Influence law of air flow and water immersion duration on the risk of secondary oxidation spontaneous combustion of coal

Abstract

To further elucidate the variations of secondary oxidation spontaneous combustion risk of lignite under different air flows and immersion time. Secondary oxidation experiments of short-term water-immersed coal and long-term water-immersed coal were conducted under four air flows. The results show that, the presence of a temperature inflection point during primary oxidation process, when coal temperature exceeds it, both the oxygen consumption rate and heat release intensity of long-term water-immersed coal are lower, furthermore, decrease in air flow leads to reduction in the temperature inflection point. The oxygen consumption rate and heat release intensity during the primary oxidation process exceed those observed during the subsequent secondary oxidation process. In the secondary oxidation process, long-term water-immersed coal exhibits higher rates of oxygen consumption and heat release intensity compared to short-term water-immersed coal. Additionally, the oxygen-consuming activation energy for oxygen consumption of long-term water-immersed coal is lower. The increase in air flow and water immersion time generally leads to the extreme value of the limit parameters, such as the local maximum of minimal thickness of residual coal and the lower limit oxygen fraction, the local minimum of the maximal air leakage intensity develops in the direction of increasing the risk of spontaneous combustion of coal in goaf.

Introduction

The example of China demonstrates that despite adjustments made to its primary energy structure and a reduction in the proportion of coal consumption, it continues to be a significant consumer and producer of coal¹. The occurrence of coal spontaneous combustion (CSC) accidents in mine incidents accounted for over 90%, resulting in economic losses of 20 billion yuan annually^2,3.The issue not only incurs substantial economic losses for enterprises, but also significantly jeopardizes the safety of underground operators and the ecological environment. In the process of coal production, transportation, and storage, it is challenging to prevent coal from being exposed to groundwater and rainwater. The likelihood of spontaneous combustion in water-immersed coal is higher compared to non-water-immersed coal⁴. The study conducted by Dong et al.⁵ revealed that coal undergoes significant expansion and softening upon immersion in water for a specific duration, resulting in the formation of distinct fragmentation patterns and detachment of smaller particles from the coal matrix. The simultaneous dissolution of certain minerals in the water leads to a reduction in the mineral content of coal, while simultaneously increasing the proportion of macroscopic pores and specific surface area⁶. Qin et al.⁷, revealed that prolonged soaking resulted in enhanced pore interfaces, as evidenced by increased average pore size, pore diameter, and micropore flow. Li et al.⁸ investigated the impact of pore structure on the properties of water-saturated coal and discovered that following a specific duration of water impregnation, the gas permeability of the coal samples increased, and the development of fractures and pores became more pronounced. Additionally, the adsorbed oxygen concentration surpasses that of raw coal, indicating an enhanced heating rate and a heightened propensity towards spontaneous combustion. According to the research conducted by Zhong et al.⁹, when the moisture content of coal samples falls within a specific range, water-immersed coal exhibits a higher susceptibility to spontaneous combustion compared to raw coal. The study conducted by Song et al.¹⁰ demonstrated that the immersion process significantly augmented the propensity for spontaneous combustion in long flame coal.

The term “secondary oxidation” refers to the phenomenon where oxidated coal, under conditions of good ventilation and heat storage, undergoes oxidation process again. This results in the coal extinguishing to normal temperature after exceeding the critical temperature, only to reignite again^11,12. In China, the issue of secondary oxidation of residual coal in goafs is particularly severe, leading to uncontrolled fires post-oxidation. Consequently, a significant number of coal mines are required to undertake well sealing and remediation measures¹³. The study conducted by Liu et al.¹⁴ demonstrated that high quality bituminous coal subjected to secondary oxidation exhibits enhanced low temperature oxidation, heightened the risk of spontaneous combustion, and increased susceptibility to spontaneous combustion. The secondary oxidation of residual coal, as demonstrated by Liang et al.¹⁵, revealed that compared to raw coal, residual coal exhibits a lower characteristic temperature and heat absorption, but higher heat release, mass loss rate, and comprehensive combustion coefficient during the secondary oxidation process. Consequently, oxidized coal resulting from primary oxidation possesses an increased risk of spontaneous combustion. Zhang et al.¹⁶ demonstrated that primary oxidation solely induced alterations in the functional group content of coal, without affecting the types of functional groups present. However, it was observed that the active structure of coal increased following primary oxidation, thereby leading to an enhanced propensity for spontaneous combustion. The research conducted by Guo et al.¹⁷ demonstrated that the onset of strong oxidation in primary oxidized coal occurred later compared to raw coal. The study conducted by Liu et al.¹⁸ revealed that coal exhibits a faster heating rate and lowers critical temperature and dry cracking temperature after undergoing primary oxidation, as compared to raw coal. Pan et al.¹⁹ showed experimentally that primary oxidized coal is more easily oxidized. The secondary oxidation of oxidized coal was found to exhibit a higher level of complexity compared to that of raw coal by Niu et al.²⁰. Tang et al.²¹ discovered that the heightened risk of spontaneous combustion in oxidized coal can be attributed to a reduction in its aromatic structure and aliphatic groups, coupled with an increase in the presence of oxygen-containing functional groups. The study conducted by Zhang et al.²² demonstrated that manipulating the air flow conditions significantly influences CSC, as evidenced by the results of the programmed temperature experiment. The research conducted by Lei et al.²³ demonstrated that as the air flow increases, there is an upward shift in the area with a high oxygen flow fraction, leading to a progressive increase in temperature within the coal. The study conducted by Liu et al.¹⁸ demonstrates that the primary oxidation process, coupled with an increase in air flow, can effectively lower the oxygen-consuming activation energy of the slow oxidation stage.

The process of CSC is a highly intricate physical and chemical phenomenon, encompassing not only physical and chemical adsorption but also formal and formless heat release. Currently, the mechanism behind CSC is still being explored, with numerous scholars investigating it under various conditions²⁴. Presently, most researchers primarily focus on studying CSC under individual conditions such as water-immersion, airflows, oxygen concentration, and secondary oxidation; however, there are limited studies on the combination of multiple conditions. This study examines the secondary oxidation and spontaneous combustion characteristics of coal with different water immersion times under varying air volume conditions to investigate the mechanism of CSC through analysis of oxygen-consuming activation energy, oxygen consumption rate, heat release intensity, and ultimate spontaneous combustion parameters.

Experimental materials and procedures

Experimental materials

The lignite produced by Zuoyun Donggucheng Coal Industry Co. Ltd. of Shanxi Coal Import and Export Group was used in this experiment. The coal samples were crushed to a particle size of less than 10 mm by applying a pressure of 25 MPa through a hydraulic press. Put 200 g of well-stirred crushed coal samples into 1 L wide-mouth plastic bottles and then pour them full of pure water to seal and store them, and then invert and shake them 3 times a day. Upon reaching the designated immersion duration, the coal sample is transferred from the wide-mouth plastic bottle to the tray. Subsequently, the tray is positioned at an angle for a period of 30 min to facilitate the drainage of excess surface moisture from the coal sample. The drained coal samples were placed horizontally in trays and subsequently transferred to a vacuum drying oven, where they were subjected to a constant temperature of 40 °C for 6–10 h to facilitate the removal of surface moisture from the coal samples. The coal samples were named according to the number of days of water-immersed, air flow, primary oxidation, secondary oxidation, and the naming rules are shown in Table 1.

Table 1.

Experimental conditions and naming symbols.

Variable indicators	Variable indicator values	Notation
Number of immersed days	Short-term (50 days) immersed coal	S
	Long-term (200 days) immersed coal	L
Air flow	200 mL/min	q1
	150 mL/min	q2
	100 mL/min	q3
	50 mL/min	q4
Oxidation process	Primary oxidation	1
	Secondary oxidation	2

Experimental methods

For the experiment, a copper canister made of red copper with inner diameter Φ = 39 mm, outer diameter Φ = 42 mm and height H = 270 mm was chosen as the coal sample canister, and the loading height h = 240 mm. The coal temperature was measured at the center of the coal sample using a type K thermocouple. The inlet air is heated by a copper inlet pipe, which has an inner diameter of Φ = 3 mm, an outer diameter of Φ = 4 mm, and a length of L = 50 m. This ensures that the temperature of the coal sample’s inlet air matches the ambient temperature. The experimental setup consisted of four parts: gas supply system, programmed heating system, temperature detection system, and gas chromatography²⁵.

The coal sample tank was connected to the air supply system, and the experimental air flow was adjusted to facilitate low-temperature primary oxidation with a temperature increase rate of 0.5 °C/min. After the heating device reaches 38 °C, the temperature is kept constant for half an hour, and the heating rate of 0.5 °C/min is continued after the coal temperature reaches 38 °C. When the temperature of the coal reaches 170 °C, heating is ceased, and the gas supply is switched from air to nitrogen. The flow rate of nitrogen is set at 250 mL/min to inhibit coal oxidation and facilitate cooling. When the coal temperature drops to room temperature, re-change the air supply and open the program again to raise the temperature of the coal samples for the second oxidation process, the secondary oxidation process of the heating rate, air flow conditions consistent with the primary oxidation process. During the experiment, the gas was collected at the air outlet at the end of the coal sample tank at intervals of 10 °C within the range of 40–170 °C, and the components and concentration of the gas were detected by gas chromatograph.

The air flow selection in similar experiments primarily focuses on the range of 50-150 mL/min^{14,17,23,26,27}. Therefore, a gradient of 50mL/min is utilized to select an air flow ranging from 50 to 200 mL/min for the experiment.

The gas samples obtained during the experiment were measured three times, and the average value was taken to obtain an accurate measurement of gas concentration.

Experimental results and analysis

Calculation of oxygen-consuming activation energy of oxygen consumption

The O₂ concentration is shown in Fig. 1.

Fig. 1.

O₂ concentration under different experimental conditions.

The oxygen-consuming activation energy of oxygen consumption is a crucial parameter for characterizing the level of oxidation difficulty. A higher value indicates a more challenging coal-oxygen recombination reaction and a reduced risk of spontaneous combustion. The equation for calculating the oxygen-consuming activation energy of coal is shown in Eq. (1)²⁸:

1

In the equation, represents the actual inlet oxygen concentration, mol/cm³; represents actual outlet oxygen concentration, mol/cm³ ; A represents pre-factor, s^–1 ; E represents oxygen-consuming activation energy, J/mol; R represents gas constant, 8.314 J/(mol k); T represents thermodynamic temperature, K; Q represents air delivery flow, cm³/s ; represents flow of coal sample, cm³.

Let , , then . Let, , then followed by

The low-temperature oxidation (40–170 °C) process of experimental coal samples can be categorized into three stages, based on the relationship between oxygen concentration and coal temperature during CSC, as depicted in Fig. 1. The stage I involves coal temperatures ranging from 40 to 90 °C, during which the oxygen consumption is relatively sluggish, and the concentration changes exhibit minimal variations; The coal temperature reaches 100–130 °C in the stage II, leading to an acceleration in oxygen consumption. As a result, the oxygen concentration rapidly declines and the disparity between each air flow increases; The stage III is characterized by a coal temperature range of 140–170 °C. Within this temperature range, the rate of oxygen consumption accelerates, leading to a significant decrease in oxygen concentration and an increase in the disparity between each air flow. A linear fit with as the horizontal coordinate and as the vertical coordinate was performed to obtain the and R² for each segment as shown in Fig. 2, followed by the oxygen-consuming activation energy as shown in Fig. 3. The closer R² approaches 1, the stronger the correlation between the equation and observed data.

Fig. 2.

Fitting of coal samples to 1/T under different conditions

Fig. 3.

Oxygen-consuming activation energy of coal samples under different experimental conditions.

During the primary oxidation of the coal samples, the oxygen-consuming activation energy of long-term water-immersed coal decreased by 85.81%, 84.58%, 47.08%, and 80.02% under q₁, q₂, q₃, and q₄ conditions in stage I respectively, compared to that of short-term water-immersed coal; the oxygen-consuming activation energy of long-term water-immersed coal decreased by 43.87%, 77.06%, and 78.81% under q₁, q₂, and q₃ conditions in stage II, respectively, while it increased by 81.61% under q₄ conditions compared to short-term water-immersed coal; the apparent activation energies of long-term water-immersed coal under q₁ and q₂ conditions decreased by 29.07% and 5.76%, respectively, compared to those of short-term water-immersed coal in stage III; The long-term water-immersed coal under q₃ and q₄ conditions resulted in a respective increase of 2.40% and 19.59% in the oxygen-consuming activation energy during stage III.

During the secondary oxidation of the coal samples, the apparent activation energies of the long-term water-immersed coal under q₁, q₂, q₃, and q₄ conditions in stage I were reduced by 75.81%, 45.45%, 14.84%, and 7.37% respectively compared to those of the short-term water-immersed coal; the apparent activation energies of long-term water-immersed coal under q1 conditions exhibited a 6.78% increase, while those under q₂, q₃, and q₄ conditions in stage II showed reductions of 68.28%, 30.70%, and 39.11% respectively when compared to the short-term water-immersed coal; the oxygen-consuming activation energy of long-term water-immersed coal decreased by 52.32%, 54.80%, and 59.05% under q₁, q₂, and q₃ conditions, respectively, in stage III compared to that of short-term water-immersed coal. Additionally, the oxygen-consuming activation energy of long-term water-immersed coal increased by 154.39% under q₄ conditions in stage III compared to that of short-term water-immersed coal.

During the experimental process of short-term water-immersed coal, the apparent activation energies of the coal samples in stage I of the secondary oxidation process under q₁, q₂,q₃, and q₄ conditions were reduced by 49.20%, 74.55%, 71.47%, and 18.59% respectively compared to those observed during the primary oxidation process; the oxygen-consuming activation energy of coal samples during stage II of secondary oxidation, under q₁, q₂, and q₃, is reduced by 42.78%, 55.25%, and 52.97% respectively compared to the primary oxidation process. Additionally, the oxygen-consuming activation energy of coal samples under q₄ is increased by 63.69% compared to the primary oxidation process; the oxygen-consuming activation energy of the coal sample in stage III of the secondary oxidation process under q₁ is reduced by 36.37% compared to that of the primary oxidation process, while it increases by 16.42%, 46.45%, and 65.54% under q₂, q₃, and q₄ respectively.

During the experimental process of long-term water-immersed coal, the oxygen-consuming activation energy in the initial stage of secondary oxidation for coal samples under q₁, q₃, and q₄ conditions decreased by 72.08%, 39.39%, and 75.46% respectively compared to the primary oxidation process; the oxygen-consuming activation energy of the coal sample in the initial stage of secondary oxidation increased by 85.51% compared to that of primary oxidation under q₂; the oxygen-consuming activation energy of the coal sample in stage II of the secondary oxidation process is reduced by 1.91%, 48.74%, and 54.95% under q₁, q₂, and q₃, respectively, compared to that in the primary oxidation process, under q₄, it increases by 10.95% compared to the primary oxidation process; the oxygen-consuming activation energy of coal samples in stage III of secondary oxidation is observed to be 19.06%, 30.08%, and 27.60% lower than that of primary oxidation under q₂, q₃, and q₄ conditions, respectively; conversely, under the condition of q₁, the oxygen-consuming activation energy in stage III of secondary oxidation is found to be 11.48% higher than that in primary oxidation.

In summary, when the coal temperature exceeds 100 °C, 140 °C, and 140 °C respectively under air flow conditions of 50, 100, and 150 mL/min, the short-term activation energy for secondary oxidation of water-immersed coal is higher than that for primary oxidation. The oxygen-consuming activation energy of secondary oxidation in long-term water-immersed coal was observed to be lower than that of primary oxidation throughout the entire process of oxidation under all air flow conditions.

In the primary oxidation process, when the air flow was set at q₁ and q₂, it was observed that the long-term water-immersed coal exhibited higher reactivity compared to the short-term water-immersed coal once the coal temperature exceeded 100 and 140 °C respectively. Additionally, in other temperature ranges, the oxygen-consuming activation energy of the long-term water-immersed coal remained low. However, when the air flow exceeded q₂, all segments of coal temperature between 40 and 170 °C showed a consistent trend of low activation energy for long-term water-immersed coal. Furthermore, during the secondary oxidation process, all experimental conditions with varying air flows demonstrated reduced reactivity for long-term water-immersed coal.

Calculation of oxygen consumption rate

The oxygen consumption rate of the coal samples was calculated according to the oxygen consumption rate Eq. (2)²⁹, and its variation with temperature is shown in Fig. 4.

Fig. 4.

Oxygen consumption rate under different experimental conditions.

2

In the equation, represents oxygen consumption rate, mol/(cm³ s); Q represents air flow, cm³/s; represents flow of coal samples, cm³; represents actual inlet oxygen concentration, mol/cm³; represents actual outlet oxygen concentration, mol/cm³.

The oxygen consumption rate of the primary oxidation process of short-term water-immersed coal was consistently higher than that of the secondary oxidation process under the conditions of air flows q₁, q, and q₃. Moreover, this difference increased with temperature, particularly when the coal temperature exceeded 100 °C, where it became more significant. However, under the condition of air flow q₄, the oxygen consumption rate of the primary oxidation was generally lower than that of the secondary oxidation process.

The oxygen consumption rate of short-term water-immersed coal in an air flow of q₂–q₄ follows a similar pattern to that of long-term water-immersed coal under the same air flow conditions. However, the primary oxygen consumption rate is generally higher than the secondary oxygen consumption rate, and this difference increases with temperature, with a significant inflection point at 110 °C. In terms of overall performance, both primary and secondary oxidation rates increase with larger air flows.

In the primary oxidation process, within the range of q₂–q₄ for air flow, as the coal temperature increases, the oxygen consumption rate ratio of short-term immersed coal and long-term immersed coal under the same air flow condition gradually increases with rising coal temperature. At low coal temperatures, the oxygen consumption rate of short-term immersed coal is lower than that of long-term immersed coal. However, when the coal temperature reaches a certain turning point, the oxygen consumption rate of short-term immersed coal becomes higher. The temperature turning points for air flows q₄, q₃ and q₂ are 160 °C, 130 °C and 120 °C respectively. The transition temperature point, at which the oxygen consumption rate of short-term immersed coal exceeds that of long-term immersed coal during primary oxidation under an air flow ranging from q₂ to q₄, decreases with decreasing air flow. However, the oxygen consumption rate of short-term immersed coal remains consistently lower than that of long-term immersed coal when the air flow is set at q₁. The oxygen consumption rate of long-term immersed coal is generally higher than that of short-term immersed coal during the process of secondary oxidation, given the same air flow.

In the primary oxidation process, within the range of air flow q₂–q₄, with the increase of coal temperature, the ratio of the oxygen consumption rate of short-term water-immersed coal and long-term water-immersed coal under the same air flow condition increases gradually with the increase of coal temperature in general, and the oxygen consumption rate of short-term water-immersed coal is lower than that of long-term water-immersed coal in the case of lower coal temperature, and the oxygen consumption rate of short-term water-immersed coal starts to be higher than that of long-term water-immersed coal when the coal temperature reaches a certain temperature turning point. rate, for air flows q₁, q₂ and q₃, the temperature turning points are 160, 130 and 120 °C, respectively. That is to say, the turning temperature point at which the oxygen consumption rate of short-term water-immersed coal is higher than that of long-term water-immersed coal during primary oxidation with air flow in the range of q₂–q₄ decreases with the decrease of air flow, while the oxygen consumption rate of short-term primary oxidation of water-immersed coal with an air flow of q₁ is always lower than the oxygen consumption rate of long-term water-immersed coal. In the secondary oxidation process, the oxygen consumption rate of long-term water-immersed coal is basically higher than that of short-term water-immersed coal under the same air flow condition.

Calculation and analysis of CO and CO2 production rates

CO, CO₂ generation rate can characterize the intensity of coal-oxygen complexation. Based on the experimentally determined O₂, CO, and CO₂ concentrations, Eqs. (3) and (4) were calculated in conjunction with the CO and CO₂ generation rates²⁷:

3

4

In equations, represents the rate of production of carbon monoxide, mol/(cm³ s); represents the rate of production of carbon dioxide, mol/(cm³ s); represents actual outlet carbon monoxide concentration, mol/cm³; represents actual outlet carbon dioxide concentration, mol/cm³; represents the flow of the reactor, (cm³).

The rates of CO and CO₂ production in the coal samples during the programmed warming are shown in Figs. 5 and 6 respectively.

Fig. 5.

CO production rate of coal samples under different conditions.

Fig. 6.

CO₂ production rate of coal samples under different conditions.

The rate of CO generation from short-term water-immersed coal is higher than that from long-term water-immersed coal during both primary and secondary oxidation. The rate of CO generation from short-term and long-term immersed coal generally decreases as the air flow decreases. When the air flow is q₁, the CO generation rate of short-term water-immersed coal in the primary oxidation process is lower than that in the secondary oxidation process before 140 °C. When the air flow is q₂ and q₄, the CO generation rate of short-term water-immersed coal in the secondary oxidation process significantly exceeds that in the primary oxidation process. When the air flow is q₃, the CO generation rate of short-term immersed coal in the primary oxidation process surpasses that in the secondary oxidation process. The CO generation rate of long-term water-immersed coal in the primary oxidation process consistently outperforms that in the secondary oxidation process, with an increasing disparity as temperature rises.

When the air flow is q₃, the CO₂ generation rate of short-term water-immersed coal in the primary oxidation process is basically larger than that of long-term water-immersed coal, while the CO₂ generation rate in the secondary oxidation process is basically smaller than that of long-term water-immersed coal; when the air flow is q₄, the CO₂ generation rate of short-term water-immersed coal in the primary oxidation process is basically smaller than that of long-term water-immersed coal, while it is basically larger than that of long-term water-immersed coal in the secondary oxidation process. The change of CO₂ generation rate with the change of air flow in long and short-term water-immersed coal is like that of CO generation rate, which is reduced with the decrease of air flow. Except for the short-term water-immersed coal under the condition of q₂ air flow, the CO₂ generation rate in the primary oxidation process was slightly smaller than that in the secondary oxidation, the long and short-term water-immersed coal under the rest of the conditions showed that the CO₂ generation rate in the primary oxidation process was larger than that in the secondary oxidation.

Calculation and analysis of the upper limit of exothermic intensity

The heat released by coal-oxygen composite action is the main heat source of spontaneous combustion of coal, and the exothermic intensity is its important index. The upper limit of exothermic intensity is calculated by the Eq. (5)²⁶.

5

In the equation , represents upper limit of exothermic intensity, kJ/(cm³ s); represents average heat of reaction of CO, = 311.9 kJ/mol; represents average heat of reaction of CO₂, = 446.7 kJ/mol.

The upper limit of the exothermic intensity of the coal samples during the programmed warming is shown in Fig. 7.

Fig. 7.

Upper limit of exothermic intensity of coal samples under different conditions.

The exothermic intensity increases with the increase in air flow during oxidation processes, however, there is no significant difference in exothermic intensity between air flows q₂ and q₃. The upper limit of exothermic intensity in the primary oxidation process of short-term and long-term immersed coal generally exceeds that in the secondary oxidation process under equivalent air flow conditions, which contradicts the observed trend where the oxygen-consuming activation energy of long-term water-immersed coal is lower in the secondary oxidation process compared to that in short-term water-immersed coal. This discrepancy can be attributed to a compensatory effect between the pre-exponential factor A and the oxygen-consuming activation energy E.

During the secondary oxidation process, under identical air flow conditions, there is an increasing trend in the exothermic intensity ratio between short-term water-immersed coal and long-term water-immersed coal as temperature rises. Except for the coal samples under q₄ within a range of 110–140 °C showing a ratio between 1.0 and 1.2, all other tested coals display ratios below 1.0. This clearly indicates that short-term water-immersed coals generally exhibit lower exothermic intensities compared to their long-term counterparts. The rule aligns with the correlation between oxygen consumption rate and factors such as air flow, temperature, and immersion time.

In summary, as the air flow increases, both the rate of oxygen consumption and the upper limit of coal exothermic intensity increase with rising temperature. Furthermore, during both primary and secondary oxidation processes under identical air flow time and air flow conditions, these two variables exhibit higher values in the former. This is because after the primary oxidation, the number of functional groups in oxidized coal that can react with oxygen decreases, so that the coal-oxygen recombination reaction in the secondary oxidation process is less complete than that in the primary oxidation, and the oxygen consumption rate and heat release intensity are reduced. The oxygen consumption rate and the upper limit of exothermic intensity during the primary oxidation process are generally lower for short-term immersed coal at air flow of q₁ compared to long-term immersed coal, the same pattern also applies in the low temperature when the air flow rates are q₂, q₃, and q₄. However, there is a temperature inflection point (120 °C, 130 °C, and 160 °C) that increases with increasing air flow rate, when the coal temperature exceeds this inflection point, both the upper limit of oxygen consumption rate and exothermic intensity during short-term immersion oxidation process are higher than those during long-term immersion oxidation process. The upper limit of oxygen consumption rate and heat release intensity of long-term water-immersed coal is generally higher than that of short-term water-immersed coal under the same air flow during the process of secondary oxidation.

Calculation and analysis of limiting parameters

CSC is a result of the joint action of intrinsic and extrinsic factors of coal, and CSC may occur when both intrinsic and extrinsic factors fulfill the conditions. The limit value of external conditions under which coal can spontaneous combustion is called CSC limiting parameter, which mainly includes minimal thickness of residual coal, limit oxygen concentration and lower limit air leakage intensity. The calculation equations for the minimal thickness of residual coal, the lower limit oxygen concentration, and the maximal air leakage intensity are shown in Eqs. (6),  (7), and  (8)^31,32, respectively.

6

7

8

In equations, represents minimal thickness of residual coal, cm ; represents air density, kg/m³; represents specific heat capacity of air, J/(kg K); q represent exothermic intensity, cm/s; represents temperature of the coal body enclosure, °C; T represents the air flow temperature, °C; represents equivalent thermal conductivity of the loose coal body, J/(cm s K); represents exothermic intensity of the loose coal body at temperature T, J/(cm³ s); represents low limit oxygen flow fraction, %; represents oxygen concentration in the air, %; h represents thickness of the loose coal body, cm; represents maximal air leakage intensity, cm/s.

As shown in Figs. 8, 9 and 10. The minimal thickness of residual coal, the lower limit oxygen flow fraction, and the maximum air leakage intensity under corresponding conditions are calculated and obtained by taking a 90 cm thickness of residual coal in the goaf of a coal mine, an air leakage intensity of 0.025 cm/s, and a surrounding rock temperature of 25 °C as an example. This calculation is combined with experimental results on the change rules of oxygen concentration and exothermic intensity.

Fig. 8.

Minimal thickness of residual coal for each condition.

Fig. 9.

Low limit oxygen flow fraction for each condition.

Fig. 10.

Maximal air leakage intensity for each condition.

Figures 8 and 9 demonstrate that as the coal temperature increases, there is an initial increase followed by a decrease in both the minimal thickness of residual coal and the low limit oxygen flow fraction. In addition to the primary oxidation process of water-immersed coal under air flows of q₃ and q₂, the minimal thickness of residual coal and low limit oxygen flow fraction at the spontaneous combustion starting temperature (40 °C) of water-immersed coal decrease as the air flow increases. That is, the more serious the air leakage, the smaller the amount of coal left behind required to trigger spontaneous combustion, the lower the oxygen concentration, the larger the scope of the hazardous area for spontaneous combustion to occur in the goaf of coal mine, and the higher the risk of spontaneous combustion. The minimal thickness of residual coal and the lower limit oxygen fraction for spontaneous combustion initiation (40 °C) in long-term water-immersed coal decreased significantly compared to the occurrence of short-term water-immersed coal, indicating that under the experimental conditions, the longer the water immersion time, the smaller the residual flow of coal and the lower oxygen fraction required to initiate spontaneous combustion, the greater the range of the risk of spontaneous combustion in the goaf of coal mine, and the greater the danger of spontaneous combustion. Short-term water-immersed CSC initiation (40 °C) in the air flow of q₂, q₄ conditions of primary oxidation of the minimal thickness of residual coal, the lower limit oxygen fraction concentration is less than the secondary oxidation, the rest of the air flow conditions on the contrary. And the minimal thickness of residual coal and the low limit oxygen flow fraction for the secondary oxidation of long-term water-immersed coal are greater than the primary oxidation. That is, under the condition of q₂ and q₄ air flow of short-term water-immersed coal secondary oxidation requires a smaller amount of residual coal and lower oxygen concentration, that the risk range of spontaneous combustion in the airspace is larger, and the risk of spontaneous combustion is greater. The remaining conditions of water-immersed coal secondary oxidation requires a greater amount of residual coal, higher oxygen concentration, the risk of spontaneous combustion in the goaf of coal mine is smaller in scope, and the risk of spontaneous combustion is smaller.

Whether the phenomenon of CSC can be sustained should be considered the extreme value of the minimal thickness of residual coal and the lower limit oxygen flow, when the thickness of residual coal and the oxygen concentration are greater than extreme value is a necessary condition for it to be able to spontaneous combustion and can be sustained³³. The maximum value of minimal thickness of residual coal and low limit oxygen fraction of the experimental coal samples decreased with the increase of air flow, i.e., the greater the air leakage, the greater the risk of spontaneous combustion. Under the same water immersion time conditions, the minimal thickness of residual coal and the lower limit oxygen flow fraction of secondary oxidation are greater than that of primary oxidation, which indicates that the spontaneous combustion hazard of primary oxidation is greater. Under the same oxidation conditions, the minimal thickness of residual coal and the low limit oxygen flow fraction of long-term water-immersed coal are smaller than that of short-term water-immersed coal, indicating that the spontaneous combustion hazard of long-term water-immersed coal is greater.

Consistent with the pattern of spontaneous combustion hazard exhibited by the minimal thickness of residual coal and the low limit oxygen flow fraction. As shown in Fig. 10, the maximal air leakage intensity showed a decrease to a very small value and then an increase with increasing temperature. In addition to the short-term water-immersed coal in the air flow of q₂ and q₃ primary oxidation process, in the water-immersed CSC initiation (40 °C) the maximal air leakage intensity increases with the increase in air flow. That is, the more serious the air leakage, the greater the range of air leakage intensity that can trigger spontaneous combustion, the greater the range of hazardous areas in the goaf of coal mine where spontaneous combustion can occur, and the higher the risk of spontaneous combustion. The maximal air leakage intensity for spontaneous combustion initiation (40 °C) of long-term water-immersed coals increased significantly compared with that of short-term water-immersed coals, indicating that under the experimental conditions, the longer the submergence time, the greater the maximal air leakage intensity capable of initiating spontaneous combustion, the greater the scope of the hazardous area of the goaf of coal mine capable of spontaneous combustion, and the higher the risk of spontaneous combustion. The maximal air leakage intensity of short-term water-immersed coal was higher than that of secondary oxidation for primary oxidation under air flows of q₂ and q₄, and the remaining air flows were opposite. In contrast, the maximal air leakage intensity of the secondary oxidation of the long-term water-immersed coal was lower than that of the primary oxidation in all cases. That is, under the condition of air flow of q₂ and q₄ short-term water-immersed coal secondary oxidation of the leakage intensity range is larger, the hazardous area of the goaf of coal mine can occur spontaneous combustion range is larger, and the risk of spontaneous combustion is greater. The range of leakage intensity of secondary oxidation under the remaining conditions is smaller compared to primary oxidation, and the range of hazardous areas in the extraction zone where spontaneous combustion can occur is smaller, with a lower risk of spontaneous combustion.

Similarly, whether the CSC phenomenon can be sustained should also consider the maximal air leakage intensity of the very small value, on-site air leakage intensity is lower than the very small value of the coal remains in the goaf of coal mine before spontaneous combustion is likely to occur and sustained. The maximal air leakage intensity of the experimental coal samples decreased with the decrease in air flow, i.e. the larger the air leakage, the greater the spontaneous combustion risk. Under the same water-immersed duration and air flow, the maximal air leakage intensity of the second oxidation of coal samples is lower than that of the first oxidation, which indicates that the spontaneous combustion hazard of the first oxidation of coal samples is greater. Under the same oxidizing conditions, the maximal air leakage intensity of long-term water-immersed coal is greater than that of short-term water-immersed coal, indicating that the spontaneous combustion risk of long-term water-immersed coal is greater.

Conclusion

1. The oxygen-consuming activation energy of the secondary oxidation of short-term water-immersed coal is higher than that of the primary oxidation when the coal temperature exceeds 100, 140, and 140 °C under air flows of 50, 100, and 150 mL/min respectively. However, under an air flow of 200 mL/min, the secondary oxidation activation energy of short-term water-immersed coal is lower than that of the primary oxidation. The secondary oxidation of long-term water-immersed coal exhibits a lower rate compared to the primary oxidation when exposed to an air flow ranging from 40 to 170 °C. The activation energy of long-term water-immersed coal during primary oxidation is higher than that of short-term water-immersed coal when the coal temperature exceeds 100 and 140 °C, respectively, under air flows of 50 and 100 mL/min. However, at other temperature ranges, the activation energy of long-term immersed coal is lower. The oxygen-consuming activation energy of long-term water-immersed coal is relatively low when the air flow rate exceeds 100 mL/min and the coal temperature ranges from 40 to 170 °C. The findings indicate that, under the experimental condition of maintaining a constant stroke flow during the oxidation process, the oxygen-consuming activation energy of coal that has been submerged in water for an extended period is significantly diminished, thereby making the conditions necessary for spontaneous combustion more readily attainable.

2. In different oxidation processes, the principles governing exothermic intensity and oxygen consumption rate are essentially identical, with primary oxidation is higher than secondary oxidation. This is since following primary oxidation, the quantity of functional groups capable of engaging in secondary oxidation reactions diminishes. When the air flow rate is 100, 150, and 200 mL/min, respectively, there exists a temperature inflection point (120 °C, 130 °C, and 160 °C) that increases with the increase in air flow rate. When the coal temperature exceeds the temperature inflection point, both exothermic intensity and oxygen consumption rate during the primary oxidation process of short-term water-immersed coal are higher than those of long-term water-immersed coal. However, when the air flow rate is set at 50 mL/min, both exothermic intensity and oxygen consumption rate during the primary oxidation process of short-term water-immersed coal are lower compared to those of long-term water-immersed coal. In the secondary oxidation process, the exothermic intensity and oxygen consumption rate of the long-term water-immersed coal are greater than that of the short-term water-immersed coal.

3. The maximal value of minimal thickness of residual coal and low limit oxygen fraction generally increase with the decrease of air flow, and the maximal air leakage intensity decreases with the decrease of air flow; under the condition of the same air flow and the number of oxidizations, the maximal value of the minimal thickness of residual coal and the low limit oxygen fraction of long-term water-immersed coal are smaller than that of short-term water-immersed coal, and the minimal value of maximal air leakage intensity is smaller than that of short-term water-immersed coal; the maximal value of the minimal thickness of residual coal and the low limit oxygen fraction of secondary oxidization are larger than that of primary oxidization, and the minimal value of maximal air leakage intensity is smaller than that of primary oxidization. The increase in air flow and prolonged immersion time will exacerbate the risk of spontaneous combustion of abandoned coal in goaf, whereas the risk of spontaneous combustion of immersed coal in goaf decreases after primary oxidation, suggesting that the immersion factor of water will exert a more significant influence on the risk of spontaneous combustion during coal secondary oxidation.

Author contributions

Yu. Dong. Zhu. and Zhao. wrote the main manuscript text, Yu. Dong. Kong. and Zhang. carried out experiments and Yu. Dong. and Zhu. processed the data.All authors reviewed the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (grant number 51804107), the Natural Science Foundation of Hunan Province (grant number 2020JJ4260).

Data availability

All data generated or analyzed during this study are included in this published article.

Competing interests

The authors declare no competing interests.