Prediction of Coal Spontaneous Combustion Risk under Poor Oxygen Concentration Based on Fuzzy Clustering and Lattice Tightness

Abstract

To study the risk of coal spontaneous combustion (CSC) in goafs under poor oxygen concentrations, lignite, gas coal, and fat coal were selected as experimental samples for thermal analysis. The thermogravimetric curves and kinetic parametric equations of coal with different metamorphisms at oxygen concentrations of 18%, 14%, 10%, 5%, and 3% were studied. The results showed that the higher the degree of coal metamorphism, the lower the tendency for the oxidation reaction and spontaneous combustion. With the decrease of oxygen concentration, the weight loss rate of coal gradually decreased, and the apparent activation energy gradually increased. However, the heat release of CSC first increased and then decreased, with the greatest heat release when HM was at a 14% oxygen concentration, QM at 10%, and FM at 18%. On this basis, the thermal analysis parameters of CSC under different metamorphisms and oxygen concentrations were analyzed by fuzzy clustering, and coal was divided into two categories: spontaneous combustion risk and no spontaneous combustion risk. Combined with lattice tightness, the risk of CSC under different metamorphisms and oxygen concentrations can be determined.

1. Introduction

Coal spontaneous combustion (CSC), as one of the five major mining disasters, not only threatens the life and health of mine workers but also easily leads to the collapse of goafs, the erosion of surface soil, and the destruction of groundwater resources. − Nearly 60% of mines in China have mine fires, most of which are caused by spontaneous combustion of coal seams. − CSC is a highly intricate process involving dynamic physical and chemical reactions, primarily taking place in concealed areas like goafs, sealed fire zones, fractured coal pillars, and other dangerous zones of spontaneous combustion. These areas are prone to heat accumulation and decreased oxygen concentration due to slow wind flow. The oxygen concentration of the goaf is generally poor, and its oxygen concentration is lower than 21% in a normal atmosphere. Different depths of the goaf correspond to different oxygen concentrations. Coal oxidation in the goaf is influenced by factors such as the oxygen supply, heat release, and heat dissipation characteristics of coal. − Therefore, exploring the characteristics of CSC under different poor oxygen concentrations is extremely important for the prevention and control of CSC.

To take effective measures to predict CSC, many scholars have carried out some studies, mainly through the weight loss rate, heat release, activation energy, and so on, to study the thermal characteristics of coal. − The generation and accumulation of heat is the main direct cause of CSC. Exploring the basic thermal parameters of CSC can provide a reliable theoretical basis for the accurate prediction of mine fires. The generation and accumulation of heat is the major direct cause of CSC. Thermal parameters such as characteristic temperature, mass loss, thermal strength, and activation energy of CSC are affected by oxygen concentration. ,

However, previous studies are lacking in explaining the change of the thermal effect of CSC in anoxic environments. Oxygen concentration plays an important role in the process of CSC, affecting the oxidation capacity and heat release intensity of coal. Yutao et al. calculated the kinetic parameters of coal oxidation and found that as oxygen concentrations decreased, both the apparent activation energy and prefinger factor of coal oxidation also decreased. , This indicated that lowering the oxygen concentration can effectively suppress the risk of CSC. As the oxygen concentration decreased, the heat flow curve significantly decreased and the characteristic temperature increased. Additionally, the low oxygen environment markedly reduced the risk index of CSC. , Zhao et al. studied the thermal reaction of long flame coal in the heating process under different oxygen concentrations and obtained the effects of oxygen concentration on characteristic temperature and related parameters. Yang et al. constructed a mathematical model incorporating parameters such as apparent activation energy, heat capacity, heat release, and thermal conductivity and conducted precise measurements of the characteristic parameters associated with CSC. Although there are some studies on CSC at poor oxygen concentration, many thermal characteristics have been studied to predict CSC, but the in-depth research on the mathematical correlation and law between CSC parameters is still insufficient. Furthermore, to minimize the incidence of mine fires, it is essential to establish a prediction model of CSC based on the thermal parameters under different poor oxygen concentrations, so as to further improve the prediction method of CSC and more effectively prevent the disaster of CSC.

In this study, three coal samples with different metamorphic degrees under five different low oxygen concentrations were selected. Then, the thermal analysis experiments were conducted to investigate CSC, focusing on the change law of thermal parameters such as weight loss rate, heat release, and activation energy during the coal oxidation process. The mathematical relationship of characteristic parameters of the CSC under different metamorphisms and oxygen concentrations was analyzed, and the prediction model of the CSC was established. This study is of significant importance for the prevention and control of CSC.

2. Experiment and Method

2.1. Sample Selection and Preparation

The coal samples used in this study were brown coal (HM) from Yangchangwan in the Lingwu Mining Area, gas coal (QM) from Donghuantuo in the Tangshan Mining Area, and fat coal (FM) from Qianjiaying in the Tangshan Mining Area. Following collection from the mine, the coal was rapidly preserved under sealed conditions to avoid oxidation. Subsequently, the coal was pulverized and screened to a powder of less than 200 mesh particle size for the experiment. The proximate analyses of the coal samples are listed in Table .

1. Proximate Analysis of Coal Samples.

coal samples	M ad (%)	A d (%)	V ad (%)	FCdaf (%)
HM	6.27	3.22	29.88	70.12
QM	1.54	7.69	45.83	73.39
FM	0.68	14.96	26.61	54.17

2.2. Apparatus and Procedure

The experimental instrument is a thermogravimetric analyzer of STA-449-F3 in Figure , which mainly includes a TG test system and oxygen tanks with different concentrations. There are microbalances and differential thermocouples in the thermogravimetric analyzer, and the TG curve can be drawn by measuring the mass changes of coal samples in the thermogravimetric analyzer.

1.

A thermogravimetric analyzer of STA-449-F3.

Before conducting a thermogravimetric experiment, the samples were placed in a DZF-6020 vacuum drying oven and dried at room temperature for 12 h. Then, 10 mg of dried coal samples with a mesh size of over 200 was weighed and placed in an alumina crucible. Oxygen concentrations of 18%, 14%, 10%, 5%, and 3% were injected into the instrument. The injection flow rate was adjusted to 10 mL/min, and the samples were heated from 30 to 800 °C under controlled heating at 10 °C/min. After reaching the temperature, the experiment was stopped and the experimental data was obtained.

3. Results and Discussion

3.1. TG–DTG Curve Analysis

Thermal gravimetric experiments were conducted on coal samples with different metamorphic degrees at oxygen concentrations of 18%, 14%, 10%, 5%, and 3%. TG curves representing the mass fractions were obtained. The first derivative of the TG curve was calculated to obtain a DTG curve representing the rate of weight loss change with temperature. The changes in TG and DTG curves of coal with different metamorphic degrees were relatively consistent at different oxygen concentrations. Figure presents the DG and DTG curves of HM at an 18% oxygen concentration, as well as the division of characteristic temperature points (CTPs) at different stages.

2.

TG and DTG curves of HM at an 18% oxygen concentration.

The initial temperature (T ₀) refers to the room temperature during the experiment. The critical temperature (T ₁) denotes the temperature at which the first minimum point appears on the DTG curve. The dry-cracking temperature (T ₂) is the characteristic temperature corresponding to the TG curve when the DTG curve value is 0. The pyrolysis temperature (T ₃) signifies the point on the thermogravimetric curve where the oxygen absorption and weight gain of coal reach a second maximum, marking the end of the oxygen-absorption stage. The ignition temperature (T ₄) is the temperature at which coal begins to burn, which is the intersection point between the tangent of T ₃ on the thermogravimetric curve and the tangent of the thermogravimetric curve at the same temperature as that of the maximum weight loss temperature (T ₅). T ₅ corresponds to the lowest point on the DTG curve, where the mass of coal decreases the fastest. The burnout temperature (T ₆) is the temperature at which the mass of the coal sample remains unchanged after the combustion.

According to the CTP of coal during heating, the entire process of CSC can be roughly divided into four stages: the dehydration and desorption stage (T ₀ to T ₂), the oxidation stage (T ₂ to T ₄), the combustion stage (T ₄ to T ₆), and the burnout stage (T ₆ to the end). The oxidation stage comprises the oxygen adsorption stage (from T ₂ to T ₃) and the pyrolysis stage (from T ₃ to T ₄). Based on the above CTP and reaction stage division, Table shows the characteristic temperatures of samples at oxygen concentrations of 18%, 14%, 10%, 5%, and 3%.

2. Characteristic Temperature Points of Different Coal Samples.

coal sample	oxygen concentration (%)	T 1 (°C)	T 2 (°C)	T 3 (°C)	T 4 (°C)	T 5 (°C)	T 6 (°C)
HM	18	82.4	169.7	226.9	330.1	410.6	585.6
	14	78.4	179.1	228.7	331.2	423.2	601.9
	10	63.7	160.5	254.5	335.4	437.9	622
	5	52	142.1	240.9	336.4	445.4	666
	3	54.5	144.6	233.7	348.6	475.9	734.8
QM	18	102.5	162.8	284.3	358.7	473.5	664.2
	14	52.6	117.9	258.4	354.3	451.6	673.5
	10	44.5	92.4	277.6	362.7	452.6	699.6
	5	87	121	282	366.6	527.3	718.9
	3	84.6	130.5	278.3	378	479.9	735.9
FM	18	45.7	71.1	280.4	375.6	472.6	618.6
	14	54.6	127.3	315.3	361.9	514.8	645.4
	10		145.7	310.6	376.9	513	678.3
	5		110.4	324.8	397.2	567.9	775.1
	3		101.7	325.8	405.9	562.7	784.1

According to Table , it can be seen that the CTP of CSC is different due to the differences in metamorphic degree and oxygen concentration. The structure of HM with the lowest metamorphic degree is composed of many oxygen-containing active functional groups. In contrast to the other two coal samples, the dehydration and desorption stage (Stage I) requires a lower temperature (52 °C) and demonstrates a greater propensity for oxidation reactions. The T ₁ of HM at oxygen concentrations of 3% to 5% is 52 to 54.5 °C, which is reduced by about 25 °C compared to other oxygen concentrations. The T ₃ and T ₄ of HM are lower compared to those of QM and FM, which have a higher metamorphic degree. This suggests that coals with a lower metamorphic degree are more susceptible to spontaneous combustion. The metamorphic degree of QM is higher than that of HM, and the characteristic temperature point T ₁ is the lowest at 44.5 °C at a 10% oxygen concentration. The main body of the QM structure is stable, but there is an unstable side-chain structure. When the oxygen concentration is about 10%, the oxygen attacks the unstable side-chain structure of coal most violently, and the coal–oxygen reaction is the most intense. FM, as the most stable structure, has a low content of surface active structure and rarely undergoes dehydration, desorption, and oxidation reactions at relatively poor oxygen concentrations (<14%). Overall, oxidation reactions of fat coal require higher oxygen concentration and temperature than the others with different metamorphisms.

Figure shows the TG curves of coal samples under different oxygen concentrations. It is found that there are differences in the mass changes of the reaction under different oxygen concentrations.

3.

TG curves of coal samples (a) HM, (b) QM, and (c) FM.

Because the research focus is on the differences in the characteristics of CSC with different metamorphisms, a temperature range of T ₀ to T ₄ (the stages I to III) was selected for analysis during the study. As illustrated in Figure , coal with a lower metamorphic degree is more susceptible to oxygen-induced oxidation and spontaneous combustion reactions. HM has a greater mass reduction at oxygen concentrations of 3% and 5% than others, and overall, the mass reduction is greater than that of QM and FM. As observed, the structure of HM with a low metamorphic degree is unstable, rendering it prone to thermal cracking that produces active intermediates capable of reacting with oxygen. After the oxygen concentration reached 5%, the extent of HM fragmentation was maximized. As the oxygen concentration increases, oxygen attacks the molecules of HM fragments to cause structural changes and generate new active products to react with them, deepening the mass reduction of lignite. The mass reduction of QM at an oxygen concentration of 10% or 14% is greater than that at other concentrations. This is because the metamorphic degree of QM is higher than that of HM, and its main structure is relatively stable, but the side-chain structure is unstable. As the oxygen concentration gradually increases, the rate of oxygen attack on the side-chain structure of coal increases, making it easier for the coal oxygen reaction to occur. FM has the highest metamorphic degree, and there is no significant difference in quality reduction under different oxygen concentrations. Therefore, it can be seen that the structure of FM is the most stable and not easily affected by temperature and oxygen.

Comparing Figure a–c, it is found that as the metamorphic degree of coal increases, the processes of each stage of the coal oxygen reaction are correspondingly prolonged, most notably in the pyrolysis stage. This is because the higher the metamorphic degree of coal, the fewer the number of active groups in the structure of coal, the greater the content of aromatic hydrocarbon, the fewer the side chains prone to the cracking reaction and the active groups prone to oxidation reaction with oxygen, and the corresponding ignition temperature T ₄ also shows hysteresis with the increase of the metamorphism degree of coal.

3.2. DSC Curve Analysis

The DSC curve of lignite at an 18% oxygen concentration is shown in Figure . By integrating the DSC curve, the heat absorption and release curves of coal with different metamorphic degrees under different oxygen concentrations can be obtained. In a high-temperature environment, coal will always absorb heat and lead to spontaneous combustion. In the initial stage of the thermogravimetric experiment, coal absorbs heat, resulting in the removal of bound water and the release of small molecular gases (T ₀∼T ₂). With the increase of temperature (T ₂∼T ₃), the coal structural groups undergo cracking reactions (T ₃∼T ₄), generating active fragments that react with oxygen (T ₄∼T ₅), followed by chemical adsorption and reactions to release heat (T ₅∼T ₆).

4.

DSC curve of HM.

The variation trend of DSC curves for coal with different metamorphic degrees under different oxygen concentrations is consistent, as demonstrated in the DSC curve in Figure . With decreasing oxygen concentration, the curve transitions from a convex peak to a smoother profile, accompanied by the corresponding changes in the heat release of the coal sample. As demonstrated in Figure , the total heat release of coal with different metamorphisms is generally affected by oxygen concentration. However, the heat release of coal and the change in oxygen concentration are not always positively correlated.

5.

Heat release of coal with different metamorphic degrees.

When the oxygen concentration of HM increases from 3% to 18%, its heat release gradually increases and then decreases, reaching a maximum of 602.3 J/g. According to the coal oxygen composite theory, this phenomenon is due to the unstable structure of HM, which is easily affected by temperature to produce reactive intermediates. The reaction of the reactive intermediate with oxygen needs to release a substantial quantity of heat. With the increase of oxygen concentration, the production rate of reactive intermediates cannot keep up with the reaction rate of oxygen and reactive intermediates, leading to the gradual reduction of heat release.

The maximum heat release of QM is 631.5 J/g when the oxygen concentration is 10%. This is because the QM structure is relatively stable, and there are fewer reactive intermediates due to the influence of temperature at the stage of poor oxygen concentration. As the oxygen concentration increases to about 10%, the speed of oxygen attack on the coal side chain is accelerated, and the coal oxygen reaction is intensified. With the further increase of the oxygen concentration, the active structure of the side chain is consumed, and the oxygen molecules begin to attack the aromatic hydrocarbon structure. Because the aromatic hydrocarbon structure of the QM is relatively stable, the heat release begins to decrease.

As the molecular structure of high metamorphic coal, FM is not easily cracked under the influence of temperature. As the oxygen concentration increases, the heat release increases dramatically. The lower the metamorphic degree of coal, the easier it is to react with oxygen and the higher the release of heat.

3.3. Kinetic Analysis

The activation energy serves as an indicator of the tendency of CSC, and the lower the activation energy, the higher the tendency of CSC. During the T ₂ to T ₄ stages, coal absorbs heat and undergoes a coal oxygen composite reaction, gradually reaching a temperature that can cause coal to decompose upon heating. At this stage, the internal structure of coal will be affected by temperature to break the chemical bond and generate active fragments, which will react with oxygen to accelerate the decomposition of the coal. Therefore, studying the apparent activation energy at this stage is more meaningful than at other stages and can provide guidance for dividing the oxygen concentration of CSC under oxygen-deficient environments.

The Coats Redfren integration method is used to calculate the integration of the oxygen absorption and weight gain stages and the thermal decomposition stages of coal, as shown in eq

$$\ln \left[\frac{G(\alpha )}{T^2}\right]=\ln \frac{AR}{\beta E}-\frac{E}{RT}$$ 1

where α is the conversion rate, %; β is the heating rate, K/min; A is the pre factor, min^–1, E is the activation energy, J/mol.

The ln–ln­(1 – α)/T ² and 1/T curves of coal with different metamorphic degrees under different oxygen concentrations according to eq are shown in Figure . The activation energy E can be calculated based on the slope of the fitted line.

6.

Kinetic correlation curves of coal (a) HM, (b) QM, and (c) FM.

Table shows the changes in apparent activation energy and the correlation coefficient R ² of the coal oxygen reaction during the T ₂ to T ₄ stages of coal with different degrees of metamorphism under different oxygen concentrations.

3. Dynamic Parameters of Coal with Different Metamorphic Degrees.

	HM		QM		FM
oxygen concentration (%)	R 2	E (kJ/mol)	R 2	E (kJ/mol)	R 2	E (kJ/mol)
18	0.972	6.26	0.981	26.70	0.992	43.64
14	0.984	7.89	0.981	15.18	0.998	37.67
10	0.989	9.30	0.983	14.63	0.986	53.08
5	0.997	9.94	0.971	31.79	0.989	65.00
3	0.993	18.26	0.981	41.76	0.984	67.43

From Table , it can be seen that as the degree of coal metamorphism increases, the activation energy required for the CSC under variable oxygen conditions becomes higher and higher. It can be seen that coal has a high metamorphic degree and stable molecular structure, so more energy is required for the cracking reaction.

The fitting curve R ² values of lignite, gas coal, and fat coal under different oxygen concentrations are all greater than 0.97, indicating that the linear fitting effect is good at these oxygen concentrations. The apparent activation energy of coal can be obtained on the basis of the fitted slope: lignite: 6.26 kJ/mol (minimum), gas coal: 14.63 kJ/mol (minimum), and fat coal: 37.67 kJ/mol (minimum). The reason for this phenomenon may be due to the stronger structural activity of lignite compared with gas coal and fat coal. When the oxygen concentration is at 3%, the coal structure begins to be affected by temperature to break bonds and undergo a coal oxygen reaction with oxygen; the side chain structure of gas coal is unstable and prone to bond breakage, resulting in the formation of small-molecule compound structures. With the addition of oxygen, oxygen attacks small-molecule compounds to generate active fragments, requiring a large amount of activation energy, reaching a maximum of 41.76 kJ/mol. After the oxygen concentration reaches 10%, the coal oxygen reaction rate accelerates and the required energy decreases to 14.63 kJ/mol. The small-molecule compounds generated by the side chains are not enough to react with oxygen, and oxygen begins to attack the main structure of coal, requiring energy to gradually increase to 26.7 kJ/mol. This is why the apparent activation energy gradually increases when the oxygen concentration exceeds 10%; as a high metamorphic coal, the structure of fat coal is stable. When oxygen is added, it attacks the side-chain structure of fat coal, causing bond breakage and an atomic torsion reaction. This stage consumes the maximum energy, reaching 67.43 kJ/mol. When the oxygen concentration reaches 14%, the speed of the oxygen attack on the fatty coal side chain increases. At this time, the fatty coal side chain structure undergoes structural adjustment and generates active groups for aerobic reactions. Because of the high activity of the groups, the energy required for the reaction is reduced to 37.67 kJ/mol.

3.4. Fuzzy Clustering Prediction Method of CSC

3.4.1. Establishing a Fuzzy-Pattern Library of CSC

According to the analysis of the thermal characteristics of coal with different degrees of metamorphism, it can be concluded that the severity of the coal oxygen reaction varies with different degrees of metamorphism under different oxygen concentrations, which can lead to differences in the tendency of CSC with different degrees of metamorphism under different oxygen concentrations. In order to identify the tendency of others’ CSC with the same metamorphic degree under different oxygen concentrations, the fuzzy clustering method is selected to predict them. − Fuzzy clustering analysis refers to the method of classifying objects according to certain characteristics and specific requirements.

First, the fuzzy matrix similarity is established by using the sum of squares of differences. r _ij ∈ [0,1] is used to connect the correlation between x _i and x _j . The specific formula for constructing a fuzzy matrix is eq .

$$r_{\mathrm{i}\mathrm{j}}=1-c·\sqrt{\sum _{\mathrm{k}=1}^m{(x_{ik}-x_{jk})}^2}$$ 2

Among them, c > 0 is a constant, which can be selected according to the actual situation. This article takes c = 0.005.

The fuzzy matrix is calculated according to eq . The original data of the thermal characteristic parameters and the calculated fuzzy matrix are shown in Table .

4. Thermal Characteristic Parameters of Coal Samples.

oxygen concentration (%)	coal sample	T 4 (°C)	heat release (J/g)	apparent activation energy (kJ/mol)
18	HM1	330.1	572.6	6.26
	QM2	358.7	608	26.7
	FM3	375.6	641.5	43.64
14	HM4	331.2	602.3	7.89
	QM5	354.3	614.7	15.18
	FM6	361.9	623.7	37.67
10	HM7	335.4	541.5	9.3
	QM8	362.7	631.5	14.63
	FM9	376.9	577.1	53.08
5	HM10	336.4	523.6	9.94
	QM11	366.6	561.1	31.79
	FM12	397.2	545.6	65
3	HM13	348.6	473.2	18.26
	QM14	378	490.8	41.76
	FM15	405.9	512.8	67.43

After establishing the fuzzy matrix, the data are normalized using the range transformation method, as shown in eq .

$$X_{\mathrm{i}\mathrm{j}}^{\prime }=\frac{X_{\mathrm{i}\mathrm{j}}-\min \{X_{\mathrm{i}\mathrm{j}}\}}{\max \{X_{\mathrm{i}\mathrm{j}}\}-\min \{X_{\mathrm{i}\mathrm{j}}\}}\left[\begin{array}{l}i=1,2,...,n\\ j=1,2,...,n\end{array}\right]$$ 3

The fuzzy matrix obtained by normalizing the original data of the thermal characteristic parameters of CSC is shown in Table .

5. Fuzzy Matrix Obtained from Original Data.

number	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	1
2	0.75	1
3	0.55	0.79	1
4	0.85	0.83	0.65	1
5	0.75	0.93	0.78	0.86	1
6	0.66	0.90	0.88	0.76	0.87	1
7	0.84	0.64	0.43	0.70	0.62	0.55	1
8	0.66	0.87	0.83	0.78	0.91	0.88	0.53	1
9	0.67	0.78	0.67	0.65	0.71	0.74	0.65	0.66	1
10	0.75	0.56	0.36	0.61	0.54	0.47	0.91	0.44	0.60	1
11	0.77	0.76	0.59	0.70	0.71	0.68	0.78	0.64	0.86	0.74	1
12	0.53	0.59	0.50	0.48	0.52	0.55	0.58	0.47	0.80	0.58	0.76	1
13	0.55	0.39	0.20	0.41	0.36	0.30	0.71	0.27	0.49	0.80	0.61	0.55	1
14	0.49	0.40	0.25	0.37	0.36	0.33	0.63	0.28	0.56	0.69	0.64	0.69	0.81	1
15	0.43	0.43	0.33	0.35	0.37	0.39	0.52	0.32	0.64	0.55	0.64	0.83	0.57	0.78	1

According to the given order of the coal sample and oxygen concentration, X = {component 1, component 2, component 3, component 4, component 5, component 6, component 7, component 8, component 9, component 10, component 11, component 12, component 13, component 14, component 15} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}.

According to the definition of fuzzy matrix, r _ij ≠ 0, sorted 1 > 0.93 > 0.91 > 0.90 > 0.88 > 0.87 > 0.86 > 0.85 > 0.84 > 0.83 > 0.80 > 0.79 > 0.78 > 0.77 > 0.76 > 0.75 > 0.74 > 0.71>······>0.24 > 0.21 > 0.14.

Taking 0.93 < a ≤ 1, X can be divided into 15 categories:

{1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {10}, {11}, {12}, {13}, {14}, and {15}.

Taking 0.91 <a ≤ 0.93, X can be divided into 14 categories:

{1}, {2, 5}, {3}, {4}, {6}, {7}, {8}, {9}, {10}, {11}, {12}, {13}, {14}, and {15}.

Taking 0.90 < a ≤ 0.91, X can be divided into 12 categories:

{1}, {2, 5, 8}, {3}, {4}, {6}, {7, 10}, {9}, {11}, {12}, {13}, {14}, and {15}.

Taking 0.88 < a ≤ 0.90, X can be divided into 11 categories:

{1}, {2, 5, 6, 8}, {3}, {4}, {7, 10}, {9}, {11}, {12}, {13}, {14}, and {15}.

Taking 0.86 < a ≤ 0.88, X can be divided into 10 categories:

{1}, {2, 3, 5, 6, 8}, {4}, {7, 10}, {9}, {11}, {12}, {13}, {14}, and {15}.

Taking 0.85 < a ≤ 0.86, X can be divided into 8 categories:

{1}, {2, 3, 4, 5, 6, 8}, {7, 10}, {9, 11}, {12}, {13}, {14}, and {15}.

Taking 0.84 < a ≤ 0.85, X can be divided into 7 categories:

{1, 2, 3, 4, 5, 6, 8}, {7, 10}, {9, 11}, {12}, {13}, {14}, and {15}.

Taking 0.83 < a ≤ 0.84, X can be divided into 6 categories:

{1, 2, 3, 4, 5, 6, 7, 8, 10}, {9, 11}, {12}, {13}, {14}, and {15}.

Taking 0.80 < a ≤ 0.83, X can be divided into 6 categories:

{1, 2, 3, 4, 5, 6, 7, 8, 10}, {9, 11}, {12, 15}, {13}, and {14}.

Taking 0.79 < a ≤ 0.80, X can be divided into 2 categories:

{1, 2, 3, 4, 5, 6, 7, 8, 10}, {9, 11, 12, 15}, {13}, and {14}.

Taking 0.78 < a ≤ 0.79, X can be divided into 2 categories:

{1, 2, 3, 4, 5, 6, 7, 8, 10}, {9, 11, 12, 15}, and {13, 14}.

Taking 0.77 < a ≤ 0.78, X can be divided into 2 categories:

{1, 2, 3, 4, 5, 6, 7, 8, 10} and {9, 11, 12, 13, 14, 15}.

Finally, the above two types of samples are combined to form a fuzzy-pattern library {S ₁, S ₂}, where S ₁ is a collection of prone to spontaneous combustion patterns and S ₂ is a collection of prone to nonspontaneous combustion patterns.

The average values of T ₄, heat release, and apparent activation energy of fuzzy-pattern library indicators S ₁ and S ₂ are shown in Table .

6. Fuzzy-Pattern Library Indicator Data.

sample	T 4	heat release	apparent activation energy
S 1	349.59	595.49	19.02
S 2	378.87	526.77	46.22
standardized S 1	1.00	1.00	0.00
standardized S 2	0.00	0.00	1.00

According to eq , the standardized fuzzy-pattern library indicator data are obtained in Table . After obtaining a standardized fuzzy database, the test data can be tested to see its tendency toward spontaneous combustion.

3.4.2. Determining the Tendency of CSC by Lattice Tightness

When detecting the spontaneous combustion tendency of the test data, we need to choose a fuzzy recognition mode. The mode selected in this article is lattice tightness, as shown in eq .

$$\sigma (A,B)=\frac{1}{2}[A·B+(1-A\odot B)]$$ 4

where A,B is a fuzzy subset on the domain U, and σ­(A,B) is called the degree of fit between A and B; A·B are called the “inner product” of A and B, A·B = ∨(A(X _i )∧B(X _i )); A⊙B are called the “outer product” of A and B, A⊙B = ∧(A(X _i )∨B(X _i )).

The larger the value of σ­(A,B), the closer A is to B.

According to eq , the fit degree between the coal sample data that has been determined to have a certain degree of metamorphism and the standardized fuzzy data can be calculated to determine the spontaneous combustion tendency of the data to be tested.

4. Conclusion

This study investigated the thermal characteristic parameters of CSC with different metamorphic degrees under poor oxygen concentrations and established a fuzzy clustering prediction method of CSC.

• 1The CSC tendency decreased with a higher coal metamorphism. The reduction of oxygen concentrations suppressed oxidation, raising the activation energy for the oxidation of coal. Heat release exhibited nonlinear behavior, peaking at 14%, 10%, and 18% of oxygen concentration for lignite, gas coal, and fat coal, respectively.
• 2Lower metamorphism coals (lignite) showed a minimal activation energy (6.26 kJ/mol), indicating higher CSC susceptibility, while high metamorphism coals (fat coal) required up to 67.43 kJ/mol. The Coats–Redfern model reliably described reaction kinetic behaviors (R ² > 0.97).
• 3Fuzzy clustering effectively categorized coals under different poor oxygen concentrations into high-risk (S ₁) and low-risk (S ₂) groups based on thermal parameters. The lattice tightness method quantified risk levels, offering a practical predictive method.

These results provide critical insights for CSC prevention in goafs, emphasizing the importance of conducting risk assessments based on different coal types and poor oxygen concentrations. Future work should focus on field validation and the integration of real-time monitoring.

All data supporting the findings of this study are fully available within the article. No additional public data repository deposition is required.

Dong Gao: writingreview and editing, resources, funding acquisition, data curation. Jianxin Li: writing original draft, methodology, investigation. Fusheng Wang: supervision, methodology, conceptualization. Yanlei Guo: resources, data curation. Liwen Guo: methodology, conceptualization. Wei Sun: investigation, data curation.

The authors declare no competing financial interest.