Gas Permeability Change With Deformation and Cracking of a Sandstone Under Triaxial Compressiongas Permeability Change With Deformation and Cracking of a Sandstone Under Triaxial Compression

-Abstract: 51 In this paper, a THMC (Thermal-Hydrological-Mechanical-Chemical) multi-field coupling 52 triaxial cell was used to systematically study the evolution of gas permeability and the 53 deformation characteristics of sandstone. The effects of confining pressure, axial pressure, and 54 air pressure on gas permeability characteristics were fully considered in the test. The gas 55 permeability of sandstone decreases with increasing confining pressure. When the confining 56 pressure is low, the variation of gas permeability is greater than the variation of gas permeability 57 at high confining pressure. The gas injection pressure has a significant effect on the gas 58 permeability evolution of sandstone. As the gas injection pressure increases, the gas 59 permeability of sandstone tends to decrease. At the same confining pressure, the gas 60 permeability of the sample during the unloading path is less than the gas permeability of the 61 sample in the loading path. When axial pressure is applied, it has a significant influence on the 62 permeability evolution of sandstone. When the axial pressure is less than 30 MPa, the gas 63 permeability of the sandstone increases as the axial pressure increases. At axial pressures 64 greater than 30 MPa, the permeability decreases as the axial pressure increases. Finally, the 65 micro-pore/fracture structure of the sample after the gas permeability test was observed using 66 3D X-ray CT imaging. 67


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In this paper, a THMC (Thermal-Hydrological-Mechanical-Chemical) multi-field coupling 52 triaxial cell was used to systematically study the evolution of gas permeability and the 53 deformation characteristics of sandstone. The effects of confining pressure, axial pressure, and 54 air pressure on gas permeability characteristics were fully considered in the test. The gas 55 permeability of sandstone decreases with increasing confining pressure. When the confining 56 pressure is low, the variation of gas permeability is greater than the variation of gas permeability 57 at high confining pressure. The gas injection pressure has a significant effect on the gas 58 permeability evolution of sandstone. As the gas injection pressure increases, the gas 59 permeability of sandstone tends to decrease. At the same confining pressure, the gas 60 permeability of the sample during the unloading path is less than the gas permeability of the 61 sample in the loading path. When axial pressure is applied, it has a significant influence on the 62 permeability evolution of sandstone. When the axial pressure is less than 30 MPa, the gas 63 permeability of the sandstone increases as the axial pressure increases. At axial pressures 64 greater than 30 MPa, the permeability decreases as the axial pressure increases. Finally, the 1 Introduction 70 Natural gas is considered to be a cleaner and more efficient energy source than oil and coal.

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Unconventional resources, such as tight sandstone gas, are at the bottom of the global natural 72 gas resource pyramid. However, its potential resources are considerably greater than the 73 conventional natural gas reserves (Khlaifat et al., 2011). At present, although the exploitation 74 of tight sandstone gas is still in its early stages, its reserves are relatively large, with recoverable 75 reserves of approximately 1/3 of the total amount of natural gas. Sandstone gas is a typical 76 unconventional natural gas resource stored in low-permeability or ultra-low-permeability tight 77 sandstone reservoirs. Sandstone gas is difficult to mine by conventional techniques. Therefore, 78 it is usually necessary to produce natural gas of economic value through large-scale fracturing 79 or special gas recovery process technology (

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Results indicate that crack closure primarily causes the reduction in the effective permeability 87 of the gas due to the increase in the confining pressure under the condition of constant water 88 content. In addition, studies have also found that some samples even have a large dispersion of 89 initial effective permeability. However, there is a confining pressure-saturation threshold, and 90 when this threshold is exceeded, the effective gas permeability of the samples decreases 91 abruptly Fu et al., 2015;Wang et al., 2017b). However, these studies have 92 neglected the evolution of gas permeability after sample fracture. In mining, the gas 93 permeability of sandstone after fracturing is a highly important parameter that cannot be 94 ignored. In addition, the microscopic pore structure after fracturing is of great significance for

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In this paper, we focused on the evolution of gas permeability during cyclic loading and 101 unloading and considered the effect of air pressure on gas permeability characteristics.

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Furthermore, we also studied the evolution law of gas permeation of sandstone during 103 fracturing and reconstructed the fractured specimen by CT scanning to observe the internal pore 104 fracture structure. The permeability calculation was performed using the steady-state method, which works well 125 for samples with a permeability higher than 10 -19 m 2 and has been used widely in many 126 studies (Liu et al., 2020;Liu et al., 2015). Another reason is that we need to carry out 127 Klinkenberg (or slip) experiments, and the steady-state method is easier to implement. This 128 study also applied this method combined with our gas permeability test device ( Figure 3). The 129 servo system controls the confining pressure/axial pressure. To ensure safety, Argon was 130 chosen and injected from the gas source into a set volume cylinder (0.4 ml). The gas was later 131 injected into a triaxial pressure chamber at a given pressure 1 , and the gas pressure drop ∆ 132 was recorded over time ∆ . The average pressure ( P mean ) in the cylinder during ∆ is -2 -P mean = 1 − ∆ /2. Darcy's law states that the formula for determining the effective gas 134 permeability (k eff) is as follows: where is the fluid's dynamic viscosity (2.2 × 10 5 Pa • s), 0 is buffer reservoir's volume, is the intrinsic permeability; l is the average free path of the gas molecule; r is the pore 151 radius; c is the scale factor; b is the Klinkenberg coefficient or the slip factor, and P is the pore 152 pressure. The slip factor is defined as where κ is the Boltzmann constant, and T is the absolute temperature.

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Similarly, when the confining pressure is less than 5 MPa, the deformation of the sample is -2 -large. Above 5 MPa, the deformation of the sample is less sensitive to the confining pressure.

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In the second loading and unloading cycle, the deformation of the sample is mainly in the elastic 205 range, and some deformation is unrecoverable compared with the first cycle.  After the gas permeability test, sample C1 was scanned using a 3D X-ray Microanalyser. The 269 image resolution was 53.14 µm, which was scanned a layer at a time from top to bottom. After 270 the scanning was completed, a total of 500 slices were selected. Before reconstruction, image 271 enhancement and threshold segmentation are required. The whole process is shown in Figure   272 9. These slices were three-dimensionally reconstructed by a compiled algorithm to obtain a 273 three-dimensional reconstruction model of the sample. 274 275 Figure 9 Flow chart of 3D reconstruction of the digital core.
-2 -As shown in Figure 10, there is a macroscopic crack in the height direction at an angle of 277 45℃ + 2 ( is internal friction angle). CT scanning can identify rock fracture surfaces when 278 only macro cracks can be visible on the surface. This is primarily due to rock shear failure.

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With the gradual increase in axial pressure in the static condition confining pressure, the friction 280 between the particles in the rock mass also gradually increases. When it reaches a certain value, 281 the rock mass particles will dislocate, and shear failure occurs. In addition to the shear fracture 285 Figure 11 shows the evolution of the crack generation and permeability. Phase I: in the initial 286 stage, the stress on the pore structure of the sample is weak due to the small axial pressure.

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Therefore, the permeability remains largely unchanged. Phase II: as the axial pressure 288 increases, the micro-crack appears in the sample, and the gas permeability increases gradually.

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When a crack (shear failure) is generated at an angle of 45℃ ± 2 degree in the height 290 direction, the gas permeability is maximized. Phase III: as the axial pressure increases, the axial 291 pressure will compress the crack, decreasing permeability. Therefore, the evolution of 292 permeability during the complete process varies as follows: stable → slowly increasing → we make a comparative analysis of different algorithms. Figure 12

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Where is the pore connectivity, is the total volume of the connected pores, and is 318 the total pore volume. The calculated pore connectivity of the sample is 64.41%. According to 319 Figure

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Especially at the initial loading stage (confining pressure less than 5 MPa), the gas permeability 329 decreased by 7.59 and 2.27 times for samples C1 and C2, respectively. From 5 MPa to 20 MPa, 330 the gas permeability decreased only a little. This means that most of the pores in the initial stage 331 that allow the gas to flow have been closed, and subsequent pressurization has less effect on 332 the deformation of the pore structure. After two loading and unloading cycles, the gas 333 permeability recovered to 4.07×10 -16 m 2 (C1) and 2.51 ×10 -16 m 2 (C2), which is fairly different 334 from the initial value. This finding indicates that some of the pores have been plastically 335 deformed and cannot be recovered.

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When axial pressure is applied, the gas permeability gradually increases due to the expansion 337 of the crack. When macroscopic cracks are generated, the permeability reaches a maximum.

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The axial pressure increased further, and the permeability reduced due to the compaction of the 339 axial pressure on the macro crack. Based on microscopic CT images, the cracks are mainly 340 oriented at a 45 ℃ -degree angle along the height direction. Further quantitative analysis -2 -revealed that the porosity was approximately 7.28%, which was relatively tight and indirectly 342 verified the phenomenon of low macroscopic gas permeability. In addition, different algorithms 343 have a greater impact on digital image characterization, and further research is needed.

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In addition, we also considered the Klinkenberg (gas slippage) effect and found that when the 345 gas pressure exceeds 2 MPa, the change in gas pressure has little effect on the permeability.

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There is no significant difference in the gas slippage effect under different confining pressures, 347 and the slippage effect in the loading stage is clearer than that in the unloading stage. Studies 348 have also found that the slip factor tends to increase as the intrinsic permeability decreases.

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This phenomenon can be primarily attributed to the pore structure being subjected to pressure 350 and causing the pore size to decrease. As a result of this increased collision frequency between 351 the gas molecules and the inner wall of the pores, the gas exhibits a slip phenomenon and 352 increasing the slip factor.