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. 2024 Apr 22;9(17):19657–19668. doi: 10.1021/acsomega.4c01754

Effect of Stress Relief on Coal Seam Gas Migration: Experiment and Application Discussion

Yang Zhao †,‡,*, Hong Zhang †,‡, Ting Liu §, Baiquan Lin §, Chunshan Zheng †,‡, Yuannan Zheng †,‡
PMCID: PMC11064015  PMID: 38708245

Abstract

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Stress relief-induced enhanced permeability is one of the crucial measures for promoting gas desorption flow and strengthening gas extraction. In order to examine the impact of stress relief and its magnitude on gas migration, this article explores the gas desorption flow during the stress relief process and elucidates the influence of stress relief degree on gas extraction. The results indicate that considering the analysis of the pore structure effect on gas seepage, the four coal samples' permeability is ranked as PDS > CSL > JZS > GHS. Throughout the stress relief process, the gas desorption rates of different coal samples under various stress paths exhibit varying degrees of increase. As an illustration, following 3600 s of stress alterations, the gas desorption rate of CSL1# experiences a notable increase, surging by 2.57 times; PDS2# shows 55.93 times increase after 4200 s, and JZS3# exhibits 3.13 times increase after 5400 s. A stress relief degree model is established to investigate the variation of horizontal stress and stress relief degrees under different borehole spacings, vertical stresses, cohesion, and internal friction angles for various borehole diameters (coal output). Optimal stress relief is achieved with a borehole diameter greater than 1.52 m with a borehole spacing set at 4 m. When the stress relief degree exceeds 30%, the corresponding borehole diameter ranges for different vertical stresses are 1.49–1.6 m. Similarly, for cohesion, the ranges are 1.25–1.68 m, and for internal friction angles, the ranges are 1.39–1.53 m. The research results can provide valuable insights for determining parameters in the on-site construction of stress relief boreholes.

1. Introduction

Coal serves as the cornerstone of energy security in China.1−5 For the past few years, as coal mining has moved into deeper layers, the conditions surrounding coal seam occurrence and extraction have become increasingly complex. During the mining process, various hazards pose threats, with different disasters interacting with and influencing each other. Among these, the situation of gas disaster prevention and control is particularly severe, seriously jeopardizing the safety of coal mine operations.6−8 Coal seam gas is not only a disaster-causing source and greenhouse gas but also a clean energy resource.9−11 Nevertheless, the efficient extraction of gas faces substantial challenges due to the high stress, strong plasticity, and low permeability characteristics inherent in deep coal seams.

In the pursuit of optimizing the extraction efficiency of deep coal seams, a spectrum of methodologies has been deployed to improve coal permeability. Presently, the available measures include protective layer mining, hydraulic slotting, hydraulic fracturing, hydraulic flushing, and loose blasting technologies. The different technologies have significant differences in application conditions due to their different principles.12,13 Among these, protective layer mining, hydraulic flushing, and hydraulic slotting belong to the stress relief-induced permeability enhancement approach, while hydraulic fracturing and loose blasting belong to the stress boosting-induced permeability enhancement approach. Protective layer mining stands out as a proven and effective gas control technology under the conditions of coal seam groups.14,15 Nevertheless, as mining depths increase, first-mined layers transform into outburst-prone coal seams. Additionally, numerous single coal seams lack the prerequisites for protective layer mining. Hydraulic slotting, loose blasting, and hydraulic fracturing are generally considered suitable for hard coal seams. For soft single coal seams, the fractures induced by these methods tend to compact under the impact of high stress.16−19 Hydraulic flushing technology has emerged prominently for stress relief-induced permeability enhancement in deep single soft and low-permeability coal seams. Through cyclic high-pressure water flushing of boreholes, this methodology effectively enlarges the borehole radius, achieving stress relief-induced permeability enhancement in the surrounding area.20,21 Liu et al.22 formulated a gas flow-geomechanics coupling model, delving into the influence of hydraulic flushing on the permeability and gas migration of coal through numerical simulations. The study revealed a more pronounced enhancement of permeability in soft coal as a result of borehole flushing. Zhang et al.23 innovatively developed a directional hydraulic flushing technique, substantiating its efficacy through numerical simulations and on-site engineering experiments. This technique significantly augments stress relief and gas flow capabilities in composite soft and hard coal seams. Yang et al.24 devised a model for hydraulic flushing gas extraction considering plastic damage. Their numerical simulations characterized the flushing damage zone, analyzed the enhancement of coal seam permeability stemming from flushing, and delineated the optimal borehole layout for flushing.

Through analysis and summary of the previous research, it has been determined that stress relief can significantly enhance the efficiency of gas extraction. However, how does stress relief affect coal seam gas migration? How does it promote coal seam gas desorption? Li et al.25 used testing methods such as mercury intrusion, methane isothermal adsorption, and liquid nitrogen to explore the micropore structure and methane adsorption performance of coal after hydraulic flushing. The findings suggest that hydraulic flushing is a highly effective method for enhancing the internal pore channels of coal, significantly enhancing the methane adsorption performance. Jiang et al.26 investigated the pore structure and desorption flow after damage under various stress relief conditions. The findings indicate that rapid stress relief can significantly increase the pore volume and desorption rate. Zhang et al.27 conducted gas extraction experiments under different unloading paths. The results show that during the gas extraction process gas pressure decreases rapidly and then slows down. Different unloading stress paths exert significant effects on gas flow characteristics. Liu et al.28 explored the features of coal seam gas desorption and diffusion under varying stress paths, highlighting the critical role of stress relief in significantly enlarging fracture openings and enhancing desorption rates.

In summary of the current research status, implementing stress relief measures is essential for extracting gas from deep coal seams. These measures aim to enhance coal seam permeability by improving the coal pore–fracture structure, thereby facilitating the gas flow.29 In practical engineering, the degree of stress relief induced by flushing is commonly quantified by the borehole coal output. A higher borehole coal output typically signifies a more substantial level of stress relief achieved through flushing. However, it is essential to note that the borehole coal output is closely tied to construction time and costs during on-site operations, and a higher borehole coal output does not necessarily guarantee improved gas extraction efficiency.22,30 Therefore, determining an appropriate borehole coal output that aligns with the needs of underground gas extraction becomes crucial. This article aims to establish a meaningful correlation between gas migration during stress relief and the degree of stress relief in boreholes. In this article, based on the stress evolution characteristics around boreholes resulting from hydraulic flushing, the gas migration of coal under stress relief conditions is studied, a model of the stress relief degree is established, and the effective stress relief degree is determined by combining with the experimental, thereby examining the correlation between stress relief degree and borehole coal output. The findings offer valuable guidance for determining the optimal parameters in on-site borehole flushing operations.

2. Experimental Sample and Method

2.1. Samples and Basic Parameters

To investigate the effect of stress relief on gas migration, this study selected coal samples from four mining areas: Chensilou Mine (CSL), Pingdingshan Mine (PDS), Guhanshan Mine (GHS), and Jiaozishan Mine (JZS). These four coal samples come from different mining areas, and all four mining areas are characterized by high gas and outburst mines. Before conducting the experiments, the basic parameters tests were carried out on four coal samples, as shown in Table 1. It is evident from Table 1 that the CSL, GHS, and JZS samples are all anthracite, while the PDS sample is bituminous coal.

Table 1. Basic Parameters Results of Four Coal Samples.

coal sample moisture/% ash/% volatile matter/% fixed carbon/% vitrinite reflectance/% cohesion/MPa internal friction angle/°
CSL 1.66 7.49 8.14 82.70 2.59 0.59 29.37
PDS 0.79 12.47 23.58 63.16 1.31 1.03 34.40
GHS 2.47 6.42 8.55 82.57 3.09 1.73 36.99
JZS 1.67 12.58 7.62 78.13 2.81 0.97 32.16
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2.2. Experiments

2.2.1. Method for Testing the Pore–Fracture Structure of Samples

Coal exhibits high heterogeneity as a complex porous medium, characterized by numerous irregular pores and fracture structures.31,32 Recently, researchers have explored the characteristics of coal pore–fracture structure using various testing methods.33−35 Among them, nuclear magnetic resonance (NMR) testing is commonly employed. This method not only comprehensively reflects the pore distribution characteristics of samples but also offers benefits such as a brief testing duration and minimal sample damage. The theory of low-field nuclear magnetic resonance testing is as follows:

An expression for the total relaxation time T2 is given by36−38

2.2.1. 1

where ρ2 is transverse surface relaxation rate, m/s; D is diffusion coefficient, m2/s; γ is spin-to-magnetism ratio, T2S is surface relaxation time, s; T2D is diffusion relaxation time, s; S/V is ratio of the pore surface area and volume; T2B is free relaxation time, s; MHz/T; G is field strength gradient, T/m; and TE is the echo spacing, s.

Due to T2B is much larger than T2, and 1/T2D is 0 under a uniform magnetic field. Assuming the coal consists of a single type of pore structure, eq 1 can be streamlined to39−41

2.2.1. 2

where r is pore diameter, m; Fs is geometry factor.

2.2.2. Method and System for Stress Relief Gas Desorption Experiments

After hydraulic flushing and stress relief, the stress distribution around the borehole undergoes a rearrangement, as illustrated in Figure 1.6,42 Considering the stress distribution characteristics, to analyze the impact of stress evolution on gas migration, we redefined three regions. Region ①, both vertical stress and horizontal stress gradually reduce; in Region ②, vertical stress gradually rises, and horizontal stress gradually reduces; and in Region ③, vertical stress remains relatively constant, and horizontal stress gradually reduces.

Figure 1.

Figure 1

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Stress distribution around stress relief borehole and the variation of vertical and horizontal stresses under different stress paths.

With the above-defined stress evolution regions, three experimental stress paths were established. Four coal samples were subjected to gas desorption experiments under these three stress paths. The specific stress variations are depicted in Figure 1, where the initial values and changing gradients of vertical and horizontal stresses are determined based on the sample’s inherent properties. During the experiments, the time interval for each step of stress variation was set to Δt = 10 min, and the entire process recorded gas desorption data.

The experimental system is depicted in Figure 2, representing a stress-constrained coal gas desorption and diffusion test system designed and assembled by the laboratory. The experimental procedures and data recording are as follows: Before the experiment, the entire test system is evacuated using a vacuum pump for at least 6 h. After the axial and confining stresses are adjusted to 3 MPa, the adsorption pressure is kept constant at 2 MPa, and adsorption is conducted for 48 h. Upon completion of adsorption, the axial and confining stresses are gradually changed according to the set stress path, with desorption conducted for 10 min at each step. The desorption amount is monitored and recorded at each step until the completion of a set of experiments.

Figure 2.

Figure 2

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Experimental system for gas desorption and diffusion in stress-constrained coal sample.

3. Experimental Results and Discussion

3.1. Characteristics of Coal Sample Pore–Fracture Structure

Figure 3 depicts the T2 distribution spectra and cumulative amplitude for the four samples. In Figure 3a, representing the CSL coal sample, the pores exhibit a three-peak distribution primarily dominated by micropores. A distinct boundary between micropores and meso–macro pores suggests limited connectivity between them, while mesopores show relatively good connectivity with macropores. Figure 3b showcases the PDS coal sample displaying a three-peak pore distribution. Micropores and macropores are distributed relatively evenly, with fewer mesopores. The continuity between peaks suggests good pore distribution connectivity across micropores, mesopores, and macropores. Figure 3c displays the GHS coal sample with a bimodal pore distribution, predominantly featuring micropores. A clear boundary between micropores and meso–macro pores indicates limited connectivity, while mesopores exhibit relatively good connectivity with macropores. Figure 3d illustrates the JZS coal sample, revealing a three-peak pore distribution primarily dominated by micropores. A distinct boundary between micropores and meso–macro pores suggests limited connectivity, while mesopores exhibit relatively good connectivity with macropores.

Figure 3.

Figure 3

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T2 spectra and cumulative amplitude of four coal samples: (a) CSL coal sample. (b) PDS coal sample. (c) GHS coal sample. (d) JZS coal sample.

Figure 4 displays the cumulative amplitude values and proportions of pores on different scales for the four coal samples. In Figure 4a, showing cumulative amplitude values for various pore scales, CSL, GHS, and JZS coal samples exhibit a relatively similar pore distribution, predominantly characterized by micropores, with fewer meso- and macropores. Conversely, the PDS coal sample demonstrates the highest content of macropores followed by micropores and the least content of mesopores. Figure 4b illustrates the proportions of pores on different scales. The micropore proportions for CSL, PDS, GHS, and JZS coal samples are 78.2, 37.9, 89.5, and 89.7%, respectively. The mesopore proportions are 13.1, 14.9, 1.4, and 3.6%, while the macropore proportions are 8.7, 47.2, 9.1, and 6.7%. Analysis of the results indicates that GHS and JZS coal samples have nearly identical micropore proportions. The CSL coal sample has the second highest micropore proportion, while the PDS coal sample has the least. The PDS coal sample has the highest proportion of meso–macro pores followed by CSL and JZS coal samples, and the GHS coal sample has the least. Combining the results from Figure 4a, it is evident that the JZS coal sample has the highest micropore content followed by GHS and CSL coal samples, and the PDS coal sample has the least micropores. The PDS coal sample has the highest content of meso-macro pores followed by CSL and JZS coal samples, and the GHS coal sample has the least. Analyzing the effect of pore structure on gas adsorption alone, the adsorption capacities rank as JZS > GHS > CSL > PDS. Analyzing the effect on coal seam gas seepage based on pore structure alone, the seepage capacities rank as PDS > CSL > JZS > GHS.

Figure 4.

Figure 4

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Accumulation amplitude and proportion of different scale pores of four coal samples. (a) Accumulation amplitude. (b) Pore proportion.

3.2. Evolutionary Characteristics of the Gas Desorption Rate under Stress Paths

Figure 5 illustrates the variation of gas desorption rates(Qt) for four coal samples under three stress paths. 1# Coal Sample: Experiences a gradual reduction in both vertical and horizontal stresses. Initial vertical stresses for CSL1#, PDS1#, GHS1#, and JZS1# are set at 20, 18, 22, and 18 MPa, respectively, while the initial horizontal stress remains constant at 10 MPa for all samples. Undergoes a rise in vertical stress with a simultaneous reduction in horizontal stress. Both vertical and horizontal stresses initiate at 10 MPa for all four coal samples. 3# Coal Sample: Maintains a constant vertical stress while gradually reducing horizontal stress. Initial vertical stresses for CSL3#, PDS3#, GHS3#, and JZS3# are set at 20, 18, 20, and 20 MPa, respectively, with a consistent initial horizontal stress of 10 MPa across all samples. Each step of the three stress paths has a variation range of 1 or 2 MPa in stress. Considering the significant effect of horizontal stress on permeability and the consistent initial horizontal stress of 10 MPa across all coal samples subjected to various stress paths, this work focuses on the evolution of horizontal stress and analyzes its influence on gas desorption rates.

Figure 5.

Figure 5

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Evolution characteristics of gas desorption rates observed in four coal samples under distinct stress paths. (a–c) The gas desorption rate for CSL coal samples under three stress paths. (d–f) The gas desorption rate for PDS coal samples under three stress paths. (g–i) The gas desorption rate for GHS coal samples under three stress paths. (j–l) The gas desorption rate for JZS coal samples under three stress paths.

To examine the impact of various stress evolution stages on the desorption of gas, the cumulative desorption amount of gas curves underwent differentiation. Due to the short interval of the data recording time frequency of 1 s, a large number of the same cumulative desorption amount of data existed during the recording time. For this reason, the differential curves were subjected to second-order smoothing, and although there were some numerical differences between the smoothed gas desorption rates and the original data, the trend of the treated gas desorption rates with stress was more significant. As illustrated in Figure 5, the gas desorption rates for distinct coal samples under varying stress paths exhibit a rapid decline as desorption time increases. Subsequently, they exhibit a stagewise fluctuation pattern as stress varies, characterized by both ascending and descending trends. Overall, the initial desorption rate is highest for PDS coal samples, followed by CSL and JZS coal samples, with GHS coal samples showing the lowest initial desorption rate. This indicates that the initial permeability of the four coal samples follows the order PDS > CSL > JZS > GHS, consistent with the results of the pore structure analysis. Consequently, during the initial gas extraction process, the pore structure proves to be a critical factor influencing gas desorption and migration.

In Figure 5a, the initial Qt of CSL1# is observed to be 0.303 mL/s. Commencing at 1200 s, Qt notably rises with stress variation. Following the stress change at 3600 s, the Qt rapidly increases from 0.021 to 0.054 mL/s, indicating a 2.57 times increase. In Figure 5b, CSL2# exhibits an initial Qt of 0.365 mL/s. The stress change after 4200 s gradually influences the Qt, leading to a 1.92 times increase after 5400 s. As seen in Figure 5c, CSL3# displays an initial Qt of 0.13 mL/s. From 1800 s onward, stress variation gradually impacts the Qt. Following the stress change at 5400 s, Qt increases by 3.08 times.

From Figure 5d, the Qt rate of PDS1# is 0.532 mL/s. Starting from 1200 s, Qt initially increases with stress and then gradually decreases. After 3000 s, Qt increased by 2.41 times. According to Figure 5e, the initial Qt of PDS2# is 0.416 mL/s, and after 4200 s, the Qt increased by 55.93 times. Figure 5f indicates that the initial Qt of PDS3# is 0.303 mL/s. Starting from 2400 s, the stress variations significantly altered the Qt. After the stress change corresponding to 6000 s, Qt increased by 4.97 times.

In Figure 5g, the initial Qt of GHS1# is 0.112 mL/s. Commencing at 1800 s, stress variations significantly altered the Qt. After 3600 s, Qt increased by 3.1 times. According to Figure 5h, the initial Qt of GHS2# is 0.091 mL/s. Starting from 600 s, stress variations consistently changed the Qt, and after 6000 s, the Qt increased by 6 times. Figure 5i indicates that the initial Qt of GHS3# is 0.035 mL/s. Beginning at 1800 s, stress variations altered the Qt. After the stress change at 6000 s, the Qt increased by three times.

From Figure 5j, the initial Qt of JZS1# is 0.244 mL/s. After 1800 s, the stress variations significantly altered the Qt. After 4200 s, Qt increased by 2.62 times. According to Figure 5k, the initial Qt of JZS2# is 0.196 mL/s. Starting from 1800 s, stress variations noticeably changed the Qt. After the stress change corresponding to 6000 s, Qt increased by 1.95 times. Figure 5l indicates that the initial Qt of JZS3# is 0.187 mL/s. Starting from 1800 s, the stress variations significantly altered the Qt. After the stress change corresponding to 5400 s, the Qt increased by 3.13 times.

The above analysis reveals that under stress relief conditions, the Qt of different coal samples exhibits a certain degree of increase, and the magnitude of the increase is significant. Thus, it can be inferred that stress relief effectively promotes the gas desorption flow. However, how the experimental results can guide on-site construction is a key issue in this article. During the stress relief process, how much reduction in horizontal stress is needed to achieve effective stress relief? How to establish a correlation between the degree of stress relief and the optimal borehole coal output during hydraulic flushing?

3.3. Discussion

Based on the above issues, an in-depth analysis of the data trends in Figure 5 was conducted to explore the points of integration between the experiments and on-site construction. According to the above experimental results, the dynamic change in Qt is a process of gradually decreasing the horizontal stress. To correlate the stress changes during the experimental process with the stress changes around the borehole, the process of reducing horizontal stress is analogized to the stress relief process surrounding the borehole. However, what level of horizontal stress relief is needed to achieve effective stress relief? Due to the relatively small scale of the coal samples in the experimental process and the varying impact of horizontal stress on the Qt among various coal samples, this section defines the degree of stress relief corresponding to the initial increase in Qt as the effective stress relief degree and the degree of stress relief corresponding to the surge in Qt as the complete stress relief degree. Based on this, a stress relief degree model is constructed.

3.3. 3

where d1 is the effective stress relief; d2 is the complete stress relief; σh0 is the initial stress of various coal samples; σh1 is the stress when the Qt of various coal samples increases for the first time; and σh2 is the stress when the Qt of various coal samples experiences a sudden increase.

The stress relief degrees for four coal samples under various conditions in Figure 5 were calculated using eq 3, and the results are presented in Table 2. From Table 2, the stress relief degrees vary for different coal samples, and even for the same coal sample, there are differences in stress relief degrees. The effective stress relief degrees for different coal samples range from 10 to 70%, while the complete stress relief degrees range from 80 to 95%. Over one-third of the coal samples, exhibiting a 30% stress relief degree, lie within the effective stress relief range. Although complete stress relief can significantly increase Qt, it also leads to an increase in engineering time and a substantial cost escalation. Therefore, this article suggests that achieving an effective stress relief degree is reasonable during engineering practice.

Table 2. Stress Relief Degrees for Different Coal Samples under Stress Paths.

coal d1 d2 coal d1 d2 coal d1 d2 coal d1 d2
CSL1# 40% 95% PDS1# 40% 90% GHS1# 60% 95% JZS1# 60% 95%
CSL2# 70% 95% PDS2# 70% 80% GHS2# 10% 95% JZS2# 30% 95%
CSL3# 30% 90% PDS3# 50% 95% GHS3# 30% 95% JZS3# 30% 95%
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Based on the above results, it is evident that a stress relief degree exceeding 30% can lead to effective stress relief. It should be noted that the conclusions regarding the effective stress relief degree in this article are based on preliminary findings from the experiments. Subsequent verification can be carried out through extensive laboratory and engineering experiments. The findings of this article contribute theoretical insights that can guide further research in the field.

Analysis of the aforementioned results indicates that Qt increases with a higher stress relief degree. However, this article focused on standard coal samples, and the results can only characterize the gas migration around a single borehole under stress relief conditions. In actual coal seam gas extraction, the primary method involves extracting gas from a group of boreholes, and it is crucial to consider whether the extraction areas between boreholes meet the required standards, as indicated by the red dotted lines in Figure 6. Figure 6 illustrates the variation in vertical stress around coal seams for different borehole diameters (representing different degrees of stress relief). Figure 6 reveals that, with a constant distance between boreholes, a rise in borehole diameter results in a reduction in vertical stress around the borehole. However, it is noteworthy that the vertical stress between two boreholes also increases. This leads to a decrease in permeability in the intermediate region between the boreholes, resulting in a reduced gas migration capacity. Consequently, in the gas extraction process from a group of boreholes, a higher degree of borehole stress relief does not necessarily translate to improved gas extraction efficiency. However, how to integrate the degree of borehole stress relief with on-site engineering practices and how to guide on-site borehole construction parameters are questions addressed by this article. To explore this, a numerical simulation study on the stress evolution of stress-relieved boreholes was conducted. Based on the defined stress relief degree, this article investigated the variation of horizontal stress and stress relief degree between boreholes with different diameters and analyzed the key factors influencing the stress relief degree.

Figure 6.

Figure 6

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Analysis of the effect of stress relief degree on gas extraction.6,30,42

4. Stress Evolution Simulation Study of Stress-Relieved Coal

4.1. Physical Model of Stress-Relieved Coal

Different borehole diameters represent varying borehole coal outputs, reflecting the degree of stress relief of the borehole. In practical engineering, the borehole coal output is frequently employed to characterize the degree of stress relief in boreholes. To investigate the relationship between the defined stress relief degree in this article and borehole coal output, a hydraulic flushing borehole model was constructed based on FLAC 3D. The model simulated and analyzed the relationship between different borehole diameters and the horizontal stress and stress relief degree between boreholes. The geometric model is illustrated in Figure 7. The model dimensions are 40 × 40 × 5 m, the top is a vertical stress boundary, the four sides are zero-displacement roller support boundaries, and the bottom is a fixed constraint boundary. The elastic modulus is 2 GPa, and Poisson’s ratio is 0.3. As shown in Figure 7, the yellow dots between two boreholes represent horizontal stress monitoring points. If the middle position of the borehole reaches effective stress relief, then it indicates that the region between the boreholes has achieved effective stress relief.

Figure 7.

Figure 7

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Hydraulic flushing geometric model.

Table 3 shows the simulated borehole coal output for different diameters with a simulated coal density of 1400 kg/m3. The study simulated the variation in horizontal stress between two boreholes, which ranged from 0.2 to 1.8 m in diameter.

Table 3. Different Borehole Diameters and Corresponding Coal Output.

borehole diameter 0.2 m 0.4 m 0.6m 0.8 m 1 m 1.2 m 1.4 m 1.6 m 1.8 m
coal output 0.04 t/m 0.18 t/m 0.4 t/m 0.7 t/m 1.1 t/m 1.58 t/m 2.16 t/m 2.81 t/m 3.56 t/m
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To explore the key factors influencing borehole stress relief, this article analyzes the variation of horizontal stress between boreholes under different borehole spacings, vertical stresses, cohesions, and internal friction angle conditions. This article also calculates the stress relief degree with respect to borehole diameter under different parameter settings, as shown in Table 4. When simulating the impact of a specific parameter change on the horizontal stress between boreholes, other parameter values are kept constant with the bolded parameters in Table 4 being fixed.

Table 4. Model Simulation Parameters.

parameters variable
borehole spacing 4 m 6 m 8 m 10 m
vertical stress 16 MPa 18 MPa 20 MPa 22 MPa
cohesion 0.5 MPa 1 MPa 2 MPa 3 MPa
internal friction angle 30° 35° 40° 45°
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4.2. Simulation Results and Discussion

This section primarily analyzes the variations in horizontal stress and stress relief degree between boreholes under different borehole diameters (borehole coal output). The analysis is based on external parameters of the coal (borehole spacing and vertical stress) and internal parameters of the coal (cohesion and internal friction angle).

Figure 8 illustrates the variation of horizontal stress and stress relief degrees between boreholes under different borehole spacings with respect to the borehole diameter. In Figure 8a, a notable difference in the horizontal stress between boreholes is evident for various spacings. At borehole diameters less than 0.8 m, the horizontal stress between boreholes gradually increases with an increase in spacing. For borehole diameters larger than 0.8 m, the horizontal stress between boreholes initially rises and then reduces with rising spacing. As a rise in borehole diameter, the variation trends of horizontal stress between boreholes under different spacings are inconsistent. For a borehole spacing of 4 m, the horizontal stress between boreholes gradually decreases with the increase in borehole diameter, reducing by 42.71% at a borehole diameter of 1.8 m in comparison to 0.2 m. At a borehole spacing of 6 m, the horizontal stress between boreholes initially decreases, then gradually increases, and decreases again with the increase in borehole diameter. This results in a 4.12% reduction in horizontal stress at a borehole diameter of 1.8 m in comparison to 0.2 m. For a borehole spacing of 8 m, the horizontal stress between boreholes initially decreases and then gradually increases as the borehole diameter increases, resulting in a 6.14% increase in horizontal stress at a borehole diameter of 1.8 m in comparison to 0.2 m. Similarly, at a borehole spacing of 10 m, the horizontal stress between boreholes initially decreases, then gradually increases, resulting in a 4.31% increase in horizontal stress at a borehole diameter of 1.8 m compared to a borehole diameter of 0.2 m. From Figure 8b, the stress relief degree varies differently with an increase in borehole diameter under different spacing conditions. At a spacing of 4 m, the stress relief degree of boreholes gradually increases with a rise in borehole diameter, reaching over 30% when the corresponding borehole diameter is greater than 1.52 m. For a spacing of 6 m, the stress relief degree of boreholes initially rises, then decreases before rising again with a rise in borehole diameter. At a spacing of 8 m, the stress relief degree rises as the borehole diameter rises at a diameter less than 0.8 m and reduces as the borehole diameter rises at a diameter greater than 0.8 m. For a spacing of 10 m, the stress relief degree rises as the borehole diameter rises at a diameter less than 1 m and reduces as the borehole diameter rises at a diameter greater than 1 m.

Figure 8.

Figure 8

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Variation of results with borehole diameter under different borehole spacings: (a) Horizontal stress. (b) Stress relief degree.

Figure 9 illustrates the variation of horizontal stress and stress relief degree around boreholes under different vertical stresses with respect to the borehole diameter. From Figure 9a, it can be observed that for the same borehole diameter the horizontal stress between boreholes varies under different vertical stresses. As the borehole diameter increases, the trend of horizontal stress between boreholes under different vertical stresses is generally consistent, gradually decreasing with an increase in diameter, although the magnitude of decrease varies. For instance, at a vertical stress of 16 MPa, the horizontal stress between boreholes with a diameter of 1.8 m is reduced by 38.83% compared to a borehole diameter of 0.2 m. At vertical stresses of 18, 20, and 22 MPa, the corresponding reductions at a borehole diameter of 1.8 m are 40.95, 42.71, and 43.47%, respectively. It can be observed that with larger vertical stress, the reduction in horizontal stress between boreholes is more pronounced with an increase in diameter. This indicates that for the deeper coal seams, the more the borehole coal output under the corresponding borehole spacing, the better the effect of stress relief. From Figure 9b, as the borehole diameter increases, the stress relief degree under different vertical stresses gradually increases but with some differences. When the borehole diameter is less than 1 m, stress relief degree under different vertical stresses is essentially consistent. However, at a borehole diameter of 1.2 m, lower vertical stress corresponds to greater stress relief degree, while a borehole diameter greater than 1.4 m leads to higher stress relief degree under higher vertical stress. When relief depth exceeds 30%, the corresponding borehole diameter range for different vertical stresses is from 1.49 to 1.6 m and above.

Figure 9.

Figure 9

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Variation of results with borehole diameter under different vertical stresses: (a) Horizontal stress. (b) Stress relief degree.

Figure 10 depicts the variation of horizontal stress and stress relief degree between boreholes under different cohesions concerning borehole diameter. In Figure 10a, it is evident that, for the same borehole diameter, the horizontal stress between boreholes differs under different cohesion. As the borehole diameter increases, the trend of horizontal stress between boreholes under different cohesion is generally consistent, gradually decreasing with an increase in diameter but with varying magnitudes of reduction. For instance, when the cohesion is 0.5 MPa, the horizontal stress between boreholes with a diameter of 1.8 m is reduced by 54.18% compared to that of a borehole diameter of 0.2 m. At a cohesion of 1 MPa, the reduction is 42.71%. With a cohesion of 2 MPa, the reduction is 35.04%, and with a cohesion of 3 MPa, the reduction is 32.54%. This indicates that a smaller cohesion leads to a greater reduction in the horizontal stress between boreholes with an increase in diameter. From Figure 10b, as the borehole diameter increases, the stress relief degree under different cohesion gradually increases but with some differences. With an increase in diameter, the difference in stress relief degree between different cohesions gradually enlarges. When the stress relief degree exceeds 30%, the corresponding borehole diameter range for different cohesion is from 1.25 to 1.68 m and above.

Figure 10.

Figure 10

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Variation of results with borehole diameter under different cohesion. (a) Horizontal stress. (b) Stress relief degree.

Figure 11 illustrates the variation of horizontal stress and stress relief degree between boreholes under different internal friction angles concerning borehole diameter. From Figure 11a, it can be observed that at the same borehole diameter, the horizontal stress differs under different internal friction angles. As the borehole diameter increases, the trend of horizontal stress under different internal friction angles is generally consistent, gradually decreasing with the increasing borehole diameter but with varying reduction magnitudes. For example, with an internal friction angle of 30°, the horizontal stress at a borehole diameter of 1.8 m decreases by 42.71% compared to a borehole diameter of 0.2 m. With an internal friction angle of 35°, the corresponding reduction is 34.59%. For an internal friction angle of 40°, the reduction is 39.58%, and for 45°, it is 37.78%. This indicates that the impact of the internal friction angle on horizontal stress is relatively complex. From Figure 11b, with a rise in borehole diameter, the stress relief degree under different internal friction angles gradually increases but with some differences. At a borehole diameter of less than 1 m, a larger internal friction angle corresponds to a higher stress relief degree. However, when the borehole diameter exceeds 1 m, the relationship between the stress relief degree and internal friction angle becomes more complex. For stress relief degrees above 30%, the corresponding borehole diameter ranges for different internal friction angles are from 1.39 to 1.53 m and above.

Figure 11.

Figure 11

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Variation of results with borehole diameter under different internal friction angles. (a) Horizontal stress. (b) Stress relief degree.

By analyzing the impact of borehole diameter (coal output), borehole spacing, vertical stress, cohesion, and internal friction angle on borehole stress relief, it is evident that the borehole diameter, borehole spacing, and cohesion are crucial factors affecting borehole stress relief. In the process of stress relief and enhanced gas extraction for different strength coals, it is necessary to adjust the borehole parameters, such as borehole diameter and spacing, based on the strength of the coal seam to achieve optimal stress relief effects. The optimal borehole diameter obtained in this article is calculated based on the simulated parameters and does not represent a specific coal seam. The simulation results can provide guidance and insights for on-site borehole construction.

5. Conclusions

This work studied the gas desorption characteristics during the stress relief process. A stress relief degree model was established to study the correlation between the stress relief degree and on-site engineering practices. The numerical simulations were performed to unveil the impact of the borehole stress relief degree on gas extraction. The main conclusions are as follows:

  • 1.

    Examining the effect of pore structure on gas adsorption, the adsorption capacity of the four coal samples was in the order of JZS > GHS > CSL > PDS. The PDS coal sample had the highest macropore content followed by CSL and JZS coal samples, with the GHS coal sample having the least macropore content. Examining the effect of pore structure on gas seepage, the seepage capacity of the four coal samples was in the order of PDS > CSL > JZS > GHS.

  • 2.

    The initial desorption rate of the PDS coal sample was the highest followed by the CSL and JZS coal samples, with the GHS coal sample having the lowest initial desorption rate. This indicates that the initial permeability of the four coal samples follows the order of PDS > CSL > JZS > GHS, consistent with the results of the pore structure analysis. During the stress relief process, gas desorption rates of different samples under various stress paths increased to varying degrees. For example, following 3600 s of stress alterations, the gas desorption rate of CSL1# experiences a notable increase, surging by 2.57 times; PDS2# shows a 55.93-times increase after 4200 s, and JZS3# exhibits 3.13 times increase after 5400 s. Therefore, stress relief significantly promotes gas migration.

  • 3.

    Based on experimental and numerical simulation results, a stress relief degree model was constructed, defining effective stress relief degrees. Optimal stress relief is achieved with a borehole diameter greater than 1.52 m with a borehole spacing set at 4 m. When the stress relief degree exceeds 30%, the corresponding borehole diameter ranges for different vertical stresses are 1.49–1.6 m. Similarly, for cohesion, the ranges are 1.25–1.68 m, and for internal friction angles, the ranges are 1.39–1.53 m. The research results can provide guidance for determining on-site borehole parameters.

Acknowledgments

This work was supported by the Natural Science Research Project of Anhui Educational Committee (2022AH050812), National Natural Science Foundation of China (52304199), Anhui Provincial Natural Science Foundation (2308085QE153), Open Research Grant of Joint National-Local Engineering Research Centre for Safe and Precise Coal Mining (EC2023018), and Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology (2022yjrc114).

The authors declare no competing financial interest.

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