Analysis of Influencing Factors and Application of Gas Drainage Effect in Longitudinal Drifts with Sequential Longhole Drilling

Abstract

Gases are prone to accumulating in mines. Untimely gas drainage can easily trigger gas outbursts, which may further lead to gas explosions, directly endangering personnel lives and mine safety. Therefore, gas control during gob-side entry driving (roadway excavation adjacent to the goaf) in high-gas mines is crucial to ensuring successful and safe mining and excavation. The 110505 track haulage gateway is a typical high-gas gob-side driving gateway. The measured maximum gas content of the lower No.5 coal seam is 6.0289 m³/t. At present, without a scientific basis for optimizing core parameters, such as the spacing and diameter of gas drainage boreholes, gas drainage is incomplete, and triangular gas pressure zones are likely to form between boreholes. As a result, the risk of gas accumulation is high. This not only exacerbates the danger of unpredicted gas outbursts but also seriously hinders the rapid excavation of the gateway and the progress of mining and further excavation. Based on a mechanical framework coupling coal seam and methane migration, and focusing on the relationships between factors such as borehole spacing, borehole aperture, methane drainage duration, and overall gas drainage efficiency, a model incorporating dual pore distribution and unified permeability characteristics was constructed. Numerical modeling was performed using the COMSOL Multiphysics platform to examine the influences of different borehole spacings and apertures on underground gas drainage in coal seams. The results indicate that reducing borehole spacing contributes to a more pronounced decline in gas pressure and a lower peak pressure between neighboring boreholes. When an interval spacing of 0.3 m was adopted for the drilling layout arrangement, the peak gaseous potential within the surrounding rock matrix dropped to 0.48 MPa following continuous drainage over a duration of 20 days, a reduction of 44%, and there was no obvious triangular zone of pressure. In contrast, borehole diameter had a minor effect on gas drainage efficiency, and the maximum gas pressure after 20 days was less than 0.52 MPa under different borehole diameters. This work establishes a theoretical foundation and offers practical guidance for high-efficiency gas drainage during gob-side entry driving, which is of vital importance for achieving safe and rapid excavation in high-gas mines.

1. Introduction

As the “ballast stone” of energy security in China, coal was the predominant energy source in 2024, constituting 53.2% of China’s national primary energy supply [1]. Nearly half of the underground coal mining facilities nationwide exploit methane-rich coal seams or formations prone to dynamic methane ejection hazards [2]. This substantial fraction dictates that safe and efficient production from high-gas coal mines is not only directly related to the stability of China’s energy supply [3] but also plays a crucial role in safe mine production and the security of mine personnel. Generally, coal seams in high-gas mining areas in western China are characterized by dense coal matrices and poorly developed fractures, with a gas desorption rate of only one-third to one-half that of soft coal seams. Thus, in-seam gas drainage is an effective approach to controlling gas outburst risks. However, in high-gas environments, gas tends to accumulate in the coal around roadways. As in-seam gas drainage is the primary means of controlling gas outburst risks and ensuring safe roadway excavation, the rationality of parameter design for this process directly determines emissions efficiency and safety performance. Poor design of parameters such as borehole spacing and the aperture for gas drainage [4] can increase the likelihood of forming triangular zones of pressure or invalidating engineering work, which not only increases the gas overrun rate but also reduces roadway excavation speed. Therefore, there is an urgent need to optimize in-seam gas drainage parameters.

A large number of scholars have conducted relevant research by means of numerical simulation. Kang et al. [5] examined the evolution of the distance influencing effective gas drainage using a numerical simulation, determining that the distance reaches about 1.52 m after half a year of continuous gas drainage. Chen et al. [6] examined the impacts of spatial parameters including the dimensions, intervals, and quantity of hydraulic slots on gas drainage efficiency. They established 3D numerical models and fluid–solid coupling models and conducted field tests at Wangxingzhuang Coal Mine, clarifying that optimizing these parameters can significantly enhance gas drainage performance. Zhang et al. [7] analyzed the influence of gas drainage time, borehole spacing, and arrangement method on gas drainage performance by means of COMSOL numerical simulation and elucidated the law of correlation between the borehole superposition effect and drainage efficiency. Chen et al. [8] explored the impact of the quantity and layout interval of in-seam boreholes on gas drainage efficiency by performing numerical simulations with a hydro-mechanical coupling theoretical framework. They found that the minor semi-axis of the elliptical isobaric contours corresponding to five drilling arrangements exceeded the valid gaseous attenuation coverage by 59%, while an interval spacing of 4 m delivered optimal performance over a 90-day continuous removal timeframe. Su et al. [9] investigated the gas drainage performance and surrounding rock failure of cross-measure boreholes in deep inclined coal seams through coupled numerical simulations. Experimental observations revealed that extending the duration of drainage effectively reduces gas pressure and enhances coal seam permeability. Furthermore, the borehole arrangement alters in situ stress distribution and expands the plastic zone of the surrounding rock. Wang et al. [10] revealed that borehole diameter, coal seam permeability, and initial gas pressure determine the gas drainage range under stress–seepage coupling conditions. A larger aperture and higher permeability can effectively expand the pressure relief radius and improve drainage efficiency. Du et al. [11] examined the effects of gas drainage duration and borehole interval on the effective gas drainage scope, determining that a borehole spacing of 5 m is optimal for 140 days of gas drainage. Hosseini A et al. [12] developed a three-dimensional numerical representation tailored to gas drainage and further specified the suitable separation distance of extraction boreholes on the basis of the cross-borehole arrangement technique. Leśniak G [13] validated the feasibility of adopting long-distance directional boreholes for gas drainage within fractured gob zones of adjacent coal strata and explored the intrinsic mechanism governing how key controlling parameters (vertical and horizontal borehole layout configurations, reservoir lithology indicators, and the orientation of maximum horizontal in situ stress) affect overall extraction performance. Zhang et al. [14] confirmed that a superposition effect occurs for pressure drop zones when multiple boreholes are used for gas drainage simultaneously, thereby significantly expanding the overall effective gas drainage range, and pointed out that borehole spacing based on the traditional single-borehole model is too conservative and can be optimized and reduced. Many studies rely on field data and new technologies to carry out exploration. Wang et al. [15] investigated the effects of permeability, gas pressure, and burial depth on gas drainage performance using field data collected from Xuehu Coal Mine. Experimental observations revealed that a pronounced positive correlation between seam permeability parameters and gas removal efficacy weakens as burial depth increases continuously, whereas relevant beneficial connections related to seam gaseous potential are gradually enhanced. Furthermore, burial depth exhibits an inverse correlation with overall underground gas control effectiveness. Karacan et al. [16] clarified the roles of factors such as borehole arrangement method, gas drainage stage, borehole length, and location in gas drainage performance. Aminossadati S.M. et al. [17] found that fiber optic sensing technology can not only measure the borehole flow rate but also simultaneously monitor the internal conditions of the borehole, thereby improving gas drainage efficiency.

Some scholars combine multiple research methods and intelligent algorithms to optimize relevant parameters. Cheng et al. [18] combined response surface methodology (RSM) with numerical simulation to establish a highly accurate predictive model that links multiple controlling variables to the effective influence zone of gas drainage, finding that the initial permeability of coal strata strongly affects the overall seam gas removal range and that interactive coupling relationships between such permeability parameters and drainage duration exhibited outstanding sensitivity, thereby promoting considerable improvements in in-seam gas control efficiency. Zheng et al. [19] adopted an approach integrating response surface methodology (RSM) with orthogonal experimental design to explore how the duration of gas drainage, original gas pressure, inherent coal seam permeability, and borehole aperture determine the effective radius of gas drainage. Their findings indicated that the original gas pressure has the greatest impact on the target radius. Wang et al. [20] studied the influence of borehole diameter, spacing, and extraction negative pressure on gas drainage via fluid–solid coupling simulation and gray correlation analysis. They found that borehole aperture has the greatest influence, followed by borehole spacing, while extraction negative pressure has the least effect. They reported that the optimal parameters were an aperture of 8 cm, spacing of 3 m, and negative pressure of 50 kPa; meanwhile, the gas pressure drops rapidly in the early drainage stage and tends to stabilize after 30 days. Hosseini A et al. [21] established an ANN-GWO algorithm model. Relying on the nonlinear fitting and prediction capabilities of the ANN and the global optimization advantage of GWO, the model was developed and optimized for the key factors influencing coal mine gas drainage, such as borehole layout, gas drainage negative pressure, and gas drainage time. In addition to borehole parameters, hole-sealing work also plays a vital role in gas drainage. Importantly, the hole-sealing technology applied should not be overlooked. Yao et al. [22] analyzed air leakage characteristics during the hole-sealing procedure and identified a key pattern, reporting that for a 9 m wide cracking zone within the rock mass adjacent to the roadway, the depth of hole sealing should be optimized to 9–10 m. Lou et al. [23] developed an innovative dynamic plugging material based on the idea of “solid sealing fluid and liquid sealing gas”. Field tests demonstrate that this material is capable of dynamically plugging regenerated fractures in the vicinity of gas drainage boreholes, efficiently blocking air seepage pathways, increasing the gas drainage purity from 8% to 24%, and remarkably enhancing the overall drainage efficiency. Zhou et al. [18] established a mathematical model of how hole-sealing techniques affect gas drainage.

In summary, to address the problem of gas control in goaf-side entry driving, this study was conducted to optimize critical technical indicators for underground methane drainage, employing COMSOL Multiphysics 5.6 numerical simulation software, and construct a “dual-porosity single-permeability” coal–gas solid coupling model. Further, it systematically explores how borehole spacing and aperture govern drainage performance and identifies the optimal combination of operational indicators. This study offers technical guidance for the rapid excavation of the 110505 track haulage gateway and offers a theoretical reference and engineering guidance for gas control in goaf-side entry driving in similar high-gas coal seams.

2. Model Establishment

Numerical simulations were performed using COMSOL Multiphysics 5.6 (COMSOL Inc., Stockholm, Sweden). This software was selected because it can support fully coupled multi-physics analysis, which is essential for modeling the interaction between coal deformation, gas seepage, and matrix diffusion in fractured coal seams. It enables flexible definition of partial differential equations and custom coupling between solid mechanics and fluid flow fields, making it a popular choice for solving coal mine gas drainage and multi-field coupling problems. Relevant engineering studies demonstrate that this simulation tool can accurately reflect gas migration rules inside coal seams, and the calculated data maintain good consistency with measured and experimental outcomes, proving its reliability for practical simulation research [24,25,26].

In this study, a coal–gas gas–solid coupling model was established based on the “dual-porosity single-permeability” system. This model can effectively separate fracture seepage and matrix diffusion processes, which is consistent with the real-world mechanism of gas migration in coal seams. It offers a simple means of setting parameters and stable computing performance and is widely applicable to engineering multi-physics coupling simulation [27,28,29]. This model assumes inherent isotropic permeability and ignores directional seepage differences caused by oriented fractures; however, it has limitations in describing the nonlinear mass transfer of a heterogeneous coal mass [30]. Considering the above model characteristics and to simplify numerical calculation, the following reasonable simplifications are proposed [31,32,33]: The immediate strata overlying and underlying coal seams have low permeability and remain devoid of accumulated gas. Coal seam gas is treated as an ideal gaseous medium, while its migration within coal strata presents laminar seepage characteristics, following Darcy’s classical criterion. Evolution of seepage throughout the coal seam is assumed under constant thermal boundary conditions. It is worth mentioning that gas desorption is an endothermic process, which can cause local temperature reductions inside coal. Temperature variation needs to be considered independently in high-gas-concentration seams under certain circumstances. The area of migration generated by borehole drainage is regarded as a radial migration zone, within which gaseous migration occurs as radial seepage. Along the drilling boundary, the sorbed gaseous potential maintains equilibrium with the fracture internal energetic magnitude. Initial modeling conditions assume consistent gaseous potential magnitudes within fracture networks and pore matrix structures; both characteristic values match the original seam gaseous baseline prevailing within coal strata. The content of adsorbed gas conforms to the Langmuir equation. Gas migration occurs in two sequential processes. First, coal seam gaseous components migrate from the coal matrix system to fracture networks, following typical Fickian diffusion patterns. Then, they are discharged into the borehole through fractures via Darcy seepage. The specific mathematical model is given below.

2.1. Deformation Equation of Gas-Bearing Coal Mass

Based on effective stress principles governing dual-medium systems, an equation defining the displacement-based deformation of coal strata was derived by integrating stress equilibrium relations, geometric formulations, and the generalized Hooke criterion [34,35]. Within this expression, G represents the shear modulus parameters of the rock mass [34], in MPa; u_i,jj corresponds to the displacement component along the horizontal i-direction; u_j,ji corresponds to the displacement component along the horizontal j-direction; v represents Poisson’s ratio; Fi denotes the component of the body force in the i-direction, in MPa; β_f represents the Biot effective stress coefficient corresponding to fractures [36]; p_f is the fracture gas pressure [34], in MPa; β_m represents the Biot effective stress coefficient corresponding to pores [36]; and p_m is the matrix gas pressure, in MPa.

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

(1)

2.2. P-M Permeability Model

P-M permeability models are theoretical models often used to describe the evolution of permeability in coalbed methane drainage. These models assume that the coalbed methane reservoir exists under uniaxial strain [37] and that the overburden load remains constant. In light of real-world engineering practices for regional pre-mining gas drainage in first-mined coal seams, analysis demonstrates that the stress regime within deep first-mined coal seams fulfills the modeling prerequisites of a P-M permeability model [37].

The formulation of the proposed P-M theoretical framework was grounded in classical single-porosity poroelastic principles [37]. For a coal mass regarded as a pore–fracture dual medium, the double-porosity poroelastic theory is most applicable to solving the variation in fracture porosity with effective stress [37]. An equation for fracture porosity was established on this basis [38], in which k₀ denotes the initial intrinsic permeability within intact coal matrix masses, m² [39]; k corresponds to the intrinsic permeability within intact coal matrix masses, m² [39]; ϕ_f denotes the inherent fracture porosity within intact coal matrix masses, representing the fracture porosity of the coal mass [38], %; ϕ_f0 denotes the initial fracture porosity of the coal mass, % [39]; M is the axial constraint modulus, MPa, and $M={\displaystyle \frac{E_c\left(1-\nu \right)}{\left(1+\nu \right)\left(1-2\nu \right)}}$ [38]; K is the bulk modulus; p_L is the Langmuir pressure constant, MPa [20]; and ε_L is the constant Langmuir volumetric strain at infinite pore pressure [20].

$${\displaystyle \frac{{\varphi }_f}{{\varphi }_{f_0}}}=1+{\displaystyle \frac{1}{M_{{\varphi }_{f_0}}}}\left[{\beta }_f\left(p_f-p_{f_0}\right)+{\beta }_m\left(p_m-p_{m_0}\right)\right]+{\displaystyle \frac{{\epsilon }_L}{{\varphi }_{f_0}}}\left({\displaystyle \frac{K}{M}}-1\right)\left({\displaystyle \frac{p_m}{p_L+p_m}}-{\displaystyle \frac{p_{m_0}}{p_L+p_{m_0}}}\right)$$

(2)

Considering double-porosity poroelastic theory, the fracture porosity varies dynamically with effective stress. A permeability model can be derived by incorporating the cubic law [40,41]:

$${\displaystyle \frac{k}{k_0}}={\left({\displaystyle \frac{{\varphi }_f}{{\varphi }_{f_0}}}\right)}^3={\left\{\left.\begin{array}{l}1+{\displaystyle \frac{1}{M{\varphi }_{f_0}}}\left[{\beta }_f\left(p_f-p_{f_0}\right)+{\beta }_m\left(p_m-p_{m_0}\right)\right]+\\ {\displaystyle \frac{{\epsilon }_L}{{\varphi }_{f_0}}}\left({\displaystyle \frac{K}{M}}-1\right)\left({\displaystyle \frac{p_m}{p_L+p_m}}-{\displaystyle \frac{p_{m_0}}{p_L+p_{m_0}}}\right)\end{array}\right\}\right.}^3$$

(3)

2.3. Matrix Gas Diffusion Equation

The pressure of gas adsorbed within the coal matrix evolves dynamically over time, as described by Fick’s Second Law. Within this expression, V_M is the molar volume of methane under standard conditions, m³/mol; ρ_c is the coal density, kg/m³; R is the universal gas constant, 8.314 J·mol⁻¹·K⁻¹; T is the temperature, K; τ is the sorption time constant, s; ϕ_m is the coal matrix porosity.

$${\displaystyle \frac{{\partial }_{pm}}{{\partial }_t}}={\displaystyle \frac{V_M\left(p_m-p_f\right){\left(p_m+p_L\right)}^2}{\tau V_{L}RT{P}_L{\rho }_C+\tau {\varphi }_m{V}_M{\left(p_m+p_L\right)}^2}}$$

(4)

2.4. Fracture Gas Seepage Equation

Building upon the principle of mass preservation and the fundamental framework of Darcy’s theory [42], an equation describing fracture gas pressure was derived by incorporating the mass supply associated with matrix diffusion [42]. Within this expression, k_e is the effective gas permeability, m²; μ is the methane viscosity, Pa·s.

$${\varphi }_f{\displaystyle \frac{{\partial }_{Pf}}{{\partial }_t}}+p_f{\displaystyle \frac{{\partial }_{{\varphi }_f}}{{\partial }_t}}=\nabla \left({\displaystyle \frac{k_e}{\mu }}{p}_f\nabla p_f\right)+{\displaystyle \frac{1}{\tau }}\left(1-{\varphi }_f\right)\left(p_m-p_f\right)$$

(5)

In summary, a coal–gas gas–solid coupling model was formulated by combining Equations (1), (4) and (5), incorporating the effects of gas desorption–diffusion, coal skeletal deformation, and matrix volume shrinkage [43], as presented in Equation (6).

$$\left\{\begin{array}{l}G{u}_{i,jj}+{\displaystyle \frac{G}{1-2v}}{u}_{j,ji}-{\beta }_{\mathrm{f}}{p}_{\mathrm{f},i}-{\beta }_{\mathrm{m}}{p}_{\mathrm{m},i}+F_i=0\\ {\displaystyle \frac{\partial {\varphi }_f}{\partial t}}={\displaystyle \frac{1}{M}}\left({\beta }_f{\displaystyle \frac{\partial p_f}{\partial t}}+{\beta }_m{\displaystyle \frac{\partial p_m}{\partial t}}\right)+{\displaystyle \frac{{\epsilon }_L{P}_L}{{\left(P_L+p_m\right)}^2}}\left({\displaystyle \frac{K}{M}}-1\right){\displaystyle \frac{\partial p_m}{\partial t}}\\ {\displaystyle \frac{\partial p_m}{\partial t}}=-{\displaystyle \frac{V_M\left(p_m-p_f\right){\left(p_m+P_L\right)}^2}{\tau V_{L}RT{P}_L{\rho }_c+\tau {\varphi }_m{V}_M{\left(p_m+P_L\right)}^2}}\\ {\varphi }_f{\displaystyle \frac{\partial p_f}{\partial t}}+p_f{\displaystyle \frac{\partial {\varphi }_f}{\partial t}}=\nabla \left({\displaystyle \frac{k_e}{\mu }}{p}_f\nabla p_f\right)+{\displaystyle \frac{1}{\tau }}\left(1-{\varphi }_f\right)\left(p_m-p_f\right)\end{array}\right.$$

(6)

2.5. Construction of Coal Seam Gas Drainage Numerical Model and Numerical Model of Boundary Conditions

2.5.1. Initial and Boundary Conditions

For the gas diffusion module within coal matrix systems, zero-flux constraints are enforced across all exterior boundaries of the computational domain [44]. Initial pressure magnitudes are calibrated in accordance with the in situ gas pressure within the coal seam formation [44]. Meanwhile, the drilling periphery is designated as a first-type boundary condition, where gaseous potential matches the negative suction level imposed during drainage procedures.

For the fracture network gas migration module, impermeable boundary constraints are enforced across all peripheral extents throughout the computational domain. All pressure values in this model are defined as relative pressures with atmospheric pressure as the reference zero point. According to the geological occurrence data of the study coal seam, the initial gas pressure of coal matrix and fracture system is uniformly set to 1.20 MPa, which is consistent with the in situ gas pressure within stratigraphic seam formations. Borehole sidewalls are set to a constant pressure of 15 kPa (drainage negative pressure) referring to conventional engineering parameters, and gas mainly migrates from coal matrix diffusion. A quasi-static method is adopted for the time-dependent calculation in this model.

For the structural mechanical module governing fractured rock assemblages, the basal boundary undergoes full displacement constraint, lateral extents are assigned sliding support configurations, and uniformly distributed stress loads act upon the top boundary to characterize native in situ stress conditions within geological strata.

2.5.2. Basic Parameters

Critical parameters were identified using field geological data and laboratory measurements and are presented in

Table 1. Relevant parameters of gas drainage by boreholes in heading roadway.

Parameters	Values	Parameters	Values
Langmuir Volume Constant (m3/t)	13.9138	Poisson’s Ratio of Coal	0.32
Langmuir Pressure Constant (MPa)	1.2582	elastic modulus of coal (MPa)	3.3
Molar Volume of Gas under Standard Conditions (m3/mol)	22.4	apparent density of coal (t/m3)	1.29
Apparent Density of Coal Mine Gas under Standard Conditions (kg/m3)	0.716	elastic modulus of coal matrix (MPa)	8.4
Matrix Size (mm)	10	gas diffusion coefficient of coal matrix (m2/s)	5.6 × 10−12
molar mass of methane (kg/kmol)	16.0428	limiting adsorption swelling strain of coal mass	0.02295
initial absolute permeability of coal seam (m2)	4.936 × 10−17	Klinkenberg factor (Pa)	0.251
initial fracture porosity of coal seam (%)	5.5	universal gas constant (J·mol−1·K−1)	8.41351
coal seam temperature (K)	293.15	dynamic viscosity of coal mine gas (Pa·s)	1.08 × 10−6

.

2.5.3. Simulation Design

To determine a suitable gas drainage borehole layout and achieve optimal drainage, numerical simulations were carried out for the gas drainage conditions corresponding to different borehole spacing and aperture values.

A numerical simulation was carried out to analyze the impact of borehole size parameters on in-seam gas drainage. In this study, borehole layout schemes with a fixed diameter of 94 mm and spacings of 0.15 m, 0.30 m, and 0.45 m were used to investigate the gas drainage efficiency of the 110505 pre-excavated track haulage gateway under 15 kPa of drainage negative pressure. The relevant schemes are illustrated in Figure 1.

The same simulation was applied to examine the effect of borehole size on gas drainage performance. Borehole layouts with sequential borehole apertures of 72 mm, 94 mm, and 112 mm and a fixed borehole spacing of 0.3 m were adopted to assess the gas drainage efficiency of the 110505 pre-excavated track haulage gateway under 15 kPa of drainage negative pressure. The detailed layouts and corresponding analysis results are provided in Figure 2.

The detailed rotation angles and designed lengths of each comparative borehole are listed in

Table 2. Rotation angles and designed lengths of boreholes.

Drilling Site	Borehole No.	Rotation Angle/°	Horizontal Control Distance/m	Designed Borehole Length/m
First layer	X-4#	4°50′	64	64.2
	X-5#	3°00′	64	64.1
	X-6#	2°00′	64	64.0
	X-7#	1°16′	64	64.0
Second layer	2-1#	17°26′	90	94.4
	2-2#	11°00′	70	71.3
	2-3#	7°36′	64	64.6
	2-4#~2-7#	5°00′	64	64.2
Third layer	3-1#	31°30′	90	105.4
	3-2#	19°00′	70	74.0
	3-3#	12°31′	64	65.5
	3-4#~3-7#	8°11′	64	64.7

, corresponding to the borehole layouts illustrated in Figure 1 and Figure 2.

3. Analysis of In-Seam Gas Drainage Effect

3.1. Influence of Borehole Spacing on Gas Drainage Performance

Numerical simulations of gas drainage via long boreholes drilled into the coal seam were conducted to clarify the effect of inter-borehole distance on gas drainage behavior. Contour maps for the pore pressure distribution of coal seams under varying drainage durations and borehole spacing values were plotted, as illustrated in Figure 3.

The contours of pore pressure distribution in the coal seam under various gas drainage periods and borehole intervals, shown in Figure 3, reveal that the gas pressure increases gradually with increasing borehole spacing. After 10 d and 20 d of gas drainage, among the three groups of working conditions with borehole spacings of 0.15 m, 0.30 m, and 0.45 m, the coal seam gas pressure corresponding to a borehole spacing of 0.15 m is the lowest in both drainage periods, indicating optimal gas drainage performance. When the borehole spacing is set at 0.45 m, low gas pressure is detected in areas adjacent to the boreholes. With an increase in borehole depth, triangular zones of high gas pressure develop between adjacent boreholes, resulting in unsatisfactory gas drainage. These results confirm that borehole spacing has a pronounced effect on the effectiveness of gas drainage. The duration of gas drainage is also proven to influence gas drainage effectiveness. When boreholes are arranged at spacings of 0.30 m, the seam gaseous pressure declines within the safe threshold range after 20 days of drainage. When the borehole spacing is 0.45 m, the gas pressure after 20 d of gas drainage is much lower than that after 10 d of drainage.

The pressure distribution of the 110505 pre-excavated roadway under different borehole spacings is presented in Figure 4.

It can be concluded from the pressure distribution of the 110505 pre-excavated roadway under different borehole spacings in Figure 4 that a smaller borehole spacing leads to better gas drainage performance. After 20 d of gas drainage, a gas pressure of 0.77 MPa is recorded for a borehole spacing of 0.45 m. When the spacing is set to 0.30 m, the gas pressure is 0.43 MPa, representing a reduction of 44%. For a borehole spacing of 0.15 m, the gas pressure is 0.29 MPa, a reduction of 62%.

The gas pressures corresponding to the latter two spacing schemes are both lower than 0.5 MPa, indicating that the gas pressure has been reduced to the safe range (below the critical outburst pressure of 0.74 MPa). In contrast, the gas pressure at a spacing of 0.45 m remains fairly high. Meanwhile, under identical spacing configurations, lower gaseous potential magnitudes can be achieved with prolonged drainage. Early in the gas drainage period, the gas pressure within the coal seam drops swiftly due to the strong driving force associated with a high pressure gradient. As gradient magnitudes progressively decrease, the attenuation rate of gaseous potential is steadily lowered, and the gas drainage process can be stabilized accordingly. Meanwhile, with radial spacing extending outward around drilled openings, both gaseous differential gradients and corresponding attenuation trends are gradually mitigated throughout the surrounding coal strata. This phenomenon indicates that borehole spacing has a significant and obvious influence on gas drainage efficiency. Technically, smaller spacing accelerates the decline in coal seam gas pressure and achieves better drainage performance. In practical engineering, however, both technical performance and economic cost must be taken into account. Although a spacing of 0.15 m achieves the best drainage effect, it increases the construction workload and cost. A spacing of 0.45 m can reduce investment but fails to meet underground safety excavation requirements. Because it comprehensively balances technical requirements and economic benefits, 0.3 m is the optimal borehole spacing.

3.2. Influence of Borehole Aperture on Gas Drainage Performance

Parametric numerical assessments of seam gas drainage with extended underground boreholes were implemented to clarify how hole aperture governs real-world drainage efficiency. Contour maps depicting seam gaseous potential profiles for varied drainage durations and borehole apertures were derived from numerical simulations and are illustrated in Figure 5.

In the front section of boreholes, better drainage of the surrounding gas is achieved with a larger borehole aperture, due to the narrow spaces between neighboring boreholes. As methane drainage continues, methane stress around the drilling holes is gradually attenuated, accompanied by a corresponding expansion of the influence scope. Meanwhile, negligible discrepancies in methane magnitude are observed across varying borehole aperture specifications.

The pressure distribution in the 110505 pre-excavated roadway under different borehole apertures is illustrated in Figure 6.

From the pressure distribution in the 110505 pre-excavated roadway under different borehole apertures, shown in Figure 6, it can be concluded that there is no significant difference in gas drainage among borehole apertures. The gas pressure associated with the borehole apertures declines gradually as gas drainage continues over time. After 20 d of gas drainage, the gas pressure is reduced to 0.5 MPa when the borehole aperture is 72 mm; it is 0.48 MPa for an aperture of 94 mm and 0.45 MPa for an aperture of 112 mm. After 10 d of gas drainage, measurements show that the gas pressure corresponding to all three borehole apertures is roughly 0.5 MPa. As gas drainage proceeds, boreholes of varying apertures all have a noticeable gas-pressure-reducing effect. Therefore, using the conventional borehole diameter of 94 mm avoids additional costs due to customized drilling tools, special construction equipment, and extended construction time. Compared with the use of non-conventional borehole diameters, the traditional scheme reduces the cost of drilling and the construction period, improving overall economic benefit without worsening gas drainage. Therefore, adopting a universal borehole diameter of 94 mm offers better economic benefits in field engineering.

To quantitatively analyze the influence of various parameters on gas pressure, data normalization and single-factor sensitivity analysis were adopted in this study. The relevant calculation formulas are as follows.

The sensitivity coefficient was used to quantify the influence degree of each parameter, and its calculation formula is presented below:

$$P={\displaystyle \frac{\Delta Y/Y_0}{\Delta X/X_0}}$$

(7)

where X₀ and ΔX are the baseline value and variation in the parameter; Y₀ and ΔY are the initial gas pressure and its variation. A larger absolute value of S means a more remarkable influence on gas pressure.

To unify the data range for intuitive comparison, gas pressure values were processed via min–max normalization:

$$P^{*}={\displaystyle \frac{P-P_{\min }}{P_{\max }-P_{\min }}}$$

(8)

where P* is the normalized gas pressure, P is the original gas pressure, and P_max and P_min stand for the maximum and minimum pressure in simulation cases. The field-measured gas pressure data was obtained by the GPD60 intrinsic safety gas sensor manufactured by CCTEG Chongqing Research Institute, Chongqing, China.

On the basis of the above formulas, we calculated the normalized pressure data and sensitivity coefficients of borehole spacing, borehole diameter and extraction time. The overall variation trend and comparative results are visualized in Figure 7 for further analysis.

3.3. Discussion

• Core mechanism of action of layout parameters

Differing from the superficial variation law described above, the effectiveness of gas drainage is essentially governed by the coal–rock mass stress state and gas seepage dynamics. The adjustment of borehole spacing directly changes the spatial distribution of the pressure relief field, which further influences the degree of connectivity of gas flow channels in coal seams. This is why spacing plays a predominant role in improving gas control. In contrast, the borehole diameter only affects local flow conditions near boreholes, which cannot alter the overall trend of seepage field evolution; therefore, its potential to regulate drainage is limited.

2.

Theoretical explanation of staged drainage characteristics

The staged decline law of gas pressure reflects not only a simple change in data but also the process of conversion of free and adsorbed gas in coal. In the early stage, free gas is discharged preferentially with large pressure differences, showing a rapid drop in pressure. In the later stage, gas desorption speed restricts its overall migration efficiency, which leads to the gradual stabilization of pressure. This conclusion is consistent with the basic gas laws.

3.

Parameter optimization priority determination

As illustrated in Figure 7, each construction parameter imposes a regular influence on gas pressure evolution. Consistent with the above mechanism analysis, increased borehole spacing weakens the overall pressure relief and drainage performance, whereas larger borehole diameter and prolonged extraction time facilitate gas pressure reduction.

Quantitative calculation further distinguishes the comprehensive influence of different parameters. The sensitivity coefficients of borehole spacing, extraction time, and borehole diameter are 0.583, 0.48, and 0.092, respectively. Such numerical differences fundamentally correspond to the inherent action characteristics of each parameter. Borehole spacing governs the overall seepage and stress field distribution, thereby exhibiting the most prominent regulatory effect. Extraction time cooperates with the staged gas desorption and migration process, maintaining a stable regulatory capacity throughout the drainage cycle. In comparison, borehole diameter only functions on local flow conditions near the borehole, resulting in the lowest sensitivity and limited overall regulation potential.

4. Engineering Application

4.1. Basic Roadway Conditions

As shown in Figure 8, the 110503 panel is an active longwall working face. The upper part is the 110501 goaf, and the coal body below is the research object of this paper. Gas drainage is implemented here to support the excavation of the 110505 track transport roadway. The 110505 track haulage gateway operates as a gob-side entry-driving roadway, with a planned strike length of 1284 m. This roadway has a rectangular sectional configuration with a transverse span of 5.8 m and a vertical elevation of 3.4 m and advances along the basal stratum belonging to the No. 5 coal seam formation. On average, the coal seam has a mean thickness of 9.17 m, with its dip angle ranging from 9° to 13°. The rock assemblages constituting the immediate overlying and underlying strata consist mainly of fine-grained arenite and silty rock formations, which are classified as low-strength rocks characterized by poor water-resistance properties. Situated to the north of this roadway is the 110503 half belt haulage gateway. A 64 m wide sectional coal pillar is retained between the two roadways. Large-scale drilling sites were established via the 110503 half belt haulage gateway to implement gas pre-drainage within a 25 m zone along the 110505 track haulage gateway. Field measurements reveal that the 110505 high-gas gob-side entry-driving roadway has a maximum gas content of 6.0299 m³/t, an initial gas pressure of 0.48 MPa, and a maximum initial gas emission velocity of 12.4 m³/(min·m) (exceeding 10 m³/min). The gas content is verified to exceed the specified safety control standard.

4.2. Borehole Layout Scheme

To achieve effective gas pre-drainage within the 25 m range on the side of the 110505 track haulage gateway during the excavation of the 110503 belt haulage gateway, the following scheme is developed in light of the findings obtained from the numerical simulation. Considering the key outcomes of the numerical simulation, including that triangular pressure zones are prone to forming at a borehole spacing of 0.45 m, that single-layer boreholes are unable to cover the average coal seam thickness of 8.5 m, and that a borehole aperture of 94 mm balances gas drainage performance and economic efficiency, the optimal borehole spacing of 0.3 m, optimal borehole aperture of 94 mm, and optimal three-layer fan-shaped borehole arrangement were determined. Three-stage lug drilling fields, namely No.1, No.2, and No.3, are arranged at the heading face of the 110503 belt haulage gateway. A spacing of 2 m was established between the No.1 drilling field and the No.2 and No.3 drilling fields. Lug drilling fields are arranged on both sides of the No.3 drilling field. The No.1 drilling field is designed to control a range of 15 m beyond the roadway contour line, the No.2 drilling field is specially constructed to cover the 25 m core pre-drainage zone, and the No.3 drilling field offers auxiliary supplementation. The in-seam strip pre-drainage boreholes were arranged to control a range of 90 m in front of the roadway. A total of 21 boreholes were constructed in both the No.1 and No.2 drilling fields, with drilling workloads of 1393 m and 1335 m, respectively. Nine boreholes were constructed in the No.3 drilling field, with a drilling workload of 705 m. In total, 51 boreholes were designed and constructed, with an overall drilling workload of 3433 m, so as to ensure no gas drainage blind zone at the borehole spacing of 0.3 m. The three-layer fan-shaped boreholes were designed with different inclination angles for complete coverage of the coal seam: the first layer was arranged at angles ranging from 4°50′ to 1°16′, the second layer from 17°26′ to 5°, and the third layer from 31°30′ to 8°11′. A ZBQ-27/1.5 pneumatic grouting pump was used for hole sealing, and bagged polyurethane was used as sealing material with a sealing depth of 20 m. A Model 2BEF80 high-negative-pressure water-ring vacuum pump, with a rated rotational speed of 270 r/min, a flow rate of 710 m³/min, and a power of 900 kW, was employed to provide stable negative pressure for gas drainage. Meanwhile, a Φ720 mm seamless steel main pipeline was selected to ensure the real-world gas drainage performance aligned with the simulation results. A diagram of the layout of the in-seam strip gas pre-drainage boreholes for the 110503 belt haulage gateway is shown in Figure 9.

4.3. Gas Monitoring

To monitor the gas content in the 110505 track haulage gateway and its surrounding coal mass after implementing in-seam gas pre-drainage technology, on-site measurements were performed to quantify the residual gas content present in the 110505 track haulage gateway coal seam and its surrounding coal mass.

Specifically, forty-five effect inspection boreholes were constructed downward from the 110503 belt haulage gateway. These boreholes were distributed at different positions along the 110503 belt haulage gateway, with a sampling depth of approximately 24 m. Their scope encompassed a critical zone extending 15 m beyond the contour of the lower rib in the 110505 track haulage gateway. A schematic diagram of the layout of these boreholes is provided in Figure 10. The DGC coal seam gas content tester was used for the inspection. Through on-site rapid desorption testing of drill cuttings, estimation of gas loss, and laboratory measurement of remnant gas content, the gas content within the 110505 track haulage gateway and its surrounding coal body was precisely determined so as to confirm whether the gas content in the coal mass following pre-drainage had been decreased to the required safety control standard.

No abnormal events such as hole blowout, drill sticking, or drill pushing occurred during the test. The residual gas content at different measurement points is presented in Figure 11.

As shown in Figure 9, the residual gas content at various locations in the 110505 track haulage gateway was found to fluctuate significantly with distance but is concentrated within the range of 3.5~5.5 m³/t in most areas. For the section ranging from 0 to 200 m away from the roadway opening, the gas content is relatively low, approximately 3.5~4 m³/t, indicating a comparatively stable gas pre-drainage effect. For the section from 400 to 800 m, the gas content shows a trend of fluctuating upward and stays within the interval of 4~5 m³/t. An obvious peak appears near the 1000 m position, with a peak value of 5.6692 m³/t. This represents the region with the highest gas content in the figure, which is close to the red control line. The gas content decreases after 1000 m. Although fluctuations still exist in the subsequent sections, high peaks no longer occur. The developed coal–gas gas–solid coupling model employs a dual-porosity single-permeability structure, and the numerical gas drainage results derived accordingly exhibit favorable accuracy.

4.4. Model Reliability Verification

To verify the rationality of parameter selection and the accuracy of the simulation results, the measured residual gas content was used to inversely calculate the gas pressure for model validation.

4.4.1. Calculation Formula

The classical gas content formula is applied:

$$X={\displaystyle \frac{abp}{1+bp}}·{\displaystyle \frac{100-A_{ad}-M_{ad}}{100}}·{\displaystyle \frac{1}{1+0.31M_{ad}}}+{\displaystyle \frac{100Kp}{\rho }}$$

(9)

where X is the gas content of coal seam, m³/t; a and b are adsorption constants with units of m³/t and MPa⁻¹, respectively; p is the absolute gas pressure in MPa; A_ad is the ash content in %; M_ad is the % moisture content; ρ is the apparent density; and K is the pore volume of the coal in m³/m³.

4.4.2. Parameter Setting and Calculation Result

The uniform coal physical parameters were determined as follows:

a = 13.91 m³/t, b = 1.26 MPa⁻¹, A = 12%, M = 1.5%, K = 0.0739 m³/m³, ρ = 1.30 t/m³

The measured residual gas content was X = 5.6692 m³/t, and the inversely calculated actual residual gas pressure is 0.4640 MPa.

4.4.3. Error Analysis

The residual gas pressure obtained by inversion of field data is 0.4640 MPa. Combined with the numerical simulation results, the stable residual gas pressure of the coal seam after gas drainage is 0.48 MPa. The relative error between the simulated value and the inversely calculated value is calculated as follows:

$$\delta =\left|{\displaystyle \frac{p_{sim}-p_{mea}}{p_{mea}}}\right|\times 100\%$$

(10)

where P_sim is the simulated residual gas pressure, MPa; and P_mea is the residual gas pressure obtained by formula inversion, MPa. The final relative error is 3.45%. The error is extremely small and fully within the allowable range of engineering numerical simulation research. It shows that the simulated gas pressure results are highly consistent with the actual field conditions.

4.4.4. Verification Conclusion

The calculated data agree well with the simulation results, indicating that the established numerical model and selected parameters are reasonable and reliable. The simulated variation law of gas pressure is capable of accurately reflecting real-world field conditions.

5. Conclusions

According to the simulation results, the following three parameters differ greatly in their impact: borehole spacing has the greatest influence, followed by pre-drainage time, and borehole diameter has the weakest effect. Reducing borehole spacing and extending the drainage time can effectively reduce gas pressure in the coal seam, but changing the borehole diameter results in negligible improvement.

(1)

Borehole spacing is the dominant parameter. Smaller spacing contributes to far better gas pressure reduction performance under the same conditions. With a fixed diameter and drainage time, smaller borehole spacing produces a larger drop in gas pressure and a wider area of pressure relief. Increasing the spacing will weaken the superposition effect and greatly slow the pressure reduction rate, which has a strong influence on overall drainage.

(2)

Within the scope of this research, borehole diameter had a negligible impact on gas pressure variation. When spacing and drainage duration remained unchanged, adjusting the borehole diameter resulted in only very small differences in gas pressure. No obvious change was observed in gas seepage velocity and the pressure relief range. Enlarging the borehole diameter alone is insufficient to improve gas control.

(3)

Drainage time exerts a strong regulating effect. A longer drainage time reduces gas pressure, with a typical staged decline. In the early stage of drainage, a high pressure gradient accelerates gas flow and causes a rapid pressure drop. In the later stage, the pressure difference gradually decreases, and the pressure reduction speed tends to be stable. Reasonably prolonging the drainage time, an approach second only to reducing the borehole spacing, can steadily reduce gas pressure to acceptable levels.

In practical engineering applications, borehole spacing should be regarded as the primary optimization index to improve gas drainage efficiency. A scientific and reasonable drainage cycle shall be formulated to sustain the long-term and stable operation of drainage work. Since borehole diameter has a negligible regulatory effect, conventional standard parameters can be adopted in field construction without additional modification. This optimization scheme can ensure favorable gas drainage performance, reduce construction difficulty and engineering investment, and possesses prominent practical value for on-site production.