Fractal Pore and Its Impact on Gas Adsorption Capacity of Outburst Coal: Geological Significance to Coalbed Gas Occurrence and Outburst

Abstract

Pore structure and methane adsorption of coal reservoir are closely correlated to the coalbed gas occurrence and outburst. Full-scale pore structure and its fractal heterogeneity of coal samples were quantitatively characterized using low-pressure N₂ gas adsorption (LP-N₂GA) and high-pressure mercury intrusion porosimetry (HP-MIP). Fractal pore structure and adsorption capacities between outburst and nonoutburst coals were compared, and their geological significance to gas occurrence and outburst was discussed. The results show that pore volume (PV) is mainly contributed by macropores (>1000 nm) and mesopores (100–1000 nm), while specific surface area (SSA) is dominated by micropores (<10 nm) and transition pores (10–100 nm). On average, the PV and SSA of outburst coal samples are 4.56 times and 5.77 times those of nonoutburst coal samples, respectively, which provide sufficient place for gas adsorption and storage. The pore shape is dominated by semiclosed pores in the nonoutburst coal, whereas open pores and inkbottle pores are prevailing in the outburst coal. The pore size is widely distributed in the outburst coal, in which not only micropores are dominant, but also, transition pores and mesopores are developed to a certain extent. Based on the data from HP-MIP and LP-N₂GA, pore spatial structure and surface are of fractal characteristics with fractal dimensions $D_{m 1}$ (2.81–2.97) and $D_{n}$ (2.50–2.73) calculated by Menger model and Frenkel–Halsey–Hill (FHH) model, respectively. The pore structure in the outburst coal is more heterogeneous as its $D_{n}$ and $D_{m 1}$ are generally larger than those of the nonoutburst coal. The maximum methane adsorption capacities ( $V_{L}$ : 15.34–20.86 cm³/g) of the outburst coal are larger than those of the nonoutburst coal ( $V_{L}$ : 9.97–13.51cm³/g). The adsorptivity of coal samples is governed by the micropores, transition pores, and $D_{n}$ because they are positively correlated with the SSA. The outburst coal belongs to tectonically deformed coal (TDC) characterized by weak strength, rich microporosity, complex pore structure, strong adsorption capacity, but poor pore connectivity because of inkbottle pores. Therefore, the area of TDC is at high risk for gas outburst as there is a high-pressure gas sealing zone with abundant gas enrichment but limited gas migration and extraction.

1. Introduction

Coalbed methane is a serious safety hazard in coal mines [1, 2], while it is also an important economical natural gas supply [3, 4]. The mechanism of gas occurrence, emission, and outburst is not only controlled by macroscopic geological factors [5, 6] but also closely correlated to the microscopic structure in coal reservoirs [7, 8]. The effects of geological factors on gas occurrence and outburst have been studied extensively [9–11]. However, it is still necessary to further study geological significance from the perspective of porosity and adsorptivity in coal reservoirs. The solid-gas coupling between coal and methane is essentially the interaction between gas and inner pores [12], and pore structure directly influences the occurrence of adsorbed gas and free gas in coal seams [13–19]. Therefore, the investigation into pore structure and methane adsorption capacity of coal is the key to analyzing the microscopic mechanism of coalbed gas occurrence and outburst, which is critical to safety mining and coalbed methane resource evaluation.

Coal is a type of porous medium, in which the well-developed pore network provides the storage place and seepage channel for gas [20–24]. The decimal classification is widely adopted in coal pore research [25], namely, micropores (<10 nm), transition pores (10–100 nm), mesopores (100–1000 nm), and macropores (>1000 nm). Generally, pore structure in coal reservoirs can be characterized by image analysis [18, 26], fluid intrusion [27, 28], gas adsorption [13, 15, 29], small-angle scattering of X-rays (SAXS), and neutrons (SANS) [30, 31]. Among them, high-pressure mercury intrusion porosimetry (HP-MIP) has been commonly used in pore characterization for obtaining quantitative information in a wide pore size range (3 nm–100 μm) [28, 32]. It should be pointed out that the mercury intrusion pressure is extremely high in determining nanopores. For example, the maximum intrusion pressure can reach 413.7 MPa, which corresponds to a pore size of 3 nm. The high-pressure mercury may destroy the original pore structure. Furthermore, the compression effect on coal matrix intensifies at high pressures [13, 33]. Consequently, HP-MIP is recommended for the characterization of pores with a diameter above 50 nm because of the practical errors in characterizing pores with smaller sizes [8, 14]. However, low-pressure N₂ gas adsorption (LP-N₂GA) can accurately measure nanopores in coal reservoirs, which overcomes the limitation of HP-MIP. Therefore, the advantages of HP-MIP and LP-N₂GA should be combined to achieve the full-scale pore characterization in coal samples and obtain accurate details, such as specific surface area (SSA), pore volume (PV), pore size distribution (PSD), pore shape, pore openness, and connectivity.

Due to the complexity of the pore network in coal, the heterogeneity of pore structure is difficult to be described in light of the traditional Euclidean geometry theory, while with the application of modern fractal theory, fractal dimension can quantitatively characterize the complexity of pore structure [16, 34]. Adopting Frenkel-Halsey-Hill (FHH) and Menger models to analyze the data from LP-N₂GA and HP-MIP, Yao et al. [15, 28] described the fractal characteristics of nanoscale pores (<100 nm) and micron-scale pores (>100 nm) for different-rank coal, respectively. The fractal heterogeneity of coal pores leads to differences in SSA and gas adsorption capacity [35]; thus, it is necessary to perform a comparative study on fractal pore characteristics between outburst and nonoutburst coals.

Methane is mainly stored in coal as patterns of adsorbed gas, free gas, and dissolved gas [36]. Adsorbed gas accounts for 80%–90% of the total gas content in coal reservoirs [14, 37]. The methane adsorptivity of coal is vital to gas content and gas pressure. Usually, adsorption isotherms are obtained from methane adsorption experiments in the laboratory [20, 38], and adsorption parameters are calculated by fitting an appropriate adsorption model to quantify the adsorption capacities of coal samples. The gas adsorption capacities for coal reservoirs are not only affected by external conditions such as pressure, temperature, and moisture content [39, 40] but also closely related to coal properties including coal rank, maceral composition, pore parameters, and fractal dimension [16, 41, 42]. Tectonically deformed coal (TDC) is prevalent in China, which is usually associated with coal and gas outburst [12, 43]. The coal strength, pore structure, and fractal heterogeneity all changed significantly from the native structure (primary coal) to TDC [12, 43, 44]. However, the pore structure and fractal heterogeneity caused by tectonic deformation and their influence on gas adsorption and occurrence still need to be further studied.

This study focuses on the fractal pore and gas adsorption capacity of the outburst coal and their geological significance to coalbed gas occurrence and outburst. HP-MIP and LP-N₂GA were performed to jointly characterize the full-scale pore structure in coal samples. According to the branches of mercury intrusion and nitrogen adsorption, the fractal dimensions were calculated to study the fractal heterogeneity of microscopic pore structure. Isothermal adsorption experiments were performed to determine methane adsorption capacities of coal samples and discover the effects of pore structure and fractal dimension on gas adsorptivity. Moreover, we compared the difference of fractal pores and adsorbability between the outburst coal and nonoutburst coal and revealed their geological significance to gas occurrence and outburst. This study helps to understand coalbed gas geological occurrence and prevent coal and gas outburst.

2. Samples and Methodology

2.1. Geological Background and Sampling

The study area is located in the Qianjiaying coal mine, Kaiping coalfield, China (Figure 1(a)). Main coal seams are distributed in the Upper Carboniferous to Lower Permian Damiaozhuang Formation, and the study area is structurally located in the southeastern Kaiping syncline (Figure 1(b)). The burial depth of coal seam increases from southeast to northwest. The content and pressure of coalbed gas are generally consistent with the variation trend of burial depth, as well as gas occurrence closely controlled by folds and faults. There are two high-risk areas of coal and gas outburst delineated based on gas content, gas pressure, structural complexity, and variation coefficient of coal thickness, comprehensively. The study area had experienced a gas anomaly and outburst, with a volume of 7380 m³ gas emission and 489 t of pulverized coal and rock block ejection at the main crosscut on the -850 m level (Figure 1(c)), which provides a good comparative object for the present study.

Figure 1

Location of the study area (a, b), structural outline map of the coal mine (c), and macroscopic and microscopic characteristics of the coal samples (d).

Eight coal samples were collected from the gas anomaly and outburst area and nonoutburst area (Table 1). The coal samples from gas anomaly and outburst areas mainly belong to scaly coal and wrinkle coal because of the tectonic deformation and coal seam rheology, whereas the samples from nonoutburst areas are mainly primary coal and cataclastic coal (Figure 1(d)). Compared with the primary coal, TDC in the outburst area is characterized by low strength, low firmness, and poor stability through the observation on sample specimen. According to microscopic observation, there are rare microfractures and a few crossed microfractures in primary coal and cataclastic coal, respectively. However, abundant and various microfractures formed a complex network connecting pores in the scaly coal and wrinkle coal from the gas outburst area (Figure 1(d)). The coal samples belong to coking coal with measured vitrinite reflectance ( $R_{o, \max}$ ) ranging within 1.29%–1.58% (Table 1). According to the proximate analysis, all the coal samples are characterized by low moisture content, as well as high ash and volatile content. Coal rank and coal quality have significant effects on gas adsorption. Due to the small-scale alteration for the above two properties among the samples, we focus on the effect of fractal pore structure on methane adsorption capacities of the coal samples.

Table 1

Basic information and testing data of the coal samples.

Sample ID	Sampling location	Tectonically deformed types	$R_{o, \max}$	Proximate analysis (%)
Sample ID	Sampling location	Tectonically deformed types	$R_{o, \max}$	$M_{ad}$	$A_{ad}$	$V_{daf}$	FC_ad
ZC-S5	Nonoutburst area	Primary coal	1.32	2.02	22.7	23.44	51.84
ZC-S8		Primary coal	1.29	1.13	20.83	24.75	53.29
ZC-Q9		Cataclastic coal	1.49	1.10	21.12	29.96	47.82
ZC-S12		Cataclastic coal	1.55	1.43	21.16	27.81	49.60

TC-1	Gas anomaly and outburst area	Scaly coal	1.33	0.35	15.79	28.27	55.59
TC-2		Scaly coal	n/a	0.44	23.51	26.49	49.56
TC-3		Wrinkle coal	1.58	1.08	23.25	28.15	47.52
TC-4		Wrinkle coal	n/a	0.87	18.84	31.33	48.96

Notes: n/a: no available data; $M_{ad}$ : moisture content, air dry basis; $A_{ad}$ : ash content, air dry basis; $V_{daf}$ : volatile content, air dry basis; FC_ad: fixed carbon, air dry basis.

2.2. Experimental Methods

2.2.1. High-Pressure Mercury Intrusion Porosimetry

HP-MIP experiments were conducted using an AutoPore 9510 mercury porosimeter (Micrometrics Instrument, USA) at the Key Laboratory of Coalbed Methane Resources and Reservoir Formation Process, China University of Mining and Technology. According to the China National Standard GB/T 21650.1-2008, coal samples were broken down to about $2 \times 2$ mm. Then, 3–5 g granular sample was oven-dried at 110°C for 12 h to remove moisture and impurity gas. Afterwards, the instrument was vacuumized before testing and loaded with the dry samples for the experiment. Mercury was injected into the coal samples with the pressure range from 690 Pa to 413.7 MPa, corresponding to the lower limits of detected pore size 3 nm. Owing to the effect of the surface tension, the relationship between the pressure of intrusion mercury and pore size can be expressed by the Washburn equation [45]. The amount of intrusion and extrusion mercury at different pressures was recorded to calculate the parameters of pore structure. Meanwhile, the results with pore size greater than 100 μm should be removed, which are considered to be interfered by particle accumulation or surface cracks.

2.2.2. Low-Pressure N₂ Gas Adsorption

LP-N₂GA measurements were carried out at the Key Laboratory of Coal Preparation & Purification, China University of Mining and Technology, using a specific surface and pore size analyzer (Autosorb IQ, Quantachrome, USA), which can detect the pore size ranging within 0.35–200 nm. The resolution of the microporous test can reach 0.02 nm, and the minimum detectable SSA and PV are 0.0005 m²/g and 0.0001 cm³/g, respectively. Based on the China National Standard GB/T19587-2004, the coal samples were crushed into 0.18–0.25 mm (60–80 mesh). Then, 5–8 g coal powder samples were dried at 110°C for 12 h in an oven to remove impurity fluids including water vapor. After sample drying, all coal powders were evacuated for complete outgassing in a high vacuum system within 5 h. Using N₂ gas with a purity of 99.99%, adsorption and desorption isotherms of coal powders were measured successively with the relative pressures ( $P / P_{0}$ : 0.009–0.998) at the temperature of 77.4 K. According to the N₂ adsorption branch, the multipoint Brunauer-Emmett-Teller (BET) model and Barrett-Joyner-Halenda (BJH) model [46–48] were chosen to calculate the SSA and PV, respectively. The PSDs were derived based on the density functional theory (DFT) model [49, 50].

2.2.3. Methane Adsorption Experiment

Isothermal adsorption experiments were carried out adopting an IS-300 volumetric adsorption and desorption analyzer (TerraTek, USA) at the Key Laboratory of Coalbed Methane Resources and Reservoir Formation Process, China University of Mining and Technology. Firstly, the coal samples were crushed into 0.18–0.25 mm (60–80 mesh). Secondly, 120–150 g pulverized coal powder was prepared as the equilibrium water sample at the relative humidity of 98%. Lastly, using the pure methane gas (purity: 99.99%), adsorption measurements were performed with pressures ranging within 0–8 MPa at a constant temperature (30°C). The pressure data of both the sample cell and reference cell was recorded to calculate the adsorbed methane content of the coal samples. The Langmuir model (Equation (1)) [51] was chosen to fit the adsorption data and further determine the relevant parameters and isotherms for the coal samples: $\begin{matrix} (1) & V = \frac{{P V}_{L}}{P + P_{L}}, \end{matrix}$ where $P$ is testing pressure, MPa; $V$ is methane adsorption content at the pressure P, cm³/g; $V_{L}$ is the Langmuir volume, which reflects the maximum methane adsorption capacity, cm³/g; and $P_{L}$ is the Langmuir pressure, MPa.

2.3. Fractal Dimension Analysis

Based on the fractal theory, the heterogeneity and complexity of pore structure can be quantitatively evaluated with fractal dimension. In this study, the fractal dimensions with different pore size ranges were determined based on the HP-MIP and LP-N₂GA data, denoted as $D_{m}$ and $D_{n}$ , respectively. The Menger sponge model was applied to $D_{m}$ calculation [28], which is expressed as $\begin{matrix} (2) & \ln (\frac{{d V}_{p}}{d P}) \propto (D_{m} - 4) \ln P, \end{matrix}$ where $D_{m}$ is the fractal dimension calculated from HP-MIP data, dimensionless; $P$ is the intrusion mercury pressure, MPa; and $V_{p}$ is the cumulative mercury volume at the pressure $P$ , mL/g.

As long as the fractal characteristics exist in the pore structure, $\ln (d V_{p} / d P)$ and $\ln P$ exhibit a linear correlation. Furthermore, the slope $K_{m}$ of the linear correlation can be obtained to calculate the fractal dimension $D_{m}$ .

The Frenkel-Halsey-Hill (FHH) model was widely adopted for fractal dimension determination, which is shown in the following equation: $\begin{matrix} (3) & \ln (V) = (D_{n} - 3) \cdot \ln [\ln (\frac{P_{0}}{P})] + C, \end{matrix}$ where $D_{n}$ is the fractal dimension calculated from LP-N₂GA data, dimensionless; $C$ is a constant dimensionless; $P / P_{0}$ is relative pressure, dimensionless; and $V$ is the adsorbed gas volume at $P / P_{0}$ , cm³/g.

If the pore structure is characterized by fractal heterogeneity, $\ln V$ exhibits a linear correlation with $\ln [\ln (P_{0} / P)]$ . Solving the slope $K_{n}$ of the linear correlation, the fractal dimension $D_{n}$ can be further calculated, and the fractal dimension is generally divided into two stages ( $D_{n 1}$ and $D_{n 2}$ ). It should be noted that both the $D_{m}$ and $D_{n}$ values should be between 2 and 3 [52, 53], and a larger fractal dimension indicates a stronger fractal heterogeneity of pore structure.

3. Results

3.1. Pore Characterization Using HP-MIP

The mercury intrusion and extrusion curves are illustrated in Figure 2 for all the coal samples. For the nonoutburst coal samples, the amount of mercury intrusion increased slowly at the low pressures but increased rapidly while pressure is over 5000 psi, indicating that micropores are relatively rich compared to larger-size pores. Both mercury intrusion branch and extrusion branch are concave-up curves, and hysteresis loops are narrow for nonoutburst coal samples. It is speculated that semiclosed pores are dominant in the nonoutburst coal samples, resulting in poor openness and connectivity. For the outburst coal samples, the amount of mercury intrusion increases consistently with pressure from the initial stage to the high-pressure stage, indicating that the PSDs are relatively uniform in the samples. With the decrease of pressure, the mercury extrusion curves initially decreased rapidly, then tended to be flat (sample TC-3 and TC-4), and finally presented a sharp decline with the upper convex shape (sample TC-1 and TC-2). The hysteresis loops are relatively wide for outburst coal samples as a result of the considerable difference in the volume between mercury intrusion and extrusion. Hence, the outburst coal mainly contains open pores, but the inkbottle pores with narrow throats occupy a substantial proportion, which leads to poor pore connectivity.

Figure 2

Mercury intrusion and extrusion curves of the coal samples.

The parameters of pore structure obtained from HP-MIP are shown in Table 2. The measured porosity of coal samples varies between 2.24% and 7.29%. The PV of macropores and mesopores range within 0.0012–0.0174 cm³/g and 0.0006–0.0170 cm³/g, respectively. And the SSAs of macropores and mesopores are 0.001–0.015 m²/g and 0.012–0.249 m²/g, respectively. The relationship between incremental intrusion volume and pore size is plotted in Figure 3. The PSDs are unimodal for the nonoutburst coal samples (Figure 3(a)), and incremental intrusion volume possesses a peak at the range of micro- and transition pores. However, the PSDs are relatively uniform for the outburst coal samples (Figure 3(b)), showing a multimodal distribution, and two major peaks appear in micropores and mesopores. It should be noted that HP-MIP has advantages in macro- and mesopore characterization, though the accuracy is questionable in characterizing pores with a diameter below 50 nm. So the PSDs of pores (<50 nm) should be further analyzed in combination with LP-N₂GA.

Table 2

Pore structure parameters of the coal samples measured by HP-MIP and LP-N₂GA.

Sample	Porosity (%)	Pore volume (cm³/g)				Specific surface area (m²/g)				Total PV (cm³/g)	Total SSA (m²/g)
Sample	Porosity (%)	Macropores HP-MIP	Mesopores HP-MIP	Transition pores LP-N₂GA BJH	Micropores LP-N₂GA BJH	Macropores HP-MIP	Mesopores HP-MIP	Transition pores LP-N₂GA BET	Micropores LP-N₂GA BET	Total PV (cm³/g)	Total SSA (m²/g)
ZC-S5	3.06	0.0017	0.0013	0.0008	0.0002	0.002	0.023	0.130	0.266	0.0041	0.421
ZC-S8	2.24	0.0012	0.0006	0.0005	0.0001	0.001	0.012	0.074	0.052	0.0024	0.139
ZC-Q9	3.92	0.0040	0.0020	0.0010	0.0004	0.006	0.034	0.164	0.435	0.0074	0.640
ZC-S12	3.98	0.0039	0.0022	0.0012	0.0005	0.004	0.037	0.182	0.389	0.0078	0.612
TC-1	5.31	0.0092	0.0060	0.0023	0.0014	0.010	0.088	0.381	1.578	0.0188	2.057
TC-2	7.29	0.0140	0.0170	0.0036	0.0014	0.011	0.249	0.602	1.837	0.0360	2.699
TC-3	4.69	0.0174	0.0040	0.0028	0.0013	0.015	0.061	0.444	1.868	0.0255	2.388
TC-4	6.79	0.0089	0.0071	0.0027	0.0022	0.007	0.137	0.444	2.706	0.0208	3.294

Figure 3

Relationship between incremental intrusion volume and pore size for nonoutburst coal samples (a) and outburst coal samples (b).

(b)

3.2. Pore Characterization Using LP-N₂GA

LP-N₂GA results show that N₂ adsorption curves are in reverse “S” shape for all the coal samples (Figure 4). The shape of adsorption curves depends on the interaction between nitrogen and pore surface in different pressure ranges [54]. When $P / P_{0} < 0.01$ , the adsorption branches rise sharply because of micropore filling, indicating well-developed micropores in the coal samples. Then, the adsorption curves present a knee-bend shape at the stage of $0.01 < P / P_{0} < 0.05$ , which indicates the monolayer adsorption process of nitrogen molecules covering the entire pore surface based on the technical report proposed by the International Union of Pure and Applied Chemistry (IUPAC) [48, 54]. Subsequently, the adsorbed volume increases slowly as a result of the transition from monolayer adsorption to multilayer adsorption. Finally, at high relative pressures ( $P / P_{0} > 0.9$ ), the adsorption curves rise remarkably and fail to reach adsorption saturation even if $P / P_{0}$ approaches 1.0, indicating the capillary condensation occurs in pores. There are hysteresis loops between adsorption and desorption branches (Figure 4) because of the capillary condensation. The hysteresis loops are relatively narrow for nonoutburst coal samples as their adsorption curves almost overlap with desorption curves. In the light of the hysteresis loop classification recommended by IUPAC [54], the hysteresis loops of the nonoutburst coal are similar to the type H4 hysteresis loop, implying that the narrow slit-like pores, wedge pores, and conical pores are prevailing in the nonoutburst coal. However, the hysteresis loops of the outburst coal possess larger width and appear to have a sharp decline at the $P / P_{0}$ of 0.5, which are similar to type H2(b) based on the classification, as well as present the characteristics of type H3 hysteresis loop at high pressures. Therefore, there are plate-shaped pores, cylindrical pores with open ends, and inkbottle pores with a wide body but a narrow throat in the outburst coal samples.

Figure 4

N₂ adsorption and desorption isotherms of the coal samples.

According to the results measured by LP-N₂GA (Table 2), the PV of micro- and transition pores in the coal samples are 0.0001–0.0022 cm³/g and 0.0005–0.0036 cm³/g, respectively. The SSAs of micro- and transition pores are 0.052–2.706 m²/g and 0.074–0.602 m²/g, respectively. LP-N₂GA has an advantage in the characterization of PSDs of the micro- to transition pores. According to the PSDs calculated using the DFT model presented in Figure 5, the PSDs of the nonoutburst coal samples show multimodal with the peaks in the pore size ranges of 18–20 nm, 30–50 nm, and 70–80 nm (Figure 5(a)). Although the multimodal feature of the PSDs is apparent for the outburst coal samples (Figure 5(b)), the peaks are distributed over a relatively wide pore size range (3–80 nm).

Figure 5

Relationship between incremental adsorbed volume and pore size for nonoutburst coal samples (a) and outburst coal samples (b).

(b)

3.3. Pore Fractal Heterogeneity of the Coal Samples

Based on the data from mercury intrusion branches of the coal samples, the correlations between $\ln (d V_{p} / d P)$ and $\ln P$ are plotted in Figure 6. Two different linear correlations are shown at pressure ranges of 0.01–24 MPa and 24–413.7 MPa, and the pore size at the transition point between the two linear correlations is approximately 50 nm. When the pore diameter is over 50 nm ( $D > 50$ nm), there is a strong linear relationship between $\ln (d V_{p} / d P)$ and $\ln P$ with the coefficient of determination ( $R^{2}$ ) above 0.96 for all the coal samples (Table 3). Furthermore, the fractal dimension $D_{m 1}$ was calculated according to the Menger model (Equation (2)), which ranges from 2.81 to 2.97. The values of $D_{m 1}$ are close to the upper limit 3, indicating that the pore structure ( $D > 50$ nm) is relatively complex in the coal samples. Nevertheless, for the pore diameter of 3–50 nm, the correlations between $\ln (d V_{p} / d P)$ and $\ln P$ are relatively weak, especially for sample ZC-S8 ( $R^{2} = 0.3823$ ) and sample TC-2 ( $R^{2} = 0.4517$ ). In addition, the calculated fractal dimension values $D_{m 2}$ range from 3.63 to 3.83, which all exceed the upper limit 3 and become invalid. The previous studies have shown that the compressibility of coal presents a remarkable impact on the HP-MIP data when mercury intrusion pressure is beyond 20 MPa [13, 16]. For HP-MIP measurements at high pressures, the mercury intrusion volume per unit pressure is larger than the actual pore volume because of matrix compression in the coal samples, resulting in errors in $D_{m 2}$ calculation for the pores below 50 nm. Thus, our results also confirmed that HP-MIP is inadequate in the characterization of pores below 50 nm.

Figure 6

Plots of $\ln (d V / d P)$ and $\ln (P)$ of the representative coal samples based on the HP-MIP measurements.

Table 3

Calculated results of fractal dimensions based on HP-MIP and LP-N₂GA.

Sample	HP-MIP						LP-N₂GA
	$D > 50$ nm			$D = 3 - 50$ nm			$D = 1 - 50$ nm
	$K_{m 1}$	$D_{m 1}$	$R^{2}$	$K_{m 2}$	$D_{m 2}$	$R^{2}$	$K_{n}$	$D_{n}$	$R^{2}$
ZC-S5	-1.18	2.82	0.9719	-0.21	3.79	0.6842	-0.42	2.58	0.9995
ZC-S8	-1.11	2.89	0.9818	-0.17	3.83	0.3823	-0.50	2.50	0.9993
ZC-Q9	-1.19	2.81	0.9728	-0.25	3.75	0.8549	-0.38	2.62	0.9992
ZC-S12	-1.19	2.81	0.9671	-0.29	3.71	0.8841	-0.39	2.61	0.9877
TC-1	-1.10	2.90	0.9772	-0.28	3.72	0.9308	-0.33	2.67	0.9968
TC-2	-1.07	2.93	0.9691	-0.32	3.68	0.4517	-0.36	2.64	0.9984
TC-3	-1.15	2.85	0.9830	-0.29	3.71	0.8876	-0.27	2.73	0.9985
TC-4	-1.03	2.97	0.9699	-0.37	3.63	0.9305	-0.30	2.70	0.9803

Notes: $D_{m 1}$ and $D_{m 2}$ are the fractal dimensions calculated based on HP-MIP data with pore size greater than 50 nm and 3–50 nm, respectively. $D_{n}$ is the fractal dimension calculated based on LP-N2GA data with pore size 1–50 nm. $K_{m 1}$ , $K_{m 2}$ , and $K_{n}$ are the corresponding fitting parameters.

To overcome the limit of fractal dimension calculation in pores ranging within 3–50 nm from HP-MIP data, the fractal dimension $D_{n}$ of pores ranging within 1–50 nm was calculated based on N₂ adsorption branches (Table 3). As exhibited in Figure 7, the correlations between $\ln V$ and $\ln [\ln (P_{0} / P)]$ are linear with $R^{2}$ above 0.98 for all the coal samples. According to the FHH model (Equation (3)), the fractal dimension $D_{n}$ was calculated with the value of 2.50–2.73. Comparatively, the $D_{n}$ is smaller than $D_{m 1}$ , which reflects that the heterogeneity of pores above 50 nm is stronger than that of pores ranging within 1–50 nm.

Figure 7

Plots of $\ln V$ and $\ln [\ln (P_{0} / P)]$ of the representative coal samples based on the LP-N₂GA measurements.

3.4. Adsorption Isotherms of the Coal Samples

As illustrated in Figure 8 and Table 4, the methane adsorption capacities of all the coal samples were determined through methane adsorption experiments on the equilibrium water samples at 30°C. The adsorption isotherms were well fitted adopting the Langmuir model (Equation (1)), with $R^{2}$ above 0.99 for all the coal samples, and the adsorption parameters were further obtained. The Langmuir volume ( $V_{L}$ ) of coal samples ranges from 9.97 cm³/g to 20.86 cm³/g, and the Langmuir pressure ( $P_{L}$ ) ranges from 0.93 MPa to 1.42 MPa (Table 4). Obviously, the $V_{L}$ of the outburst coal samples (15.34–20.86 cm³/g) is larger than that of the nonoutburst coal samples (9.97–13.51 cm³/g), which indicates that the outburst coal possesses stronger methane adsorption capacities.

Figure 8

Methane adsorption isotherms of the coal samples.

Table 4

Fitting results of adsorption parameters for the coal samples.

Sample	$V_{L}$ (cm³/g)	$P_{L}$ (MPa)	$R^{2}$
ZC-S5	11.35	1.40	0.9965
ZC-S8	9.97	1.38	0.9976
ZC-Q9	13.10	1.42	0.9962
ZC-S12	13.51	1.20	0.9980
TC-1	15.34	0.98	0.9965
TC-2	19.43	0.93	0.9997
TC-3	17.99	1.50	0.9981
TC-4	20.86	1.39	0.9992

4. Discussion

4.1. Effect of Pore Structure on Methane Adsorption Capacity

The adsorption capacity of coal is an important factor affecting the gas content in the coal mine. As the place where gas interacts with coal matrix, the pore properties are the most direct factor affecting the methane adsorption in coal reservoir. Also, coal rank, maceral, and other factors can indirectly affect the adsorption performance of coal by controlling the pore structure [13, 41]. According to the scatter diagrams of total PV and SSA versus the maximum methane adsorption capacities of the coal samples (Figure 9), there is a strong positive correlation between $V_{L}$ and SSA ( $R^{2} = 0.9410$ ). The maximum methane adsorption capacities increase with the increase of the SSA (Figure 9(b)). Therefore, the adsorptivity of the coal sample is directly controlled by the SSA as it reflects the abundance of adsorption sites for methane molecules. Compared with the SSA, total PV weakly correlates with the $V_{L}$ , especially for the outburst coal samples with high methane adsorption capacities (Figure 9(a)). Considering the different effects of pores with different sizes on methane adsorption, the correlations between the maximum methane adsorption capacities and the PV of micro-, transition-, meso- and macropores are illustrated in Figure 10. The results show that the maximum methane adsorption capacities exhibit a positive linear correlation with the micropore volume ( $R^{2} = 0.8757$ ) and transition pore volume ( $R^{2} = 0.8386$ ), respectively (Figure 10(a)), while the data points representing the maximum methane adsorption capacity versus meso- and macro- pore volumes are relatively scattered without obvious correlation (Figure 10(b)).

Figure 9

Correlations between the maximum methane adsorption capacity and total pore volume (a) and total specific surface area (b).

(b)

Figure 10

Correlations between the maximum methane adsorption capacity and pore volume of micro- and transition pores (a) and meso- and macropores (b).

(b)

The pores with different sizes differ in the contribution to the PV and SSA. As shown in Figure 11(a), the total PV of the coal samples is mainly provided by macropores and mesopores. Macropores occupy the largest percentage of the total PV, i.e., 41.4%–59.7% (average: 48.3%), followed by mesopores with the percentage of 19.9%–47.2% (average: 31.3%). However, the total SSA is mainly contributed by micropores and transition pores (Figure 11(b)). The micropores dominated the total SSA with the percentage of 37.3%–82.0% (average: 67.2%), followed by transition pores with the percentage of 13.5%–53.3% (average: 26.6%). On the one hand, given the same total PV, the micro- and transition pores can provide a larger surface area than meso- and macropores for methane adsorption. On the other hand, the distance is relatively short between the pore walls in micro- and transition pores. It may cause the van der Waals force field to overlap between the pore walls, resulting in the larger adsorption potential in nanopores [16, 55]. Therefore, micropores and transition pores are the governing factors on gas adsorption capacity in coal seams. The well-developed micro- and transition pores in the outburst coal are accompanied by a rich internal surface, which enhances the gas adsorption capacity and expansion potentiality.

Figure 11

Pore volume (a) and specific surface area (b) distributions for different pore sizes in the coal samples.

(b)

4.2. Effect of Fractal Dimension on Methane Adsorption Capacity

The complexity of the pore structure is another key factor affecting the gas adsorption capacity [13, 35, 42, 56]. Even if coal samples have the same PV or SSA, the pore complexity may be completely different, which is expressed by fractal dimensions $D_{n}$ ( $D < 50$ nm) and $D_{m 1}$ ( $D > 50$ nm) in this study. It can be seen from Figure 12 that the $V_{L}$ presents a positive relationship with $D_{n}$ ( $R^{2} = 0.6969$ ), as the maximum methane adsorption capacity increases with the increasing $D_{n}$ of the coal samples. However, the correlation is unobvious between the maximum adsorption capacity and $D_{m 1}$ . The physical meanings represented by $D_{n}$ and $D_{m 1}$ are different. The $D_{n}$ was calculated based on the N₂ adsorption branch and FHH model, and $D_{m 1}$ was obtained according to the mercury intrusion branch and Menger model. As LP-N₂GA measurement mainly indicates the interaction between nitrogen molecules and the pore surface of coal matrix [54], $D_{n}$ describes the complexity and roughness of the pore surface. Nevertheless, the HP-MIP experiment is a process that the mercury fluid flows through the pore throat and injects into the pore body via pressure elevation [27, 28]; thus, $D_{m 1}$ reflects the complexity and irregularity of the spatial structure. Therefore, fractal dimension $D_{n}$ of the pore surface is closely related to gas adsorption capacities, whereas fractal dimension $D_{m 1}$ of the pore spatial structure presents an unobvious effect on gas adsorptivity.

Figure 12

Relationship between the maximum methane adsorption capacity and fractal dimensions.

We further analyze the effect of the fractal dimension on the methane adsorption capacities by plotting the $D_{n}$ and total SSA of the coal samples (Figure 13). The results show that the total SSA presents a positive correlation with $D_{n}$ , which also proves that the $D_{n}$ mainly reflects the complexity and roughness of the pore surface. The coal sample with a higher $D_{n}$ value possesses a larger specific surface area, thereby facilitating the methane adsorption capacity.

Figure 13

Relationship between total specific surface areas and fractal dimension $D_{n}$ .

4.3. Fractal Pore Structure of Outburst Coal and Its Geological Significance

4.3.1. Comparison of Fractal Pore Characteristics between Outburst and Nonoutburst Coals

The pore structure and fractal heterogeneity of the coal reservoir are closely related to the gas occurrence since they affect the methane adsorption capacities of the coal samples. The differences of pore structure (including porosity, PV, SSA, PSD, and pore shape) and fractal characteristics between the outburst coal and nonoutburst coal were compared, and their geological significance was analyzed. The porosity, PV, and SSA of the outburst coal samples vary from 4.69% to 7.29%, 0.0188–0.0360 cm³/g, and 2.388–3.294 m²/g, respectively (Table 2). The porosity, PV, and SSA of the nonoutburst coal samples are 2.24%–3.98%, 0.0024–0.0078 cm³/g, and 0.139–0.640 m²/g, respectively. Compared to the nonoutburst coal samples, the porosity, PV, and SSA of outburst coal samples are significantly higher (Figure 11). Quantitatively, the porosity, PV, and SSA of the outburst coal are 1.82 times, 4.56 times, and 5.77 times those of the nonoutburst coal on average, respectively. The well-developed porosity of the outburst coal has two aspects of geological significance to coalbed gas occurrence and outburst. On the one hand, the larger PV leads to the thinner coal skeleton in unit volume, and thus, the coal body is characterized by low strength and fragile structure. On the other hand, the rich surface area inside the outburst coal provides sufficient adsorption sites for methane molecules, and the large pore volume provides sufficient space for gas storage. Therefore, gas is easy to accumulate in the outburst coal seam, which increases gas pressure and outburst tendency.

The pore shape of coal can be analyzed based on the hysteresis loops determined by the mercury intrusion/extrusion and the N₂ adsorption/desorption [35, 54]. Yao and Liu [57] concluded that the open pore and inkbottle pore can retain mercury and lead to a hysteresis loop, while the semiclosed pore cannot. Taking samples ZC-S8 and TC-4 as an example, the difference of pore shape between the outburst coal and nonoutburst coal can be analyzed. As shown in Figure 14(a), the hysteresis loops of the nonoutburst coal are narrow or inconspicuous. Accordingly, the nonoutburst coal is dominated by semiclosed pores, including narrow slit-like pores, wedge-shaped pores, and conical/tubular pores with a closed end. This type of pore system is of poor openness and connectivity, which is not conducive to gas occurrence and enrichment. However, the hysteresis loops of the outburst coal are wide, and the N₂ desorption branch presents a sharp decline (Figure 14(b)). Therefore, the pores in the outburst coal are mainly open pores, including parallel plate-like pores open on all sides and cylindrical pores open at both ends. In addition, there are a certain number of inkbottle pores with narrow throats and wide bodies, which limit the pore connectivity. This type of pore structure is beneficial to gas enrichment and storage, and abundant gas can be stored in the wide bottle body of the inkbottle pores. More importantly, the narrow pore throat restricts the gas seepage. Thus, the gas does not migrate but accumulates locally to form a high-pressure gas zone.

Figure 14

Schematic diagram of pore shape for the nonoutburst coal (a) and outburst coal (b) based on the HP-MIP and LP-N₂GA data.

(b)

PSD is directly related to the occurrence and migration of coalbed gas. Micro- and transition pores provide the primary space for adsorbed gas, while meso- and macropores mainly constitute the diffusion and seepage space for free gas [15, 28]. LP-N₂GA and HP-MIP were combined to characterize PSD in pore sizes ranging from 1 to 50 nm and >50 nm, respectively, according to their advantages. As the full-scale PSDs are shown in Figure 15, the nonoutburst coal is dominated by micropores. However, the pore size is widely distributed in the outburst coal, in which not only micropores are dominant, but also, transition pores and mesopores are developed to a certain extent. The difference of PSDs between outburst and nonoutburst coals is mainly affected by tectonic deformation. As the degree of tectonic deformation increases (sequence from primary coal, cataclastic coal, scaly coal, to wrinkle coal), the micropores in TDC increase significantly because of the squeezing action [12], which corresponds to the narrow throat of the inkbottle pores in the outburst coal. In addition, new macropores and microfractures were formed in TDC under the tectonic deformation, which provides a favorable channel for rapid and instantaneous gas release in gas outburst.

Figure 15

The pore size distribution of the coal samples from HP-MIP and LP-N₂GA data.

According to the comparison of the fractal dimensions between the nonoutburst coal and outburst coal (Figure 16), $D_{n}$ and $D_{m 1}$ of the nonoutburst coal samples vary from 2.50 to 2.62 (2.58 on average) and 2.81–2.89 (2.83 on average), respectively, while $D_{n}$ and $D_{m 1}$ of the outburst coal samples range within 2.64–2.73 (2.69 on average) and 2.85–2.97 (2.91 on average), respectively. Both $D_{n}$ and $D_{m 1}$ of the outburst coal are generally larger than those of the nonoutburst coal, which suggests that the pore structure in the outburst coal is more complex and heterogeneous. Additionally, with the increase of the degree of tectonic deformation, $D_{n}$ shows an increasing trend (Figure 16), while the changing trend is less evident for $D_{m 1}$ . Therefore, the fractal heterogeneity of pores below 50 nm is more sensitive to tectonic deformation than that of pores above 50 nm.

Figure 16

Fractal dimensions of the coal samples with different tectonically deformed types.

4.3.2. Geological Implication of Fractal Pore Structure on Gas Occurrence and Outburst

The coal and gas outburst occurred in the zone of TDC including scaly coal and wrinkle coal in the study area. Meanwhile, there are significant differences in pore structure between TDC and primary coal as mentioned in Section 4.3.1. To reveal the relationship between tectonic deformation and gas outburst, the combined effect of tectonic deformation, pore structure, and adsorption capacity of coal reservoir on gas occurrence and outburst was summarized. Under the tectonic deformation, the primary coal transits to TDC accompanied by the direct effect on the physical properties and pore structure (Figure 17). Firstly, the coal strength is reduced yielding low hardness and brittle structure, thus forming the zone of soft and broken coal. Secondly, TDC is characterized by abundant PV and SSA and developed microporosity and strong fractal heterogeneity, resulting in a large number of internal surfaces for methane adsorption. Accordingly, the gas adsorption capacities of TDCs are remarkably enhanced. Thirdly, inkbottle pores with narrow throats emerge under the tectonic deformation, resulting in poor pore connectivity, which is unfavorable for gas migration and extraction. In addition, the TDC area is also a geostress concentration zone with high stress and high energy. Cheng and Lei [58] also suggested that in situ coal reservoirs in the TDC area possess low permeability as the fracture system was severely squeezed. Therefore, TDC is of strong adsorption capacity but poor permeability, and coalbed gas is enriched to form a high-pressure gas sealing zone.

Figure 17

The combined effect of tectonic deformation, pore structure, and gas adsorptivity on coalbed gas occurrence and outburst.

In fact, coal and gas outburst can be regarded as a combined action of gas, the porous medium of coal/rock, and underground stress according to the integrated factor outburst hypothesis [11]. Li [59] proposed that, for coal and gas outburst, high-pressure gas is an essential factor, while coal structure is an obstacle, and underground stress acts as a dynamic factor. The place, where TDC is well-developed, is in an unstable state due to the combination of soft and deformed coal zone, high-pressure gas sealing zone, and underground stress concentration zone (Figure 17). Once the triggering factors (excavating disturbance, rock burst, active geological structure, temperature anomaly, etc.) break the original equilibrium state, the adsorbed gas is desorbed to free gas rapidly, resulting in a gas expansion in the coal reservoir. Ultimately, high-pressure free gas and crushed coal powder/block are released instantaneously driven by stress energy, which leads to abnormal gas emission, even continuous coal fragmentation, and gas outburst. In summary, weak coal structure, abundant gas enrichment, and concentrating underground stress are the prerequisites for coal and gas outburst. The risk of gas outburst in the zone of TDC is higher than that in the zone of primary coal.

5. Conclusions

In this work, qualitative description, quantitative experiments, and fractal dimension calculation have been carried out to compare the pore structure and methane adsorption capacity between outburst and nonoutburst coals. Further, the effects of fractal pore on gas adsorption capacity and its geological significance to coalbed gas occurrence and outburst were discussed. The following conclusions can be drawn from the present study. (1)

On average, the PV and SSA of outburst coal samples are 4.56 and 5.77 times those of nonoutburst coal samples, respectively. The pore size is widely distributed in the outburst coal compared with the nonoutburst coal. Developed porosity in the outburst coal is beneficial to gas enrichment but leads to weak coal strength. Meanwhile, the considerable inkbottle pores in the outburst coal restrict gas migration and extraction, which is an important microscopic factor leading to gas outburst

(2)

Pore structure in coal reservoir exhibits fractal characteristics. The fractal dimensions $D_{n}$ ( $D < 50$ nm) and $D_{m 1}$ ( $D > 50$ nm) can be calculated based on HP-MIP and LP-N₂GA, respectively. The pore structure of the outburst coal is more complex and heterogeneous as its $D_{n}$ and $D_{m 1}$ values are generally larger than those of the nonoutburst coal. In addition, the $D_{n}$ is more sensitive to tectonic deformation than $D_{m 1}$

(3)

The methane adsorption capacities of the coal samples are governed by micropores and transition pores and affected by the fractal dimension $D_{n}$ as well. The rich micro- and transition pores and complex pore surface are accompanied by abundant internal surface area, resulting in the significantly stronger gas adsorption capacity of the outburst coal than that of the nonoutburst coal

(4)

The outburst coal is mostly scaly coal and wrinkle coal with tectonic deformation in the study area. The TDC is characterized by weak coal strength, complex pore structure, and strong adsorption capacity but limited permeability. Therefore, the area of TDC is at high risk for gas outburst, where there is a combination of soft coal zone, high-pressure gas sealing zone, and underground stress concentration zone

Footnotes

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This research was jointly supported by the National Natural Science Foundation of China (Grant Nos. 42202190, 42172156, and 42072199); the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20221147); and the Fundamental Research Funds for the Central Universities (Grant No. 2022-11247).

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Fractal Pore and Its Impact on Gas Adsorption Capacity of Outburst Coal: Geological Significance to Coalbed Gas Occurrence and Outburst

Abstract

1. Introduction

2. Samples and Methodology

2.1. Geological Background and Sampling

2.2. Experimental Methods

2.2.1. High-Pressure Mercury Intrusion Porosimetry

2.2.2. Low-Pressure N2 Gas Adsorption

2.2.3. Methane Adsorption Experiment

2.3. Fractal Dimension Analysis

3. Results

3.1. Pore Characterization Using HP-MIP

3.2. Pore Characterization Using LP-N2GA

3.3. Pore Fractal Heterogeneity of the Coal Samples

3.4. Adsorption Isotherms of the Coal Samples

4. Discussion

4.1. Effect of Pore Structure on Methane Adsorption Capacity

4.2. Effect of Fractal Dimension on Methane Adsorption Capacity

4.3. Fractal Pore Structure of Outburst Coal and Its Geological Significance

4.3.1. Comparison of Fractal Pore Characteristics between Outburst and Nonoutburst Coals

4.3.2. Geological Implication of Fractal Pore Structure on Gas Occurrence and Outburst

5. Conclusions

Footnotes

Data Availability

Conflicts of Interest

Acknowledgments

References

2.2.2. Low-Pressure N₂ Gas Adsorption

3.2. Pore Characterization Using LP-N₂GA