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

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.

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 scholars[18−20] have conducted numerous studies on the tendency of coal spontaneous combustion. Nimaje and Tripathy[21] 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 Prasad[23] 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 Perlmutter[29] 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. Tang[37] 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, Wang[50] 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. Zhang[51] 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.

Experiments and Methods

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 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

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 –3.[19,54,55]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(O 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(O and W 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 .

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

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 .

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

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.

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 .

Figure 1

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 –8.

Figure 2

Peak-fitting FTIR figure of S1.

Figure 8

Peak-fitting FTIR figure of S7.

Peak-fitting FTIR figure of S2.

Peak-fitting FTIR figure of S3.

Peak-fitting FTIR figure of S4.

Peak-fitting FTIR figure of S5.

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 .

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

Results and Discussion

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 that the Rr of the samples increased with increasing metamorphism. The CJI values of the samples were calculated by eqs –3. The results are displayed in Table . 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 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 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.

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 X(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 X(k)* are shown in Table . Grey relational coefficients for normalized data were computed using eqs –7.[62]where k is the number of coal samples; i is the number of parameters; X0(k)* is the normalized reference sequence; X(k)* is the normalized comparative sequence. Δ(k) is the deviation sequence of the reference sequence and comparability sequence. R(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

Note: X is X(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 . The grey relational grade was between 0 and 1. Using eq to average the grey relational coefficients, the results are displayed in Table .[62]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

As shown in Table , 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. Agnieszka[28] 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. Zhong[14] 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.

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 , and the multiple regression variable data of the seven coal samples is displayed in Table .

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

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 is as followswhere 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 , 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

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 , 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

As shown in Table , 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 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

According to the data in Table , 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

The collinearity diagnosis of the model was validated by data in Table . 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 , 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

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

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 .

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

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 .

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

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.

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.