Threshold Determination for Effective Water Injection in Coal Seams: Insights from Numerical Simulation

Abstract

Coal seam water injection is the most basic and effective dust control technology used on the coal mining face. Numerical simulations are helpful for predicting the humidity range of coal seam water injection. The results can provide guidance for the field design of coal seam water injection process parameters. In order to understand the influence of coal seam water injection pressure and water injection time on the coal seam wetting effect, this paper uses the Fluent 17.0 software system to study the process parameters of the coal seam water injection seepage process under different conditions. It is found that in the process of coal seam water injection, with the increase in water injection pressure and the prolongation of water injection time, there is a specific threshold value for the change in coal seam permeability. Only when the water injection pressure and time increase to the threshold value will the permeability of the coal seam be significantly enhanced and the wetting effect improved. The pressure threshold of the mine is 15 MPa–20 MPa, and the time threshold is the first 42 h.

1. Introduction

Coal is the primary energy source in China, accounting for approximately two-thirds of the country’s total primary energy consumption [1,2,3,4,5]. Coal mining processes can lead to a variety of environmental issues and natural disasters, including roof collapse, natural gas leaks, fires, and dust pollution [6,7,8]. In recent years, the rapid development of coal mining technology and the widespread use of high-powered mining machinery have dramatically increased the amount of dust produced in coal mines. This has resulted in a deteriorating work environment, posing a serious threat to the safety of mining operations and the health of workers [9,10,11,12].

According to the occupational disease statistics report released by the National Health Commission of China, the number of new annual pneumoconiosis cases in China is significant. In 2018, there were 23,497 new cases of occupational diseases, of which 19,468 were pneumoconiosis, which accounted for 82.85% of the total reported cases. In terms of industrial distribution, new pneumoconiosis cases are mainly concentrated in the coal mining and non-ferrous metal mining industries, with the coal mining industry accounting for approximately 40% of the total reported pneumoconiosis cases [13,14,15].

Currently, coal seam water injection dust reduction is considered to be the most proactive and effective method of controlling dust sources at their origin. This method is highly valued and widely promoted in various countries worldwide. By pre-wetting the coal seam through water injection before mining and excavation activities, the amount of dust generated during these operations can be effectively reduced [16,17,18,19,20,21]. As early as the 1960s, the German Mining Authority mandated water injection before mining operations in coal mines [22]. Coal seam gas injection equipment includes pneumatic pumps, constant flow control valves, and hydraulic expansion sealing devices [23]. The Institute of Mining Mechanics at the Ukrainian Academy of Sciences developed the YHP-type water injection pump, which can automatically adjust water injection parameters based on the permeability characteristics of the coal seam [24]. The French Coal Center developed flow controllers and continuous water injection devices to automate coal seam water injection [25]. In the 1970s, China began promoting the use of coal seam water spray dust suppression technology [26]. Zhou et al. [27] analyzed the influence of water injection systems and pressurization methods on the dust suppression effect of water injection in longwall coal seam gas. Zhou et al. [28] used a numerical method, combining the stress–strain relationship with the computational fluid dynamics software ANSYS, to simulate the pressure field and velocity field of the coal seam under different water injection pressures to determine the optimal water injection parameters. Zhang [29] analyzed the three stages of hydraulic wetting—wetting, soaking, and spreading—using the Gibbs function, supplementing the mechanism of hydraulic wetting to prevent coal and gas outbursts. Li et al. [30] used the MTS electro-hydraulic servo rock testing system to study the permeability characteristics of deep coal and rock samples under high pore water pressure. Wang [31] proposed a method of using CO₂ cyclic cold soaking to improve the water absorption rate and wetting efficiency of coal. Xu et al. [16] used CFD numerical simulations to consider the deformation parameters of coal and obtained the stress and strain laws of the coal seam water injection effect on the coal seam. Sun [32,33] introduced 2-acrylamido-2-methylpropanesulfonic acid and itaconic acid into the polymer chain of sodium alginate in different combinations and added the anionic surfactant sodium dodecyl sulfate and the non-ionic surfactant fatty alcohol polyoxyethylene ether in different proportions to obtain three high-efficiency wetting promoters.

Coal seam water injection has long been recognized as an effective dust control and permeability enhancement technique in coal mining operations. Previous studies have explored various aspects of this process, including the effects of injection pressure, water flow rates, and the mechanical properties of coal seams. Notable works have focused on optimizing water injection parameters through experimental and simulation methods to improve the efficiency and safety of mining operations. However, despite these advances, there remains a significant gap in understanding regarding the precise thresholds of injection pressure and time that are critical for achieving optimal permeability enhancement. Therefore, this paper intends to conduct a numerical simulation study on the in-seam deep hole sealing area of difficult-to-inject coal seams. Based on this, it will utilize computational fluid dynamics software to study the radial seepage pressure field, seepage velocity field, and seepage flow distribution under different injection times and pressures. Additionally, it will investigate the pressure and time thresholds of injection process parameters to provide theoretical guidance for improving permeability enhancement technology in difficult-to-inject coal seams and reducing the occupational hazard of dust in mining and excavation faces.

2. Numerical Simulation Modeling and Boundary Conditions

Both physical experiments and numerical simulations serve as effective alternatives to directly monitoring the permeability enhancement effects of hydraulic fracturing in difficult-to-inject coal seams. They are widely employed in dust suppression research. As Fluent 17.0 software inherently incorporates heterogeneity coefficients, it can accurately simulate the non-uniformity of rock and coal masses. Roof fracturing for permeability enhancement involves initially fracturing the roof strata to establish a water injection pathway between the roof and the coal seam, followed by permeability enhancement of the coal seam. Given the involvement of multiple rock components in the simulation process, Fluent 17.0 software was chosen for this numerical simulation analysis.

2.1. Physical Model

Geological data from a mining face in Shanxi were collected and analyzed. Using the Fluent 17.0 software, a three-dimensional seepage model of a water-injected coal seam as a porous medium was established. We selected a rectangular parallelepiped with dimensions of 100 m × 150 m × 3 m as the calculation area. A hole with a length of 85 m, a diameter of 75 mm, and a sealed length of 10 m was modeled with the starting face of the injection hole centered 1.5 m above the bottom of the coal seam (i.e., the center of the borehole is located at the center of the side of the coal seam). The mesh software was used to divide the calculation area into an unstructured tetrahedral mesh. According to calculations, the total number of nodes in the unstructured tetrahedral mesh is 49,312 and the total number of elements is 255,360. To simplify the simulation process, the mesh was divided from the radial plane of the borehole as shown in Figure 1:

Darcy’s law: Darcy’s law applies to low-speed fluid flow in porous media. The expression for Darcy’s law in one-dimensional form is

$$q=vS=-{\displaystyle \frac{\pi r^{2}K}{\mu }}{\displaystyle \frac{𝜕p}{𝜕\chi }}={\displaystyle \frac{\pi r^{2}K\left(p_0-p_1\right)}{\mu L}}$$

(1)

In the equation, v represents the seepage velocity, which is the volume of fluid passing through a unit cross-sectional area per unit time, expressed in m³/(s m²); q is the water injection rate, in m³/s; S is the cross-sectional area, in m²; r is the radial distance from the center of the borehole, in cm; p = p(r,t) is the fluid pressure at a distance r (m) from the borehole and at time t (s), in atm; p_i is the initial fluid pressure in the original formation, in atm; K is the permeability of the formation, in Darcy; L is the length, in cm (μ, pa*s).

Equation of state: The equation of state describes the relationship between the density $\rho$ of a substance and its pressure p and temperature T. Fluid seepage in the seam can be regarded as taking place under isothermal conditions, so the equation of state only needs to state the relationship between fluid and pressure. The equation of state for a fluid is

$$\rho ={\rho }_0{e}^{C\left(\rho -{\rho }_0\right)}$$

(2)

where C is the compression coefficient, in atm⁻¹; $\rho$ is the density of the fluid, in g/cm³, ${\rho }_0$ is the value of ${\rho }_0$ at P = P₀.

Continuity equation: the continuity equation of radial flow is

$${\displaystyle \frac{1}{r}}{\displaystyle \frac{𝜕\left(r{v}_t\rho \right)}{𝜕r}}={\displaystyle \frac{𝜕\left(\phi \rho \right)}{𝜕t}}$$

(3)

where the porosity of the formation is written as a %; $\rho$ is the density of the fluid, in g/cm; v_t is the radial percolation volume velocity of the inflow unit, in cm³/(s cm²); t is the time, in second; and r is the distance from the borehole axis along the radial direction to a point, in cm.

Differential equations: Based on Darcy’s law, the equation of state, and the continuity equation, the basic differential equations of coal–rock seepage are deduced.

$${\displaystyle \frac{{𝜕}^{2}p}{𝜕r^2}}+{\displaystyle \frac{1}{r}}{\displaystyle \frac{𝜕p}{𝜕r}}={\displaystyle \frac{\varphi \mu C_t}{K}}{\displaystyle \frac{𝜕p}{𝜕t}}$$

(4)

Boundary conditions: Assume that there is a borehole in an infinite homogeneous medium, and that the borehole is filled with water at the moment t = 0 (s), at a constant injection pressure Pw (atm); there is no liquid pressure (zero) in the whole medium before the injection. These conditions can be represented by the following initial and boundary conditions:

$$\begin{gathered} p\left(t=0,r\right)=0 \\ p\left(t=0,r=\infty \right)=0 \\ p\left(t=0,r=r_w\right)=p_w \end{gathered}$$

(5)

Theoretical solutions of the basic differential equations were obtained by the Polubarinova–Kochina method according to the initial and boundary conditions:

$$p={\displaystyle \frac{p_w}{\mathrm{Ei}\left(-\frac{\varphi \mu C_r{r}_w^2}{4Kt}\right)}}\mathrm{Ei}\left(-{\displaystyle \frac{\varphi \mu C_r{r}_w^2}{4Kt}}\right)$$

(6)

2.2. Parameterization

After establishing the mathematical model for coal seam water injection and permeability enhancement, the seepage patterns around the borehole under different water pressures and stress conditions were analyzed. The relationship between coal sample permeability and water pressure is illustrated in Figure 2. Subsequently, a comparative analysis was conducted to examine the impact of injection pressure on the radial seepage pressure and velocity around the borehole, assuming constant porosity. Based on the relationship between coal and rock permeability and pore water pressure under in situ stress conditions, a User-Defined Function (UDF) was implemented to incorporate permeability variations. This allowed us to analyze the effects of injection pressure on radial seepage pressure, seepage velocity, and water content around the borehole under varying permeability conditions. This analysis provides valuable insights into the relationship between injection pressure, flow rate, and the uniformity and extent of wetting, offering a reference for optimizing field process technologies.

After the grid is divided, the relevant parameters are set: the laminar flow model is set as a viscous model, and the convergence accuracy of the calculation adopts the default value of 0.001. The fluid material is added and the physical properties of the fluid are set; this paper researches the seepage movement of water injection in the coal seam and determines the density of its physical properties as 1000 kg/m³; the boundary properties and conditions are set; the upper and lower boundaries of the injection boreholes and the left and right boundaries are set to be the constant-pressure permeability boundaries, and the total pressures of inlet and outlet are calculated according to the standard atmospheric pressure. The total pressure is injected in amounts of 4, 10, 15, 20, and 25 MPa. The total pressure at the exit is calculated according to the standard atmospheric pressure, the boundary conditions of the wall are kept unchanged at the default value, the fluid is set to be a porous medium model, and the parameters such as porosity are set as shown in

Table 1. Initial parameter setting for numerical simulation of coal bed water injection.

Parameter Indicator	Parameter Value	Parameter Unit
Water viscosity coefficient	1.04 × 10−3	Pa·s
Water density	1.0 × 103	kg/m3
Absolute permeability of coal seam	7.526 × 10−18	m2
Initial porosity of coal bed	6.3586	%
Density of coal seam	1.43 × 103	kg/m3
Poisson’s ratio	0.32	/
Modulus of elasticity of coal seam	2.6 × 103	MPa
Tensile strength	1.0 × 104	Pa

.

A numerical simulation analysis of water injection was conducted using five water pressure measurements of 4, 10, 15, 20, and 25 MPa. The ground stress condition was set as the original rock stress, which assumed that the coal body did not undergo volume deformation and that the initial porosity was maintained. The pressure, velocity, and water distribution law within the coal body around the borehole were analyzed following 12, 36, and 72 h of water injection.

3. Numerical Simulation Results and Analysis

3.1. Simulation Analysis of Radial Seepage Pressure Field of Coal Bed Water Injection Borehole under Different Pore Water Pressure

A numerical simulation was conducted on a unidirectional injection borehole with a length of 85 m. A cross-section was set at a radial distance of 1.5 m from the injection borehole to analyze the temporal variation of the seepage pressure around the borehole under different injection pressures. The simulation results are presented in Figure 3.

The pressure around the injection wellbore changes over time, as shown in Figure 4. Under injection pressures of 4 MPa and 10 MPa, the pressure distribution around the wellbore remains relatively stable for the first 36 h, with a small range of influence. When the injection pressure reaches 15 MPa, the pressure distribution around the wellbore becomes noticeably wider and more uniform after 36 h. As the pressure continues to rise, the injection pressure increases to 20 MPa and the pressure distribution around the wellbore continues to widen and become more uniform after 36 h. As the pressure increases further, the injection pressure increases to 25 MPa, and through the color width of the pressure distribution around the wellbore, the range of influence changes relatively little.

Through numerical simulation, it can be found that during the coal seam injection process, the changes in coal seam permeability are not continuous with increasing injection pressure, but rather depend on a specific threshold. Only when the injection pressure exceeds this threshold does the coal seam’s permeability exhibit a significant increase. Based on the numerical simulation results, the threshold pressure for increasing permeability in this coal seam is found to be between 15 MPa and 20 MPa.

3.2. Analysis of Radial Seepage Velocity Field of Coal Bed Water Injection Borehole under Different Pore Water Pressure

A numerical simulation was conducted on a unidirectional injection borehole with a length of 85 m. A cross-section was set at a radial distance of 1.5 m from the injection borehole to analyze the temporal variation of seepage velocity around the borehole under different injection pressures. The simulation results are presented in Figure 5. The data regarding the temporal variation of seepage velocity around the borehole were then compiled and plotted as a curve graph, as shown in Figure 6.

Based on an analysis of the contour plots depicting the temporal variation of seepage velocity around the borehole under different injection pressures, it is evident that the moisture migration range expands radially around the borehole within the first 36 h, accompanied by a decrease in average seepage velocity. During the initial stage of water injection, the seepage range of moisture within the coal seam is relatively limited, but the seepage velocity under high water pressure is significantly higher. At an injection pressure of 25 MPa, the average seepage velocity around the borehole is approximately 22.55 m/s, whereas under a low injection pressure of 4 MPa, it is approximately 1.64 m/s. This observation suggests that high-pressure water injection can effectively increase water volume, expand the wetting range, and shorten the injection time, thereby saving construction time.

Figure 6 illustrates the temporal variation of seepage velocity around the borehole. The curve representing 4 MPa exhibits a distinct inflection point at 18 h, while the 10 MPa curve shows an inflection point at 24 h. The 15 MPa curve displays inflection points at 18 h, 24 h, and 36 h, while the 20 MPa curve exhibits inflection points at 24 h, 36 h, and 42 h. The 25 MPa curve shows inflection points at 12 h and 24 h. All curves demonstrate a significant flattening after 42 h, indicating a slow decline in flow velocity within the coal seam surrounding the borehole. Therefore, 42 h represents the time threshold for injection pressure. Within this timeframe, the wetting effect of water injection is pronounced under all injection pressures, whereas the effect becomes less evident beyond 42 h.

3.3. Analysis of Water Distribution Law of Radial Seepage in Borehole under Different Pore Water Pressure

To better illustrate the wetting effect of coal seam water injection, a numerical simulation was conducted on a unidirectional injection borehole with a length of 85 m. A cross-section was set at a radial distance of 1.5 m from the injection borehole to analyze the temporal variation in moisture increase around the borehole under different injection pressures. The simulation results are presented in Figure 7.

The simulation results demonstrate that the increase in moisture content within the coal seam under different injection parameters is reflected by the turbulent dissipation of the fluid. The red areas represent maximum dissipation, indicating a higher fluid flow around the borehole, while the blue areas represent minimal dissipation, indicating lower fluid flow. During borehole injection, the fluid initially passes through a solid section. At injection pressures of 4 MPa and 10 MPa, the fluid dissipation gradually decreases, resulting in a less effective moisture enhancement effect. At an injection pressure of 4 MPa, as the injection time increases, the color contour plots clearly indicate a higher fluid flow dissipation within the injection borehole at 12 h, leading to a more pronounced moisture enhancement effect. At this point, the moisture increase within the borehole is approximately 0.4%. Under an injection pressure of 10 MPa, the moisture enhancement effect is approximately 3–4 times greater.

For injection pressures of 15 MPa, 20 MPa, and 25 MPa, a certain degree of dissipation occurs at the borehole entrance as the water is injected at an injection time of 36 h. Higher injection pressures result in more pronounced dissipation. Notably, the moisture enhancement effect under 15 MPa is approximately twice that of 10 MPa. Furthermore, starting from an injection pressure of 15 MPa, the analysis of color changes in the images reveals that fluid flows more easily during the early stages of injection, and the moisture increment increases with higher injection pressures. Taking the 12-hour injection time as an example, the moisture increment within the borehole under 15 MPa is approximately 1.2%, which is higher than the 0.8% observed under 4 MPa. Under 25 MPa, the moisture increment within the borehole can reach 1.8%, which is higher than the 1.4% observed under 4 MPa.

4. Conclusions

This study established a radial seepage model for coal seam water injection boreholes. Based on this model, computational fluid dynamics software was employed to investigate the radial seepage pressure field, seepage velocity field, and seepage flow distribution around the borehole under different injection times and pressures. The analysis of the numerical simulation results yielded the following main conclusions:

(1) The study identified that the permeability of the coal seam does not continuously increase with rising water injection pressure. Instead, a specific pressure threshold exists between 15 MPa and 20 MPa, beyond which the permeability significantly enhances. This finding is critical for optimizing water injection processes in coal seams and should be considered in the design of field operations.

(2) The analysis revealed that the radial seepage velocity around the borehole stabilizes after 42 h, regardless of the injection pressure. This indicates that 42 h is the time threshold for achieving an effective wetting effect in the coal seam. Injection beyond this period does not contribute significantly to further wetting, highlighting the importance of time management in water injection practices.

(3) The identified thresholds for pressure and time are essential for improving the efficiency of water injection in coal mining. These thresholds should be directly applied in field operations to enhance coal seam permeability and wetting effectiveness.