Characterization of Gas Seepage in the Mining Goaf Area for Sustainable Development: A Numerical Simulation Study

Abstract

An in-depth understanding of gas (oxygen and methane) seepage characteristics in coal mine goafs is essential for the safe production of mines and for advancing sustainable development practices within the mining industry. However, the gas distribution and its flow processes still remain ambiguous. In this article, we developed a three-dimensional porous media mining goaf mathematical model (considering the heterogeneity) to analyze the methane and oxygen flow features. Firstly, based on the variation laws of the “three zones”—the free caving zone, fracture zone, and subsidence zone—porosity changes in the vertical direction were set. A three-dimensional physical model of a fully mechanized caving mining area with a “U”-shaped ventilation system was established as the basis, and a COMSOL Multiphysics multi-field coupled model was built. Secondly, based on the established model, the characteristics of porosity distribution, mixed gas pressure changes, and the volume fraction of oxygen in the goaf were analyzed. The results show that as the distance from the working face increases, the compaction intensity in the mined-out area gradually rises, resulting in a decreasing porosity trend. The porosity distribution characteristics significantly impact the mechanical behavior and gas flow. The gas pressure inside the mined-out area is much higher than the surroundings, decreasing with depth. The upper and middle parts have the highest-pressure concentrations, requiring focused assessment and targeted monitoring measures based on the pressure characteristics of different regions. The oxygen concentration gradually decreases with depth due to poor ventilation, leading to potential explosive gas mixtures, necessitating ventilation system optimization, enhanced monitoring, and emergency preparedness. The gas exhibits vertical stratification, with higher concentrations in the upper and deep regions. Targeted drainage and ventilation methods can effectively control the gas concentration and ensure production safety.

1. Introduction

Coal is the dominant energy source China [1,2,3], which will still play a dominant role in the future of economic development. Most coal mines in China are deep, and the coal seams are highly impermeable, unlike many mines in the US and Australia [4,5]. With the depth of coal mining continuously increasing, the weight of the overlying strata and area distribution in goafs also increase, directly resulting in the danger of coal and gas outbursts. Additionally, continuous mining can also lead to an increase in the scope of caving in abandoned mining areas—more gas outbursts and more serious leakage in the working face, resulting the abandoned coal mine being prone to spontaneous combustion [6,7,8,9,10]. Methane emissions from mined-out areas, as a more potent greenhouse gas compared to carbon dioxide, have a significant impact on global climate change. According to evaluations by the Kyoto Protocol and the Intergovernmental Panel on Climate Change (IPCC), the global warming potential of methane is about 84–87 times that of carbon dioxide over a 20-year time frame and about 28–36 times over a 100-year time frame. Therefore, controlling methane emissions is crucial to mitigating climate warming and enhancing environmental sustainability. The release of CO₂ from residual coal in goaf areas contributes to the greenhouse effect by adding to atmospheric CO₂ levels [11,12,13,14,15,16,17]. In the mining process, voids and cracks formed in mined-out areas become the main channels for methane accumulation and release. By thoroughly studying the migration patterns of these gases, we can effectively predict and assess methane emissions, providing a theoretical basis for formulating scientific control strategies that support sustainability. Understanding methane migration mechanisms helps develop new capture and utilization technologies, increase resource recovery rates, reduce environmental pollution, and lower safety risks in coal production. Therefore, strengthening research on gas migration in mined-out areas not only aids in environmental protection and safety production but also significantly contributes to the sustainable development of coal mines. Especially in the context of sustainability, scientific gas management strategies and technological innovations can not only reduce greenhouse gas emissions and protect the environment but also achieve resource recycling, promoting green development and long-term sustainability in the mining sector [18,19,20,21,22,23,24,25,26]. Addressing these challenges through sustainable development practices, such as improving mining techniques to minimize environmental impact and utilizing advanced technologies for gas management, is essential for ensuring the long-term viability of the coal mining industry while mitigating its environmental footprint.

Relying solely on man-made experience to understand and deal with gas problems (gas outburst and spontaneous combustion) is far from enough. It is an essential and critical issue to apply a systematic scientific method to continuously deepen the understanding and mastery of the intrinsic laws of gas flow in abandoned mining areas. Comparing existing empirical methods, the proposed scientific method should have the following characteristics: such as actively adopting scientific, quantitative, and more effective forecasting, which has important academic value and practical significance. Overall, in the past few decades, the previous literature on gas flow characterization has focused on just coal seam gas [27]. The theory of coal seam gas migration has also become relatively mature, playing a huge role in the prevention and control of coal mine gas. However, the development of the theory of gas migration in abandoned mining areas or goaf area was relatively less, and further in-depth research is still needed.

The fractured, irregular structure of goaf zones hampers effective ventilation, leading to uneven gas distribution and unclear concentrations of hazardous gases like methane and CO₂. Monitoring systems often lack comprehensive coverage due to the complexity and size of these areas, creating blind spots where gas buildup or subsidence may go undetected. Additionally, extreme conditions in deep mines, such as high temperatures and humidity, can impair monitoring equipment, reducing the reliability of real-time data. These challenges highlight the need for more advanced ventilation and monitoring solutions to ensure safety and environmental protection. Currently, most numerical simulations of mined-out areas tend to simplify key factors such as porosity by assuming homogenous distributions, which can lead to discrepancies between simulated results and actual field conditions. This assumption of homogeneity overlooks the complex, highly heterogeneous nature of goaf zones, where varying porosity and permeability can significantly affect gas migration and storage behavior. Additionally, existing tools often focus on single-field coupling (e.g., fluid flow) rather than multi-field coupling (e.g., the interaction between thermal, hydraulic, and mechanical processes), which limits their ability to capture the full complexity of the goaf environment. Another limitation is the low degree of visualization in many of these simulations, making it difficult to fully interpret and communicate the dynamic processes occurring within mined-out areas. By addressing these gaps, our research brings innovation through enhanced multi-field coupling and improved modeling of heterogeneity, as well as a higher degree of visualization to more accurately reflect the behavior of gases in goaf areas. Zhang Wei conducted physical similarity experiments to determine the swelling coefficients in various zones of the overlying strata of the goaf, using FLUENT 2024 R2 to investigate the gas concentration distribution under both gas drainage and non-drainage conditions. By adjusting porosities, he successfully modeled the heterogeneity of the goaf [28]. However, the permeability of the “three horizontal zones” was found to be discontinuous. Building on the distribution patterns of the goaf leakage airflow field and the three-zone spontaneous combustion model, a goaf model under high-drainage roadway conditions was developed, revealing that the width of the oxidation and heat accumulation zones expanded with increasing drainage flow rates, providing valuable methods for goaf fire prevention [29]. Further studies using FLUENT software simulated changes in the leakage airflow field within the goaf based on varying particle sizes, finding that an average particle size of 0.1 m closely aligns with actual field conditions and significantly affects airflow distribution across the working face [30]. A multi-field coupled goaf model established using COMSOL Multiphysics 6.2 indicated that the gas volume fraction and its gradient are inversely proportional, with minimal discrepancies between simulation results and field measurements confirming the model’s accuracy [31]. Additionally, simulations of gas migration patterns under nitrogen injection conditions showed that the minimum oxygen concentration required for a gas explosion is negatively correlated with the nitrogen injection position [32]. Finally, the division of the three zones and the distribution of multiple fields in shallow coal seam conditions revealed the necessity of considering surface leakage airflow in oxygen concentration analyses, with CO₂ concentration distribution closely mirroring that within the goaf [33].

Subsequently, the finite element methods were applied for establishing mathematical models for gas seepage in the abandoned mining area by considering the abandoned mining area as a porous medium. In addition, based on the established theories which related to porous medium seepage and dynamic diffusion, the laws of mixed gas variable density non-linear seepage–diffusion in the abandoned mining area or goaf area were analyzed in-depth. However, for the research object presented in this article (i.e., the Huainan mining area of China), the numerical simulation studies on gas migration in abandoned mining areas are relatively rare at the current stage. It is also worth noting that the previous numerical simulation models have often ignored the influence of the height of the abandoned mining area—treating the study of the laws of gas migration in the abandoned mining area as a planar problem. Furthermore, the actual abandoned mining area is a three-dimensional (3D) space, although some numerical simulation models were established by considering the abandoned mining area 3D distributions, but the migrations of gas in these 3D spaces were not clearly revealed. Additionally, a significant discrepancy between the computational results and the actual conditions often occurred, as well as poor convergence of the gas composition distribution solutions. The reasons included the improper selection of fluid parameters, and the technical handling in the simulation software. At the same time, it has been found that the software’s calculations are highly dependent on the technical handling of the caved media in the mined-out area. Under the mentioned such circumstances, the results of numerical simulations are difficult to be representative and reliable. Thus, improving the applicability of gas drainage technology by studying the gas migration patterns in the goaf is of great significance for ensuring the safe production of coal.

In this article, we first analyzed the porosity changes in the vertical direction of a coal mine goaf based on the variation laws of the “three zones” (i.e., the free caving zone, fracture zone, and subsidence zone). Secondly, a three-dimensional physical model of a fully mechanized caving mining area was developed on the basis of a “U”-shaped ventilation system. Finally, by introducing the COMSOL Multiphysics software, the characteristics of multiple fields, such as leakage air flow, oxygen, and gas, in a three-dimensional state of the fully mechanized caving mining area, were obtained. The numerical simulation presented in this article could provide a reference for optimizing gas extraction in mined-out areas and promote the national energy security cause.

2. Materials and Methods

2.1. Study Area

In this article, the Huainan mining area was chosen as research region; various kinds of numerical simulations were conducted by considering the actual characteristics of coal reservoir in our research object. Here, we briefly introduce the regional geological and geographical features.

The Huainan mining area is located within the city of Huainan, Anhui Province, China, and is one of the important energy bases in China [34]. The coal resources in this mining area are abundant, and it is an important coal production base in the East China region. The Huainan mining area is one of the key national coal-production bases and has maintained a relatively high level of coal production for many years, providing important coal supply for the power industry, and other sectors in the East China region. The Huainan mining area is an important energy base in China, but its special geological conditions and severe gas problems have always been the key challenges, restricting the safe production of the mining area. Scientific mining and management measures need to be taken to ensure its long-term stable development [35,36,37,38,39,40].

The Huainan mining area is located in the central and northern part of Anhui Province, in the interior of East China. It administratively belongs to the cities of Bengbu, Huainan, and Fuyang, with the main part located within the jurisdiction of Huainan City, on the north bank of the middle reaches of the Huaihe River. It extends eastward from the Changfen–Luohe Town line to the Zhumaodian–Tangdian line in the west, where it connects with the Xin’ji mining area. It is bounded by the Bagong Mountain and Shuneng Mountain ranges in the south, and the Changxing Town–Tangji Town line in the north. It is approximately 70 km long from east to west and 40 km wide from south to north, covering an area of around 1600 km². Its geographic coordinates are 116°20′ to 117°03′ E and 32°34′ to 32°55′ N (Figure 1).

In general, the Huainan mining area has abundant mineral resources and a long history of mining. However, this has also resulted in the formation of a certain number of abandoned mining areas. The schematic diagram of the distribution of abandoned mining areas is shown in Figure 2.

2.2. Physical Model Construction

The real working face in the Huainan mining area is characterized as a “U”-shaped ventilation mode, and the air volume supplied to the working face is ~1600 m³/min. According to the actual site conditions, the mined-out area can be reasonably simplified as length of ~1000 m, width of ~200 m and height of ~75 m. The detailed geometric parameters of the mined-out area model constructed in this article were shown in

Table 1. Geometric parameters of the model.

Name	Parameter (X × Y × Z)
Goaf	1000 m × 200 m × 75 m
Working Face	5 m × 200 m × 3 m [5]
Intake Airway and Return Airway	20 m × 5 m × 3 m [5]
Gas Emission	15.8 m3/min (field acquisition)

. The grid sizes of the roadways, working face, and residual coal on the floor are refined. The three-dimensional model and grid division of the mined-out area are shown in Figure 3.

2.3. Simulation Parameters and Boundary Conditions Setup

The selection of the main computational conditions and simulation parameters follows the actual site conditions of the working face. The fixed gas source term is set as a constant value, and the absolute gas outburst rate of the goaf as ~15.8 m³/min. The gas source term is set as 1 × 10⁻⁷ kg/(m³·s). The intake airflow temperature was set at 38 °C based on the measured temperature, with a depth of approximately 800 m. The oxygen concentration in the intake airway was set as the standard air composition, with an O₂ volume fraction of 21% and an N₂ volume fraction of 79%. The default boundary conditions for the adjacent regions are set as internal boundaries. The return airway is set as the free outlet, and the velocity at the duct walls is set as 0, with no-slip conditions. Considering that the goaf gas still contains a small amount of gas, the residual gas concentration in the goaf is set to 0.6 mol/m³ based on the field data.

In actual situations, the working face in the mining environment is extremely complex, and it is very difficult to completely simulate the shape of the working face and the impact of equipment. Therefore, it is necessary to make reasonable assumptions for the later numerical simulations, which can be seen as follows:

(1)

The goaf gas was considered as an ideal gas—it did not undergo compression during the flow process and conforms to the seepage law.

(2)

The gas concentration emitted from the goaf is 100%, and it does not contain other gas components.

(3)

The gas emission source from the goaf is simplified as a whole, and the gas emission rate is assumed to be uniformly distributed in the goaf, with the gas emission rate and gas parameters being fixed constants.

(4)

The influence of the mining equipment on the gas flow in the working face is ignored, and the goaf, intake, and return air roadways, as well as the working face, are assumed to be rectangular, with the model size and related parameters set according to the actual situation.

(5)

The parameters such as the porosity of the fractures in the goaf are functions of space and do not change with the mining time.

2.4. Theoretical Governing Equations for Mixed Gas Flow in the Goaf Area

Building on the robust built-in interfaces provided by COMSOL Multiphysics software, the integration of the coupled Brinkman and Navier–Stokes equations offers a sophisticated method to more accurately describe the intricate characteristics of non-Darcy fast seepage in fractured caved areas. This approach is particularly effective when accounting for the complex conditions presented by porous media. By leveraging these advanced computational models, researchers and engineers can gain deeper insights into the fluid dynamics at play, ensuring that the interplay between the porous matrices and the fracture networks is comprehensively captured. This methodology not only enhances the precision of simulations but also provides a more detailed understanding of the flow behaviors in such challenging geological environments [41].

$$\left\{\begin{array}{l}{\displaystyle \frac{1}{\varphi }}{\rho }_f{\displaystyle \frac{\partial u}{\partial t}}=\nabla \cdot \left[-PI+K\right]-\left(k^{-1}\mu +\beta {\rho }_{\mathrm{f}}\left|u\right|+{\displaystyle \frac{Q_m}{{\varphi }^2}}\right)u+F+{\rho }_{f}g\\ {\rho }_f\left(\nabla \cdot u\right)=Q_m\\ K=\mu {\displaystyle \frac{1}{\varphi }}\left(\nabla u+{\left(\nabla u\right)}^T\right)-{\displaystyle \frac{2}{3}}\mu {\displaystyle \frac{1}{\varphi }}\left(\nabla \cdot u\right)I\\ \beta ={\displaystyle \frac{1.75\left(1-\varphi \right)}{D_p{\varphi }^3}}\end{array}\right.$$

(1)

where p represents the pressure, Pa; K represents the stress tensor, Pa; I is the imaginary unit; u is the velocity vector, m/s; μ is the dynamic viscosity, Pa·s; k is the permeability, m²; ρ_f is the fluid density, kg/m³; β is the inertial resistance coefficient, dimensionless; F is the body force, kg/m²/s²; and Q_m is the source term, kg/m³/s.

$$\varphi {\displaystyle \frac{\partial c_i}{\partial t}}+\nabla \cdot \left(-D_i\nabla c_i\right)+u\cdot \nabla c_i=S_i$$

(2)

where c_i represents the concentration, mol/m³; D_i represents the diffusion coefficient of gas component i, m²/s; and S_i represents the source term, in mol/m³/s.

Through the analysis of coal sample data from the mining face, the coal’s oxygen consumption rate was calculated under different oxygen concentration conditions as

$$V_{O_2}=0.00099{\displaystyle \frac{c_1}{c_0}}exp(0.01633\cdot T)$$

(3)

where V_O2 represents the oxygen consumption rate, kg/(m³·s); c₀ represents the inlet oxygen concentration, %; c₁ represents the outlet oxygen concentration, %; and T represents the temperature in the goaf, K.

3. Results

3.1. Establishment of a Three-Dimensional Continuum Model for the Goaf Area

The goaf is a common site for spontaneous coal combustion in mines. Understanding the heterogeneous collapse conditions and the variation law of porosity in the porous medium of the goaf plays a crucial role in further exploring the self-ignition of residual coal and the distribution characteristics of multi-field phenomena in the goaf.

The porosity distribution in the goaf is described by a mathematical model determined by the three-dimensional dilation coefficient [1]. The three-dimensional dilation coefficient distribution function for rock collapse is shown in the following equation:

$$K_p=K_{p,min}+\left[\left(K_{p,max1}-K_{p,min}\right)+{\varphi }_1\left(K_{p,max2}-K_{p,max1}\right)e^{-a_2{d}_2}\right]e^{-a_1\left(d_1+b_1\right)\left(1-e^{-{\varphi }_0{a}_0\left(d_0+b_0\right)}\right)}$$

(4)

where K_p is the distribution function of the bulking coefficient of the caved rock blocks in the gob area; K_p,min is the bulking coefficient of the compacted and broken rock blocks, which is taken as 1.1; K_p,max1 is the bulking coefficient of the rock near the lower part of the working face, and K_p,max2 is the bulking coefficient of the initial caved rock, with the relationship K_p,min < K_p,max1 < K_p,max2; d₀, d₁, and d₂ are the distances from the point (x, y, z) to the working face, the surrounding walls of the gob area, and the floor, respectively, in meters; b₀ is the control parameter for adjusting the depth of the old gob area, and its corresponding attenuation rate a₀ is used to fit the porosity change at the working face and the cut-through eye, with the units being m and m⁻¹, respectively; b₁ is the control parameter for adjusting along the working face direction, and its corresponding a₁ is used to fit the porosity change in the “triangular zone” on both sides of the gob area, with the units being m and m⁻¹, respectively; a₂ is the attenuation rate with respect to the distance from the top of the old gob area, in m⁻¹; ϕ₀ represents the parameter for adjusting the porosity distribution to be more blunt, and ϕ₁ is determined based on the field conditions. Combining the relevant literature [1], the values of a₀, a₁, a₂, b₀, b₁, ϕ₀, and ϕ₁ are obtained as 0.0386 m⁻¹, 0.286 m⁻¹, 0.16 m⁻¹, 4 m, 7 m, 0.23, and 0.85, respectively.

Based on the calculation of the bulking coefficient after coal and rock caving, the porosity function can be expressed as follows:

$$\varphi =1-{\displaystyle \frac{1}{K_p}}$$

(5)

Based on the Ergun model, the permeability function can be calculated as follows:

$$k={\displaystyle \frac{{D_p}^2{\varphi }^3}{150{\left(1-\varphi \right)}^2}}$$

(6)

where D_p is the average harmonic particle diameter, in meters.

As shown in Figure 4, Figure 5 and Figure 6, the porosity distribution characteristics of the caved zone calculated using the COMSOL software are presented.

From Figure 4, it can be observed that along the horizontal direction, at the same vertical height, the porosity decreases continuously as the distance from the working face increases. When x = 50 m, the porosity along the strike direction has already become very small, with a range of 0.09 to 0.30. When x = 100 m, the compaction strength of the caved zone increases, and the porosity becomes even smaller, with a range of 0.09 to 0.26.

From Figure 5, it can be observed that when Z = 1 m, the porosity in the region closer to the working face is relatively high. At Z = 10 m, the porosity has decreased significantly, as the expansion coefficient of the overlying rocks in the caved zone is not very large. At the fractured zone at Z = 40 m, the porosity ranges from 0.09 to 0.13.

In the horizontal direction, most of the area has been completely compacted, with a small porosity. A small “O-shaped” ring remains near the coal wall, and the porosity gradually increases from the center towards the two ends of the caved zone. In the vertical direction, the porosity gradually increases from top to bottom.

From Figure 6, it can be seen that in the horizontal direction, most of the area has a high degree of compaction and a small porosity. A small “O-shaped” ring remains near the coal wall, and the porosity gradually increases from the center towards the two ends of the caved zone, with a maximum of 34%, while the minimum in the central area is only 10%.

3.2. Simulation Analysis of the Leakage Pressure Field in the Goaf Area

From Figure 7, it can be seen that in the horizontal direction, the pressure is relatively high in the lower corner on the intake side of the working face, while it is relatively low in the upper corner. In the vertical direction, as the height increases, the porosity decreases, and the resistance increases, leading to a gradual decrease in pressure.

Specifically, at Z = 1 m, the pressure distribution map shows that there is a relatively high pressure value near the caved zone, indicating that the region close to the top of the caved zone is subjected to a relatively high pressure load. The pressure value gradually decreases with increasing horizontal distance, suggesting a significant pressure transfer and dispersion effect. This layer is located in the upper part of the caved zone, and the pressure concentration characteristics are relatively prominent, requiring special attention and evaluation of the stability in this region.

At Z = 10 m, the pressure value has decreased compared to the 1 m depth, but it is still relatively high, especially in the area directly above the caved zone. The distribution range of the pressure values has expanded, indicating that the pressure transfer and dispersion effect has further developed at this depth. This layer is located in the middle part of the caved zone, and its bearing capacity and deformation characteristics need to be monitored, and the overall stability of the middle region needs to be evaluated.

At Z = 40 m, the pressure value has further decreased, and the distribution range has also expanded. The pressure value directly above the caved zone is relatively high, but the overall pressure level has decreased. This layer is located in the lower part of the caved zone, and the degree of pressure concentration is relatively relieved compared to the previous two layers, but it still requires special attention.

At Z = 70 m, the pressure value has further decreased, and the distribution range has become even more extensive. The pressure value directly above the caved zone has already become relatively low, and the overall pressure level has decreased significantly.

From Figure 8, it can be seen that the compaction degree of the “two-coal” residual coal in the strike direction of the caved zone is smaller than that inside the caved zone, resulting in a not-so-obvious pressure reduction gradient along the strike direction of the caved zone over a long distance. Numerical calculations show that the pressure difference between the two ends of the working face is 483 Pa.

3.3. Simulation Analysis of the Oxygen Distribution Field in the Goaf Area

According to Figure 9, the oxygen concentration is higher on the intake side than on the return side. The fresh airflow entering the working face carries oxygen that flows into the caved zone from the lower corner and exits the caved zone from the upper corner. Therefore, the oxygen concentration is relatively high in the lower corner of the caved zone, with a maximum total volume fraction of up to 20%. The oxygen concentration is relatively low in the upper corner of the caved zone, and it gradually decreases in a radial pattern from the lower corner to the upper corner.

Due to the gradual compaction of the collapsed coal and rock in the deep part of the caved zone, there is essentially no flowing airflow, so the oxygen concentration in the deep part of the caved zone is lower than that in the part of the caved zone closer to the working face, and the oxygen concentration decreases gradually with increasing depth of the caved zone.

Based on the division of the caved zone into “three zones” according to the oxygen concentration, the range of the heat dissipation zone in the caved zone is 0–139 m, the range of the oxidation and heating zone is 120–147 m, and the maximum width of the asphyxiation zone is 75–246 m.

3.4. Simulation Analysis of the Gas Distribution Field in the Goaf Area

According to Figure 10, the methane concentration in the lower part and intake side of the caved zone is below 5%, indicating good ventilation. The methane concentration in the upper part and return side of the caved zone is 8–12%, suggesting poor ventilation in these areas. The methane concentration in the deep part of the caved zone is 10–18%, indicating serious methane accumulation.

From Figure 11, we can see that at Z = 1 m, the overall methane concentration is relatively low, all below 10%, with a slight increase in the return airway. At Z = 10 m, the methane concentration distribution is similar to that at Z = 1 m, but the methane concentration in the upper corner is higher than at Z = 1 m. At Z = 40 m, the methane concentration in the upper corner can reach around 17%, and at Z = 70 m, the methane concentration in the upper corner further increases, but the distribution range does not expand significantly.

From Figure 10 and Figure 11, we can see that under the influence of gravity, there is an overall upward migration of methane in the caved zone, with the methane volume fraction in the intake side of the caved zone significantly lower than in the deep part of the caved zone, and the methane volume fraction in the upper part of the caved zone higher than in the lower part.

Combining Figure 4, Figure 5, Figure 6, Figure 10 and Figure 11, we can see that based on the three-dimensional porosity distribution, the high methane volume fraction is not only accumulated at the top of the caved zone, but also at a certain height above the floor, as the methane has already migrated and accumulated.

Integrating Figure 10 and Figure 11, the distribution of methane concentration in the caved zone is influenced by the flow of leakage airflow within the caved zone. The fresh airflow entering the working face from the intake airway flows into the lower corner of the caved zone and carries away a portion of the methane through the upper corner of the caved zone towards the working face, resulting in a lower methane concentration in the lower corner of the caved zone and a higher methane volume fraction in the upper corner. Due to the gradual compaction of the collapsed coal and rock in the deep part of the caved zone, there is essentially no airflow, so the methane volume fraction in the deep part of the caved zone is higher than that in the part of the caved zone closer to the working face, and the methane volume fraction increases gradually with the increasing depth of the caved zone.

4. Discussion

4.1. Variation Characteristics of Porosity and Permeability in the Mined-Out Area

According to the porosity change patterns shown in Figure 4, Figure 5 and Figure 6, it can be observed that as the distance from the working face of the mined-out area increases, the compaction intensity gradually increases, leading to a decrease in porosity. This phenomenon can be attributed to the fact that after the initial collapse of the rock in the mined-out area, it is further compacted by the overlying strata, resulting in the compression of the pore space.

Regarding the figure, the regions closer to the working face have a relatively higher porosity, while the porosity decreases significantly as the distance from the working face increases. This is because the initial bulking factor is larger in the areas closer to the working face, leading to a higher porosity in this region. However, as the height continues to increase, the porosity changes gradually stabilize.

Overall, in the horizontal direction, most of the area has already been fully compacted, resulting in a relatively low porosity. There is a small “O-shaped” ring remaining near the coal wall, and the porosity gradually increases from the center towards the ends of the mined-out area. In the vertical direction, the porosity gradually increases from top to bottom.

This phenomenon can be explained by the fact that as the depth increases, the compaction degree of the rock in the mined-out area decreases, leading to an increase in porosity in the lower regions.

In summary, the distribution of porosity in the mined-out area is influenced by multiple factors. In the horizontal direction, the compaction intensity is the primary factor, while in the vertical direction, the changes in the bulking factor play a crucial role. Additionally, the “O-shaped” ring structure near the coal wall and the relatively smaller bulking factor changes in the bending and subsidence zones also have a significant impact on the porosity distribution. These findings are important for better understanding the mechanical behavior and gas flow characteristics of mined-out areas.

4.2. Characteristics of Distribution and Variation of Air Leakage Pressure Field in the Mined-Out Area

From the overall gas pressure distribution map shown in the figure, it can be seen that the pressure inside the mined-out area is significantly higher than the surrounding areas. This is mainly due to the accumulation and confined nature of the gas within the mined-out area. As the depth increases, the gas pressure exhibits a gradually decreasing trend, which may be attributed to the diffusion and permeation effects of the gas.

Analyzing the gas pressure characteristics of different depth regions, the upper part of the mined-out area (Z = 1 m, Z = 10 m) has the highest concentration of gas pressure, which requires focused attention and safety assessment. In the middle part of the mined-out area (Z = 20 m), the gas pressure has decreased to some extent, but the potential presence of high-concentration gases still needs to be monitored. The gas pressure concentration in the lower part of the mined-out area (Z = 40 m) has been alleviated, but it also requires focused attention. As for the deep-seated areas away from the mined-out area (Z = 70 m), the dispersing effect of the gas pressure is more evident.

To further evaluate and improve the safety of the mined-out area, it is recommended to conduct more detailed gas component analysis and concentration monitoring, especially in the high-pressure upper and middle regions, to assess their flammability, toxicity, and other characteristics. Measures such as ventilation and displacement can be taken to reduce the gas concentration and pressure in these areas. For the lower and deep-seated regions, the monitoring intensity can be appropriately reduced, but the overall safety needs to be ensured.

Additionally, gas concentration and pressure monitoring equipment should be installed at key locations to continuously monitor the gas changes in the mined-out area. Based on the monitoring data, timely analysis and judgment of the safety status should be conducted, and corresponding early warning measures should be developed. In the event of abnormal conditions, immediate emergency measures should be taken to ensure the safety of the operating personnel. Overall, targeted monitoring and control measures should be implemented based on the pressure characteristics of different depth regions to ensure the long-term safety and stability of the mined-out area.

As mentioned in Figure 8, when Z = 1 m, the gas pressure distribution in the mined-out area indeed exhibits a “two-track” characteristic. That is, the pressure gradient changes are not very obvious along the strike direction of the mined-out area, while the pressure gradient changes are more significant in the dip direction. This distribution pattern is related to the difference in the compaction degree of the residual coal mentioned earlier. Specifically, along the strike direction of the mined-out area, the relatively smaller compaction degree of the residual coal leads to lower resistance to gas diffusion and flow in this direction, resulting in a relatively “gentle” pressure distribution. In the dip direction, the higher compaction degree of the residual coal hinders gas diffusion and flow, leading to a more pronounced pressure gradient and a steeper distribution pattern.

This uneven pressure distribution pattern means that the areas with relatively higher pressure along the strike direction may have the risk of a high concentration of flammables, which require focused monitoring and control. Additionally, the regions with a large pressure gradient in the dip direction may have the risk of local leakage and diffusion, which need to be promptly detected and addressed. Specifically, the ventilation system of the mined-out area should be optimized to improve the uniformity of gas flow and reduce the risks in the high-pressure regions. More detailed emergency plans should be developed and differentiated emergency measures should be taken according to the pressure characteristics of different regions.

4.3. Characteristics of Oxygen Field Distribution Changes in the Mined-Out Area

In the deep mined-out area, the oxygen concentration gradually decreases with increasing depth due to poor air flow, which reflects the uneven ventilation in the mined-out area. For the heat dissipation zone, the oxygen concentration is relatively high, which is conducive to heat dissipation and does not pose a risk of spontaneous combustion. In the oxidation and heating zone, the oxygen concentration gradually decreases, making it easy for oxidation reactions to occur and cause temperature rise, posing a risk of spontaneous combustion. In the suffocation zone, the oxygen concentration is relatively low, and the risk of spontaneous combustion may not be high.

Based on previous research, increasing the ventilation rate significantly expands the oxidation zone on the intake side, while the change in the oxidation zone on the return side is minimal. This makes it more challenging to prevent spontaneous combustion on the intake side of the goaf. Overall, the uneven distribution of oxygen concentration may lead to the formation of explosive gas mixtures in local areas, posing safety hazards. The temperature rise in the oxidation and heating zone may trigger spontaneous combustion accidents, endangering the safety of the entire mined-out area. The low oxygen concentration in the deep mined-out area may also lead to asphyxiation accidents, threatening the life safety of the operating personnel. It is necessary to optimize the ventilation system design, improve the air flow in the mined-out area, reduce the difference in oxygen concentration, strengthen the gas monitoring and early warning in key areas, timely identify and address safety hazards, and take targeted emergency rescue measures to enhance the emergency response capability. At the same time, it is also important to reasonably plan the use of the mined-out area and avoid long-term stay of personnel in dangerous areas.

4.4. Analysis of Gas Distribution in the Mined-Out Area

Due to the effect of gravity, gas in the mined-out area exhibits a distinct vertical stratification characteristic. The gas concentration is relatively low in the areas near the intake side, but gradually increases with the distance from the intake side, particularly prominent in the top part of the mined-out area, where the gas concentration is significantly higher than the bottom, forming a clear gas enrichment layer. The presence of leakage airflow within the mined-out area causes the fresh airflow to mainly concentrate in the lower corner region, carrying away a portion of the gas in that area, resulting in a relatively low gas concentration. In the upper corner region, however, due to the lack of effective leakage airflow, gas tends to accumulate, forming a gas enrichment zone. In the deep part of the mined-out area, the lack of flowing airflow prevents the effective dispersion of gas, leading to higher gas concentrations that increase with depth.

The leakage characteristics within the mined-out area are also an important factor influencing the gas distribution. As the mined-out area becomes more compacted over time, the leakage performance in the deep region deteriorates, which is unfavorable for gas drainage and results in higher gas concentrations in the deep areas. In contrast, the regions near the working face have relatively better leakage performance, which can promote gas drainage and lead to lower gas concentrations.

To address the gas enrichment in the top and deep regions of the mined-out area, targeted gas drainage measures can be taken to effectively control the gas concentration. For the lower corner region with relatively low gas concentration, strengthening ventilation can be an effective approach to ensure safe production.

In summary, the in-depth analysis and understanding of the gas distribution patterns in the mined-out area provide important theoretical guidance and technical support for gas management, ventilation system optimization, gas drainage, and safety monitoring in actual production, which is of great significance for ensuring safe coal mining.

5. Conclusions

Adhering to the goal of sustainable development, based on the actual geological conditions of a mining area in the Huainan coalfield, this study uses numerical simulation to establish a fluid–solid coupling model. By fully considering the characteristics of the “three zones” in the goaf area and the residual coal, we investigated the fluid distribution characteristics and seepage patterns within the goaf. The aim is to provide a basis for optimizing gas extraction. The conclusions are as follows:

(1)

Away from the working face, the compaction intensity in the mined-out area increases, leading to a decrease in porosity. Horizontally, most areas are well compacted, except for a small “O-shaped” ring near the coal wall with higher porosity. Vertically, porosity increases from top to bottom. These porosity patterns significantly affect the mechanical and gas flow behaviors of the mined-out area.

(2)

The gas pressure in the mined-out area is notably higher than in surrounding areas and decreases with depth. The upper and middle sections have the highest pressures, requiring focused safety assessments. Lower and deeper regions have lower pressures but still need monitoring. The gas pressure distribution shows a “two-track” pattern, with less gradient change along the strike and more significant changes in the dip direction, influenced by the compaction of residual coal. Targeted monitoring and control measures should be applied based on depth-specific pressure characteristics to ensure long-term safety and stability.

(3)

Oxygen concentration in the mined-out area decreases with depth due to poor ventilation, leading to uneven oxygen distribution. This can cause explosive gas mixtures in some areas, posing safety risks. Improving ventilation design, enhancing airflow, reducing oxygen concentration differences, and strengthening gas monitoring and emergency measures are crucial for enhancing safety and response capabilities.

(4)

Gas in the mined-out area shows distinct vertical stratification, with higher concentrations in upper and deep regions and lower concentrations in the lower corner. This relates to changes in leakage characteristics within the area. Implementing targeted gas drainage and ventilation strategies can effectively manage gas concentrations and ensure production safety.