Pore Structure, Fractal Dimension, and Methane Adsorption Capacity of Coals: A Case Study from the Huaibei Coalfield, China

Abstract

The Huaibei Coalfield hosts abundant coalbed methane (CBM) resources, yet its heterogeneous pore structure poses challenges for efficient development. In this study, the multiscale pore structure was characterized using field-emission scanning electron microscopy (FE-SEM), mercury intrusion porosimetry (MIP), and N₂/CO₂ adsorption experiments, and fractal dimensions were quantified to reflect pore heterogeneity, and methane adsorption capacity was tested with the improved Langmuir equation. The results indicate that the coal samples are medium-rank bituminous coal, with a maximum vitrinite reflectance (R _o,max) of 0.73%–0.96%. Vitrinite constitutes the major maceral component, while mineral contents remain low. FE-SEM and EDS analyses reveal highly heterogeneous pore fractures and mineral compositions. Of the total pore volume, micropores and macropores together account for approximately 90.81%, with volumes of 0.72–1.86 cm³/100 g (average of 1.24 cm³/100 g) and 0.32–4.99 cm³/100 g (average of 1.54 cm³/100 g), respectively. The specific surface area of micropores is 18.13–48.94 m²/g (average of 32.21 m²/g), which accounts for 99.55% of the total on average. In addition, the coal rank promotes micropore development, whereas the inertinite content negatively correlates with macropore volume. Methane adsorption capacity is 0.81–1 mmol/g (average of 0.92 mmol/g), which is primarily controlled by the volume and specific surface area of micropores but shows no relationship with the maceral or mineral component. Moreover, methane adsorption capacity shows positive correlations with fractal dimensions D _N21 and D _CO2 but a negative correlation with D _N22. From a kinetic perspective, mesopores and macropores can accelerate gas transport and shorten equilibrium time. This study offered scientific support for CBM assessment and exploitation in the Huaibei Coalfield.

1. Introduction

As a major clean energy source, coalbed methane (CBM) plays a key role in energy optimization, pollution reduction, and the sustainable development. , In China, the discovery of high-yield CBM wells in regions such as the eastern margin of the Ordos Basin has further demonstrated the enormous resources. The Huaibei Coalfield, as an important coal production base in the Huainan–Huaibei region, is endowed with abundant CBM resources. However, the complex and highly heterogeneous pore structure of coals has severely hindered an in-depth understanding of CBM occurrence and migration mechanisms. − Accordingly, systematic characterization of the pore structure and its correlation with methane adsorption capacity have become an urgent task.

The pore structure includes several key parameters, such as pore type, pore size distribution, specific surface area, pore volume, and connectivity, which directly control methane adsorption, desorption, diffusion, and seepage capacities. , Extensive research has focused on pore structure characterization using multiple approaches and can be classified into image observation techniques, fluid intrusion methods, and nondestructive physical approaches. Image observation techniques, such as field-emission scanning electron microscopy (FE-SEM) and atomic force microscopy (AFM), provide direct visual evidence of the geometry and spatial arrangement of pores and fractures. , However, their limitations in observation scope and resolution make it difficult to achieve statistical representativeness and accurate characterization of nanoscale pores. , Reliable experimental datasets obtained under carefully controlled laboratory conditions remain essential for validating pore characterization techniques and improving the interpretation of coupled physical processes in geomaterials. , Fluid intrusion techniques, represented by mercury intrusion porosimetry (MIP) and N₂/CO₂ adsorption, are widely employed for quantitative analysis of pore structure parameters. , Although each technique covers a distinct pore size interval, individual methods possess inherent limitations. For example, MIP may cause compression of the coal matrix and reduce the data accuracy of micropores (<2 nm) and mesopores (2–50 nm). N₂ adsorption exhibits insufficient sensitivity to micropores, while CO₂ adsorption is limited to the characterization of mesopores and macropores (>50 nm). , Nondestructive physical methods, such as nuclear magnetic resonance (NMR) and small-angle X-ray scattering (SAXS), allow for noninvasive characterization of pore structures, , yet they still face challenges in achieving comprehensive coverage of multiscale pore characterization.

Fractal theory, with its unique advantage in describing complex and irregular structures, has been increasingly applied in the study of coal pore structures. − Fractal dimensions can effectively quantify the surface roughness and structural heterogeneity of pores and are associated with methane adsorption and migration capacities. , Various fractal models, such as the Frenkel–Halsey–Hill (FHH) model and Menger model, have been developed to analyze pore complexity. − In terms of methane adsorption capacity, traditional models such as the Langmuir model have been widely used. However, they tend to simplify the actual adsorption process, which can lead to deviations between predicted data and actual adsorption capacity. ,, The dominant factors influencing the methane adsorption capacity include the pore structure, fractal dimensions, macerals, and minerals. , For instance, vitrinite dominates the adsorption behavior due to its abundant micropores and sufficient adsorption sites. However, the isolated pore structure of inertinite restricts effective gas adsorption, and the compact organic texture of exinite leads to a weak methane adsorption capacity. Additionally, the mineral occupies internal pore spaces, which is responsible for the reduced adsorption capacity of coals. In addition to material composition, the pore structure plays a dominate role in methane storage. Previous studies have shown that micropores are the main sites for methane adsorption, while mesopores and macropores serve as migration channels to accelerate gas transfer and reduce the time required to reach adsorption equilibrium from a kinetic viewpoint. Nevertheless, most previous regional studies on coals of the Huaibei Coalfield discussed equilibrium methane adsorption capacity and rarely systematically linked full-scale pore heterogeneity and fractal features to gas dynamic migration behaviors, which leaves space for further comprehensive evaluation of CBM adsorption characteristics in this area. ,

In this study, we systematically characterized full-range pore structures, fractal features, and their effects on the methane adsorption capacity of coals in the Huaibei Coalfield. FE-SEM, MIP, and N₂ and CO₂ adsorption were combined to obtain multiscale pore parameters, and fractal theory was used to quantify pore heterogeneity. Methane adsorption tests were performed, and correlations between coal properties and pore structure parameters were analyzed. The effects of pore volume, specific surface area, macerals, and fractal dimensions on methane storage capacity were further discussed. Beyond equilibrium adsorption, we qualitatively interpreted the dual roles of mesopores and macropores in methane mass transport and adsorption kinetics by published diffusion theories. Thereby, this study provides scientific guidance and technical support for the accurate assessment and efficient exploitation of CBM resources in the Huaibei Coalfield.

2. Geological Setting

The Huaibei Coalfield is located on the southeastern margin of the North China Plate and the eastern part of the Yu-Huai Depression (Figure ), with regional tectonics predominantly governed by EW and NE trending faults as well as the Xusu structure. Subjected to multistage tectonic events, major faults within the study area were well-developed and spatially intertwined. − The coal-bearing strata are Carboniferous and Permian. The Carboniferous Taiyuan Formation contains 5–6 coal seams, which are mainly distributed in the upper and lower parts and are thin, unstable, and unmineable.

1.

Geological structure, coalmine distribution, and sampling sites of the Huaibei Coalfield.

The Permian coal-bearing strata are divided into the Shanxi Formation, the Lower Shihezi Formation, and the Upper Shihezi Formation. The Shanxi Formation has a thickness of 100–130 m and contains No. 10 and 11 coal seams. The Lower Shihezi Formation has a thickness of 180–240 m, with lithology mainly composed of sandstone, siltstone, and mudstone. It is the main coal-bearing rock series, containing 6–12 layers from No. 4 to 9 coal seams. Among them, the No. 8 coal seam is the main mining coal seam. The Upper Shihezi Formation has a thickness of about 380–700 m and contains No. 1 to 3 coal seams. Among them, the No. 3 coal seam is locally mineable with a thickness of 0–1.89 m.

3. Samples and Methods

3.1. Sample Collection

As illustrated in Figure , a total of 12 fresh coal samples were collected from 9 sampling sites within the Guoyang, Linhuan, and Suzhou mining areas. These samples represent typical coal-bearing seams of the above three mining subareas. Given the geological heterogeneity of the Huaibei Coalfield, the present results are mainly applicable to the sampled areas. All coal samples were immediately sealed and stored in the laboratory to minimize oxidation and ensure the reliability of subsequent experimental tests. Prior to sampling, information including the sampling site, sample number, and coal seam was recorded and is listed in Table . Subsequently, three key tests were carried out on all coal samples, namely, proximate analysis, maceral analysis, and maximum vitrinite reflectance (R _o,max) test, which was conducted in accordance with the Chinese National Standard GB/T 212–2008, GB/T 8899–2013, and GB/T 6948–1998, respectively. Moreover, the remaining samples were prepared according to the required weight and mesh size for pore structure analysis.

1. Sample Sites and Basic Parameters of the Collected Coal Samples from the Huaibei Coalfield .

			proximate analysis (%)			maceral analysis (%)
sample site	coal seam	sample No.	M ad	A d	V daf	vitrinite	inertinite	exinite	mineral	R o,max (%)
Renlou	8	RL-22–2	1.06	12.35	32.36	65.32	19.27	6.64	8.75	0.95
Xinhu	3	XH-3	0.78	14.93	29.37	80.38	12.31	4.27	3.04	0.73
Xutuan	7	XT-1	1.34	24.03	38.15	75.09	12.64	5.10	7.17	0.83
Xutuan	3	XT-4	1.22	15.65	36.93	74.34	13.46	6.58	5.62	0.82
Jiegou	7	JG-1	0.80	18.98	31.37	69.27	14.63	6.09	10.01	0.96
Qi’nan	7	QN-4	1.05	22.49	38.27	67.05	19.67	6.88	6.40	0.78
Luling	10	LL-1	0.98	17.20	37.21	83.70	10.71	0.99	4.60	0.75
Zhuxianzhuang	8	ZXZ-1	2.59	18.75	34.44	77.21	16.24	3.24	3.31	0.83
Zhuxianzhuang	10	ZXZ-2	1.71	22.12	41.75	72.40	13.70	8.60	5.30	0.74
Qidong	7	QD-1	1.18	20.72	37.32	61.03	24.92	8.02	6.03	0.84
Qidong	8	QD-2	0.68	25.22	37.84	64.50	27.86	9.08	4.67	0.86
Taoyuan	10	TY-1	1.16	15.90	39.62	71.13	14.24	9.05	5.58	0.76

^aNote: M _ad = moisture content; A _d = ash content; V _daf = volatile matter content; and R _o,max = maximum vitrinite reflectance.

3.2. FE-SEM Characterization

Zeiss Gemini 300 SEM equipment (Germany) integrated with an energy dispersive spectrometer (EDS) was employed to capture the images of the pore fracture structure of selected coal samples according to the Chinese Oil and Gas Industrial Standard SY/T 5162–2014. The pore fracture morphologies represent natural cross sections of coal, which were pretreated with gold sputtering coating. All SEM observations were performed at a temperature of 24 °C and a relative humidity of 35%, and pore features were inferred and analyzed based on the acquired FE-SEM images. In addition, EDS was applied to identify mineral components in selected regions.

3.3. MIP Analysis

MIP tests were executed on a Micromeritics AutoPore IV 9505 mercury porosimeter (USA) in accordance with the Chinese National Standard GB/T 21650–2008. All coal samples were first dried at 105 °C for 12 h, and test specimens with a particle size of 1–2 mm and a mass of 10–15 g were then prepared. The measurements were carried out at a temperature of 24 °C, with a maximum pressure of 60,000 psia. This measurement quantitatively characterized the macropore structures of coal samples, and a relative standard deviation of ≤5% was maintained to ensure the reliability and repeatability of experimental results.

3.4. Low-Pressure N₂/CO₂ Adsorption Analysis

In line with the Chinese National Standard GB/T 19587–2004, a Micromeritics ASAP 2460 surface area analyzer (USA) was used for low-pressure CO₂ and N₂ adsorption experiments. For sample pretreatment, 1–2 g of 40–60-mesh powdered coal samples was dried at 105 °C for 24 h to thoroughly remove adsorbed moisture and atmospheric gases. In experimental data processing, the Brunauer–Emmett–Teller (BET) and Barrett–Joyner–Halenda (BJH) models were applied to estimate mesopore structural parameters based on N₂ adsorption data, and the Dubinin–Radushkevich (D–R) and Dubinin–Astakhov (D–A) models were used to process CO₂ adsorption data.

3.5. Methane Adsorption Analysis

Methane adsorption isotherms of coal samples were tested by a Beishide 3H-2000PH high-temperature and high-pressure gas adsorption analyzer (China) in accordance with the Chinese National Standard GB/T 19560–2004. Coal samples were pulverized to 60–80 mesh and 2–3 g of each sample was prepared for the experiment. Prior to the adsorption tests, coal samples were dried at a constant temperature of 60 °C for 24 h to remove moisture and eliminate its interference on the test results. All methane adsorption measurements were carried out at a constant temperature of 30 °C and a maximum pressure of 10 MPa. Adsorption measurements yield excess adsorption data, whose deviation from true absolute adsorption values grows with increasing pressure. Since the conventional Langmuir model assumes absolute adsorption and fails to correct this bias, an improved Langmuir equation with a density correction term is adopted. It transforms excess adsorption experimental results into absolute adsorption parameters and provides reliable fitting for high-pressure methane adsorption isotherms. The improved equation is shown in eq ,

$$V_{\mathrm{e}\mathrm{x}}=\frac{V_{\mathrm{L}}P}{P_{\mathrm{L}}+P}\left(1-\frac{{\rho }_{\mathrm{g}}}{{\rho }_{\mathrm{a}}}\right)$$ 1

where V _L is the Langmuir volume, m³/t; P _L is the Langmuir pressure, MPa; P is the equilibrium pressure, MPa; V _ex is the excess adsorption volume, m³/t; ρ_g is the gas phase density, t/m³; and ρ_a is the adsorbed phase density, t/m³.

Notably, the methane adsorption capacity of each sample was converted to mmol/g at standard temperature and pressure, with the molar volume of methane taken as 22.414 cm³/mmol for unit conversion. The equation is given as follows

$$M_{\mathrm{L}\mathrm{C}}=\frac{V_{\mathrm{e}\mathrm{x}}}{22.414}$$ 2

where M _LC is the converted Langmuir volume, mmol/g.

3.6. Fractal Dimension Calculation of Pore Fracture Structures

For FE-SEM images, the box-counting method was employed for fractal dimension calculation mainly due to its effectiveness in characterizing the heterogeneous pore fracture distribution on coal surfaces. The equations are as follows in eqs and ,

$$D_{\mathrm{FE}}=-\lim \delta \to \infty \frac{\ln (N(\delta ))}{\ln \delta }$$ 3

$$\ln (N(\delta ))=-D_{\mathrm{FE}}\ln \delta +C$$ 4

where D _FE is the fractal dimension, N(δ) is the quantity required to fully cover the binary image, and C is a constant value based on the linear plot of ln­(N(δ)) vs lnδ.

As for MIP data, the Menger sponge model was applied to calculate the fractal dimension, given as follows in eq ,

$$\ln \left(\frac{\mathrm{d}V}{\mathrm{d}P}\right)=\ln B+(D_{\mathrm{M}\mathrm{I}\mathrm{P}}-4)\ln P$$ 5

where P is the mercury intrusion pressure, V is the cumulative volume, D _MIP is the fractal dimension, and B is the slope based on the plot of In­(dV/dP) vs ln P.

Fractal dimensions of N₂ adsorption results were determined using the FHH model. The fractal method is expressed as follows in eq

$$\ln \left(\frac{V}{V_{\mathrm{m}}}\right)=A\ln \left[\ln \left(\frac{P_0}{P}\right)\right]+C$$ 6

where V is the adsorbed volume under equilibrium pressure (cm³/g), V _m is the monolayer coverage volume under equilibrium pressure (cm³/g), and A is derived from the plot of ln­(ln­(P ₀/P)) vs ln­(V). Here, P is the equilibrium adsorption pressure (MPa), P ₀ is the saturation adsorption pressure (MPa), and C is a constant. Eqs and were used to calculate the fractal dimensions of mesopores, which are expressed as follows

$$D_{\mathrm{N}2}=A+3$$ 7

$$D_{\mathrm{N}2}=3(A+1)$$ 8

Specifically, eq is suitable for conditions controlled by capillary condensation, and eq is typically used for those governed by van der Waals forces. For coal and shale, the fractal dimension ranges from 2 to 3. In addition, D _N21 and D _N22 refer to the fractal dimensions calculated by eq .

Regarding micropore structures, fractal dimensions were calculated from CO₂ adsorption data using the volume–specific surface area (V–S) model, as described in eq

$$\ln V=\frac{3}{D_{\mathrm{CO}2}}\ln S+C$$ 9

where V and S represent the cumulative pore volume (cm³/g) and specific surface area (m²/g), respectively, D _CO2 is the fractal dimension, and C is a constant.

4. Results

4.1. Basic Information on Coal Samples

The data of basic tests are shown and listed in Table . The maximum vitrinite reflectance (R _o,max) of collected samples is in the range of 0.73–0.96% (average of 0.82%), which corresponds to medium-rank bituminous coal. Maceral analysis shows that vitrinite is 61.03%–83.70% (average of 71.79%). Inertinite accounts for 10.71%–27.86% (average of 16.65%), and exinite accounts for 0.99%–9.08% (average of 6.25%). Proximate analysis shows that coal samples have low moisture content (M _ad) overall, with a value of 0.68%–2.59% (average of 1.21%). Ash content (A _d) is between 12.35% and 25.22% (average of 19.03%) and shows obvious variation among different sampling sites. In addition, volatile matter content (V _daf) falls between 29.37% and 41.75% (average of 36.22%).

Notably, despite the similar coal rank, maceral composition and proximate analysis indexes vary among different sampling sites and coal seams. Sample LL-1 exhibits the highest vitrinite content (83.70%) and the lowest exinite content (0.99%). In contrast, sample QD-2 shows the highest inertinite content (27.86%) and exinite content (9.08%). As for proximate analysis, samples ZXZ-1, QD-2, and ZXZ-2 record the highest moisture content (2.59%), ash content (25.22%), and volatile matter content (41.75%), respectively.

4.2. CH₄ Adsorption Capacity

CH₄ adsorption capacity was determined and fitted with eqs and . Figure shows that CH₄ adsorption volume increases sharply first, followed by a slow-rising trend with increasing equilibrium pressure. Academically, CH₄ adsorption of coal increases with pressure to a constant with isotherms being Type I. As shown in Table , the converted Langmuir volume is 0.81–1.00 mmol/g (average of 0.92 mmol/g) and Langmuir pressure is 1.98–3.92 MPa (average of 2.96 MPa). The No. 8 coal seam has a relatively higher adsorption capacity, with the sample RL-22–2 reaching the maximum value of 1.00 mmol/g. Overall, the adsorption capacity varies slightly among samples, with minor differences in the same seam from different coalmines.

2.

CH₄ adsorption isotherms at 30 °C and 10 MPa fitted by an improved Langmuir equation of coals from the Huaibei Coalfield.

2. CH₄ Adsorption Capacity of Coals from the Huaibei Coalfield .

sample site	coal seam	sample no.	M CL (mmol/g)	P L (MPa)
Renlou	8	RL-22–2	1.00	3.46
Xinhu	3	XH-3	0.81	3.38
Xutuan	7	XT-1	0.99	2.76
Xutuan	3	XT-4	0.97	2.40
Jiegou	7	JG-1	0.95	3.92
Qi’nan	7	QN-4	0.83	2.61
Luling	10	LL-1	0.88	3.33
Zhuxianzhuang	8	ZXZ-1	0.89	2.69
Zhuxianzhuang	10	ZXZ-2	0.84	2.83
Qidong	7	QD-1	0.98	2.81
Qidong	8	QD-2	0.87	1.98
Taoyuan	10	TY-1	0.98	3.00

^aNote: M _LC = converted Langmuir volume and P _L = Langmuir pressure.

4.3. FE-SEM Results

FE-SEM observations and EDS analysis are shown in Figure . Overall, various pores and microfractures were observed in all samples, and the size varies from nanometers to micrometers. As shown in Figure a,g, tissue pores occur in fusinite, telinite, and phyllovitrinite. Within the latter two macerals, some tissue pores still preserve plant cell structures. Gas pores are elliptical metamorphic pores aligned in a preferred orientation within vitrinite, with widths exceeding 0.1 μm (Figure b). In contrast, gas pores of coals in the Huainan Coalfield are 0.1–1 μm in diameter and distributed in clusters, and crescent-shaped pores were observed due to the high lithostatic pressure. As illustrated in Figure c, pores display considerable morphological diversity, including circular, elliptical, and irregular geometries. As shown in Figure d–f, microfractures are randomly and irregularly distributed and vary in morphology and size. With a maximum width of nearly 1 μm, they are short and straight and show preferred orientation (Figure d,e). Under external stress, some become oriented and elongated into “X”-shaped patterns (Figure e). In vitrinite, well-developed microfractures are clearly visible and have excellent connectivity and can significantly enhance permeability.

3.

SEM images and EDS analyses of coals from the Huaibei Coalfield.

As shown in Figure g–i, quantitative analysis of mineral elements was performed using EDS on three distinct regions of two samples from the Qidong Coalmine. Specifically, the marked region in Figure g is dominated by the major elements C, Ca, O, and Ti, accompanied by lower contents of Rb and Al. As shown in Figure h, the region primarily consists of O, C, Rb, and Al and a minor amount of Ti. As shown in Figure i, the major elements are O, Rb, Al, and C, with trace amounts of Ti and Ca. Overall, these results reveal clear differences among the regions in terms of morphological features, elemental composition, and modes of mineral occurrence, which highlight the strong heterogeneity of multiphase components in coal and the complexity of its diagenetic environment.

In this study, high-contrast binary images were derived from raw FE-SEM micrographs using software ImageJ (USA), where white zones correspond to the coal matrix and black zones are pore fracture systems (Figure ). Quantitative fractal characterization was subsequently conducted using the box-counting approach based on eqs and . The calculated fractal dimensions for the samples TY-1, XT-1, and ZXZ-2 are 1.8924, 1.8337, and 1.8769, respectively. Collectively, the result illustrates that the pore fracture system in coal samples demonstrates distinct fractal characteristics.

4.

Binary images (a–c) and fractal dimension (d–f) of coals from the Huaibei Coalfield. Note: Figures 4a–c were derived from Figure a,b,f.

4.4. Characteristics of Macropores

Pore structure parameters of macropores based on MIP curves are listed in Table . The porosity is 1.86–10.04% (average of 4.08%). The volume and specific surface area of macropores are 0.32–4.99 cm³/100 g (average of 1.54 cm³/100 g) and 0.03–0.68 m²/g (average of 0.14 m²/g), respectively. The minimum macropore volume (0.32 cm³/100 g) and specific surface area (0.03 m²/g) both appear in the sample QD-1 from the No.7 coal seam of the Qidong Coalmine. In contrast, the maximum values of these two parameters are recorded in sample QD-2 from the No.8 coal seam. Extreme values of the macropore parameters all concentrate in samples from the Qidong Coalmine, which indicates a consistent variation trend of macropore properties.

3. Pore Structure Parameters of Coals from the Huaibei Coalfield.

				pore volume (cm3/100 g)				specific surface area (m3/g)
sample site	coal seam	sample No.	porosity (%)	MIP	N2	CO2	Total	MIP	N2	CO2	total
Renlou	8	RL-22–2	3.30	0.75	0.06	1.86	2.67	0.10	0.17	48.94	49.21
Xinhu	3	XH-3	4.31	1.85	1.07	0.92	3.84	0.09	6.49	23.84	30.42
Xutuan	7	XT-1	3.71	1.15	0.08	1.63	2.86	0.06	0.21	42.93	43.20
Xutuan	3	XT-4	4.39	1.68	0.05	1.25	2.98	0.11	0.15	32.61	32.87
Jiegou	7	JG-1	3.11	1.79	0.06	1.45	3.30	0.09	0.26	35.70	36.05
Qi’nan	7	QN-4	3.51	1.06	0.09	0.72	1.87	0.10	0.42	18.13	18.65
Luling	10	LL-1	5.41	2.47	0.19	0.96	3.62	0.16	0.19	24.49	24.84
Zhuxianzhuang	8	ZXZ-1	2.87	0.69	0.23	1.26	2.18	0.08	1.03	33.18	34.29
Zhuxianzhuang	10	ZXZ-2	3.33	0.96	0.14	0.79	1.89	0.10	0.45	20.07	20.62
Qidong	7	QD-1	1.86	0.32	0.81	1.52	2.65	0.03	3.78	41.24	45.05
Qidong	8	QD-2	10.04	4.99	0.32	1.25	6.56	0.68	1.58	33.13	35.39
Taoyuan	10	TY-1	3.09	0.76	0.23	1.21	2.20	0.10	1.22	32.22	33.54

Clear hysteresis is observed between the intrusion and extrusion curves of coal samples (Figure ). Two explanations for this phenomenon have been reported, namely, contact angle fluctuations during MIP tests and the pore structure. However, contact angle-induced hysteresis alone cannot fully explain the observed features, as mercury intrusion and extrusion are essentially governed by the pore structure of coal. As for pore morphology and MIP measurement, mercury intrusion into blind-end slit and ink bottle-shaped pores is dominated by pore throat size, while the extrusion process is constrained by the pore body. ,

5.

Mercury intrusion/extrusion curves based on the cumulative intrusion volume vs pressure of MIP results.

As shown in Figure , pore size distributions were plotted. Multipeaked distributions exhibit at pore sizes of 5–10 nm, 30–50 nm, 100–300 nm, 0.40–3 μm, and 10–40 μm. For samples ZXZ-2 and QD-1, mesopores account for a relatively higher proportion, while macropores are poorly developed, a structural feature that is unfavorable for methane desorption. Sample QD-2 shows a moderate proportion of both mesopores and macropores, which creates favorable conditions for methane desorption.

6.

Pore size distribution based on MIP results of coals from the Huaibei Coalfield.

4.5. Characteristics of Mesopores

As shown in Table , the volume and specific surface area of mesopores are 0.05–1.07 cm³/100 g (average of 0.28 cm³/100 g) and 0.15–6.49 m²/g (average of 1.33 m²/g), respectively. Distinct from the macropore structure parameters of samples QD-1 and QD-2, the extremum indices are distributed in Xutuan and Xinhu Coalmines, which reflects the independent structural development of mesopores and macropores. Based on the International Union of Pure and Applied Chemistry (IUPAC) classification, H3 hysteresis loops appear in the moderate relative pressure range and correspond to bottleneck-shaped mesopores, while ink bottle-shaped mesopores generate characteristic H2 hysteresis loops. Figure shows the N₂ adsorption/desorption isotherms for six representative coal samples. Three key regions are identified based on the relative pressure: low (P/P ₀ < 0.1), moderate (0.1 < P/P ₀ < 0.9), and high (P/P ₀ > 0.9). In the low-pressure region, the overlap of adsorption/desorption branches implies that the dominant pore type is characterized by poorly connected and semiopen pores. Within the moderate-pressure region, adsorption volume shows little change with rising P/P ₀, suggesting the dominance of bottleneck-shaped mesopores. As for sample QD-1, the highest adsorption volume is observed in Figure e with an H2 hysteresis loop, whereas that of sample LL-1 is the H3 type. In addition, the adsorption curve rises sharply as P/P ₀ nears 1; this indicates the existence of well-developed, highly connected mesopores and macropores.

7.

N₂ isotherms of coals from the Huaibei Coalfield.

As shown in Figure , all six samples exhibit dominant peaks at a pore size range of 2–50 nm; it suggests that mesopores are the main storage space. Sample XH-3 shows sharp, single peaks, which reflects the narrow and homogeneous pore structures (Figure a). Conversely, sample QD-1 shows a broadened profile with elevated dV/dD values, indicative of aggregative pores with a broader size distribution (Figure e). In addition, sample QN-4 exhibits a relatively wide single peak (Figure b), and samples LL-1, ZXZ-2, and QD-2 displays a bimodal or highly broadened peak (Figure c,d,f).

8.

Pore size distribution based on the N₂ adsorption results of coals from the Huaibei Coalfield.

4.6. Characteristics of Micropores

As shown in Table , the volume and specific surface area of micropores are 0.72–1.86 cm³/100 g (average of 1.24 cm³/100 g) and 18.13–48.94 m²/g (average of 32.21 m²/g), respectively. The minimum volume and specific surface area both appear in sample QN-4 from the No.7 coal seam of the Qi’nan Coalmine. By contrast, the maximum values of these two parameters are recorded in sample RL-22–2 from the No.8 coal seam of the Renlou Coalmine. The extreme values of the CO₂-determined parameters are distributed in different coalmines and coal seams, which indicates an obvious spatial variation characteristic of micropore properties.

In addition, CO₂ adsorption isotherms show similar morphological characteristics, which are Type I isotherms (Figure ). This result demonstrates that no unbalanced capillary condensation occurs during the micropore filling process. As shown in Figure , the main peaks of pore size distribution are concentrated within the narrow interval of 1.0–1.3 nm. Samples XH-3 and ZXZ-2 show secondary peaks at 1.4–1.8 nm, which presents a slight multipeak distribution characteristic. Additionally, sample QD-1 features the highest development degree of the dominant micropores, while sample XH-3 is the weakest.

9.

CO₂ adsorption isotherms of coals from the Huaibei Coalfield.

10.

Pore size distribution based on the CO₂ adsorption results of coals from the Huaibei Coalfield.

4.7. Results of Fractal Dimensions Based on Fluid Invasion Methods

4.7.1. MIP

Based on MIP data and eq , fractal dimension calculation and pore structure characterization were conducted for all samples. The R ² values of linear fitting for ln­(dV/dP) vs ln P range from 0.9036 to 0.9859; this verifies that pore structures exhibit distinct fractal characteristics (Figure a,b). In addition, the fractal dimension D _MIP was obtained and is listed in Table , which ranges from 2.7562 to 2.9758 (average of 2.8591). In addition, the slope (D _MIP–4) of ln­(dV/dP) vs ln P spans from −1.2438 to −1.0083.

11.

Fractal dimension fitting plots based on MIP (a, b) and N₂ (c, d) and CO₂ (e, f) adsorption data of selected coals from the Huaibei Coalfield.

4. Calculation Result of Fractal Dimensions Based on MIP Data.

sample No.	linear relationship	D MIP–4	D MIP	ln B	R 2
RL-22–2	ln(dV/dP) = −1.0804 ln P −7.4324	–1.0804	2.9196	–7.4324	0.9036
XH-3	ln(dV/dP) = −1.2113 ln P −6.6734	–1.2113	2.7887	–6.6734	0.9859
XT-1	ln(dV/dP) = −1.1398 ln P −7.2801	–1.1398	2.8602	–7.2801	0.9325
XT-4	ln(dV/dP) = −1.1604 ln P −6.6738	–1.1604	2.8396	–6.6738	0.9781
JG-1	ln(dV/dP) = −1.0685 ln P −7.2641	–1.0685	2.9315	–7.2641	0.9779
QN-4	ln(dV/dP) = −1.1055 ln P −7.1984	–1.1055	2.8945	–7.1984	0.9479
LL-1	ln(dV/dP) = −1.0411 ln P −5.9861	–1.0411	2.9589	–5.9861	0.9707
ZXZ-1	ln(dV/dP) = −1.0479 ln P −7.3293	–1.0479	2.9521	–7.3293	0.9595
ZXZ-2	ln(dV/dP) = −1.0083 ln P −7.0869	–1.0083	2.9117	–7.0869	0.9584
QD-1	ln(dV/dP) = −1.0242 ln P −7.9574	–1.0242	2.9758	–7.9574	0.9851
QD-2	ln(dV/dP) = −1.2438 ln P −5.1732	–1.2438	2.7562	–5.1732	0.9724
TY-1	ln(dV/dP) = −1.0917 ln P −5.6984	–1.0917	2.9083	–5.6984	0.9499

4.7.2. N₂ Adsorption

Based on the FHH model and N₂ adsorption data, fractal characterization analysis of the pore structure was carried out on collected coal samples. The finding reveals that the R ² value obtained by the plot of ln­(V) vs ln­(ln­(P/P ₀)) is ≥ 0.93 at P/P ₀ intervals of 0–0.5 and 0.5–1.0 (Figure c,d), which confirms that pore structures of samples exhibit distinct FHH fractal characteristics. Notably, the fitting stability is enhanced in the high relative pressure range. This is because monolayer adsorption in the low relative pressure range is affected by micropore heterogeneity, while multilayer adsorption and capillary condensation better capture the overall fractal characteristics of the pore structure in the high relative pressure range. Combined with eqs –, the fractal dimensions D _N21 and D _N22 were calculated and are listed in Table , which are 2.383–2.870 (average of 2.592) and 2.432–2.689 (average of 2.582), respectively.

5. Calculation Result of Fractal Dimensions Based on N₂ Adsorption Data.

	P/P 0 = 0–0.50			P/P 0 = 0.50–1.00
sample no.	A 1	D N21 = 3 + A 1	R 2	A 2	D N22 = 3 + A 2	R 2
RL-22–2	–0.130	2.870	0.98	–0.473	2.527	0.99
XH-3	–0.544	2.456	0.99	–0.311	2.689	0.99
XT-1	–0.288	2.712	0.96	–0.568	2.432	0.99
XT-4	–0.228	2.772	0.93	–0.503	2.497	0.99
JG-1	–0.672	2.328	0.98	–0.507	2.493	0.99
QN-4	–0.381	2.519	0.99	–0.338	2.662	0.99
LL-1	–0.617	2.383	0.99	–0.342	2.658	0.99
ZXZ-1	–0.492	2.508	0.99	–0.38	2.62	0.99
ZXZ-2	–0.455	2.545	0.99	–0.391	2.609	0.99
QD-1	–0.476	2.724	0.99	–0.329	2.571	0.98
QD-2	–0.469	2.531	0.99	–0.377	2.623	0.99
TY-1	–0.579	2.754	0.99	–0.399	2.601	0.99

4.7.3. CO₂ Adsorption

Based on CO₂ adsorption data, the V-S model was adopted to calculate the fractal dimensions of micropore structures with the corresponding linear fitting relationship applied (Figure e,f). The R ² values of linear fitting for all samples range from 0.9989 to 0.9998; this attests to excellent fitting accuracy and confirms distinct fractal characteristics in micropore structures. Linear fitting yields a 3/D _CO2 value of 1.0588–1.1128, and the constant C values range from −8.3233 to −8.1063. The fractal dimension D _CO2 was calculated by eq and is listed in Table , with the values ranging from 2.7332 to 2.8959 (average of 2.8073).

6. Calculation Result of Fractal Dimensions Based on CO₂ Adsorption Data.

sample no.	linear relationship	3/D CO2	D CO2	C	R 2
RL-22–2	ln V = 1.0832 ln S −8.2681	1.0832	2.8696	–8.2681	0.9997
XH-3	ln V = 1.0771 ln S −8.1720	1.0771	2.7853	–8.1720	0.9997
XT-1	ln V = 1.1128 ln S −8.3233	1.1128	2.8959	–8.3233	0.9992
XT-4	ln V = 1.0847 ln S −8.3233	1.0847	2.8184	–8.2159	0.9993
JG-1	ln V = 1.0588 ln S −8.1063	1.0588	2.8334	–8.1063	0.9989
QN-4	ln V = 1.0857 ln S −8.1285	1.0857	2.7332	–8.1285	0.9991
LL-1	ln V = 1.0679 ln S −8.1437	1.0679	2.8064	–8.1437	0.9998
ZXZ-1	ln V = 1.1067 ln S −8.1437	1.1067	2.7908	–8.3079	0.9996
ZXZ-2	ln V = 1.0917 ln S −8.1870	1.0917	2.748	–8.1870	0.9996
QD-1	ln V = 1.0833 ln S −8.2841	1.0833	2.8293	–8.2841	0.9994
QD-2	ln V = 1.0957 ln S −8.2770	1.0957	2.738	–8.2770	0.9992
TY-1	ln V = 1.0952 ln S −8.2916	1.0952	2.8392	–8.2916	0.9991

5. Discussion

5.1. Pore Structure Characterization

In this study, the pore structure of the coal samples was characterized through a combination analysis of MIP and N₂ and CO₂ adsorption experiments. By integrating the optimal characterization intervals, pore structure parameters were accurately obtained throughout the full pore size range of coal samples. − , Statistical results of pore structure parameters were listed and are plotted in Table and Figure . In terms of pore volume, the value of micropores is 0.72–1.86 cm³/100 g (average of 1.24 cm³/100 g), and those of mesopores and macropores are 0.05–1.07 cm³/100 g (average of 0.28 cm³/100 g) and 0.69–4.99 cm³/100 g (average of 1.54 cm³/100 g), respectively. In addition, the total pore volume is 1.87–6.56 cm³/100 g (average of 3.05 cm³/100 g). As for specific surface area, the value of micropores is 18.13–48.94 m²/g (average of 32.21 m²/g), and those of mesopores and macropores are 0.15–6.49 m²/g (average of 1.33 m²/g) and 0.06–0.68 m²/g (average of 0.14 m²/g), respectively. The total specific surface area is 18.65–49.21 m²/g (average of 33.68 m²/g).

12.

Percentages of pore volume (a) and specific surface area (b) of coal samples from the Huaibei Coalfield.

As shown in Figure a, micropores and macropores account for 19.05–69.66% (average of 44.38%) and 28.09%–76.07% (average of 46.43%) of the total pore volume, respectively. Comparatively, the proportion of mesopores is 1.68%–30.57% (average of 9.19%). On the whole, the contribution of various pore types to the total follows the order of mesopores < micropores < macropores. On the other hand, the contributions of micropores and macropores are roughly equivalent, with their combined mean value of 90.81%. As shown in Figure b, the proportion of micropores is 78.37%–99.45% (average of 99.55%), whereas mesopores and macropores are 0.35%–21.33% (average of 4.00%) and 0.07%–1.92% (average of 0.45%), respectively. This indicates that micropores are the predominant contributors to the specific surface area.

As illustrated in Figure , pore size distributions based on pore volume were constructed by the curves of MIP and CO₂ and N₂ adsorption techniques, which exhibit multipeak characteristics at 1.0–2.0 nm, 30–50 nm, 0.1–1 μm, 1–3 μm, and >100 μm. Notably, sample QD-1 displays a left-skewed pattern with two distinct peaks observed in the ranges of 1.0–2.0 nm and 30–50 nm (Figure e). This highlights the crucial role of micropores and mesopores in governing the total pore volume. In contrast, sample QD-2 exhibits a macropore-dominated distribution with a right-skewed tendency (Figure f). Its primary peak shifts to the range of 0.1–1 μm, while a secondary peak appears in the micropore range. In addition, samples QN-4, LL-1, and ZXZ-2 show “U”-type patterns with pronounced peaks in micropore and macropore ranges (Figure b–d). Moreover, sample XH-3 exhibits three comparable peaks in the full-size range (Figure a).

13.

Pore structure distributions based on the pore volume of MIP and N₂ and CO₂ adsorption curves.

Figure illustrates a unimodal pore size distribution of specific surface area with the main peak centered between 1.0 and 2.0 nm. Beyond 2 nm, the marginal contribution to specific surface area declines sharply, while mesopores and macropores contribute negligibly. This finding confirms that micropores account for most of the specific surface area in all coal samples. As shown in Figure a,c, samples XH-3 and LL-1 exhibit secondary peaks in the range of 2–10 nm and 100–200 nm, respectively. However, such variations do not alter the unimodal pattern dominated by micropores.

14.

Pore structure distributions based on the specific surface area of MIP and N₂ and CO₂ adsorption curves.

5.2. Impacts of Coal Basic Parameters on the Pore Structure

Based on the tested data, relationships between pore structure parameters and basic data of coal samples were established and are plotted in Figure . As shown in Figure a,b, ash content has no relationship with the volume and specific surface area of multiscale pores. By contrast, ash content of coals from the Huainan Coalfield has positive correlations with mesopores and macropores, as evidenced by mineral-filled pore fractures observed in FE-SEM images. As shown in Figure c, except for sample QD-2, the macropore volume exhibits a negative correlation with the inertinite content. This observation reveals that a higher inertinite proportion corresponds to lower macropore volume. However, no significant linear correlation exists between the inertinite content and specific surface area (Figure d).

15.

Relationships between the pore volume, specific surface area and ash content (a, b), inertinite content (c, d), and R _o,max (e, f) of selected coals in the Huaibei Coalfield.

As shown in Figure e,f, R _o,max exhibits positive correlations with the volume and specific surface area of micropores but shows no such correlations with those of mesopores and macropores. This phenomenon indicates that an increase in the coal rank promotes micropore development and thus enhances the specific surface area. In fact, the volume and specific surface area of mesopores and macropores have no correlation with R _o,max. During coalification, the aromatization and polycondensation of coal molecules were accompanied by the escape of small molecular gases, which generated many secondary micropores. In contrast, the development of mesopores and macropores is largely controlled by the primary structure and tectonic processes of coal, and the increase in the coal rank exerts a weak modification effect on them.

5.3. Impacts of the Pore Structure and Maceral on Methane Adsorption Capacity

As illustrated in Figure a, methane adsorption capacity is positively correlated with micropore volume but shows no correlations with the volumes of mesopores and macropores. Similarly, a strong positive correlation exists between the methane adsorption capacity and specific surface area of micropores, whereas no relationship is found for mesopores and macropores (Figure b). Given that micropores are the primary contributors to the specific surface area (Figure ), this confirms that methane molecules are primarily adsorbed on the abundant sites provided by their extensive internal surface area. ,

16.

Correlations between the methane adsorption capacity and pore volume (a) and specific surface area (b) of selected coals in the Huaibei Coalfield.

Figure shows the plots of methane adsorption capacity versus coal macerals and mineral matter. As illustrated in Figure a–c, no obvious linear relationships exist between vitrinite, inertinite, or exinite and methane adsorption capacity. For mineral matter (Figure d), data points are broadly scattered, and only a faint upward trend can be perceived. These results suggest that no single component can accurately describe the methane adsorption behaviors of coal. According to the above analysis, the coal rank, pore structure, and various maceral combinations collectively control methane adsorption characteristics.

17.

Correlations between methane adsorption capacity and vitrinite (a), inertinite (b), exinite (c), and mineral contents (d).

Methane adsorption behavior in the coal matrix includes the equilibrium storage capacity and dynamic adsorption process. The former one determines the methane storage potential, while adsorption kinetics reflect methane diffusion velocity and equilibrium attainment time, with both governed by the full-scale pore structure of coal. Liu et al. have confirmed that micropores provide massive adsorption sites and dominate saturated methane adsorption capacity, which explains why the present study primarily highlights the positive correlation between micropore parameters and methane adsorption capacity. Nevertheless, as pointed out by previous research, mesopores and macropores exert negligible effects on ultimate equilibrium adsorption volume yet serve as dominant mass transfer pathways to facilitate methane diffusion and improve adsorption kinetics. The underlying reason is that they greatly reduce methane migration distances, speed up gas mass transport, and shorten the time to reach adsorption equilibrium. Notably, no independent dynamic adsorption tests were performed to capture kinetic profiles or rate constants in this study. By integrating the measured data with pore diffusion theories reported in existing studies, we qualitatively interpret the dual regulatory roles of mesopores and macropores in methane storage capacity and adsorption kinetics for coals in the Huaibei Coalfield.

5.4. Impacts of Fractal Dimensions on Methane Adsorption Capacity

As shown in Figure a, the fractal dimension D _MIP has no relationship with methane adsorption capacity; this suggests that the development of macropores in the selected coals has no controlling effect on methane adsorption capacity. Figure b shows that the fractal dimension D _N21 has a positive correlation with methane adsorption capacity. Generally, the higher the fractal dimension D _N21, the more irregular the pore surface and abundant adsorption sites, thus significantly improving the methane adsorption capacity. Figure c indicates that the fractal dimension D _N22 exhibits a negative correlation with methane adsorption capacity. As the fractal dimension D _N22 increases, the complexity of the pore structure is enhanced, while the connectivity deteriorates, which reduces the efficiency of gas migration within the pores. This poor pore connectivity further hinders methane diffusion and slows down the adsorption equilibrium process from a kinetic perspective, consistent with the widely recognized pore-controlled gas transport theory in coals. Figure d shows that the fractal dimension D _CO2 is positively correlated with methane adsorption capacity. D _CO2 reflects the structural characteristics of micropores and refers that micropores provide the main sites for methane adsorption. The more complex the micropore surface, the stronger the methane adsorption capacity, which is consistent with the variation trend of D _N21.

18.

Correlations between the methane adsorption capacity and D _MIP (a), D _N21 (b), D _N22 (c), and D _CO2 (d) of selected coals in the Huaibei Coalfield.

6. Conclusions

This study systematically analyzed the full-size pore structure, fractal characteristics, and their correlations with the methane adsorption capacity of coal samples in the Huaibei Coalfield by using a combination of multiple characterization methods and fractal theory, and conclusions are as follows:

• (1)FE-SEM and EDS identify heterogeneous nanomicron pores, microfractures, and minerals in the coal matrix. The fractal dimensions of pore fracture systems range from 1.8337 to 1.8924. The total pore volume and specific surface area are 1.87–6.56 cm³/100 g (average of 3.05 cm³/100 g) and 18.65–49.21 m²/g (average of 33.68 m²/g), respectively. Micropores dominate the specific surface area, and micropores and macropores account for 90.81% of the total pore volume.
• (2)All samples are medium-rank bituminous coal with an R _o,max of 0.73%–0.96% (average of 0.82%) and an A _d of 12.35%–25.22% (average of 19.03%). Coal basic properties have different effects on the multiscale pores of coals. Separately, R _o,max is positively correlated with micropore volume and specific surface area, whereas the inertinite content presents a negative correlation with the macropore volume. In addition, ash content has no linear correlation with the pore structure.
• (3)The Langmuir volume is 0.81–1 mmol/g (average of 0.92 mmol/g) and Langmuir pressure is 1.98–3.92 MPa (average of 2.96 MPa). Methane adsorption capacity rises with micropore volume and specific surface area due to abundant adsorption sites. A single maceral or mineral cannot independently control adsorption volume, which is jointly governed by coal rank, pore structure, and maceral combinations.
• (4)Multiscale pores of coal samples exhibit distinct fractal characteristics. D _N21 and D _CO2 exhibit positive effects with methane adsorption capacity. Conversely, D _N22 displays a negative correlation due to the increased structural complexity of mesopores. In addition, mesopores and macropores accelerate gas transport and shorten equilibrium time from a kinetic perspective.

The authors declare no competing financial interest.