*3.1. AE Counting and Energy Analysis during Spontaneous Combustion and Heating of Coal*

Through the two aspects of AE characteristic parameters and spectrum, the data obtained by the large-scale coal spontaneous combustion AE test system are analyzed. The characteristic parameters are selected for counting and energy. The current research on coal spontaneous combustion shows that the occurrence and development of coal spontaneous combustion have stage characteristics in different temperature bands [33]. Based on this, the experimental process in Figures 2 and 3 is divided according to the temperature stages, and the change law of the AE signal is analyzed. The third stage of the sample has entered the high-temperature state after rapid warming, and the subsequent warming is slower [10]. Figure 2 shows the law of the change of AE counts with time during the heating process of coal.

**Figure 2.** AE count and cumulative count plot.

**Figure 3.** AE energy and cumulative energy map.

As can be obtained from Figure 2, with the progress of the experiment, there is a gradual increase in the AE count in the initial heating stage of 0~5000 s due to the low temperature. The coal body has not obtained enough energy, and the thermal stress is not enough to destroy the coal body itself. Only more fine cracks are generated. Therefore, the integrity of the coal sample is better, and the AE signal is less. In the continuous heating stage of 5000~15,000 s, the coal body has a higher temperature. With the increase in temperature, the thermal stress of the coal body is enough to destroy the weaker structure, and the internal pore system of the coal body is reconstructed. The native cracks and new cracks inside the coal sample expand and develop at this stage. Hence strong AE signals are generated. In the subsequent heating stage of 15,000~20,000 s, the surface temperature of the coal sample continues to rise. More and more particles beyond the yield stress are inside the coal sample, so the destruction of pore structure and crack expansion are also increasing, the integrity of the coal body is seriously damaged, and the AE signal is further enhanced.

The cumulative count curve of AE is fitted to obtain a univariate linear regression curve with a slope of 5.316 and an apparent linear law, indicating that with the increase of temperature during the heating of the coal body, the AE signal continues to increase, and the level of AE count continues to increase.

As can be seen from Figure 3, with the progress of the experiment, the AE signal intensity shows a significantly enhanced trend. It has good consistency with the AE cumulative count diagram. In the initial heating stage of 0~5000 s, the coal body, due to the low temperature and the internal functional group of the coal body, failed to achieve the required activation energy. At this time, the redox reaction is weak, the coal body structure does not change significantly, and the AE energy is weak. In the continuous heating stage of 5000~15,000 s, the coal body has a higher temperature, the redox reaction of the coal body itself is more active, and the structure of the coal body is slightly damaged, so the AE signal energy is strong. In the subsequent heating stage of 15,000~20,000 s, the surface temperature of the coal sample continues to rise, the coal body obtains sufficient activation energy, and the internal structure is continuously decomposed and converted so that the coal structure is damaged. The AE energy continues to increase.

The cumulative energy curve of AE is fitted to obtain a univariate linear regression curve with a slope of 3.294 and an apparent linear law, indicating that with the increase of temperature during the heating of coal, the level of AE energy continues to increase, and the AE signal continues to increase.

In order to obtain the difference between the AE signal data at different temperatures, the AE counts and energy data of 5 min before and after 30 ◦C, 50 ◦C, 100 ◦C, 200 ◦C, and 300 ◦C are intercepted and plotted in Figures 4 and 5 below.

**Figure 4.** 600 s AE count of different temperature stages in the spontaneous combustion process of coal.

**Figure 5.** 600 s AE energy map of different temperature stages in the process of coal spontaneous combustion.

It can be seen from Figure 5 that there are fewer overall AE events at 30 ◦C and 50 ◦C. More AE signals at low counting points are generated, indicating that due to the lower temperature in the temperature band, the internal thermal expansion of the coal body is weaker, and the AE events are fewer. At 100 ◦C, there are more AE events, and a higher count of AE signals appear, indicating that in this temperature segment, a large amount of crystalline water disappears by heat evaporation of the coal body, resulting in more AE signals, and more pores have appeared on the surface of the coal sample, and the pore cracks are gradually increasing with the increase of temperature. At 200 ◦C, the internal

moisture of the coal body is tiny, and the thermal rupture phenomenon begins to appear. Hence, a robust AE signal appears, and the cracks on the surface of the coal sample expand and develop in this temperature segment. At 300 ◦C, the AE event of the coal body is more active, but the AE signal is also stronger, the thermal rupture phenomenon in the temperature band is completed, the thermal decomposition begins to appear, and the integrity of the coal sample at this time is seriously damaged, and it can be seen from the AE count data that the increase in temperature has a promoting effect on the generation of AE signals.

As shown in Figure 5, at 30 ◦C and 50 ◦C, the overall performance is relatively calm, a relatively small number of high-energy events occurred, and the overall energy amount value is low. At 100 ◦C, the coal body began to surge, the AE activity was active, and the AE signal at this time mainly came from the expansion and closure of the native fissure during the thermal expansion of the coal sample. At 200 ◦C, the AE activity is more active, with more high-energy events. The AE signal at this time mainly comes from the thermal expansion and rupture of the coal body, resulting in many pore fractures. At 300 ◦C, the AE activity is still relatively active. However, the intensity is slightly lower, indicating that the hot expansion material inside the coal body at this time has been completely expanded. A large number of cracks appear on the surface of the coal body, and the AE signal is mainly caused by the oxidative decomposition of the coal body by heat.

In order to explore the variation law of the maximum count and maximum energy in different temperature bands, the maximum values of the count and energy in the five temperature bands are selected and plotted, as shown in Figure 6 below.

**Figure 6.** Maximum count and maximum energy of AE in different temperature segments.

Figure 6 is a graph of the maximum count and maximum energy change in the five temperature bands, and it can be seen from the figure that with the increase in temperature, the maximum count of AE shows a gradual increase trend, indicating that the temperature has a promoting effect on the AE signal. The maximum increase in the 30 ◦C–100 ◦C section is slight, indicating that the AE signal of the coal body is small and the change of the coal structure is small during this stage. In the temperature range of 100 ◦C to 200 ◦C, the maximum count of coal bodies increased significantly, indicating that during this time period, the rupture state of coal bodies changed, the AE signal was more active, and the internal structure of coal bodies changed greatly. There is still a slow growth trend in the maximum count of coal bodies at 300 ◦C, indicating that the coal body is in the same rupture state at 200 ◦C–300 ◦C. The maximum energy is in the temperature range of 30 ◦C to 100 ◦C. There is a slow growth trend, indicating that the coal structure changes little at

this stage. In the temperature range of 100 ◦C to 200 ◦C, the maximum energy growth of the coal body is large, indicating that in this temperature range, the rupture mode of the coal body changes so that the energy is greater. At 300 ◦C, the maximum energy of the coal body still increases compared with 200 ◦C, indicating that the structural evolution of the coal body is continuing.

#### *3.2. Time-Frequency Analysis of AE Signals during Coal Spontaneous Combustion Heating*

The measured data are analyzed using a fast Fourier transform (FFT), and the following is an introduction to the principle of FFT [34,35]:

$$\mathbf{x}(k) = \sum\_{n=0}^{N-1} \mathbf{x}(n) e^{-2j\pi nk/N} \tag{1}$$

The inverse transformation is:

$$\mathbf{x}(k) = \frac{1}{\mathcal{N}} \sum\_{n=0}^{N-1} x(k) e^{2j\pi nk/N} \tag{2}$$

where: *x(k)* is the *k*th value of the discrete spectrum, *k* = 0, 1, ..., *N* − 1; *x(n)* is the *n*th value of time domain sampling, *n* = 0, 1, ..., *N* − 1.

The original waveform signals emitted by sound emissions from five different temperature bands during the heating process are extracted. Fast Fourier transforms (FFT) are performed to obtain a two-dimensional spectrogram.

The four small plots in the four typical power spectra of Figure 7 are interpreted for the four states. The main frequency of AE (peak frequency) corresponds to the maximum amplitude in the two-dimensional spectrogram. The main frequency and secondary frequency not in the same main peak is called a double peak, and the same main peak is called a single peak. When the frequency of the second frequency is higher than the main frequency, it is called high frequency, and when the frequency of the second frequency is lower than the main frequency, it is called low frequency. In this paper, eight AE events are selected around the five temperatures, and the probability of occurrence of each type of frequency is obtained by the fast Fourier transform, as shown in Table 2.

**Table 2.** Power spectrum probability table for different temperature types.


From Table 2 above, it can be seen that the number of occurrences of high bimodal frequency and bimodal low frequency measured in the experiment is more. The single peak high frequency and single peak low frequency are less. Fourier transform through MATLAB was used to obtain the main frequency amplitude of five temperatures. The AE signal at 30 ◦C–100 ◦C is mainly low frequency, the amplitude is slightly increased, and at 200 ◦C, it is mainly based on low frequency and high amplitude. At 300 ◦C, the AE signal is mainly based on high frequency and low amplitude. The difference between the main frequency and the amplitude category at different temperatures is large. It shows that with the increase of temperature, the probability of higher frequency main frequency AE signal will also increase, and there will be almost no high-frequency main frequency AE event before 50 ◦C, and when the temperature exceeds 50 ◦C, the high-frequency AE events

begin to appear. Thus, the AE frequency provides certain conditions for coal spontaneous combustion monitoring and early warning.

**Figure 7.** Spectrograms of four typical power articles. (**a**) double peak low frequency; (**b**) double peak high frequency; (**c**) single peak high frequency; (**d**) single peak low frequency.

The average frequency of the main frequency of the AE signal of five coal samples is calculated, and the average frequency fitting curve of coal at different temperatures is plotted, as shown in Figure 8. The fitting curve of the main frequency average frequency of coal at different temperatures shows that with the increase of temperature, the average frequency of the main frequency of AE gradually increases, so it can be known that the main frequency of AE shows a positive correlation with temperature, and this law can be used as the basis for judging the temperature change of the goaf area under the coal mine.

**Figure 8.** The average frequency of the main frequency of coal under different temperature conditions.

### **4. Study on the Fractal Law of Coal Spontaneous Combustion Heating Process**

#### *4.1. Fractal Law of Pore Structure of Coal Body after Treatment at Different Temperatures*

In this paper, the fractal dimension "A = D − 3" is calculated by using the FHH model and capillary force. The nitrogen adsorption curve is divided into two parts at P/P0 = 0.5; the fractal dimension calculated from the P/P0 < 0.5 curve part is recorded as D2 as the fractal dimension of the pore surface. The fractal dimension calculated from the P/P0 > 0.5 curve part is the fractal dimension of the pore structure is recorded as D1. The fractal calculation of the coal samples treated at four different temperatures is performed, and the obtained data is plotted in Figure 9 below.

**Figure 9.** Fractal dimension fitting curve after different temperature treatments.

D1 and D2 are obtained from the fractal dimension fitting curve of Figure 9, where D1 is the fractal dimension of the high-pressure segment, that is, the fractal dimension of the pore structure. D2 is the fractal dimension of the low-pressure segment, that is, the fractal dimension of the pore surface. In Table 3, fractal dimensions of different pore sizes are obtained by different temperature treatments.

**Table 3.** Fractal dimensions after different temperature treatments.


It can be seen from the table that with the increase of temperature, the fractal dimension of pore structures D1 and D2 are the same, in the temperature range from 30 ◦C to 100 ◦C; as the temperature rises due to thermal evaporation, the coal structure gradually becomes more complex, the pore structure continues to increase, and D1 increases. In the temperature section of 100~300 ◦C, the internal moisture of the coal body has been volatilized in large quantities, and the thermal expansion phenomenon of coal has begun to appear, resulting in the squeezing and closing of some pores and the reduction of D1. Coal

pore surface fractal dimension D2 generally showed an upward trend, indicating that the coal surface pore fracture structure tends to be complex. With the temperature of 30 ◦C to 200 ◦C, the surface moisture and volatile substances of the coal body are heated and evaporated so that the number of pores on the surface of the coal increases, and the coal surface structure is more complex. When the temperature reaches 200 ◦C, D2 shows a downward trend indicating that the coal surface structure tends to be flattened at this temperature. The surface part of the pore cracks is squeezed and closed due to heat expansion, resulting in a decrease in the complexity of the coal surface structure. D2 is reduced accordingly.
