1. Introduction
China currently produces approximately half of the total worldwide coal energy [
1]. Coal spontaneous combustion (CSC) is a major hazard of coal mining [
2,
3,
4], resulting in production losses, environmental pollution, and casualties [
5,
6,
7,
8]. CSC has the characteristics of making it difficult to detect, locate, prevent, and control the fire source. Most coal mine fires in China are caused by CSC [
9]. The amount of coal lost due to CSC reaches 4.42 million tons every year. CO
2 and CH
4 produced by CSC have a certain impact on global warming, and H
2S and SO
2 produced by CSC pose great harm to the human body [
10,
11]. Understanding the spontaneous combustion process is therefore important for predicting and mitigating potential hazards.
The spontaneous combustion of coal is a complex physical and chemical reaction process, ultimately driven by the thermal effect of oxidation, which is reflected in the intensity of heat released [
12,
13,
14,
15]. In the 1980s, Luo et al. [
16,
17], Fushun Branch of Coal General Hospital, took the lead in testing the CSC tendency by the chromatographic oxygen absorption identification method to characterize the thermal effect of coal oxidation and spontaneous combustion, and implemented it as a national standard in 2006 (GB/T20104-2006). In the laboratory, quantifying the thermal effects of oxidation is typically accomplished with thermal analysis techniques, including thermogravimetric analysis, differential thermal analysis, and differential scanning calorimetry [
18,
19,
20,
21,
22]. The Merrick model [
23] relates the heat transfer process in coal pyrolysis. Li et al. [
24] quantified the controlling parameters and variability of the exothermic intensity of spontaneous combustion through large-scale laboratory experiments. In order to explore the law of CSC, Cao and Wang [
25] carried out an experimental study on coal exothermic characteristics under lean oxygen conditions by using an adiabatic spontaneous combustion device. Hu [
26] carried out a study on the microscopic physical and chemical characteristics and macroscopic thermal effect of coal during spontaneous combustion and oxidation in a gas-containing atmosphere. Li [
27] studied the thermal oxidation reaction, thermal effect, heat conduction, and dynamic characteristics of coal under different oxygen deprivation levels by combining experimental tests and theoretical analysis. Pan et al. [
28] studied the maximum exothermic temperature, heat absorption, and heat release in the process of coal oxidation by using a differential scanning calorimetry (DSC) experiment of coal temperature-programmed oxidation, and calculated the activation energy in the oxidation process according to the thermal effect data of the DSC experiment. Fan et al. [
29] monitored the variation in the heat flow and heat release of coal samples at different oxygen concentrations in the process of gradual warming. Chen [
30] studied the combustion process of white anthracite oxidation by a C80 microcalorimeter, and analyzed its exothermic characteristics and activation energy changes. Kuchta J.M. et al. [
31] proposed characterizing the thermal effect of CSC with the gas production rate.
Simulating CSC in the laboratory is an effective method for better understanding the underlying processes. Aiming at the problems existing in the research field of the thermal effect of coal spontaneous combustion and oxidation, based on the leading heating and reference test methods, this paper effectively tests the thermal effect of coal spontaneous combustion by constructing a physical similarity reference test experimental system. This can effectively test the macroscopic characteristic parameters in the process of coal spontaneous combustion. On this basis, more in-depth research is carried out. Through theoretical analysis and a self-made small coal quantity test bench, combined with the microstructure change characteristics of the coal low-temperature oxidation process, the thermal effect of coal spontaneous combustion is tested quickly and accurately, and the basic theory of coal spontaneous combustion is further improved and enriched. We provide basic parameters for predicting the spontaneous combustion law under real conditions. This provides basic theoretical support and solutions for on-site prevention and control, and has high basic theoretical value and important scientific and practical significance.
2. Theory
During heating, there is a positive temperature difference between the coal sample and the surrounding experimental apparatus. To facilitate calculation and theoretical derivation, the different types of heat in the system are defined as follows. We maintain the total heat of the coal sample as
Qc, which is the sum of
Qm (total heat of self-oxidation of coal sample) and
Qk (compensation heat of coal sample by experimental system). From these definitions, the relationship between these values is given by
Heat may be transferred to the sample by conductive heat (
Qd) and radiation (
Qf,) of the coal sample tank to the coal sample, and convective heat dissipation of the air current to the coal sample (
Qs) [
32,
33]. Other heat during coal spontaneous combustion is
Qt. The relationship of these values is thus
Heat transferred to the sample by conduction, radiation, and convection is straightforward to quantify, but other heat (
Qt) is difficult to calculate from theory. The contribution from this heat (
Qk) may, however, be empirically determined by heating a material that is physically similar to coal but which does not react with oxygen or combust. If the properties of this reference material (i.e., the thermal conductivity and density) change with temperature in a manner similar to that of coal, the factor
Qk can be assumed to be equal for both samples. Then, the total heat of self-oxidation of coal sample (
Qm) can be expressed as
The relationship between the total heat of the coal sample (
Q) and the temperature difference of a system during heating (Δ
T) is given by
where
C represents the specific heat capacity (J/g∙°C);
M represents the mass of the coal sample (g). Defining the final temperature of the coal sample reached as
Tf allows for Δ
T to be written as
A function for the final temperature with respect to time can be obtained empirically from the experimental data, and expressed as
. Combining this with Equations (4) and (5) results in an expression for maintaining the total heat (
Qc) of the coal sample:
where the superscript
b denotes the reference coal sample. A similar expression can be written for the comparison material, denoted with the superscript
u, which does not have a
Qm component:
If
Cb =
Cu and
Mb =
Mu, according to Equations (3), (6), and (7),
Qm can be written:
Thus, the heat released by the coal sample during heating (Qm) can be determined from and , which can be experimentally determined.
The heat release intensity of the coal sample (
q0t) is defined as the heat released per unit time, so the relationship between the heat release and the heat release intensity can be expressed as
During the experiment, as the temperature increases, the coal sample first undergoes physical and chemical adsorption with oxygen supplied by inflowing air, which generates adsorption heat. When the temperature reaches a critical temperature, the coal begins to chemically react with oxygen. In this process, oxygen is consumed while producing CO, CO2, and other gases, and releasing chemical reaction heat.
If it is assumed that the thermal effects of coal all result from the reaction of coal with oxygen, and we assume that all consumed oxygen has reacted to oxidize the coal, the calculated thermal effect is too large. Similarly, if it is assumed that the oxygen consumed is incorporated into the production of CO and CO
2, with only the remaining fraction chemically adsorbed, the calculated thermal effect is too small. Therefore, without considering the error introduced by the temperature differences of the experimental apparatus, the
q0t should be between these constraints, the minimum heat release intensity of the coal sample (
qmin) and the maximum heat release intensity of the coal sample (
qmax). That is, the relationship between the three should be
Thus, if the value of q0t calculated from the experimental data satisfies Equation (10), the accuracy of the method of heating a physically similar reference material would be verified.