Mine disasters are complex and varied, and fires caused by coal spontaneous combustion (CSC) are one of the most serious mine disasters (Liu et al., 2020; Onifade et al., 2020; Ren et al., 2022), which are highly susceptible to human casualties, environmental pollution and property damage (Deng et al., 2017; Wu et al., 2018; Li et al., 2019; Song et al., 2020). CSC is difficult to detect, locate, prevent and control the source of fire, and most coal mine fires in China are caused by CSC (Liu et al., 2022). Data show that fire accidents caused by CSC account for more than 90% of all mine fires (Wang et al., 2022), and the annual coal loss due to CSC amounts to 4.42 million tons. The process of CSC and oxidation is very complex and the exothermicity of oxidation is influenced by the intrinsic physicochemical properties, coal particle size, moisture in the coal, air humidity and oxygen concentration (Lei et al., 2023). Therefore, it is of great importance to understand the macro-featured parameters of CSC.

By studying the characteristics of CSC and accurately determining the exothermic intensity, reaction rate and other key parameters in the process of CSC, it can not only reflect the changes of coal in this period, but also accurately calculate the spontaneous combustion period of coal or the shortest experimental spontaneous combustion period (Ma et al., 2019; Zhai et al., 2020; Zhang et al., 2021a). Zhang et al. (2021b) established a large coal spontaneous combustion experimental bench to test the oxidative heating properties of Huangling coal, revealing the spatial and temporal evolution characteristics of the temperature field. Li et al. (2022) studied and experimentally verified the relationship between O₂, CO and CO₂ concentrations and temperature based on a mathematical model of the temperature field. Zuo et al. (2021) studied the temperature rise during the natural oxidation of coal using a self-built experimental platform and analyzed the variation of oxygen consumption and exothermic intensity with coal temperature by varying different air volumes and found that the exothermic intensity increased exponentially with the increase of temperature. Zeng et al. (2018) investigated the oxidative spontaneous combustion characteristics of ultra-thick coal seams in the Junggar coalfield using temperature programmed experiments and thermogravimetric analysis, and quantitatively studied many parameters, such as O₂ consumption rate, CO and CO₂ generation rate, and coal reaction activation energy. Deng et al. (2015) conducted a large-scale coal spontaneous combustion test based on a large 15t experimental furnace and studied the changes in temperature, gas ratio, oxygen consumption and exothermic intensity. Zhang et al. (2021) analyzed the oxidation properties of functional groups during CSC and their relationship with the macroscopic properties of CSC using the differential scanning thermal method.

The adiabatic oxidation method was first proposed by Davis for the study of low-temperature oxidation properties of coal (Davis et al., 2010). The adiabatic oxidation of coal is usually divided into large, medium and small samples according to the amount of experimental coal, with large samples usually requiring hundreds of kilograms or even tens of tons (Martini, 2008). Zhang et al. (2020) conducted adiabatic oxidation experiments with a small combustion furnace to analyze the changes of temperature, O2 and CO during CSC under pure oxygen adiabatic conditions. Chen et al. (2018) designed and built a small combustion furnace for CSC and studied macroscopic characteristic parameters such as temperature, gas ratio, oxygen consumption, exothermic intensity and limiting parameters. Xiao et al. (2017) constructed an experimental furnace for spontaneous combustion of 15t coal, Lei et al. (2018) built an experimental furnace for spontaneous combustion of 2t coal, Wen et al. (2017) based on an experimental furnace for spontaneous combustion of 1.5t coal, and they investigated the oxidation and self-heating characteristics of loose coal by combining various gas flow equations.

Although the adiabatic oxidation method with a small amount of coal samples cannot fully reflect the temperature field distribution in the process of CSC in real situations, it can simulate the temperature rise characteristics of the self-heating center of coal during CSC in a more realistic way, and also can truly reflect the essential properties of the difficulty of CSC. The determination of macro-featured parameters of CSC characteristics with kilogram-level coal volume natural oxidation adiabatic heating experimental system is rarely reported and needs further in-depth study. In this paper, an adiabatic oxidation loading experimental setup is designed based on a small coal volume experimental firing period test bench. The experimental system is loaded with small coal volume, small particle size, and the coal sample is dried and treated, and oxygen is introduced during the experiment, and the experimental data can better determine the propensity of coal to spontaneous combustion. The study is dedicated to solving the problem of rapid and accurate determination of the natural ignition period of coal in coal mines, and better serve coal mine safety production.

As in Figure 1, for the broken loose coal body (void ratio of n) micro-metasome, coal in the atmospheric pressure state, you can ignore the thermal resistance of contact between coal solid particles, and the low-temperature oxidation of coal can also ignore the radiation heat exchange of coal, micro-metasome particles and the gas in the void obey the law of energy conservation, the coal body exists the following relationship: Q m − Q d + Q f = E m (1)

Where, Q m is the difference between the heat inflow and heat outflow from the coal particles on the surface of the micro-metasome per unit time, kJ·mol^-1·s^-1; Q d is the convective heat exchange between the particles and the gas in the pores per unit time, kJ·mol^-1·s^-1; Q f is the exothermic intensity per unit time, kJ·mol^-1·s^-1; E m is the energy change rate of the micro-metasome per unit time, kJ·mol^-1·s^-1.

The gas in the pores within the micro-metasome obeys energy conservation: Q g − Q h + Q d = E g (2)

Where, Q g is the difference between the heat inflow and heat outflow from the micro-metasome surface particles per unit time, kJ·mol^-1·s^-1; Q h is the enthalpy change of pore gas occurring in the particles per unit time, kJ·mol^-1·s^-1; E g is the rate of energy change of the micro-metasome per unit time, kJ·mol^-1·s^-1.

The difference between the heat inflow and heat outflow from the coal particles on the surface of the micro-metasome per unit time can be expressed as: Q m = ∂ ∂ x 1 − n ⋅ λ m ∂ T m ∂ x + ∂ ∂ y 1 − n ⋅ λ m ∂ T m ∂ y + ∂ ∂ z 1 − n ⋅ λ m ∂ T m ∂ z d x d y d z (3)

Convective heat exchange between coal particles and pore gas per unit time is the result of the joint action of thermal conductivity and convection, and gas-solid heat exchange is known through Newton’s cooling theorem: Q d = α m T m − T g d x d y d z (4)

Where, α m is the convective heat transfer coefficient of coal. T m 、 T g indicate the coal surface, gas medium related temperature parameters.

The standard exothermic intensity of the coal body per unit volume per unit time is expressed as q 0 T , then: Q f = q 0 T d x d y d z (5)

The rate of energy change of the exothermic coal body can be expressed as: E m = d E d τ = D D τ ρ m ⋅ C m ⋅ 1 − n ⋅ T m d x d y d z (6)

Where, C m is the heat capacity of solid coal, J⋅g^-1⋅°C⁻¹; ρ m is the density of solid coal, g⋅cm^-1; E is the internal energy of coal, J⋅kmol^-1; τ is the time, s.

Substituting Equations 3–6 into Equation 1, the simplification gives: ∂ ∂ x λ m 1 − n ∂ T m ∂ x + ∂ ∂ y λ m 1 − n ∂ T m ∂ y + ∂ ∂ z λ m 1 − n ∂ T m ∂ z − α m T m − T g + q 0 T = D D τ ρ m C m 1 − n T m (7)

In actual coal: ∂ x ∂ τ = ∂ y ∂ τ = ∂ z ∂ τ = 0 (8)

Therefore: div λ m 1 − n g r a d T m − α m T m − T g + q 0 T = ∂ ∂ τ ρ m C m 1 − n T m (9)

In Equation 2, the difference between the heat inflow and heat outflow of the pore gas per unit time is: Q g = ∂ ∂ x λ g ⋅ n ⋅ ∂ T g ∂ x + ∂ ∂ y λ g ⋅ n ⋅ ∂ T g ∂ y + ∂ ∂ z λ g ⋅ n ⋅ ∂ T g ∂ z d x d y d z (10)

The difference between the inflow and outflow enthalpy of the pore gas per unit time is: Q h = ∂ ∂ x n ⋅ ρ g ⋅ C g ⋅ u ¯ ⋅ T g + ∂ ∂ y n ⋅ ρ g ⋅ C g ⋅ v ¯ ⋅ T g + ∂ ∂ z n ⋅ ρ g ⋅ C g ⋅ w ¯ ⋅ T g d x d y d z (11)

The rate of change of pore gas energy per unit time within the micro-metasome is: E g = ∂ ∂ τ n ⋅ ρ g ⋅ C g ⋅ T g d x d y d z (12)

Substituting Equation 4 and Equation 10–12 into Equation 2 gives: div n ⋅ λ g ⋅ g r a d T g − div n ⋅ ρ g ⋅ C g ⋅ U ⇀ ⋅ T g + α m T m − T g = ∂ ∂ τ n ⋅ ρ g ⋅ C g ⋅ T g (13)

Under normal conditions, the wind flow velocity inside the broken coal is small and the broken coal particles are isotropic. When the environment is determined, λ, ρ, C do not vary with time and space, and the temperature of solid coal, broken coal and pore gas is approximately considered the same, i.e., T c ≈ T m ≈ T g ≈ T . Eq. 12 can be simplified as: ρ c ⋅ C c ∂ T ∂ τ = λ c div g r a d T + q 0 T − n ⋅ ρ g ⋅ C g div U ⇀ ⋅ T g (14)

Where, T c is the temperature of the broken coal, °C; λ c is the thermal conductivity of the broken coal, J⋅cm^-1⋅°C⁻¹⋅s^-1; T m is the temperature of the solid coal, °C; λ m is the thermal conductivity of the solid coal, J⋅cm^-1⋅°C⁻¹⋅s^-1; T g is the gas temperature, °C; λ g is the thermal conductivity of the air, J·cm^-1·°C⁻¹·s^-1; U ⇀ is the air flow rate, m·s^-1; q is the exothermic intensity of coal body, J·cm^-3·s^-1; ρ c is the density of broken coal, g·cm^-3; C m is the specific heat of solid coal, J·g^-1·°C⁻¹; ρ m is the density of solid coal, g⋅cm^-3; C c is the specific heat of broken coal, J⋅g^-1⋅°C⁻¹; ρ g is the density of air, g⋅cm^-3; C g is the specific heat of air, J⋅g^-1⋅°C⁻¹; n is the void ratio of coal body, %; τ is the time, s.

Therefore, the conditions that cause thermal heating of the coal body storage are: ρ c ⋅ C c ∂ T ∂ τ = λ c ⋅ div g r a d T + q 0 T − n ⋅ ρ g ⋅ C g div U ⇀ ⋅ T ≥ 0 (15)

At room temperature, the oxidation exothermic intensity of broken coal body is generally (1–100) × 10⁻⁶ J cm^-3·s^-1; the thermal conductivity of broken coal body is generally (8.6–13.4) × 10⁻⁴ J cm^-1·°C⁻¹·s^-1; the heat dissipation by conduction of broken coal body is generally (25.8–40.2) × 10⁻⁴ × ∂ 2 T ∂ r 2 J·cm^-3·s^-1 (by spherical stacking); air enthalpy becomes 1.2 × 10⁻³ × U ⇀ × ∂ T ∂ r (J·cm^-3·s^-1, r is the radius of the sphere).

According to the coal samples used in the experiment and the experimental scheme, the experimental temperature starts from 30 °C, the starting air leakage intensity during the experiment is controlled at about Q ¯ = 0.015 (cm³·cm^-2·s^-1), the oxidation exothermic intensity of coal is taken as q = 7.5 × 10⁻⁶ (J·cm^-3·s^-1) at 30 °C with reference to the previous experiments done by XK-III of Xi’an University of Science and Technology, the solid coal thermal conductivity λ m = 1.2 × 10⁻³ (J·cm^-1·s^-1·°C⁻¹), the thermal conductivity of air λ g = 2.65 × 10⁻⁴ (J·cm^-1·s^-1·°C⁻¹), and the void ratio of experimental coal n = 0.37, according to the formula of thermal conductivity of coal: ρ c ⋅ C c ∂ T ∂ τ = λ c ⋅ div g r a d T + q 0 T − n ⋅ ρ g ⋅ C g div U ⇀ ⋅ T ≥ 0 (16)

Calculated as: λ c = 8.54 × 10 − 4 , J ∙ cm − 1 ∙ s − 1 ∙ ℃ − 1 (17)

Considering the experimental model of CSC by a spherical shape, the temperature difference between the center of the sphere and the boundary is kept below 2 °C. Then the minimum amount of coal that causes warming is estimated according to Equation 16, and converting Equation 16 into a difference equation and organizing it gives: 6 × λ c × T 0 − T r r 2 + C g × ρ g × Q ¯ × T 0 − T r r − 7.5 × 1 0 − 6 ≤ 0 (18)

Where, T 0 、 T r denote the temperature at the center of the ball and the boundary, respectively, °C; Q ¯ is the air leakage intensity, cm³⋅cm^-2⋅s^-1; r is the radius of the ball, cm.

By calculation, when the temperature difference between the inside and outside of the experimental coal is less than 2 °C, the minimum radius of the sphere that causes heating is 39.40cm, and thus the minimum amount of coal that causes heat storage and heating is 137.12 kg. If the temperature difference between the inside and outside of the coal is controlled at 0.5 °C, the minimum radius of the sphere that causes heating is 19.08cm, and the minimum amount of coal that causes heat storage and heating is 15.57 kg When the temperature difference between the inside and outside of the coal is 0.2 °C, the minimum radius of the sphere that causes heating is 11.93cm, and the minimum amount of coal that causes heat storage and heating is 3.81 kg. If the temperature difference between the inside and outside is 0.1 °C, the minimum radius of the sphere that causes CSC is 8.38cm, and the minimum amount of coal that causes thermal heating is 1.32 kg.

In this paper, the main macroscopic characterization parameters of coal spontaneous combustion were determined by testing Huangling No.2 coal using a self-designed kilogram-level coal spontaneous combustion experimental device, and the main conclusions were obtained as follows.

(1) The minimum amount of coal that causes thermal storage and warming is 1.32 kg, and the experimental system of natural oxidation and adiabatic heating of kilogram-level coal is designed, and the amount of coal required for the experiment is only 7–8 kg. Completed a small sample natural ignition test of Huangling No.2 coal, and measured the experimental natural ignition period of 34 days for this coal sample.