# Experimental Study and Percolation Analysis on Seepage Characteristics of Fractured Coal and Sandstone Based on Real-Time Micro-CT

Authors: Zhaoxing Lv; Qianqian Ji; Weijie Ren
Journal: Geofluids
 (2020)

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## Abstract

Sandstone and coal are the two most common types of reservoirs in nature. The permeability of sandstone in oil-bearing formations controls its oil and gas production; the permeability of the coal seam containing gas has a crucial influence on the gas drainage efficiency. One of the main factors affecting rock permeability is the spatial distribution and connectivity of pores and fissures in the rock. In this paper, a small-sized sample with a diameter of 5 mm and a height of 10 mm was used for the test. The rock samples under different stress states were scanned in real-time during the seepage testing. Based on 2D images, a 3D digital sample was reconstructed. We extracted the pores and fissures from the 3D digital sample, studied the size and distribution of the largest cluster in the sample, and revealed the influence of confining pressure and seepage pressure on the percolation probability and permeability of the sample. The research results show that brittle sandstone and plastic coal, two types of rocks with completely different properties of mechanics, have obvious differences in the spatial distribution of the largest clusters. Under the same stress state, in brittle sandstone-like rocks, the connectivity of the fissures is the primary factor affecting permeability, and the pores are the auxiliary factor; for plastic rocks such as coal, the situation is just the opposite, pores are the primary factor affecting permeability, and fissures are the auxiliary factor. The research results answer the question: Hydraulic fracturing technology can increase the oil and gas production of sandstone reservoirs but cannot increase the drainage efficiency of coalbed methane.


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## Body

## 1. Introduction

Rock is a natural porous medium material with a large number of randomly distributed pores and fissures inside, pores and fissures constitute the voids in the rock, and the distribution and connectivity of these voids have a vital impact on the permeability of the rock. Besides, rocks are rich in energy resources, especially sedimentary rocks such as sandstone and coal. The permeability of these rocks is of great significance to the extraction of oil, natural gas, and methane. Therefore, the permeability of sandstone and coal and the distribution of pores and fissures have long been the research focus of scholars.Pores and fissures in rocks provide storage space and transport passage for fluids, so studying the distribution characteristics of pore fissures is a basic work. The current experimental methods used to study pores and fissures mainly include the following: mercury intrusion porosimetry (MIP) [1, 2], gas adsorption (N2/CO2) [3, 4], computerized tomography (CT) [5–8], and nuclear magnetic resonance (NMR) [9–11]. But these methods have certain limitations; MIP is highly likely to destroy the pore structure due to the high-pressure injection of mercury, which may result in some misleading information on the pores [12–14]. The gas adsorption method cannot destroy the pore structure, but it can only be used for dry rock samples and not for water-bearing samples [15], and it is assumed that the shape of the pores is cylindrical [4]; NMR is a fast, nondestructive method for characterizing porous media microstructures. However, in terms of microstructure characterization, NMR has a poor recognition effect on macropores. Moreover, the metal minerals in the sample may affect the NMR relaxation time T2 distribution [16, 17]. Compared with the above methods, micro-CT is a nondestructive and high-precision visualization scanning technology [5, 18], which has been widely used. Micro-CT not only makes it possible to analyze pores and fissures with a spatial resolution of several microns but also obtains pore-throat size distribution information such as pore diameter, throat duct length, and pore connectivity [19, 20]. Wang et al. [7, 21] studied the microscopic structure, coal deformation, and water transport behaviors of heterogeneous coal by using micro-CT. Shi et al. [22] analyzed the detailed structure of microfractures in different rank coals through micro-CT scanning and determined the effects of coal rank on the physical properties of microfractures.In the study of rock permeability, Heiland [23] used sandstone as the research object to study the permeability characteristics during deformation and failure processes and the evolution of rock permeability before and after failure; Chen et al. [24] also used sandstone in a triaxial compression test to conduct experimental research on the deformation characteristics, permeability change law, and acoustic emission characteristics of the confining pressure unloading process, and the test results illustrated a correlation between the deformation characteristics, acoustic emission, and permeability of the rock during unloading; Wang et al. [25] used a rock mechanic test system to conduct triaxial compression tests on sandstone and limestone; their results revealed the evolutionary characteristics of permeability during rock failure and the relationship between rock strength, deformation, and permeability before and after failure.In terms of rock seepage research based on micro-CT, the current main research idea is to obtain a 3D digital rock sample through CT scanning of the rock sample, then use the numerical simulation method to study the change law of the permeability of the digital rock sample, and finally establish the rock seepage model by comparing the simulation results with the actual seepage test results [26–28]. Because of the lack of seepage experiment equipment that can perform real-time CT scanning, there are few studies on how the distribution and connectivity of pores and fissures change with the increment of confining pressure and seepage pressure during the seepage test and what is the relationship between the connectivity of pores and fissures and rock permeability.To solve the above problems, in this paper, we newly developed a set of special experimental equipment, which can scan rock samples with micro-CT while conducting seepage tests, and studied the distribution and connectivity of pores and fissures in the rock samples, and the relationship between the connectivity of pores and fissures and confining pressure and seepage pressure based on real-time micro-CT scan.


## 2. Experiment

### 2.1. Sample Preparation

The yellow sandstone used in this test was collected from a quarry in the suburbs of Neijiang city, Sichuan Province; this sandstone, with medium compressive strength, good homogeneity, and few visible natural fissures, is an ideal material for studying the permeability of the brittle rock. The coal samples were retrieved from an underground mine located in the Qinshui Basin in the southeastern part of Shanxi Province in China, coated with wax, and transported to the laboratory. The coal categorized as anthracite has low strength, uniform texture, high porosity, and abundant natural microfissures; it is a plastic rock.The main reasons for choosing these two kinds of rocks as research objects are as follows: The main purpose of this paper is to study the influence of confining pressure and seepage pressure on 1the permeability of brittle and plastic rocks after failure, to obtain the changing pattern of the connectivity of pores and fissures with the increment of stresses. For brittle rocks, sandstone with no obvious bedding meets this requirement. At the same time, it contains a large number of uniformly distributed pores, so the yellow sandstone used in the experiment is an ideal rock for studying seepage [29–31]. For plastic rocks, coal is a kind of rock with obvious plastic deformation characteristics. However, in most types of coals, joints and bedding are developed and unevenly distributed, which will affect the test results; in order to eliminate this effect, we selected this kind of anthracite with high porosity and relatively good homogeneity as the research object. The processed coal samples and sandstone samples with a diameter of 5 mm and a height of 10 mm are shown in Figure 1.Figure 1
Yellow sandstone samples and coal samples.


### 2.2. Experimental Apparatus

#### 2.2.1. High-Resolution Micro-CT System

The model of the high-resolution micro-CT system used in this test isμCT225kvFCB. The system consists of an X-ray source, an amorphous silicon flat-panel detector, and a sample stage. The amorphous silicon flat-panel detector used for image acquisition is composed of 3200×2232 pixels, and the size of each pixel is 127 μm, as shown in Figure 2. Digital control is adopted to move the sample stage in the three directions of X, Y, and Z, which can realize high-precision positioning.Figure 2
High-resolution micro-CT system.The main parameters of scanning are operating current of 120μA, working voltage of 100 kV, the exposure time of 2 s per image, and the geometric magnification of 36.04; the resolution of each pixel was 5.38 μm, which means that the smallest pore size that can be identified was 5.38 μm. During the scanning, the rotation angle of the sample stage was 0.9° for each projection, the sample stage was rotated 360°, and the number of projections was 400.


#### 2.2.2. Mini Triaxial Seepage Testing Machine

The testing machine used in this test is newly developed by our research team; it is developed for miniature rock sample (5-7 mm in diameter and 10-20 mm in height). This machine can be used for uniaxial compression experiments, triaxial compression experiments, seepage experiments, and real-time CT scanning. The stiffness of the testing machine is0.8×104kN/m, the elastic modulus of the loading device is 206 GPa, the shear modulus is 80 GPa, and Poisson’s ratio is 0.26. The elastic modulus of the applicable sample is 0.25-5 GPa, Poisson’s ratio is 0.11-0.25, and the stiffness is 0.1−1×102kN/m.The mini triaxial seepage testing machine consists of an axial loading device, axial stress sensor, axial stress display, confining pressure input port, seepage pressure input port, and triaxial pressure chamber, as shown in Figure3.Figure 3
Mini triaxial seepage testing machine: ① rock sample, ② seepage pressure input, ③ axial stress display, ④ triaxial pressure chamber, ⑤ confining pressure input, ⑥ axial stress sensor, and ⑦ axial loading device.


#### 2.2.3. Seepage Test System for Real-Time CT Scanning

The system can perform a CT scan of the sample in real-time while conducting the seepage test and obtain the variation trend of the connectivity of pores and fissures in the rock sample in different stress fields. This system is shown in Figure4.Figure 4
Seepage test system for real-time CT scanning and its schematic: ① water pump, ② accumulator, ③ pressure meter, ④ and ⑤ valve, ⑥ mini triaxial seepage testing machine, ⑦ confining pressure input line, and ⑧ seepage pressure input line.Confining pressure and seepage pressure are loaded with a water pump, and the loading medium is distilled water. When confining pressure needs to be applied, close the valve ⑤, open the valve ④, and pressurize with a high-precision water pump ①; when seepage pressure needs to be applied, close the valve ④ and open the valve ⑤. In this way, the system can switch freely between the two pressure lines. To ensure the stability of the pressure on the line, an accumulator is connected to each line. During the seepage test, the mini triaxial seepage testing machine ⑥ is fixed on the sample stage of the micro-CT to perform real-time scanning.


### 2.3. Experimental Method

One of the research objects in this paper is the seepage characteristics of rock samples after failure. Therefore, before the seepage test, an increasing axial load is applied to the sample under prefixed confining pressure until the sample reaches the strength limit and fails. Then, keep the axial strain constant, unload the confining pressure, start reloading the confining pressure and seepage pressure, measure the permeability of the rock sample, and perform real-time CT scanning.3D digital rock samples can be reconstructed based on 2D grayscale images obtained by CT scanning; in digital rock samples, the higher the gray value, the greater the density of the pixel. To study the connectivity of pores and fissures under different stress conditions, it is first necessary to identify and extract the pores and fissures; the most commonly used method is to binarize the digital sample. In this process, the selection of threshold is a very important step, which determines the accuracy of identifying pores and fissures. Here, the method of segmentation of the DTM threshold is used [32]. Figure 5 is a comparison of sandstone images before and after binary processing.Figure 5
Sandstone images before and after binary processing.
(a)
Before binary processing(b)
After binary processingAccording to the method above, a spatial skeleton composed of pores is reproduced. In the skeleton, all of the adjacent pores formed a connected cluster, and there are lots of clusters in the 3D digital sample. We called the cluster that contains the largest number of pore pixels “the largest cluster.” As the porosity of the sample increases, the number of pore pixels contained in the largest cluster will increase [33]. The percolation probability of the 3D digital sample can be expressed by the following formula:(1)P=MN,where P is the percolation probability. M is the number of pore pixels contained in the largest cluster. N is the total number of pixels in the 3D digital sample.


## 2.1. Sample Preparation

The yellow sandstone used in this test was collected from a quarry in the suburbs of Neijiang city, Sichuan Province; this sandstone, with medium compressive strength, good homogeneity, and few visible natural fissures, is an ideal material for studying the permeability of the brittle rock. The coal samples were retrieved from an underground mine located in the Qinshui Basin in the southeastern part of Shanxi Province in China, coated with wax, and transported to the laboratory. The coal categorized as anthracite has low strength, uniform texture, high porosity, and abundant natural microfissures; it is a plastic rock.The main reasons for choosing these two kinds of rocks as research objects are as follows: The main purpose of this paper is to study the influence of confining pressure and seepage pressure on 1the permeability of brittle and plastic rocks after failure, to obtain the changing pattern of the connectivity of pores and fissures with the increment of stresses. For brittle rocks, sandstone with no obvious bedding meets this requirement. At the same time, it contains a large number of uniformly distributed pores, so the yellow sandstone used in the experiment is an ideal rock for studying seepage [29–31]. For plastic rocks, coal is a kind of rock with obvious plastic deformation characteristics. However, in most types of coals, joints and bedding are developed and unevenly distributed, which will affect the test results; in order to eliminate this effect, we selected this kind of anthracite with high porosity and relatively good homogeneity as the research object. The processed coal samples and sandstone samples with a diameter of 5 mm and a height of 10 mm are shown in Figure 1.Figure 1
Yellow sandstone samples and coal samples.


## 2.2. Experimental Apparatus

### 2.2.1. High-Resolution Micro-CT System

The model of the high-resolution micro-CT system used in this test isμCT225kvFCB. The system consists of an X-ray source, an amorphous silicon flat-panel detector, and a sample stage. The amorphous silicon flat-panel detector used for image acquisition is composed of 3200×2232 pixels, and the size of each pixel is 127 μm, as shown in Figure 2. Digital control is adopted to move the sample stage in the three directions of X, Y, and Z, which can realize high-precision positioning.Figure 2
High-resolution micro-CT system.The main parameters of scanning are operating current of 120μA, working voltage of 100 kV, the exposure time of 2 s per image, and the geometric magnification of 36.04; the resolution of each pixel was 5.38 μm, which means that the smallest pore size that can be identified was 5.38 μm. During the scanning, the rotation angle of the sample stage was 0.9° for each projection, the sample stage was rotated 360°, and the number of projections was 400.


### 2.2.2. Mini Triaxial Seepage Testing Machine

The testing machine used in this test is newly developed by our research team; it is developed for miniature rock sample (5-7 mm in diameter and 10-20 mm in height). This machine can be used for uniaxial compression experiments, triaxial compression experiments, seepage experiments, and real-time CT scanning. The stiffness of the testing machine is0.8×104kN/m, the elastic modulus of the loading device is 206 GPa, the shear modulus is 80 GPa, and Poisson’s ratio is 0.26. The elastic modulus of the applicable sample is 0.25-5 GPa, Poisson’s ratio is 0.11-0.25, and the stiffness is 0.1−1×102kN/m.The mini triaxial seepage testing machine consists of an axial loading device, axial stress sensor, axial stress display, confining pressure input port, seepage pressure input port, and triaxial pressure chamber, as shown in Figure3.Figure 3
Mini triaxial seepage testing machine: ① rock sample, ② seepage pressure input, ③ axial stress display, ④ triaxial pressure chamber, ⑤ confining pressure input, ⑥ axial stress sensor, and ⑦ axial loading device.


### 2.2.3. Seepage Test System for Real-Time CT Scanning

The system can perform a CT scan of the sample in real-time while conducting the seepage test and obtain the variation trend of the connectivity of pores and fissures in the rock sample in different stress fields. This system is shown in Figure4.Figure 4
Seepage test system for real-time CT scanning and its schematic: ① water pump, ② accumulator, ③ pressure meter, ④ and ⑤ valve, ⑥ mini triaxial seepage testing machine, ⑦ confining pressure input line, and ⑧ seepage pressure input line.Confining pressure and seepage pressure are loaded with a water pump, and the loading medium is distilled water. When confining pressure needs to be applied, close the valve ⑤, open the valve ④, and pressurize with a high-precision water pump ①; when seepage pressure needs to be applied, close the valve ④ and open the valve ⑤. In this way, the system can switch freely between the two pressure lines. To ensure the stability of the pressure on the line, an accumulator is connected to each line. During the seepage test, the mini triaxial seepage testing machine ⑥ is fixed on the sample stage of the micro-CT to perform real-time scanning.


## 2.2.1. High-Resolution Micro-CT System

The model of the high-resolution micro-CT system used in this test isμCT225kvFCB. The system consists of an X-ray source, an amorphous silicon flat-panel detector, and a sample stage. The amorphous silicon flat-panel detector used for image acquisition is composed of 3200×2232 pixels, and the size of each pixel is 127 μm, as shown in Figure 2. Digital control is adopted to move the sample stage in the three directions of X, Y, and Z, which can realize high-precision positioning.Figure 2
High-resolution micro-CT system.The main parameters of scanning are operating current of 120μA, working voltage of 100 kV, the exposure time of 2 s per image, and the geometric magnification of 36.04; the resolution of each pixel was 5.38 μm, which means that the smallest pore size that can be identified was 5.38 μm. During the scanning, the rotation angle of the sample stage was 0.9° for each projection, the sample stage was rotated 360°, and the number of projections was 400.


## 2.2.2. Mini Triaxial Seepage Testing Machine

The testing machine used in this test is newly developed by our research team; it is developed for miniature rock sample (5-7 mm in diameter and 10-20 mm in height). This machine can be used for uniaxial compression experiments, triaxial compression experiments, seepage experiments, and real-time CT scanning. The stiffness of the testing machine is0.8×104kN/m, the elastic modulus of the loading device is 206 GPa, the shear modulus is 80 GPa, and Poisson’s ratio is 0.26. The elastic modulus of the applicable sample is 0.25-5 GPa, Poisson’s ratio is 0.11-0.25, and the stiffness is 0.1−1×102kN/m.The mini triaxial seepage testing machine consists of an axial loading device, axial stress sensor, axial stress display, confining pressure input port, seepage pressure input port, and triaxial pressure chamber, as shown in Figure3.Figure 3
Mini triaxial seepage testing machine: ① rock sample, ② seepage pressure input, ③ axial stress display, ④ triaxial pressure chamber, ⑤ confining pressure input, ⑥ axial stress sensor, and ⑦ axial loading device.


## 2.2.3. Seepage Test System for Real-Time CT Scanning

The system can perform a CT scan of the sample in real-time while conducting the seepage test and obtain the variation trend of the connectivity of pores and fissures in the rock sample in different stress fields. This system is shown in Figure4.Figure 4
Seepage test system for real-time CT scanning and its schematic: ① water pump, ② accumulator, ③ pressure meter, ④ and ⑤ valve, ⑥ mini triaxial seepage testing machine, ⑦ confining pressure input line, and ⑧ seepage pressure input line.Confining pressure and seepage pressure are loaded with a water pump, and the loading medium is distilled water. When confining pressure needs to be applied, close the valve ⑤, open the valve ④, and pressurize with a high-precision water pump ①; when seepage pressure needs to be applied, close the valve ④ and open the valve ⑤. In this way, the system can switch freely between the two pressure lines. To ensure the stability of the pressure on the line, an accumulator is connected to each line. During the seepage test, the mini triaxial seepage testing machine ⑥ is fixed on the sample stage of the micro-CT to perform real-time scanning.


## 2.3. Experimental Method

One of the research objects in this paper is the seepage characteristics of rock samples after failure. Therefore, before the seepage test, an increasing axial load is applied to the sample under prefixed confining pressure until the sample reaches the strength limit and fails. Then, keep the axial strain constant, unload the confining pressure, start reloading the confining pressure and seepage pressure, measure the permeability of the rock sample, and perform real-time CT scanning.3D digital rock samples can be reconstructed based on 2D grayscale images obtained by CT scanning; in digital rock samples, the higher the gray value, the greater the density of the pixel. To study the connectivity of pores and fissures under different stress conditions, it is first necessary to identify and extract the pores and fissures; the most commonly used method is to binarize the digital sample. In this process, the selection of threshold is a very important step, which determines the accuracy of identifying pores and fissures. Here, the method of segmentation of the DTM threshold is used [32]. Figure 5 is a comparison of sandstone images before and after binary processing.Figure 5
Sandstone images before and after binary processing.
(a)
Before binary processing(b)
After binary processingAccording to the method above, a spatial skeleton composed of pores is reproduced. In the skeleton, all of the adjacent pores formed a connected cluster, and there are lots of clusters in the 3D digital sample. We called the cluster that contains the largest number of pore pixels “the largest cluster.” As the porosity of the sample increases, the number of pore pixels contained in the largest cluster will increase [33]. The percolation probability of the 3D digital sample can be expressed by the following formula:(1)P=MN,where P is the percolation probability. M is the number of pore pixels contained in the largest cluster. N is the total number of pixels in the 3D digital sample.


## 3. Experimental Results and Analyses

The permeability of the rock is affected by confining pressure and seepage pressure. In order to figure out the influence of these two types of pressures on the permeability changes of the rock, the seepage tests and real-time micro-CT scanning are performed on sandstone and coal, which have different mechanical properties.


### 3.1. Influence of Confining Pressure on Sandstone Permeability

Firstly, the confining pressure of 2.5 MPa and the seepage pressure of 2 MPa are applied to the sandstone sample, and then, the axial pressure is slowly loaded until the sample fails. The fractured sandstone sample is shown in Figure6. Keep the seepage pressure unchanged at 2 MPa and start to increase the confining pressure step by step. Measure the flux of water discharged from the outlet under each confining pressure and perform real-time micro-CT scanning. The test results are shown in Figure 7.Figure 6
The fractured sandstone sample.Figure 7
Dependence of sandstone permeability on confining pressure.It can be seen from Figure7 that when the seepage pressure keeps constant, the permeability decreases with the increment of the confining pressure. It indicates that when the confining pressure increases, the original fissures in the sample are compressed, and the width of the fissures decreases, which ultimately leads to poor permeability. Fitting the curve in Figure 7 shows that the relationship between permeability and confining pressure is a power-law relationship.


### 3.2. Influence of Confining Pressure on Sandstone Percolation Probability

Under different confining pressures, the real-time micro-CT scans are performed on sandstones to reconstruct 3D digital samples. Based on the digital samples, we extract the skeleton of pores and fissures, obtain the largest connected clusters, and calculate the percolation probability. Figure8 shows digital samples and the spatial distribution of the largest clusters under different confining pressures.Figure 8
The 3D digital sample and the spatial distributions of the largest clusters.Comparing the fissures in the digital samples and the largest clusters in Figure8, it can be seen that the spatial forms of the fissures and the largest clusters are similar. As the confining pressure increases, the small fissures are compressed and closed firstly, and the width of the large fissures becomes smaller and smaller. The size of the largest cluster gradually decreases with the increase of the confining pressure. Counting up the size of the largest clusters and calculating the percolation probability under different confining pressures, the results are shown in Figure 9.Figure 9
Variation of percolation probability with confining pressure.


### 3.3. Influence of Seepage Pressure on Coal Permeability

The confining pressure of 4.5 MPa and the seepage pressure of 0.5 MPa are applied to the coal sample, and then, the axial pressure is slowly loaded until the sample fails. The fractured coal sample is shown in Figure10. Keep the confining pressure at 2 MPa and start to increase the seepage pressure step by step. Measure the flux of water discharged from the outlet under each confining pressure, and perform real-time micro-CT scanning. The test results are shown in Figure 11.Figure 10
The fractured coal sample.Figure 11
Variation of coal permeability with seepage pressure.Figure11 shows that as the seepage pressure increases, the permeability of the coal sample first decreases and then increases; when the seepage pressure is 2 MPa, the permeability reaches the minimum. The reasons for this change in permeability are as follows. At the beginning phase of the test, the relatively high confining pressure puts the fissure surface in a compressed state. Besides, the low strength of the coal matrix causes the occurrence of significant deformation under confining pressure, which causes the fissures to close and the connectivity of fissures becomes worse. Another reason for the decrease in permeability is that water can only permeate a small portion of the fissure surface when the value of seepage pressure is very small. In this situation, the outward opening force generated by the seepage pressure acting on the fissure surface is very small compared to the closing force due to the confining pressure, so the fissure cannot be opened further. Therefore, before the seepage pressure is sufficiently high enough to open the fissure, the seepage pressure can be regarded as the axial pressure acting on the end of the sample, which increases the volumetric stress on the sample, resulting in a decrease in permeability. When the seepage pressure reaches 2 MPa, the pressure is already high enough to cause the fissures to slowly open; therefore, the permeability of the coal sample starts to increase accordingly.


### 3.4. Influence of Seepage Pressure on Coal Percolation Probability

Under different seepage pressures, the real-time micro-CT scans are performed on coal samples to reconstruct 3D digital samples. Based on the digital samples, we obtain the skeleton of pores and fissures, the largest connected clusters, and calculate the percolation probability. Figure12 shows the spatial distribution of the largest clusters under different seepage pressures.Figure 12
The spatial distributions of the largest clusters in coal samples.Comparing Figure12 above with Figure 8, we can see that the largest clusters in coal and sandstone have a completely different spatial form. In the coal sample, the distribution of the largest cluster is relatively homogeneous, and its structure is like randomly distributed pores, which is sponge-like, and the existence of fissures is almost invisible. In the sandstone sample, the form of the largest cluster is firmly controlled by the fissures, and its structure is the same as the fissure structure in the sample. This indicates that the main factors controlling the permeability of the plastic rock and brittle rock are different; in brittle sandstone-like rocks, the connectivity of the fissures is the primary factor affecting permeability, and the pores are the auxiliary factor; in plastic rocks such as coal, the situation is just the opposite, pores are the primary factor affecting permeability, and fissures are the auxiliary factor.A lot of engineering practical experience shows that the hydraulic fracturing technology can significantly increase the oil and gas production in sandstone reservoirs but cannot increase the gas drainage efficiency of coalbed. The reason lies in the fact that the coalbed is a plastic rock layer, and its permeability is mainly controlled by pores rather than fissures. The weak coal undergoes large deformation under the action of the overlying rock, and the fissures generated by high-pressure water close again quickly. For brittle rocks such as sandstone, as mentioned above, the main control factor on its permeability is the fissures rather than the pores; after being fractured, the sandstone has a large number of fissures, which significantly increases the permeability.The variation of percolation probability with seepage pressure is shown in Figure13.Figure 13
Variation of percolation probability with seepage pressure.It can be seen from Figure13 that the percolation probability increases exponentially with the increment of seepage pressure. Furthermore, by comparing Figures 13 and 11, when the seepage pressure is greater than 2 MPa, the percolation probability and permeability both increase with the increment of seepage pressure, and the variation pattern is the same. However, when the seepage pressure is less than 2 MPa, the changing trend of percolation probability and that of permeability is inconsistent; the reason is that the seepage pressure is relatively smaller than the confining pressure; at this time, its main function is to increase the volumetric stress at the end of the coal sample, resulting in a decrease in permeability.


## 3.1. Influence of Confining Pressure on Sandstone Permeability

Firstly, the confining pressure of 2.5 MPa and the seepage pressure of 2 MPa are applied to the sandstone sample, and then, the axial pressure is slowly loaded until the sample fails. The fractured sandstone sample is shown in Figure6. Keep the seepage pressure unchanged at 2 MPa and start to increase the confining pressure step by step. Measure the flux of water discharged from the outlet under each confining pressure and perform real-time micro-CT scanning. The test results are shown in Figure 7.Figure 6
The fractured sandstone sample.Figure 7
Dependence of sandstone permeability on confining pressure.It can be seen from Figure7 that when the seepage pressure keeps constant, the permeability decreases with the increment of the confining pressure. It indicates that when the confining pressure increases, the original fissures in the sample are compressed, and the width of the fissures decreases, which ultimately leads to poor permeability. Fitting the curve in Figure 7 shows that the relationship between permeability and confining pressure is a power-law relationship.


## 3.2. Influence of Confining Pressure on Sandstone Percolation Probability

Under different confining pressures, the real-time micro-CT scans are performed on sandstones to reconstruct 3D digital samples. Based on the digital samples, we extract the skeleton of pores and fissures, obtain the largest connected clusters, and calculate the percolation probability. Figure8 shows digital samples and the spatial distribution of the largest clusters under different confining pressures.Figure 8
The 3D digital sample and the spatial distributions of the largest clusters.Comparing the fissures in the digital samples and the largest clusters in Figure8, it can be seen that the spatial forms of the fissures and the largest clusters are similar. As the confining pressure increases, the small fissures are compressed and closed firstly, and the width of the large fissures becomes smaller and smaller. The size of the largest cluster gradually decreases with the increase of the confining pressure. Counting up the size of the largest clusters and calculating the percolation probability under different confining pressures, the results are shown in Figure 9.Figure 9
Variation of percolation probability with confining pressure.


## 3.3. Influence of Seepage Pressure on Coal Permeability

The confining pressure of 4.5 MPa and the seepage pressure of 0.5 MPa are applied to the coal sample, and then, the axial pressure is slowly loaded until the sample fails. The fractured coal sample is shown in Figure10. Keep the confining pressure at 2 MPa and start to increase the seepage pressure step by step. Measure the flux of water discharged from the outlet under each confining pressure, and perform real-time micro-CT scanning. The test results are shown in Figure 11.Figure 10
The fractured coal sample.Figure 11
Variation of coal permeability with seepage pressure.Figure11 shows that as the seepage pressure increases, the permeability of the coal sample first decreases and then increases; when the seepage pressure is 2 MPa, the permeability reaches the minimum. The reasons for this change in permeability are as follows. At the beginning phase of the test, the relatively high confining pressure puts the fissure surface in a compressed state. Besides, the low strength of the coal matrix causes the occurrence of significant deformation under confining pressure, which causes the fissures to close and the connectivity of fissures becomes worse. Another reason for the decrease in permeability is that water can only permeate a small portion of the fissure surface when the value of seepage pressure is very small. In this situation, the outward opening force generated by the seepage pressure acting on the fissure surface is very small compared to the closing force due to the confining pressure, so the fissure cannot be opened further. Therefore, before the seepage pressure is sufficiently high enough to open the fissure, the seepage pressure can be regarded as the axial pressure acting on the end of the sample, which increases the volumetric stress on the sample, resulting in a decrease in permeability. When the seepage pressure reaches 2 MPa, the pressure is already high enough to cause the fissures to slowly open; therefore, the permeability of the coal sample starts to increase accordingly.


## 3.4. Influence of Seepage Pressure on Coal Percolation Probability

Under different seepage pressures, the real-time micro-CT scans are performed on coal samples to reconstruct 3D digital samples. Based on the digital samples, we obtain the skeleton of pores and fissures, the largest connected clusters, and calculate the percolation probability. Figure12 shows the spatial distribution of the largest clusters under different seepage pressures.Figure 12
The spatial distributions of the largest clusters in coal samples.Comparing Figure12 above with Figure 8, we can see that the largest clusters in coal and sandstone have a completely different spatial form. In the coal sample, the distribution of the largest cluster is relatively homogeneous, and its structure is like randomly distributed pores, which is sponge-like, and the existence of fissures is almost invisible. In the sandstone sample, the form of the largest cluster is firmly controlled by the fissures, and its structure is the same as the fissure structure in the sample. This indicates that the main factors controlling the permeability of the plastic rock and brittle rock are different; in brittle sandstone-like rocks, the connectivity of the fissures is the primary factor affecting permeability, and the pores are the auxiliary factor; in plastic rocks such as coal, the situation is just the opposite, pores are the primary factor affecting permeability, and fissures are the auxiliary factor.A lot of engineering practical experience shows that the hydraulic fracturing technology can significantly increase the oil and gas production in sandstone reservoirs but cannot increase the gas drainage efficiency of coalbed. The reason lies in the fact that the coalbed is a plastic rock layer, and its permeability is mainly controlled by pores rather than fissures. The weak coal undergoes large deformation under the action of the overlying rock, and the fissures generated by high-pressure water close again quickly. For brittle rocks such as sandstone, as mentioned above, the main control factor on its permeability is the fissures rather than the pores; after being fractured, the sandstone has a large number of fissures, which significantly increases the permeability.The variation of percolation probability with seepage pressure is shown in Figure13.Figure 13
Variation of percolation probability with seepage pressure.It can be seen from Figure13 that the percolation probability increases exponentially with the increment of seepage pressure. Furthermore, by comparing Figures 13 and 11, when the seepage pressure is greater than 2 MPa, the percolation probability and permeability both increase with the increment of seepage pressure, and the variation pattern is the same. However, when the seepage pressure is less than 2 MPa, the changing trend of percolation probability and that of permeability is inconsistent; the reason is that the seepage pressure is relatively smaller than the confining pressure; at this time, its main function is to increase the volumetric stress at the end of the coal sample, resulting in a decrease in permeability.


## 4. Conclusions

This paper takes brittle sandstone and plastic coal as the research objects and mainly studies the seepage characteristics of these two types of rocks with completely different properties of mechanics. In the seepage test, a miniature sample was used, and a real-time micro-CT scan was performed at the same time. The percolation theory was used to analyze the size and shape changes of the largest clusters in the rock samples under different stress states, and the main control factors for the permeability of these two types of rocks were discussed. The main conclusions are as stated below.(1)
Under different confining pressures, the permeability decreases with the increment of confining pressure, and the power-law relationship between the two is satisfied; at the same time, with the increase of confining pressure, percolation probability also decreases with the increment of confining pressure; the power-law relationship is still satisfied between the two(2)
Under different seepage pressures, the permeability first increases and then decreases with the increment of seepage pressure, and the permeability reaches the minimum when the seepage pressure is 2 MPa. However, when the seepage pressure is more than 2 MPa, percolation probability increases with the increment of seepage pressure; when the seepage pressure is less than 2 MPa, there is only a slight increase in the percolation probability. The changing trend of percolation probability and permeability is inconsistent(3)
The spatial distribution of the largest cluster under different stress states indicates that the main factors controlling the permeability of the plastic rock and brittle rock are different; in brittle sandstone-like rocks, the connectivity of the fissures is the primary factor affecting permeability, and the pores are the auxiliary factor; in plastic rocks such as coal, pores are the primary factor affecting permeability, and fissures are the auxiliary factor.



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*Source: 8832946-2020-11-05.xml*