Sample preparation
The four samples for the experiment were obtained from the DaTong Coal Mine in the central and southern Qinshui Basin, Shanxi Province, and are numbered Coal-1, Coal-2, Coal-3, and Coal-4, respectively. The industrial component data for the coals are listed in Table 1. The key to the success of porosity and permeability tests is the preparation of suitable plunger samples. Cores along the vertical bedding direction were obtained with a drilling machine and the coal face was ground using the wire-cutting method. The length of each coal core was 70 mm and their diameter was 38 mm.
Table 1
Coal industrial component data
| Sample | M (%) | Mad (%) | Ad (%) | Vd (%) | Fcd (%) |
| Coal-1 | 87.09 | 0.85 | 12.06 | 8.48 | 78.61 |
| Coal-2 | 89.36 | 1.03 | 9.61 | 9.99 | 79.37 |
| Coal-3 | 88.29 | 0.95 | 8.76 | 10.25 | 80.04 |
| Coal-4 | 82.64 | 1.04 | 12.22 | 9.6 | 78.04 |
| Note: M is the content of organic matter, Mad is the moisture content of the air-drying base, Ad is the ash content of the air-drying base, Vd is the volatile content of the air-drying base, and Fcd is the carbon content of the air-drying base. |
Experimental methods
CT scanning technology has the advantages of being nondestructive, fine, and quantitative and offering three-dimensional digitization (Li et al. 2014, Deng et al. 2017). Open pores, connected pores, and closed pores of coal can be scanned to accurately display the pore distribution and connectivity (Song et al. 2013). The principle of CT scanning entails conducting tomographic scanning of coal samples, obtaining two-dimensional section images reflecting the distribution characteristics of coal pores by using different absorption rates of X-rays between the coal skeleton and pores, and displaying them in high-resolution digital images (Liu et al. 2017, Fang et al. 2018). In this study, CT scanning and digital image processing technology were used to scan and reconstruct coal samples to obtain the three-dimensional spatial distribution of coal pores and then analyse the internal microstructure, pore connectivity, and seepage characteristics of coal. The permeability was obtained using an NER Benchlab 7000EX instrument.
CT scanning experiment
Phoenix v | tome | x m microfocus CT scanning was used. The working voltage was 300 kV, the working power was 500 W, and the highest magnification was 100⋅. The coal samples were scanned after drying at 80 ℃ for 24 h, and a total of 1368 two-dimensional CT slices with a resolution of 14.57 mm were obtained.
Digital core technology is an important method used to analyse pore structure, rock physical properties, and microscopic seepage laws. Image processing includes filtering, threshold segmentation, and three-dimensional reconstruction, as shown in Fig. 1. Median filtering was used to protect pore integrity, smooth the transition pore and matrix of coal rock, and retain important feature information in the image (Wang et al. 2020, Wang et al. 2021). The watershed algorithm was adopted for threshold segmentation. This is a mathematical morphology segmentation method based on topological theory, and it has good recognition ability for weak edges (Wang et al. 2023). Adjusting the interactive threshold is the basis for analysing the pore structure parameters of different kinds of coal. Coal is a porous solid material composed of organic matter, minerals, and voids (pores and fissures). The two-dimensional CT sections exhibited three shades of gray, with bright colours representing minerals, gray representing substrates, and black representing pores and fissures.
Permeability testing experiment
The NER Benchlab 7000EX permeability measuring system (New England Research, Inc.) was used for the permeability experiments. The hardware setup included the confining pressure and pore pressure and source and response systems. Complex transient permeability in the range of 5 nD to 5 µD under hydrostatic stress conditions up to 10,000 psi was measured. This can be done with pore pressures up to 10,000 psi when using liquid and 2,000 psi when using gas. The heated pressure vessel could be used for measurements of up to 120 ℃. Multifield coupling of the sample permeability evolution under stress and temperature loading was obtained.
Helium gas was used for the permeability experiments. The initial confining pressure was 2 MPa, and then the confining pressure was gradually increased to 3, 4, 5, 6, 7, 8, 9, and 10 MPa. The pore pressure was maintained at 2 MPa, and the test temperature was 25 ℃. The transient measurement method was based on Darcy's law; therefore, the permeability k can be expressed as
$$k=\frac{{2\mu Q{P_0}L}}{{(P_{2}^{2} - P_{1}^{2})S}}.$$
1
where m is the helium gas viscosity, S is the cross-sectional area of the coal sample, P0 is the standard atmosphere, L is the core length, Q is the gas velocity, P1 is the inlet gas pressure, and P2 is the outlet gas pressure.
CT scanning to analyse the internal microstructure characteristics of coal rock
Three-dimensional pore distribution space
Coal is a porous medium with strong heterogeneity, complex pores, and fissures (Van Krevelen 1993, Palmer 2009). To reveal the differences in the pore structures of different kinds of coal, CT scanning was conducted on four samples. Three-dimensional reconstruction of two-dimensional CT slices was performed to obtain the three-dimensional spatial distribution of different coal structures, including three-dimensional digital model building, image binarisation, pore extraction, and three-dimensional redrawing of pores. Figure 2 shows three-dimensional visualisation diagrams of the pores; these clearly show the pore distribution characteristics of coal from two perspectives. Compared with the Coal-1 sample, the pore structure of the Coal-4 sample has a wide distribution and complexity, and corresponds to a greater porosity. The pore size, pore volume, pore number, and porosity data of different coal structures were quantitatively analysed, as listed in Table 2.
Table 2
Basic parameters of the pore distribution obtained from CT scanning
| Sample | Coal size (mm) | Coal volume (mm3) | Number | Porosity (%) |
| max | min | mean | max | min | mean |
| Coal-1 | 24.26 | 0.44 | 0.89 | 3291.50 | 1.38 | 7.22 | 5075 | 9.97 |
| Coal-2 | 33.09 | 1.05 | 1.76 | 4624.50 | 3.14 | 10.98 | 4185 | 11.83 |
| Coal-3 | 39.99 | 1.34 | 1.97 | 5386.30 | 3.21 | 12.99 | 4189 | 12.84 |
| Coal-4 | 50.58 | 2.03 | 2.95 | 7669.50 | 5.54 | 19.32 | 5276 | 15.33 |
Digital image processing technology was used to extract and calculate the microscopic pore structures of the different kinds of coal. Figure 3 shows the contribution to the pore volume, which is the proportion of pore volume of different pore sizes to the total pore volume. A pore size of < 1 mm in the Coal-1 sample makes the greatest contribution to the pore volume, accounting for 43.83%. Pore sizes of 1.0 to 2.0 mm make the greatest contribution for the Coal-2 and Coal-3 samples to the pore volume, accounting for 39.29% and 33.79%, respectively. However, compared with Coal-2, a pore size of > 2 mm of the Coal-3 sample makes a greater pore volume contribution and has a greater average pore size. Pore sizes of 2.0 to 3.0 mm for the Coal-4 sample makes the greatest contribution to the pore volume, accounting for 42.27%. Therefore, the large pore size distribution corresponds to the greater pore volume contribution to the high porosity of coal.
Feature analysis of the pore network model
The operation module Separate Objects in Avizo software was used to separate the pore space into a group of connected and labelled spheres. Furthermore, the operation module Generate Pore Network was used to build an equivalent pore network ball-and-stick model to quantitatively characterise the pore spatial distribution of coal, as shown in Fig. 4. The colours of the pore and throat are divided according to the pore volume size and equivalent throat radius, respectively. By adjusting the pore-to-throat parameters, the three-dimensional spatial distribution of the coal pores was optimised. The pore network models of the Coal-2 and Coal-4 samples had more pores and throats and were more complex than those of the Coal-1 and Coal-3 samples. However, the pore size and throat radius of the Coal-3 sample were larger than those of the Coal-2 sample, which results in the Coal-3 sample having greater porosity.
The ball-and-stick model of the pore network mainly includes pore, throat, and connectivity parameters. The pore radius, throat radius, pore volume, and coordination number of the coal samples were obtained, as shown in Figs. 5 and 6. Figure 5 shows the pore network model parameters; the largest pore and throat radii of the Coal-1 sample are 26.83 and 4.47 mm, respectively. The largest pore and throat radii of the Coal-2 sample are 19.92 and 6.71 mm, respectively. The Coal-3 sample has the largest pore radius of 37.44 mm and the largest throat radius of 9.11 mm. The largest pore and throat radii of the Coal-2 sample are 28.97 and 8.22 mm, respectively. The pore network model parameters of the Coal-2 and Coal-3 samples indicate that the pore volume is determined by the radius and number of pore throats.
Figure 6 shows the distribution of the pore volume and coordination number. Pore connectivity can be analysed by coordination number, which is the number of connections between each pore. The pores with coordination numbers of 2 and 3 constitute the main body of the Coal-1 and Coal-3 samples. The Coal-2 and Coal-4 samples have multipore connectivity, but the Coal-4 sample has better connectivity.
The effects of pore connectivity on the permeability characteristics of coal were analysed using CT scanning technology. A value of was used as the connectivity criterion, and the objects can be connected in point contact, line contact, and surface contact. The three-dimensional connectivity evaluation equation is as follows (Nakamura et al. 2008, Zhu et al. 2020):
$$C=\frac{{{v_c}}}{v}.$$
2
where C is the connectivity factor, vc is the connected pore volume, and v is the sample volume. The pore connectivity strength is expressed by the ratio R of the pore-to-throat radius:
$$R=\frac{{{r_p}}}{{{r_t}}}.$$
3
where rp is the pore radius and rt is the throat radius. R is negatively correlated with connectivity strength.
The connectivity factor C and pore-to-throat ratio R of the samples are listed in Table 3. The greater the porosity of the coal, the better the connectivity, the smaller the pore-throat ratio, and the stronger the connectivity strength.
Table 3
Connectivity and pore-to-throat ratio data
| Sample | C (%) | R |
| Coal-1 | 0.023 | 3.79 |
| Coal-2 | 0.029 | 2.35 |
| Coal-3 | 0.031 | 1.93 |
| Coal-4 | 0.048 | 1.79 |
Analysis of coal permeability and main controlling factors
Effect of pore characteristics on permeability
The pore distribution characteristics of coal are the direct controlling factors of coal reservoir permeability; these include pore size, pore number, pore volume, pore connectivity, and connectivity strength (Zhai et al. 2018, Cheng and Pan 2020). Figure 7 shows the relationship between the measured permeability and pore structure parameters of the coal samples. Permeability is positively correlated with pore size, pore connectivity, and pore volume and negatively correlated with pore-to-throat ratio. Pore connectivity directly determines the possibility of fluid transport, and the pore-to-throat ratio determines the difficulty of fluid transport. For the coal samples tested in this study, the greater the porosity, the better the corresponding connectivity, the smaller the pore-to-throat ratio, the stronger the connectivity strength, the larger the average pore size and pore volume, and the greater the permeability.
Permeability characteristics of capillary seepage channels
By combining the Poiseuille equation of microscopic capillary seepage theory and Darcy's law of macroscopic seepage theory, Yu et al. (2002) deduced the following permeability equation of capillary porous media:
$$k=\frac{\pi }{{128}}\frac{{L_{0}^{{1 - {D_T}}}}}{A}\frac{{{D_f}}}{{3+{D_T} - {D_f}}}\lambda _{{\hbox{max} }}^{{3+{D_T}}}.$$
4
where Df is the fractal dimension of the pore size, with 1 < Df < 2 under two-dimensional conditions; DT is the fractal dimension of the tortuosity of the capillary seepage channel, with 1 < DT < 2; lmax is the maximum pore size; and L0 is the length of the coal sample. The cross-sectional area A of the porous medium is
$$A=\frac{{\pi {D_f}\lambda _{{\hbox{max} }}^{2}(1 - \phi )}}{{4 \times \phi (2 - {D_f})}}.$$
5
where f is the porosity. Substituting Eq. (5) into Eq. (4), we obtain:
$$k=\frac{{\lambda _{{\hbox{max} }}^{{1+{D_T}}}}}{{32}}\frac{{\phi L_{0}^{{1 - {D_T}}}}}{{(1 - \phi )}}\frac{{2 - {D_f}}}{{(3+{D_T} - {D_f})}}.$$
6
It can be seen from Eq. (6) that permeability is closely related to the fractal dimension of pore size, the fractal dimension of tortuosity of seepage channels, porosity, and maximum pore size. The fractal geometric structure parameters of coal are assigned according to the actual situation of the coal microstructure. The curves in Fig. 8 show the influence of different capillary seepage channel model parameters on permeability, in which the permeability is positively correlated with pore size and porosity and negatively correlated with the fractal dimension of the pore size and tortuosity. Among them, the pore size was highly sensitive to permeability. Therefore, lmax meeting the fractal characteristics directly affects the prediction accuracy of coal permeability.
Permeability analysis based on pore characteristic parameters
Yu et al. (2002) based on an equilateral triangle of the microparticle theory model, combined with the particle radius and porosity, and then calculated the average macropore size of the largest as the maximum pore size. However, for coal rock with an uneven distribution of pore sizes, this method of calculating the maximum pore size is too idealistic. It is important to consider the complexity and connectivity of the micropore structure in coal rock to analyse the transport characteristics of coal reservoir resources. With the development of CT scanning technology, based on digital image processing technology and fractal theory, and considering the complexity of coal-rock porosity and connectivity, we can optimise the calculation of the maximum pore size lmax.
Table 4 lists the pore structure parameters of the coal samples. The optimised parameters lmax, f, Df, and DT were substituted into Eq. (6) to obtain the predicted permeability values km, which were 0.0469, 0.0919, 0.1154, and 0.1914 mD, respectively. The predicted permeability values km are greater than the measured permeability values kr because the seepage channel roughness has a restricting effect on the permeability characteristics. The errors between the predicted and measured permeabilities were 2.35%, 1.85%, 1.47% and 2.40%, respectively, which verifies the accuracy and applicability of the permeability analysis by CT scanning.
Table 4
Comparison between predicted and measured permeability values
| Sample | C (%) | f (%) | lmax (mm) | Df | DT | kr (mD) | km (mD) | Error (%) |
| Coal-1 | 0.023 | 9.97 | 11.26 | 1.45 | 1.08 | 0.0469 | 0.0458 | 2.35 |
| Coal-2 | 0.029 | 11.83 | 16.09 | 1.51 | 1.10 | 0.0919 | 0.0902 | 1.85 |
| Coal-3 | 0.031 | 12.84 | 17.99 | 1.52 | 1.11 | 0.1154 | 0.1137 | 1.47 |
| Coal-4 | 0.048 | 15.33 | 23.58 | 1.58 | 1.13 | 0.1914 | 0.1868 | 2.40 |