2.1 Coal specimens

The experimental coal specimens were obtained from the II1 coal seam of Zhaogu No.2 Coal Mine in Xinxiang, Henan Province, China. The coal mass, mainly lump coal, is stable and belongs to the medium-thick coal seam with horizontal development. According to the drill core data, the lump coal yield reaches more than 80%. With a simple structure and a relatively single coal type, the seam is relatively stable. The coal mass is generally hard; the tectonic coal is not developed, with a small amount of grain-loaded coal. Resembling metallic luster, the stripes are gray-black, anthracite coal with low to medium ash, with ultra-low sulfur, low phosphorus, high softening temperature, high thermal stability, and high strength. Moreover, the coal mass is not easily broken. The industrial analysis parameters of the test coal specimens are shown in Table 1.

2.2 Experimental system and apparatus

The dynamic loading experiments were conducted using an industrial CT scanning system. The experimental system consists of industrial CT scanning and loading displacement seepage. The working principle of the industrial CT scanning system (Figure 1) involves the use of X-ray to scan coal specimens with different densities and thicknesses (Wang et al., 2021). The ray intensity passing through the coal specimen is attenuated due to the absorption or scattering of the material in the path. The projection data are obtained by collecting the attenuated rays, and the reconstruction algorithm is used to display the internal structure of the coal specimen in the form of images.

               

The loading displacement seepage experiment system is mainly composed of a triaxial pressure cell, a triaxial compression loading system, a coal specimen holder, a data acquisition system, and a gas seepage system (Saghafi & Pinetown, 2015). The triaxial pressure cell is made of carbon fiber material, which is mainly composed of a pressure chamber cylinder, a pressure piston, a rubber sleeve, O-rings, and a coal specimen chamber.

The in situ loading CT experimental procedure is as follows: First, standard coal samples are prepared in the selected coal seam for CT experiments, followed by initialization and debugging of the experimental system to ensure normal communication connection and vacuum state of the ray tube, preheating CT scanning equipment, and centered electronic beam. Then, the detected sample is placed on the CT scanning turntable and the ray source is turned on; the sample is rotated for 1 week to ensure that the projection can be fully received by the detector. When the sample is placed, the scanning parameters on the software are to be set. The parameters mainly include setting the current voltage and the approximate load required for sample failure. After the detector position is calibrated, scanning is started. When the sample is destroyed, scanning is completed. Finally, the ray source is closed and the results are stored, as shown in Figure 2.

               

3.1 CT image processing and analysis

The two-dimensional slice images obtained from the CT scan test are gray images. In order to use the three-dimensional reconstruction software to complete the subsequent operation, the images need to be analyzed and processed (Figure 3). First, gray-scale adjustment is carried out, and the internal composition structure of the coal sample can be clearly displayed. Then, the background removal step is performed to remove the black background in the two-dimensional slice in advance. Next, the median filter is used to denoise the two-dimensional slice, and the noise is removed by approximating the real value with the neighborhood value. The required gray value is selected and the pixels are binarized in the entire gray image. The final image processing results are only black and white, in which black represents pores and white represents the coal matrix and minerals.

               

3.2 Representative elementary volume (REV)

Even in the same coal mass, the porosity would vary considerably with different research volumes. It is known that there is a mesoscale range in the scale of CBM seepage from micro-definition to macro-definition. In the mesoscale range (Du et al., 2023), the seepage process of CBM in the dual structure of pores and fractures is included. When the volume Vi is less than a certain value Vmin, the value of the attribute value ni suddenly fluctuates considerably. When the value of Vi is greater than Vmin, the fluctuation of the attribute value ni disappears. At this time, the volume Vmin is defined as the meso-scale lower bound of CBM seepage in the dual structure of the coal mass pore fracture. In the macroscopic CBM injection, it is difficult to determine the size of the coal pore-fracture structure and so it is difficult to determine the specific value of the mesoscale upper bound. Researchers can also determine this according to the size of the selected coal specimen. The REV is selected to represent the permeability of coal in the meso-scale range (Liu et al., 2023). REV is the common practice in reconstruction. It is the smallest volume unit that can achieve the stability of the relevant performance of the scanned specimen. The volume unit is representative enough, and the range scale is shown in Figure 4.

               

3.3 Maximum ball algorithm

PNM is an abstraction of a porous medium into an ideal geometry, also known as a ball-and-stick model (Saghafi, 2017; Xiong et al., 2016). The complex pore space consists of interconnected pores and throats. The pore structure inside the coal mass is characterized by a sphere, and the connection channel between the pores becomes throats connecting the sphere, which is characterized by a stick. Then, the pores and throats in the coal mass can be characterized by the mathematical parameters (Yang et al., 2015) of the sphere and the stick (Figure 5).

               

The basic calculation idea of the PNM involves the maximum sphere algorithm (Figure 6). The principle involves the assumption that many spheres are placed in the center of the pores and throats, and then the volume of the sphere is increased until the edges of the spheres are infinitely close to those of the pores and throats. The edge is infinitely close, and finally the entire pore structure cannot be contained by other spheres, so the sphere covering the pore is the maximum sphere. All pore structures are treated in the same way so that the largest spheres of all pores are interconnected.

               

3.4 Numerical mesh repair

In the numerical simulation of pore-scale seepage (Liu et al., 2024; Zhao et al., 2021), in order to ensure the smooth progress and fast convergence of the simulation, it is necessary to preprocess the digital coal pore model before the simulation (Wang et al., 2019). The preprocessing process is carried out mainly to repair the geometric mesh. The calculation principles of the two software are different. It is necessary to establish the Stereo Lithography (STL) data interface through the visualization software to import the COMSOL software.

However, due to the large number of meshes in the model during the export process, the mesh division error problem will inevitably occur. Accordingly, the model mesh also needs to be repaired. The mesh repair mainly includes enhancing the mesh quality and surface repair. The repaired mesh can be successfully imported into COMSOL for further analysis. A bridge from digital coal rock to seepage simulation is built to realize data interaction. The process is shown in Figure 7.

               

3.5 Seepage simulation equation

4.1 Fracture plane structure characteristics

Under the condition of uniaxial loading, a total of five loading scans were carried out on the experimental coal specimens, and all CT images of the coal specimens from the initial state to the loading failure state process were obtained. The specific results are shown in Figure 8. In the first scanning, there are many microscopic fractures at the bottom of the initial stage of the experimental coal specimen. When the coal specimen enters the elastic stage (the second and third scanning), the primary fractures in the coal specimen first have no obvious closure, and then start to produce new fractures. After the peak stress is reached (the fourth scanning), the coal specimen begins to show signs of damage and a large number of fractures occur. In the fifth scanning after pressure relief, the coal body is completely unstable. At the same time, with a sharp decrease of stress, the new fractures are interconnected and penetrated. The number and volume of fractures reach the peak, and the experimental coal specimen is more severely damaged.

               

The coal specimens were selected for five scans from top to bottom (Figure 9). A slice at each location is presented in a row. Each column, from left to right, corresponds to one scan to analyze the fracture evolution process inside the coal with the increase of axial stress. It can be seen from the figure that there are few micro-fractures in the middle and lower parts of the test coal specimen at the initial stage. At the second scanning, there is no obvious change as a whole, but there are signs of narrowing in the lower cracks and some cracks are closed; This represents an energy accumulation process.

               

With the increase of the axial stress, when the third scanning is conducted, obvious large volume fractures begin to appear in the middle and upper parts of the coal mass. When the axial stress reaches the peak strength of the coal mass, the new fractures begin to expand obviously and new fractures also appear in the middle and lower parts. At this time, the internal fractures of the coal specimen in the compressive state expand and connect with each other, and the fractures develop in a more easily aggregated direction. The stress–strain curve decreases rapidly when the peak stress is reached. At the fifth scanning, it can be seen that the primary fractures in the coal mass further expand, the number of new fractures reaches the peak, and they are interconnected with each other. The size increases sharply, from the primary fractures in the middle of the specimen to outward expansion, extending to the edge of the coal specimen.

In order to more accurately characterize the degree of fracture development in coal specimens, the characteristic image features are extracted on the basis of 2D scanned digital images, and the gray-scale values are quantified for the images of structural changes in coal specimens during loading. When scanning in the initial state, only a small number of fractures exist at the bottom of the coal specimen. Therefore, five scanning slices of the bottom of the coal specimen are selected as samples for analysis, and the gray value statistics of the 2D image are obtained by digital image technology.

The image after the CT scan is in a 16-bit RGB format, which is transformed into an 8-bit gray-scale image by image processing software, and the statistical range of the histogram of the gray value is 0–255. The CT image has a gray value of cracks close to 0. A lower average gray value is associated with more fractures if there are more gray pixels around 0. The gray-scale standard deviation reflects the image contrast to some extent. The more the deviation, the more severe the pixel gray-level variation and the more complex the fracture pattern. The peak height (Figure 10) shows the change process near the gray value of 0, which characterizes the change process of the fracture. In the first scan, there are only a few gray value statistics near 0. In the second scan, the gray value close to 0 increases slightly, indicating that there are a few new fractures compared with the first scan. As the pressure is exerted continuously, by the third scan, the gray value near 0 increases. On reaching the peak intensity, the 0 value at the fourth scan represents a significant complex change in the fissure. Until the fifth scan after the damage of the specimen, the statistical histogram shows a peak of the protrusion near the gray level of 0, indicating that the number of cracks reaches its peak at this time.

               

The average gray value (AGV) and gray standard deviation (GSD) curve of the last layer of the selected specimen are shown in Table 2. In the second scan (7.86 MPa), the AGV decreases slightly compared with the initial state, indicating that there are new fractures, but the number is small. From the second scan (7.86 MPa) to the fourth scan (15.15 MPa), the AGV continues to decline, indicating that the coal specimen is in the elastic stage at this time, new fractures are continuously generated, fracture propagation continues, and a few fractures exist in the specimen. Finally, in the fifth scan (4.35 MPa) after the specimen is completely destroyed, the mean square deviation increases considerably, indicating that the pixel gray-level changes dramatically and the fracture morphology is more complex. The AGV decreases, indicating that the fracture development reaches the peak.

4.2 Fracture fractal dimension

In order to obtain the fractal dimension of the fracture distribution inside the coal specimen, the CT scan image needs to be processed binarily. The results obtained after binary processing are shown in Table 3. As can be seen, the binarized CT image retains well the distribution characteristics of internal fractures in the coal specimens (Figure 11). Based on the principle of the box-counting dimension method and CT image storage, the image data of the obtained series of CT 2D coal specimens are obtained using Image J software. In the slice figure obtained from the five scans of the coal specimen, 10 slices with equal spacing are selected in each group from top to bottom along the XY axis direction and their 2D fractal dimensions are calculated. From the calculation results (Figures 12 and 13), the 2D fracture fractal dimension of the coal specimen is within the range of 1.156–1.705 and the fitting correlation coefficient is above 0.92, indicating that the calculation results are effective. From the perspective of the 2D plane, the larger the fractal dimension, the more sufficient the fracture development and the more complex the distribution, and vice versa.

               

               

               

The pore-fracture network displays fractal characteristics. With the increase of the axial stress, the fractal dimension first shows a downward trend in the elastic stage (the first scan), and then shows a positive correlation with the axial stress. The scanning results under the initial state of coal specimens show that the fractal dimension of coal specimens fluctuates between 1.7369 and 1.7422, with an average value of 1.7396, and the difference between the upper and lower limits is not obvious, indicating that there are few initial fractures in the original state of coal specimens from top to bottom. At the second scan, the fractal dimension of the coal specimen fluctuates between 1.6876 and 1.7327, with an average of 1.7070, and the average fractal dimension decreases, indicating that the pore fractures in the coal specimen are compressed and closed at this stage. After the three scans, the fractal dimension increases with the increase of the axial stress, and the average fractal dimensions are 1.7537, 1.8303, and 1.9219. This shows that after the coal specimen enters the elastic stage, the initial pore fractures begin to develop and with the increase of stress, the development becomes increasingly obvious. After the damage stage, the fractures are connected as a whole and the development reaches the peak, which corresponds to the analysis of the gray value of the slice.

4.3 Fracture evolution analysis

Plane slice images can only show local information of a section of coal fractures. By contrast, 3D fractures can be more intuitive and comprehensive by showing the overall distribution and spatial morphology of coal fractures. The fractures of coal specimens were extracted to study their shape and spatial distribution. The evolution process of five scans of coal specimens is shown in Figure 14. In the figure, the 3D reconstruction process of coal specimens from the first scan to the fifth scan is presented from top to bottom. From left to right, the reconstruction model of the coal matrix, pore fracture, mineral, and the coal bulk during the five scans is shown.

               

From the fracture reconstruction of the first scan results, it can be seen that there are only a few tiny fractures in the lower part of the coal specimen at the initial stage of the coal specimen and there is no original fracture in the middle and upper parts of the coal specimen. At this time point, the total volume of fractures is 3.822 mm3. The second scan corresponds to the new fracture generation stage of coal specimen deformation. The deformation of the coal specimen increases and there are small fractures in the middle and upper parts of the coal specimen. The internal fractures are continuously developing and expanding, resulting in an increase in the total volume of the fractures. At this time point, the total volume of internal fractures in the coal specimen is 5.701 mm3.

From the acoustic emission signal in the process of coal specimen deformation under pressure, it can be easily seen that the stress–strain curve of the coal specimen in the elastic stage maintains a good linear trend, but crack propagation, connection, and extension always occur within the specimen, and internal damage continues to accumulate. When the peak stress is reached, the internal fractures of the coal specimen develop rapidly and the volume of the new fractures begins to increase sharply. Finally, multiple fractures are connected to form a new fracture surface, which results in the destruction of the coal specimen. During this period, the stress decreases and the fracture volume increases rapidly to 1018.556 mm3. When the coal specimen is completely depressurized, the internal fractures are further fully expanded, the fracture volume reaches a maximum of 1630.164 mm3, and the coal specimen is completely damaged.

Based on the voxel value and resolution of the reconstruction model, the fracture volume extracted from each scanning point is calculated, and then fracture porosity is calculated. Fracture porosity is defined as the fracture volume divided by the volume of the selected region of interest (ROI) of the coal specimen. Using the image cutting function in the three-dimensional reconstruction software, the ROI size is as close as possible to the size of the coal sample (diameter is 25 mm, height is 50 mm). And ensure that the volume of ROI extracted from different stages is as consistent as possible. The fracture volume and porosity of the coal specimens at different scanning stages are listed below (Table 4).

4.4 Pore network model

The construction process of the equivalent PNM is as follows: First, a command is included in the module after threshold segmentation is completed to remove the isolated pores in the reconstruction model. In this way, the isolated pores will not be connected to other pores and there is no throat or no ball–stick model. Then, commands are added to the maximum connected region of the model, the parameters in the commands are set, and these are rendered. From the results, the latter three groups of specimens form connected pore fractures. Accordingly, the final equivalent PNM of the three groups after coal specimen scanning can be obtained (Figure 15).

               

Table 5 shows the structural parameters of pores and throats when coal specimens are in different stages. In terms of the average number of pores and throats, the average radius of the pore structure of the elastic stage (S3) is smaller than that of the postpeak stress stage and the pressure relief stage (S4 and S5), but the number of pores and throats is considerably higher than that of the other two groups. This is because in the elastic stage (S3) of the loading process, a lot of new pores are gradually produced. With the increase of load, the shape and distribution of the pore structure are changed, so many small pores are connected to each other and form large pores, even fractures. Therefore, the postpeak stress stage and the pressure relief stage (S4 and S5) have large pore volume but small numbers in 3D reconstruction.

The coordination number is a microscopic parameter characterizing the connectivity of the pore network, which reflects the connectivity effect of the pores. The density of the connection between the spheres and the number of seepage channels can be reflected by the size of the coordination number. The pores are connected to adjacent pores through throats, and the number of connected throats is different. In closed pores, some pores are not connected with other pores, so the coordination number is 0. Such pores are called isolated pores, which contribute little to the formation of seepage channels. Some pores are connected to more pores. The smaller the coordination number, the poorer the pore connectivity and the smaller the number of seepage channels.

4.5 Seepage simulation

After generating the model through commands, the calculation module is used to obtain the streamline distribution map of the fluid flowing along the Z-axis direction. The color of the line in the figure represents the flow rate. From blue to red, the color represents the rising trend of the flow rate of the streamline. The Z-axis velocity field streamline distribution of the crack expansion and generation of the seepage stage (S3, S4, and S5) is as follows.

The simulated streamline of the seepage path during the loading process is shown in Figure 16. In the elastic stage (S3) of the initial loading process, the streamlines are mostly blue and green, the number of connected pores and fissures is small, and the streamlines are not straight. Only a small number of streamlines run through from top to bottom, indicating that although the seepage channel has been formed inside the coal body at this stage, the development of the channel is slow. Accordingly, the gas migration process is not smooth. It can also be seen from Table 7 that the maximum flow rate in the elastic stage (S3) is 3.84 m/s and the absolute permeability is 0.083 μm2.

               

After reaching the peak stress stage (S4), the main seepage channels inside the coal have completely opened and the streamline runs through the whole specimen from top to bottom, forming the main seepage channel. The streamline at this time is denser than that in the previous stage and it can be seen from the color of the streamline that obvious red color begins to appear, indicating that the flow rate at this time point also increases rapidly. The maximum flow rate can reach 42.12 m/s and the absolute permeability at this time point is 1.57 μm2.

In the pressure relief stage (S5), after the coal specimen is fully damaged, both the density of the streamline and the flow rate reach the peak and a large number of red streamlines appear. At this time point, the maximum flow rate is 46.25 m/s, which is 42.41 m/s higher than when the channel is just formed, and the absolute permeability is 2.57 μm2. This shows that with the continuous increase of load, the pore structure inside the coal mass also changes. When many large pore structures are interconnected with each other, the main fracture, or the main channel of gas seepage in the coal, is formed. Also, it will gradually increase until the coal specimen is damaged and the gas would gush out via the fracture channel.

The seepage simulation pressure distribution map of different loading stages is shown in Figure 17. The closer the color is to red, the higher the pressure in this area. The pressure mainly acts on the middle of the specimen. In the elastic stage (S3) of the initial loading stage, the pressure of the coal mass from top to bottom is almost the average pressure. This is mainly due to the fact that the fracture structure is not perfect at this time point. There are many isolated pore structures, so the pressure cannot be effectively released. When the peak stress stage is reached (S4), the pressure distribution changes obviously. At this time, the main fracture has formed and the effective seepage channel has opened. In this case, the seepage channels have converged to form the main channel. Although the pressure in the middle of the specimen hardly changes, the pressure at the upper and lower ends of the specimen changes significantly. At the S5 stage, after complete damage, although the pressure distribution is almost the same as that in the postpeak stress stage (S4), the pressure value decreases obviously. This shows that the smaller the pore pressure, the more developed the pore-fracture structure of coal, which is more conducive to the seepage of fluid.

               

On comprehensive comparison of the data changes (Figure 18), it can be found that when the absolute permeability increases, the tortuosity and flow rate tend to decrease. The absolute permeability is negatively correlated with tortuosity, indicating that as tortuosity decreases, the connected pore structure becomes simpler and the absolute permeability increases.

               

As the load increases (Table 6), the pressure value of the pore structure inside the coal mass decreases continuously from an average pressure value of 1.128 MPa in the elastic stage (S3) to 1.103 MPa in the pressure relief stage (S5). This is mainly due to the increase of the connectivity between the pore structures. The number of isolated pores decreases and the pressure is effectively released. However, with the increase of load, the seepage velocity of fluid in the coal mass also increases, from 1.26 m/s in the elastic stage (S3) to 33.26 m/s in the pressure relief stage (S5). This indicates that the volume and radius of new cracks in the coal mass increase with increasing load. As a result, the main seepage channel is formed inside, which changes the path and characteristics of gas migration.

It can be seen from Table 7 that the error between the simulated permeability value and the experimental test value is between 3.08% and 9.21% and the average error is 5.73%, indicating that the evolution process of the numerical simulation seepage field is consistent with the evolution process of the fracture field. Therefore, the permeability of coalbed methane can be accurately predicted and the permeability change law of loaded coal rock can be effectively described.

4.6 Pressure and velocity fields of seepage

Seepage often acts on the interconnected pore-fracture structure. The pressure and velocity of seepage are important factors in studying the seepage law in space. Therefore, the maximum connected pore clusters of coal samples at each scanning stage were simulated in the finite element software and then used to describe the variation of pore pressure and seepage velocity during the seepage of methane in the pore-fracture space.

Although the pressure at the input and output ports of the reconstruction structure model of coal at different stages remains the same, the internal pressure field is completely different. This indicates that the pore-fracture structure inside the coal increases with increasing load (Figure 19). In the elastic stage (S3), the maximum pressure in the coal mass is 116 052 Pa and the minimum value is 102 578 Pa; by contrast, in the pressure relief stage (S5), the maximum pressure in the coal mass is 109 528 Pa and the minimum value is 96 713 Pa. In the process of gas seepage, the fluid pressure is attenuated along the direction of flow.

               

The velocity of gas along the direction of seepage gradually increases (Figure 20). Due to the heterogeneity of the pore-fracture structure, the seepage velocity of each part of the coal model is different and the velocity increases rapidly at the fracture. When the fracture channel shrinks, the gas flow velocity increases sharply. In the pressure relief stage (S5), the seepage velocity reaches a maximum of 45.28 m/s, but the seepage path does not cover the entire pore-fracture space. This is because the geometric complexity of the pore structure will inevitably lead to some pore stagnation, in which no seepage occurs.

               

In general, the results of the pressure distribution and the streamline velocity of the gas seepage field obtained by finite element software are basically the same as those obtained by Visual, which confirms the accuracy of the 3D reconstruction structure and provides a research method for the coal mass at the micro scale.