low temperature environments.

2. Materials and Methods

2.1. Specimen Preparation

Two types of granite were selected for this study: a coarse-grained granite sourced from Hunan Province, China, and a fine-grained granite from Fujian Province, China. All rock specimens were machined into standard cylindrical shapes with a diameter of 50 mm and a height of 100 mm, in accordance with the specifications recommended by the International Society for Rock Mechanics (ISRM). To ensure specimen quality, the non-parallelism and surface flatness of the end faces were maintained below 0.02 mm, while the angular deviation from perpendicularity between the specimen axis and end faces was kept below 0.25°. In addition to the standard specimens, a subset was fabricated into hollow cylindrical specimens by drilling a central hole with a diameter of 10 mm through the entire 100 mm height. The standard cylindrical specimens were used for freeze–thaw cycling tests, whereas the hollow specimens were employed in real-time low-temperature testing, as illustrated in Figure 1.

Before and after the freeze–thaw cycles, all specimens underwent saturation and drying procedures using a high-pressure vacuum saturator and a drying oven, respectively. The dry and saturated masses of the specimens were recorded before and after the tests to determine porosity changes. The basic physical parameters of the coarse- and fine-grained granites are summarized in

Table 1. Basic physical parameters.

Particle	Natural Density	Dry Density	Saturation Density	Porosity
	(g/cm3)	(g/cm3)	(g/cm3)	(%)
Coarse-grained granite	2.638	2.637	2.645	0.83
Fine-grained granite	2.808	2.806	2.811	0.45

. Mineralogical compositions were identified using X-ray diffraction (XRD) analysis, and the primary mineral constituents of both granite types are presented in

Table 2. Mineral composition of the samples.

Particle	Quartz	Muscovite	Albite	Potassium Feldspar
Coarse-grained granite	23.16%	18.45%	30.37%	28.02%
Fine-grained granite	14.5%	27.02%	58.47%

and Figure 2. The equipment used was a Malvern Panalytical third-generation Empyrean Sharp-Shooter X-ray diffractometer, with a scanning angle range of 5° to 90° and a scanning speed of 5° per minute.

It should be noted that the coarse-grained granite used in this study is primarily composed of quartz, muscovite, albite, and potassium feldspar, while the fine-grained granite does not contain potassium feldspar. Experimental mineralogical studies have confirmed that quartz, being a relatively stable mineral, exhibits excellent thermal stability in the temperature range of −196 °C to 25 °C, with a volumetric expansion coefficient of less than 1.2 × 10⁻⁶/°C. In contrast, muscovite, potassium feldspar, and albite may undergo lattice distortion in ultra-low temperature environments (i.e., <−150 °C), potentially leading to the initiation of microcracks.

2.2. Freeze–Thaw Cycle Test

In this study, freeze–thaw cycle tests were conducted on granite specimens with two distinct grain sizes: coarse-grained and fine-grained. Prior to the tests, the initial 1D gas permeability of the oven-dried specimens (at 105 °C) was measured using a 1D gas permeation apparatus. Based on the initial gas permeability results obtained at room temperature, each granite type was categorized into five groups, with each group comprising two standard cylindrical specimens. These grouped specimens were then subjected to a series of freeze–thaw cycling tests. The freeze–thaw cycle test was conducted using the B-DW-120W118 low-temperature preservation chamber manufactured by Shanghai Boyi Test Equipment Co., Ltd. (Shanghai, China) The internal dimensions of the chamber were 500 mm × 400 mm × 560 mm, and the temperature setting range spanned from −20 °C to −150 °C.

Based on previous studies [6,11,31] and practical considerations, a freezing rate of 0.5 °C/min and a freezing duration of 4 h were selected. The freeze–thaw cycle testing procedure was conducted as follows:

(1)

Specimens were saturated in an ultra-high-pressure vacuum saturation apparatus for 72 h to ensure full water saturation.

(2)

Freezing was performed at target temperatures of −20 °C, −40 °C, −60 °C, −90 °C, and −120 °C, with a controlled cooling rate of 0.5 °C/min. Once the desired temperature was reached, specimens were maintained at the set temperature for 4 h using a cryogenic freezer.

(3)

Thawing was conducted under natural ambient conditions.

(4)

Steps (1) through (3) were repeated for a total of 20 freeze–thaw cycles.

Following completion of the freeze–thaw cycling, the granite specimens were oven-dried and subjected to 1D gas permeability testing.

2.3. 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 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 × 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 m². 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 Darcy’s law as the theoretical foundation [32,33].

The 1D gas permeability was calculated using the following equation:

$$K_x={\displaystyle \frac{\mu 2h{Q}_x{P}_0}{A\left(P_{ini}^2-P_0^2\right)}}$$

(1)

where K_x is the gas permeability coefficient, Q_x is the volumetric gas flow rate at the outlet, μ 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 P₀ 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. To account for this phenomenon—commonly referred to as the gas slip effect—Klinkenberg et al. [34] introduced a slip correction factor, denoted as β. By incorporating this factor, Equation (1) is modified to calculate the specimen’s intrinsic gas permeability, as follows:

$$K_{app}=K_{int}\left(1+{\displaystyle \frac{\beta }{P_m}}\right)$$

(2)

where K_app is the apparent gas permeability coefficient, K_int is the intrinsic gas permeability coefficient, β is the Klinkenberg slip factor, and P_m is the average gas pressure within the specimen.

2.4. Two-Dimensional Gas Permeability Test

Three hollow specimens, each of coarse-grained and fine-grained granite, were first tested to determine the 2D gas permeability under ambient conditions. Following this, 2D gas permeability tests were conducted under real-time low-temperature conditions at −20 °C, −40 °C, −60 °C, −90 °C, and −120 °C in sequence. Prior to each test, the specimens were oven-dried to ensure uniform starting conditions, allowing for the determination of the real-time low-temperature 2D gas permeability at each of the specified temperatures.

In this study, the 2D gas permeability of granite was investigated using the radial seepage method without applying confining pressure. The test apparatus consists of two primary components: a gas transmission system and a fixture that holds the specimens without confining pressure. Each granite specimen was drilled through the center and placed in the fixture, which was secured with four fastening bolts. The fixture was sealed with upper and lower covers to prevent any gas leakage. The upper cover was designed with a gas seepage channel that was connected to the gas transmission system, allowing controlled gas flow during testing, and the simplified diagram of the test principle is shown in Figure 4.

During the 2D radial permeation tests, higher inlet gas pressures were applied within the cavities of the hollow granite specimens, and the pressure decrease over time was monitored. The gas passed through the annular specimen in a radial direction, and its permeability was considered as the 2D radial gas permeability [35].

The 2D radial gas permeability was calculated using the following equation:

$$K_r={\displaystyle \frac{\mu V}{\pi h}}{\displaystyle \frac{\ln \left(R\right)}{P^2-1}}{\displaystyle \frac{∆p}{∆t}},\left(R={\displaystyle \frac{r_2}{r_1}},P={\displaystyle \frac{p_1}{p_a}}\right)$$

(3)

where K_r is the 2D radial gas permeability coefficient; V is the volume of the gas buffer bottle; h is the height of the specimen; r₁ and r₂ are the inner and outer radii of the annular cavity, respectively, and p₁ and p_a are the corresponding pressures at the inner and outer boundary conditions, respectively.

The gaseous fluid flows radially out of the annular cavity, with fluid flow from the top and bottom of the cavity ideally neglected.

The Knudsen number K_n is commonly used to categorize flow regimes in small pores [36]. It is expressed using the following form:

$$K_n={\displaystyle \frac{\mathsf{\lambda }}{d}}$$

(4)

$$\lambda ={\displaystyle \frac{\mathsf{\mu }}{P}}\sqrt{{\displaystyle \frac{\pi R_{g}T}{2M}}}$$

(5)

where K_n is the Knudsen number; λ is the average free range of gas molecules; d is the average pore diameter of the specimen; μ is the gas viscosity coefficient of the gas at P (pressure) and T (temperature); R_g is the universal gas constant; M is the gas molecular mass. According to the Knudsen number K_n, the gas flow regime can be categorized into continuous/Darcy flow (K_n < 0.001); slip flow (0.001 < K_n < 0.1); transition flow (0.1 < K_n < 10); and free molecular (Knudsen) flow (K_n > 10) [37].

The temperature range for the 2D gas permeability test was from 20 °C to −120 °C, with an air pressure range of 5 to 15 bar. Based on Equations (4) and (5), the calculated Knudsen number ranged from 0.00223 to 0.0128 for coarse-grained granite and from 0.0685 to 0.395 for fine-grained granite. Both ranges can be corrected for permeability using the Klinkenberg equation.

2.5. Nuclear Magnetic Resonance Test

In this test, granite specimens were analyzed using the CPMG pulse sequence on a 2 MHz NMR spectrometer manufactured by Limmecho Technology Co., Ltd., Beijing, China. During the NMR measurements, the temperatures of both the magnet and the probe coil were maintained at 20 ± 1 °C.

Nuclear magnetic resonance (NMR) techniques can be used to characterize the pore structure of porous media by measuring the transverse relaxation time (T₂) of hydrogen nuclei in the fluids within the porous material. Fluids in rock voids exhibit three distinct relaxation mechanisms: free relaxation, surface relaxation, and diffusion relaxation. For general fluids in porous media, free and diffusive relaxation are significantly weaker than surface relaxation and, therefore, can be neglected in the study and application of porous media. As a result, the T₂ relaxation time of fluids in pores can be expressed by the following equation:

$${\displaystyle \frac{1}{T_2}}={\displaystyle \frac{1}{T_{2B}}}+{\displaystyle \frac{1}{T_{2S}}}+{\displaystyle \frac{1}{T_{2D}}}\approx {\displaystyle \frac{1}{T_{2S}}}={\rho }_2{\displaystyle \frac{S}{V}}={\displaystyle \frac{F}{R}}$$

(6)

where T₂ is the relaxation time; T_2B is the free relaxation time; T_2S is the surface relaxation time; T_2D is the diffusion relaxation time; ρ₂ is the transverse surface relaxation strength, which takes the value of 10 μm/s; S is the surface area of the pore; V is the pore volume; F is the pore shape factor of the rock, which takes the value of 2; and R is the pore radius.

From Equation (6), it is evident that the transverse relaxation time T₂ depends on the ratio of the pore surface area to its volume. Therefore, a larger T₂ value corresponds to a larger pore size, while a smaller T₂ value indicates smaller pores.

Equation (6) can be further expressed as:

$$R={\rho }_{2}F{T}_2$$

(7)

Thus, the pore structure distribution of the specimen can be determined by measuring its transverse relaxation time T₂. The granite cylindrical specimens, with a diameter and height of 25 mm, used for the NMR tests are shown in Figure 5.

3. Results and Discussion

3.1. Change in Porosity

The changes in porosity of individual specimens are analyzed using the rate of change in porosity, which is defined as follows:

$$∆N={\displaystyle \frac{n_f-n_0}{n_0}}\times 100\%$$

(8)

where ∆N is the rate of change in porosity of the specimen, n_f is the porosity after the freeze–thaw cycle, and n₀ is the porosity before the freeze–thaw cycle.

Figure 6 displays the rate at which the porosity of the two granite specimens changed at various freezing temperatures throughout the freeze–thaw process. The porosity change rate of coarse-grained granite increased from 2.93% to 23.64%, while that of fine-grained granite increased from 2.35% to 27.45% as the temperature dropped from −20 °C to −120 °C. Additionally, the rate of porosity change in fine-grained granite was higher than in coarse-grained granite. This difference is primarily due to the lower initial porosity of fine-grained granite, which undergoes a more noticeable shift in porosity following the freeze–thaw cycle. In contrast, coarse-grained granite had an initial porosity of 0.83% and 0.45%.

When the freezing temperature ranged from −60 °C to −90 °C, the porosity of coarse-grained granite increased more slowly. Meanwhile, the porosity of fine-grained granite did not change significantly within the temperature range of −40 °C to −60 °C. Since different pore sizes correspond to different freezing points of pore water [38], the freeze–thaw cycle during the initial phase of temperature drop leads to a faster rate of rock damage. Once the water in the larger pores of the rock has completely frozen, the freeze–thaw damage gradually reaches a saturated state. Due to the higher proportion of small pores in fine-grained granite, its freeze–thaw damage reaches saturation earlier. As the temperature continues to decrease, the water in the smaller pores of the granite begins to freeze, resulting in a significantly accelerated increase in porosity for both types of granite.

In conclusion, the porosity change rate of both coarse-grained and fine-grained granite increases as the freezing temperature decreases. The rate of increase shows notable variations across different temperature intervals, following a pattern of rapid increase, stability, and then a rapid increase once more.

3.2. One-Dimensional Gas Permeability

3.2.1. One-Dimensional Intrinsic Gas Permeability

The intrinsic gas permeability coefficients of the two granite specimens were determined by applying corrections to the apparent gas permeability values, and the results are presented in Figure 7.

Figure 8 shows the 1D intrinsic gas permeability of granite before freeze–thaw cycles at different confining pressures. The dispersion of intrinsic gas permeability in coarse-grained granite under various confining pressures (5 MPa, 10 MPa, and 15 MPa) is minimal. This suggests that the internal pore structure of coarse-grained granite is relatively consistent across specimens. In contrast, the intrinsic gas permeability of fine-grained granite exhibits greater dispersion under varying confining pressures, indicating a lack of stability compared to coarse-grained granite. This is particularly evident at a confining pressure of 5 MPa, where the intrinsic gas permeability of different specimens varies by an order of magnitude. However, Figure 8b shows that, under a confining pressure of 5 MPa, the intrinsic gas permeability of fine-grained granite is concentrated in the range of 4 × 10⁻²⁰ to 1.5 × 10⁻¹⁹, and the degree of dispersion decreases as the confining pressure increases. This suggests that fine-grained granite possesses a more complex pore structure than coarse-grained granite.

To facilitate a more comprehensive analysis of the effect of low temperatures on the gas permeability of granite in subsequent tests, the intrinsic gas permeability at a confining pressure of 5 MPa was used as the standard, and the fine-grained granite specimens were divided into two groups: Group 1 (PB1, PB2, PB3, PB4, PB5) and Group 2 (PC1, PC2, PC3, PC4, PC5).

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:

$$N_T={\displaystyle \frac{K_f-K_s}{K_s}}$$

(9)

where N_T is the rate of change in intrinsic gas permeability (a positive value indicates an increase in intrinsic gas permeability); K_f is the intrinsic gas permeability of granite after freeze–thaw cycle, K_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 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 °C to −40 °C, the rate of change in intrinsic gas permeability shows a clear upward trend. When the temperature falls further into the −60 °C to −90 °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 °C to −120 °C, the rate of permeability change increases sharply again. This is because water in macropores typically freezes near 0 °C, whereas water in nanopores requires cooling to approximately −90.91 °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. In other words, the denser the granite microstructure, the more susceptible it is to freeze–thaw-induced degradation.

3.2.3. Effect of Confining Pressure on Intrinsic Gas Permeability

Based on the results of intrinsic gas permeability measurements before and after freeze–thaw cycles, the variation curves of granite’s intrinsic gas permeability with confining pressure at different freezing temperatures are plotted in Figure 10. Overall, both coarse- and fine-grained granite exhibit a similar trend: intrinsic gas permeability decreases with increasing confining pressure, and the rate of this decrease gradually diminishes as the pressure continues to rise. Among the fine-grained granite specimens, the reduction in intrinsic gas permeability in Group B is more pronounced than that in Group C.

Before freeze–thaw cycling, the intrinsic gas permeability of the three granite types decreased by 55.59%, 79.32%, and 76.74%, respectively, as confining pressure increased from 5 MPa to 15 MPa. After freeze–thaw cycling, the average reduction in intrinsic gas permeability for coarse-grained granite at freezing temperatures of −20 °C, −40 °C, −60 °C, −90 °C, and −120 °C was 63.80%, 59.72%, 59.09%, 58.50%, and 59.57%, respectively. For fine-grained granite, Group B exhibited reductions of 81.66%, 78.61%, 76.38%, 84.55%, and 80.21%, while Group C showed corresponding reductions of 75.36%, 64.18%, 86.74%, 78.25%, and 78.93%.

The primary determinant of freeze–thaw damage to rocks is their lithology [44]. Due to differences in mineral composition and particle size between coarse- and fine-grained granite, the damage mechanisms under freeze–thaw cycles also differ. After freeze–thaw cycling, all granite specimens exhibited increased permeability reductions compared to those at room temperature. Coarse-grained granite showed a greater increase in permeability decline, while fine-grained granite exhibited a more moderate change. This is likely because coarse-grained granite, having lower strength and stiffness, is more susceptible to internal stress caused by the repeated expansion and contraction associated with ice–water phase transitions. These stresses promote pore propagation and the formation of new pores. In contrast, fine-grained granite, with its higher strength and more compact structure, primarily experiences widening of existing pores rather than the formation of new ones.

Therefore, the freeze–thaw damage in coarse-grained granite is mainly manifested through the initiation and propagation of new pores, which results in an increase in smaller, interconnected pores. At low confining pressure (5 MPa), these new pores contribute to permeability. However, at higher confining pressure (15 MPa), many of these small pores are compressed and closed, leading to a more significant reduction in permeability after freeze–thaw cycling. Conversely, for fine-grained granite, since the primary damage mechanism involves the expansion of existing pores with limited formation of new flow paths, the permeability decrease with increasing confining pressure is less affected by the freeze–thaw cycle.

3.3. Two-Dimensional Gas Permeability

3.3.1. Two-Dimensional Intrinsic Gas Permeability

Table 3. Two-Dimensional gas permeability of coarse-grained granite(m²).

Specimen No.	Apparent Permeability			Intrinsic Permeability
	5 Bar	10 Bar	15 Bar
TA1	3.25 × 10−18	2.75 × 10−18	2.49 × 10−18	2.16 × 10−18
TA2	3.83 × 10−18	3.32 × 10−18	2.97 × 10−18	2.59 × 10−18
TA3	2.94 × 10−18	2.86 × 10−18	2.58 × 10−18	2.45 × 10−18

and

Table 4. Two-Dimensional gas permeability of fine-grained granite(m²).

Specimen No.	Apparent Permeability			Intrinsic Permeability
	5 Bar	10 Bar	15 Bar
TB1	2.52 × 10−19	1.89 × 10−19	1.74 × 10−19	1.27 × 10−19
TB2	4.92 × 10−19	3.52 × 10−19	2.93 × 10−19	1.88 × 10−19
TB3	1.58 × 10−19	1.26 × 10−19	1.07 × 10−19	8.59 × 10−20

present the 2D intrinsic gas permeability measurements of granite hollow specimens with coarse and fine particle sizes. The average 2D intrinsic gas permeability values for coarse-grained and fine-grained granite are 2.40 × 10⁻¹⁸ and 1.34 × 10⁻¹⁹ m², respectively. These results are consistent with the 1D gas permeability findings, which are also on the order of 10⁻¹⁸ and 10⁻¹⁹ m², respectively, indicating a difference of approximately one order of magnitude. Similarly, the 2D intrinsic gas permeability of coarse-grained granite exhibits greater stability compared to that of fine-grained granite, further suggesting that the internal pore structure of coarse-grained granite is relatively uniform across specimens.

3.3.2. Changes in 2D Intrinsic Gas Permeability

The scatter plot illustrating the relationship between 2D gas permeability of granite and freezing temperature is shown in Figure 11. The corresponding fitted curves and coefficients of determination (R²) are also provided. The results indicate a linear increase in 2D gas permeability with decreasing freezing temperature for both types of granite. This is because the test was conducted using dry specimens, and the dry specimens’ gas permeability was affected by real-time low temperatures. Change is primarily caused by the rock’s contraction and deformation during the freezing process; the rock’s pores will widen as a result of the contraction of the rock skeleton. The differing thermal contraction coefficients of the mineral phases lead to incompatible deformations during freezing, disrupting the internal structure and generating additional permeable pathways, thereby increasing the gas permeability.

The fitted relationship between 2D gas permeability and freezing temperature is described by a first-order linear function. The slope of the fitting curve reflects the rate at which the 2D gas permeability increases with decreasing temperature—the steeper the slope, the more sensitive the granite is to real-time low-temperature conditions. The 2D gas permeability of coarse-grained granite exhibits a more pronounced increasing trend compared to fine-grained granite. This can be attributed to the denser solid skeleton of fine-grained granite, which undergoes more uniform strain under real-time low-temperature conditions, leading to less significant changes in the internal pore structure. This behavior contrasts with the one-dimensional gas permeability observed in granite specimens subjected to freeze–thaw cycles. The differing trends in gas permeability under these two testing conditions can be explained by the fact that dry granite specimens, when exposed to real-time low temperatures, experience damage primarily due to the cold contraction of the rock. In contrast, saturated granite specimens subjected to freeze–thaw cycles undergo additional complex damage due to the water-ice phase transition, which further contributes to the degradation of the rock’s internal structure.

3.4. NMR Test Results

3.4.1. Analysis of T₂ Distribution Curve

Nuclear magnetic resonance (NMR) tests were conducted on water-saturated granite specimens before and after freeze–thaw cycles, resulting in T₂ distribution curves for granite samples with different particle sizes. As shown in Figure 12, the T₂ values for coarse-grained granite ranged from 0.01 to 1000 ms, while those for fine-grained granite ranged from 0.01 to 100 ms. This indicates that, compared to fine-grained granite, coarse-grained granite exhibits a broader pore size distribution and a larger maximum pore radius.

The T₂ distribution curves of fine-grained granite before and after the freeze–thaw cycles were primarily characterized by two peaks, with the first peak showing a significantly higher signal intensity than the second. This suggests that the internal pore structure of fine-grained granite is dominated by small-sized pores. As the freezing temperature decreased, the position of the first peak shifted slightly to the right, while its amplitude remained largely unchanged. In contrast, the second peak not only shifted to the right but also increased in intensity. These observations imply that the pore size corresponding to the first peak increased after the freeze–thaw cycle, though the quantity of these pores remained stable, whereas both the size and number of pores associated with the second peak increased.

For coarse-grained granite, the T₂ distribution curve before the freeze–thaw cycle also displayed two distinct peaks. However, when the freezing temperature was reduced to between −20 °C and −90 °C, the curve exhibited three peaks, indicating the emergence of a new class of pores. When the temperature was further reduced to −120 °C, the number of peaks reverted to two. This suggests that the freeze–thaw process led to the development of a new range of pore sizes in coarse-grained granite, resulting in significant alterations to its pore structure. Notably, at −120 °C, the pore structure of the coarse-grained granite appeared to be more fully developed, with enhanced connectivity between pores.

The microstructural changes observed in both granite types after freeze–thaw treatment align with the trends in intrinsic gas permeability under varying confining pressures, thereby validating the consistency between microscopic pore evolution and macroscopic permeability behavior.

The total area under the T₂ distribution curve can be used to represent the porosity of the rock, serving as a critical indicator of changes in pore volume. The variation in the total area of the T₂ distribution curves with freezing temperature is shown in Figure 13. As the freezing temperature gradually decreases, pore initiation and propagation occur within both granite types due to the combined effects of the water-ice phase transition and the contraction and deformation of mineral particles. This leads to an upward trend in the total area of the T₂ distribution curve, indicating a significant increase in pore volume as a result of freeze–thaw-induced damage.

Under identical freeze–thaw conditions, coarse-grained granite consistently exhibits a larger total T₂ area compared to fine-grained granite, suggesting that the latter has a lower porosity and a denser pore structure. As freezing temperature decreases, the total T₂ area for both granite types generally follows a pattern of increase–decrease–increase. Compared to the range of −20 °C to −60 °C, a more substantial increase in the total T₂ area is observed when temperatures drop to −90 °C and −120 °C, and a declining trend is seen in the −40 °C to −60 °C range. It coincides with the law that the rate of change of 1D gas permeability of granite changes with temperature. Therefore, this phenomenon can be attributed to variations in the freezing point of pore water across different pore sizes, which results in minimal changes to the granite’s pore structure within the temperature range of −40 °C to −60 °C.

By comparing the rate of change in the total T₂ area between the two granite types, it is evident that fine-grained granite experiences a more pronounced increase in pore volume after undergoing freeze–thaw cycles. This trend closely mirrors the changes observed in the 1D intrinsic gas permeability of granite, further reinforcing the relationship between microstructural pore evolution and macroscopic permeability behavior.

3.4.2. Changes in Pore Size Distribution

Based on the data presented in Figure 13 and Equation (7), the pore size distribution of coarse and fine granite before and after freeze–thaw cycles can be derived. In this study, granite rock pores are classified into three categories: micropores (r < 0.1 μm), mesopores (0.1 μm ≤ r ≤ 1 μm), and macropores (r > 1 μm) as per previous studies [45]. The area under the curves in Figure 14 directly reflects the trend of changes in various pore sizes within the granite specimens.

The pore volume of the granite specimens correlates positively with the area of the pore size distribution curve. By integrating the area of the three pore size intervals shown in Figure 14, the volume occupied by each pore type can be calculated. The variation trends in pore volume and the proportion of each pore type with temperature for the two granites are shown in Figure 15, Figure 16 and Figure 17. The volume proportion of macropores in coarse-grained granite is the largest, followed by mesopores, while micropores constitute the smallest proportion. From the pore distribution changes in Figure 15 and Figure 17, it can be seen that when the temperature is higher than −20 °C, new micropores form within coarse-grained granite, while mesopores expand and transition into macropores. This results in an increase in both the volume and proportion of micropores and macropores, while the volume and proportion of mesopores decrease. As the freezing temperature decreases further, micropores continue to form and gradually develop into mesopores, resulting in the stabilization of micropore volume, although its proportion decreases. Simultaneously, the volume of macropores increases, but their volume proportion decreases, indicating that mesopores continue to expand into macropores, although the rate of increase in macropore volume is slower than that of mesopores. Therefore, at lower freezing temperatures, the freeze–thaw damage to coarse-grained granite is primarily characterized by the continuous formation of micropores, which subsequently develop into mesopores.

Fine-grained granites do not have macropores within them and contain only micropores and mesopores. The change in pore volume inside fine-grained granite takes −60 °C as the cut-off point; when the freezing temperature is higher than −60 °C, the volume of micropores inside fine-grained granite increases, and there are no mesopores. When the freezing temperature dropped below −60 °C, the volume of micropores began to decrease, while mesopores began to appear and gradually increased in volume, and finally the proportion of mesopore volume exceeded that of micropores at −120 °C. This suggests that new micropores are constantly produced inside the fine-grained granite when the freezing temperature is high. With the further decrease in temperature, these micropores gradually developed and expanded into mesopores, resulting in a continuous increase in mesopore volume. The decrease in the volume of micropores further suggests that the freeze–thaw damage of fine-grained granite at lower freezing temperatures is mainly reflected in the transformation and expansion of micropores into mesopores.

When considering the effects of confining pressure and temperature on the gas permeability of granite after freeze–thaw cycles, it is observed that at higher freezing temperatures, only the water in the smaller pores of both granite types freezes into ice. As a result, freeze–thaw damage is minimal, leading to the formation of only tiny pores in both types of granite. However, as the temperature decreases from −60 °C to −90 °C, the larger pores in the granite begin to gradually freeze, which increases the freeze–thaw damage in both granite types. Coarse-grained granite, due to its relatively lower strength, is unable to withstand the freezing and expansion of ice as well as the contraction of rock particles. This results in the separation of pore tips, creating new pores, which then continue to expand and propagate. This process is manifested as the continuous formation of micropores, which then develop into mesopores. And due to the higher strength and stiffness of fine-grained granite, the freezing and expansion of ice as well as the contraction of rock particles can only widen most of the original pores in fine-grained granite, not enough to produce new pores; i.e., it is manifested as a process of transformation and expansion of micropores to mesopores.

3.5. Relationship Between Pore Structure and Permeability

3.5.1. Contributing Porosity of Granite

In practical applications, although porosity may be consistent, different pore size distributions within a rock can lead to variability in permeability. Therefore, it is crucial to consider both pore size and porosity when assessing permeability. Zhang et al. [46] introduced a metric called “contributing porosity,” defined as the product of porosity and the proportion of relevant pore size to overall porosity within a given size range. This metric quantifies the proportion of pores within a specified size range, reflecting the combined effect of pore size and porosity on gas permeability. The contributing porosities for different pore size ranges before and after freeze–thaw cycling in granite are presented in

Table 5. Contributing porosity (%) of granite in different pore size ranges.

Particle	Coarse-Grained Granite			Fine-Grained Granite
Temperature	Pore Size Distribution Range
	<0.1 μm	0.1~1 μm	>1 μm	<0.1 μm	0.1~1 μm
20 °C	0.003	0.030	0.793	0.449	0.000
−20 °C	0.040	0.035	2.857	2.353	0.000
−40 °C	0.015	0.176	5.129	13.498	0.000
−60 °C	0.076	0.451	11.503	9.125	4.116
−90 °C	0.039	0.944	13.693	10.416	9.874
−120 °C	0.049	1.437	22.154	8.446	19.003

.

3.5.2. Relationship Between Pore Size Distribution and Gas Permeability

To gain a deeper understanding of how low temperatures affect the gas permeability properties of granite, the 1D intrinsic gas permeability before and after freeze–thaw cycles is analyzed in conjunction with the contributing porosity. This investigation explores how freeze–thaw cycles alter the pore structure within granites of two different grain sizes, coarse and fine, leading to changes in its permeability properties. The relationship between each contributing porosity and the permeability of granite before and after freeze–thaw cycling can be determined across different pore size distributions. Based on the findings in Section 3.4.2, it is evident that the pore size distribution of both granites shows a clear distinction at −60 °C. Therefore, when analyzing the relationship between pore size distribution and gas permeability of granite before and after freeze–thaw cycles, the analysis should be conducted with −60 °C as the cut-off point.

The 1D intrinsic gas permeability under a confining pressure of 5 MPa is studied as an example. The relationship between each contributing porosity and the permeability of granite is shown in Figure 18 and Figure 19. As shown in Figure 18, within the freezing temperature range of 20 °C to −40 °C, a strong positive correlation exists between the contributing porosity of macropores (pore size >1 μm) and intrinsic gas permeability, with a correlation coefficient of 0.989. The correlation coefficients for macropores with a pore size of <0.1 μm and mesopores (pore size between 0.1 μm and 1 μm) are 0.152 and 0.709, respectively. This indicates that, in the temperature interval from 20 °C to −40 °C, the change in intrinsic gas permeability of coarse-grained granite is primarily controlled by macropores during freeze–thaw cycles. In the temperature range from −60 °C to −120 °C, both mesopores and macropores show highly correlated positive relationships with intrinsic gas permeability, with correlation coefficients of 0.992 and 0.944, respectively. This suggests that during this temperature range, freeze–thaw cycling affects the intrinsic gas permeability of coarse-grained granite through a combined influence of mesopores and macropores.

From Figure 19, it can be observed that in the temperature range from 20 °C to −40 °C, the contributing porosity of micropores and the intrinsic gas permeability exhibit a strong positive correlation, with a correlation coefficient of 0.998. In contrast, the correlation coefficient for mesopores is only 0.319. This suggests that, in the temperature interval from 20 °C to −40 °C, the changes in the intrinsic gas permeability of fine-grained granite are primarily controlled by micropores. When the temperature ranges from −60 °C to −120 °C, the contributing porosity of mesopores and the intrinsic gas permeability show a highly correlated positive relationship, with a correlation coefficient of 0.985. This indicates that, within this temperature range, the changes in the intrinsic gas permeability of coarse-grained granite due to freeze–thaw cycles are primarily controlled by mesopores.

4. Conclusions

In this paper, 1D intrinsic gas permeability tests and nuclear magnetic resonance (NMR) tests were conducted before and after freeze–thaw cycles on coarse- and fine-grained granite. The effect of low temperature on the gas permeability of different particle sizes was analyzed in conjunction with 2D intrinsic gas permeability tests under real-time low-temperature conditions. The main conclusions drawn are as follows:

(1)

The low dispersion of the 1D and 2D gas permeability test results of coarse-grained granite in the initial state indicates that the pore structure between different specimens of coarse-grained granite is more stable than that of fine-grained granite. As the freezing temperature decreases, the 1D intrinsic gas permeability of granite increases. Due to differences in the freezing point of pore water corresponding to pores of different sizes, the change trend in intrinsic gas permeability in different freezing temperature intervals varies significantly. At the same freezing temperature, the change in intrinsic gas permeability of fine-grained granite is significantly higher than that of coarse-grained granite, indicating that fine-grained granite is more sensitive to freeze–thaw damage.

(2)

In real-time cryogenic environments, both granites exhibit a linear increase in 2D gas permeability with a gradual decrease in freezing temperature. Additionally, the greater the 2D gas permeability of the granite at room temperature, the faster the rate of increase in permeability with decreasing temperature.

(3)

In real-time cryogenic environments, the two granites exhibited a linear increase in 2D gas permeability with a gradual decrease in freezing temperature. In addition, the greater the 2D gas permeability of the granite at room temperature, the faster the rate of increase in permeability with decreasing temperature.

(4)

Coarse-grained granite contains micropores (r < 0.1 μm), mesopores (0.1 μm ≤ r ≤ 1 μm), and macropores (r > 1 μm), with macropores being the dominant pore structure. In contrast, fine-grained granite consists of micropores and mesopores, with mesopores occupying a dominant position. As the freezing temperature decreases, the volume proportion of micropores and macropores in coarse-grained granite decreases, while mesopores increase. In fine-grained granite, the volume proportion of micropores decreases, and mesopores increase.

(5)

Among the factors influencing freeze–thaw damage in rocks, lithology plays a dominant role. When the freezing temperature is relatively low, the two types of granite exhibit distinct patterns of freeze–thaw damage evolution. In coarse-grained granite, the damage is primarily manifested in the initiation and expansion of newly formed pores, with new micropores continuously forming and developing into mesopores. In contrast, the freeze–thaw damage in fine-grained granite is more prominently reflected in the intensified expansion of pre-existing pores, with original micropores continuously developing and eventually transforming into mesopores.

(6)

In the temperature range of 20 °C to −20 °C, the intrinsic gas permeability of coarse-grained granite is primarily controlled by macropores, while fine-grained granite is dominated by micropores. When the temperature decreases further to the −60 °C to −120 °C interval, the intrinsic gas permeability of coarse-grained granite is influenced by a combination of mesopores and macropores, whereas fine-grained granite is primarily controlled by mesopores.

5. Engineering Implications

(1)

The significant increase in gas permeability with decreasing freezing temperature, particularly for fine-grained granite, indicates that temperature fluctuations in cryogenic environments must be carefully considered when designing underground LNG storage facilities. Fine-grained granite’s higher sensitivity to freeze–thaw damage could lead to higher permeability and potential leakage risks over time. Thus, temperature control and monitoring strategies are critical to mitigate such risks.

(2)

The distinct patterns of freeze–thaw damage between coarse-grained and fine-grained granite emphasize the need for tailored materials in LNG storage construction. Coarse-grained granite, with its focus on macropores, may be more resilient to freeze–thaw cycles, while fine-grained granite, with its pre-existing micropores, may undergo more significant damage. This should influence the selection of materials for long-term underground storage, particularly in regions where temperature cycling is a concern.

6. Outlook

(1)

The operating temperature of underground LNG is approximately −162 °C, while the lowest temperature in this study is −120 °C. Future research could explore gas permeability at temperatures as low as −162 °C or even lower.

(2)

In future microstructural studies, it may be valuable to incorporate experimental methods such as scanning electron microscopy (SEM) and computed tomography (CT), with a particular emphasis on −60 °C as a critical threshold. Robust and efficient vision-based models, such as DeepLab [47] and EfficientNet [48], could be utilized to carefully examine the damage effects of low temperatures on the microstructure of rocks.