Fractal Analysis and Classification of Pore Structures of High-Rank Coal in Qinshui Basin, China

Abstract

The influence of high-rank coal’s pore characteristics on the physical properties, gas-bearing properties, and exploitation of coal reservoirs is becoming more and more prominent. How to establish the classification to describe the pore networks combining quantitative and qualitative characteristics has emerged as a major problem, which may offer a scientific foundation to deepen the understanding of this issue. In this research, the structure and fractal characteristics of reservoir pores were determined after analyzing 20 high-rank coal samples from Xinjing Coal Mine in the Qinshui Basin with the application of the high-pressure mercury intrusion method (HPMI) and argon ion polishing–field emission scanning electron microscopy (AIP–FESEM). The results show that the tested coal samples were bipolar distributed, with transitional pores and micropores dominating the pore volume, followed by macropores. The Menger sponge fractal models manifested two or three distinct straight-line segments with demarcation points of 65 nm and 1000 nm. A natural classification with three major pore types of diffusion pores (D-pores), seepage pores (S-pores), and pico pores (P-pores), demarcated by pore size intervals of 65 nm and 1 nm and seven sub-types, was established to relate pores to pore networks based on these fractal characteristics and the kinetic characteristics of methane molecules. This classification scheme can characterize the relationship between pore types and the corresponding major occurrence and transport mechanisms of the gas. In addition, P-pores and D-pores are predominately nanoscale OM pores with three major genetic types of organic constituent interparticle pores (5–200 nm), metamorphic pores (<5 nm), and intermorphic pores (<5 nm). S-pores are more complex in origin and shape features, and the major types include outgas pores, plant tissue residual pores, mineral-related pores, and microfractures. The mean radius (Pa), total pore volume (Vt), apparent porosity (Φ), and volume ratio of macro- and mesopores were positively correlated with the fractal dimension D1 of S-pores (>65 nm). Since fractal analysis is a more comprehensive characterization of reservoir structure and quantitatively reflects the pore structure, undulating state, and roughness of the inner surface, fractal parameters can be used as an important index to describe the pore structure characteristics of high-rank coal reservoirs.

1. Introduction

China has the world’s third largest resource of coalbed methane (CBM). Furthermore, China’s CBM reserves exceed those of shale and tight gas, the other two unconventional gases [1]. Therefore, there has been a lot of interest in CBM’s exploitation and utilization. Coal is a heterogeneous and anisotropic porous media with complicated pore structure of dual porosity, namely microporous matrix and microporous cleats [2]. Pore structures are usually characterized by pore size, shape, volume, surface area, and spatial distribution [3]. All of these are key influencing factors and critical evaluating parameters of the storage capacity and migration efficiency of CBM [4,5]. Moreover, micropores are the material foundation for CH₄ replacement by CO₂. Thus, the study of the pore structures of coal can provide a basis for the further development of CO₂ geological storage technology [6,7,8,9,10].

Coal, as an unconventional reservoir, has much smaller pore sizes when compared to conventional reservoirs. Pore sizes are usually in the nanoscale, especially for high-rank coal [11,12]. The pore structure of coal has been investigated with a number of methods: scanning electron microscopy (SEM), mercury intrusion porosimetry (MIP), small-angle X-ray scattering (SAXS), N₂ gas adsorption method, etc. [13,14]. However, the ultra-small scale of pore size creates difficulties in the description of pore structure. Due to sample preparation and resolution limitations, few imaging methods and instruments can achieve nanoscale pore presentation. The large pore size distribution range of coal also makes it difficult to directly describe pore structure with any single method of MIP, N₂ gas adsorption method, atomic force microscopy (AFM), and SAXS. The application of argon ion polishing (AIP), which is used for the preparation of the high-quality surface for samples, and field emission scanning electron microscopy (FESEM) has contributed to the image observation of nanoscale pores in shale reservoirs [15,16,17]. The same method has been successfully applied to the study of nanoscale pores in coals with various ranks [18,19,20,21,22], providing a direct analysis of nanoscale pores and fractures. Scholars have conducted numerous studies on coal structure and pores (Table 1), revealing the basic characteristics of the pore system and its complex influencing factors [23,24,25,26,27,28,29]. These studies have accumulated significant experience in investigating the fine characteristics of coal pores, but there are still issues with the characterization techniques now in use. For example, there is an inability to comprehend pore genesis in terms of pore size distribution characteristics. In addition, different methods result in differences in characterization results. Last but not least, a pore classification framework that can compare the results of different research is still absent, which causes incompatibility in the application of pore study results to resource evaluation and prediction. The qualitative observation scale is frequently different from the quantitative characterization scale in many research, thus affecting the discussion of the combined qualitative–quantitative analysis. New techniques including modeling methods based on experimental test data are continuously applied to the characterization and evaluation of pores in unconventional oil and gas reservoirs, and the quantitative understanding of reservoir pore structure has consequently deepened [28].

Table 1. Representative research progress on structure and classification research of coal pores in recent years.

Samples	Source	Methods	Pore Size Characterization	Research Objective and Parameters	Literature
Anthracite, Low-/Medium-/High-volatile bituminous, Lignite coal	The northern China mining area	LP-N2GA, SEM	Pore images at micron scale; PSDs: <30 nm	Pore shape, specific surface area, pore volume	[23]
Tectonically deformed coals	Several collieries in north China	AFM	Pore images and corresponding PSDs: <15 nm	Tectonically deformed nanoscale pore structure and shape	[24]
Low-rank coals	The Erlian Basin, Hailar Basin, the Junggar Basin, and the Ordos Basin	MIP, NMR, SEM	Pore images at micron scale; Differentiated PSDs by each method	Pore structure evolution	[25]
Middle- and high-rank coals	Eastern Yunnan and Western Guizhou, China	MIP, LP-N2GA, Fractal Analysis	PSDs	Fractal characteristics of pore structure	[26]
Bituminous coals covering a wide range of rank	Poland, the US (Appalachian), New Zealand, and Australia (Bowen and Sydney Basins)	Neutron scattering measurements USANS and SANS	PSDs: 5 nm–7 μm, No image observation	PSDs and accessible PSDs in bituminous coals	[27]
Not mentioned	The Fucheng Colliery, Qiwu Colliery, and Cuizhuang Colliery in China	MIP, LP-N2GA, Fractal Analysis	Differentiated PSDs by each method	Pore structure and adsorption characteristics of destructed coals	[28]
Anthracite and semi-anthracite coal	The southern Qinshui Basin in China	FIB-SEM and X-ray CT	Differentiated PSDs by each method	Interconnected pores in coal	[29]
Anthracites	The Qinshui Basin in China	HPMI, AIP–FESEM, Fractal Analysis	Qualitative–quantitative combined method and corresponding PSDs	Pore size classification related to gas behavior	This research

Table 1. Representative research progress on structure and classification research of coal pores in recent years.

Samples	Source	Methods	Pore Size Characterization	Research Objective and Parameters	Literature
Anthracite, Low-/Medium-/High-volatile bituminous, Lignite coal	The northern China mining area	LP-N2GA, SEM	Pore images at micron scale; PSDs: <30 nm	Pore shape, specific surface area, pore volume	[23]
Tectonically deformed coals	Several collieries in north China	AFM	Pore images and corresponding PSDs: <15 nm	Tectonically deformed nanoscale pore structure and shape	[24]
Low-rank coals	The Erlian Basin, Hailar Basin, the Junggar Basin, and the Ordos Basin	MIP, NMR, SEM	Pore images at micron scale; Differentiated PSDs by each method	Pore structure evolution	[25]
Middle- and high-rank coals	Eastern Yunnan and Western Guizhou, China	MIP, LP-N2GA, Fractal Analysis	PSDs	Fractal characteristics of pore structure	[26]
Bituminous coals covering a wide range of rank	Poland, the US (Appalachian), New Zealand, and Australia (Bowen and Sydney Basins)	Neutron scattering measurements USANS and SANS	PSDs: 5 nm–7 μm, No image observation	PSDs and accessible PSDs in bituminous coals	[27]
Not mentioned	The Fucheng Colliery, Qiwu Colliery, and Cuizhuang Colliery in China	MIP, LP-N2GA, Fractal Analysis	Differentiated PSDs by each method	Pore structure and adsorption characteristics of destructed coals	[28]
Anthracite and semi-anthracite coal	The southern Qinshui Basin in China	FIB-SEM and X-ray CT	Differentiated PSDs by each method	Interconnected pores in coal	[29]
Anthracites	The Qinshui Basin in China	HPMI, AIP–FESEM, Fractal Analysis	Qualitative–quantitative combined method and corresponding PSDs	Pore size classification related to gas behavior	This research

The fractal characterization of porous media as an applicable tool has been well documented [30]. Fractal was initially developed to describe self-similarity and statistical irregularities of geometrics at all scales [31]. It has been demonstrated that porous materials including shale, coal, and tight sandstone are all fractal. [32,33]. In order to measure the degree of complexity, fractal dimension has been induced as a ratio that could provide a statistical index of complexity and compare how the detail in a pattern changes with the scale at which it is measured. Fractal dimension (D) could be measured by experimental results from HPMI, N₂ gas adsorption, SEM image, and SAXS [33,34,35,36]. The Menger sponge model derived from HPMI data has been widely used to calculate D due to its simple calculation process and accurate pore structural characterization [37,38]. The fractal theory builds a bridge between micromorphology (shape, pore size distribution, and pore connectivity) and macroperformance (porosity and permeability) [39,40]. By assigning fractal dimensions to the data, coal pore structure can be quantitatively characterized.

The exploration, utilization, and evaluation of coal and coalbed methane are affected by complex factors [41,42,43,44]. Researchers have identified coal reservoir pores as playing a crucial role in the storage, migration, and formation of coalbed methane, based on research on the pore characteristics and its influence on the reservoir properties, gas bearing properties, and coalbed methane’s exploitation [43,44,45]. High-rank coal has exceptionally developed nanopores and is confronted with the “bottleneck” issues in the exploitation of coalbed methane [16,34]. Therefore, it is crucial to conduct extensive research on the high-rank coal’s pores. In this research, 20 coal samples were collected from the Qinshui Basin, China. All samples were subjected to FESEM image analysis and MIP tests in order to characterize pore structure. Moreover, fractal characteristics were analyzed by establishing the Menger sponge model from MIP data. The pore classification methodology was established according to pore morphologies and fractal dimensions. Subsequently, the diffusion and adsorption features of coal were discussed by explaining the relationship between fractal dimensions and the pore parameters used to characterize pore structures, such as porosity, permeability, and specific surface area. This research is aimed to address the pore structure and pore classification problem from the perspective of fractal theory and deepen the understanding of the characteristics of pores in high-rank coals.

The pore classification and its relationship with gas storage and migration mechanism established in this research can be widely applied to characterize, compare, and quantitatively evaluate the coal pore system and provide support for the resource evaluation and prediction of coalbed methane. Furthermore, although rich coalbed methane is present in China’s high-rank coal, its exploitation is complicated by issues, such as limited mining capacity and rapidly declining productivity. Therefore, this study can help to explain the mechanisms of the “bottleneck” problems in China’s Qinshui Basin and other high-rank coal reservoirs. It should be noted that in the expanding application in various high-rank coal reservoirs, the coal samples used should be coal matrix samples that are not impacted by tectonical stress and other unique variables. The main tasks of the research include: (1) The systematical investigation into pore structural and fractal characteristics of high-rank coal samples and the establishment of pore natural classification related to the occurrence and migration of CBM with the combination of the kinetic characteristics of methane molecules. (2) The identification of predominately genetic types in a different pore size range through the combination of qualitative observation and quantitative test on the basis of a classification scheme. (3) The identification of the influencing factors of the structural and fractal characteristics and the advantages to integrate fractal parameters into the index to describe pore structure characteristics and heterogeneity degree of high-rank coal reservoirs.

2. Geological Setting

Qinshui Basin is one of the most important coalbed methane (CBM) exploration and exploitation areas in China (Figure 1a). Its width exceeds 330 km, and its area is roughly 23.5 × 103 km² [46,47,48]. All samples were taken from the Xinjing Coal Mine, which is located in the Shouyang–Yangquan monocline zone at the northeastern margin of the Qinshui Basin (Figure 1b). Coal-bearing strata in the research area mainly consist of the Taiyuan Formation and Permian Shanxi Formation, with an overall average thickness of over 150 m [49]. In particular, the thick widespread coal-bearing strata of the Taiyuan Formation are deposited on the area of marshes of tidal flats and delta plains [48]. The Taiyuan Formation mainly consists of coal seams, mudstone and sandstone, with a thickness ranging within 30–70 m in the study area (Figure 1c).

3. Materials and Methods

3.1. Samples

A total of 20 samples from the No. 15 coal seam of the Taiyuan Formation were directly taken from the working faces of Xinjing Coal Mine in Yangquan Area, Qinshui Basin (Figure 1a,b). The No. 15 coal seam is stable in the study area with thickness between 0.4 m and 8.7 m (average, 6.14 m). The basic information of the selected samples is shown in

Table 2. Proximate analysis and basic information of high-rank coal samples.

Sample	Ro, Max (%) a	Coal Type b	Maceral Compositions (Vol.%)
			Vitrinite	Exinite	Inertinite	Mineral
M1	2.22	Anthracite C	82.13	1.19	5.14	11.54
M2	2.94	Anthracite C	69.98	0.80	9.15	18.69
M3	3.41	Anthracite B	85.18	0.00	14.03	0.59
M4	2.39	Anthracite C	77.65	0.98	11.18	10.00
M5	3.49	Anthracite B	76.07	0.19	23.15	0.39
M6	4.37	Anthracite A	80.65	0.00	6.83	9.59
M7	3.67	Anthracite B	71.27	0.19	25.93	2.61
M8	2.40	Anthracite C	70.94	0.00	15.63	13.43
M9	2.27	Anthracite C	77.01	0.00	18.47	4.32
M10	2.83	Anthracite C	75.64	0.00	12.67	11.69
M11	2.99	Anthracite C	71.23	0.00	16.63	12.13
M12	2.87	Anthracite C	67.96	0.19	28.54	3.11
M13	2.52	Anthracite C	86.07	0.57	10.88	2.48
M14	2.91	Anthracite C	80.46	0.00	10.46	9.07
M15	3.15	Anthracite B	71.92	0.00	21.63	6.26
M16	3.05	Anthracite B	70.50	0.00	24.16	5.34
M17	2.91	Anthracite C	76.60	0.00	15.63	7.38
M18	3.64	Anthracite B	84.45	0.00	8.83	6.72
M19	3.07	Anthracite B	82.14	0.00	3.69	13.98
M20	3.25	Anthracite B	73.42	0.00	9.37	17.21
Average value	3.02	Anthracites	76.56	0.2055	14.6	8.3265

^a Ro, max (%): Mean maximum reflectance of vitrinite; ^b Coal type classified according to ISO 11760 (2005).

. All samples belong to anthracites based on ISO-11760 (2005) [50], with a Ro, max (%) value of 2.22–4.37%. As shown in Table 1, the maceral compositions (Vol.%) are mainly vitrinite (67.97–86.07%; average, 76.56%) with a small amount of inertinite (3.69–28.54%; average, 14.6%) and mineral content (0.39–18.69%; average, 8.3265%). However, exinite compositions are rarely found (0–1.19%; average, 0.2055%). Thus, all samples were vitrinite-rich coals, indicating a good capacity for methane due to the microporosity of vitrinite [51].

3.2. Methods

A combined analysis using HPMI and FESEM was chosen for the full-scale natural classification of the micro-reservoir space. Other methods, such as N₂ gas adsorption, can also characterize nanoscale pores in unconventional oil and gas reservoirs, and it has a good performance in the pore size of 2~50 nm. However, pores need to be analyzed and compared over a larger range. FESEM features significant multiscale analysis capability by using the image analysis technique, and the HPMI test results correspond better to the pore size range analyzed by FESEM. Therefore, this research performed the fractal analysis on HPMI data to realize the pores’ natural classification and compares it with the results from FESEM analysis. The comprehensive study combining HPMI, FESEM, and fractal model integrates qualitative observation and quantitative analysis and provides a more inclusive understanding of the pore structural characteristics of high-rank coal.

The AIP–FESEM experiment was conducted at Harbin Institute of Technology. A flat surface of 16 mm² was prepared for argon ion polishing (AIP), forming a polished section of Gaussian shape with extremely high surface quality. The Helios Nanolab 600i focused ion dual beam scanning electron microscope and S-4700 Field-Emission scanning electron microscope were used to image pores on the polished section. The polished surface was sprayed with gold before field emission electron microscopy observation. The thickness of the gold film was about 10 nm. The pore type classification carried out in this research was mainly based on the genesis and spatial location of pore development. Therefore, material component types on which the pore development is based are the key to confirming the pore type. In the pore classification, the identification of images and Energy Dispersive Spectroscopy (EDS) test data were used to clarify material components and consequently the type of pore. The scanning methods of EDS were divided into point scan, line scan, and surface scan. In the process of material component determination, the surface scan was used to clarify the planar distribution, and the point scan was applied to identify the specific mineral component type.

The HPMI experiment was conducted in the Key Laboratory of CBM Resources and Reservoir Formation Process, Ministry of Education (China University of Mining and Technology) using the AutoPore IV 9500 V1.09 analyzer of Micromeritics. The analyzer had four low-pressure ports and two high-pressure ports with a test pore size ranging within 3.600–0.003 µm. Before the HPMI test, the selected samples were dried for 24 h to remove the effect of bound water. When describing the PSDs and other structure characteristics, the pore size classification by Hodot (1966) was adopted to classify the reservoir pores into macropores >1000 nm, mesopores ranging within 100–1000 nm, transitional pores ranging within 10–100 nm, and micropores <10 nm, respectively [52].

HPMI data could describe pore structure characteristics in the range from nanoscale to micron- scale. Therefore, fractal modeling based on mercury intrusion data could provide a more comprehensive understanding of coal pore structure. Menger sponge fractal analysis generated 3D model on the nonlinear coal pore structures, which involved a correlation between gas flow capacity through coal porous medium and pore size distribution characteristics. Thus, the fractal dimension of coal pore characteristics including pore structure, range of pore sizes, and pore volume was systematically analyzed for their influence on coal permeability.

Fractal dimension can be calculated by establishing the Menger sponge model from HPMI data [34,40,53,54]. The original solid cube element with an intrinsically porous structure (side length of R) was split into 27 subcubes. Seven of the 27 subcubes were removed on the nucleus and center of each face. Twenty subcubes were left to do the same process, and after k times, a Menger sponge fractal model was established with a cube number of N_k and a side length r_k of R/mk. However, the development of the Menger sponge was dimensionally limited to the edge of the remaining subcubes [55]. After k times of the same process, the relationship between N_k and r_k can be described as Equation (1), according to the definition of fractal dimension:

$$N_k=R^D\cdot r_k^{-D}$$

(1)

In Equation (1), D is the fractal dimension.

Total pore volume V_k and total pore specific surface area S_k were described as:

$$V_k=N_k\cdot \frac{4}{3}\pi r_k^3=C{r}_k^{3-D}$$

(2)

$$S_k=N_k\cdot 4\pi r_k^2=C{r}_k^{2-D}$$

(3)

In Equations (2) and (3), C was a constant. The derivation on r_k in Equations (2) and (3):

$$\frac{d{V}_k}{d{r}_k}\propto r_k^{2-D}$$

(4)

$$\frac{d{S}_k}{d{r}_k}\propto r_k^{1-D}$$

(5)

The derivation on two sides of the Washburn’s equation based on the HMPI data and the relationship between the pore radius increment d_rk and pressure increment dP_(rk) can be described as:

$$d{r}_k=-\frac{r_k}{P(r_k)}\cdot dP(r_k)$$

(6)

In Equation (6), σ and cosθ were constants related to the surface tension of mercury and the nonwetting contact angle under laboratory conditions. Equation (6) and the Washurn equations were taken into Equations (4) and (5), and the logarithms were taken on both sides of the equation. The general formula, which describes the relationship between volume increment in fixed stress (dV/dP) and pressure (P), was established based on fractal theory and the Washurn equation [22]:

$$\lg \left[\frac{d{V}_k}{dP(r_k)}\right]\propto (D-4)\lg P(r_k)$$

(7)

$$\lg \left[\frac{d{S}_k}{dP(r_k)}\right]\propto (D-3)\lg P(r_k)$$

(8)

where D was the fractal dimension; V was the volume of the pore at each equilibrium pressure (P), which could be obtained via the incremental pore volume of mercury injection, and P was the equilibrium pressure. Thus, the relation curve of dV/dP and P could be drawn in the double logarithmic coordinate, according to Equation (7). The slope k of the linear part of the curve could be calculated based on Equation (7), and the fractal dimension D could be obtained as:

D = 4 + k

(9)

4. Results

4.1. Morphological Characteristics

Previous studies classified pores in unconventional reservoirs as mineral matrix pores, organic pores, and fracture pores, based on FESEM images [18,56]. The FESEM imaging results indicate that pores in coal were grouped into particle-related pores (organic pores in or around micro-organic components and mineral-related pores) and fracture pores. Figure 2 presents the FESEM images of different porous areas at nanoscale. Organic matter-hosted pores, pores in the mineralogical edge, and clay mineral pores were the major pore types in the tested coal samples. However, organic matter-hosted pores were the most common pore types in coal [57] (Li et al., 2017) due to the low content of minerals in coal (Table 1).

Mineral-related pores in coal were mainly developed within or on the mineralogical edge of clay minerals and other particle minerals, such as quartz. However, even in mineral rich areas, nanoscale organic matter-hosted pores were well-developed (Figure 2a). Figure 2b presents the image processing result of Figure 2a, showing the coexistence of organic matter pores, pores in the mineralogical edge, and clay mineral pores in this microarea. Organic matter-hosted pores were the predominant pores in coal with a pore size ranging from 10 nm to more than 500 nm (Figure 2c,d). Most of these clay mineral pores were intergranular pores of authigenic minerals, such as kaolinite (Figure 2e,f). Compared with the intergranular pores of clay minerals, pores in the mineralogical edge were developed with a relatively larger pore size (Figure 2g,h).

The morphological characteristics of organic matter-hosted pores were significantly different from the intergranular pores of clay minerals. Unlike organic matter pores in shale, which had a spherical or ellipsoidal morphology, nanoscale organic matter-hosted pores in coal usually had an irregular shape (Figure 2c,d). However, outgas pores in the microscale were developed in spherical or ellipsoidal shapes. The crescent or elongated shapes of clay mineral pores were controlled by the orientation of clay sheets (Figure 2e,f). It is hard to find a common shape from pores in the mineralogical edge, since these pore shapes are controlled by the morphology and contact mode of particles (Figure 2g,h). In the microscopic observations, the strong nonhomogeneity of pore development at the microscopic level should be noted. For example, in the observation area of a section of microscopic organic constituents in Figure 2d, pores in the mineralogical edge and clay minerals were not developed. However, in Figure 2e, pores in clay minerals were developed, while the organic pores were not developed in their adjacent organic matter.

4.2. Pore Structure Characteristics

The HMPI analysis results for pore structure characteristics are presented in

Table 3. Pore structure characteristics of the HPMI analysis of coal samples.

Samples	Vt/cm3/g	St/m2/g	Pa/nm	Φ/%	Eex/%	Vma/vol.%	Vme/vol.%	Vtr/vol.%	Vmi/vol.%
M1	0.0554	24.058	9.2	4.23668363	0.693971	0.141391	0.133841	0.405132	0.594868
M2	0.0437	23.442	7.5	2.875017847	0.836646	0.050663	0.049563	0.327251	0.572524
M3	0.0671	26.425	10.2	5.243544874	0.662968	0.095449	0.209747	0.282208	0.412595
M4	0.0361	19.257	7.5	2.483028784	0.837087	0.129555	0.049703	0.243811	0.576931
M5	0.0435	23.911	7.3	2.784934146	0.850978	0.10488	0.041491	0.258232	0.595397
M6	0.0302	16.468	7.3	2.142209757	0.835817	0.123626	0.039652	0.248222	0.5885
M7	0.0463	24.181	7.7	3.106191827	0.797199	0.085255	0.061752	0.295108	0.557885
M8	0.0417	21.796	7.7	3.178743539	0.81445	0.126779	0.063328	0.242133	0.56776
M9	0.031	17.817	7	2.038316061	0.888077	0.082111	0.038966	0.257422	0.621501
M10	0.0269	15.304	7	2.273857933	0.890588	0.071168	0.045663	0.266526	0.616642
M11	0.049	22.265	8.8	3.809653428	0.713238	0.187692	0.080622	0.24131	0.490376
M12	0.0401	19.237	8.3	3.007224346	0.768682	0.162004	0.068018	0.252918	0.51706
M13	0.0494	21.584	9.1	3.910959308	0.662878	0.149132	0.077111	0.312709	0.461048
M14	0.044	18.615	9.5	3.586923412	0.653708	0.219241	0.107855	0.218769	0.454135
M15	0.0547	19.835	11	4.991520702	0.529635	0.233452	0.140195	0.243524	0.382829
M16	0.0415	22.134	7.5	2.719432336	0.851428	0.125044	0.044963	0.254698	0.575295
M17	0.041	23.165	7.1	2.540655263	0.889488	0.087397	0.0346	0.266363	0.61164
M18	0.0428	22.574	7.6	2.846067496	0.827288	0.119889	0.052287	0.257824	0.57
M19	0.0357	20.007	7.1	2.340004794	0.8762	0.101501	0.036536	0.256486	0.605478
M20	0.0406	21.757	7.5	2.7318207	0.822922	0.100303	0.061896	0.261411	0.57639
Average	0.043035	21.1916	8.095	3.142339509	0.785162	0.124827	0.071889	0.269603	0.547443

Vt, total pore volume; St, total specific surface area; Pa, average pore diameter; Φ, apparent porosity, pore volume of pores with diameter >7.2 nm; E_ex, ejection efficiency; V_ma, volume ratio of macropores; V_me, volume ratio of mesopores; V_tr, volume ratio of transitional pores; V_mi, volume ratio of micropores.

. The volume of transitional pores (V_tr) and micropores (V_mi) varied from 21.88–40.51 vol.% to 38.28–62.15 vol.%, respectively. Macropores had a certain development degree (V_ma value of 5.07–23.35 vol.%, with a mean value of 12.48 vol.%). Mesopores were not developed with the smallest content of 3.46–20.97 vol.%, with a mean value of 7.19 vol.%. The apparent porosity (Φ) ranged from 2.04% to 5.24%, indicating the low porosity and limited reservoir space development of the tested high-rank coal samples. The HPMI total pore volume of the samples ranged from 0.0269 cm³/g to 0.0671 cm³/g, with an average of 0.0430 cm³/g, and the total specific surface area ranged from 15.304 m²/g to 26.425 m²/g, with an average of 21.1916 m²/g. The average pore size was at nanoscale, with a mean value of <10 nm.

Among the intrusion and extrusion curves in Figure 3, the lower ones are mercury intrusion curves obtained under pressurized conditions, while the upper ones are mercury extrusion curves acquired under pressure relief conditions. In the HPMI test, the liquid mercury entered pores as the pressure increased. After reaching its peak, the pressure was gradually released, leaving some liquid mercury in the pore system. Through the analysis of the relationship between the liquid mercury and the pore system under different pressure conditions, quantitative parameters could be provided for understanding the pore characteristics. Note that the pressure in the figure refers to absolute pressure. According to the HPMI intrusion and extrusion curves, these high-rank coal samples can be divided into two groups (Figure 3). Group a was more significantly noncoincident between the intrusion and extrusion curves when compared to group b (Figure 3). In addition, the intrusion and extrusion curves of group b samples were more reversible at whole range and more horizontal in shape. The differences between these two groups may correlate with the different connectedness and pressure sensitivity of the coal matrix.

PSDs are key influencing factors on the gas behavior of CBM [13], and the HPMI method has advantages in measuring PSDs in bigger pore size ranges when compared with N₂/CO₂ adsorption [58]. As shown in Figure 4, the PSDs of all tested high-rank coal samples were bipolar distributed with well-developed micropores, transitional pores, and macropores. However, the development of mesopores was limited. Incremental intrusion plots using HMPI data (Figure 4) suggest a significant pore volume in the nanoscale pore size range <100 nm. Sample M3 showed the largest pore volume, while sample M6 showed the least pore volume. High-rank coal samples shared similar uni- or multimodal PSDs with well-developed nanopores <100 nm and macropores, except for the M3 sample, which was relatively better developed at a pore size range of 100–1000 nm. Based on the fine observation of geological features, this sample exhibited a relatively low mineral content, while outgas pores were highly developed under SEM. The main pore sizes of outgas pores fell in the range of 100–1000 nm. Therefore, during the HPMI testing, the liquid mercury entered outgas pores under pressure, resulting in a relatively higher incremental pore volume in this range. All samples had a broad pore peak <15 nm and a minor but prominent peak >10 µm. The development of the minor peak may correlate with the microfractures and cleats or stress–relaxation fractures of the samples [59], while the development of the major peak may correlate with the nanoscale OM pores [40,60]. It was notable that pore structure distortion may occur when characterizing pores <3 nm due to the compressibility effects [61].

4.3. Fractal Characteristics

According to the Menger sponge fractal model, a plot of lg(P) vs. lg(dV/dP) showed a linear relationship, and the slope k was used to calculate the fractal dimension D: D = k + 4. The coal fractal analysis of 20 high-rank coal samples was performed through the lgP−lg(dV/dP) curve based on theoretical foundations. The results are illustrated in

Table 4. Fractal characteristics of the HPMI analysis of coal samples.

Sample	D1	R12	V1/cm3/g	S1/m2/g	D2	R22	Vm+h/cm3/g	Sm+h/m2/g
M1	3.1384	0.9528	0.0174	0.241	3.7041	0.9304	0.038	23.817
M2	2.7643	0.9173	0.0063	0.15	3.7207	0.9151	0.0374	23.292
M3	3.2413	0.8649	0.0244	0.477	3.5809	0.8769	0.0427	25.948
M4	3.0927	0.9125	0.0072	0.073	3.8973	0.6492	0.0289	19.184
M5	2.865	0.8289	0.0074	0.09	3.8831	0.6366	0.0361	23.821
M6	2.7485	0.9133	0.0056	0.057	3.9087	0.6736	0.0246	16.411
M7	3.0175	0.8226	0.0084	0.147	3.7392	0.9041	0.0379	24.034
M8	2.6392	0.9762	0.0089	0.097	3.8856	0.7237	0.0328	21.699
M9	2.8944	0.8913	0.0044	0.059	3.9171	0.591	0.0266	17.758
M10	2.8717	0.9162	0.0037	0.054	3.8856	0.6295	0.0232	15.25
M11	2.9264	0.8971	0.0144	0.132	3.8015	0.8584	0.0346	22.133
M12	3.0327	0.9095	0.0103	0.108	3.7927	0.8611	0.0298	19.129
M13	3.0206	0.8976	0.0136	0.21	3.6791	0.9384	0.0358	21.374
M14	3.2243	0.6911	0.0155	0.13	3.8142	0.9337	0.0285	18.485
M15	3.2443	0.7248	0.0231	0.274	3.7506	0.8869	0.0316	19.561
M16	2.8332	0.9331	0.008	0.088	3.8787	0.7721	0.0335	22.046
M17	2.7342	0.8887	0.0059	0.08	3.8826	0.8605	0.0351	23.085
M18	2.616	0.9223	0.0084	0.097	3.8599	0.8549	0.0344	22.477
M19	2.8068	0.8024	0.0057	0.066	3.9096	0.6417	0.03	19.941
M20	3.0736	0.8169	0.0075	0.091	3.8787	0.756	0.0331	21.666
Average	2.9393	0.8740	0.010305	0.13605	3.8185	0.7947	0.03273	21.05555

D₁, fractal dimension at lower pressure; R₁², correlation coefficient of lg(P) vs. lg(dV/dP) at lower pressure; V₁, pore volume of pores at lower pressure; S₁, specific surface area at lower pressure; D₂, fractal dimension at higher pressure; R₂², correlation coefficient of lg(P) vs. lg(dV/dP) at higher pressure; V_m+h, pore volume of pores at middle and high pressure; S_m+h, specific surface area at middle and high pressure.

and Figure 5.

From the plots of lgP−lg(dV/dP) (Figure 5), two or three distinct straight-line segments with different slopes were observed at the whole pressure range. That is, there were two or three nonscale ranges of dimension in the plots of lgP−lg(dV/dP), which corresponded to two or three different intervals of pore diameters and fractal dimensions, respectively. Most of the samples, except for sample M1 and sample M4, which had two segments, could be divided into three segments with two demarcation points. For samples with three segments (M2, M3, and M5–M20), the first demarcation point between the first and second segments of the pore diameter was for lg(P) in intervals from −0.3966 to −0.4758 (corresponding to the pore radius of 60–72 nm, with a mean value of 65 nm). The second demarcation point was in intervals from −0.7543 to −4.9728 (corresponding to the pore radius of 921.7–1027.1 nm, with a mean value of 1000 nm). When lg(P) < −0.3966, which corresponded to the third segment with a pore diameter >1,000 nm, the pore structure was significantly fractal for the average relative coefficient R₁² between the lgP and lg(dV/dP) of the samples, which was 87.4%. Meanwhile, the slope (k) of these lines in the third segments varied from −0.7557 to −1.3608, with calculated fractal dimensions (D1) ranging from 2.616 to 3.0927. The volume of pores in the third segments with a pore diameter of >1000 nm (V₁) at lower pressure ranged from 0.0037 to 0.0244 cm³/g, and the specific surface area varied from 0.057 to 0.274 m²/g. When lg(P) was within −0.3966 to −0.7543, which corresponded to the second segment with a pore diameter of 65–1000 nm, the pore structure was not fractal. Thus, for samples with three segments, the first and third segments had a good linear correlation. When lg(P) > −0.7543, which corresponded to the first segment with a pore diameter <65 nm, the mean value of the fractal dimensions and slope (k) of the line were 3.8185 and 0.1815, respectively. Compared with pores >1000 nm, the pore volume and specific surface area of pores <1000 nm (V_m+h and S_m+h) were significantly higher.

Curves between specific surface area increments in fixed stress (dS/dP) and pressure (P) in the double logarithm coordinates of the coal samples were established based on Equation (8) (Figure 6). As shown in Figure 6, the specific surface area distributions of pores smaller than 150 nm (lgP > 3) were significantly fractal. A previous fractal analysis revealed that the volume increment in fixed stress (dV/dP) declined with decreasing pressure and was phased-based on the plots of lgP−lg(dV/dP), indicating that the pore structure was also phase-based [22,44]. Pores < 150 nm were not phase-based and had significant fractal characteristics on a specific surface area in this study, indicating that the pores in this size range belonged to one pore system with a similar predominate genetic formation mechanism and development characteristics.

5. Discussion

5.1. The Structural Characteristics and Natural Classification of Pores

As the fractal geometry theory has pointed out, the more homogeneously distributed the pores are, the bigger the fractal dimension [62]. In the first line segment, all prepared samples similarly exhibited that the structure of pores with a diameter of over 65 nm was extremely complicated because the fractal dimension was closed to three, whereas the fractal dimensions of the second line segment were universally over three, which was unpractical, indicating that the structure of pores with a diameter below 65 nm was relatively not fractal, or the Menger model was inapplicable to the structural characterization of these pores. All samples revealed a catastrophic point in pore size, which ranged within 60–72 nm on the plots of lgP−lg(dV/dP), dominating the diffusion and adsorption features of methane in the reservoir [40]. The interval of 60–72 nm in the fractal analysis using China’s high-rank coal samples was also indicated by Zhao et al. [63] and Fu et al. [34].

A natural classification was helpful in correlating pores in different scales with pore networks in unconventional reservoirs [64]. As shown in Figure 7, scholars have put forward different classifications of pores in coal (Figure 7), which were mostly based on pore sizes [49,64,65] or pore types [32]. However, how to correlate pore classification with gas behavior remained a problem. Fractal analysis is a useful tool to build a bridge between structural characteristics and gas behavior [34,47].

In this research, three groups were demarcated by pore size intervals of 65 nm and 1 nm, namely diffusion pores, seepage pores (D-pores), and pico pores. They are shown as the 4th classification in Figure 7. Compared with previous classification schemes, this classification scheme synthesized pore size and gas migration mechanism (Figure 7).

The subinterval-division was based on the kinetic characteristics of methane molecules in coal [5,66,67,68,69,70,71,72]. The gas in P-pores was mostly stored in the absorption state, and the major transport mechanism was surface diffusion (Figure 8a). In the pore size range of D-pores (1–65 nm), the microreservoir space was subdivided into DI-pores, DII-pores, and DIII-pores, with pore size intervals of 5.3 nm and 15 nm, respectively. According to Knudsen diffusion, DI-pores with a pore size of <5.3 nm belonged to free molecular pores (Knudsen number [k_n] > 10 k_n is used to describe the transport mechanism incorporating Knudsen diffusion and viscous flow), with a major transport mechanism of molecular diffusing in the adsorption phase and solid solution phase (Figure 8b) [73,74,75]. A pore size interval of 15 nm was the pore diameter that had a significantly specific surface area and pore volume increment based on HPMI data. The major molecular diffusion in DII-pores and DIII-pores belonged to Knudsen diffusion, with a k_n value ranging from 1 to 10 (Figure 8c).

According to the HPMI analysis, DI-pores and DII-pores were the most developed types that contributed to the major pore volume and gas adsorption points, followed by SIII-pores. Pores in the pore size range of DIII-pores, SI-pores, and SII-pores (15–1000 nm) were relatively not well-developed. Thus, the tested high-rank coal samples had good storage capacity in nanopores, relatively good seepage capacity for viscous gas flow in macropores and fractures, and weak seepage capacity from major microreservoir spaces of micro- and transitional pores to macropores and microfractures. Thus, the special structural characteristics of pores in high-rank coals would lead to the “bottle-neck” problem of CBM productivity in high-rank coal reservoirs [76].

5.2. Genetic Types and Subtypes of Pores

The combination of qualitative observation and quantitative testing helped to deepen the understanding of unconventional reservoir pores [77]. AIP–FESEM was used to perform nanoscale observations on typical samples. Pores with different genetic types had distinct morphological characteristics, and six subtypes had predominant genetic types, respectively. Thus, the shapes of these pores in the fractal-based natural classification can be revealed through images (Figure 9).

According to the FESEM images and previous literature [59,78], P-pores and D-pores in the studied samples were predominately nanoscale OM pores, which included three major genetic types of interparticle pores: organic constituents (5–200 nm), metamorphic pores (<5 nm), and intermorphic pores (<5 nm). Thus, the predominant pore types of P-pores and DI-pores were metamorphic pores (<5 nm) and intermorphic pores (<5 nm), which had a complex shape [32,78]. Most DII-pores and DIII-pores fell into interparticle pores of organic constituents with triangular, slit-shaped, or quadrilateral pore topographies and a relatively simple pore structure (Figure 9f–h). Compared with D-pores, S-pores were more complex in genetic type and shape features (Figure 9a–f).

SI-pores (65–150 nm) had a similar major genetic type of interparticle pores of organic constituents (Figure 9f). However, SII-pores and SIII-pores had different major genetic types: outgas pores (100 nm–2 µm with spherical or ellipsoidal morphology), plant tissue pores (>500 nm with the complex shape), mineral-related pores (mostly intergranular pores of clay minerals with a sheet-like shape and pores on the mineralogical edge), and microfractures (Figure 9a–c). In the pore size range of SII-pores, the microreservoir space was mainly contributed by outgas pores, mineral-related pores, and plant tissue pores, while SIII-pores were mostly mineral dissolution pores and microfractures (Figure 9c).

5.3. The Relationship between Fractal Dimensions and Pore Parameters

Fractal analysis is a comprehensive and quantitative study of the complex pore structure of coal, which is affected by shape and spatial development characteristics. The influencing factors of the fractal and structural characteristics can be revealed by analyzing the relationship between fractal dimensions and structural indexes of pore volume, specific surface area, and pore size.

The fractal dimension value and pore parameters of high-rank coal samples are shown in Table 4. The mean radius (Pa) and total pore volume (Vt) showed a positive correlation with the fractal dimension D1 of S-pores (>65 nm), indicating that the higher the mean radius and total pore volume, the larger the fractal dimension of the S-pore (Figure 10a,c). It has generally been assumed that as the pore radius decreases, the structure heterogeneity increases, and the pore structure becomes more complex, increasing the fractal dimension. As the value of D1 becomes larger, the apparent porosity (Φ) became larger (Figure 10d), and the pore surface became rougher [31]. However, no significant correlation was found between the total specific surface area (St) and D1 (Figure 10b), suggesting that the impact of the specific surface area on the fractal dimension was limited.

It can be found that the higher the fractal dimension of D1, the higher the volume ratio of macropores (V_ma) and mesopores (V_me) and the smaller the volume ratio of micropores (V_mi) (Figure 10e,g,k). However, the correlation was not significant between D1 and the volume ratio of transitional pores (V_tr) (Figure 10i). This indicated that the higher the D1 value, the more developed the macro- and mesopores became. Furthermore, the fractal dimensions of D2 only showed a positive correlation with the volume ratio of micropores (V_mi) (Figure 10f,h,j,l). It is noteworthy that the relationships among pore volume, surface area, and fractal dimension were different with scale (Figure 10m–p). For seepage pores with a larger pore size, the more developed the S-pore pore volume (V1) and surface area (S1), the higher the fractal dimension (D1). On the contrary, for the absorption pores with nanoscale pore sizes, the indexes of the pore volume and surface area revealed a negative relationship with the fractal dimension (D2). The explanation for this phenomenon was that on a larger scale, the development of pores with large pore sizes reduced the total heterogeneity of the pore structure, whereas nanopores with heterogeneous spatial distributions might increase the pore structure’s complexity (Figure 11).

Fractal dimension quantitatively reflected the pore structure, the undulating state, and the roughness of the inner surface, while the pore structure influenced the adsorption and seepage capacities of the coal matrix [79,80,81]. Pores not only contributed significantly to reservoir space, but also influenced its permeability. As indicated by previous studies, the permeability contributed by seepage pores generally covered 10%–30% of the entire permeability [28]. The fractal-based classification was useful as a basis for evaluating seepage pores and matrix seepage ability. Furthermore, the fractal dimension was correlated with both structural parameters and other reservoir factors, such as reservoir material composition and formation conditions [47,81]. Fractal analysis was a more comprehensive characterization of reservoir structure, which could be used as an important index to describe pore structure characteristics and heterogeneity degree [82,83].

In the future, observed images and data of pores will continue to be collected on the basis of the established high-rank coal pore classification, and the growing data will further validate the current research. In addition, the outcome of the research will be applied to the evaluation, characterization, and exploitation of technology research of the Qinshui Basin and other high-rank coal reservoirs. A new method for reservoir pore structure comparison will also be explored on the basis of the pore size classification proposed in this study. By comparing the pore structure differences of reservoirs with different physical properties, gas-bearing characteristics, and development effect, the key factors and mechanisms affecting the high-rank coal production capacity at the microscopic scale will thus be identified.

6. Conclusions

The structural and fractal characteristics of reservoir pores in high-rank coal samples were analyzed using quantitative HPMI and qualitative AIP–FESEM observations. The conclusions drawn from these experimental results and fractal model are as follows:

(1)

The coal samples are bipolar distributed, and the majority of the pore volume is dominated by transitional pores and micropores, followed by macropores. The mesoporosity of high-rank coal is limited. The specific surface area is concentrated in micropores. The samples can be divided into two groups, according to the different shapes of HPMI: intrusion and extrusion curves.

(2)

Menger sponge fractal models are established by analyzing the plots of lgP-lg(dV/dP), showing two or three distinct straight-line segments with demarcation points of 65 nm and 1000 nm. Pores > 1000 nm are significantly fractal with the calculated fractal dimensions of D1, which vary from 2.616 to 3.0927. Pores of 65–1000 nm are not fractal, while pores <65 nm are relatively weakly fractal, with D2 values larger than 3.

(3)

A natural classification with three major types and seven subtypes is established based on the fractal characteristics and kinetic characteristics of methane molecular, which is correlated with pores in different scales, as well as pore networks and gas behavior. Diffusion pores (D-pores), seepage pores (S-pores), and pico pores (P-pores) are demarcated by pore size intervals of 65 nm and 1 nm.

(4)

P-pores and D-pores are predominately nanoscale OM pores with three major genetic types: interparticle pores of organic constituents (5–200 nm), metamorphic pores (<5 nm), and intermorphic pores (<5 nm). S-pores are more complex in genetic type, with the major genetic types of SII- and SIII-pores being outgas pores, plant tissue residual pores, mineral-related pores, and microfractures.

(5)

The mean radius (Pa), total pore volume (Vt), apparent porosity (Φ), and the volume ratio of macro- and mesopores are positively correlated with fractal dimension D1 of S-pores (>65 nm). Fractal parameters reflect the pore structure, the undulating state, and the roughness of the inner surface. These can be used as an important index to describe the pore structure characteristics. The fractal analysis of pore structure characteristics and natural classification also provides a novel approach for the study of microstructures and their influence on gas migration of high-rank coal reservoirs, which is helpful for revealing the origin of the “bottleneck” problem in both the Qinshui Basin and other high-rank CBM-bearing strata in China.