Optimization and Application of Drilling Parameters Based on Gas–Solid Coupling Simulation

Abstract

The layout of directional high-level long boreholes in fracture zones for extracting pressure-relieved gas from goaf is a key technology to address the gas concentration exceedance in upper corners. To solve the gas exceedance issue at Fengtai Mine’s upper corner, this study established a gas–solid coupling model using COMSOL Multiphysics 6.3 based on actual mine parameters. The research investigated the influence patterns of different extraction parameters (negative pressure, borehole diameter, and extraction duration) on coal seam gas pressure and effective extraction radius (critical gas pressure 0.74 MPa). The results demonstrate the following. The effective extraction radius shows positive correlations with extraction negative pressure, borehole diameter, and extraction time while exhibiting a negative correlation with gas pressure. When borehole diameter exceeds 203 mm, extraction negative pressure surpasses 25 kPa, and extraction duration extends beyond 90 days; the effective extraction radius stabilizes, with the gas pressure influence range ceasing to decrease significantly with further parameter increases. Field validation results showed that, during the observation period, both pure gas extraction volume and mixed gas volume exceeded those of high-level drainage galleries. The gas concentrations in both the upper corner and return airflow remained within safe limits, effectively resolving the gas exceedance issue. This achievement not only established an efficient gas control system for the Fengtai Mine but also provides valuable parameter optimization methods and engineering experience for similar coal mines. The implementation has significantly enhanced gas control efficiency and safety production levels in the mining area.

1. Introduction

With the continuous development of the economy, coal resources have long maintained a dominant position in China’s energy system and remain central in the primary energy consumption structure [1,2]. As shallow coal resources gradually deplete and mining depths continue to increase, coal mines are commonly confronted with complex “three highs and one low” geological conditions—specifically, high tectonic stress, high gas pressure, high formation temperature, and low permeability [3,4,5]. These conditions significantly increase the probability of coal–rock–gas dynamic disasters. The instantaneous release of enormous energy not only severely threatens the safety of underground workers but also tends to trigger chain reactions, such as mine ventilation system failures and equipment damage, making it the primary technical bottleneck restricting safe and efficient coal resource extraction [6]. The arrangement of directional high-level long boreholes in overlying strata for pressure-relief gas drainage enables coordinated coal and gas extraction, effectively addressing this challenge [7]. Directional high-level long boreholes demonstrate technical advantages, including rapid drilling speed, low construction costs, high drainage efficiency, and effective mitigation of mining succession tensions [8]. Therefore, research on the layout horizons and parameters of such boreholes holds significant importance for resolving gas overlimit issues and guiding subsequent working face arrangements.

Yang et al. [9] combined a gas pressure drop method with borehole gas flow analysis to determine the effective drainage radius of gas extraction boreholes in Tian’an Coal Mine through simultaneous measurement of gas pressure and flow in pressure-testing holes. Xu et al. [10] derived the effective drainage radius and critical gas pressure in the Wudong mining area, analyzing gas pressure variations under different initial gas pressures, borehole diameters, and drainage negative pressures using COMSOL Multiphysics simulation. Wang et al. [11] designed orthogonal experiments to analyze the influence of various borehole parameters on effective drainage radius, identifying optimal parameters validated through grey correlation analysis and a sulfur hexafluoride (SF₆) tracer method. Zhang and Wang [12] established a dynamic permeability model and employed FLAC3D numerical simulation to optimize borehole diameter and spacing, achieving a 29.7% improvement in gas concentration through their research outcomes. Yan et al. [13] developed a gas–solid coupling model incorporating coal–rock deformation and matrix-fracture seepage-diffusion fields, demonstrating that equilateral triangular borehole arrangements effectively eliminate drainage blind zones. Xue et al. [14] constructed a hydraulic fracturing gas–solid coupling model, revealing fracture development patterns in overlying strata and clarifying coal seam parameter impacts on fracturing-gas drainage processes. Zhang et al. [15] investigated a model considering matrix-fracture interactions and fluid exchanges. Through COMSOL simulations and field tests, Zhou et al. [16] optimized borehole spacing and negative pressure in Inner Mongolia mines while establishing a three-dimensional gas distribution model for goaf areas. Shang et al. [17] identified enhanced initial permeability as the key factor for improving drainage radius. Chen’s experiments [18] under confining pressure revealed decreasing coal permeability with increasing pore pressure during gas injection. Mohammad Hatami et al. [19] developed a numerical simulation model considering viscous flow and Knudsen diffusion and investigated the effects of several factors, such as nanometer pore size, pressure-dependent viscosity, number of adsorbed gas layers, and temperature, on shale permeability. Javadpoure, F [20] proposed an equation for gas flow in nanopores based on Kundsen diffusion as well as a slip flow to study the influence of pore size on the variation in permeability.

The aforementioned research achievements have provided theoretical foundations for the efficient application of gas drainage. However, gas flow in coal seams constitutes a complex physical process. Most researchers primarily focus on constructing theoretical analytical models to investigate porosity and permeability evolution during gas drainage or studying the impact of individual parameters on drainage efficiency. Consequently, it is imperative to conduct comprehensive simulation analyses integrating multiple influencing factors to determine optimal borehole parameters and validate their rationality through engineering practices.

To address the unresolved problem of excessive gas concentration in the upper corner of Fengtai coal mine in Pingding County, Yangquan City, Shanxi Province, China, this study used COMSOL numerical simulation software to analyze the variations in gas pressure and effective extraction radius under different borehole parameters, including diameter, negative extraction pressure, and extraction duration. This study determined the optimal borehole configuration through systematic simulation and subsequently carried out on-site verification through engineering practice to validate the theoretical results.

2. Coupled Gas–Solid Modeling of Gas Extraction

2.1. Physical Model

Gas exists in coal seams through multiple occurrence states. The primary form is the adsorbed state, where gas molecules are tightly bound to micropore surfaces of coal matrices via van der Waals forces, forming monolayer or multilayer adsorption. The secondary form is the free state, where gas resides as a free phase within fractures, pores, and other interconnected voids, its distribution governed by pore connectivity and external pressure. A minimal fraction exists as a dissolved state, dissolved in water or organic matter within the coal seam. The internal fracture network and pore structure of coal collectively form the gas storage and migration system [21,22].

Gas migration in coal involves multiple coupled mechanisms. Under undisturbed conditions, adsorbed gas remains in equilibrium with the coal matrix. However, mining-induced disturbances, temperature fluctuations, or pressure changes trigger desorption, converting adsorbed gas into free gas. Free gas migrates via seepage through fractures under pressure gradients, while in micropores or low-permeability zones, diffusion dominates due to concentration gradients [22]. Coal matrix swelling caused by stress redistribution or gas desorption dynamically alters fracture apertures and pore connectivity, creating a “self-regulating” effect on migration pathways. Additionally, geological structures (e.g., faults, folds) guide fracture development, significantly influencing gas migration routes, with localized stress concentrations potentially forming preferential flow channels. Thus, gas occurrence and migration represent a dynamic equilibrium governed by adsorption–desorption, diffusion–seepage, coal deformation, and geological conditions.

To simplify the complex gas migration process, the following assumptions are adopted in this study [23]:

(1)

The coal body is a continuous, homogeneous medium, ignoring the inhomogeneity of the microscopic pore structure;

(2)

The deformation of the coal body is much smaller than its geometric size, ignoring its plastic deformation and large deformation;

(3)

The mechanical properties of the coal rock body are isotropic, ignoring the anisotropic characteristics of joints and fissures;

(4)

Only gas flow is considered, ignoring the influence of water or other fluids;

(5)

Gas seepage in the coal body conforms to Darcy’s law, and gas diffusion conforms to Fick’s law;

(6)

The temperature is constant during gas flow.

2.2. Mathematical Model

2.2.1. Gas Diffusion Control Equation

The porosity, permeability, initial permeability, and initial porosity of gas in a coal body conform to the cubic law. The cubic law formula is shown in Equation (1):

$${\displaystyle \frac{\mathsf{\phi }}{{\mathsf{\phi }}_0}}={\displaystyle \frac{{\mathsf{\varphi }}^3}{{\mathsf{\varphi }}_0^3}}$$

(1)

where $\mathsf{\phi }$ is permeability; $\mathsf{\varphi }$ is porosity; ${\mathsf{\phi }}_0$ is initial permeability; and ${\mathsf{\varphi }}_0$ is initial porosity.

During gas extraction, mass exchange occurs between the coal matrix and the fissures. The mass exchange equation is shown in Equation (2):

$${\mathrm{Q}}_{\mathrm{S}}=\mathrm{D}\mathsf{\xi }\left({\mathsf{\rho }}_{\mathrm{m}}-{\mathsf{\rho }}_{\mathrm{f}}\right)$$

(2)

where ${\mathrm{Q}}_{\mathrm{S}}$ is the mass exchange between the coal matrix and the fissure; D is the gas diffusion coefficient; $\mathsf{\xi }$ is the shape factor of the coal matrix; and ${\mathsf{\rho }}_{\mathrm{m}}$ and ${\mathsf{\rho }}_{\mathrm{f}}$ are the densities of gas in the coal matrix and the fissure in the standard state.

The coal matrix shape factor needs to be determined by adsorption tests. The coal matrix shape factor is calculated as shown in Equation (3):

$$\mathsf{\xi }={\displaystyle \frac{1}{\mathsf{\tau }\mathrm{D}}}$$

(3)

where $\mathsf{\tau }$ is the adsorption time.

Associative Formulas (2) and (3) are derived as follows:

$${\mathrm{Q}}_{\mathrm{S}}={\displaystyle \frac{1}{\mathsf{\tau }}}\left({\mathsf{\rho }}_{\mathrm{m}}-{\mathsf{\rho }}_{\mathrm{f}}\right)$$

(4)

Under ideal conditions and ignoring the effect of temperature variations, the gas in the coal seam conforms to the ideal gas equation of state. The density of gas in the coal matrix is shown in Equation (5), and the density of gas in the coal fissure is shown in Equation (6):

$${\mathsf{\rho }}_{\mathrm{m}}={\displaystyle \frac{{\mathrm{M}}_{\mathrm{c}}}{\mathrm{RT}}}{P}_m={\displaystyle \frac{{\mathrm{M}}_{\mathrm{c}}}{{\mathrm{V}}_{\mathrm{m}}}}$$

(5)

$${\rho }_f={\displaystyle \frac{M_c}{RT}}·P_f$$

(6)

where ${\mathrm{M}}_{\mathrm{c}}$ is the molar mass of gas; $\mathrm{R}$ is the ideal gas molar constant; $\mathrm{T}$ is the coal seam temperature; ${\mathrm{P}}_{\mathrm{m}}$ and ${\mathrm{P}}_{\mathrm{f}}$ are the coal matrix and fissure gas pressures; and ${\mathrm{V}}_{\mathrm{m}}$ is the molar volume of gas in the standard state.

The total mass of gas within the coal matrix consists of both adsorbed and free gas [10]. The total mass of gas in the coal matrix is calculated as shown in Equation (7):

$${\mathrm{m}}_{\mathrm{m}}={\mathrm{m}}_{\mathrm{mm}}+{\mathrm{m}}_{\mathrm{mf}}={\displaystyle \frac{{\mathrm{M}}_{\mathrm{c}}{\mathsf{\rho }}_{\mathrm{c}}}{{\mathrm{V}}_{\mathrm{m}}}}{\displaystyle \frac{{\mathrm{V}}_{\mathrm{L}}{\mathrm{P}}_{\mathrm{m}}}{{\mathrm{P}}_{\mathrm{L}}+{\mathrm{P}}_{\mathrm{m}}}}+{\displaystyle \frac{{\mathsf{\varphi }}_{\mathrm{f}}{\mathrm{M}}_{\mathrm{c}}{\mathrm{P}}_{\mathrm{m}}}{\mathrm{RT}}}{\mathrm{v}}_{\mathrm{f}}=-{\displaystyle \frac{{\mathsf{\phi }}_{\mathrm{f}}}{\mathsf{\mu }}}\nabla {\mathrm{P}}_{\mathrm{f}}$$

(7)

where ${\mathsf{\rho }}_{\mathrm{c}}$ is the density of coal; ${\mathrm{V}}_{\mathrm{L}}$ is the Langmuir volume constant; and ${\mathrm{P}}_{\mathrm{L}}$ is the Langmuir pressure constant.

Mass exchange of gas in the coal matrix and coal fissures follows the law of conservation of mass. The law of conservation of mass is shown in Equation (8):

$${\displaystyle \frac{\partial {\mathrm{m}}_{\mathrm{m}}}{\partial \mathrm{t}}}=-{\mathrm{Q}}_{\mathrm{S}}=-{\displaystyle \frac{{\mathrm{M}}_{\mathrm{c}}}{\mathsf{\tau }\mathrm{RT}}}\left({\mathrm{P}}_{\mathrm{m}}-{\mathrm{P}}_{\mathrm{f}}\right)$$

(8)

The diffusion equation of gas in the coal matrix is obtained by joining Equations (7) and (8). The gas diffusion equation in the coal matrix is shown in Equation (9):

$${\displaystyle \frac{\partial }{\partial \mathrm{t}}}\left({\displaystyle \frac{{\mathrm{M}}_{\mathrm{c}}{\mathsf{\rho }}_{\mathrm{c}}}{{\mathrm{V}}_{\mathrm{m}}}}{\displaystyle \frac{{\mathrm{V}}_{\mathrm{L}}{\mathrm{P}}_{\mathrm{m}}}{{\mathrm{P}}_{\mathrm{L}}+{\mathrm{P}}_{\mathrm{m}}}}+{\displaystyle \frac{{\mathsf{\varphi }}_{\mathrm{f}}{\mathrm{M}}_{\mathrm{c}}{\mathrm{P}}_{\mathrm{m}}}{\mathrm{RT}}}\right)=-{\displaystyle \frac{{\mathrm{M}}_{\mathrm{c}}}{\mathsf{\tau }\mathrm{RT}}}\left({\mathrm{P}}_{\mathrm{m}}-{\mathrm{P}}_{\mathrm{f}}\right)$$

(9)

2.2.2. Equation of Control for Gas Seepage

Gas seepage in coal fractures conforms to Darcy’s law. Darcy’s law is shown in Equation (10):

$${\mathrm{v}}_{\mathrm{f}}=-{\displaystyle \frac{{\mathsf{\phi }}_{\mathrm{f}}}{\mathrm{u}}}\nabla {\mathrm{P}}_{\mathrm{f}}$$

(10)

where ${\mathrm{v}}_{\mathrm{f}}$ is the gas seepage velocity and $\mathrm{u}$ is the gas dynamic viscosity coefficient.

According to the law of conservation of mass, the difference between the mass of gas diffusing from the coal matrix into the coal fissures and the mass of gas seeping from the coal fissures into the coal matrix is the amount of change in the coal seam gas. The formula for calculating the amount of gas change in the coal seam is shown in Equation (11), and the formula for calculating the gas content in the coal fissure is shown in Equation (12):

$${\displaystyle \frac{\partial {\mathrm{m}}_{\mathrm{f}}}{\partial \mathrm{t}}}+\nabla \left({\mathrm{v}}_{\mathrm{f}}{\mathsf{\rho }}_{\mathrm{f}}\right)={\mathrm{Q}}_{\mathrm{S}}$$

(11)

$${\mathrm{m}}_{\mathrm{f}}={\displaystyle \frac{{\mathsf{\varphi }}_{\mathrm{f}}{\mathrm{M}}_{\mathrm{c}}{\mathrm{P}}_{\mathrm{f}}}{\mathrm{RT}}}$$

(12)

The gas seepage equation within the fissure is obtained by associating Equations (9)–(12) when the effect of temperature variation is neglected. The coal fissure gas seepage equation is shown in Equation (13):

$${\mathsf{\varphi }}_{\mathrm{f}}{\displaystyle \frac{\partial {\mathsf{\rho }}_{\mathrm{f}}}{\partial \mathrm{t}}}-\nabla \left({\displaystyle \frac{{\mathsf{\phi }}_{\mathrm{f}}}{\mathrm{u}}}\nabla {\mathrm{P}}_{\mathrm{f}}{\mathsf{\rho }}_{\mathrm{f}}\right)=--{\displaystyle \frac{1}{\mathsf{\tau }}}\left({\mathsf{\rho }}_{\mathrm{m}}-{\mathsf{\rho }}_{\mathrm{f}}\right)$$

(13)

2.2.3. Coal Body Deformation Control Equation

After the coal body is affected by mining, the original stress equilibrium state is broken, and the coal body is deformed under the influence of mining stress and ground stress. The geometric equation of the coal body is shown in Equation (14):

$${\mathsf{\epsilon }}_{\mathrm{ij}}={\displaystyle \frac{{\mathsf{\mu }}_{\mathrm{ij}}+{\mathrm{u}}_{\mathrm{ji}}}{2}}$$

(14)

where ${\mathsf{\epsilon }}_{\mathrm{ij}}$ is the coal body strain tensor; $\mathsf{\mu }$ is the displacement component; and $\mathrm{i}$ and $\mathrm{j}$ are the horizontal and vertical directions, respectively.

Gas-bearing coals are in a state of stress equilibrium. The coal body stress balance equation is shown in Equation (15):

$${\mathsf{\sigma }}_{\mathrm{ij},\mathrm{j}}=-{\mathrm{F}}_{\mathrm{i}}$$

(15)

where ${\mathsf{\sigma }}_{\mathrm{ij},\mathrm{j}}$ is the stress tensor component and ${\mathrm{F}}_{\mathrm{i}}$ is the volumetric force component.

In the previous section, it is assumed that the coal rock body is isotropic material, and the effect of temperature change is neglected; therefore, its deformation follows Hooke’s law, and in the three-dimensional coordinate system, the deformation components of the coal rock body are the same in the x, y, and z directions. The coal body eigenstructure equation is shown in Equation (16) [24]:

$${\mathsf{\epsilon }}_{\mathrm{i},\mathrm{j}}={\displaystyle \frac{{\mathsf{\sigma }}_{\mathrm{i},\mathrm{j}}}{2\mathrm{G}}}-\left({\displaystyle \frac{1}{6\mathrm{G}}}-{\displaystyle \frac{1}{9\mathrm{K}}}\right){\mathsf{\sigma }}_{\mathrm{jj}}{\mathsf{\delta }}_{\mathrm{ij}}+{\displaystyle \frac{\mathsf{\alpha }}{3{\mathrm{K}}_{\mathrm{m},\mathrm{i}}}}{\mathrm{P}}_{\mathrm{m},\mathrm{i}}+{\displaystyle \frac{\mathsf{\beta }}{3\mathrm{K}}}{\mathrm{P}}_{\mathrm{f},\mathrm{i}}{\mathsf{\delta }}_{\mathrm{ij}}+{\displaystyle \frac{{\mathsf{\epsilon }}_{\mathrm{s}}}{3}}{\mathsf{\delta }}_{\mathrm{ij}}$$

(16)

where $\mathrm{G}=\mathrm{E}/2\left(1+\mathsf{\upsilon }\right)$ is the shear modulus of the coal rock mass; $\mathrm{K}=\mathrm{E}/3\left(1-2\mathsf{\upsilon }\right)$ is the bulk modulus of the coal rock mass; ${\mathsf{\epsilon }}_{\mathrm{s}}$ is the adsorption strain of the coal rock mass; $\mathsf{\alpha }=1-\mathrm{K}/{\mathrm{K}}_{\mathrm{m}}$ and $\mathsf{\beta }=1-\mathrm{K}/{\mathrm{aK}}_{\mathrm{m}}$ are the Biot effective stress coefficient of the coal matrix and fissures, respectively; $\mathrm{E}$ is the elastic modulus of the coal; and and $\mathsf{\upsilon }$ is the Poisson’s ratio.

The coal body deformation control equations can be obtained by associating Equations (14)–(16) [23]:

$${\mathrm{Gu}}_{\mathrm{i},\mathrm{jj}}+{\displaystyle \frac{\mathrm{G}}{1-2\mathsf{\upsilon }}}{\mathrm{u}}_{\mathrm{j},\mathrm{ji}}-{\mathsf{\alpha }\mathrm{P}}_{\mathrm{m},\mathrm{i}}-{\mathrm{P}}_{\mathrm{f},\mathrm{i}}-{\mathrm{K}\mathsf{\epsilon }}_{\mathrm{s},\mathrm{i}}+{\mathrm{F}}_{\mathrm{i}}=0$$

(17)

The combination of Equations (9), (13) and (17) is the gas extraction gas–solid coupling model.

3. Numerical Simulation

3.1. Geometric Modeling and Boundary Conditions

The three-dimensional geometric model was simplified to a two-dimensional planar model using COMSOL numerical simulation software. A square model with a side length of 10 m was established. The boundaries around the gas seepage field model were set as zero flux (used to simulate impermeable geologic barriers (e.g., dense rock formations, faults, or geologic formations) to stop gas flow), the left and right boundaries were set as roller supports (used to simulate a model that is constrained on both sides by the surrounding rock (e.g., horizontal geopathic stress effects) but can settle or expand in the vertical direction due to gas extraction), the upper boundary was applied with a constant load (vertical pressure applied to the top of the model to simulate self-weight or tectonic stresses in the overlying rock formation) of 6.3 Mpa, the lower boundary was set as a fixed support (acts on the bottom of the model to simulate the support of the upper strata by a stable rock layer unaffected by mining), and the boundaries of the extraction boreholes were set as the Dirichlet boundary conditions (used to simulate the active extraction of gas by negative extraction pressure in extraction boreholes).

In order to improve the accuracy and efficiency of the simulation, a triangular mesh was used to refine the model. Figure 1 shows the geometric model and boundary conditions.

3.2. Numerical Simulation Parameter Setting

Table 1. Model parameter settings.

Parameters	Numerical Value	Parameter Unit
Initial gas pressure of coal seam	1 × 106	Pa
Initial fracture rate	0.040
Initial permeability	3 × 10−17	m2
Initial porosity	0.10
Klinkenberg factor	1.44 × 105	Pa
Molecular mass of methane gas	16	g/mol
Gas state constant	8.413510	J/mol/K
Seam temperature	293	K
Methane kinetic viscosity coefficient	1.08 × 10−5	mu
Langmuir constant (limiting adsorption capacity)	0.02	m3/kg
Langmuir constant (pressure)	3.03	MPa
Molar volume of methane at standard conditions	22.4	L/mol
Apparent density of coal	1.41	kg/m3
Poisson’s ratio of coal	0.3	GPa
Limiting adsorption deformation	0.005
Modulus of elasticity of coal matrix	8200	MPa
Modulus of elasticity of coal	2800	MPa

lists the global parameters required for COMSOL Multiphysics numerical simulation software, with all parameters in the table being measured data from actual experiments.

4. Analysis of Numerical Simulation Results

The “Rules for Prevention and Control of Coal and Gas Outbursts” states that, when the gas pressure in a coal seam is greater than 0.74 Mpa or the gas content is greater than 8 m³/t, there is a danger of protrusion, and therefore, the reduction in gas to below 0.74 Mpa is used as a criterion for determining the effective extraction radius.

4.1. Analysis of the Effect of Negative Extraction Pressure on Gas Pressure

The simulated working conditions are as follows: the initial gas pressure is 1 Mpa: the negative pressure of extraction is set to 10 kPa, 15 kPa, 20 kPa, 25 kPa, 30 kPa, and 35 kPa; the diameter of the borehole is 120 mm; and the extraction time is 50 d.

Figure 2 shows the cloud diagram of gas pressure change in the coal body around the drill hole when the negative pressure of extraction is 10 kPa, 15 kPa, 20 kPa, 25 kPa, 30 kPa, and 35 kPa, respectively. According to the analysis of Figure 2, when extracting the gas from the coal body, due to the existence of the pressure difference between the negative pressure of extraction and the gas pressure of the coal seam, the gas pressure of the coal body around the drill hole decreases more, and the gas pressure of the coal body far away from the drill hole decreases slightly but is basically equal to the initial gas pressure of the coal seam. The gas pressure is slightly decreased but basically equal to the initial gas pressure of the coal seam, and the gas pressure is basically negatively correlated with the negative pressure of extraction.

Figure 3 shows the variation in effective extraction radius at different extraction negative pressures (10 kPa, 15 kPa, 20 kPa, 20 kPa, 25 kPa, 30 kPa) and at different extraction times (30 d, 50 d, 70 d), and

Table 2. Effective pumping radius over time.

Extraction Time	Effective Extraction Radius
30 d	1.39–1.55
50 d	1.96–2.40
70 d	2.87–4.38

shows the variation in effective extraction radius under different extraction times. According to Figure 3 and Table 2, it can be seen that the effective extraction radius changes in the range of 1.39 m–1.55 m, 1.96 m–2.40 m, and 2.87 m–4.38 m under the extraction times of 30 d, 50 d, and 70 d, corresponding to the negative pressures of 10 kPa, 15 kPa, 20 kPa, 25 kPa, 30 kPa, and 35 kPa respectively, and the effective extraction radius changes in the range of 1.39 m–1.55 m, 1.96 m–2.40 m, and 2.87 m–4.38 m, respectively, when the extraction time is the same; the higher the negative pressure of extraction, the larger the effective extraction radius is. When the extraction time is the same, the higher the negative pressure, the larger the effective extraction radius, but with the increasing negative pressure, the effective extraction radius increases, but when the negative pressure increases to a certain critical value, the effective extraction radius rate decreases significantly.

At a certain extraction time, when the negative extraction pressure varies between 10 kPa and 25 kPa, the faster the rate of gas pressure decrease around the borehole, the more obvious the growth rate of the effective extraction radius, but after the negative extraction pressure is greater than 25 kPa, with the increase in negative extraction pressure, the rate of gas pressure decreases, and the growth rate of the effective extraction radius decreases significantly.

In actual mine gas extraction, increasing the negative pressure of extraction will significantly increase equipment operation and maintenance costs, and the negative pressure of extraction will cause turbulence of the air flow in the working face [25]. Therefore, the best negative pressure for gas extraction should be 25 kPa.

4.2. Analysis of the Effect of Borehole Diameter on Gas Pressure

The simulated working conditions are as follows: initial gas pressure 1 Mpa; pumping negative pressure is 25 kPa; and borehole diameters are 120 mm, 153 mm, 203 mm, and 253 mm.

Figure 4 shows the cloud diagram of gas pressure change around the drill hole when the drill hole diameter is 120 mm, 153 mm, 203 mm, and 253 mm, respectively. Figure 5 shows the variation in effective extraction radius under different drill hole diameters. According to Figure 4 and Figure 5, the maximum effective extraction radius is 4.35 m, 4.58 m, 4.87 m, and 4.90 m when the diameter of the drill hole is 120 mm, 153 mm, 203 mm, and 253 mm, respectively, and the effective extraction radius is the smallest when the diameter of the drill hole is 120 mm and is the maximum when the diameter of the drill hole is 253 mm, which shows a positive correlation between the diameter of the drill hole and effective extraction radius. The effective extraction radius is the smallest when the borehole diameter is 120 mm and is the largest when the borehole diameter is 253 mm, and the positive correlation between the borehole diameter and the effective extraction radius is shown, but when the borehole diameter increases from 203 mm to 253 mm, the effective extraction radius only increases by 0.03 m, and the effective extraction radius has no obvious change.

In addition, in the actual drilling construction and subsequent gas extraction process, the increase in drilling diameter will lead to serious collapse and poor sealing effect [26]; the construction of the 253 mm drill hole needs to be reamed twice, and the reaming will affect the stability of the original drill hole. For the above numerical simulation analysis and the actual situation, the optimal diameter of the drill hole is 203 mm.

4.3. Analysis of the Effect of Extraction Time on Gas Pressure

The simulated working conditions are as follows: initial gas pressure 1 MPa; extraction negative pressure is 25 kPa; borehole diameter is 203 mm; and extraction time is 30 d, 60 d, 90 d, and 120 d.

Figure 6 shows the variation in gas pressure around the borehole at different extraction times (30 d, 60 d, 90 d, 120 d) when the diameter of the borehole is 203 mm and the negative extraction pressure is 25 kPa. Figure 7 shows the variation in gas pressure at different distances (0.5 m, 1.0 m, 1.5 m, 2.0 m, 2.5 m, 3.0 m, 3.5 m, 4.0 m, 4.5 m, 5.0 m) from the center of the borehole with different extraction times (30 d, 60 d, 90 d, 120 d). According to Figure 6 and Figure 7, it can be concluded that the longer the extraction time, the larger the decrease in gas pressure, the faster the decrease rate, and the larger the effective extraction radius, which is basically a positive correlation, and the change in gas pressure is more obvious with the increase in extraction time. When the extraction time is 30 d, the change in gas pressure is small, and it only decreases in the range of 2.5 m in the borehole, and there is no significant change in the gas pressure in the rest of the range; when the extraction time is 60 d, the effect of gas extraction improves compared to 30 d, and it can satisfy the expected effect of extraction, but the scope of influence of extraction is limited; when the extraction time is 90 d, the effect of extraction improves significantly compared to 60 d, and the scope of influence of extraction increases, but the extraction time increases, the effective extraction radius increases, and with the increase in extraction time, the gas pressure changes more significantly. When the extraction time is 90 d, the extraction effect is obviously improved compared with 60 d, and the influence range of extraction is increased, but after the extraction time is more than 90 d, the gas pressure decreases, and the influence range is obviously reduced.

Ideally, the longer the extraction time, the better the gas extraction effect, but in actual engineering practice, one needs to consider time, equipment operation, labor costs, and other factors. Increasing the extraction time will slightly improve the extraction effect but significantly increase the cost. Based on the principle of cost-effective optimization, the extraction time is 90 d.

5. Engineering Practice

5.1. Mine Overview and Drill Layout

Fengtai Coal Mine in Pingding County, Yangquan City, Shanxi Province, is currently mining the No. 15 coal seam, with an average dip angle of 5°, an average seam thickness of 6.06 m, and a maximum gas pressure of 1.0 MPa. According to the mine’s gas outflow prediction report, the gas content of the coal seam is 5.04 m³/t, and the maximum absolute gas outflow of the 15101 working face is 27.07 m³/min, which is the largest gas outflow of a mine in the world. Due to the existence of the 12#, 13#, and 14# unmineable neighboring coal seams in the 15101 working face, the mine is in danger of gas overlimit and coal and gas protrusion.

To address the aforementioned challenges, four directional high-level long boreholes were constructed in the Fengtai Coal Mine to mitigate the gas overlimit risks and reduce the coal and gas outburst potential. Integrated analysis of theoretical research and field conditions determined the optimal drainage parameters: a negative pressure of 25 kPa, borehole diameter of 203 mm, and extraction duration of 90 days, achieving an effective drainage radius of approximately 4.8 m. To ensure operational reliability while accounting for permeability variations in overlying strata, fault influences, and inter-borehole interference, the borehole spacing was finalized at 4 m, informed by empirical data from adjacent mines and theoretical safety margins.

The drilling arrangement is shown in plan view, and the sections are shown in Figure 8 and Figure 9.

Table 3. Directional high-level long borehole solid drilling parameters.

Drill Hole Number	Hole Diameter/mm	Drilling Depth/m	Distance to the Roof/m	Level Distance to the Lower Gang of the Return Trench/m
1#	203	329	39	28
2#	203	333	43	32
3#	203	342	47	36
4#	203	345	51	40

shows the actual drilling parameters of the directional high-level long boreholes.

5.2. Analysis of Pumping Effects and Technological Advantages

5.2.1. Analysis of Extraction Effects

For working face 15101, the mineable length is approximately 270 m, with a daily advance rate of 3.4 m. The directional high-level long borehole coverage section was fully extracted within 80 days of mining activity. Consequently, an 80-day observation period was conducted on the gas extraction performance of the directional boreholes, during which key parameters including pure gas extraction volume, mixed gas volume, gas concentration at the upper corner, and gas concentration in the return airflow were systematically recorded.

Figure 10 illustrates the variation curves of mixed gas volume (pure gas volume) in the directional high-level long borehole extraction section, while Figure 11 presents the gas concentration variation curves at the upper corner (return airflow).

According to the analysis of Figure 10 and Figure 11, the mixed volume of the directional high-level long boreholes ranges from 16.50 m³/min to 24.21 m³/min, with an average mixed volume of 21.16 m³/min; the pure volume ranges from 0.93 m³/min to 11.14 m³/min, with an average pure volume of 8.23 m³/min; the gas concentration in the upper corner ranges from 0.14% to 0.25%, and that in the return airflow ranges from 0.03% to 0.10%. The gas concentration in the upper corner ranges from 0.14% to 0.25%, and the gas concentration in the return airflow ranges from 0.03% to 0.10%.

The mixed volume and pure volume of gas extraction from the directional high-level long drill holes will change with the advancement of the working face. At the early stage of work face mining, the coal seam and overlying rock layer are less affected by mining, and due to the small advancement distance of the work face, the fissure development of the overlying rock layer is incomplete, the tiny fissures formed between the collapse zone and the fissure zone are not effectively guided, and the unpressurized gas affected by the mining is unable to be extracted in the fissure zone under the negative pressure.

Due to the air leakage in the mining area, the gas accumulates in the upper corner to form a vortex, which is not easy to be extracted; therefore, in the 1–10 d observation stage, the pure and mixed amount of gas extracted is small, and the concentration of gas in the upper corner rises. As the working face advances continuously, the area of the overhanging airspace area increases continuously, and when the self-weight of the rock layer overlying the airspace area exceeds its strength limit, the roof plate breaks and collapses under the initial pressure, the fissures in the rock layer overlying the airspace area are fully developed, and the number of fissures increases and conduction occurs so that the pure quantity and mixed quantity of the gas extracted increases continuously. After 14 days of mining, with the periodic collapse of the overlying rock layer, the pure volume and mixed volume of gas extraction showed cyclic changes as the working face advanced. Observation results show that, during the observation period, after the initial collapse of the roof slab, the extraction and mixing volume was stabilized at about 21 m³/min. During the period of 20 to 34 days, due to the hardness of the roof layer in this section and the increase in the cyclic pressure step, the roof slab failed to collapse in time, which resulted in the lower extraction and mixing volume, but at this stage, the gas outflow from the K₂ and K₃ limestone above the face was larger; therefore the change in the pure extracting volume was smaller. During the period of 34 days to 70 days, the top slab collapsed in time through manual intervention to force the roof release, and the extraction mixed volume increased significantly.

At the later stage of the extraction phase (71 to 80 days), as the working face was about to advance to the stopping line, there were some abandoned roadways around the drill holes, which caused the gas to leak into the abandoned roadways, and the directional high-level long boreholes could not effectively extract the gas in the fissure zone; therefore, the extraction mix and the pure volume of the extraction showed a significant downward trend during the period of 71 to 80 days.

5.2.2. Comparison of Technical Advantages

(1) Deploying directional high-level long boreholes via directional drilling rigs to extract pressure-relief gas at the upper corner eliminates the risks associated with constructing high-level drainage galleries, such as accidental exposure to outburst-prone coal seams, faults, or aquifers during roadway development. This approach significantly enhances mine safety and ensures efficient production continuity.

(2) Unlike fixed-location high-level drainage galleries, directional boreholes can be strategically positioned across different strata horizons based on site-specific geological conditions. This enables precision extraction of gas from multiple emission sources, effectively maintaining low gas concentrations in the upper corner, working face, and return airflow, thereby reducing drainage workload.

(3) The adoption of directional high-level long boreholes significantly enhances operational productivity, with directional drilling rigs achieving a daily advance rate of 80–100 m, far exceeding the 5 m/day rate of conventional rock roadway development. This high-efficiency drilling method allows for parallel execution of gas drainage and roadway layout tasks, thereby substantially shortening project timelines. Additionally, the elimination of rock roadway excavation reduces associated infrastructure costs (e.g., pipelines, ventilation systems) and minimizes waste rock generation, lowering both haulage expenses to the surface and long-term maintenance demands, collectively yielding considerable economic advantages.

(4) Directional boreholes minimize surface waste rock stockpiling, preventing environmental hazards such as spontaneous combustion of waste rock or contamination of soil and groundwater by sulfur-bearing toxic substances, thereby delivering substantial ecological and societal benefits.

(5) By eliminating roadway development, waste rock haulage, conveyor system management, and long-term roadway maintenance, directional boreholes drastically lower operational and administrative costs compared to traditional gallery-based systems.

According to

Table 4. Comparative analysis of technical advantages.

Technology Type	Directional High-Level Long Boreholes	High-Level Drainage Galleries
Roadway section area/m2		5.5
Quantity of work/m	1349	300
Project unit price/CNY	749.86	8000
Total project price/CNY	1,011,600	2,400,000
Amount of gangue/ton		2733.5
Gangue treatment cost/CNY		218,680
Construction period/d	15	84

, the use of directional high-level long boreholes instead of high-level drainage galleries for gas extraction can reduce the construction cost by 69.42%, reduce the amount of gangue by 2733.5 tons, and reduce the cost of gangue transportation by 218,680 CNY, and the construction period can be saved by 82.14%.

6. Conclusions

By establishing a gas–solid coupling model for gas drainage and employing COMSOL numerical simulation software, this study investigates the impacts of extraction negative pressure, borehole diameter, and extraction duration on coal seam gas pressure. Field validations were conducted, yielding the following conclusions:

(1) By analyzing the change in gas pressure and effective extraction radius around the drill hole using the three influencing factors of different drill hole diameters, extraction times, and negative pressures, we came up with the optimal drill hole arrangement parameters: drill hole diameter of 203 mm, negative pressure of 25 kPa, and extraction time of 90 d.

(2) The optimal drilling arrangement parameters obtained from the numerical simulation results are used to verify the extraction effect in the Fengtai coal mine through 80 days of observation and data recording of the pure volume of gas extraction, mixing volume, the upper corner, and the concentration of gas in the return airflow: the mixing volume of the directional high-level long boreholes ranged from 16.50 m³/min to 24.21 m³/min, and the pure volume of the extraction ranged from 0.93 m³/min to 11.14 m³/min; the gas concentration in the upper corner ranged from 0.14% to 0.25%, and the gas concentration in the return airflow ranged from 0.03% to 0.10%. The gas concentration in the upper corner was between 0.14% and 0.25%, and the gas concentration in the return airflow was between 0.03% and 0.10%. The gas limit in the 15101 face was not exceeded, which further verified the rationality of the drilling parameters.

(3) Adopting directional high-level long boreholes instead of high-level drainage galleries for gas extraction can reduce the construction cost by 69.42%, reduce the amount of gangue by 2733.5 tons, reduce the cost of gangue transportation by 218,680 CNY, and reduce the construction time by 82.14%.

Deficiencies in the current research are as follows:

(1) The gas–solid coupling model fails to consider temperature variations’ impacts on gas adsorption–desorption behavior. In practical coal mining scenarios, dynamic temperature fluctuations during extraction activities may influence gas migration patterns.

(2) The adoption of a two-dimensional planar model overlooks the effects of vertical permeability and three-dimensional fracture network distribution on gas drainage efficiency.

(3) Field validations were exclusively conducted in a single mine (Fengtai Coal Mine), lacking verification in complex geological conditions (e.g., high tectonic stress zones, multi-fault coal seams), thereby limiting the universal applicability of the research findings.

(4) There was a failure to place drill holes that effectively detect gas pressure to validate the rationality of the model

Future research directions are as follows:

(1) Develop a three-dimensional gas–solid coupling model incorporating heterogeneous coal masses, large deformation theory, temperature fields, dynamic permeability, and geological structures to enhance numerical simulation authenticity for gas drainage.

(2) Validate model rationality in mines featuring multiple faults, high geothermal gradients, and intense tectonic stresses while investigating correction requirements for optimal borehole parameters under diverse geological conditions.

(3) Establish a parameter adjustment database by compiling research outcomes from varied mine types, ultimately formulating standardized gas drainage technical specifications adaptable to different geological settings.

(4) Lay out the effective detection pressure monitoring drill holes and organize the subsequent workings and similar geological conditions of the mine pumping data for comparison to verify the rationality of the model and the applicability of the research results.