Skip to main content
NCBI home page
ACS Omega logoLink to ACS Omega
. 2021 Mar 5;6(10):6736–6746. doi: 10.1021/acsomega.0c05736

Study on the Spontaneous Combustion Tendency of Coal Based on Grey Relational and Multiple Regression Analysis

Dong Gao †, Liwen Guo †,‡, Fusheng Wang †,‡,*, Zhiming Zhang †
PMCID: PMC7970494  PMID: 33748587

Abstract

graphic file with name ao0c05736_0011.jpg

The correlation between the spontaneous combustion tendency of coal and its properties are of great importance for safety issues, environmental concerns, and economic problems. In this study, the relationship between multiple parameters, different from the previous single parameter, and the spontaneous combustion tendency was analyzed. The comprehensive judgment index (CJI), which indicates the tendency of coal spontaneous combustion, was obtained for samples collected from different mines. The CJI was measured by the cross-point temperature and had a negative correlation with the spontaneous combustion tendency. Physical pore structures and chemical functional groups were characterized based on cryogenic nitrogen adsorption and Fourier transform infrared spectroscopy measurements, respectively. For analyzing the effect of coal properties on the spontaneous combustion tendency, the grey relational grade was determined by the grey relational analysis between the CJI and the pore structures and functional groups of coal. The grey relational grade of the benzene substituent with CJI had a maximum of 0.8642, and the macropores had the minimum, 0.4169. The higher the gray relational grade was, the more relevant the spontaneous combustion tendency was, indicating that the benzene substituent was the most relevant. To better predict the spontaneous combustion tendency, the average pore diameter, hydroxyl, methyl, methylene, and benzene substituent with a high grey relational grade were selected. Finally, the multiple regression prediction model of CJI was established. The R squared coefficient, significance level, F-distribution, t-distribution, collinearity diagnosis, and residual distribution of the model met the requirements. In addition, two coal samples were selected to verify the spontaneous combustion tendency model. The relative errors between the predicted CJI value and the experimental CJI value were 1.42 and 4.25%, respectively. These small relative errors verified the reasonableness and validity of the prediction model.

1. Introduction

Spontaneous combustion, which generally exists in coal mines, is one of the five major mine natural disasters. Additionally, spontaneous combustion of coal has caused safety accidents,1−5 economic losses,6,7 and environment issues.8−12 Hence, it is of great significance to assess the extent of the spontaneous combustion tendency for reducing spontaneous combustion of coal.13,14

The inherent properties of coal, oxygen concentration, and moisture content are the major factors for influencing the tendency of spontaneous combustion within extremely complex physicochemical processes.15−17 Domestic and international scholars18−20 have conducted numerous studies on the tendency of coal spontaneous combustion. Nimaje and Tripathy21 found that the Olpinski index, which was obtained by the statistical analysis of coal parameters, could be used to evaluate the spontaneous combustion tendency of Indian coals. Pattanaik et al.22 concluded that the intrinsic properties of the coal (vitrinite, exinite, and inertinite) had significant correlations with the tendency of spontaneous combustion. The tendency of coal spontaneous combustion decreased with decreasing vitrinite and exinite but increased with the decrease of inertinite content. Chandra and Prasad23 suggested that the susceptibility proneness to coal spontaneous combustion slowly decreased from high to moderate to low with an increase of coalification.

The effect of pore structures on spontaneous combustion of coal is important for the current work.24−28 Pores are the pathways through which oxygen transports within coal, which determine the amount of oxygen exposed to the coal surface. Karsner and Perlmutter29 demonstrated that the oxidation rate increased with an increase of gas diffusion rate within coal particles. Zhang et al.30 concluded that the heterogeneity of pore distribution reduced the spontaneous combustion tendency by virtue of the pore size distribution through multiscale and multifractal analyses. The oxidation rate of coal had a significant correlation with the densification on lignite; when the densification increased, the number of active sites on coal surface capable of reacting with oxygen molecules decreased, and in addition, the oxidation rate decreased.13 The oxidation rate of coal was influenced by the oxygen concentration that reacted with the coal. However, when the oxygen concentration was below a threshold value, the oxidation reaction was inhibited.31,32 Therefore, the pore structure affects the reaction rate between coal and oxygen, which consequently affects the tendency of coal spontaneous combustion.

The activity and content of each functional group directly affect the spontaneous combustion tendency of coal.33−35 Zhang et al.36 found that during the spontaneous combustion of coal, −OH had dominant effects on the emanating heat from coal. Tang37 concluded that the increases in the content of aliphatic hydrocarbon and oxygen-containing functional groups increased the probability of coal spontaneous combustion. Li et al.38 found that active sites, which were generated from the thermal decomposition of oxygen-containing groups, accelerated the oxidation of coal. Zhong et al.14 found that the increasing content of the aliphatic hydrocarbon group and hydroxyl group resulted in an accelerated oxidation reaction rate, which was more likely to result in spontaneous combustion. Therefore, different functional groups have different effects on the low-temperature oxidation of coal spontaneous combustion, resulting in different tendency of coal spontaneous combustion.

The moisture content of coal has a complex influence on the spontaneous combustion.39−41 Clemens et al.42 found that moisture could inhibit the production of stabilized radicals and quicken the oxidation of coal. Wu et al.43 indicated that the mechanism for moisture to influence upon spontaneous combustion changed with the reaction stage.

The inherent properties of coal determine the degree of difficulty in spontaneous combustion. At present, methods that evaluate the spontaneous combustion trend of coal have not been generally accepted. Researchers have proposed numerous research methods to analyze the oxidation rule of coal spontaneous combustion. These include low-temperature oxidation,44 adiabatic oxidation,20 thermal gravity analysis,45 and crossing point temperature methods.21,30,46 Nevertheless, few studies have examined the relationship between multiattribute coupling and spontaneous combustion tendency.

Grey relational analysis was appropriate to resolve the complex interrelationships between multiple factors and research objects.47−49 In the past few years, grey relational analysis has been widely used in coal spontaneous combustion for research and prediction. By using grey relational analysis, Wang50 calculated the grey correlation degree of index gas at different characteristic temperatures, optimized the early prediction index gas of coal spontaneous combustion at different temperature stages, and established perfect index gas systems. Zhang51 analyzed various functional groups in the infrared spectra of different coal samples by means of grey relational analysis and obtained the quantitative variation law of different functional groups with temperature. The root cause of coal spontaneous combustion was the reaction and exothermic heat between oxygen and functional groups. Therefore, the tendency of coal spontaneous combustion is related to the pore structure, functional groups, and other coal parameters. Based on the grey relational analysis, we try to establish a multiparameter model to quantify the probability for the spontaneous combustion tendency of coal. The cross-point temperature (CPT) is used to measure the spontaneous combustion tendency of coal to verify the accuracy of the model.

The objective of this study was to establish a multiparameter model to comprehensively and systematically analyze the spontaneous combustion tendency of coal. The experiments utilized CPT measurements, cryogenic nitrogen adsorption measurements, and Fourier transform infrared (FTIR) spectroscopy. To effectively eliminate the complicated effect of water during spontaneous combustion, samples were dried in a vacuum oven at 60 °C for 24 h to ensure that the moisture content was approximately consistent. Subsequently, pore structures and functional groups of the samples were obtained. Thereafter, the grey relational grade between the spontaneous combustion tendency and the pore structures and functional groups of coal was analyzed by grey relational analysis. Eventually, a new model describing the coal spontaneous combustion tendency was established by multiple regression analysis.

2. Experiments and Methods

2.1. Coal Samples

Fresh coal samples were directly collected from coalfields throughout northern China following the Chinese standard (GB/T 19222-2003)52 and were carefully sealed and transported to the laboratory for experiments. Subsequently, the samples were crushed and screened out with different particle sizes. In accordance with the Chinese standard (GB/T 6948-2008),53 the vitrinite random reflectance (Rr) of all coal samples on corresponding polished sections was measured with a photometer microscope. Table 1 provides the coal coalfield location and the coal rank of samples in this experiment.

Table 1. Coal Ranks of the Samples.

samples coalfield Rr (%) coal ranks
S1 Huolinhe 0.36 lignite
S2 Linnancang 0.68 gas coal
S3 Donghuantuo 0.74 gas coal
S4 Tangshan (7 coal seam) 0.90 1/3 coking coal
S5 Qianjiaying 1.24 coking coal
S6 Xingtai 2.21 meager coal
S7 Yangquan 2.51 anthracite
Open in a new tab

2.2. CPT Measurement

This experiment was conducted by the self-developed device based on program heating technology. Samples with a mass of 50 ± 0.1 g and a particle size of 50–80 mesh were placed in the container with a heating rate of 0.8 °C/min, and the temperatures of coal and oven were recorded. From initiation, the container was continuously filled with high-purity nitrogen for 5 min to remove the impurity gas. Then, dry air, instead of high-purity nitrogen, at a flow rate of 96 mL/min was established and then adjusted to 8 mL/min when the coal sample temperature reached 35 °C. When the coal temperature caught up with the oven temperature, samples reached the CPT. In CPT measurements, the spontaneous combustion tendency was described by the comprehensive judgment index (CJI). CJI of the coal was calculated by the following eqs 1–3.19,54,55

2.2. 1
2.2. 2
2.2. 3

where I is the CJI; φ(O2) is the oxygen concentration at the outlet of the coal sample tank in the container when the coal temperature is 70 °C; TCPT is the CPT; Iφ(O2) is the oxygen concentration index at the outlet of the coal sample tank when the coal temperature is 70 °C; ITCPT is the temperature index of the CPT; Wφ(O2) and WTCPT are the weights of low-temperature and rapid oxidation stage, respectively, and their values are 0.6 and 0.4; φ is the amplification factor, 40; 300 is the correction factor.

When I < 600, 600 < I < 1200, and I > 1200, the tendency of coal spontaneous combustion is easy to spontaneous combustion, spontaneous combustion, and difficult to spontaneous combustion, respectively.

Obtained by experiment and calculation, the CJI and other parameters of the spontaneous combustion tendency are shown in Table 2.

Table 2. CJI and Other Parameters in the CPT Experiment.

samples φ(O2) Iφ(O2) TCPT ITCPT I
S1 20.07 29.48 154.8 10.57 531.76
S2 19.83 27.94 166.1 18.57 667.59
S3 20.41 31.68 178.3 27.36 873.36
S4 19.20 23.87 192.1 37.21 868.24
S5 19.06 22.97 206.0 47.14 1005.51
S6 20.70 33.55 202.3 44.50 1217.16
S7 20.73 33.74 214.2 53.00 1357.81
Open in a new tab

2.3. Cryogenic Nitrogen Adsorption Experiment

Nitrogen adsorption–desorption was carried out on a Micromeritics JW-BK112 static nitrogen adsorption apparatus to determine the Brunauer–Emmett–Teller (BET) specific surface areas and pore size distributions of the samples. The experimental samples selected had a mass of approximately 2.5 g with a particle size of 24–50 mesh. The samples were degassed and dehydrated. The pore parameters obtained from the cryogenic nitrogen adsorption experiment are shown in Table 3.

Table 3. Pore Structure Parameters of Coala.

samples V1 cm3/g V2 cm3/g V3 cm3/g SBET m2/g Dap nm Vt cm3/g
S1 0.0030 0.0041 0.0024 4.53 12.26 0.00949
S2 0.0005 0.0002 0.0001 0.31 11.63 0.00081
S3 0.0003 0.0002 0.0001 0.47 8.01 0.00054
S4 0.0027 0.0017 0.0007 0.24 7.43 0.00512
S5 0.0003 0.0002 0.0001 0.17 8.20 0.00059
S6 0.0005 0.0003 0.0002 5.18 6.22 0.00097
S7 0.0030 0.0021 0.0008 3.01 6.15 0.00598
Open in a new tab
a

Note: V1, V2, and V3 are the pore volumes of micropores (<10 nm), mesopores (10–50 nm), and macropores(>50 nm), respectively. SBET is the BET specific surface area; Dap is the average pore diameter; Vt is the single point adsorption total pore volume.

2.4. FTIR Spectroscopy Experiment

Each group in the coal molecule has different vibration modes when subject to a light source with a continuous wavelength, and the same groups also have varying vibration forms. Therefore, FTIR spectroscopy was used to analyze the content of the functional groups. First, 1 mg of the sample with 150 mg of KBr were uniformly ground for 2 min and pressed into a pellet. Subsequently, the samples were dried in a vacuum oven under 60 °C for 12 h. Finally, FTIR spectra of the samples were obtained by a FTIR spectrometer (FTIR-8400, Shimadzu, Japan) with spectral region 400–4000 cm–1and resolution 0.4 cm–1, which are displayed in Figure 1.

Figure 1.

Figure 1

Open in a new tab

FTIR spectra of the samples.

In order to better analyze the content of functional groups in the FTIR diagram, Peak Fit v4.12 was used for the peak fitting of the FTIR sample data. First, after the infrared data is imported, automatic smoothing correction is performed. Next, AutoFit Peaks II Second Derivative method is chosen for peak fitting. Finally, we manually repeat this until r2 > 0.99 stops fitting and save the corresponding data. The peak-fitting figures of the FTIR are displayed in Figures 2–8.

Figure 2.

Figure 2

Open in a new tab

Peak-fitting FTIR figure of S1.

Figure 8.

Figure 8

Open in a new tab

Peak-fitting FTIR figure of S7.

Figure 3.

Figure 3

Open in a new tab

Peak-fitting FTIR figure of S2.

Figure 4.

Figure 4

Open in a new tab

Peak-fitting FTIR figure of S3.

Figure 5.

Figure 5

Open in a new tab

Peak-fitting FTIR figure of S4.

Figure 6.

Figure 6

Open in a new tab

Peak-fitting FTIR figure of S5.

Figure 7.

Figure 7

Open in a new tab

Peak-fitting FTIR figure of S6.

For analyzing the content of functional groups after peak fitting more intuitively, the representatives of the main functional groups with the most reactivity were selected to calculate the content relative of peak area,56−58 and the results are shown in Table 4.

Table 4. Peak Area Content of Main Functional Groups in Each Coal Sample.

  functional groups and corresponding peak area content
samples hydroxyl methyl, methylene carboxyl aromatic hydrogen carbon–carbon double bond benzene substituent
S1 0.1968 0.0552 0.0100 0.0352 0.0297 0.0270
S2 0.1767 0.0377 0.0081 0.0294 0.0357 0.0302
S3 0.1753 0.0355 0.0233 0.0263 0.0272 0.0285
S4 0.1656 0.0350 0.0038 0.0262 0.0478 0.0312
S5 0.1624 0.0298 0.0000 0.0202 0.0102 0.0336
S6 0.1537 0.0332 0.0145 0.0159 0.0107 0.0374
S7 0.1525 0.0140 0.0148 0.0153 0.0120 0.0465
Open in a new tab

3. Results and Discussion

3.1. Experimental Analysis

The Rr of samples in different areas ranged from 0.36 to 2.51 and were obtained by vitrinite random reflectance. It can be concluded from Table 1 that the Rr of the samples increased with increasing metamorphism. The CJI values of the samples were calculated by eqs 1–3. The results are displayed in Table 2. The spontaneous combustion tendency of S1 was easy to spontaneous combustion, of S2, S3, S4, and S5 was spontaneous combustion, and of S6 and S7 was difficult to spontaneous combustion. The degree of metamorphism was positively correlated with the CJI of spontaneous combustion tendency. Specifically, the lower the coal rank, the smaller the value of CJI and the stronger the spontaneous combustion tendency. Table 3 shows the pore structure parameters for the cryogenic nitrogen adsorption experiment. The average pore diameter was negatively correlated with the CJI of the coal spontaneous combustion tendency. The correlation between other pore parameters of coal and CJI was not significant. Table 4 shows the peak area content of the main functional groups for the FTIR spectroscopy experiment. The hydroxyl, methyl, methylene, and carbon–carbon double bonds were negatively correlated with the CJI values. The benzene substituent was positively correlated with the CJI values.

However, the spontaneous combustion tendency of coal should be determined by the coupling of multiple factors such as its chemical composition and physical structure. Therefore, it was necessary to comprehensively study the combined effect of the internal composition and structure of coal on the spontaneous combustion tendency. In addition, determining the correlation between each factor and the spontaneous combustion tendency, finding out the key influencing factors, and establishing a multifactor comprehensive prediction model of spontaneous combustion tendency are also necessary.

3.2. Grey Relational Analysis

Grey system theory was initially proposed by Professor Deng in 1982 to solve situations where information was partly available and unavailable.59 Grey relational analysis was appropriate to resolve the complex interrelationships between multiple factors and research objects.47−49,60,61 In our study, grey relational analysis was used to determine the complicated relationships between multiple parameters for the spontaneous combustion tendency of coal.

The CJI (I) was selected to be the reference sequence X0(k). The basic parameters of coal samples were selected to be the comparison sequence Xi(k). The data obtained from the experiments were normalized to ensure that the scatter range of the sequence was small. The maximum method was used for normalization, and the results of X0(k)* and Xi(k)* are shown in Table 5. Grey relational coefficients for normalized data were computed using eqs 4–7.62

3.2. 4
3.2. 5
3.2. 6
3.2. 7

where k is the number of coal samples; i is the number of parameters; X0(k)* is the normalized reference sequence; Xi(k)* is the normalized comparative sequence. Δi(k) is the deviation sequence of the reference sequence and comparability sequence. Ri(k) is the grey relational coefficient. q is the distinguished coefficient where q ∈ [0,1]; generally speaking, the stability of the coefficient is the most moderate when q is equal to 0.5.

Table 5. Normalized Parameters of Coal Samplesa.

samples X0(k)* X1(k)* X2(k)* X3(k)* X4(k)* X5(k)* X6(k)* X7(k)* X8(k)* X9(k)* X10(k)* X11(k)* X12(k)*
S1 0.39 1.00 1.00 1.00 1.00 0.87 1.00 1.00 1.00 0.43 1.00 0.62 0.58
S2 0.49 0.17 0.05 0.04 0.09 0.06 0.95 0.90 0.68 0.35 0.83 0.74 0.65
S3 0.64 0.10 0.05 0.04 0.06 0.09 0.65 0.89 0.64 1.00 0.75 0.57 0.61
S4 0.64 0.90 0.41 0.29 0.54 0.05 0.61 0.84 0.63 0.16 0.75 1.00 0.67
S5 0.74 0.10 0.05 0.04 0.06 0.03 0.67 0.83 0.54 0.00 0.57 0.21 0.72
S6 0.90 0.17 0.07 0.08 0.10 1.00 0.51 0.78 0.60 0.62 0.45 0.22 0.80
S7 1.00 1.00 0.51 0.33 0.63 0.58 0.50 0.78 0.25 0.63 0.43 0.25 1.00
Open in a new tab
a

Note: Xi is Xi(k) by normalization. X0(k) is the CJI; X1(k) is the micropore parameter; X2(k) is the mesopore parameter; X3(k) is the macropore parameter; X4(k) is the parameter of the single point adsorption total pore volume; X5(k) is the parameter of the BET specific surface area; X6(k) is the parameter of the average pore diameter; X7(k) is the parameter of the hydroxyl content; X8(k) is the parameter of the methyl and methylene contents; X9(k) is the parameter of the carboxyl content; X10(k) is the parameter of the aromatic hydrogen content; X11(k) is the parameter of the carbon–carbon double bond content; finally, X12(k) is the parameter of the benzene substituent content.

The grey relational grade is a numerical measure of similarity between the reference sequence and the comparison sequence. On averaging the grey relational coefficients, the overall grey relational grade was obtained by eq 8. The grey relational grade was between 0 and 1. Using eq 8 to average the grey relational coefficients, the results are displayed in Table 6.62

3.2. 8

where m is the experimental number of coal samples. γ is the integral grey relational grade.

Table 6. Grey Relational Grade between Each Parameter and CJI.

parameters X1(k) X2(k) X3(k) X4(k) X5(k) X6(k) X7(k) X8(k) X9(k) X10(k) X11(k) X12(k)
γ 0.5368 0.4436 0.4169 0.4814 0.4924 0.6566 0.6370 0.6693 0.5914 0.5942 0.5449 0.8642
Open in a new tab

As shown in Table 6, macropores (X9(k)) with a value of 0.4169 and benzene substituent (X12(k)) with a value of 0.8642 are the minimum and maximum grey relational grades, respectively. The greater the grey relational grade value, the better the represented relationship between each parameter and CJI. The parameter effects and the optimal level of each parameter can be determined on the basis of grey relational grade.

In terms of physical structure, the pore diameter was highly correlated with the CJI of spontaneous combustion tendency. Agnieszka28 suggested that the spontaneous combustion tendency decreased with the decrease of the macropore diameter. With the deepening of the degree of coalification, the pore diameter decreased, while the macropores decreased and the mesopores developed. The gas flow in the pore changed from laminar permeability to molecular diffusion. The gas flow capacity weakened, which reduced the tendency of coal spontaneous combustion.

In terms of molecular composition, the functional groups, benzene substituent, hydroxyl groups, methyl groups, and methylene groups, were highly correlated with CJI for spontaneous combustion tendency. The essence of coal oxidation was the stretching vibration and bending vibration of the functional groups. Zhong14 suggested that the content of the oxygen functional group and the aliphatic hydrocarbon group affects the tendency of coal spontaneous combustion. Hydrogen on methyl and methylene initially reacted with oxygen to produce carbon-free radicals, while the methyl and methylene that provided hydrogen react with hydroxyl groups on the oxygen functional groups to produce water and a large number of carbon-free radicals. The hydroxyl group continuously participated in the reaction to form the carbon radical and the oxygen-containing radical. Furthermore, carbon-free radicals combined with oxygen to release gas in an exothermic reaction. Once the heat accumulated, coal may be oxidized or even burned.

In conclusion, the CJI of coal spontaneous combustion tendency was related to various property parameters of coal, which was not simply determined by one coal parameter but by the coupling of multiple parameters. We propose a multiparameter coupled prediction model for the spontaneous combustion tendency of coal.

3.3. Multiple Regression Analysis

Multiple regression analysis is a regression analysis method to study the relationship between a dependent variable and multiple independent variables.48,63−65 The dependent variable is predicted by a multiple regression model with independent variable parameters. The spontaneous combustion tendency of coal was influenced by numerous parameters; therefore, we established a multiple regression model by the grey relational grade between each factor and CJI of coal spontaneous combustion tendency. The greater the grey relational grade, the greater the improvement in the modeling accuracy. Therefore, parameters quantifying the average pore diameter, hydroxyl, methyl, methylene, and benzene substituent of seven coal samples were selected as the explaining variables, and the comprehensive determination index was selected as the explained variable. The initial multiple regression model is eq 9, and the multiple regression variable data of the seven coal samples is displayed in Table 7.

3.3. 9

Table 7. Multiple Regression Variable Data of Samplesa.

samples Y X1 X2 X3 X4
S1 531.76 12.26 0.1968 0.0552 0.0270
S2 667.59 11.63 0.1767 0.0376 0.0301
S3 873.36 8.01 0.1753 0.0355 0.0285
S4 868.24 7.43 0.1656 0.0350 0.0312
S5 1005.51 8.20 0.1624 0.0298 0.0336
S6 1217.16 6.22 0.1537 0.0332 0.0374
S7 1357.81 6.15 0.1525 0.0140 0.0465
Open in a new tab
a

Note: Y is the CJI; X1 is the parameter of the average pore diameter; X2 is the parameter of the hydroxyl content; X3 is the parameter of methyl and methylene contents; X4 is the parameter of the benzene substituent content.

The matrix expression of eq 9 is as follows

3.3. 10

where Y is the explained variable; X is the explaining variables; β is the regression coefficient; ε is the random error.

Results were obtained by using IBM SPSS Statistics 21 software. This includes regression fitting, regression equation, and corresponding analysis results. However, the accuracy of the regression equation must be verified by statistical test of the results.

As one may observe in Table 8, all four variables requested entered the model, and none was eliminated.

Table 8. Input/Removed Variable.

variables entered variables removed method
X1, X2, X3, X4 none enter
Open in a new tab

The determination coefficient represents the fitting effectiveness of the model to accurately summarize the data. To verify the fitting goodness of the model, the determination coefficient should be examined. The closer the determination coefficient was to 1, the more accurate the fitting effect was. According to the data in Table 9, the determination coefficient R is 0.989, R square is 0.978, and adjusted R square is 0.933. All these parameters were closer to 1 at high values, indicating that the regression equation had a high degree of fitting accuracy.

Table 9. Model Summary.

R R squared adjusted R Squared std. error of the estimate
0.989 0.978 0.933 74.936
Open in a new tab

As shown in Table 10, the value of F was 22.011, and the given significance level of α was 0.05. Obtaining a value for F from a test threshold table, F0.05(4, 2) = 19.247, it is evident that F > Fα(k, n–k–1)(k is the number of parameters; n is the number of coal samples). The significance level shown in Table 9 was 0.044 less than 0.05. This indicates that the model was statistically significant. Consequently, the above indicated that the linear relationship of the model was significantly established at the confidence level.

Table 10. Anova.

parameter variance sum of squares df mean square F sig.
regression 494410.952 4 123602.738 22.011 0.044
residual 11230.899 2 5615.450    
total 505641.851 6      
Open in a new tab

According to the data in Table 11, the t values of the four explaining variables (X1, X2, X3, and X4) obtained were |t1| = 1.832, |t2| = 0.53, |t3| = 0.191, and |t4| = 2.268, respectively. The given significance level of α was 0.05, and the degree of freedom (df) was 2 (n–k–1 = 2). When t0.025(2) = 6.205 was calculated, it can be observed that the values of all four variables were less than the critical value; therefore, the null hypothesis was rejected. In other words, the four explaining variables introduced in the model all had significant influence under the level. All explaining variables passed the significance test of variables.

Table 11. Coefficient.

  unstandardized coefficients
 standardized coefficients
   collinearity statistics
model B std. error β T sig. tolerance VIF
constant 1176.737 965.864   1.218 0.347    
X1 –52.79 28.82 –0.446 –1.832 0.208 0.187 5.341
X2 –3290.75 6203.861 –0.175 –0.53 0.649 0.102 9.824
X3 1228.511 6434.105 0.051 0.191 0.866 0.154 6.511
X4 21528.54 9491.253 0.496 2.268 0.151 0.232 4.304
Open in a new tab

The collinearity diagnosis of the model was validated by data in Table 11. The variance inflation factors (VIFs) of the four explaining variables were all less than 10, indicating that the model did not contain multicollinearity problem.

The normal P–P plot of the regression standardized residual is the relationship between the accumulative proportion of variables and the accumulative proportion of normal distribution. In Figure 9, the predicted points are distributed on both sides of the line without significant deviation, which indicate that the random variables were well-described by the normal distribution, and the residual distribution is also approximately normal.

Figure 9.

Figure 9

Open in a new tab

Normal P–P plot of regression standardized residual.

In conclusion, the model satisfied the significance test with high reliability, and the variables were randomly distributed and independent. The model passed the regression coefficient and residual analysis test, and the regression equation was statistically significant. In summary, we determined the multifactor prediction model of coal spontaneous combustion tendency as follows

3.3. 11

To verify the practicability of the model, fresh coal samples from Tangshan mine (8 coal seam) and Chengde mine were selected. According to the same experimental operation, corresponding experimental data of coal spontaneous combustion tendency and influencing factors are obtained, as shown in Table 12.

Table 12. Experimental Data of Coal Samples in Tangshan Mine and Donghuantuo Mine.

coal coalfield X1 X2 X3 X4 Y
Tangshan (8 coal seam) 8.16 0.1645 0.0314 0.0337 983.43
Chengde 8.35 0.1693 0.0327 0.0268 765.29
Open in a new tab

The experimental data obtained from coal samples and used for verification were substituted into the formula for the multifactor prediction model of spontaneous combustion tendency. The actual and predicted CJI values of coal spontaneous combustion tendency were calculated, as shown in Table 13.

Table 13. Practical Application of the Prediction Model.

coal coalfield experimental value predicted value absolute error value relative error (%)
Tangshan(8 coal seam) 983.43 969.47 13.96 1.42
Chengde 765.29 797.84 32.55 4.25
Open in a new tab

By calculating the CJI for the coal seam spontaneous combustion tendency, both coal mine (8 coal seam) and Chengde mine demonstrate a tendency for spontaneous combustion. By comparing the predicted value and the experimental value, the relative errors of two coal samples of the model were 1.42 and 4.25%, respectively. These small relative errors verified the reasonableness and validity of the prediction model.

4. Conclusions

In this study, the influence of multiple parameter coupling on the tendency of coal spontaneous combustion was studied.

By the measure of vitrinite random reflectance, the Rr of each coal sample increased with an increasing metamorphism degree. Meanwhile, the CJI of coal spontaneous combustion tendency increased with Rr.

According to grey relational analysis, the grey relational grades between CJI and the parameters of coal samples were obtained. The grey relational grade between each parameter and CJI was in the descending order: benzene substituent, methyl, methylene, average pore diameter, hydroxyl, aromatic hydrogen, carboxyl, carbon–carbon double bond, micropores, BET specific surface area, single point adsorption total pore volume, mesopores, and macropores. Among these parameters, the benzene substituent had the maximum grey relational grade of 0.8642 and carboxyl had the minimum grey relational grade, 0.4169.

Based on the results from the SPSS Statistics software for regression fitting, the prediction model was established. The R squared value of model was 0.978. The significance level, the F-distribution, the t-distribution, the collinearity diagnosis, and the residual distribution of the model satisfied all verification requirements. In addition, two coal samples were selected to verify the model to compare the measured values and predicted values of the multiple regression equation. The relative errors for CJI found in this verification were 1.42 and 4.25%, respectively. This suggests that the multiple regression model had higher prediction accuracy and relatively smaller error ranges. This results in an improvement in the application of predicting the spontaneous combustion tendency of coal.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (grant no. 51974128) and Natural Science Foundation of Hebei Province, China (grant no. E2020209111).

The authors declare no competing financial interest.

References

  1. Song Z.; Kuenzer C. Coal fires in China over the last decade: A comprehensive review. Int. J. Coal Geol. 2014, 133, 72–99. 10.1016/j.coal.2014.09.004. [DOI] [Google Scholar]
  2. Eckhoff R. K.; Rolf K. Dust Explosion Prevention and Mitigation, Status and Developments in Basic Knowledge and in Practical Application. Int. J. Chem. Eng. 2009, 1–12. 10.1155/2009/569825. [DOI] [Google Scholar]
  3. Zhang J.; Fu J.; Hao H.; Fu G.; Nie F.; Zhang W. Root causes of coal mine accidents: Characteristics of safety culture deficiencies based on accident statistics. Process Saf. Environ. 2020, 136, 78–91. 10.1016/j.psep.2020.01.024. [DOI] [Google Scholar]
  4. Zhang J.; Xu K.; You G.; Wang B.; Zhao L. Causation Analysis of Risk Coupling of Gas Explosion Accident in Chinese Underground Coal Mines. Risk Anal. 2019, 39, 1634–1646. 10.1111/risa.13311. [DOI] [PubMed] [Google Scholar]
  5. Qin Y.; Song Y.; Liu W.; Wei J.; Lv Q. Assessment of low-temperature oxidation characteristics of coal based on standard oxygen consumption rate. Process Saf. Environ. Protect. 2020, 135, 342–349. 10.1016/j.psep.2019.12.039. [DOI] [Google Scholar]
  6. Wang Y.; Li X.; Wang W.; Guo Z. Experimental and in-situ estimation on hydrogen and methane emission from spontaneous gasification in coal fire. Int. J. Hydrogen Energy 2017, 42, 18728–18733. 10.1016/j.ijhydene.2017.04.192. [DOI] [Google Scholar]
  7. Spada M.; Burgherr P. An aftermath analysis of the 2014 coal mine accident in Soma, Turkey: Use of risk performance indicators based on historical experience. Accid. Anal. Prev. 2016, 87, 134–140. 10.1016/j.aap.2015.11.020. [DOI] [PubMed] [Google Scholar]
  8. Grossman S.; Davidi S.; Cohen H. Emission of toxic and fire hazardous gases from open air coal stockpiles. Fuel 1994, 73, 1184–1188. 10.1016/0016-2361(94)90257-7. [DOI] [Google Scholar]
  9. Karacan C. Ö.; Ruiz F. A.; Cotè M.; Phipps S. Coal mine methane: A review of capture and utilization practices with benefits to mining safety and to greenhouse gas reduction. Int. J. Coal Geol. 2011, 86, 121–156. 10.1016/j.coal.2011.02.009. [DOI] [Google Scholar]
  10. Erarslan C.; Örgün Y.; Bozkurtoğlu E. Geochemistry of trace elements in the Keşan coal and its effect on the physicochemical features of ground- and surface waters in the coal fields, Edirne, Thrace Region, Turkey. Int. J. Coal Geol. 2014, 133, 1–12. 10.1016/j.coal.2014.09.003. [DOI] [Google Scholar]
  11. Sakala E.; Fourie F.; Gomo M.; Madzivire G. Natural Attenuation of Acid Mine Drainage by Various Rocks in the Witbank, Ermelo and Highveld Coalfields, South Africa. Nat. Resour. 2021, 30, 557. 10.1007/s11053-020-09720-5. [DOI] [Google Scholar]
  12. Gielisch G.; Christian K. Coal fires a major source of greenhouse gases- a forgotten problem. Environ. Risk Assess. Rem. 2018, 2, 1972. 10.4066/2529-8046.100030. [DOI] [Google Scholar]
  13. Parsa M. R.; Tsukasaki Y.; Perkins E. L.; Chaffee A. L. The effect of densification on brown coal physical properties and its spontaneous combustion propensity. Fuel 2017, 193, 54–64. 10.1016/j.fuel.2016.12.016. [DOI] [Google Scholar]
  14. Zhong X.; Kan L.; Xin H.; Qin B.; Dou G. Thermal effects and active group differentiation of low-rank coal during low-temperature oxidation under vacuum drying after water immersion. Fuel 2019, 236, 1204–1212. 10.1016/j.fuel.2018.09.059. [DOI] [Google Scholar]
  15. Saha M.; Dally B. B.; Medwell P. R.; Chinnici A. Burning characteristics of Victorian brown coal under MILD combustion conditions. Combust. Flame 2016, 172, 252–270. 10.1016/j.combustflame.2016.07.026. [DOI] [Google Scholar]
  16. Riahi Z.; Bounaouara H.; Hraiech I.; Mergheni M. A.; Sautet J.-C.; Nasrallah S. B. Combustion with mixed enrichment of oxygen and hydrogen in lean regime. Int. J. Hydrogen Energy 2017, 42, 8870–8880. 10.1016/j.ijhydene.2016.06.232. [DOI] [Google Scholar]
  17. Schwitalla D.; Markus R.; Clemens F.; Christian W.; Matthias G.; Jin B.; Stefan G.; Markus N.; Meyer B. Ash and slag properties for co-gasification of sewage sludge and coal: An experimentally validated modeling approach. Fuel Process. Technol. 2018, 175, 1. 10.1016/j.fuproc.2018.02.026. [DOI] [Google Scholar]
  18. Cai J.; Yang S.; Hu X.; Song W.; Xu Q.; Zhou B.; Song Y. Forecast of coal spontaneous combustion based on the variations of functional groups and microcrystalline structure during low-temperature oxidation. Fuel 2019, 253, 339–348. 10.1016/j.fuel.2019.05.040. [DOI] [Google Scholar]
  19. Wang D.; Dou G.; Zhong X.; Xin H.; Qin B. An experimental approach to selecting chemical inhibitors to retard the spontaneous combustion of coal. Fuel 2014, 117, 218–223. 10.1016/j.fuel.2013.09.070. [DOI] [Google Scholar]
  20. Onifade M.; Genc B. Spontaneous combustion of coals and coal-shales. Int. J. Min. Sci. Technol. 2018, 28, 933–940. 10.1016/j.ijmst.2018.05.013. [DOI] [Google Scholar]
  21. Nimaje D. S.; Tripathy D. P. Characterization of some Indian coals to assess their liability to spontaneous combustion. Fuel 2016, 163, 139–147. 10.1016/j.fuel.2015.09.041. [DOI] [Google Scholar]
  22. Pattanaik D. S.; Behera P.; Singh B. Spontaneous Combustibility Characterisation of the Chirimiri Coals, Koriya District, Chhatisgarh, India. Int. J. Geol. 2011, 02, 336–347. 10.4236/ijg.2011.23036. [DOI] [Google Scholar]
  23. Chandra D.; Prasad Y. V. S. Effect of coalification on spontaneous combustion of coals. Int. J. Coal Geol. 1990, 16, 225–229. 10.1016/0166-5162(90)90047-3. [DOI] [Google Scholar]
  24. Cui X.; Zhang J.; Guo L.; Gong X. The Effect of Static Blasting Materials on Coal Structure Changes and Methane Adsorption Characteristics. Adv. Mater. Sci. Eng. 2020, 2020, 1–12. 10.1155/2020/2858621. [DOI] [Google Scholar]
  25. Zhang Y.; Dong J.; Guo F.; Chen X.; Wu J.; Miao Z.; Xiao L. Effects of the evolutions of coal properties during nitrogen and MTE drying processes on the spontaneous combustion behavior of Zhaotong lignite. Fuel 2018, 232, 299–307. 10.1016/j.fuel.2018.05.169. [DOI] [Google Scholar]
  26. Shi Q.; Qin B.; Liang H.; Gao Y.; Bi Q.; Qu B. Effects of igneous intrusions on the structure and spontaneous combustion propensity of coal: A case study of bituminous coal in Daxing Mine, China. Fuel 2018, 216, 181–189. 10.1016/j.fuel.2017.12.012. [DOI] [Google Scholar]
  27. Liu G.; Benyon P.; Benfell K. E.; Bryant G. W.; Tate A. G.; Boyd R. K.; Harris D. J.; Wall T. F. The porous structure of bituminous coal chars and its influence on combustion and gasification under chemically controlled conditions. Fuel 2000, 79, 617–626. 10.1016/s0016-2361(99)00185-4. [DOI] [Google Scholar]
  28. Dudzińska A. The Effect of Pore Volume of Hard Coals on Their Susceptibility to Spontaneous Combustion. J. Chem. 2015, 1–7. 10.1155/2014/393819. [DOI] [Google Scholar]
  29. Karsner G. G.; Perlmutter D. D. Reaction regimes in coal oxidation. AIChE J. 1981, 27, 920–927. 10.1002/aic.690270607. [DOI] [Google Scholar]
  30. Zhang D.; Wang W.; Deng J.; Wen H.; Zhai X.; Shu C.-M. Thermokinetic Characteristics of Jurassic Coal Spontaneous Combustion Based on Thermogravimetric Analysis. Sci. Rep. 2020, 10, 1–15. 10.1080/00102202.2020.1821002.31913322 [DOI] [Google Scholar]
  31. Deng J.; Ren L.-F.; Ma L.; Lei C.-K.; Wei G.-M.; Wang W.-F. Effect of oxygen concentration on low-temperature exothermic oxidation of pulverized coal. Thermochim. Acta 2018, 667, 102–110. 10.1016/j.tca.2018.07.012. [DOI] [Google Scholar]
  32. Lü H. F.; Xiao Y.; Deng J.; Li D.; Yin L.; Shu C. Inhibiting effects of 1-butyl-3-methyl imidazole tetrafluoroborate on coal spontaneous combustion under different oxygen concentrations. Energy 2018, 186, 115907. 10.1016/j.energy.2019.115907. [DOI] [Google Scholar]
  33. Xu T.; Xie Q.; Kang Y. Heat effect of the oxygen-containing functional groups in coal during spontaneous combustion processes. Adv. Powder Technol. 2017, 28, 1841. 10.1016/j.apt.2017.01.015. [DOI] [Google Scholar]
  34. Xu Q.; Yang S.; Tang Z.; Cai J.; Zhong Y.; Zhou B. Free Radical and Functional Group Reaction and Index Gas CO Emission during Coal Spontaneous Combustion. Combust. Sci. Technol. 2017, 190, 834–848. 10.1080/00102202.2017.1414203. [DOI] [Google Scholar]
  35. Geng W.; Nakajima T.; Takanashi H.; Ohki A. Analysis of carboxyl group in coal and coal aromaticity by Fourier transform infrared (FT-IR) spectrometry. Fuel 2009, 88, 139–144. 10.1016/j.fuel.2008.07.027. [DOI] [Google Scholar]
  36. Zhang Y.; Yang C.; Li Y.; Huang Y.; Zhang J.; Zhang Y.; Li Q. Ultrasonic extraction and oxidation characteristics of functional groups during coal spontaneous combustion. Fuel 2019, 242, 287–294. 10.1016/j.fuel.2019.01.043. [DOI] [Google Scholar]
  37. Tang Y. Analysis of Coals with Different Spontaneous Combustion Characteristics Using Infrared Spectrometry. J. Appl. Spectrosc. 2015, 82, 316–321. 10.1007/s10812-015-0105-0. [DOI] [Google Scholar]
  38. Li J.; Li Z.; Yang Y.; Niu J.; Meng Q. Room temperature oxidation of active sites in coal under multi-factor conditions and corresponding reaction mechanism. Fuel 2019, 256, 115901. 10.1016/j.fuel.2019.115901. [DOI] [Google Scholar]
  39. Kadioğlu Y.; Varamaz M. The effect of moisture content and air-drying on spontaneous combustion characteristics of two Turkish lignitesa. Fuel 2003, 82, 1685–1693. 10.1016/s0016-2361(02)00402-7. [DOI] [Google Scholar]
  40. Huang Z.; Li J.; Gao Y.; Shao Z.; Zhang Y. Thermal Behavior and Microscopic Characteristics of Water-soaked Coal Spontaneous Combustion. Combust. Sci. Technol. 2020, 1–19. 10.1080/00102202.2020.1777993. [DOI] [Google Scholar]
  41. Arisoy A.; Akgün F. Modelling of spontaneous combustion of coal with moisture content included. Fuel 1994, 73, 281–286. 10.1016/0016-2361(94)90126-0. [DOI] [Google Scholar]
  42. Clemens A. H.; Matheson T. W. The role of moisture in the self-heating of low-rank coals. Fuel 1996, 75, 891–895. 10.1016/0016-2361(96)00010-5. [DOI] [Google Scholar]
  43. Wu Y.; Zhang Y.; Wang J.; Zhang X.; Wang J.; Zhou C.; Sciubba E. Study on the Effect of Extraneous Moisture on the Spontaneous Combustion of Coal and Its Mechanism of Action. Energy 2020, 13, 1969. 10.3390/en13081969. [DOI] [Google Scholar]
  44. Wang D.-m.; Xu-yao Q.; Xiao-xing Z.; Jun-jie G. Test method for the propensity of coal to spontaneous combustion. Procedia Earth Planet. Sci. 2009, 1, 20–26. 10.1016/j.proeps.2009.09.006. [DOI] [Google Scholar]
  45. Ban Y.-p.; Tang Y.-h.; Wang J.; Han M.-x.; Te G.-s.; WANG-Yan Y.; He R.-x.; Zhi K.-d.; Liu Q.-s. Effect of inorganic acid elution on microcrystalline structure and spontaneous combustion tendency of Shengli lignite. J. Fuel Chem. Technol. 2016, 44, 1059–1065. 10.1016/s1872-5813(16)30047-0. [DOI] [Google Scholar]
  46. Mohalik N. K.; Lester E.; Lowndes I. S. Development a modified crossing point temperature (CPTHR) method to assess spontaneous combustion propensity of coal and its chemo-metric analysis. J. Loss Prev. Process 2018, 56, 359–369. 10.1016/j.jlp.2018.09.001. [DOI] [Google Scholar]
  47. Qu X.; Qiu M.; Liu J.; Niu Z.; Wu X. Prediction of maximal water bursting discharge from coal seam floor based on multiple nonlinear regression analysis. Arabian J. Geosci. 2019, 12, 1–20. 10.1007/s12517-019-4748-7. [DOI] [Google Scholar]
  48. Kanchana J.; Prasath B.; Krishnaraj B.; Geetha B.; Priyadharshini B. Multi response optimization of process parameters using grey relational analysis for milling of hardened Custom 465 steel. Procedia Manuf. 2019, 30, 451–458. 10.1016/j.promfg.2019.02.064. [DOI] [Google Scholar]
  49. Sarraf F.; Shabnam H. N. Improving performance evaluation based on balanced scorecard with grey relational analysis and data envelopment analysis approaches: Case study in water and wastewater companies. Eval. Progr. Plann. 2020, 79, 101762. 10.1016/j.evalprogplan.2019.101762. [DOI] [PubMed] [Google Scholar]
  50. Wang L. Study on gas forecasting indexes of coal spontaneous combustion based on grey correlative analysis. ICMHPC 2007, 54–59. [Google Scholar]
  51. Zhang W. Q.; Jiang S. G.; Wang L. Y.; Wu Z. Y.; Shao H.; Wang K. B-Mode Grey Relational Analysis of Surface Functional Groups Change Rules in Coal Spontaneous Combustion. Adv. Mater. Res. 2011, 236-238, 762–766. 10.4028/www.scientific.net/amr.236-238.762. [DOI] [Google Scholar]
  52. Sampling of Coal Petrology, GB/T 19222-2003, China, AQSIQ, 2003.
  53. Method of Determining Microscopically the Reflectance of Vitrinite in Coal, GB/T 6948-2008, China, AQSIQ, 2009.
  54. Xuyao Q.; Wang D.; James A. M.; Zhong X. Crossing point temperature of coal. Miner. Process. Technol. 2011, 21, 255–260. 10.1016/j.mstc.2011.02.024. [DOI] [Google Scholar]
  55. Zhong X.; Wang D.; Qi X.; Gu J. Research on Oxidation Kinetics Test Methods Concerning the Spontaneous Combustion of Coal. J. China Univ. Min. Technol. 2009, 38, 789–793. [Google Scholar]
  56. Li L.; Tahmasebi A.; Dou J.; Lee S.; Li L.; Yu J. Influence of functional group structures on combustion behavior of pulverized coal particles. J. Energy Inst. 2020, 93, 2124–2132. 10.1016/j.joei.2020.05.007. [DOI] [Google Scholar]
  57. Zhai X.; Ge H.; Wang T.; Shu C.; Li J. Effect of water immersion on active functional groups and characteristic temperatures of bituminous coal. Energy 2020, 205, 118076. 10.1016/j.energy.2020.118076. [DOI] [Google Scholar]
  58. Behera D.; Nandi B. K.; Bhattacharya S. Variations in combustion properties of coal with average relative density and functional groups identified by FTIR analysis. Int. J. Coal Prep. Util. 2020, 1–17. 10.1080/19392699.2020.1755661. [DOI] [Google Scholar]
  59. Deng J. Introduction to Grey system theory. J. Grey Syst. 1989, 1, 1–24. [Google Scholar]
  60. Gugulothu B.; Rao G. K. M.; Bezabih M. Grey relational analysis for multi-response optimization of process parameters in green electrical discharge machining of Ti-6Al-4V alloy. Mater. Today 2020, 1–10. 10.1016/j.matpr.2020.06.135. [DOI] [Google Scholar]
  61. Khan Z. A.; Siddiquee A. N.; Khan N. Z.; Khan U.; Quadir G. A. Multi Response Optimization of Wire Electrical Discharge Machining Process Parameters Using Taguchi based Grey Relational Analysis. Procedia Mater. Sci. 2014, 6, 1683–1695. 10.1016/j.mspro.2014.07.154. [DOI] [Google Scholar]
  62. Tzeng C.-J.; Lin Y.-H.; Yang Y.-K.; Jeng M.-C. Optimization of turning operations with multiple performance characteristics using the Taguchi method and Grey relational analysis. J. Mater. Process. Technol. 2009, 209, 2753–2759. 10.1016/j.jmatprotec.2008.06.046. [DOI] [Google Scholar]
  63. Algina J.; Olejnik S. Sample Size Tables for Correlation Analysis with Applications in Partial Correlation and Multiple Regression Analysis. Multivar. Behav. Res. 2003, 38, 309–323. 10.1207/s15327906mbr3803_02. [DOI] [PubMed] [Google Scholar]
  64. Im K.; Lee J. M.; Yoon U.; Shin Y. W.; Kim S. I. Fractal dimension in human cortical surface: Multiple regression analysis with cortical thickness, sulcal depth, and folding area. Hum. Brain Mapp. 2006, 27, 994–1003. 10.1002/hbm.20238. [DOI] [PMC free article] [PubMed] [Google Scholar]
  65. Xie G.; Wang Z.; Hei X.; Takahashi S.; Nakamura H.. Data-Based Axle Temperature Prediction of High Speed Train by Multiple Regression Analysis. 2016 12th International Conference on Computational Intelligence and Security (CIS), 2017; pp 349–353.

Articles from ACS Omega are provided here courtesy of American Chemical Society

RESOURCES