Changes in Pore Structure and Gas Adsorption–Desorption Characteristics of Coal Under High-Voltage Electric Pulses

Abstract

High-voltage electrical pulses (HVEPs), a new technology designed to enhance the permeability of coal seams, have received significant attention for their application in gas extraction from low-permeability coal seams. This study designed a high-pressure adjustable electrical pulse experimental system to investigate the effects of HVEPs on the pore structure and gas adsorption–desorption characteristics of bituminous coal samples. The results revealed that HVEPs effectively restructured pore morphology in coal samples through the opening of previously sealed and partially enclosed pores. This led to a significant increase in the average pore diameter, total pore volume, and porosity. However, the increase in total specific surface area was minimal. Moreover, the connectivity of pores was continuously enhanced. As the discharge voltage increased, the pore structure significantly improved. However, HVEP treatment slightly increased the adsorption pores (micropores and transition pores) and significantly increased the seepage pores (mesopores and macropores), which facilitated the free flow of gas within the coal samples. Additionally, HVEP treatment significantly reduced both the adsorption rate and the maximum gas adsorption capacity of the coal samples, indicating a strong inhibitory effect of HVEPs on gas adsorption. Conversely, HVEPs significantly increased the gas desorption capacity and desorption rate, suggesting that HVEPs facilitated the rapid desorption and release of gas from the coal samples. Furthermore, HVEP treatment increased the gas diffusion coefficient of the coal samples, which reduced their resistance to free diffusion after desorption and promoted gas extraction from the coal seam.

1. Introduction

With the continuous advancement of China’s industrialization and modernization, the imbalance between energy supply and demand has become increasingly pronounced. The development of domestic conventional oil and gas resources is insufficient to sustain economic growth. Therefore, expanding the exploration and utilization of unconventional natural gas resources is crucial for the sustainable growth of China’s energy sector [1]. Coalbed methane (CBM), which is a high-quality and clean form of unconventional natural gas, has been extensively explored and developed. However, 95% of China’s recoverable coal seams exhibit low permeability, with values between 0.1 × 10⁻⁵ and 0.1 × 10⁻³ µm². These coal seams face significant technical challenges such as complex geological conditions, high gas content, deep mining depths, and high in situ stress. These challenges obstruct the efficient extraction of CBM and increase the risk of gas-related accidents, posing a significant threat to safe production [2,3,4]. To improve CBM recovery, artificial enhancement techniques are commonly used based on the occurrence and migration characteristics of coal seams. These techniques can improve the fracture structure of coal reservoirs and increase their permeability. Currently, the main approaches for enhancing coal seam permeability include hydraulic techniques (such as hydraulic fracturing, hydraulic slotting, and hydraulic drilling), waterless fracturing methods (injection of CO₂, N₂, or air injection), ultrasonic waves, microwave radiation, fluidized mining, acid washing, microbial technology, and controllable shock waves. Additionally, combined enhancement techniques (such as integrated hydraulic fracturing and slotting or integrated hydraulic drilling and fracturing) have been developed to improve efficiency [5,6,7,8,9]. These methods have proven effective in modifying formation stress, expanding the pressure relief zone, and increasing coal seam permeability. However, these methods have certain limitations in their applicability. For example, hydraulic fracturing and slotting technologies are widely used, but they require large amounts of water, are prone to water lock effects, and are limited by water resource availability. Deep-hole blasting involves complex procedures and poses safety risks such as difficulties in explosive delivery, coal seam outbursts, and micro-earthquakes. Conventional borehole drainage requires extensive engineering work, while acidification technology faces challenges such as environmental pollution, equipment corrosion, and high transportation costs [10]. Therefore, developing new methods to increase coal seam permeability is crucial for ensuring the safe and efficient extraction of CBM.

High-voltage electric pulse (HVEP) technology, as an emerging method, has attracted widespread attention from researchers owing to its advantages, including a simple process, wide operating range, low energy consumption, and environmental friendliness. The fracturing effect of HVEP on solid materials was first discovered by accident in the 1950s and 1960s [11]. As HVEP rock-breaking technology gradually matured, the former Soviet Union began applying it in the 1970s to enhance permeability and unblock reservoirs during the exploitation of low-permeability oil layers to achieve noticeable increases in production [12,13,14]. The success of HVEP technology in enhancing oil reservoir permeability, unblocking flow channels, and increasing production and injection rates has prompted some researchers in the coal industry to explore its application for improving gas extraction from low-permeability coal seams. Zhang et al. [15,16,17] conducted a series of experimental investigations to analyze the alterations in coal permeability induced by HVEP treatment under diverse axial pressures, gas pressures, and confining pressures. The results showed that this technology, which is based on electrical discharge principles, can increase coal seam permeability by more than two orders of magnitude. Zhu et al. [18] studied the microscopic characteristics of anthracite coal samples treated with HVEP and found that the influence of elements such as C and O in the HVEP-treated coal samples, which constitute oxygen-containing groups, on gas adsorption slightly decreased. The cumulative pore volumes, including both micropores and macropores, were consistently greater in the coal samples compared to the raw coal samples. Lu et al. [19,20] investigated that HVEP based on the liquid electric effect can also significantly crack coal samples, and the more times of the HVEP treatment, the higher the density of fractures and the more interconnected the fracture network in coal samples. At the same time, the presence of weak structural parts such as pores and fractures in coal samples can facilitate fractures propagation. Li et al. [21,22] found that the volume of pores in the mesopore and macropore range within coal samples exhibited a notable increase under the action of repeated pulse strong shock waves, with a porosity increase of up to 74%. The pore size distribution range gradually became continuous from initially dispersed and isolated, and the count of open pores grew, resulting in enhanced connectivity of pores. Lin et al. [23,24,25] found that the adsorption hysteresis phenomenon of the HVEP-treated bituminous coal samples was more obvious, the pore volume and pore area increased, the micropore size expanded, and the pore structure was significantly improved. Jiang et al. [26,27,28] compared the evolution of pore and fracture structures and changes in permeability of coal samples soaked with KCl, MgCl₂, and FeCl₃ solutions after HVEP treatment, and found that FeCl₃ had the best improvement effect on anthracite coal samples, while MgCl₂ had the best improvement effect on bituminous coal samples. Bao et al. [29] conducted hydraulic fracturing experiments on coal and rock using a HVEP combined with hydraulic fracturing device and found that as the discharge voltage increased, the length, width, area, and complexity of the generated fractures all increased to varying degrees. Yan et al. [30,31,32] studied how HVEP processing modifies pore structure and permeability in anthracite, demonstrating significantly enhanced total porosity in treated versus untreated coal samples, especially with significant effects on mesopores and macropores. Ma et al. [33] developed a coal seam increased permeability test system based on HVEP and studied the displacement and propagation of fractures in coal seams when subjected to water shock wave effects. The results indicated that it was capable of substantially altering coal reservoirs’ pore and fracture structure, thereby enhancing the effectiveness of permeability improvement in coal seams.

Overall, HVEP technology has significant potential for enhancing coal seam permeability. However, further research is needed to elucidate the underlying mechanisms and engineering applications of this technology. The pore structure of coal significantly influences its gas adsorption–desorption behavior and determines the flow characteristics of gas within the coal seam. This study involved conducting fracturing experiments using a self-developed high-voltage adjustable electrical pulse experimental system to investigate the impact of HVEPs on the adsorption–desorption behavior of coal. Additionally, variations in the pore structure of the coal samples before and after HVEP treatment were analyzed via mercury intrusion porosimetry (MIP). This system has advantages, including safety, environmental protection, energy efficiency, repeatable discharge, and high energy output. These results provide a scientific foundation for elucidating the mechanism of coal permeability enhancement via HVEP treatment and its potential engineering applications.

2. Experimental

2.1. Material Preparation

The bituminous coal samples used in this experiment were obtained from the Qiyuan Coal Mine located in Shanxi Province. Large coal samples were extracted from the mining site, wrapped and sealed with cling film, and transported to the surface wellhead. The samples were then loaded into wooden boxes and transported to the processing plant. To minimize damage from handling and transport, large intact coal samples were selected and cut into cube-shaped blocks (~20 cm × 20 cm × 20 cm) using a cutting machine along the parallel bedding direction. During cutting, the sample surfaces were rinsed with water to smoothen them. A total of 12 coal samples were prepared and divided into 4 groups, with 3 coal samples in each group. The corresponding group numbers were A0, A1, A2, and A3. Industrial analysis, elemental analysis, and vitrinite reflectance measurements were conducted using an automatic industrial analyzer (SX2-10-12N, Yiheng Company, Shanghai, China), an organic elemental analyzer (PE2400-Ⅱ, PerkinElmer (Suzhou) Company, Suzhou, China), and a micro photometer (Leitz MPV-3, Leitz Company, Wetzlal, Germany), respectively, according to relevant national standards. The results are presented in

Table 1. Properties of the coal samples.

Sample	Proximate Analysis (wt%)				Coal Rank	Ultimate Analysis (%)
	Cad	Had	Oad	Nad		Aad	Vdaf	Mad	FCad
QY	88.68	3.61	4.78	2.93	Bituminous	21.19	11.84	6.59	60.38

.

2.2. Experimental System

A self-designed HVEP system, which was developed to meet the specific requirements of this research, was used in the experiment. This system mainly comprises a high-voltage charging power supply, an energy storage capacitor, an output control cabinet, a trigger control device, a discharge switch, a high-voltage electrode, a safety protection device, and a high-voltage cable (Figure 1). The boosting system includes a step-up transformer and a rectifier silicon stack, which convert 220 V/50 Hz AC power to the rated voltage for capacitor charging. The energy storage system comprises multiple capacitors connected in parallel. The discharge control system features a series of discharge switches, enabling both manual and automatic operation. The safety protection system mainly consists of a grounding system to ensure secure operation.

2.3. Experimental Procedures

The entire experimental procedure was as follows (Figure 1):

(1)

The prepared coal blocks were submerged in tap water for 24 h to ensure complete saturation, thereby minimizing strength variations during HVEP treatment.

(2)

The coal blocks were placed horizontally, parallel to the bedding direction, at the base of an integrated stainless steel water tank. To prevent the movement of the coal blocks during the experiment, the water tank was securely welded to an outer stainless-steel layer. Positioning the coal blocks horizontally ensured that the electrical pulse shock wave aligned with the bedding plane of the coal layer, thereby effectively simulating the actual depositional environment of a coal reservoir.

(3)

The electrodes connected to the high-voltage cable were slowly placed in the water tank, ensuring that the electrode gaps aligned with the center of the coal blocks. A fixing bracket was used to secure the electrodes in a vertical position, ensuring that the shock wave release window remained centered on the coal blocks during discharge.

(4)

Water was added to the tank until it reached 20 cm above the coal blocks. The high-voltage charging power supply was subsequently turned on to charge the energy storage capacitor bank. Once the predetermined voltage was reached, the power supply was deactivated, and the discharge switch was triggered to start the HVEP discharge process. The oscilloscope data were recorded. After each discharge, the electrodes and brackets were inspected for looseness and re-secured if necessary. This process was repeated until the set number of discharges (five in this experiment) was completed. Finally, the coal blocks were removed, and the fracturing conditions were recorded.

(5)

The coal samples were replaced, and the discharge voltage was adjusted. Three discharge voltages—8, 10, and 12 kV—were selected for the fracturing experiments. The corresponding coal samples were labeled A1, A2, and A3. Coal samples that were not exposed to HVEPs were designated as A0. After the experimental procedure outlined in steps 2 to 4, all coal samples underwent HVEP treatment sequentially. The pore structure parameters of the coal samples were examined both before and after the HVEP treatment.

3. Results and Discussion

3.1. Impact of HVEPs on Coal Pore Morphology

MIP was used to analyze the pore structure, morphology, porosity, and connectivity of the coal samples. In this study, the decimal pore size classification method introduced by B.B. Hottot [34] was used to classify pores into four types: micropores (<10 nm), small pores (10–100 nm), medium pores (100–1000 nm), and large pores (>1000 nm). Coal pores can be categorized into four types based on connectivity: through pores, interconnected pores, semi-closed pores, and closed pores. Particularly, through pores and cross-linked pores were typically regarded as open pores. Because mercury cannot penetrate closed pores, the data obtained from MIP can only be used to analyze the characteristics of open and semi-open pores. Owing to the pore shielding effect, mercury injection and ejection curves typically do not overlap, forming a hysteresis loop. This hysteresis behavior can be used to assess the pore morphology of the coal [35,36]. The mercury intrusion equipment used in this paper is the Autopore IV 9510 mercury instrument (produced by the Micromeritics Company, Norcross, GA, USA), with a pore size measurement range of 30 angstroms to 1000 μm. It has two low-pressure stations and one high-pressure station. The volume accuracy for advancing and retreating mercury is below 0.1 μL, and the working pressure ranges from 0.1 to 414 MPa. Figure 2 displays the MIP curves of the coal samples before and after HVEP treatment. At an injection pressure below 10 MPa, the A0 coal sample exhibited slight hysteresis between the mercury injection and ejection curves (Figure 2a). As the injection pressure exceeded 10 MPa, the curves nearly overlapped, indicating the disappearance of the hysteresis loop effect. A pressure of 10 MPa corresponded to a pore diameter of 124.7 nm (calculated using Equation (3) in ref. [10]). This indicates that in bituminous coal, micropores and small pores exhibit relatively poor connectivity and are classified as semi-closed pores. Conversely, medium and large pores display higher connectivity and are considered semi-open pores. However, the overall connectivity of these pores remained low.

After HVEP treatment, the mercury injection and ejection curves of A1, A2, and A3 samples exhibited significant hysteresis and a higher mercury injection volume compared with A0. This indicates that the total pore volume in the coal samples increased after the electrical pulse treatment, along with improved pore connectivity. At a discharge voltage of 8 kV, the mercury injection volume of sample A1 increased from 176.32 × 10⁻³ mL/g before HVEP treatment to 230.26 × 10⁻³ mL/g, representing an increase of 53.94 × 10⁻³ mL/g and a growth rate of 30.59%. Similarly, the mercury-ejection volume of the coal sample significantly increased from 40.81 × 10⁻³ to 87.99 × 10⁻³ mL/g, reflecting an increase of 47.18 × 10⁻³ mL/g. The HVEP-treated samples exhibited a more distinct hysteresis loop and greater mercury injection and ejection volumes than A0. Additionally, the mercury-ejection curve lagged behind the mercury injection curve across the entire mercury pressure range. This indicates that HVEP treatment altered the pore structure of the coal sample. Moreover, the pore at all size levels expanded, leading to an overall increase in total pore volume. Some semi-sealed pores transformed into open pores, which increased the number and volume of open pores. At 10 kV, the mercury injection volume of A2 increased to 257.05 × 10⁻³ mL/g, which is an increase of 80.73 × 10⁻³ mL/g compared with the A0 sample (45.79%). Furthermore, the mercury-ejection volume increased to 108.25 × 10⁻³ mL/g, reflecting an increase of 67.44 × 10⁻³ mL/g compared with A0. The hysteresis loop between the mercury injection and ejection curves further widened, indicating a continuous increase in pore size, total pore volume, and the proportion of open pores. At 12 kV, the mercury injection volume of the A3 sample further increased to 283.24 × 10⁻³ mL/g compared with A2. The injection volume of A3 exceeded that of the A0 sample by 106.92 × 10⁻³ mL/g, reflecting a 60.64% increase. The hysteresis loop between the mercury injection and ejection curves reached its maximum, indicating that the coal sample pores were largely open with enhanced interconnectivity.

These results indicate that HVEP-induced fracturing significantly modified the pore structure of the coal samples. The shock waves caused previously closed and semi-closed pores to expand into interconnected, open pores, which facilitated the formation of a pore-fracture network. As the discharge voltage increased, the mercury content in the coal samples continuously increased, leading to a gradual increase in total pore volume, pore number, and pore diameters across all levels. Additionally, pore connectivity continuously improved, providing crucial pathways for CBM extraction.

3.2. Effect of HVEPs on the Coal Pore Structure

The degree of pore development, permeability, and connectivity in coal can be assessed using key pore structure parameters [37,38].

Table 2. Pore structure parameters analyzed via MIP.

Coal Sample	Total Pore Volume (10−3 mL/g)	Average Pore Diameter (nm)	Total Specific Surface Area (m2/g)	Pore Volume (10−3 mL/g)				Porosity (%)	Pore Proportion (%)
				Micropore	Transition Pore	Mesopore	Macropore		Adsorption Pore	Seepage Pore
A0	176.32	15.62	32.55	83.80	60.26	25.92	6.33	6.24	81.71	18.29
A1	230.26	23.71	33.86	87.07	72.57	55.33	15.30	9.33	68.33	30.67
A2	257.05	32.47	34.12	90.87	75.62	69.75	20.81	13.96	64.77	35.23
A3	283.24	46.53	35.05	97.79	83.07	78.06	24.32	17.37	63.85	36.15

summarizes the fundamental parameters of pore structure for each coal sample, including average pore diameter, total pore volume, specific surface area, stage pore volume, and porosity, derived from mercury intrusion experiment results. Figure 3 illustrates the changes in these parameters across the coal samples. HVEP treatment significantly altered the pore structure of coal (Table 2 and Figure 3). After HVEP treatment, the average pore diameter, porosity, total pore volume, and specific surface area increased compared with the pre-fracturing conditions. The specific changes are as follows:

(1)

Total pore volume, average pore diameter, and porosity

After HVEP treatment, the changes in total pore volume, average pore diameter, and porosity of the coal samples were strongly correlated. This indicates a consistent increase with increasing discharge voltage. At discharge voltages of 8, 10, and 12 kV, the total pore volume increased from 176.32 × 10⁻³ mL/g (before HVEP treatment) to 230.26 × 10⁻³, 257.05 × 10⁻³, and 283.24 × 10⁻³ mL/g, respectively. Similarly, the average pore diameter increased from 15.62 nm to 23.71, 32.47, and 46.53 nm, while the porosity increased from 6.24% to 9.33%, 13.96%, and 17.37%.

These results indicate that HVEP treatment effectively increased the pore volume in the coal. Theoretically, a larger total pore volume can enhance the coal reservoir capacity to store CBM. Although HVEPs increased the total pore volume, they caused small pores to fracture and merge into larger ones, thereby increasing the proportion of larger-diameter pores. During this process, many closed pores in the coal sample transformed into semi-open or open pores, which enlarged the pore throats between them. This change resulted in an enlargement of the average pore size and an increase in porosity within the coal sample. Consequently, this improved structure facilitated the diffusion and movement of CBM, thereby enhancing permeability in the coal reservoir.

(2)

Specific surface area

After HVEP treatment, the specific surface areas of A1, A2, and A3 slightly increased compared with A0. This was due to the HVEP-induced formation of larger diameter pores in the coal. However, with increasing pore diameter, the specific surface area decreased, which limited the overall enhancement of the specific surface area. With increasing discharge voltage, the specific surface area exhibited a continuous but gradual increase. As the discharge voltage increased to 12 kV, the specific surface area of the coal sample increased from 32.55 m²/g before HVEP treatment to 35.05 m²/g, reflecting a 7.68% increase. Generally, the gas adsorption capacity of coal is influenced by its specific surface area. Although increasing the specific surface area is theoretically expected to improve gas adsorption capacity, HVEP shock waves opened closed pores, forming numerous interconnected semi-open and open pores that facilitate gas diffusion and migration. Additionally, the repeated oscillating stress waves and continuous friction of internal fluids within the coal reduced pore surface roughness, further promoting gas desorption and migration.

3.3. Impact of HVEPs on Gas Adsorption Characteristics

The coal contains a complex and diverse network of pore structures. Various forces act on the pore surfaces, creating a surface force field. As gas molecules migrate to the pore surface, the coal spontaneously adsorbs these molecules to reduce surface energy and balance the unsaturated force field. The Langmuir model is the most commonly used theoretical framework for investigating gas–solid two-phase adsorption. Research has shown that under constant temperature and equilibrium pressure conditions, the gas adsorption capacity of the coal can be expressed using the following equation [39,40,41]:

$$Q={\displaystyle \frac{abP}{1+bP}}$$

(1)

Here, Q denotes the equilibrium pressure gas adsorption volume (cm³/g), a represents the maximum gas adsorption capability (cm³/g), b indicates a constant in the adsorption model that describes the rate of gas adsorption by coal at the low-pressure stage (MPa⁻¹), and P denotes the gas pressure at equilibrium adsorption (MPa).

The adsorption experiments on coal samples were performed using the BSD-PHD fully automatic high-temperature and high-pressure adsorption–desorption instrument (Beside Instrument Technology (Beijing) Co., Ltd., Beijing, China). The measurement accuracy is less than ±2%, the pressure range is from high vacuum to 690 bar, and the temperature range is from −196 °C to 900 °C. Similar to conventional gas adsorption–desorption systems in laboratories, this instrument requires coal samples to be ground into a powder form with a particle size ranging from 60 to 80 mesh. For coal samples near the discharge channel after HVEP treatment, only small coal fragments need to be selected. For coal samples that have not undergone HVEP treatment, the sample preparation involves hammering the coal into small pieces. These small coal pieces are then crushed into 60–80 mesh coal powder using a crusher for experimental testing. Figure 4 shows the scatter plots of the gas isothermal adsorption amounts of coal samples before and after HVEP treatment under different discharge voltages, along with the corresponding fitted Langmuir curves. Before and after HVEP treatment, the gas isothermal adsorption curves of the coal samples followed the same trend. Specifically, as the adsorption equilibrium pressure increased, the gas absorption amount increased progressively. Once the equilibrium pressure surpassed 6.0 MPa, the adsorption amount of each coal sample stabilized, reaching equilibrium. The analysis of the entire gas adsorption equilibrium pressure range revealed that within 0–2.0 MPa, the gas adsorption rate was relatively fast, leading to a significant increase in the adsorption quantity. However, within the 2.0–7.0 MPa range, as the equilibrium pressure continuously increased, the adsorption rate gradually decreased, and the increase in adsorption amount diminished, approaching equilibrium. Moreover, the correlation coefficients for fitting the gas adsorption amounts of each coal sample using the Langmuir model exceeded 0.96, indicating a strong fit. This confirms the suitability of the Langmuir model for analyzing gas adsorption in coal samples before and after HVEP treatment, provided the adsorption equilibrium pressure remains below 7.0 MPa.

Figure 5 shows the variation patterns of the ultimate gas adsorption capacity (a) and the adsorption constant (b) of coal samples both before and after HVEP treatment. After HVEP treatment, the coal samples exhibited a lower ultimate gas adsorption capacity than the unfractured samples, indicating a reduction in coal gas adsorption capacity due to HVEP treatment. This reduction was mainly attributed to changes in the coal pore structure resulting from the fracturing process. Despite the increase in total pore volume, the average pore diameter expanded, and pore connectivity improved. Additionally, the repeated shock waves reduced the pore surface roughness, leading to a decrease in the adsorption force exerted by gas molecules onto the coal pore surface. The heat energy from the discharge process and the high temperature from the cavitation bubble collapse further reduced the gas adsorption capacity of the coal sample. Comparative analysis further revealed that as the discharge voltage increased, both the ultimate gas adsorption capacity and the adsorption constant (b) of the coal samples decreased progressively. The adsorption constant (b) reflects the speed at which gas is absorbed by the coal, with smaller values indicating slower adsorption under the same conditions. After HVEP treatment, the decrease in the adsorption constant (b) suggested that HVEPs reduced coal gas adsorption capacity.

3.4. Impact of HVEPs on Gas Desorption Characteristics

Gas desorption experiments were conducted on coal samples both before and after HVEP treatment using the BSD-PH fully automatic high-temperature and high-pressure adsorption–desorption instrument. Figure 6 shows the isothermal gas desorption curves of the coal samples both before and after treatment. The gas desorption amount of both untreated and treated samples increased over time. During the first 20 min, the desorption rate was rapid. After 20 min, the desorption rate gradually slowed and approached equilibrium. At the early stage of desorption, the coal samples exhibited a higher gas desorption amount after HVEP treatment than before treatment. However, as desorption progressed, the amount of gas desorbed from the fractured samples gradually decreased and eventually became lower than that of the unfractured samples. After 120 min of desorption, the untreated coal samples exhibited a higher gas desorption amount than the treated samples. Higher discharge voltages led to lower gas desorption amounts.

This phenomenon was due to HVEPs causing the shock waves to enlarge smaller pores in the coal into larger pores, which enhanced the connectivity between pores. Upon exiting from the coal, the gas encounters less resistance, which facilitates the formation of a concentration gradient during the early stage of desorption. This promoted rapid gas desorption, leading to a relatively higher initial gas desorption amount. After a period of desorption, the unfractured coal sample exhibited a higher gas desorption amount than the fractured coal sample. This was due to the greater number of semi-sealed pores and rougher pore surfaces in the unfractured samples compared with the fractured samples. Under the same adsorption equilibrium pressure, the unfractured coal sample had a higher gas adsorption capacity than the fractured coal sample. As desorption progressed, the gas amount in the pores of the fractured coal gradually decreased, which reduced its ability to maintain a significant gas concentration gradient, causing the gas desorption to reach equilibrium. However, the unfractured coal sample retained sufficient gas to sustain desorption, enabling a continuous gas source. Consequently, after a specific desorption period, the amount of gas desorbed from the unfractured coal sample gradually exceeded that from the fractured coal sample.

Moreover, the gas desorption capacity increased steadily over time (Figure 6). The shape of the isothermal desorption curve was similar to that of the Langmuir adsorption isotherm. This suggests that the desorption of coal can be described using the Langmuir empirical formula, consistent with previous research findings [42,43]. The expression is as follows:

$$Q_t={\displaystyle \frac{Q_{\infty }bt}{1+bt}}$$

(2)

Here, Q_t represents the total amount of gas desorbed at a certain point in time (mL/g), Q_∞ denotes the final gas desorption quantity as time approaches infinity (mL/g), and b indicates a time constant related to the desorption rate (min⁻¹).

The reciprocal of both sides of Equation (2) results in

$${\displaystyle \frac{1}{Q_t}}={\displaystyle \frac{1}{Q_{\infty }bt}}+{\displaystyle \frac{1}{Q_{\infty }}}$$

(3)

$$k={\displaystyle \frac{1}{Q_{\infty }b}},m={\displaystyle \frac{1}{Q_{\infty }}}$$

(4)

With Q_t as the abscissa and t as the ordinate, the ultimate gas desorption amount Q_∞ and the time constant b are determined via linear regression using the slope and intercept of the regression line from the gas desorption data (Equations (3) and (4)). The fitting calculation results are presented in Figure 6.

The R² values for the fitting curves of the desorption data from each coal sample before and after HVEP treatment exceeded 0.97. This indicates that the Langmuir equation accurately describes the isothermal gas desorption process. To analyze the effect of HVEP treatment on gas desorption, bar charts were created to compare the gas limit desorption amount Q_∞ and the time constant b of coal samples at different discharge voltages (Figure 7).

The fractured coal samples exhibited a lower gas limit desorption quantity Q_∞ than the unfractured coal samples, consistent with the previous analysis (Figure 7). As the discharge voltage increased, the gas limit desorption quantity Q_∞ gradually decreased, reaching a minimum of 11.29 mL·g⁻¹ at 12 kV. Additionally, with increasing discharge voltage, the desorption time constant b of the coal samples progressively increased, reaching a maximum of 0.14 min⁻¹ at 12 kV. Moreover, the HVEP-treated coal samples exhibited a higher desorption time constant b than the untreated samples. A larger b value indicates a faster desorption rate. Although the gas limit desorption quantity decreased after HVEP treatment, the desorption rate increased, thereby facilitating the quick discharge of gas from the coal and improving gas flow within the coal reservoir.

3.5. Impact of HVEPs on Gas Diffusion Characteristics

The diffusion coefficient is a key parameter for assessing the gas diffusion capability within coal. The diffusion coefficient is strongly associated with the pore structure and the interconnectedness of pores within the coal. Investigating the variation in the diffusion coefficient of coal samples before and after HVEP treatment is crucial for elucidating the effect of HVEPs on the coal pore structure. Li et al. [44] developed a dynamic gas diffusion coefficient model for multi-scale pores in coal particles to address the limitations of classical diffusion models, which cannot accurately describe gas diffusion over time. The model is expressed as follows:

$${\displaystyle \frac{Q_t}{Q_{\infty }}}=1-{\displaystyle \frac{6}{{\pi }^2}}{\displaystyle \sum }_{n=1}^{\infty }{\displaystyle \frac{1}{n^2}}exp\left({\displaystyle \frac{-D{n}^2{\pi }^{2}t}{r_0^2}}\right)$$

(5)

Here, r represents the radius of coal particles (μm), D denotes the diffusion coefficient of gas (μm²/min), and t indicates the desorption time, (min).

Nie et al. [45] suggested that at a relatively short desorption time (within 10 min), Equation (5) can be simplified as follows:

$$\eta ={\displaystyle \frac{Q_t}{Q_{\infty }}}={\displaystyle \frac{6}{r_0}}\sqrt{{\displaystyle \frac{Dt}{\pi }}}$$

(6)

At this stage, the relevant parameters are substituted into Equation (6) to yield the expression for the diffusion coefficient.

$$D={\displaystyle \frac{\pi K^2{r}_0^2}{36}}$$

(7)

Edward et al. [46] proposed that for desorption times below 10 min, the constant “a” can be considered the initial desorption rate of gas. Therefore, “a” and “b” can be calculated from the gas desorption data within the first 10 min, followed by linear fitting between them. The gas diffusion coefficient (often referred to as the initial gas diffusion coefficient) can be determined from the slope of the fitted straight line. The gas diffusion coefficients of coal samples both before and after HVEP treatment were calculated using the gas desorption experimental data in Section 3.4. A strong linear relationship was observed between “a” and “b”, with the goodness of fit exceeding 0.93.

Figure 8 shows the variation in the gas diffusion coefficient (D) of coal samples changes before and after HVEP treatment. After HVEP treatment, the gas diffusion coefficient (D) of the coal samples increased (

Table 3. Calculation results of the gas diffusion coefficient (D) for coal samples before and after HVEP treatment.

Coal Sample	Fitting Formula	Fitting Degree R2	Slope K	D/(μm2·min)
A0	η = 0.1447t0.5	0.9576	0.1447	83.678
A1	η = 0.1686t0.5	0.9461	0.1686	113.603
A2	η = 0.1946t0.5	0.9641	0.1946	151.342
A3	η = 0.2204t0.5	0.9338	0.2204	194.132

and Figure 8). This increase was due to the creation of new pores and fractures in the coal triggered by the shock waves from HVEPs. These pores were interconnected, forming pore-fracture networks. These networks provided favorable pathways for the unrestricted diffusion of gas within the coal, thereby enhancing the gas diffusion coefficient of the fractured coal samples. With increasing discharge voltage, the gas diffusion coefficient within the fractured coal samples gradually increased (Figure 8). At a discharge voltage of 8 kV, the A1 coal sample had a gas diffusion coefficient of 113.603 μm²·min, reflecting a 35.76% increase. However, at 12 kV, the gas diffusion coefficient for the A3 coal sample increased to 194.32 μm²·min, representing a maximum increase of 131.99%. These findings indicate a reduction in the resistance to gas desorption and free diffusion within the coal body, which facilitated gas migration and the extraction of coal seam gas.

4. Conclusions

This study systematically investigated the impact of HVEP treatment on the pore structure of coal and methane adsorption and desorption performance. The key findings are as follows:

(1)

The MIP results revealed that after HVEP treatment, some closed and semi-closed pores within the coal samples transformed into interconnected and open pores. Consequently, the pore quantity, average pore diameter, total pore volume, and total specific surface area of the coal samples increased, along with improved pore connectivity. After HVEP treatment, the adsorption pores in the coal samples slightly increased, while the seepage pores significantly increased, which facilitated the free flow of gas within the samples.

(2)

The HVEP-treated coal samples exhibited significantly smaller ultimate gas adsorption capacity and a lower gas adsorption rate than the untreated samples. These results indicate that HVEPs significantly inhibited gas adsorption in the coal samples.

(3)

HVEPs facilitated gas desorption dynamics within the coal samples. In the early stage of desorption, the HVEP-treated coal samples had a higher gas desorption capacity and desorption rate than the untreated samples. This suggests that HVEPs promoted the rapid desorption and release of gas from the coal.

(4)

After HVEP treatment, the coal samples exhibited a significantly higher gas diffusion coefficient, indicating a reduction in their resistance to gas diffusion after desorption. This enhancement facilitated gas diffusion and migration within the coal seam, thereby promoting CBM extraction.