Numerical Simulation of Gas Drainage via Cross-Measure Boreholes in Deep Inclined Coal Seams

Abstract

This study addresses gas drainage challenges in the Pingdingshan NO.10 mine JI_15-16 coal seam through coupled COMSOL-FLAC^3D numerical simulations. The research evaluates the effectiveness of a cross-measure borehole drainage system. It analyzes the failure mechanisms of the surrounding rock in both the machine roadway and floor roadway of the 24130 working face under the influence of boreholes. The results demonstrate that extended drainage duration progressively reduces both gas content and pressure within the borehole-affected zone of the coal seam while enhancing the effective permeability of the JI_15-16 coal stratum. The operational system extracted 1,527,357 m³ of methane, achieving a pre-drainage efficiency of 59.18% through cross-measure boreholes. The measured gas content aligns with simulated predictions, though field-recorded gas pressure registered slightly higher than modeled values. This validated drainage design complies with the Pingmei Group’s regulations for coal and gas outburst prevention. Critically, cross-measure boreholes alter stress distribution around both coal and floor roadways, promoting plastic zone expansion. Consequently, during the development of the 24130 working face’s machine roadway, intensified ground pressure monitoring is essential near borehole locations in the roof, floor, and rib strata. Supplementary support reinforcement should be implemented when required to prevent rib spalling and roof collapse incidents.

1. Introduction

The permeability of coal seams in China is generally low. With the advancement of coal mining technologies and production methods, due to intensive extraction, shallow coal resources are being rapidly depleted, prompting a shift in coal mining to deeper areas. As mining depth increases, the stress on the coal seam significantly increases, resulting in a further decrease in the permeability of the coal seam and an increase in gas pressure. These conditions may trigger severe gas disasters [1,2,3,4]. Gas extraction through boreholes in outburst-prone seams is the most direct and effective method to eliminate coal and gas outburst risks and reduce related accidents [5,6,7]. Deep-buried coal seams exhibit intrinsically low permeability under in situ stress constraints, necessitating dense borehole arrays for enhanced gas extraction efficacy. Such intensive drilling operations induce complex coal–rock deformation and failure patterns surrounding boreholes through coupled gas–drainage interactions. These mechanisms impose significant challenges on dynamic disaster mitigation (e.g., rock bursts) and roadway support systems while concurrently impairing long-term drainage efficiency. Consequently, systematic investigation into borehole extraction dynamics and surrounding failure characteristics becomes imperative. Defining the causal relationship between drainage efficiency and progressive coal–rock failure is pivotal for optimizing gas control strategies and eliminating coal and gas outburst risks in deep mining environments.

Owing to the inherent coal and gas outburst hazards in deep coal seams, direct roadway construction or gas control measures within outburst-prone strata are prohibited. Consequently, gas extraction roadways are strategically deployed in underlying stable rock strata. From these rock tunnels, cross-measure boreholes are drilled to implement remote methane drainage, effectively reducing coal seam gas pressure to mitigate outburst risks. Regarding the effectiveness of cross-measure borehole gas extraction, significant research achievements have been made globally. For instance, He et al. [8] developed a large-diameter cross-seam borehole technology for gas extraction. Their work demonstrated that large-diameter cross-seam boreholes maintain stable geometry and deliver consistent gas drainage performance, representing an up-and-coming gas extraction technique. Du et al. [9] employed the average-angle method to calculate trajectory deviation data and constructed a relationship diagram between the drilling trajectory and the three-dimensional stratigraphic position of coal and rock to ensure expected extraction efficiency. Sun [10] studied the gas extraction radius and extraction effect of trans-layer boreholes in coal seam groups through numerical simulation and field test methods. Lu et al. [11] analyzed the variation law of coal seam gas pressure in single-hole and multi-hole extraction and obtained the relationship between the spacing of holes and the extraction radius of a single hole. Cui et al. [12] performed a comparative evaluation of two borehole layout patterns under identical spacing conditions to quantify their extraction performance differences. Wang et al. [13] systematically investigated the influence of gas pressure on coal permeability characteristics through theoretical analysis and experimental data validation. In a complementary study, Qi et al. [14] analyzed the evolution law of coal seam gas pressure around an extraction borehole in time and space through theoretical analysis and numerical simulation methods and applied it to coal seam gas extraction. Chen et al. [15] investigated the impact of mining-induced disturbances on gas pressure distribution ahead of the working face during gas extraction. Their study revealed that the zone of gas pressure concentration progressively diminished in spatial extent and exhibited forward migration toward the working face. Meng et al. [16] observed that coal permeability and gas slippage effects increase with declining pore pressure. In a mechanistic study, Wang et al. [17] established that gas pressure influences coal permeability through three distinct pathways: (i) adsorption-induced swelling deformation, (ii) effective stress variations, and (iii) the Klinkenberg effect.

Furthermore, studies have demonstrated that the presence of boreholes significantly alters the surrounding rock’s failure characteristics. Xue et al. [18] revealed that cross-seam boreholes promote late-stage fracture development in surrounding rock. Zheng et al. [19] developed a novel outburst prevention method combining cross-seam grouting reinforcement with hydraulic flushing, demonstrating that this coupled approach effectively reduces coal seam gas content and pressure, enhances coal strength, and mitigates roadway deformation.

Existing research has developed simultaneous extraction technology for coal seams groups using cross-measure boreholes, revealing gas migration patterns and borehole-surrounding deformation–failure characteristics. However, for deep-buried low-permeability coal seam groups, systematic coupling mechanisms between gas seepage and borehole-surrounding failure during synchronous extraction require further exploration. The mutual interaction between gas drainage and borehole deformation needs further investigation. Based on this, this paper takes the Pingdingshan NO.10 mine JI_15-16 coal seam as the research object. It employs a numerical simulation method, combining COMSOL 5.9 and FLAC^3D 7.0, to systematically investigate the gas drainage effect of the borehole through the stratum and the deformation and failure mechanisms of the rock surrounding the roadway to provide a theoretical basis for safe production in coal mines.

2. Technical Route

Figure 1 presents the research’s technical route. Aimed at gas control and outburst hazard elimination in deep-buried low-permeability coal seam groups, we defined the research background/significance, established the theoretical framework, and determined methodologies. For the study, we first proposed cross-measure dense borehole arrays for the synchronized extraction of coal seam groups, then developed FEM-FDM numerical models to predict gas migration processes while optimizing the control parameters. A field validation of gas extraction effectiveness was subsequently conducted. Further investigation revealed deformation and failure mechanisms in coal–rock masses under dense borehole extraction. In final part of the paper, the alignment between the research outcomes and objectives is discussed, limitations are identified through a comparison with existing studies, and future research directions are proposed.

3. Theoretical Analysis and Simulation Modeling

3.1. Theoretical Analysis

3.1.1. Stress Field Control Equation

Research demonstrates that the mechanical behavior and deformation characteristics of coal undergo significant alterations under coupled gas–geostress interactions in deep coal seams, consequently modulating borehole gas drainage performance. Thus, establishing deformation control equations for gas-saturated coal under stress is imperative, comprising a stress equilibrium equation, geometric kinematic equation, and constitutive material equation.

Effective stress constitutes the foundation for establishing coal deformation control equations. Building upon the fractured porous media theory, the modified Terzaghi effective stress equation is introduced as follows [20,21]:

$${\sigma }_{ij}^{\mathrm{e}}={\sigma }_{ij}-\left({\beta }_f{p}_f+{\beta }_m{p}_m\right){\delta }_{ij}$$

(1)

In the formula, ${\sigma }_{ij}^e$ = effective stress (MPa); ${\sigma }_{ij}$ = total stress; ${\delta }_{ij}$ = the Kronecker delta tensor; $p_f$ = fracture gas pressure (MPa); $p_m$ = matrix gas pressure (MPa); ${\beta }_f$ = Biot’s effective stress coefficients for fractures; and ${\beta }_m$ = Biot’s effective stress coefficients for a matrix [22,23].

$$\left\{\begin{array}{l}{\beta }_{\mathrm{f}}=1-K/K_{\mathrm{m}}\\ {\beta }_{\mathrm{m}}=K/K_{\mathrm{m}}-K/K_{\mathrm{s}}\end{array}\right.$$

(2)

In the formula, K = the bulk modulus of the coal mass (MPa); K_m = the bulk modulus of the coal matrix (MPa); and K_s = the bulk modulus of the coal skeleton (MPa).

Coal is conceptualized as a fractured porous medium, wherein matrix deformation induced by gas desorption and in situ stress constitutes infinitesimal strain. The geometric equations governing gas-saturated coal are thus derived as follows:

$${\epsilon }_{ij}={\displaystyle \frac{1}{2}}\left(u_{ij}+u_{ji}\right)$$

(3)

Coal contains heterogeneous multiphase systems primarily composed of methane with admixtures such as carbon dioxide and water within its pores and fractures. Based on governing momentum conservation principles for multiphase media, the balance equation for methane-saturated coal is expressed as follows:

$${\sigma }_{ij,j}+f_i=0$$

(4)

Assuming gas-bearing coal is an isotropic linear elastic material, then its deformation follows the generalized Hooke’s law:

$${\sigma }_{ij}=2G{\epsilon }_{ij}+{\displaystyle \frac{2G\nu }{1-2\nu }}{\epsilon }_{\mathrm{v}}{\delta }_{ij}-{\beta }_{\mathrm{f}}{p}_{\mathrm{f}}{\delta }_{ij}-{\beta }_{\mathrm{m}}{p}_{\mathrm{m}}{\delta }_{ij}$$

(5)

Combining these equations yields the Navier-type deformation equation for coal accounting for pore pressure effects [24,25]:

$$G{u}_{i,jj}+{\displaystyle \frac{G}{1-2\nu }}{u}_{j,ji}-{\beta }_{\mathrm{f}}{p}_{\mathrm{f},i}-{\beta }_{\mathrm{m}}{p}_{\mathrm{m},i}+F_i=0$$

(6)

In the formula, G = the shear modulus (Pa) and e_i,ij = the tensor quantity (e can be displacement u, pressure p, and strain ε). The first subscript represents the i-direction component of the variable e. The second subscript indicates the partial derivative in the direction of i with respect to e_i. The third subscript indicates the partial derivative in the j direction with respect to e_i,ij (Pa); v = Poisson’s ratio and F_i = body force (Pa).

3.1.2. Control Equations for Gas Diffusion

During gas extraction, borehole drainage disrupts the initial equilibrium of gas pressure in the coal seam. The differential flow velocities between the fracture network and matrix system establish a pressure gradient (p_matrix > p_fracture); the adsorbed gas in the matrix diffuses into the fracture system. Within the matrix pores, adsorbed gas desorbs into free gas, migrates via diffusion into the fractures, and finally flows through the fractures to the extraction borehole [26]:

$$Q_{\mathrm{s}}={\displaystyle \frac{M_{\mathrm{c}}}{\tau RT}}(p_{\mathrm{m}}-p_{\mathrm{f}})$$

(7)

The total gas storage capacity per unit volume of coal matrix is given by the following equation [27]:

$$m_{\mathrm{m}}={\displaystyle \frac{M_c{V}_{\mathrm{L}}{p}_{\mathrm{m}}}{V_M\left(p_{\mathrm{m}}+P_{\mathrm{L}}\right)}}{\rho }_{\mathrm{c}}+{\varphi }_{\mathrm{m}}{\displaystyle \frac{M_{\mathrm{c}}}{RT}}{p}_{\mathrm{m}}$$

(8)

In the formula, $m_m$ = the total gas storage capacity per unit volume of coal matrix, kg/m³; V_L = the Langmuir volume constant (m³/kg); ${\rho }_c$ = coal’s apparent density (kg/m³); ${\varphi }_m$ = the matrix porosity (%); $V_M$ = the molar volume of gas under standard conditions (m³/mol); $\tau$ = the adsorption constant; $M_c$ = the molar mass of methane (kg/mol); R = the universal gas constant (J/mol·K).

Based on mass conservation principles, the dynamic equation governing the temporal evolution of matrix gas pressure per unit volume is derived as follows:

$${\displaystyle \frac{\partial p_{\mathrm{m}}}{\partial t}}=-{\displaystyle \frac{V_{\mathrm{M}}(p_{\mathrm{m}}-p_{\mathrm{f}}){(p_{\mathrm{m}}+P_{\mathrm{L}})}^2}{\tau V_{\mathrm{L}}RT{P}_{\mathrm{L}}{\rho }_{\mathrm{c}}+\tau {\varphi }_{\mathrm{m}}{V}_{\mathrm{M}}{(p_{\mathrm{m}}+P_{\mathrm{L}})}^2}}$$

(9)

3.1.3. Control Equation for Gas Flow

Deep low-permeability coal seam groups exist as virgin strata unperturbed by large-scale mining-induced stresses, with near-constant overburden loading. Given that the thickness of coal seams is much smaller than their horizontal length, lateral strain can be neglected. Consequently, the state may be idealized as uniaxial strain. Based on this uniaxial strain condition and uniform vertical loading assumption, the permeability and fracture porosity of coal exhibit a functional dependence on effective stress, conforming to the cubic law relationship as follows [28]:

$${\displaystyle \frac{k}{k_0}}={\left({\displaystyle \frac{{\varphi }_{\mathrm{f}}}{{\varphi }_{\mathrm{f}0}}}\right)}^3={\left\{\begin{array}{l}1+{\displaystyle \frac{1}{M{\varphi }_{\mathrm{f}0}}}\left[{\beta }_{\mathrm{f}}\left(p_{\mathrm{f}}-p_{\mathrm{f}0}\right)+{\beta }_{\mathrm{m}}\left(p_{\mathrm{m}}-p_{\mathrm{m}0}\right)\right]+\\ {\displaystyle \frac{{\epsilon }_L}{{\varphi }_{\mathrm{f}0}}}\left({\displaystyle \frac{K}{M}}-1\right)\left({\displaystyle \frac{p_{\mathrm{m}}}{P_L+p_{\mathrm{m}}}}-{\displaystyle \frac{p_{\mathrm{m}0}}{P_L+p_{\mathrm{m}0}}}\right)\end{array}\right\}}^3$$

(10)

In the formula, k = coal’s absolute permeability (m²); k₀ = coal’s initial absolute permeability (m²); ϕ_f = coal’s fractured porosity (%); ϕ_f0 = coal’s initial fractured porosity (%); M = the constrained axial modulus (MPa); ε_L = coal’s limiting adsorption expansion deformation quantity.

Due to the intrinsically low permeability in deep-buried coal seams, gas slippage effects within the coal fracture network induce increased transport resistance. This results in a non-negligible sensitivity of effective permeability to pore pressure, exhibiting the following nonlinear relationship governed by the Klinkenberg effect [29]:

$$k=k_{\infty }\left(1+{\displaystyle \frac{b}{p_f}}\right)$$

(11)

In the formula, b = the Klinkenberg coefficient (Pa); the value of b can be calculated as b = a_kk_∞^−0.36, where a_k is an experimental fitting coefficient, taking a value of 0.251.

Considering the gas slippage effect and Darcy’s law for gas seepage in coal fractures, the control equations for gas transport in both matrix and fracture systems can be expressed as follows [30]:

$${\varphi }_{\mathrm{f}}{\displaystyle \frac{\partial p_{\mathrm{f}}}{\partial t}}+p_{\mathrm{f}}{\displaystyle \frac{\partial {\varphi }_{\mathrm{f}}}{\partial t}}=\nabla \left({\displaystyle \frac{k_{\mathrm{e}}}{\mu }}{p}_{\mathrm{f}}\nabla p_{\mathrm{f}}\right)+{\displaystyle \frac{1}{\tau }}(1-{\varphi }_{\mathrm{f}})(p_{\mathrm{m}}-p_{\mathrm{f}})$$

(12)

On this basis, this study establishes a dual-porosity gas–solid coupling model for deeply buried gas-bearing coal that dynamically couples gas desorption diffusion processes, effective stress variations, matrix shrinkage, and the Klinkenberg effect. Figure 2 illustrates the interactive coupling relationships between coal deformation, gas diffusion, and gas flow fields. When gas flows from fractures into the borehole under a pressure gradient, the gas pressure within the fracture system gradually decreases, inducing variations in effective stress. This phenomenon leads to borehole-surrounding coal matrix deformation, altering the coal’s permeability and consequently affecting the gas flow behavior in the fracture network. Moreover, the reduction in gas pressure within the fracture system accelerates gas desorption from the coal matrix. The desorbed gas subsequently diffuses into the fractures under the influence of the concentration gradient. The variation in effective stress induced by changes in gas pressure, combined with matrix shrinkage effects, leads to coal deformation and alters matrix porosity. These transformations ultimately exert a significant influence on the gas diffusion behavior within matrix pores of deeply buried low-permeability coal.

3.2. Model Establishment

3.2.1. Cross-Measure Borehole Gas Extraction Model

The Pingdingshan NO.10 mine JI_15-16 coal seam has a burial depth of approximately 1000 m, with a dip angle of 15°, a gas pressure of 1.25 MPa, a gas content of 8.09 m³/t, and a permeability coefficient of 1.86 m²/(MPa²·d). To eliminate the outburst risk during the development of the tailgate in the JI_15-16-24130 working face, gas drainage from the surrounding coal seam is required. Extraction plan: A floor roadway was constructed in the JI₁₈ coal seam and adjacent rock strata. From this floor roadway, cross-measure boreholes were drilled to extract gas around the JI_15-16-24130 tailgate. The pattern consists of 13 boreholes per row with a diameter of 94 mm, under a drainage negative pressure of 15 kPa, and 6 m spacing between adjacent rows. Figure 3 illustrates the layout of the cross-measure boreholes, while

Table 1. Parameter table of boreholes.

Borehole No.	Dip Angle (°)	Opening Position (m)	Planned Depth (m)
1	L30.2	0.3 from left rib	31.0
2	L38.4	0.7 from left rib	27.0
3	L47.4	1.0 from left rib	24.5
4	L57.2	1.3 from left rib	22.5
5	L67.4	1.7 from left rib	21.5
6	L77.7	2.0 from left rib	21.0
7	L87.9	2.3 from right rib	21.5
8	R82.0	2.0 from right rib	22.5
9	R72.3	1.7 from right rib	24.0
10	R63.3	1.3 from right rib	27.0
11	R55.1	1.0 from right rib	30.5
12	R47.9	0.7 from right rib	35.5
13	R41.7	0.3 from right rib	42.0

provides detailed parameters of the borehole dimensions.

COMSOL was employed for numerical modeling as a robust multiphysics coupling simulation platform. Utilizing the Finite Element Method (FEM), its flexible modeling workflow and advanced solvers enable comprehensive solutions for diverse scientific and engineering challenges. These features ensure compatibility with complex fluid–solid coupling processes during coal seam gas extraction and deformation. This study developed a gas drainage model with cross-measure boreholes in the coal seam based on field conditions at Pingdingshan No. 10 Mine using COMSOL, as illustrated in Figure 4. To improve numerical simulation accuracy, a local engineering section was selected to establish the model. The computational model comprises seven strata layers with dimensions of 70 m × 50 m × 60 m (length × width × height).

Five rows of boreholes (94 mm diameter) were arranged in the central zone with 6 m row spacing. Roller supports were applied at the bottom and sides, while a vertical load ${\sigma }_{\mathrm{z}}$ was imposed on the top surface of 25 MPa. The initial coal seam gas pressure was set at 1.25 MPa, with zero-flux boundaries on all sides. The drainage negative pressure was maintained at 15 kPa at boreholes. Considering the significant influence of extraction pressure, the adsorbed gas pressure at borehole walls was assumed to be equal to the fracture gas pressure. Both diffusion and seepage equations share identical fixed-pressure boundaries at borehole walls. Initial displacements were set to 0. The Langmuir constant of coal, coal bed permeability, and coal seam temperature, among other parameters, were obtained through laboratory experiments, geological reports, field tests, and other methods. The detailed parameters are listed in

Table 2. Parameter and variable settings.

Variable	Parameter	Value	Unit
E0	Young’s modulus of coal	2713	MPa
Em	Young’s modulus of coal skeleton	8469	MPa
vc	Poisson’s ratio of coal	0.35
vR	Poisson’s ratio of rock	0.30
ϕf0	Initial porosity of fracture	0.018
ϕm0	Initial porosity of matrix	0.034
μ	Gas dynamic viscosity	1.84 × 10−5	Pa∙s
ρc	Density of coal skeleton	1420	kg/m3
PL	Langmuir pressure constant	1.094	MPa
VL	Langmuir volume constant	0.0204	m3/kg
Mc	The gas-based molecular mass of the methane	0.016	kg/mol
R	Gas state constant	8.1431	J/mol/K
T	Initial temperature in coal seam	306.15	K
Vm	Molar volume of methane in the standard condition	22.4	L/mol
p0	Initial gas pressure in coal seam	1.25	MPa
kf0	Initial permeability in coal seam	0.033 × 10−17	m2
εL	Langmuir volumetric strain constant	0.004

.

3.2.2. Borehole-Surrounding Coal–Rock Deformation and Damage Model

The FLAC^3D numerical model was developed to simulate the stress redistribution and plastic zone evolution in the surrounding rock of both floor drainage roadways and coal roadways following cross-measure borehole extraction. FLAC^3D 7.0 (Fast Lagrangian Analysis of Continua in 3 Dimensions) is a widely adopted numerical simulation software tool in geotechnical engineering. Developed using an explicit finite difference scheme, it enables accurate and efficient simulation and prediction of large deformations and failure behaviors in coal–rock masses.

The FLAC3D model was constructed with dimensions of 100 m (length) × 130 m (width, corresponding to the working face advance direction) × 55 m (height). A vertical compressive stress of 24.5 MPa was applied to the upper free boundary to simulate overburden loading conditions, while initial velocity and displacement fields were initialized to zero. Geometric modeling and mesh generation were performed using Rhinoceros software ver. 7.4. Due to the significant scale discrepancy between borehole diameters and model dimensions, a tetrahedral mesh scheme was adopted for global discretization, with localized mesh refinement implemented in borehole-intensive regions (Figure 5). The complete set of material parameters used in the simulation is provided in

Table 3. Rock stratum parameters for the FLAC^3D model.

Lithology	Thickness (m)	Compressive Strength (MPa)	Simulated Strength (MPa)
Overburden strata	19.6	37.4	0.249
15-16 coal seam	3.2	1.6	0.011
Sandy mudstone	4.3	8.6	0.057
17 coal seam	2.2	2.1	0.014
Sandstone	7.0	79.3	0.529
18 coal seam	1.8	1.6	0.011
Underlying strata	16.9	20.0	0.133

.

4. Results and Discussion

4.1. Efficiency Analysis of Gas Extraction Through Cross-Seam Boreholes in Inclined Coal Seams

Figure 6 presents the gas pressure contour maps of cross-measure borehole drainage in the JI_15-16 and JI₁₇ coal seams at different extraction times. A comparative analysis was conducted using pressure evolution contours at 30, 60, 120, and 180 days. As shown in Figure 5, the gas content in the borehole-affected zone gradually decreases with prolonged drainage time. During the initial extraction phase, the gas pressure near cross-measure boreholes progressively declines, forming low-pressure zones primarily distributed around individual boreholes, while inter-borehole regions maintain relatively higher pressure. With prolonged gas drainage duration, the gas pressure surrounding boreholes decreases further, and the low-pressure zones progressively expand outward. Consequently, the high-pressure regions between boreholes gradually diminish, with partial interconnection of low-pressure zones emerging between adjacent boreholes. At 120 days of drainage, the gas content in the borehole-affected zone decreases significantly, showing the complete interconnection of low-pressure zones across all five borehole rows and the virtual elimination of high-pressure regions. After 180 days of gas extraction, the pressure contours exhibit intensified color gradation, indicating a decrease in the pressure decline rate as the gas pressure progressively stabilizes.

Gas pressure evolution curves were plotted using monitoring data collected from preinstalled measurement lines, as presented in Figure 7. Consistent with the stress contour results from gas extraction, the gas pressure demonstrates a systematic decline from 0.97 MPa at 30 days to 0.57 MPa at 180 days, representing a 41.2% reduction rate and 52.5% cumulative change. The central boreholes exhibit slightly lower pressure (average: 0.52 MPa) compared to peripheral boreholes (average: 0.61 MPa), attributable to enhanced drainage efficiency in the densely clustered central region where higher borehole density facilitates greater gas flow velocity. Furthermore, according to the coal and gas outburst prevention regulations established by the Pingmei Group, which specify that the residual gas pressure after drainage must not exceed 0.6 MPa and the residual gas content must remain below 6 m³/t as the compliance threshold, Figure 6 demonstrates that the 0.6 MPa warning line is reached after 180 days of extraction, indicating satisfactory gas drainage performance.

Figure 8 shows the effective permeability curves of the JI_15-16 coal seam at different drainage times. The analysis reveals that the coal seam permeability generally increases with prolonged gas extraction duration, rising from 1.005 at 30 days to 1.025 at 180 days, representing a 2% increase in effective permeability. Notably, the permeability exhibits more significant changes during the first 120 days of extraction, followed by a continued but slower increasing trend beyond 120 days. This behavior suggests that as gas extraction progresses, the reduced gas content and declining gas pressure within the coal seam lead to an increase in effective permeability. When the gas content decreases below a critical threshold, the permeability stabilizes, meeting the required standards for roadway excavation in the working face.

Figure 9 presents the cumulative gas drainage volume curves of the JI_15-16 coal seam at different extraction times. The analysis reveals that the total gas drainage volume exhibits an initial rapid increase followed by stabilization. During the first 60 days of extraction, the drainage volume rises sharply from 0 m³ to 6.22 m³, accounting for 41.47% of the total gas content. From day 30 to day 180, the drainage rate gradually decreases, with the total volume reaching 11.97 m³, a 48.04% increase compared to the 60-day value. By day 180, the residual gas content stabilizes, and the simulation results confirm that it meets the required standard of less than 6 m³/t.

4.2. Application in Inclined Coal Seam Gas Drainage Projects

Based on the proposed scheme and simulation results, Pingmei No. 10 Mine constructed a floor roadway in the JI₁₈ coal seam, from which cross-measure boreholes were drilled to extract gas from the JI_15-16 coal seam. The boreholes covered a 90 m range along the working face dip direction. As shown in

Table 4. Table of pre-drainage of boreholes.

	Parameters	Methane Concentration (%)	Mixed Gas Flow Rate (m3/min)	Pure Methane Flow Rate (m3/min)	Monthly Extraction Volume (m3)	Cumulative Extraction Volume (m3)
Time
7 July~September 2016		10.20	10.50	1.05	271,600.00	1,527,357.00
October~November 2016		13.50	9.70	1.26	264,400.00
January~March 2017		11.42	12.20	1.34	378,100.00
April~June 2017		12.33	9.00	1.08	382,600.00
July~October 2017		10.81	8.10	0.81	230,657.00

, the floor roadway boreholes extracted a total of 1,527,357 m³ of gas from July 2016 to October 2017, achieving a gas pre-drainage efficiency of 59.18%.

Inspection boreholes were systematically arranged in the floor roadway to measure post-drainage residual gas pressure and content, with a configuration of two boreholes per row spaced at 50 m intervals. The measurement results for the JI_15-16-24130 working face, presented in Figure 10, demonstrate that the stabilized residual gas pressure ranges from 0.32 to 0.42 MPa, while the residual gas content varies between 3.17 and 4.76 m³/t. These parameters fully comply with the coal and gas outburst prevention standards established by Pingdingshan No. 10 Mine, thereby verifying the safety conditions for tailgate development in the specified working face.

The field measurements show good agreement with numerical simulation results, particularly in terms of gas content prediction. However, the measured gas pressures are marginally higher than simulated values, with an average discrepancy of approximately 0.05 MPa. This minor deviation can be attributed to the inherent limitations of numerical modeling, which operates under idealized conditions compared to the complex and variable geological conditions encountered in actual mining operations. The consistency between predicted and observed gas content values nevertheless confirms the reliability of the simulation approach for practical engineering applications.

4.3. Fracture Mechanism of Roadway Surrounding Rock Under Cross-Measure Borehole Drainage

4.3.1. Evolution Mechanism of Plastic Zone in Roadway Surrounding Rock

Figure 11 displays the evolution of plastic zones in the coal roadway and floor roadway at varying distances from the dense borehole zone. Analysis of the figures indicates a general trend of progressive expansion in the plastic zone distribution surrounding roadways as the distance to the dense borehole cluster decreases. Notably, significant enlargement occurs in the roof of floor roadways and both the ceiling and floor of coal roadways. At a critical distance of 5 m from the borehole zone, distinct borehole-aligned plastic zones develop in the ribs and roof–floor strata of coal roadways. Comparative analysis reveals a marked increase in roof plastic zone depth at 5 m versus 20 m, accompanied by localized shear-dominated damage regions surrounding boreholes in the ribs. For floor roadways at 5 m proximity, while moderate expansion of the rib plastic zones is observed (approximately 12–15% increase), the roof plastic zone demonstrates pronounced extension with failure patterns exhibiting precise directional alignment with borehole orientation.

4.3.2. Stress Field Analysis of Surrounding Rock in Coal Roadway and Floor Roadway

Figure 12 shows contour plots of maximum and minimum principal stress distribution in coal roadways and floor roadways at varying distances. The analysis in Figure 12 reveals that with increasing distance from the dense borehole zone, the concentration of maximum and minimum principal stresses in the ribs and roof of the coal roadway shows significant variation. In contrast, the stress concentration range in the roof, floor, and ribs of the floor roadway gradually decreases. The coal roadway exhibits asymmetric distribution characteristics of principal stresses, with stress concentrations primarily occurring near borehole locations in the roof, floor, and ribs. Particularly under the influence of Borehole 7, a notable concentration of minimum principal stress is observed in the floor stratum. Similarly, the floor roadway demonstrates asymmetric principal stress distribution patterns, with stress concentrations predominantly located near cross-measure boreholes in the roof.

The principal stress distribution ahead of the dense borehole zone exhibits consistent evolutionary patterns across varying distances, differing primarily in stress magnitude rather than distribution characteristics. This phenomenon indicates that cross-measure gas extraction induces stress concentration around the roadways due to borehole influence, which promotes the expansion of plastic zones in the surrounding rock mass and ultimately compromises its stability.

Figure 13 presents contour maps of vertical and horizontal principal stress distributions in both coal and floor roadways at varying distances from the borehole cluster. Analysis reveals that as the distance from the dense borehole zone increases, the stress concentration intensity of vertical and horizontal principal stresses in the coal roadway ribs and roof shows significant deviation, while the stress concentration range in the floor roadway roof, floor, and ribs gradually diminishes. The coal roadway exhibits asymmetric distribution characteristics of both vertical and horizontal principal stresses, with stress concentrations predominantly localized near borehole positions in the roof, floor, and ribs. Notably, under the influence of Borehole 7, a pronounced concentration of minimum principal stress is observed in the floor stratum. Similarly, the floor roadway demonstrates analogous asymmetric patterns in vertical and horizontal principal stress distribution, with stress concentrations primarily clustered around cross-measure boreholes in the roof region.

4.4. Discussion

This study addresses gas pre-drainage challenges in the JI_15-16 coal seam of Pingdingshan No. 10 Mine by developing a cross-measure borehole system. The designed scheme utilizes 13 boreholes per row drilled from the floor roadway with 6m row spacing, which has been successfully implemented onsite. The gas extraction system complies with coal and gas outburst prevention regulations at Pingdingshan No. 10 Mine and has been effectively applied during the development of the Ji_15-16-24130 working face’s machine roadway.

Mechanical analysis of surrounding rock failure mechanisms following cross-measure borehole completion reveals significant disturbances to the roadway stress field distribution. The findings of He et al. also illustrate this pattern [30]. These stress perturbations promote the progressive expansion of plastic zones in both coal and floor roadways. Consequently, during the excavation of the 24130 working face machine roadway, enhanced ground pressure monitoring is recommended near cross-measure boreholes in the roof, floor, and rib areas. When necessary, supplementary reinforcement support should be implemented to prevent potential rib spalling and roof collapse incidents.

The measured gas content demonstrates substantial equivalence with simulated data obtained from extraction results, while the measured gas pressure exhibits a moderate surplus over simulation values. The difference magnitude remains negligible, thereby confirming the numerical model’s predictive accuracy for field operations [21]. This discrepancy primarily stems from idealized conditions assumed in numerical modeling, whereas actual field conditions entail complex geological factors and uncertainties that impact extraction efficiency [12]. Additionally, limitations in modeling methodology and mesh generation, including marginally insufficient mesh refinement and the exclusive consideration of cross-measure borehole effects during roadway development, contribute to these variations [31]. Future research should employ a numerical analysis method combining PFC and FLAC^3D modeling [32] to better characterize fracture development patterns in the surrounding rock of roadways under borehole influence and develop corresponding control measures.

5. Conclusions

In order to rapidly and efficiently eliminate coal and gas outburst risks in deep-buried coal seam groups, a gas–solid coupling model consistent with the medium characteristics of deep-buried coal seams was established. A joint simulation method based on the Finite Element Method (FEM) and Finite Difference Method (FDM) was proposed to study the gas extraction and coal–rock deformation evolution during cross-measure borehole extraction in deep-buried coal seam groups. The evolution patterns of extraction pressure, extraction concentration, and coal seam permeability during extraction were analyzed, obtaining the deformation and failure characteristics of coal–rock strata under dense borehole extraction. The results provide a theoretical basis for gas extraction parameter optimization and in situ stress prediction in deep, low-permeability coal seams. Future research should introduce the Discrete Element Method (DEM) to further investigate the coupling mechanism between gas extraction and fracture development.

The main conclusions are as follows:

(1)

With increasing gas drainage duration, both gas content and pressure within the borehole-affected zone exhibit progressive reduction, while the effective permeability of the JI_15-16 coal seam shows a corresponding improvement. After 180 days of continuous extraction, the gas content decreases below the critical threshold of 6 m³/t, confirming that the implemented cross-measure drainage system fully complies with the gas outburst prevention standards established by the Pingmei Group.

(2)

The field gas extraction system successfully recovered a total of 1,527,357 m³ of methane, achieving a 59.18% pre-drainage efficiency through cross-measure boreholes. Field measurements of gas content showed good agreement with the numerical simulation results, while the measured gas pressure was slightly higher than the simulated values.

(3)

The presence of cross-measure boreholes significantly alters the stress field distribution surrounding both coal and floor roadways, leading to the progressive expansion of plastic zones. Consequently, during the development of the 24130 working face’s machine roadway, it is imperative to implement enhanced ground pressure monitoring in the roof, floor, and rib areas adjacent to borehole locations. When necessary, supplementary support reinforcement should be promptly installed to mitigate the potential hazards of rib spalling and roof collapse.