Fractal Characterization of a Multi-Scale Pore Structure in Ultra-Deep Coal Seams

Abstract

The pore–fracture structure of ultra-deep coal is critical for evaluating resource potential and guiding the exploration and development of deep coalbed methane (CBM). In this study, a coal sample was obtained from the Gaogu-4 well at a depth of 4369.4 m in the Shengli Oilfield of Shandong, China. A comprehensive suite of characterization techniques, including Field Emission Scanning Electron Microscopy (FE-SEM), X-ray diffraction (XRD), Mercury Intrusion Porosimetry (MIP), Low-temperature Nitrogen Adsorption (LT-N₂GA), and Low-pressure CO₂ Adsorption (LP-CO₂GA), were employed to investigate the surface morphology, mineral composition, and multi-scale pore–fracture characteristics of the ultra-deep coal. Based on fractal geometry theory, four fractal dimension models were established, and the pore structure parameters were then used to calculate the fractal dimensions of the coal sample. The results show that the ultra-deep coal surface is relatively rough, with prominent fractures and limited pore presence as observed under FE-SEM. Energy Dispersive Spectrometer (EDS) analysis identified the elements such as C, O, Al, Si, S, and Fe, thus suggesting that the coal sample contains silicate and iron sulfide minerals. XRD analysis shows that the coal sample contains kaolinite, marcasite, and clinochlore. The multi-scale pore–fracture structure characteristics indicate that the ultra-deep coal is predominantly composed of micropores, followed by mesopores. Macropores are the least abundant, yet they contribute the most to pore volume (PV), accounting for 70.9%. The specific surface area (SSA) of micropores occupies an absolute advantage, accounting for up to 97.46%. Based on the fractal model, the fractal dimension of the coal surface is 1.4372, while the fractal dimensions of the micropores, mesopores, and macropores are 2.5424, 2.5917, and 2.5038, respectively. These results indicate that the surface morphology and pore–fracture distribution of the ultra-deep coal are non-uniform and exhibit statistical fractal characteristics. The pore–fracture structure dominated by micropores in ultra-deep coal seams provides numerous adsorption sites for CBM, thereby controlling the adsorption capacity and development potential of deep CBM.

1. Introduction

As a clean energy, CBM recovery can reduce dependence on fossil fuels, promote the comprehensive utilization of coal resources, enhance energy efficiency, and contribute to the realization of green, low-carbon development [1,2]. Presently, commercial CBM development has been achieved in 14 countries of the whole world, and the top 4 countries with major CBM production are Australia, the United States, Canada, and China, respectively. Significant progress has been made in the exploration and development of CBM and, in the case of China [3,4], particularly with the discovery of several high-yield CBM wells in the eastern margin of the Ordos Basin, which demonstrates the vast potential of deep CBM resources [5]. The pores and fractures in coal serve as the primary storage sites and migration pathways for CBM [6,7]. Their size, shape, distribution, and connectivity directly influence processes such as adsorption, desorption, diffusion, and seepage, ultimately determining the reserves and exploitability of CBM.

Currently, the characterization of pore–fracture structure of coal primarily relies on image observation methods, fluid intrusion techniques, and non-destructive characterization methods. In image observation, techniques such as Scanning Electron Microscopy (SEM), optical microscopy, atomic force microscopy (AFM), and CT imaging allow direct visualization of pore–fracture structure of coal, morphology, and connectivity, and also enable exploration of the formation mechanisms of these pores and fractures [8,9,10]. However, the data obtained from these methods often suffer from insufficient statistical representativeness, hindering quantitative characterization [11,12]. Among fluid intrusion methods, techniques such as MIP, LT-N₂GA, and LP-CO₂GA are commonly used. MIP is mainly used to characterize larger pores with diameters greater than 50 nm, while LT-N₂GA is employed for pores in the range of 2–50 nm, and LP-CO₂GA focuses on pores with diameters below 2 nm. Fractal theory, with its advantages of practicality and simplicity, has become a significant method for investigating the fractal characteristics of coal reservoirs and explaining the complexity of pore–fracture structure of coal. A range of fractal models have been developed, including the Sierpinski model, the Frenkel–Halsey–Hill (FHH) model, the Menger model, the thermodynamic model, and the multifractal model [13,14,15]. Furthermore, the current studies demonstrated that the structure of pore–fracture in coal displays obvious fractal characteristics [16,17], which directly dominates the fractal properties on the adsorption and transport of CBM [18,19].

In recent years, numerous scholars have integrated pore–fracture characterization techniques with fractal theory to study deep coal seams, resulting in valuable findings. For instance, Wei et al. (2021) [20]. conducted an extensive study to investigate the pore structure and methane adsorption capacity of deep-buried coals from the Panji Deep Area in the Huainan Coalfield, China. A range of experimental techniques, including MIP, N₂/CO₂ adsorption, FE-SEM, and methane adsorption, were employed. The results revealed that the deep-buried coals exhibit a variety of pore types and microfractures. Micropores were found to contribute the majority of the SSA, whereas macropores predominantly governed the PV. Wang et al. (2024) [21] investigated deep coal samples from the DJ57 well using FE-SEM, LT-N₂GA, LP-CO₂GA, MIP, and micro-CT methods for quantitative characterization. Their findings revealed a variety of pore types, including primarily organic matter pores, inorganic pores (intraparticle and interparticle pores), and microfractures, with a strong connectivity network formed by the coexistence of micropores and microfractures. Zhang et al. (2024) [22] utilized X-ray diffraction (XRD), SEM, MIP, and computed tomography (CT) scanning to analyze the pore–fracture networks in deep coal samples from the Shangwan Coal Mine. They found that tectonically deformed coal exhibited more complex fissure morphologies and enhanced connectivity compared to primary structural coal, with fractal dimensions increasing as measurement scales decreased. Their study highlighted the importance of multi-scale fractal models in predicting porosity and volume fractal dimensions, thereby providing a scientific basis for coal mine safety and gas control. Similarly, Li et al. (2024) [23] investigated the full-aperture pore structures of deep coal seams using MIP, LT-N₂GA, and LP-CO₂GA methods. They observed that macropores dominated the pore volume distribution, whereas micropores and mesopores contributed significantly to the SSA. Their findings indicated that coal metamorphism significantly influenced pore structure, as evidenced by a nonlinear decrease in micropore volume and surface area with increasing volatile matter content. The study also employed sponge, FHH, and density function models to analyze pore complexity, revealing that higher degrees of coal metamorphism led to more regular microporous structures. Current research on coal PSD, morphology, and connectivity, alongside the application of fractal dimensions and models, has provided substantial theoretical foundations and technical support for CBM development and exploration. These studies have enhanced the understanding of gas adsorption–desorption dynamics, which are critical for optimizing CBM extraction and ensuring coal mine safety. However, most research on deep coal seams has focused on depths up to 3000 m, and studies on ultra-deep coal seams exceeding 4000 m remain scarce. Therefore, understanding the multiscale pore–fracture structure and fractal characteristics of ultra-deep coal seams (>4000 m) is crucial for evaluating the potential of ultra-deep CBM resources and guiding exploration and development efforts. With increasing CBM extraction depths, future research should further investigate variations in coal pore structures and fractal characteristics under diverse geological conditions at greater depths. Additionally, the impact of these variations on CBM development particularly concerning gas storage capacity, permeability, and extraction efficiency should be thoroughly examined to enhance the feasibility and sustainability of deep CBM exploitation.

By FE-SEM, XRD, MIP, LT-N₂GA, and LP-CO₂GA, this study investigates ultra-deep coal samples sourced from depths exceeding 4000 m, with the aim of analyzing surface morphology, mineral composition, and multi-scale pore structure. Additionally, pore structure parameters, including PV, SSA, and pore size distribution (PSD), are systematically evaluated. Meanwhile, based on fractal theory, quantitative analysis of the surface roughness and heterogeneity of the multi-scale pore–fracture structure of the coal is conducted, aiming to provide more precise data to support the exploration, development, and utilization of ultra-deep CMB.

2. Samples and Methods

2.1. Samples

Coal samples examined in this study were collected from the Gaogu-4 well in the Shengli Oilfield, Shandong Province, China, at a depth of 4369.36 m within the deep coal seam of the Shanxi Formation. The sampling well section spans from 4364.50 m to 4403.50 m, with a total stratigraphic thickness of 39 m. This section comprises 16.50 m of dark mudstone and 4.00 m of coal seam. Together, the thicknesses of the mudstone and coal seam account for 52.6% of the total stratigraphic thickness of this section. The mudstone, acting as a low-permeability caprock, inhibits the upward migration of coalbed methane, thereby facilitating its accumulation within the coal seam. The lithology of the well section is predominantly composed of light gray fine sandstone, fluorescent fine sandstone, and argillaceous sandstone, intercalated with dark gray mudstone, thin layers of black coal, grayish-black carbonaceous mudstone, and dark gray sandy mudstone.

Proximate analysis of the coal samples was performed in accordance with the Chinese standard GB/T 212-2008 [24], with the results summarized in

Table 1. Proximate analysis of coal sample.

ID	Mad (%)	Ad (%)	Vdaf (%)	FCad (%)
Gaogu-4	0.98	25.33	32.28	50.06

M_ad: air dry moisture content, %; A_d: dry ash yield, %; V_daf: dry ash free volatile matter, %; FC_ad: fix carbon content, %

. The analysis indicates that the coal sample exhibits a moisture content of 0.98%, an ash yield of 25.33%, a volatile matter content of 32.28%, and a fixed carbon content of 50.06%.

2.2. Experimental Methods

The International Union of Pure and Applied Chemistry (IUPAC) pore size classification scheme, i.e., micropores (<2 nm), mesopores (2–50 nm), and macropores (>50 nm), was applied in this study [25].

The qualitative characterization of the coal samples was primarily achieved through direct observation and descriptive analysis of pores using SEM. In this study, high-resolution imaging was conducted using a ZEISS Sigma 500 FE-SEM (Carl Zeiss AG, Oberkochen, Germany) to obtain detailed SEM images of the samples. The coal samples were prepared into small pieces with dimensions less than 1 cm. After drying in an oven at 60 °C for 24 h, the samples were subjected to Scanning Electron Microscopy (SEM) analysis. A relatively flat surface of the coal sample was selected for testing. A series of FE-SEM images captured at various resolutions were used to directly examine the morphological features of pores, the spatial relationships between pores and particles, and the connectivity of pore networks [21,26]. Additionally, the elemental composition of coal, including the types and contents of elements, was determined through EDS analysis.

XRD was a widely utilized technique for characterizing crystal structures, facilitating the determination of mineral composition and content in coal samples. In this study, a D8 ADVANCE X-ray diffractometer (Bruker AXS, Karlsruhe, Germany) was employed to analyze the coal samples. The instrument operated at a scanning speed of 10°/min, covering an angular range from 10° to 80°. Prior to analysis, the coal samples were sectioned into blocks not exceeding dimensions of 2 cm × 1 cm × 1 cm and positioned directly onto the diffractometer stage.

MIP determinations were conducted employing a MicroActive AutoPore V 9600 mercury porometer (Micromeritics Instrument Corp., Norcross, GA, USA). The instrument is capable of applying a maximum pressure of approximately 60,000 psi (equivalent to 414 MPa), corresponding to a minimum detectable pore size of approximately 3 nm. Prior to the experiment, the coal samples were subjected to drying in an oven at 60 °C for more than 48 h to remove any moisture content. Furthermore, a vacuum condition was meticulously maintained within the instrument throughout the testing process. Based on the data obtained from the automated recording of the mercury intrusion process, the relationship between intrusion pressure and the corresponding PD (pore diameter) was determined using the Washburn equation [27]. Consequently, pore structure parameters, including PV, SSA, and PSD, were derived from the data for the coal samples.

LT-N₂GA experiments were performed using a Anton Paar Nova 600 surface area analyzer (Anton Paar GmbH, Graz, Austria), with high-purity nitrogen as the adsorbate. Coal samples, with particle sizes ranging from 60 to 80 mesh (1–2 g), were degassed under vacuum at 105 °C for 12 h to remove moisture. Nitrogen adsorption–desorption isotherms were obtained at 77 K, with relative pressures (P/P₀) ranging from 0.001 to 0.999. The relationship between nitrogen adsorption and relative pressure was established. PV, SSA, and PSD were derived using the Brunauer–Emmett–Teller (BET) model and the Barrett–Joyner–Halenda (BJH) model [28,29,30].

LP-CO₂GA experiments were conducted using the same instrument employed for LT-N₂GA. Given that the molecular diameter of CO₂ is only 0.33 nm, CO₂ adsorption is particularly effective in characterizing the pore structure of micropores [18]. Prior to experimentation, the samples were ground to a particle size of 60–80 mesh and subsequently dried in an oven at 105 °C for 8 h. Thereafter, approximately 1–2 g of the ground sample was placed in a container and degassed for 16 h to remove moisture. Adsorption measurements were performed at 273 K, with relative pressures ranging from 0.0001 to 0.03. Data from the CO₂ adsorption experiments were analyzed using the Density Functional Theory (DFT) model, which effectively describes gas adsorption behavior and phase transitions at the molecular scale, thus providing more accurate determinations of PV, SSA, and PSD for micropores [31,32].

2.3. Fractal Theory

The fractal dimension is widely regarded as a critical parameter for characterizing the complexity of coal pore networks [33]. Several types of fractal dimensions exist, including the topological dimension, the Hausdorff dimension, the box-counting dimension, and the self-similarity dimension, among others. The box-counting dimension has been demonstrated to be an effective method for characterizing the heterogeneity of PSD on the coal surface. As is well known, PSD in coal, as observed in SEM images, is heterogeneous and exhibits fractal characteristics [34,35,36]. In this study, the widely adopted box-counting method was employed. By covering a binary image with boxes of length δ, the fractal dimension is calculated using Equation (1):

$$\mathrm{D} =-\underset{\delta \to \infty }{\lim }{\displaystyle \frac{\ln (\mathrm{N}(\delta \left)\right)}{\ln \delta }}$$

(1)

where D represents the fractal dimension and N(δ) denotes the number of boxes required to completely cover the binary images, Equation (1) can generally be expressed as follows:

$$\ln \left(\mathrm{N}\right(\delta \left)\right)=-\mathrm{Dln}\delta +\mathrm{constant}$$

(2)

Thus, the box-counting dimension can be determined from the slope of a linear plot of ln(N(δ)) against lnδ [14].

The application of the Menger sponge model in the calculation of the fractal dimension of porous media has been extensively validated by numerous researchers. In this study, the model is utilized to calculate the fractal dimension derived from MIP, with the most commonly employed mathematical expression represented by Equation (3):

$$\ln \left({\displaystyle \frac{\mathrm{d}\mathrm{V}}{\mathrm{d}\mathrm{P}}}\right)=\mathrm{lnB}+\left(\mathrm{D}-4\right)\ln \mathrm{P}$$

(3)

where P represents the mercury intrusion pressure in MPa, V denotes the cumulative volume of mercury intruded at a given pressure P in units of cm³/g, D is the fractal dimension, and B is the slope of the $\ln \left({\displaystyle \frac{\mathrm{d}\mathrm{V}}{\mathrm{d}\mathrm{P}}}\right)$ and ln P scatter plot fitting curve [37,38].

The FHH model, based on gas adsorption isotherms, is a fundamental approach for quantifying the fractal dimension of adsorptive pores in coal reservoirs. This model has been widely employed to correlate gas adsorption behavior with the fractal surfaces of solid porous media. The nitrogen adsorption–desorption isotherms of coal exhibit a distinct hysteresis loop, indicative of the formation of micropores and mesopores [39,40]. These observations are consistent with the pore size range relevant to the FHH model. Therefore, the FHH model is applied to determine the fractal dimension of the samples [41]. The FHH model can be expressed as shown in Equations (4) and (5):

$$\mathrm{lnV}=(\mathrm{D}-3)\ln \left(\ln {\displaystyle \frac{{\mathrm{P}}_0}{\mathrm{P}}}\right)+\mathrm{C}$$

(4)

$$\mathrm{D} =\mathrm{k} +3$$

(5)

where V represents the adsorption volume at equilibrium pressure P, expressed in cm³/g; P₀ denotes the saturation vapor pressure, in MPa; and C is a constant. When plotting the data from LT-N₂GA as lnV versus ln($\left(\ln {\displaystyle \frac{{\mathrm{P}}_0}{\mathrm{P}}}\right)$), the slope of the fitted line is designated as k, while D represents the fractal dimension.

The calculation of the fractal dimension of micropores using LP-CO₂GA data involves various models, including the V-S model and the Sierpinski model, among others. The V-S model, initially proposed by Mandelbrot, determines the fractal dimension of pores by analyzing the correlation between PV and SSA in solid porous media. As a porous sedimentary material, previous research has shown that the V-S model is distinguished by its high computational accuracy, as well as its exceptional fitting precision and stability when applied to the characterization of coal pore structure. The V-S model is particularly effective in determining the fractal dimension of micropores [42,43]. The equation for calculating the fractal dimension of micropores is given in Equation (6):

$$\mathrm{lnV}={\displaystyle \frac{3}{\mathrm{D}}}\mathrm{lnS}+\mathrm{K}$$

(6)

where V represents the cumulative PV, measured in cm³/g; S denotes the cumulative SSA, expressed in m²/g; D signifies the fractal dimension; and K is a constant.

3. Results and Discussion

3.1. FE-SEM Results and Fractal Characteristics

The results of FE-SEM observations are presented in Figure 1. As shown in Figure 1a,b, coal samples exhibit a complex pore structure, with pore sizes ranging from nanometers to micrometers. These pores exhibit diverse shapes, including circular, elliptical, and irregular forms, and can either be interconnected or isolated, significantly influencing the adsorption and permeability properties of coal. Figure 1c,d also reveal the presence of microfractures within the coal samples. These microfractures vary in shape, size, and origin, particularly in flaky minerals, where numerous long, narrow, plate-like microfractures with one open end are developed. Well-developed open microfractures exhibit excellent connectivity [44]. The presence of these microfractures can significantly enhance the permeability of deep coal reservoirs locally, providing effective space and pathways for the transformation of adsorbed gas to free gas and for gas migration.

The Energy Dispersive X-ray Spectroscopy (EDS) analysis using FE-SEM can quantitatively analyze the mineral elements in the coal samples. As shown in Figure 2, three distinct regions of the coal sample were chosen for microscopic analysis. The results reveal significant variations in morphological characteristics, elemental composition, and mineral occurrence, emphasizing the heterogeneity of multiphase components in coal and the complexity of the diagenetic environment. The detailed analysis is presented as follows: As shown in Figure 2a,b, this region of the coal sample primarily consists of a coal matrix, with major elements including C, O, Al, and Si, and minor amounts of S and Fe. Based on the elemental composition, this region is inferred to be dominated by silicate minerals, with trace amounts of iron sulfide minerals. As shown in Figure 2c,d, this region of the coal sample is characterized by the presence of C, O, S, and Fe as the main elements, with lower content of Al and Si and trace amounts of Na and Mg. The elemental composition suggests that this region is predominantly composed of iron sulfide minerals, with a minor presence of silicate minerals. As shown in Figure 2e,f, the elemental composition of this region is more complex, primarily consisting of C (39.60 wt%), O (38.14 wt%), Al (4.97 wt%), Si (8.71 wt%), S (2.46 wt%), Ca (2.09 wt%), and Fe (2.44 wt%), with trace amounts of Na (0.38 wt%), Mg (0.59 wt%), and K (0.62 wt%). Based on the elemental distribution, it is inferred that this region contains both iron sulfide minerals and silicate minerals, with a possible presence of minor carbonate minerals. The results of EDS analysis indicate that the ultra-deep coal contains various minerals (mainly silicate and iron sulfide minerals), which may occupy pore spaces, thereby reducing total porosity. This reduction in porosity may, in turn, decrease the storage capacity and mobility of CBM.

To further determine the mineral composition of coal samples, XRD analysis was performed, and the mineral types were semi-quantitatively assessed using Jade 6.0 software (Materials Data, Inc., Livermore, CA, USA). As depicted in Figure 3, three minerals were identified in the coal samples: kaolinite (Al₄(OH)₈(Si₄O₁₀), PDF#78-2109), marcasite (FeS₂, PDF#74-1051), and clinochlore ((Mg,Fe,Al)₆(Si,Al)₄O₁₀(OH)₈, PDF#07-0078), corresponding to silicate, sulfide, and carbonate mineral categories, respectively. These minerals exert complex influences on the pore structure of coal samples, exhibiting both beneficial and detrimental effects. Kaolinite can generate specific pores but may also impair pore connectivity through adsorption and swelling. Marcasite may occlude pores, and its oxidation can further modify the pore structure. As a silicate mineral, clinochlore tends to fill or coat the pores and fractures within coal. This filling effect significantly reduces the porosity and connectivity of coal, thereby influencing the adsorption and desorption capacity of coalbed methane. The presence and transformation of these minerals collectively shape the coal pore structure, influencing permeability, reservoir characteristics, and fluid flow properties, ultimately affecting CMB extraction [45,46].

The original grayscale FE-SEM images are unsuitable for quantitative analysis of pore structure, including PSD and fractal characteristics. To extract the fractal characteristics of the coal sample pores, the images were converted into binary format. In the FE-SEM images of the coal samples, pores typically appear as darker grayscale regions compared to the background. Consequently, pores and backgrounds can be easily differentiated based on distinct grayscale levels [47]. The global thresholding method has been demonstrated to be an effective technique for determining the appropriate grayscale threshold [48]. In this study, ImageJ version 1.54f (National Institutes of Health, Bethesda, MD, USA) was employed to process the FE-SEM images presented in Figure 1b,d, as shown in Figure 4a,b. Following the establishment of an appropriate grayscale threshold, the pores in the coal samples were segregated from the background, resulting in binary images where the coal matrix is represented in black and the pores and fractures in white. The fractal dimension was subsequently calculated using the box-counting method, with the results illustrated in Figure 4.

As depicted in Figure 4c,d, the fractal dimensions determined using the box-counting method are 1.4161 ± 5.2059 × 10⁻⁷ and 1.4582 ± 4.6061 × 10⁻⁷, respectively. These values suggest that the pore distribution on the coal surface demonstrates distinct fractal characteristics, with varying degrees of complexity in different directions. The fractal dimensions not only characterize the complexity of the pore distribution but also offer valuable insights into the heterogeneity of the coal samples.

3.2. MIP Results and Fractal Characteristics

The shapes of the mercury intrusion and extrusion curves in the MIP experiments reflect differences in the openness and connectivity of pore structures within the coal samples. Pores in coal can be classified into closed, semi-closed, and open pores based on their connectivity. Among these, open pores can form a hysteresis loop during mercury intrusion, while semi-closed and closed pores do not exhibit such a loop.

As depicted in Figure 5a, when p > 10 MPa, the discrepancy between the mercury intrusion and extrusion curves is minimal, suggesting that the coal samples primarily contain closed and semi-closed pores, with poorly developed open pore structures. The openness and connectivity of these pores are relatively low. In contrast, when p < 10 MPa, the hysteresis loop in the mercury intrusion curve becomes more pronounced, and the mercury extrusion efficiency is reduced, with a substantial amount of high-pressure mercury remaining within the coal pores. This indicates that the larger mesopores in the coal samples are predominantly open, with a high proportion of open pores and fewer semi-closed and closed pores. The connectivity of these pores is relatively well developed [49].

According to the MIP experimental results, the total PV of the coal samples is 0.086 cm³/g, the total SSA is 3.178 m²/g, the average pore size is 107.94 nm, and the porosity is 30.56%. As illustrated in Figure 5b, the peak of the PSD curve for PV occurs at 130,000 nm, suggesting that large pores contribute the most to the total pore volume. The mercury intrusion volume for large pores is 0.078 cm³/g, accounting for 91.03% of the total PV, while the intrusion volume for mesopores is 0.0088 cm³/g, representing 8.97% of the total PV. As shown in Figure 5c, the peak of the PSD curve for SSA occurs at 5 nm, indicating that mesopores account for the majority of the SSA. The SSA of mesopores is 3.11 m²/g, representing 97.87% of the total surface area, while the SSA of large pores is 0.068 m²/g, comprising 2.13% of the total surface area.

Based on the MIP experimental results and Equation (3) for calculation, Figure 5d was derived. As presented in Figure 4d, the fractal dimension of the coal samples displays a segmented characteristic. For pores larger than 50 nm (macropores), the fractal dimension is 2.5038 ± 0.04023, with a fitting degree of 0.9692, suggesting that these pores exhibit fractal characteristics and a complex pore structure. However, the fractal dimension for mesopores is not further discussed due to measurement errors arising from the compression of the coal matrix during mercury intrusion, which distorts the pore structure. These measurement errors increase as the pore size decreases [23].

3.3. LT-N2GA Results and Fractal Characteristics

The pore structure of coal demonstrates considerable complexity, exhibiting a wide PSD that spans from millimeter to nanometer scales. Due to this complexity, qualitative characterization methods alone are inadequate for fully and accurately revealing the entirety of the coal pore structure. A combination of qualitative and quantitative methods is essential to achieve a comprehensive characterization of coal pore structure. In the present study, results obtained from FE-SEM were employed for the qualitative analysis of pore and fracture morphologies on the coal surface. The observations reveal that the coal surface is relatively rough, with pores and fractures at the micrometer and millimeter scales being clearly visible, while nanometer-scale micropores remain undetectable by FE-SEM. Therefore, to overcome this limitation, LT-N₂GA and LP-CO₂GA experiments are indispensable, as they facilitate the precise characterization of micropore and mesopore structures and morphologies in coal, thereby providing critical insights into the overall understanding of coal pore structure [44,50].

IUPAC classifies adsorption–desorption isotherms into six distinct types [25]. As shown in Figure 6a, the nitrogen adsorption isotherms of the coal samples generally correspond to Type IV isotherms but exhibit notable deviations. The overall adsorption curve displays an upward trend, characterized by a lower adsorption branch and a higher desorption branch. In the low-pressure regime, the initial monolayer adsorption transitions to multilayer adsorption. As relative pressure increases, multilayer adsorption begins, with the adsorption quantity progressively increasing until multilayer adsorption is fully established. When the relative pressure exceeds 0.9, the curve exhibits a sharp rise, signifying a significant increase in adsorption quantity. This behavior suggests that in the low-pressure region, the transition from monolayer to multilayer adsorption occurs, and with increasing relative pressure, multilayer adsorption develops, leading to a gradual increase in adsorption quantity until saturation is reached at the saturation vapor pressure, at which point the adsorption layer becomes infinitely large [51,52]. The pronounced hysteresis loop and the absence of a distinct inflection point indicate the lack of ink-bottle pores. Adsorption curve and desorption are parallel, which suggests that the pore system predominantly consists of open pores, including cylindrical pores at both ends and parallel plate pores on all sides. This pore structure promotes CBM migration, demonstrating favorable permeability and connectivity.

SSA of coal samples, calculated using the BET model, is 1.31 m²/g, while that obtained using the BJH model is 1.44 m²/g. PV is 0.0028 cm³/g. PSD is broad, ranging from 1.26 nm to 127.44 nm, with an average value of 14.36 nm. As illustrated in Figure 6b,c, PSD of coal samples follows a multimodal pattern, with peaks between 1.2 nm and 4.0 nm, suggesting a higher development of micropores and mesopores within this range. According to BJH model calculations, PV for micropores is 0.00036 cm³/g, for mesopores, it is 0.00086 cm³/g, and, for macropores, it is 0.0016 cm³/g. SSA for micropores is 1.03 m²/g, for mesopores, it is 0.32 m²/g, and, for macropores, it is 0.097 m²/g. The significantly larger SSA of micropores and mesopores, compared to that of macropores, enhances the potential for CBM storage and migration.

The nitrogen adsorption–desorption isotherms obtained from LT-N₂GA experiments were used to construct a double logarithmic plot of adsorption volume versus relative pressure, as described by Equation (4). Linear regression analysis of ln(ln(P₀/P)) versus lnV provided the slope of the fitted line, which was then used to determine the fractal dimension according to Equation (5). As shown in Figure 6d, the fractal dimension fitting curve of the coal samples can be divided into distinct low-pressure and high-pressure regions. In the low-pressure regime, gas adsorption is primarily governed by van der Waals forces, the intensity of which correlates with the surface roughness of the coal samples. In contrast, in the high-pressure regime, increasing relative pressure leads to a reduction in van der Waals forces between the coal matrix and liquid nitrogen molecules. At this point, gas adsorption is predominantly driven by capillary condensation forces, which become dominant and are intricately associated with the internal pore structure of the coal. A higher fractal dimension in the low-pressure region indicates a more pronounced surface roughness of the coal samples, while a higher fractal dimension in the high-pressure region reflects a more complex distribution of internal pore structures. Specifically, in the low-pressure region (P/P₀ < 0.5), the surface fractal dimension of the coal samples is 2.3921 ± 0.05245, which is consistent with the fractal characteristics observed via FE-SEM. In the high-pressure region (P/P₀ > 0.5), the pore fractal dimension of the coal samples is 2.5917 ± 0.07165, indicating a significant degree of heterogeneity within the coal samples [23,53].

3.4. LP-CO₂GA Results and Fractal Characteristics

LT-N₂GA primarily measures pores within the size range of 1.26–127.44 nm. In materials with micropores smaller than 2 nm, interactions between the pore walls and overlapping potential energies lead to significantly higher gas adsorption quantities compared to mesoporous materials. Micropore filling occurs when P/P₀ < 0.01, and for materials with pore sizes ranging from 0.5 to 1.0 nm, P/P₀ may need to reach 10⁻⁵ to 10⁻⁷. Consequently, the analysis of micropores is more complex than that of mesopores. In this study, CO₂ adsorption experiments were conducted to characterize the pore structure of micropores with sizes less than 2 nm [54].

During LP-CO₂GA measurements, the saturation vapor pressure cannot be attained due to pressure limitations, and the samples adsorb within the relative pressure range of 0–0.03. Figure 7a presents the isothermal adsorption curves of the coal samples, where the adsorption quantity increases steadily with increasing pressure. Under low-pressure conditions, the adsorption sites on the adsorbent surface are abundant, allowing CO₂ molecules to form a uniform monolayer on the surface. The strong correlation between adsorption quantity and pressure suggests a uniform distribution of micropore structures, resulting in evenly distributed adsorption sites.

The pore size analysis in LP-CO₂GA is primarily based on DFT, with the PSD presented in Figure 7b,c. CO₂ adsorption occurs in pores with diameters ranging from 0.30 to 1.50 nm. The micropore volume of the coal samples is 0.020 m³/g, and the SSA of micropores is 56.11 m²/g, which is notably higher than the SSA derived from nitrogen adsorption. This further suggests that micropores are the primary sites for gas adsorption in coal. The micropore size distribution of the coal samples exhibits a multimodal pattern, with a high degree of consistency between the peak positions of PV and SSA. Peaks are observed at 0.45 nm, 0.60 nm, and 0.80 nm, with the micropores at 0.60 nm contributing the most to both PV and SSA. Given the well-developed micropores in the coal samples and their large SSA, these pores provide abundant adsorption sites for gas storage. Overall, the micropores in the coal samples are highly developed, with the most pronounced development observed in the pore size range of 0.45–0.80 nm.

The fractal characteristics of coal micropores are critical to gas adsorption capacity [43]. Based on the results of CO₂ adsorption experiments and Equation (6), a double logarithmic plot of cumulative PV and cumulative SSA was constructed. As shown in Figure 7d, the logarithms of cumulative PV (lnV) and cumulative SSA (lnS) exhibit a strong linear correlation, with a correlation coefficient (R² = 0.9994). The fractal dimension of the micropore structure was calculated to be 2.5424 ± 0.00496, confirming its clear fractal characteristics. This further corroborates the complex nature of the pore structure in deep coal.

3.5. Multi-Scale Pore Structure Characterization and Fractal Characteristics

The coal samples exhibit a complex pore structure, which poses significant challenges for precise characterization using a single testing method. Based on the principles of the respective tests and the characteristics of the calculation models, MIP, LT-N₂GA, and LP-CO₂GA each have specific pore size ranges in which they are most effective for accurate characterization. The LP-CO₂GA results, calculated using the DFT model, are capable of accurately characterizing pores within the size range of 0.30–1.50 nm. The LT-N₂GA results, calculated using the BJH model, are suitable for characterizing pores in the size range of 0–50 nm [55,56,57,58]. The theoretical pore size range for the MIP method spans 3.6 nm to 10 µm, covering the distribution of mesopores and macropores. However, due to the compressibility of coal under high pressure, when the mercury intrusion pressure exceeds 30 MPa (corresponding to a pore size of approximately 50 nm), the coal matrix is compressed, and micropores are also affected. Therefore, the MIP method is unsuitable for characterizing micropores and mesopores but more effective for characterizing pores within the range of 50 nm to 10 µm [55,59]. In summary, this study evaluated the optimal pore size ranges for each experimental method and selected the appropriate calculation models. The effective pore size measurement ranges from 0.31 to 1.47 nm for LP-CO₂GA and 1.26–127.44 nm for LT-N₂GA. The overlap between these two ranges is 1.26–1.50 nm, and, for this interval, the LP-CO₂GA results were used to characterize the overlapping region. The MIP results, calculated using the Washburn equation, provided an effective pore size range of 5 nm to 10 µm. The overlap with the LT-N₂GA results lies in the range of 5.0–50 nm, and for this interval, the LT-N₂GA results were used due to the matrix compression effect observed in MIP experiments at pressures exceeding 30 MPa. The multi-scale PSD characteristics of the coal samples are illustrated in Figure 8.

The multi-scale pore structure of the coal samples demonstrates a multimodal distribution, with a predominant concentration in the micropore range of 0.45–0.80 nm. A summary of the PV and SSA results across multiple scales is provided in

Table 2. PV SSA of multi-scale pore structure in coal samples.

Sample ID	PV (cm3/g)				SSA (m2/g)
	Micropores	Mesopores	Macropores	Total	Micropores	Mesopores	Macropores	Total
Gaogu-4	0.021	0.002	0.078	0.11	57.18	1.42	0.068	58.67

. The PV of the coal samples ranges from 0.002 to 0.078 cm³/g, with macropores contributing the largest proportion to the total PV at 70.9%, followed by micropores at 19.09%. Similarly, the SSA of the coal samples spans 0.068 to 57.18 m²/g, with micropores accounting for 97.46%—a contribution that significantly exceeds that of mesopores and macropores. These findings suggest that micropores are highly developed in ultra-deep coal seams, providing a larger surface area for CBM adsorption and thereby enhancing the adsorption capacity and storage potential of the coal.

The fractal dimension of coal’s multi-scale pore structure quantitatively represents the complexity of pore structures and surface roughness, which, in turn, influences the adsorption and permeability characteristics of coal. Consequently, the fractal dimension serves as a crucial indicator for describing pore structure characteristics and the extent of heterogeneity [59,60,61]. Drawing on the experimental results and the previously described fractal models, the fractal dimensions were calculated as 2.5424 for micropores, 2.5917 for mesopores, and 2.5038 for macropores. These results indicate that the pore structures of micropores and mesopores in ultra-deep coal are more complex than those of macropores.

In summary, the elevated specific surface area of micropores in ultra-deep coal offers numerous adsorption sites for CBM, markedly augmenting the coal’s adsorption capacity. The intricate fractal characteristics of micropores and mesopores, as opposed to macropores, further enhance the coal’s adsorption potential. While macropores constitute the majority of the total PV, underscoring their pivotal role in CBM permeability, the development of micropores and mesopores directly affects the adsorption and storage capacity of CBM, thus influencing the resource’s recoverability. Therefore, investigations into pore structure and fractal characteristics can inform more effective CBM development strategies. For example, augmenting coal seam permeability and refining extraction methodologies can elevate CBM recovery rates.

3.6. Implication and Limitation

The previous research mainly studied the pore structure characteristics, including the fractal characteristics of pore structure in coal seams within the depth of 3000 m, limiting the comprehensive and insightful understanding of the pore structure characteristics, due to the rare coal samples from ultra-deep coal seams exceeding the depth of 4000 m. In this study, the valuable coal sample was obtained from the Gaogu-4 well at a depth of 4369.4 m in the Shengli Oilfield of Shandong, China, providing the opportunity to explore the pore structure characteristics of the ultra-deep coal seam. Accordingly, the key pore structure characteristics were examined by a series of comprehensive measurements of FE-SEM, MIP, LT-N₂GA, and LP-CO₂GA, including the surface morphology, mineral composition, and multi-scale pore structure. The key pore structure parameters include PV, SSA, and PSD. In addition, the fractal characteristics of the multi-scale pore structure were prospected by quantitative analysis of the surface roughness and heterogeneity in the ultra-deep coal seam. The above findings can facilitate the understanding and estimating of the adsorption capacity and development potential of ultra-deep CBM [62,63,64]. All of the above contributions are devoted to providing more precise data to support the exploration, development, and utilization of the ultra-deep CMB. However, it is deduced that there are significant differences in the micropore (<2 nm), mesopore (2~50 nm), and macropore (>50 nm) structures of coal with different depths. Therefore, exploring the fractal evolutionary characteristics of coal samples with different depths in deep coal seams has important theoretical and practical guiding significance for the efficient exploitation and development of CBM in future studies.

4. Conclusions

(1) FE-SEM images reveal the pronounced heterogeneity of coal sample surfaces, with unevenly distributed pores that are typically circular, elliptical, or slit-like in shape and exhibit a relatively rough surface texture. Fractures are generally irregular in shape and partially interconnected, forming a complex pore network. The fractal dimension calculations of the coal sample surfaces indicate distinct fractal characteristics.

(2) The EDS analysis identified elements such as C, O, Al, Si, S, and Fe, confirming the presence of silicate and iron sulfide minerals. However, the restricted three samples in this analysis may introduce uncertainties regarding the representativeness of these mineralogical identifications. XRD analysis revealed that the coal sample contains kaolinite, marcasite, and clinochlore.

(3) The multi-scale pore characteristics of ultra-deep coal indicate that SSA is predominantly contributed by micropores (0.45–0.8 nm), accounting for 97.46% of the total SSA. The PV distribution follows the order of macropores > micropores > mesopores, with macropores contributing the largest proportion (70.9%).

(4) The fractal dimensions of the pore structures in ultra-deep coal were calculated as 2.5424 for micropores, 2.5917 for mesopores, and 2.5038 for macropores, indicating significant heterogeneity and pronounced multi-scale characteristics of the pore structures. The extensive development of micropores, surpassing mesopores and macropores, identifies them as the primary sites for gas adsorption. These findings are crucial for understanding the adsorption capacity and development potential of deep CBM, providing essential scientific insights for its efficient exploitation.

(5) It is noted that the analysis performed in this paper is restricted to the research samples and the theoretical model is based on only these samples. Therefore, exploring the fractal evolutionary characteristics of coal samples with different depths in deep coal seams has important theoretical and practical guiding significance for the efficient exploitation and development of CBM in future studies.