An approach for evaluation of grading forecasting index of coal spontaneous combustion by temperature-programmed analysis

Focused on the prediction and forecast index of coal spontaneous combustion, the temperature-programmed experiments were carried out to identify the releasing rule of the gaseous compounds with the consideration of coal particle sizes. Based on the method of growth rate analysis, critical and dry cracking temperatures were determined, dividing the coal low-temperature oxidation process into three stages. The critical temperature for the spontaneous combustion of the coal is in the range of 60 ~ 70 °C, with the dry cracking temperature ranging from 100 to 110 °C. It was found that the particle sizes had obvious effects on the release of gaseous compounds during the coal heating test. To reduce the influence of coal particle size on the forecasting of coal spontaneous combustion, the combination methods of coefficient of variation and the weighted grey relational analysis were proposed for the selection and evaluation of coal spontaneous combustion indexes. For the tested coal sample, CO2/CO was selected as the primary index and O2/(CO + CO2) and CO2/O2 as the alternative indexes. C2H4 and C2H6 were selected as the index gases to confirm that the coal oxidation reached the dry cracking temperature. This research could provide a reference for the determination of the grading forecasting index of coal spontaneous combustion.


Introduction
Coal spontaneous combustion is one of the major disasters that threaten the safe production of coal mines (Taraba and Michalec 2011;Kong et al. 2017). It not only causes wastage of resources (Shao et al. 2015;Wang et al. 2018a;Li et al. 2016), but also leads to gas and coal dust explosions, which threaten the health of mineworkers seriously. In addition, hazardous gas, as well as greenhouse gases, is generated (Yi et al. 2021;Xu et al. 2018;Honscha et al. 2021), thus, causing significant damage to the atmosphere and ecological environment (Wang et al. 2018b;Zhang et al. 2016;Song and Kuenzer 2014). Accurate prediction and forecasting are important to control the hazard of coal spontaneous combustion (Onifade and Genc 2020;Qu 2018). In this respect, the determination of the quantitative index to predict and forecast the coal spontaneous combustion in a complex environment becomes a research hotspot (Yuan and Smith 2011;Baris et al. 2012).
During the coal spontaneous combustion, various gas products are released, and their concentrations are positively correlated with coal temperature (Ma et al. 2019). These gases are usually used to predict and forecast coal spontaneous combustion, which is very important for mine safety (Deng et al. 2014a(Deng et al. , 2015a. Guo et al. (2019a) assessed the qualitative and quantitative analysis of the CO and C 2 H 4 formation rates, as well as various gas ratios to forecast coal spontaneous combustion. Deng et al. (2014b) proposed the growth rate analysis method to identify the characteristic temperature of spontaneous combustion. Guo et al. (2019b) found that the olefin index gas can predict coal spontaneous combustion more accurately than alkane index gas in low oxygen concentration conditions. Wen et al. (2017a) designed and manufactured the XKGW-1 type high-temperature experimental device to study the influence of the Responsible Editor: Shimin Liu oxygen concentration on the characteristic of coal spontaneous combustion. Wen et al. (2017b) made a forecast model for the concentration of CO at the air return corner under coal mine, which can be can be used to precisely evaluate the degree of coal spontaneous combustion. Ma et al. (2020) proposed a new index D-O to forecast the coal temperature during the process of coal spontaneous combustion. Zhai et al. (2021) used thermogravimetry to determine characteristic temperatures to judge low-temperature oxidation stages of water-immersion coal.
The characteristics of coal spontaneous combustion are mainly studied from two scales: micro and macro . At the microscale, the characteristics of coal spontaneous combustion are often investigated using Fourier transform infrared (FTIR) spectroscopy, thermogravimetric analyser (TGA), C80 micro-calorimeter, and other experimental methods (Wang et al. 2022). Oxidation degree feature of coal matrix was quantified by O/C ratio through XPS technique , while the metamorphic degree (Nádudvari et al. 2021), moisture content , pyrite (Deng et al. 2015b), oxygen concentration , and other factors will have a certain impact on the coal spontaneous combustion on the macroscale. The particle size is one of the main external factors affecting coal spontaneous combustion Zhang et al. 2019;Yi et al. 2014aYi et al. , 2014b. The smaller particle size could facilitate occurrence of coal spontaneous combustion (Fernandez-Anez and Garcia-Torrent 2019), enhancing the oxidizability and exothermicity of coal spontaneous combustion and releasing more gas production . Zhang et al. (2018) conducted laboratory experiments of coal spontaneous combustion under non-isothermal conditions, and the consequence showed that the total CO output of small particle size coal is more than that of larger particle size coal. Luo et al. (2019) pointed out that, as the particle size decreases, the content of CO, light hydrocarbons, and NO X precursors all showed a tendency of decrease after the increase during rapid pyrolysis of coal. Rifella et al. (2019) conducted a comprehensive analysis of the crossing-point temperature and critical self-ignition temperature and found that larger particles have a lower risk of spontaneous combustion. The integral characteristic of the low-temperature gas-phase ignition of the products of the thermal decomposition of coal particles is determined (Glushkov et al. 2015). Qin et al. (2012) proposed the oxygen consumption rate equation of coal samples with the mixed particle size, which can be used to accurately calculate the true oxygen consumption rate of coal samples. Jia et al. (2021) found that the smaller particle size of coal improves the adsorption capacity of coal and oxygen molecules and boosts the oxygen consumption rate.
To sum up, the particle size could impact the production of gas during the process of coal-oxygen compound reaction, which also affects the accuracy selection of coal spontaneous combustion indexes. To reduce the effects of particle size on predictive index of spontaneous combustion, the coefficient of variation and weighted grey relational analysis were combined to evaluate the accuracy of grading forecast of coal spontaneous combustion index by the temperature-programmed experiments in this study.

Coal samples
The coal samples used in the experiments were all collected from the mining face in the Lu'an mining area, Shanxi Province, China, sealed with multi-layer plastic bags and then shipped to the laboratory. The collected fresh coal samples were pulverized under a nitrogen atmosphere, and five particle sizes of 0 ~ 0.9 mm, 0.9 ~ 3 mm, 3 ~ 5 mm, 5 ~ 7 mm, and 7 ~ 10 mm were manually screened out and sealed for storage in the anaerobic environment. A 1-kg mixed coal sample was prepared by mixing 200 g from each of the five particle sizes.

Experimental device
This study employed the temperature-programmed experimental system developed by Xi'an University of Science and Technology. The experimental device consisted of four parts: gas channel, temperature controller, gas collection area, and gas chromatograph. The temperature-programmed experimental system is shown in Fig. 1.

Experimental process
The coal sample was placed in the experimental steel coal sample tank with a diameter of 10 cm and a length of 22 cm. To ventilate evenly, leave a space of about 2 cm at the upper and lower ends (using 100 mesh copper wire to fix the coal sample) and then ensure the airtightness of the gas path. The coal sample tank was put in the temperature control oven and injected to preheated air, followed by the collection of gases generated at different coal temperatures. During the experiment, the heating rate of the coal body was controlled to be 0.3 °C/min, and the airflow rate was 120 ml/min. Heating from 30 to 170 °C, the composition and concentration of the collected gases were analysed by gas chromatography every 10 °C during the heating process.

Characteristic temperature
Critical temperature and dry cracking temperature are two important characteristic temperatures in the process of coal spontaneous combustion. They could be used to judge the degree of coal oxidation, which provides a basis for the early grading forecast of coal spontaneous combustion Hu and Xia 2017). As the oxygen consumption rate is one of the crucial factors affecting coal self-heating capacity (Zhu et al. 2012), it can precisely correspond to the degree of coal spontaneous combustion. Therefore, in this study, the growth rate of oxygen consumption rate with temperature was used to determine the characteristic temperatures of coal spontaneous combustion (Deng et al. 2014b;Zhao et al. 2019). This method was adopted to avoid human errors and those resulting from airflow change and apparatus calibration. The equation of the growth rate is as follows: where c is the oxygen consumption rate, t is the temperature, and B is the gradient of oxygen consumption rate as the temperature rises by 10 °C.
where Z is the growth rate of oxygen consumption rate at a temperature of t i + 1 .
From Eqs. (1) and (2), Eq. (3) can be obtained: Figure 2 shows the curve of oxygen consumption rate with temperature for the coal samples.
It can be observed from Fig. 2 that the oxygen consumption rates of coal samples are positively correlated with temperature. As the coal temperature reaches 60 °C, the curve has an inflection point, and the slope of the curve increases.
Furthermore, as the coal temperature exceeds 80 °C, the inclination of the curve becomes gentle. Around 100 °C, the curve appears at the inflection point. After 110 °C, there is no inflection point on the curve. Figure 3 shows the curve of the growth rate of oxygen consumption rate with temperature for the different coal samples. Figure 3 indicates that change rules of the growth rate of oxygen consumption rate with temperature for all coal samples are similar. Coal spontaneous combustion is process of gradual acceleration, related to the reaction of coal and oxygen. The acceleration point is shown as characteristic temperature of coal spontaneous combustion. As the coal sample reaches the characteristic temperature, the coaloxygen compound reaction rises, and the amount of oxygen involved in the reaction increases greatly, increasing oxygen consumption rate suddenly, and showing an inflection The maximum point appears at t i + 1 ; it means that between t i and t i + 1 , the amount of growth of oxygen consumption rate and the slope of the curve are the largest. Therefore, the curve has an inflection point at t i , and the characteristic temperature is t i . At 70 ~ 80 °C, the first maximum value appears, followed by the second one at 110 ~ 120 °C. It indicates that the oxygen consumption rate elevates rapidly in these temperature ranges. So, 60 ~ 70 °C could be determined to be the critical temperature range for the coal sample, whereas 100 ~ 110 °C is identified as the dry cracking temperature range. Figure 4 shows the variation of CO concentration with temperature for the coal samples. It can be observed that CO gas is detected at the initial temperature (30 °C) for each coal sample. The CO concentrations for all coal sample increase with temperature. CO gas production is also impacted by particle size. For precise prediction of coal spontaneous combustion, single CO gas concentration is with errors.

C 2 H 4 and C 2 H 6
Figures 5 and 6 show the variation of C 2 H 4 and C 2 H 6 concentrations with temperature for the coal samples.
They indicate that the increasing concentration of C 2 H 4 and C 2 H 6 with temperature is associated with coal particle size. At the same temperature, the smaller particle size coal sample could generate more C 2 H 4 and C 2 H 6 gases. Both gases can be detected as the temperature reaches above 110 °C. The generation of C 2 H 6 and C 2 H 4 gases is related to the high-temperature cracking of coal. Therefore, the appearance of C 2 H 4 and C 2 H 6 can be used as the index gas to determine the dry cracking temperature.

Composite index
Due to the complex environment, such as airflow under coal mines, the air would affect the single index gas concentration. It is difficult to precisely judge the degree of coal spontaneous combustion by single gas concentration, while the composite index involving the ratio of at least two gas concentrations can reduce the influence of the environment on the indexes (Liang et al. 2019).  Figure 7 shows the variation of CO 2 /CO of all coal samples with temperature. Figure 7 indicates that there is a negative correlation between the CO 2 /CO value and temperature. It exhibits a certain degree of dispersion before 80 °C, and the curve fluctuation after 80 °C is not intuitively shown in the figure. Therefore, it is necessary to further study whether the influence of coal particle size on the variation of CO 2 /CO with temperature is within an acceptable range. Figure 8 shows the variation of O 2 /(CO + CO 2 ) of all coal samples with temperature.

O 2 /(CO + CO 2 )
The value of O 2 /(CO + CO 2 ) decreases as the temperature rises. At 80 °C, the curve approaches the inflection point, and the inclination decreases rapidly. At this stage, the coal temperature reaches the critical temperature, and the coal-oxygen reaction takes place speedily. Consequently, an increment of the oxygen consumption rate as well as the rate of production of CO and CO 2 leads to a decrease of the O 2 content and an increase of the CO and CO 2 contents, and a decreased amplitude of O 2 /(CO + CO 2 ) value increases accordingly. As the coal temperature exceeds 80 °C, the fluctuations are difficult to be judged directly from the curve; thus, it is necessary to further study the influence of coal particle size on the variation of O 2 /(CO + CO 2 ) with temperature. Figure 9 shows the variation of O 2 /CH 4 of all coal samples with temperature.

O 2 /CH 4
As observed from Fig. 8, the O 2 /CH 4 value is negatively correlated with the temperature. Below 90 °C, the coal particle size has a certain influence on the O 2 /CH 4 value, and as the temperature exceeds 90 °C, the fluctuations in the curves are not clear. Figure 10 shows the variation of CO/CH 4 with temperature. Figure 10 illustrates that the CO/CH 4 value gradually increases with the increasing temperature. The values of all coal samples exhibit a certain degree of dispersion, when the coal temperature reaches in the range of 120 ~ 140 °C. Thus, the coal particle size influences the variation of CO/ CH 4 with temperature.  Figure 11 shows the variation of O 2 /CO of all coal samples with temperature. Figure 11 indicates that there is a negative correlation between the O 2 /CO value and coal temperature for all samples. Before 80 °C, the differences among the index values of each coal sample were various, and it is difficult to observe directly from the figure after 80 °C. Figure 12 shows the variation of CO 2 /O 2 of all samples with temperature. Figure 12 shows that there is a positive correlation between the CO 2 /O 2 value and coal temperature. The particle size of coal influences the variation of CO 2 /O 2 with temperature. But, whether the degree of influence is acceptable requires further study.

Evaluation of forecast indexes for spontaneous combustion
To ascertain the reliability of the different spontaneous combustion indexes numerically, the coefficient of variation and grey relational analysis were used to evaluate the quantitative spontaneous combustion indexes. Combining with the two characteristic temperatures, three stages could be divided for the classification of coal spontaneous combustion.

Coefficient of variation analysis
The coefficient of variation (C v ) is a standardized measure of the dispersion degree for the probability distribution. It reflects the degree of difference in the size of a set of data. The C v of more than 30% usually indicates that this set of data has a large difference and a high degree of dispersion (Brown 1998;He and Oyadiji 2001). By the C v of the coal spontaneous combustion indexes at the different coal particle sizes, the influence level can be obtained. A smaller C v indicates a lower impact of particle size on the coal spontaneous combustion index. The calculate method of coefficient of variation is as Eq. (4): where C v is the coefficient of variation, n is the number of particle size, X i is the index value of spontaneous combustion of all coal samples at the same temperature, and X is the average value of X i . Figure 13 shows the C v of coal spontaneous combustion indexes with coal temperature. Figure 14 shows the average C v . Figure 13 illustrates that the C v values of CO 2 /CO, O 2 / (CO + CO 2 ), O 2 /CO, and CO 2 /O 2 at overwhelming majority temperature are less than 20%. Only a small fraction exceeds 20%. Half of the C v value of CO/CH 4 is below 20%. The C v value of O 2 /CH 4 at each temperature point is higher than 20%; furthermore, the C v value at a few temperature points is above 30%. Subsequently, Fig. 14 illustrates that the average C v value for each spontaneous combustion index was determined. Among them, C v value of O 2 /CH 4 is the highest and exceeds 30%, indicating that the dispersion degree of values of O 2 /CH 4 of each coal sample is the highest, and the coal particle size has a greater influence on it; other indexes with lower C v values are less influenced by coal particle size.

Grey relational analysis
The grey relational coefficient could be used to represent the difference degree of the geometric shapes between the curves Zhao et al. 2020). The rate of oxygen consumption can be closely associated with the coal sample temperature. Therefore, a reference series reflecting the system characteristics are determined from the rate of oxygen consumption (If the coal spontaneous combustion  indexes show a downward trend with the temperature change, the reciprocal of the rate of oxygen consumption is used as a reference series to reflect the characteristics of the system). The coal spontaneous combustion index values form the comparison series (dimensionless) and average (used in this study) value, and initial value methods are usually used to generate the reference series. The corresponding equation is as Eq. (5): where ξ i (k) is the grey relational coefficient of X i to t at time k, and ξ is the resolution coefficient (generally between 0 and 1, 0.5 in this study), where min i min k |t(k) − X i (k)| and max i max k |t(k) − X i (k) are the two-level minimum and twolevel maximum, respectively.
The grey relational coefficient γ i represents the mean value of ξ i (k). Figure 15 shows the grey relational coefficient of each coal spontaneous combustion index. Among them, except for CO/CH 4 , the grey correlation coefficients of the other indexes are higher than 0.75, which are at a relatively high level. The grey correlation coefficient of CO/CH 4 is 0.66, which is at a low level.

Optimization analysis of weighted grey relation
The influence of particle size on the variation of coal spontaneous combustion indexes with temperature cannot be ignored. In this study, the weighted grey relational analysis is used to optimize the selection of the coal spontaneous combustion index, which can make the selection of prediction and forecast index of coal spontaneous combustion more precise and reliable. The weighted of the C v is as Eq. (6): where wi is the weighted coefficient of variation .
The equation for the weighted grey relational degree can be given as Eq. (7): Figure 16 shows the weighted grey relational degree of various indexes and their ranking results. It can be seen that R CO2/CO is the highest, followed by R CO2/O2 and R O2/(CO + CO2) , and R CO/CH4 and R O2/CH4 are at a lower level, indicating that the reliability of CO 2 /CO is the highest as a coal spontaneous combustion index. As the limit value, the median R median was used to select the indexes. When the weighted grey relational degree is higher than the R median , it could be the prediction and forecast index of coal spontaneous combustion. Therefore, it is recommended to select CO 2 /CO as the primary index and CO 2 / O 2 and O 2 /(CO + CO 2 ) as the alternative indexes.
The grading forecasting index system of coal spontaneous combustion is shown in Table 1.

Conclusions
In this study, the growth rate analysis method was used to identify characteristic temperatures of the coal spontaneous combustion by temperature-programmed test. The critical temperature range for the coal sample is determined to be 60 ~ 70 °C, whereas the dry cracking temperature range is 100 ~ 110 °C. Based on the variation of CO, C 2 H 4 , and C 2 H 6 (6) during coal oxidation with consideration of particle sizes, C 2 H 4 and C 2 H 6 were selected as the confirmation indexes for the coal temperature to reach the dry cracking temperature. The coefficient of variation was used to analyse the influence of coal particle size on composite indexes, CO 2 /CO, CO 2 /O 2 , O 2 /(CO + CO 2 ), O 2 /CO, CO/CH 4 , and O 2 /CH 4 . By weighted grey relational analysis, the quantitative coal spontaneous combustion indexes were proposed: CO 2 /CO as the primary index and CO 2 /O 2 and O 2 /(CO + CO 2 ) as the alternative indexes.