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. 2024 Jul 10;9(29):31765–31775. doi: 10.1021/acsomega.4c02853

Prediction Model of Spontaneous Combustion of Lignite in Zhalainuoer Mining Area

Yanchang Li †,‡, Mingyu Jiang †,‡,*, Zehao Jing ‡
PMCID: PMC11270733  PMID: 39072113

Abstract

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A programmed temperature-increase experiment was conducted on coal samples from four coal mines in the Zhalainuoer mining area to improve the accuracy of predicting and forecasting lignite spontaneous combustion. The gases produced during the coal tests were analyzed, and logistic, exponential, Boltzmann, and fourth-degree polynomial functions were selected to develop predictive models for the gas data. Additionally, the Boltzmann function was used to predict the occurrence of fire. The results revealed that the initial appearance temperature of CO was approximately 50 °C, and it exhibited an exponential growth trend with increasing temperature. The initial appearance temperature of C2H4 was approximately 140 °C, which could serve as an indicator of coal entering the accelerated oxidation stage. Applying the selection principle to gas indicators, CO and C2H4 were identified as single gas indicators for lignite spontaneous combustion in the Zhalainuoer mining area, whereas CO/CO2 and C2H4/C2H6 were identified as composite gas indicators. Among the four functions, the Boltzmann function model exhibited the best fitting effect for CO and CO/CO2 within the temperature range of 0–200 °C. The values of the four parameters (A1, A2, dx, and x0) were determined based on their statistical characteristics, and a functional equation describing the relationship between gas concentration and coal temperature was derived. This indicates that the Boltzmann function model can be effectively used to predict the spontaneous combustion of lignite in the Zhalainuoer mining area.

1. Introduction

Coal spontaneous combustion is a common problem in many coal mines. Not only do these events result in substantial economic and resource losses but they also severely damage the environment.1−4 More than 70% of the coal mines in over 130 mining areas in 25 major coal-producing provinces and regions in China are plagued by the hidden danger of coal spontaneous combustion. Among them, 40 large and medium-sized mining areas experience severe natural coal fires.5−10 Over 200 million tons of coal resources in China have been wasted due to coal spontaneous combustion.11 Furthermore, 60% of mine fires in China are caused by coal spontaneous combustion.12 Additionally, coal spontaneous combustion often leads to gas combustion, dust explosions, and other accidents, resulting in serious casualties.13−17 The recent development of top coal caving technology and the increase in mining depth, accumulation of goaf coal, rise in temperature, and enhanced disturbances have exacerbated the problem of coal spontaneous combustion.18−22 Predicting spontaneous combustion has become crucial for preventing and controlling coal spontaneous combustion fires and the associated likelihood of mine fires caused by coal spontaneous combustion.23−26 Domestic and foreign scholars have conducted extensive research on systems for predicting coal spontaneous combustion. Coal temperature prediction in mines mainly relies on the concentration of single indicator gases released by coal spontaneous combustion, such as CO and C2H4.27−31 Qiuge et al.,32 by considering the Hequ open-pit mine as a case study, investigated the relationship between the tracking distance of internal dumping and the stability coefficient of the end slope and determined that this relationship conforms to a Boltzmann function. A reasonable tracking distance for internal dumping can enhance the end-slope stability. Ke et al.33 analyzed the conditions that model parameters should satisfy in a surface dynamic subsidence model based on the Boltzmann function. They also examined the feasibility of using this model for dynamic subsidence prediction by integrating actual field measurement data. Xin et al.34 conducted programed temperature experiments on coal samples from two mines and analyzed and predicted the oxidation of the samples using the multiparameter index method, gas growth rate analysis method, and Graham coefficient method. Hu et al.35 focused on coal samples of varying particle sizes in their analysis of temperature rise and oxidation at the Jianbei coal mine. They analyzed the changes in the volume fractions of gases such as CO and CO2 and the gas generation characteristics of coal samples with different particle sizes using the Graham fire coefficient method and select indicator gases. Yiguo36 conducted experiments on spontaneously combustible coal seams; considered CO, O2, C2H4, and other indicator gases; and dynamically identified coal spontaneous combustion hazards through field practice. Zhang et al.37 conducted a programed temperature-increase experiment using long-flame coal from Tangjiahui mine as their research subject. They analyzed the characteristics of gas generation and gas ratios with changing temperatures. This study provides both theoretical and practical foundations for preventing and controlling coal spontaneous combustion. Jun et al.38 used coal samples from the 202 working face of Wangjiashan Mine in Gansu to simulate the spontaneous combustion of coal by conducting coal spontaneous ignition tests and programmed temperature-increase experiments. They inferred the development trend of hidden dangers using logistic fitting curves. Xu et al.39 used experimental data from coal spontaneous combustion in a mine in Shandong Province to obtain the trend of the gas curve with temperature. Accordingly, they proposed a coal spontaneous combustion grading warning model that combines the Bayesian optimization method and eXtreme Gradient Boosting regression tree (XGBoost). Zhang et al.20 investigated the boundary of the fully mechanized caving face in the Jining Second Mine. They combined the generation rate of CO at different temperature thresholds with a mathematical predictive model to forecast the CO concentration at the return air corner. This aided in assessing the degree of coal spontaneous combustion in the goaf area. By analyzing the oxygen concentration limits for coal spontaneous combustion at the three zones, they identified the position of spontaneous combustion in the goaf. Jun et al.40 conducted experiments at the Zhaolou Coal Mine in Shandong by utilizing a large-scale CSC experimental setup. They derived characteristic temperatures based on the macroscopic properties of gas production and proposed a simulated annealing-support vector machine predictive model to represent the complex nonlinear mapping relationship between characteristic gases and coal temperature. Juncai et al.41 collected coal samples from the Zhaolou Coal Mine and employed gas composition analysis and a neural network algorithm to establish a BP neural network prediction model for predicting coal spontaneous combustion. Wang et al.42 proposed a model based on the sparrow search algorithm and convolutional neural network to predict the spontaneous combustion temperature of coal. Zeng et al.43 proposed a coal spontaneous combustion emergency decision-making method that integrates Grey Relational Analysis, Technique for Order Preference by Similarity to Ideal Solution, and Enhanced Prospective Theory.

Identical gas indicators exhibit significant numerical differences across different coal mines due to variations in geological structure, mining environment, and coal composition, among other factors. The threshold levels for coal spontaneous combustion grades also vary across different mines. Although gas indicator systems can predict coal spontaneous combustion, their universality is limited by the differences in coal types and geological conditions in different mining areas. Therefore, establishing a predictive model that is suitable for spontaneous combustion in lignite at the Zhalainuoer mining area is crucial to accurately identify the hidden risks of coal spontaneous combustion fires, which is critical for preventing and controlling coal mine fires.

2. Experimental Study on Gas Indicators for Coal Spontaneous Combustion

Coal samples were collected from four coal mines—Tiebei, Linglu, Lingdong, and Lingquan in the Zhalainuoer mining area. These samples were a mixture of block and powdered lignite. Industrial analysis was conducted in the laboratory on coal samples to determine their moisture content, ash content, volatile matter, and fixed carbon content, as listed in Table 1. The collected coal samples were ground to 100 mesh size (<0.15 mm), and 1 g of the ground coal was used for the experiments. The experimental setup is illustrated in Figure 1.

Table 1. Industrial Analysis Results of Coal Samples, Unit %.

coal sample moisture Mad ash content Ad volatiles Vdaf fixed carbon FCad
Tiebei coal mine 8.39 4.33 39.34 47.94
Linglu coal mine 9.69 4.69 40.55 45.07
Lingdong coal mine 9.06 5.21 38.44 47.29
Lingquan coal mine 8.31 5.69 39.81 46.19
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Figure 1.

Figure 1

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Flowchart of the coal spontaneous combustion gas product simulation experiment apparatus.

Instrument characteristics’ analysis

  • (1)

    The temperature controller consists of the upper temperature control unit and the lower pressure gauge, flow meter, purification tube, and air pump.

  • (2)

    The G2800T gas chromatograph is mainly used for analyzing the concentration changes in oxygen and nitrogen, whereas the G3800F is mainly used for analyzing the concentration changes in CO, CO2, CH4, alkanes, alkenes, and alkynes.

  • (3)

    The red and blue lines represent gas pipelines and electrical circuits, respectively.

Experimental procedure

  • (1)

    The prepared sample from Tiebei Coal Mine II3 is placed into the sample tube.

  • (2)

    The gas path of the sample tube and all electrical circuits are connected.

  • (3)

    Using a temperature controller, the furnace temperature is increased from 10 °C at a rate of 0.5 °C/min to 80 °C. At 80 °C, the heating rate is changed to 1.0 °C/min until it reaches 200 °C. Thereafter, the heating rate is changed again to 2.0 °C/min until 300 °C. An oxygen concentration of 7.9% is supplied, and the gas flow rate is adjusted to 100 cm3/min to start the experiment.

  • (4)

    The time is observed and the samples are processed using a sampling interval of 20 min.

  • (5)

    The gas chromatograph is observed to analyze the gas composition and the data is recorded.

  • (6)

    The coal is refilled, 10.0 and 20.9% oxygen concentrations are applied, and oxidation heating experiments are conducted at different oxygen concentrations.

  • (7)

    After completing a set of coal tests, the samples are replaced with Linglu Mine II3, Lingdong Mine II3, and Lingspring Mine II3 coal samples, and steps 1–6 are repeated.

3. Gas Indicator Analysis

3.1. Analysis of Single Gas Indicators

3.1.1. CO Variation Patterns

The changes in CO concentration with rising temperature during the oxidation of four coal samples from 0 to 600 °C are illustrated in Figure 2a. CO generation primarily depends on coal oxidation, pyrolysis, and the self-reaction of active functional groups. CO is continuously generated throughout the complex reactions in coal samples. Almost no CO is present in the coal seam at lower coal temperatures. Therefore, a critical temperature exists for the production of CO in all coal samples in reaction with oxygen. The experimental data reveal that the critical temperatures for the four coal samples ranged from 50 to 70 °C. Figure 2b shows that during the oxidation of the coal samples and as the temperature rises from 0 to 200 °C, the CO concentration varies with temperature. When the coal temperature reached the first slope change point (approximately 110 °C), the slope of the CO concentration growth curve increased, and the rate of CO concentration generation accelerated. This is attributable to the oxidation reactions entering the self-heating stage, and the reactions between all coal samples with oxygen accelerating, resulting in a high concentration of CO. As the coal temperature reached the second slope change point (approximately 160 °C), coal spontaneous combustion entered a phase of intense oxidation reactions, and the CO concentration exhibited a second rapid increase. CO production peaked at a coal temperature of approximately 500 °C. Because CO is present throughout the entire process of coal spontaneous combustion and exhibits a consistent pattern, it can be selected as a single gas indicator for predicting lignite spontaneous combustion in the Zhalainuoer mining area.

Figure 2.

Figure 2

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Variation of CO concentration with temperature.

3.1.2. CO2 Variation Patterns

As shown in Figure 3, the variation in CO2 concentration exhibits similarities with the changes in CO. After reaching the critical temperature for the coal–oxygen composite reaction, CO2 experienced the first accelerated growth, primarily due to the reaction of CO with O2, generating CO2. At approximately 160 °C, the rate of CO2 growth increased, and a significant increase in the concentration of CO2 production was observed at approximately 200 °C. The variation in the production of CO2 among the four coal samples was minimal between 200 and 395 °C. At approximately 550 °C, CO2 production peaked. As CO2 is a ubiquitous gas, the environment may contain high levels of CO2; therefore, it cannot be selected as a sole indicator gas.

Figure 3.

Figure 3

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Variation of CO2 concentration with temperature.

3.1.3. CH4 and C2H6 Variation Patterns

As shown in Figure 4a, the coal sample pores adsorb CH4, and thus, CH4 concentration is measured at the beginning of the experiment. Beyond the critical temperature, the concentration of CH4 gradually increased. Beyond 200 °C, a rapid growth in CH4 concentration occurred due to the accelerated thermal decomposition and coal oxidation reactions, leading to the generation of CH4. The coal samples from Tiebei and Lingdong exhibited a decreasing trend at 450 and 400 °C, whereas those from Linglu and Lingquan mines continued to exhibit an increasing trend. The variation patterns of CH4 gas produced from the four coal samples differed, and fluctuations were observed, making it impractical to consider CH4 as a singular indicative gas for predicting the spontaneous combustion of brown coal in the Zhalainuoer mining area.

Figure 4.

Figure 4

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Variation of CH4 and C2H6 concentration with temperature.

As illustrated in Figure 4b, when the coal temperature reaches approximately 200 °C, C2H6 gas exhibits a rapid increase, which is attributed to the participation of numerous active functional groups in reactions. As the coal temperature reached 300 °C, the number of active functional groups in the coal samples decreased, resulting in a decline in the concentration of C2H6 gas in the Linglu, Lingdong, and Lingquan coal mines. Some of the C2H6 in the original coal body was adsorbed in the pores, but during the crushing of the coal samples, most of the adsorbed C2H6 was released. Therefore, using C2H6 as the sole indicative gas for predicting and forecasting underground coal spontaneous combustion is not suitable.

3.1.4. C2H4 Variation Patterns

As depicted in Figure 5, all four coal samples generated C2H4 gas when the coal temperature reached approximately 160 °C. With the increase in coal temperature, the continuous degradation of aliphatic hydrocarbons and carbon atom side chains led to a rapid increase in the C2H4 gas concentration. When the coal temperature was within the range of 300–400 °C, the concentrations of C2H4 gas from the Linglu, Lingdong, and Tiebei coal samples peaked. After the coal temperature reached 400 °C, the highest concentration of C2H4 gas was observed in the coal sample from the Lingquan mine. Given that ethylene is a significant gas product of coal spontaneous combustion and reflects the extent of changes during combustion, it can be selected as an indicative gas for predicting coal spontaneous combustion.

Figure 5.

Figure 5

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Variation of C2H4 concentration with temperature.

3.2. Analysis of Composite Gas Indicators

3.2.1. CO/CO2

As shown in Figure 6, within the temperature range of 0–200 °C, the overall trend of the CO/CO2 ratio is consistent with that of the CO concentration. The CO/CO2 ratio first appeared at approximately 52 °C. As the temperature increased, the CO/CO2 ratio gradually increased, peaking at 190 °C for all four coal samples, with a range of 0.161–0.225. The complete combustion temperature of the coal samples was approximately 500 °C, with a ratio range of 0.030–0.035. The characteristic points and corresponding ratios described above suggest that the CO/CO2 ratio can be used as a composite indicative gas for assessing coal spontaneous combustion.

Figure 6.

Figure 6

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Variation of the CO/CO2 ratio with temperature.

3.2.2. C2H6/CH4

As shown in Figure 7, the C2H6/CH4 ratio exhibits an erratic variation with temperature. For all four coal samples under normal oxygen supply conditions, the C2H6/CH4 ratio first appears at approximately 130 °C. The C2H6/CH4 ratio for the Tiebei and Linglu coal samples gradually decreased with temperature, reaching its minimum value at 150 °C. In contrast, the C2H6/CH4 ratio for Lingdong and Lingquan coal samples peaked at approximately 150 °C. The variation trends of the C2H6/CH4 ratios differ among the four coal samples. At low temperatures, most of the CH4 originates from the desorption of adsorbed CH4 in coal, whereas only a small fraction is generated through coal oxidation. In practical production processes, the C2H6/CH4 ratio is easily influenced by mining activities and coal deposition time. Therefore, the C2H6/CH4 ratio is not suitable as an indicative gas for coal spontaneous combustion.

Figure 7.

Figure 7

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Variation of the C2H6/CH4 ratio with temperature.

3.2.3. C2H4/C2H6

From Figure 8, it can be inferred that the initial appearance temperature of C2H4/C2H6 in the coal samples from the four mines is approximately 160 °C, with the initial ratio data concentrated below 0.3. As the temperature of the coal increased, the C2H4/C2H6 ratio exhibited an upward trend, and the peak value corresponded to the 0.8–1.1 range. The C2H4/C2H6 ratio of the coal samples from the four mines exhibited some regularity, which can be used as an auxiliary gas index for predicting coal spontaneous combustion.

Figure 8.

Figure 8

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Variation of the C2H4/C2H6 ratio with temperature.

4. Results and Discussion

Experiments revealed that when the temperature of coal exceeded 200 °C, open flames were produced. Therefore, the gas indicators with strong regularity, CO and CO/CO2, were selected to construct the prediction model within the experimental temperature range of 0–200 °C.

4.1. Optimal Function Fitting

4.1.1. Comparison of Prediction Models for CO Concentration with Temperature

Four fitting functions, namely, logistic, exponential, Boltzmann, and fourth-degree polynomial functions, were selected to fit the selected gas indicators for the coal samples. The models were compared using the coefficient of determination (R2) and residuals to identify the optimal prediction model.

As shown in Figure 9, the relationship between the CO concentration of coal samples from the four coal mines and the variation in coal temperature is fitted using curves based on the Boltzmann, a fourth-degree polynomial, the logistic, and the exponential function models. Table 2 lists the statistics of the goodness of fit for the relationship between CO concentration and coal temperature and presents the statistics of the fitting residuals for the relationship between CO concentration and coal temperature during combustion. The analysis revealed that the fourth-degree polynomial and exponential functions had poor fitting performance, whereas the Boltzmann and logistic functions exhibited better fitting results. For the coal samples from Tiebei, Lingdong, and Lingquan, the R2 values of the fitting curves obtained using the Boltzmann function were higher than those obtained using the logistic function. However, for the coal sample from the Linglu Mine, the R2 value of the logistic function was 1, which is higher than that of the Boltzmann function. Nevertheless, the sum of squared residuals obtained using the Boltzmann function for all four coal mines was smaller than that obtained using the other three functions. Therefore, the logistic function curve for the relationship between CO concentration and coal temperature in the Linglu Mine exhibited overfitting. Thus, the Boltzmann function model is preferable for predicting the relationship between CO concentration and coal temperature within the temperature range of 0–200 °C.

Figure 9.

Figure 9

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Fitting curve depicting the relationship between CO concentration and coal temperature in the four coal mines.

Table 2. Fitting Goodness and Residual Analysis of the Relationship between CO Concentration and Coal Temperature.
  R2 (goodness of fit)
source of coal samples Boltzmann fourth-degree polynomial logistic exponential function
Tiebei 0.99995 0.99988 0.99987 0.99866
Linglu 0.99974 0.99889 1 0.99847
Lingdong 0.9996 0.98886 0.99911 0.94388
Lingquan 0.99995 0.99988 0.99987 0.99768
  sum of squared residuals
source of coal samples Boltzmann fourth-degree polynomial logistic exponential function
Tiebei 2.45 × 10–7 6.00 × 10–7 6.71 × 10–7 6.95 × 10–6
Linglu 4.22 × 10–6 4.60 × 10–6 4.92 × 10–6 6.34 × 10–6
Lingdong 1.79 × 10–6 4.93 × 10–5 3.95 × 10–6 2.48 × 10–4
Lingquan 1.18 × 10–6 3.76 × 10–6 2.96 × 10–6 2.13 × 10–5
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4.1.2. Comparison of Prediction Models for the CO/CO2 Ratio with Temperature

As illustrated in Figure 10, the fitting curves represent the relationship between CO/CO2 ratios and coal temperature variations for samples from four coal mines, derived using Boltzmann, quartic polynomial, logistic, and exponential function models. Table 3 presents the R2 values for the relationship between CO/CO2 and coal temperature and provides the residual statistics for the fitting relationship between CO/CO2 ratio and coal temperature for four coal samples. Noticeably, the Boltzmann model exhibited better fitting performance and higher goodness of fit for CO/CO2 ratios in the Tiebei, Linglu, and Lingdong coal mines than the other three function models. Additionally, the sum of squared residuals for the Boltzmann model was smaller than that of the other three fitting models. Therefore, the Boltzmann model is preferable for predicting the CO/CO2 ratios.

Figure 10.

Figure 10

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Fitting curves of the CO/CO2 ratio in four coal mines as a function of coal temperature.

Table 3. Fitting Goodness and Residual Analysis of the Relationship between CO/CO2 Ratio and Coal Temperature.
  R2 (goodness of fit)
source of coal samples Boltzmann fourth-degree polynomial logistic exponential function
Tiebei 0.99814 0.99735 0.99675 0.98293
Linglu 0.99085 0.9824 0.98916 0.93979
Lingdong 0.99803 0.99692 0.9968 0.96655
Lingquan 0.99874 0.99969 0.99819 0.99549
  R2 (goodness of fit)
source of coal samples Boltzmann fourth-degree polynomial logistic exponential function
Tiebei 6.35 × 10–5 9.07 × 10–5 1.11 × 10–4 5.83 × 10–4
Linglu 3.37 × 10–4 6.47 × 10–4 3.99 × 10–4 2.22 × 10–3
Lingdong 8.82 × 10–5 1.38 × 10–4 1.43 × 10–4 1.50 × 10–3
Lingquan 2.15 × 10–5 2.36 × 10–5 1.36 × 10–4 3.38 × 10–4
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4.2. Model Construction for Prediction

The Boltzmann function model was selected as the preferred fitting model for the variation in CO concentration and CO/CO2 ratio with temperature by fitting the experimental data of coal samples from the four mines for temperatures ranging from 0 to 200 °C. A predictive mathematical model was constructed by utilizing the obtained model parameters.

The equation for the Boltzmann function model is as follows

4.2. 1

In the equation, A1, A2, and dx represent the corresponding numerical values of the function model; x0 represents the inflection point of the function model curve; and x represents the coal temperature, which ranges from 0 to 200 °C.

To obtain the predictive model for CO concentration and CO/CO2 ratio with respect to coal temperature, the four fitting parameters were subjected to a Shapiro–Wilk normality test using SPSS software. Subsequently, the mean method was applied to calculate the CO concentration parameters, whereas the median method was used for the CO/CO2 ratio. The average values of the four parameters obtained from the four coal mine samples were taken.

4.2.1. Boltzmann Model for the Variation in CO with Temperature

The Boltzmann model for the variation in CO concentration with temperature for the four coal samples under normal oxygen concentrations is presented in Table 4. By substituting the data from the table into Equation 1, a predictive model for the numerical estimation of coal spontaneous combustion based on the variation in CO concentration with temperature can be obtained.

Table 4. Relationship between CO Concentration and Coal Temperature Fitting Parameters.
  fitting parameters
source of coal samples A1 A2 x0 dx
Tiebei 1.13 × 10–4 0.13787 191.88301 20.0501
Linglu –9.86 × 10–4 0.28184 241.11828 34.01131
Lingdong 4.53 × 10–4 0.06159 148.01638 12.4103
Lingquan –4.83 × 10–4 0.18584 192.95251 27.57905
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According to the fitting results, all models converged with 13 iterations, and parameter calculations could be performed. The normality test for variables A1, A2, dx, and x0 was conducted using the Shapiro–Wilk test method in SPSS software, and the results are listed in Table 5.

Table 5. Normality Test of the Relationship between CO/CO2 Ratio and Coal Temperature Fitting Parameters.
parameter statistics degree of freedom significance
A1 0.971 4 0.846
A2 0.996 4 0.984
x0 0.989 4 0.953
dx 0.949 4 0.709
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According to Table 5, the significance of the normality test for variables A1, A2, dx, and x0 was greater than 0.05. Additionally, all four values fell within the 95% confidence interval for a normal distribution. Taking the average of the A1, A2, dx, and x0 variables, the parameters for the Boltzmann model of the coal samples were A1 = −2.26 × 10–4, A2 = 0.16, x0 = 193.49, and dx = 23.51. Substituting these parameters into eq 1, we obtain the functional relationship between the single indicator gas CO and coal temperature in the Boltzmann model

4.2.1. 2

Equation X represents the coal temperature, which ranges from 0 to 200 °C.

4.2.2. Boltzmann Model for the Variation of CO/CO2 Ratio with Temperature

Table 6 presents the fitting parameters of the Boltzmann model for the variation in CO/CO2 ratio with coal temperature. By substituting the parameters of each coal mine into eq 1, the models for predicting the coal spontaneous combustion for the variation in CO/CO2 ratio with coal temperature can be obtained. The coal sample data for all four coal mines have valid parameter values.

Table 6. Relationship between CO/CO2 Ratio and Coal Temperature Fitting Parameters.
  fitting parameters
source of coal samples A1 A2 x0 dx
Tiebei –9.31 × 10–4 0.20693 150.00557 26.10284
Linglu 1.35 × 10–3 0.15809 119.65871 16.57236
Lingdong 6.67 × 10–4 0.19951 135.58924 19.97364
Lingquan –1.699 × 10–4 0.26501 132.16917 35.69587
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According to Table 7, the significance of the normality test for A1, A2, dx, and x0 is greater than 0.05, and all four values conform to a normal distribution within a 95% confidence interval. The median values of the four statistical parameters were utilized in the Boltzmann model of the coal samples from the four mines: A1 = 5.90 × 10–4, A2 = 0.20, x0 = 133.88, and dx = 21.34. By substituting these parameters into eq 1, the functional relationship between the composite index gas CO/CO2 and coal temperature in the Boltzmann model can be obtained

4.2.2. 3
Table 7. Normality Test of the Relationship between CO/CO2 Ratio and Coal Temperature Fitting Parameters.
parameter statistics degree of freedom significance
A1 0.987 4 0.939
A2 0.960 4 0.781
x0 0.982 4 0.916
dx 0.950 4 0.709
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Equation X represents the coal temperature, which ranges from 0 to 200 °C.

4.3. Testing the Validity of the Predictive Model

The data comparison analysis method was employed in this section to test the effectiveness and reliability of the model, as well as explore the relationship between the expected values of the model and the actual experimental data. Using Origin software, the predicted data obtained from the Boltzmann fitting model were compared with the experimental data. The changes in CO concentration with coal temperature in the four coal mines are compared in Figure 11. Similarly, Figure 12 compares the CO/CO2 ratio changes with coal temperature in the four coal mines.

Figure 11.

Figure 11

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Comparison of CO concentration variations with temperature in four coal mines.

Figure 12.

Figure 12

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Comparison of the CO/CO2 ratio variation with temperature in four coal mines.

The comparison between the predicted values of the model and the experimental true values for the two aforementioned samples revealed that the predicted values of the model were very close to the true values. The prediction models for CO concentration and CO/CO2 ratio can be effectively applied in the prediction of coal spontaneous combustion in the four coal mines, contributing to the prevention and control of coal spontaneous combustion.

5. Conclusions

  • 1.

    Experiments on coal spontaneous combustion reveal that the initial appearance temperature of CO is approximately 50 °C, and it exhibits an exponential growth trend with increasing temperature. The initial appearance temperature of C2H4 is approximately 140 °C, which indicates when coal enters the accelerated oxidation stage. The single indicator gases for the spontaneous combustion of lignite in the Zhalainuoer mining area are identified as CO and C2H4, whereas the composite indicator gases are CO/CO2 and C2H4/C2H6.

  • 2.

    Four methods are employed to fit functions for CO and CO/CO2 concentrations. The average goodness of fit for the Boltzmann model across the four coal samples was 0.99981 and 0.99644 for CO and CO/CO2, respectively. Additionally, the sum of squared residuals for the Boltzmann model was lower than that of the other three fitting models for all four coal samples. Therefore, the Boltzmann model is preferable as the predictive function model for the concentration of CO and CO/CO2 in the spontaneous combustion of brown coal in the Zhalainuoer mine area.

  • 3.

    The parameters for the Boltzmann model correlating CO concentration with coal temperature are determined as follows based on statistical characteristics: A = −2.26 × 10–4, B = 0.16, C = 193.49, and D = 23.51. Furthermore, the parameters for the Boltzmann model relating the CO/CO2 ratio to coal temperature are established as A = 5.90 × 10–4, B = 0.20, C = 133.88, and D = 21.34. The predictive accuracy of the model, when compared to actual experimental values, exhibits an average percentage error for CO concentration of 2.7% and an average percentage error for the CO/CO2 ratio of 2.1%. Therefore, the prediction based on the Boltzmann model can effectively solve the problem of spontaneous combustion of brown coal in the Zhalainuoer mining area.

  • 4.

    The focus of this study is on coal samples from the four major coal mines in the Zhalainuoer coal mining area. Future research will involve collecting samples from different types of coal mines or adjusting other relevant variables in experiments to further explore a more universally applicable model for predicting coal spontaneous combustion and developing an early warning system.

Acknowledgments

This project received funding from the National Science Foundation (52174183).

Author Contributions

§ Y.L., M.J., and Z.J. contributed equally.

The authors declare no competing financial interest.

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