Dispersion patterns of spontaneous coal combustion fumes in deep open-pit mines effects of wind direction and speed

Abstract

To explore the smoke dispersion patterns of spontaneous coal combustion in deep open-pit mines, the 13^# coal seam mining bench at Hequ open-pit mine was studied using FDS software. The analysis focused on smoke dispersion and visibility around the fire source under three wind directions and four wind speeds. A similar experiment was conducted to verify the smoke dispersion patterns. The results indicate: FDS is suitable for analyzing smoke dispersion in open-pit mines. The angle between the smoke flow and the bench surface decreases with increasing wind speed, and reverse flow occurs with leeward bench winds. The distribution range of different CO concentrations around the fire source was quantitatively analyzed. The ranges where CO concentration exceeds 200 ppm in the wind direction and vertical wind directions are as follows: 0 to 12 m, 10 m (wind facing the bench); – 3 m to 15 m, 5 m (leeward bench wind); 3 m to – 30 m, 4 m (parallel bench wind). The impact range of visibility around the smoke source decreases with increasing wind speed. The threshold wind speed for visibility impact is 0.1 m/s. Below 0.1 m/s, the impact range is similar for all three wind directions, while above 0.1 m/s, there are significant differences.

Introduction

Relevant data show that the residual coal in the shallow-buried small-kiln gob area of the merger and reorganization in the open-pit coal mine and the coal exposed before the long-term shutdown of the open-pit will spontaneously combust inside it. The resulting smoke can spread to the surface through cracks in the coal body of the bench or exposed fire surfaces (Fig. 1). Spontaneous combustion in shallow-buried small mines or open-pit coal piles not only leads to the degradation of coal resources, environmental pollution, and reduced economic value of coal, but also affects the safety of mining equipment, the health of workers, and even causes road traffic accidents. Therefore, it is of great significance to explore the dispersion patterns of spontaneous combustion flue gas of small kiln residual coal and coal pile in deep open pit mine to ensure the safety of equipment and personnel and improve the ecological protection ability of mining area.

Fig. 1.

Smoke dispersion diagram of coal spontaneous combustion in open-pit stope

Currently, scholars both domestically and internationally have conducted extensive research on coal spontaneous combustion and the dispersion of smoke from indoor and outdoor fires. The research on coal spontaneous combustion indicate that it is a complex dynamic physicochemical process^1–3, and it mostly occurs in hidden spaces such as goafs and fractured coal bodies. Researchers have revealed the characteristic parameters of coal spontaneous combustion and the effects of factors like wind speed, particle size, slope, and pile height on coal spontaneous combustion through experimental research, field testing, and numerical simulation. The main research results are:

Zhang et al.^4,5 determined the characteristic temperature and critical value of coal spontaneous combustion, as well as the indicator gas and its critical value at different oxidation stages of coal by programmed temperature rise experiments and thermal characteristic experiment of coal, analyzed the relationship between characteristic temperature and gas products, and provided an early warning method for predicting the degree of coal spontaneous combustion in mining area. Zhu Hongqing, Akgun et al.^6–11 established a mathematical model of coal pile spontaneous combustion based on the experimental study of coal oxidation reaction kinetics, and analyzed the influence of wind speed, oxygen concentration, height, porosity, slope and other variables on the spontaneous combustion of coarse coal pile by numerical software. The research on smoke dispersion mainly focuses on detection and dispersion patterns of smoke in indoor, outdoor and tunnel fires. The main research includes: Vinay et al.¹² investigated the potential issue of oxygen leakage during fires in hospital indoor environments. They used fire simulation software (FDS) to study the effects of different oxygen concentrations (21%, 22%, and 23%) on the dynamics of indoor fires in hospitals. Manea et al.¹³ used FDS to establish two fire scenarios for the fire accident of the restaurant kitchen on the first floor and the leisure bar on the second floor, analyzed the fire propagation and toxic gas ( e.g., carbon monoxide ) generation in the two scenarios, and explained the damage process of the fire. Gao et al.¹⁴ used FDS to analyze the influence of fire source location, wind speed, wind direction and its open or closed conditions on the development of dangerous goods container fires. Yinghua et al.¹⁵ used FDS to analyze the variation of smoke, temperature and CO concentration in cinema fires, and verified the reliability of the simulation results based on a 1:1 physical fire model. Shanyang Wei et al.¹⁶ used FDS to analyze the fire extinguishing effect of water mist fire extinguishing system under different working conditions in wooden stilt building. Enaru I et al.¹⁷ established a 3D model of the building based on FDS, and analyzed the evolution time, temperature and visibility of the fire. Yufeng Huang et al.^18–21 used FDS to study the fire detection process with smoke detectors placed at different locations. Elhelw Mohamed et al.²² simulated the likelihood of crude oil tank fires and the smoke temperature distribution inside and around the tanks using FDS, based on research and analysis of thermal radiation flux. Smoke is a leading cause of fatalities in fires, Gomez et al.^23–28 used FDS simulations to analyze the effects of different exhaust systems (natural or mechanical), heat release rates (HRR), ventilation, and smoke curtains on the dispersion of pollutants in buildings. At the same time, medical studies have shown that exposure to wildfire smoke or wildfire particulate matter (PM2.5) is positively correlated with all-cause mortality and respiratory diseases²⁹ .

At present, there are few reports on the study of flue smoke dispersion patterns caused by spontaneous combustion of old kilns and exposed coal bodies in deep open-pit mines. Existing literature primarily focuses on fire spread analysis in coal piles, tunnels, or flat sites, which fails to accurately reflect the impact of complex terrain, wind fields, and operational environments on smoke migration in open-pit mines. To fill this research gap, this paper takes the 13^# coal seam of the Hequ Open-pit Mine in Shanxi as the study object. Based on a year’s statistical data of wind speed and direction in the region, an FDS fire simulation model that aligns with engineering realities was constructed. The study systematically analyzes the smoke dispersion, CO concentration distribution, and visibility evolution patterns on coal mining benches under different wind conditions, and the simulation results were effectively validated through 1:100 scale model experiments.

Compared to previous studies on coal fire smoke dispersion, this paper presents significant innovations in the following areas: (1) It is the first to focus on the complex three-dimensional spatial characteristics of deep open-pit mine benches, coupling the effects of bench topography and aerodynamic disturbances on the dispersion range of smoke and CO. (2) CO concentration monitoring points are set up at different working posture heights to achieve quantitative assessment of operational risk spatial ranges. (3) Similar experiments were conducted to validate the smoke dispersion range and angle, enhancing the reliability of simulation results and their engineering guidance value. This provides theoretical support and data foundation for fire safety prevention and emergency response in deep open-pit coal mines.

Engineering background and model setting

Engineering situations

The Hequ open-pit mine is formed by the merger and restructuring of eight underground mines and contains 16 coal seams, of which 9^#, 10^#, 11^#, 12^# and 13^# are mineable coal seams. Detection results of the goaf show that the 13^# coal seam contains numerous small kiln goafs and abandoned roadways. During mining, smoke from spontaneous combustion of residual coal in these areas diffuses to the surface through fractures and joints, then spreads within the stope with atmospheric airflow. The smoke from spontaneous combustion of exposed coal in the open-pit stope mixes with atmospheric airflow at the combustion surface and disperses within the stope.

In order to enhance simulation effectiveness and speed, the model is simplified as follows: (1) Due to the large area of the deep concave open-pit coal mine, it is assumed that the wind direction and speed affecting the simulated bench are not influenced by opposite and surrounding benches. (2) The relatively thin 12^# coal seam is merged with its adjacent rock layer for simplification. The simplified slope model is shown in Fig. 2. (3) Statistics indicate that smoke point of coal spontaneous combustion in the open-pit stope are mainly concentrated at the slope top line of the coal seam benches. In the simulation, smoke points are set at the slope top line of the mining benches. (4) According to Article 86 of the Open-Pit Coal Mine Production Technical Management Regulations (Trial), road maintenance must ensure surface smoothness. Main and secondary roads should not have potholes wider than 1 m with undulations exceeding 0.15 m. In the excavation and dumping work surfaces, moving pit lines should not have potholes longer than 1 m with undulations over 0.3 m. In simulations, the coal mining bench surface is assumed to be a flat plane.

Fig. 2.

Simplified slope model diagram.

Model construction

The parameters of the slope model are as follows: the length of the floor rock is 230 m and the thickness is 15 m; the coal seam is 174.54 m long and 14 m thick. The rock layer above the coal seam is 129.44 m long and 7.68 m thick. The topsoil layer is 86.65 m long and 12.81 m thick. The slope angle of each layer is 70°, and the spontaneous combustion smoke area is located on the slope top line of the 13^# coal seam stripping bench. The coordinates of the center point are (163,30,29), and the smoke area is approximately a square with a width of 2.0 m. Bench number, airflow direction and measuring point layout are shown in Fig. 3.

Fig. 3.

Diagram of bench number, airflow direction and measuring point layout.

Fire source setting

1. Fire source parameters

The heat power of fire source and the heat release rate of fire are the key parameters to indicate the size of fire smoke. The thermal power of fire source in 13^# coal seam is determined comprehensively according to the spontaneous combustion loss measured by field investigation, laboratory test and online monitoring system of coal temperature measurement, as shown in Eqs. (1) and (2).

Fire Source Heat Power:

1

Where V is the volume of the spontaneously combusting coal in the mining bench, m³, ρ is the coal density, 1150 kg/m³, γ is the loss rate during spontaneous combustion of loose coal per unit time, 0.006^30,31.

Volume of Spontaneously Combusting Coal in the Mining Bench:

2

Where w is the width of the spontaneously combusting coal, 2 m, l is the length of the spontaneously combusting coal, 2 m, h is the thickness of the spontaneously combusting coal, 0.5 m.

By calculation Q = 357,282 kW.

The heat release rate of fire source in 13^# coal seam is determined according to the coal quality characteristics and geological data of 13^# coal seam. Finally, the heat release rate of 13^# coal seam is 80 kJ / m² and the heat release is 25,890 kJ / kg. Because the residual coal in the goaf and the exposed coal in the open air are all flammable loose broken coal, the t² medium-speed model is selected as the combustion model, the fire growth coefficient is 0.01127, and the calculated time is t = 168.5s. The area of the smoke area is set to 2.0 × 2.0 m, and the HRR curve during the simulation is shown in Fig. 4.

Fig. 4.

HRR curve diagram.

• (2)Combustion reaction equation

In order to meet the needs of simulating smoke dispersion paths on large-scale open-pit coal mining benches, this paper employs a simplified one-step global reaction kinetics model. This model is widely used in multi-field coupling simulations of coal spontaneous combustion and effectively describes heat release and smoke behavior on a macroscopic scale. It should be noted that this model cannot fully capture the multi-stage oxidation reactions and intermediate product formation during coal combustion, which presents certain limitations in accurately simulating toxic gases. Equation (3) is the one-step global reaction model proposed by Wessling et al. in their study on Wuda coal fire simulations³², and it has been validated as suitable for multi-field coupling simulations of coal spontaneous combustion.

3

Boundary condition setting

Considering the environmental characteristics of the dispersion of coal spontaneous combustion flue gas in the stripping bench of open-pit coal mine, the boundary conditions of the model are divided into two types : pressure outlet and velocity inlet. The settings are as follows:

1. Velocity inlet: The inlet surface is defined as the velocity boundary, ‘supply ‘.

2. Pressure outlet: The four surfaces except the velocity inlet are defined as pressure outlets, all of which are ‘Open ‘.

3. Model boundary: The model wall is regarded as an adiabatic surface, the ambient temperature is 20 °C, and the ambient pressure is 101.3 kPa.

4. Simulation time: The time required to reach the combustion peak when using the t2 medium-speed model simulation is t = 168.5s. In order to fully study the dispersion patterns and dispersion distance of smoke, visibility and toxic gas ( CO ), the simulation time is set to 500s to meet the needs of analyzing the CO concentration distribution at steady state.

Grid division

Reasonable meshing can not only improve the calculation speed but also greatly improve the accuracy of numerical simulation results. The mesh size of the model is determined by the characteristic diameter of the fire source. The characteristic diameter of the fire source (D) is calculated³³ See Formula (4):

4

Where D is the characteristic diameter of the fire source, m, Q is the fire source power, kW, ρ_∞ is the ambient air density, 1.2 kg/m³, C_p is the specific heat capacity of air, 1.014 kJ/(kg·K), t₀ is the ambient temperature, 293 K, g is the gravitational acceleration, 9.8 m/s².

The calculated characteristic diameter of the fire source D is approximately 10 m. According to relevant studies³⁴, the mesh size d should range between 0.06D and 0.25D to effectively capture key turbulent structures and improve simulation accuracy. Based on this, the reasonable grid size range is 0.6–2.5 m. Considering computational accuracy, time, and hardware performance, a grid size of 1 m × 1 m × 1 m was selected, with a total of 1,380,000 grid cells. The grid division of the model is shown in Fig. 5.

Fig. 5.

Model grid division diagram.

The Large Eddy Simulation (LES) turbulence model embedded in FDS will automatically activate under the aforementioned grid resolution conditions. Since the grid size used in this study is 0.1 times the fire source diameter, it meets the LES activation criteria. This allows the simulation to resolve key disturbance structures such as turbulence and recirculation in the smoke flow field, providing a more reliable fluid dynamics foundation for subsequent analysis of smoke dispersion paths and toxic gas migration patterns.

Working conditions and measuring point setting

Design of working condition

Based on the statistical data of atmospheric wind speed and direction in the Hequ area from October 2022 to October 2023 reveals that the cumulative number of days characterized by Level 1 winds (0.3–1.5 m/s), Level 2 winds (1.6–3.3 m/s), and Level 3 winds (3.4–4.4 m/s) amounted to 341 days, accounting for 93.4% of the total days in the year (365 days), as depicted in Fig. 6.

Fig. 6.

Wind statistics for the area where Hequ Open-Pit Mine is located.

The wind direction of the wind flow in this area varies greatly with the seasons. The main directions of the wind flow are northeast wind, southeast wind, northwest wind and southwest wind for 210 days, accounting for 57.5% of the total number of days ( 365 days ) in a year, as depicted in Fig. 7.

Fig. 7.

Wind direction statistics diagram.

Considering that each wind speed level covers a range and for systematic analysis, when using FDS for smoke dispersion simulation, four wind speeds are selected: level 0 winds (0.1 m/s), level 1 winds (1 m/s), level 2 winds (2.45 m/s), and level 3 winds (4.4 m/s) to analyze the dispersion law, visibility, and CO dispersion distance. The simulation Working conditions design is shown in Table 1.

Table 1.

Working conditions design Plan.

Wind speed Wind direction	0.1 m/s	1 m/s	2.45 m/s	4.4 m/s
Facing the bench wind	Flue gas dispersion patterns, visibility analysis, CO dispersion pattern and dispersion distance analysis
Leeward bench Wind
Wind parallel the bench

Layout of monitoring points

In order to study the impact of coal spontaneous combustion flue gas and toxic and harmful gas (CO) on the workers within the bench, the CO concentration monitoring sensor were set up according to the three heights of the workers squatting, standing and sitting on the truck. The heights are as follows: crouching (d) at 0.75 m, standing (s) at 1.7 m, and sitting in a truck (c) at 3 m. The layout of monitoring points is shown in Fig. 8.

Fig. 8.

Monitoring point layout diagram.

Results and verification

According to the calculation results of heat release rate per unit area ( HRR ) in 2.3, when t > 168.5s, the generation of smoke flow enters a stable phase, the dispersion patterns of flue gas and CO and the distribution of dispersion distance and visibility were analyzed at the state when the reaction reaches 500 s. In order to verify the reliability of the numerical simulation, a similar experiment was carried out using the principle of geometric and wind speed similarity.

The model was built at a ratio of 1 : 100 to build a slope model similar to Fig. 2. The four wind speeds were set at a ratio of 1:100 using a stepless speed-regulating ground-type exhaust fan. The wind speed was measured with a RA410 anemometer (range 0–45 m/s). The flue gas was provided by the coal heated by the heating plate. The experimental results are shown in Figs. 9, 10 and 11.

Fig. 9.

Flue gas dispersion diagram under different working conditions of windward bench wind.

Fig. 10.

Flue gas dispersion diagram under different working conditions of leeward bench wind.

Fig. 11.

Flue gas dispersion diagram under different working conditions of parallel bench wind.

Smoke dispersion analysis

1. Facing the bench wind

From Fig. 9, when the wind speed is 0.1 m/s in the direction of the windward bench, the wind flow has a minimal impact on smoke dispersion, causing only slight dispersion in the wind direction, with the smoke rising almost vertically. When the wind speed is 1 m/s, the smoke diffuses upward at an angle of 20°–50° relative to the bench surface, becoming closer to the benches as it rises, and at the topmost step, it diffuses upward at approximately a 25° angle. When wind speed is 2.45 m/s, the smoke almost adheres to the benches as it rises, it can be seen from the figure that under the influence of the bench, the high-concentration smoke is concentrated in the range between the middle of the bench and the smoke point, and will not spread to the slope of the upper bench. When the wind speed is 4.4 m/s, the smoke diffuses close to the bench, and the large wind speed leads to the decrease of the upward dispersion range of the smoke flow direction. The smoke is mainly concentrated above the smoke-generating bench, and it is inclined to diffuse upward in the range of 20°–30° with the bench surface.

• (2)Leeward bench wind

From Fig. 10, it is observed that when the wind speed is 0.1 m/s in the direction of leeward bench, the wind has minimal impact on smoke dispersion, causing only a slight deflection in the direction of the airflow, with the smoke rising almost vertically. When the wind speed is 1 m/s, the smoke diffuses upward at an angle of 30°–60° relative to the bench surface, the farther away from the bench, the wider and sparser the dispersion range is. At a wind speed of 2.45 m/s, the smoke diffuses upward at an angle of 20° relative to the bench surface. The figure shows that high concentrations of smoke are mainly concentrated near the emission point and the upper part of the lower bench and does not diffuse to the working face of the lower bench. When the wind speed is 4.4 m/s, the smoke is almost spread along the bench. and the smoke flow spreads to the upper part of the lower step working face which is a certain distance away from the slope of the smoking bench, posing a risk to the safety of personnel and equipment there.

• (3)Parallel bench Wind

From Fig. 11, it is observed that when the wind speed is 0.1 m/s in the parallel bench direction, the wind flow causes the smoke flow to diffuse slightly along the wind flow direction, and the upward dispersion is more obvious. When the wind speed is 1 m/s, the smoke flow spreads upwards at an angle of 30°to 60° relative to the bench surface, and the farther away from the bench, the larger and sparser the dispersion range is. When the wind speed is 2.45 m/s, the smoke flow is inclined to diffuse upward in the range of 5°–15° with the bench surface. It can be seen from the figure that the high concentration smoke is mainly concentrated in the range of 15 m from the smoke-generating point along the direction of the wind flow. When the wind speed is 4.4 m/s, the smoke diffuses almost close to the benches, and there is a risk of affecting the safety of workers and equipment in the direction of smoke flow.

From Figs. 9 and 10 and 11, it is evident that the FDS simulation results are generally consistent with the experimental results, which verifies the rationality of the simulation parameters and simulation results.

CO dispersion analysis

There is no obvious consequence within 2 h in 50 ppm CO environment, while dizziness, nausea and other adverse reactions will occur within 1 h in 100 ppm CO environment. Therefore, the dispersion of CO concentrations at 50 ppm and 100 ppm under different wind speeds and directions will be discussed.

1. Facing the bench wind

It can be seen from Fig. 12 that CO diffuses with flue gas when facing the bench wind, and the trend of CO dispersion with wind flow at different wind speeds is consistent with the trend of flue gas dispersion. When the wind speed is 0.1 m/s, CO almost diffuses upward along the vertical direction, and the wind flow only causes CO to diffuse slightly along the wind flow direction. The dispersion of CO occurs after the height of the smoke flow exceeds the bench above the smoke rising bench. When the wind speed is 1 m/s, CO is mainly concentrated in the range of 30°–60° angle with the bench surface, which is located on the outer side of the windward side of the smoke flow.When the wind speed is 2.45 m/s, CO is concentrated in the vicinity of the angle of 30° with the bench surface, which is located on the outer side of the windward side of the smoke-generating bench. The area where the CO concentration is greater than 100 ppm is located in the range of 0 –2.5 m above the smoke source. When the wind speed is 4.4 m/s, the range of CO concentration greater than 50 ppm is concentrated in the range of 5–7 m above the smoke bench, and the range of CO concentration greater than 100 ppm is concentrated in the range of 0  –2 m above the smoke source.

• (2)Leeward bench wind

Fig. 12.

CO dispersion diagram under different working conditions of facing the bench wind.

It can be seen from Fig. 13 that CO diffuses with flue gas when there is leeward -bench wind, and the trend of CO dispersion with wind flow at different wind speeds is consistent with the trend of flue gas dispersion. When the wind speed is 0.1 m/s, CO diffuses upward almost along the vertical direction, and the wind flow makes CO deflect slightly along the direction of the wind flow. Due to the dispersion of the lower benches in front of the wind flow, CO will be entrained in the opposite direction of the wind flow. When the wind speed is 1 m/s, CO is mainly concentrated in the range of 30°–60° angle with the bench surface, which is located on the outer side of the windward side of the smoke flow. When the wind speed is 2.45 m/s, the range of CO concentration greater than 50ppm is concentrated in the range of 10°–30° angle with the bench surface, which is located on the outer side of the windward side of the smoke-generating bench. The range of CO concentration greater than 100ppm is concentrated in the range of 0–2.5 m above the smoke source. When the wind speed is 4.4 m/s, CO almost diffuses along the smoke-generating bench, and CO is concentrated in the range of 0 –2 m above the smoke source.

Fig. 13.

CO dispersion diagram under different working conditions of leeward bench wind.

• (3)Parallel bench wind

According to Fig. 14, when the wind is parallel to the bench, CO diffuses with flue gas and the trend of CO dispersion with wind flow at different wind speeds is consistent with the trend of flue gas dispersion. When the wind speed is 0.1 m/s, the airflow causes the CO to diffuse slightly along the airflow direction, and the CO is concentrated in the range of 3 m near the smoke source. When the wind speed is 1 m/s, CO is mainly concentrated in the range of 40°–60° angle with the bench surface, which is located on the outer side of the windward side of the smoke flow. When the wind speed is 2.45 m/s, CO is concentrated in the range of 12 m along the wind flow direction of the smoke source, and beyond this range, it diffuses along the direction of 20° angle with the bench surface. When the wind speed is 4.4 m/s, CO diffuses along the direction parallel to the bench, and CO is concentrated in the range of 0–3 m above the bench surface.

Fig. 14.

CO dispersion diagram under different working conditions of parallel bench wind.

Visibility analysis

According to Fig. 15, the impact range of bench visibility under different wind directions and wind speeds is less than the dispersion range of flue gas and CO. With the increase of wind speed, the impact range of bench visibility gradually decreases. When the wind speed is 0.1 m/s, the influence range of visibility in three wind directions is basically the same, all of which are within the range of 3 m around the smoke source and 0–15 m in height. When the wind speed is greater than 0.1 m/s, they are different. When the wind is facing the bench, the flow dispersion is affected by the bench above the smoke point. When the wind speed is 1 m/s, the visibility of the smoke source is reduced in the range of 5 m in front of the airflow direction and 0–5 m in height. When the wind speed is greater than 2.45 m/s, the smoke dispersion velocity increases, and the visibility in the range of 4 m and 0–2 m in height around the smoke source decreases. Smoke flow is affected by the lower bench when it is leeward bench wind. When the wind speed is greater than 1 m/s, the visibility around the smoke source is reduced within 7 m around the smoke source and at a height of 0–4 m. When the wind is parallel to the bench at a speed of 1 m/s, the visibility of the smoke source is reduced in the range of 5 m in front of the airflow direction and 0–5 m in height. When the wind speed is greater than 2.45 m/s, the visibility of the smoke source is reduced in the range of 10 m in front of the airflow direction and 0–2 m in height.

Fig. 15.

Visibility of the bench under different wind speeds and directions.

CO impact range analysis

The smoke flow is fluctuating under the influence of airflow, steps, thermal buoyancy and other factors. In order to ensure the safety of personnel and equipment, the sensor set in Fig. 8 is used to monitor the change of CO concentration at each monitoring point during the simulation process, and the range of CO concentration ≥ 200ppm is analyzed (when CO concentration ≥ 200ppm, people will have headache and vertigo within 30 min ).

1. Facing the bench wind

According to Fig. 16, the closer to the smoke source point, the higher the CO concentration. The range of CO concentration reaching 200ppm is within the range of 0–12 m along the wind flow direction from the smoke source point and 10 m around the smoke source point in the vertical wind flow direction.

Fig. 16.

CO impact width under different wind speeds at the wind facing bench.

According to Fig. 17, the closer to the smoke source point, the higher the CO concentration. The range of CO concentration reaching 200 ppm is within the range of-3–15 m along the wind flow direction of the smoke source point and 5 m around the smoke source point in the vertical wind flow direction. The CO concentration within 3 m from the lower bench surface is less than 50 ppm and concentrated within 24 ppm at different distances, meeting the national standard of 24 ppm for normal work conditions³⁵. Therefore, the CO in the smoke flow will not affect the safety of workers and equipment on the lower bench surface of the smoke source bench.

Fig. 17. Leeward bench wind.

CO impact width of different wind speeds under leeward bench wind.

According to Fig. 18, the closer to the smoke source point, the higher the CO concentration. The range of CO concentration reaching 200 ppm is 3–30 m along the wind flow direction of the smoke source point, and 4 m around the smoke source point in the vertical wind flow direction.

Fig. 18. Parallel Bench Wind.

CO impact width under different wind speeds at the Parallel Benches.

Discussion

Affected by the goaf of the old kiln and the safety production management, the spontaneous combustion phenomenon of broken residual coal in the goaf of shallow buried small kiln and the coal exposed before long-term shutdown often occurs in the stope of deep concave open-pit mine. The coal mining bench of deep open pit mine is located inside the pit, and the dispersion of coal spontaneous combustion flue gas is affected by factors such as slope, wind direction and wind speed. It is of great significance to explore the dispersion patterns of coal spontaneous combustion flue gas in deep open pit mine under different wind directions and wind speeds to ensure the safety of personnel and equipment and environmental ecological protection.

Analysis of smoke dispersion range consistency

Wind speed significantly impacts the rise and dispersion characteristics of smoke plumes. Under low wind speed conditions, buoyancy plays a dominant role, causing the plume to disperse vertically. As wind speed increases, the buoyancy effect weakens, and the plume tends to disperse at an angle, with greater wind speeds leading to larger deflection angles. Figure 19 shows the comparison of smoke profiles between experiments and simulations under different wind speed conditions, demonstrating a generally consistent overall shape. At wind speeds of 0.1 m/s and 1.0 m/s, the plume primarily expands vertically, making the horizontal dispersion distance at the same elevation the focus of comparison between experiments and simulations. At wind speeds of 2.45 m/s and 4.4 m/s, the plume disperses at an angle, with the vertical rise height at fixed positions becoming the main comparison focus.

Fig. 19.

Comparison diagram of smoke dispersion range consistency.

In order to quantitatively describe the differences, this study uses metrics such as maximum (minimum) deviation, relative error, and dispersion angle for evaluation. The relative error in the horizontal direction is defined as the ratio of the relative dispersion deviation to the mining bench width, while in the vertical direction, it is the ratio of the average dispersion deviation to the experimentally measured height. At a wind speed of 4.4 m/s, the highest point of the simulated plume is slightly lower than the experimental results, which is consistent with Rinne et al.‘s finding that FDS generally underestimates smoke layer height by about 0.5 m in enclosed fire experiments³⁶.

Additionally, the FDS simulation reveals the temporal evolution characteristics of the smoke dispersion process. Taking the 4.4 m/s leeward bench wind condition as an example, the smoke undergoes a distinct transition process from initial dispersion to final stabilization. The experimental observations correspond to the “short-term stable” phase in the simulation at around 173 s, while the simulation shows a truly steady-state dispersion boundary at approximately 500 s. This difference suggests that physical experiments may have limitations in temporal observation, whereas numerical simulations can provide more comprehensive temporal information, effectively compensating for experimental limitations and enhancing the applicability of the simulation results. The comparison is shown in Table 2.

Table 2.

Smoke dispersion consistency Comparison.

Wind direction	Wind speed (m/s)	Horizontal dispersion deviation (m)				Vertical dispersion deviation (m)				Average relative error(%)		Smoke dispersion angle(°)
		Left edge		Right edge		Left edge		Right edge		Left edge	Right edge	Left edge		Right edge
		Max.	Min.	Max.	Min.	Max.	Min.	Max.	Min.			Exp.	Sim.	Exp	Sim.
Facing the bench wind	0.1	3.87	0.05	2.14	0.001	–	–	–	–	3.03	4.29	126	118	70	75
	1	1.34	0.02	3.21	0.07	–	–	–	–	1.15	8.4	151	148	107	110
	2.45	–	–	–	–	3.06	0.01	1.85	0.15	2.15	4.34	179	174	126	122
	4.4	–	–	–	–	2.94	0.008	2.69	0.002	2.1	5.03	173	175	128	122
Leeward bench wind	0.1	3.81	0.03	4.39	0.4	–	–	–	–	2.8	8.39	111	106	47	56
	1	3.9	0.45	4.2	0.02	–	–	–	–	3.98	9.86	59	61	23	27
	2.45	–	–	–	–	3.27	0.01	1.45	0.02	3.28	2.88	47	44	19	18
	4.4	–	–	–	–	2.17	0.02	2.69	0.01	2.58	4.05	40	34	3	3
Parallel bench wind	0.1	2.49	0.03	2.92	0.2	–	–	–	–	2.48	6.64	144	135	75	73
	1	2.7	0.02	2.6	0.07	–	–	–	–	2.6	6.39	156	159	135	137
	2.45	–	–	–	–	0.85	0.01	1.52	0.006	1.2	2.2	176	179	165	166
	4.4	–	–	–	–	0.64	0.001	1.63	0.1	0.925	2.29	174	179	175	177

The impact of wind direction on the dispersion patterns of flue gas in coal mining benches

Unlike open areas, the dispersion of smoke from spontaneous coal combustion on open-pit mining benches is influenced by the upper and lower benches, resulting in different dispersion effects. By analyzing the airflow and smoke forces under three wind directions—facing bench, leeward bench, and parallel to the benches—we can understand the following: When the airflow moves forward with the wind facing the bench, it is obstructed by the upper bench. This creates a vortex at the slope angle of the upper bench adjacent to the smoking bench, preventing high-concentration smoke from moving toward the slope angle. At the same time, due to the blocking effect, the dispersion width of the flue gas along the vertical wind flow direction increases. When the airflow moves forward with the leeward bench wind, the depression of the lower bench reduces the dynamic pressure, enhancing the dispersion effect of the airflow. The dispersion width of the smoke flow along the vertical direction of the wind flow is greater than the dispersion width of the smoke source point. At the same time, when the smoke flow passes through the adjacent lower step, the smoke dispersion is more uniform. When the wind is parallel to the benches, smoke dispersion is similar to that in open areas. The dispersion is entirely impacted by the buoyancy of the smoke at the emission point and the direction of the airflow. The smoke dispersion patterns in the three scenarios are as follows: In the direction of wind flow: parallel to the bench > leeward bench > facing bench. Along the direction of the vertical wind flow: facing bench > leeward bench > parallel to the bench. This is consistent with the results shown in Figs. 16 and 17 and 18.

The impact of wind speed on the flue gas dispersion and visibility in coal mining benches

The dispersion of coal spontaneous combustion flue gas in open-pit stope is the result of the combined action of flue gas buoyancy and wind speed. The buoyancy makes the flue gas diffuse upward along the vertical direction. While the wind flow makes the flue gas diffuse upward and diffuse along the direction of the wind flow. The greater the wind speed, the faster the flue gas moves along the direction of the wind flow, which shows that the greater the wind speed, the closer the wind flow is to the bench surface, and the smaller the angle between the wind flow and the bench surface.

The greater the wind speed, the faster the dispersion rate of solid particles in the flue gas of coal spontaneous combustion, and the smaller the impact on visibility. The smoke dispersion at the smoke point of the coal mining bench is affected by the adjacent upper bench and the lower bench. When the wind is facing the step, the obstruction of the adjacent upper bench makes the smoke at a certain wind speed gather near the top of the smoke source point. The concentration of toxic and harmful gases above the smoke source point increases and the visibility decreases, which affects the safety of the workers here (See Figs. 9 and 15). The adjacent lower benches make the wind flow dispersion range increase and the wind flow velocity decrease under the leeward bench wind ; the greater the wind speed, the faster the smoke dispersion speed, the more uniform, the greater the visibility. At the same time, when there is a leeward bench wind, the reduction in wind speed above the lower bench causes the smoke to spread against the wind direction., as shown in Figs. 10 and 15. The impact range of visibility in three cases is parallel bench wind > leeward bench wind > facing the bench wind. In addition, the one-step global reaction equation of coal combustion used in the simulation study is obtained through the experiment of small sample coal samples, which is not enough to truly reflect the actual situation of spontaneous combustion of coal in goaf or exposed coal seams. While a 1:100 scale model can effectively facilitate qualitative analysis of smoke dispersion patterns and validate the reasonableness of simulation results. However, due to the limitation of the model size in the quantitative analysis, it cannot meet the requirements of various monitoring probe arrangements. Therefore, it is necessary to use a similar experimental model of larger size to accurately analyze the dispersion patterns of coal spontaneous combustion flue gas.

Conclusions

1. Through similarity experiments on smoke dispersion under different wind directions and speeds, the feasibility of using FDS to simulate smoke dispersion, CO dispersion, and visibility distribution at spontaneous combustion points on open-pit coal mining benches under different wind directions and speeds was verified

2. The angle between the smoke flow and the bench surface of the smoke source point decreases with the increase of the airflow velocity. When the wind speed is greater than 2.45 m/s, the smoke flow almost spreads forward with the bench surface. CO diffuses with the smoke flow and has the same dispersion patterns as the smoke flow dispersion, and CO is located outside the windward side of the smoke flow when it diffuses.

3. The closer to the smoke point, the higher the CO concentration. The impact range of CO dispersion varies with different wind directions. The range where CO concentration reaches 200 ppm is as follows: 0 to 12 m in the wind direction and 10 m on each side around the smoke point for wind facing the bench. – 3 to 15 m in the wind direction and 5 m on each side around the smoke point for the leeward bench wind, and the maximum CO concentration above the bench surface within 0–3 m below the smoke source point approaches the maximum allowable concentration of 24 ppm for the working environment. 3 m to – 30 m in the wind direction and 4 m on each side around the smoke point for wind parallel the bench.

4. The range of visibility impact on the bench decreases as wind speed increases. When the wind speed is 0.1 m/s, the impact range for all three wind directions is similar, which is 3 m around the smoke source point and 0–15 m in height. When the wind speed exceeds 0.1 m/s, the ranges differ: For wind facing the bench at a speed of 1 m/s, the impact range is 5 m along the wind direction and a height of 0–5 m. When the wind speed exceeds 2.45 m/s, the range is 4 m around the smoke point and a height of 0–2 m. For the leeward bench wind at speeds greater than 1 m/s, the impact range is 7 m around the smoke point and a height of 0–4 m. For wind parallel to the bench at 1 m/s, the impact range is 5 m along the wind direction and a height of 0–5 m. When the wind speed exceeds 2.45 m/s, the range is 10 m along the wind direction and a height of 0–2 m.

5. This study systematically developed a smoke dispersion model for deep open-pit mine fire areas, integrating multiple factors such as wind speed and direction, terrain interference, and operational height. This enriches the application of FDS in simulating fires in complex open-pit mining environments and provides a theoretical foundation for the development of future intelligent safety management.

Author contributions

H.Z.: Writing – review & editing, Methodology, Supervision, Funding acquisition. J.R.: Writing – original draft , Visualization, Validation , Investigation, Formal analysis.All authors reviewed the manuscript.

Funding

This work was supported by the National Key R&D Program of China (No. 2022YFB4703701) and the Key Science and Technology Project of theMinistry of Emergency Management of the People’s Republic of China (No. 2024EMST080802).

Data availability

This study uses both numerical simulation and experimental research. For access to the numerical simulation program and experimental model design parameters, please contact the author directly at: chinarenjianjun@126.com.

Declarations

Competing interests

The authors declare no competing interests.