Study on the Response of Chemical Kinetics of Fragmented Coal Under Dynamic Load

Abstract

As coal resources deplete and deep mining in high-stress environments becomes more challenging, ensuring safety and sustainability in coal production is a growing concern. This study investigates the dynamic of external load on the oxidation kinetics of coal in goaf, focusing on the resulting physical and chemical changes. Thermogravimetric (TG), differential thermogravimetric (DTG), and differential scanning calorimetry (DSC) tests were conducted on long-flame coal samples under varying hammer-drop heights. Impact-loaded coal shows a shorter reaction time, higher peak intensity, and lower apparent activation energy than untreated coal. These effects intensify with increasing drop height, resulting in a 13–40% reduction in apparent activation energy. A six-step reaction pathway for pyrolysis and oxidation was developed, and kinetics parameters were determined using genetic algorithms (GA). GA-based inverse modeling produced a comprehensive reaction model for coal oxidation under dynamic load. This work presents a detailed kinetic model for coal oxidation under impact, contributing to better understanding the challenges of safety and sustainability in deep coal mining.

1. Introduction

As a key energy source for global power generation, coal demand continues to be driven by rising electricity consumption [1]. Despite significant fluctuations in the global energy market in recent years, which have introduced considerable uncertainty to the coal industry, overall trends have gradually stabilized. According to statistics, global coal consumption reached 8.7 billion tons in 2023, setting a new historical record. China’s power sector, as the largest coal consumer worldwide, accounted for one-third of total global demand [2]. Entering 2024, the resumption of China’s hydropower projects and the expansion of wind and photovoltaic power capacity have somewhat constrained the growth of coal-fired power generation. However, the rapid expansion of the service sector and increased industrial activity have driven a surge in electricity demand, resulting in sustained energy consumption growth [3,4]. According to the latest International Energy Agency (IEA) projections, global coal consumption is expected to remain stable throughout the year, with coal continuing to play a dominant role in the global energy landscape for the foreseeable future [5]. However, this growing demand comes with significant challenges, particularly in terms of sustainability. As accessible coal resources decline, the need for deeper coal mining has grown. Yet, deep mining operations are often carried out in high-stress environments, where increased coal fragmentation and evolving pore structures significantly affect the oxidation kinetics of coal under dynamic load conditions [6]. These challenges jeopardize the long-term sustainability of coal production and underscore the importance of developing safer and more sustainable mining practices. Ensuring sustainability in coal production, particularly in deep mining, is essential to maintaining coal as a viable energy source while mitigating its environmental and economic impact.

Spontaneous combustion of coal is one of the five major hazards in coal production, posing significant risks to mining operations. In China, more than 90% of coal seams are classified as spontaneous combustion-prone or highly susceptible. Statistics show that coal spontaneous combustion accounts for 85% to 90% of all mine fires, with goaf area fires contributing to more than 60% of endogenous coal mine fire incidents [7]. Each year, nearly 400 fires are directly caused by coal spontaneous combustion in China, while the potential fire risk due to natural oxidation exceeds 4000 cases. In northern China alone, coalfield fires have already resulted in over 4.2 billion tons of coal resources losses [8,9]. In recent years, as mining depth has increased, the degree of coal fragmentation has intensified, and the effects of geothermal heat and geostress have become more pronounced, further exacerbating the severity of coal spontaneous combustion [10,11,12]. Once a coal oxidation-induced fire occurs, it not only disrupts mining operations and causes substantial economic losses but also raises serious safety and environmental concerns. This phenomenon leads to substantial depletion of natural resources and the release of greenhouse gases such as CO and CO₂, which contribute to ozone layer depletion, global warming, and land desertification, posing a serious threat to the global environment [13,14].

Coal spontaneous combustion is a highly complex process, where both the intrinsic properties of coal and external factors such as dynamic load-induced stress variations interact to influence the oxidation reactions [15,16]. Its occurrence is influenced by multiple factors and can be attributed to the combined effects of intrinsic properties and external conditions. From an intrinsic perspective, the propensity for spontaneous combustion is the fundamental prerequisite, governed by chemical composition, rank, maceral content, sulfur content, particle size, porosity, and degree of fragmentation of coal [17,18,19]. In contrast, external factors, such as mine development methods, coal extraction techniques, mining environment, and ventilation conditions, can be actively managed through engineering controls. The interaction between these intrinsic and external factors creates a complex coupling effect, further increasing the likelihood and progression of coal spontaneous combustion [20,21].

While extensive studies have explored the effects of static loading and environmental factors on coal spontaneous combustion, the impact of dynamic load on the oxidation kinetics of fragmented coal remains largely unaddressed. Among these, environmental factors play a significant role. Several studies have examined the effects of temperature, humidity, and wind conditions on coal oxidation and spontaneous combustion characteristics. Carras and Akgun developed a multi-field coupled model for coal stockpile combustion, simulating real conditions driven by buoyancy and wind forces to investigate their impact on coal spontaneous combustion [22,23]. Guo et al. found that geothermal conditions significantly accelerate coal spontaneous combustion [24,25,26]. Additionally, Song, Zhong, and Zhai systematically analyzed the effects of environmental humidity on coal oxidation kinetics, spontaneous combustion mechanisms, and structural transformations [27,28,29,30,31]. Beyond environmental influences, mining techniques, mine development methods, and mining environments affect coal spontaneous combustion primarily by altering stress loads within the coal matrix. Wolf and Bruining employed goaf seepage field simulations to study stress distribution characteristics, revealing that the stress field has a significant impact on the spontaneous combustion of residual coal [32]. Chao et al. investigated the low-temperature oxidation behavior of coal under axial stress loading, demonstrating that when the temperature is below a critical threshold, increasing axial stress enhances coal oxidation. However, when the temperature exceeds the critical point, the effect of stress on oxidation shifts from promotion to inhibition. Their study further elucidated the molecular-level mechanisms by which stress influences gas production during coal oxidation [33]. Chu et al. developed an experimental system for stress loading, fragmented coal multi-field coupling, and permeability analysis, conducting low-temperature oxidation tests under six different stress states. Their results indicated that, under constant axial stress, the gas flow generated by coal oxidation decreases as temperature increases, leading to the conclusion that axial stress initially promotes but later inhibits the spontaneous combustion of fragmented coal [34]. Similarly, Pan et al. explored the effects of goaf conditions on coal oxidation, finding that increased stress alters the heat release and activation energy during coal oxidation. Their study further examined the microscopic mechanisms and macroscopic characteristics of pressure-relieved coal oxidation kinetics [35]. Additionally, Niu et al. subjected fresh coal samples to static loading–unloading cycles at pressures ranging from 4 to 16 MPa to simulate the evolution of granular coal under varying goaf loading conditions. Their findings revealed that as initial stress increases, the number of micropores and mesopores decreases, while macropores expand, accompanied by an increase in key oxygen-reactive functional groups. The pressure unloading process led to a gradual decrease in the characteristic oxidation temperature of bulk coal, but when the applied stress exceeded 8 MPa, the characteristic temperature increased, though it remained lower than that of raw coal. Based on these findings, they concluded that as the burial depth of the goaf increases, the oxidation behavior of unloaded granular coal becomes more pronounced, significantly elevating the risk of spontaneous combustion [36].

The influence of constant loading and fracture-related external factors on the spontaneous combustion characteristics of coal has been studied. Yang et al. investigated the damage evolution mechanisms of coal under cyclic loading and confining pressure, revealing the structural transformations occurring under different stress conditions [37]. Dong examined the effects of gradual compression on coal, demonstrating that the material undergoes sequential stages of compaction, densification, and fracturing. Significant variations in oxidation behavior were observed under pressure conditions ranging from 0 to 20 MPa. Further analysis indicated that 10 MPa was the optimal pressure for promoting coal oxidation, suggesting that this specific stress condition may enhance coal reactivity [38]. The evolution of pressurized coal follows four distinct stages: compaction, elastic deformation, yield, and failure, each leading to varying degrees of coal damage. Additionally, studies revealed that plastic deformation increases with unloading, yet no direct positive correlation was found between initial stress and coal oxidation propensity. Zhang et al. combined experimental studies and numerical simulations to analyze the molecular evolution of coal under stress conditions. Their findings demonstrated that stress-induced structural changes in coal led to increased CO release during oxidation, and this phenomenon was particularly pronounced in low-rank coals [39]. Furthermore, other studies examining the dynamic evolution of active functional groups, oxygen consumption rates, CO concentration, and pore structure changes during the oxidation of unloaded coal found that under different loading conditions, unloaded coal is more susceptible to oxidation than raw coal [40,41].

The interaction between the inherent physical–chemical properties of coal and the externally applied dynamic loads creates a complex coupling effect, which is crucial in determining the progression and intensity of the oxidation reactions. Coal mining involves dynamic loads on the residual coal in the goaf, caused by periodic weighting as mining progresses and roof caving in the abandoned mining area [42]. These loads can cause disruptions to the ventilation system, change the permeability of the coal seam, and ultimately affect the oxygen and temperature distribution within the coal matrix, all of which have a direct impact on the coal’s oxidation behavior [43,44,45]. As mining moves deeper, these dynamic effects become even more significant. The stresses within the coal seam increase, and the strata movements become more complex, which makes the goaf more susceptible to large-scale displacement. This results in more pronounced changes to the coal’s physical and chemical properties, including greater fragmentation, varying porosity, and shifting moisture levels. These factors all influence the coal’s tendency to undergo oxidation and spontaneous combustion. The deeper the mining, the more these dynamic forces alter the coal. Coal fragmentation, for example, increases the available surface area for oxidation, speeding up the process and making self-heating more difficult to control. The increased stress in deep mining areas also amplifies the risk of spontaneous combustion. Despite these well-known effects, research on how dynamic load in the goaf affects the physical properties of coal and influences its combustion characteristics is still limited. The mechanisms behind these changes are not fully understood and require further investigation. Given these challenges, it is crucial to better understand the impact of dynamic load on coal’s oxidation kinetics in deep mining environments. This knowledge will provide a clearer picture of the complex interactions between coal and environmental factors, improving our ability to predict and manage risks related to spontaneous combustion. Moreover, implementing preventive measures—such as optimizing ventilation systems, controlling the degree of coal fragmentation, and applying fire retardants or inert gases—will be essential to ensure safety in deep coal mining operations [46,47,48,49,50]. In order to bridge the gap in the current literature, our research utilizes TG-DSC experiments combined with inverse modeling via genetic algorithms to quantify the changes in kinetic parameters under various dynamic load conditions.

This study aims to investigate the effects of dynamic load in the goaf on the oxidation kinetics of fragmented coal and construct a global empirical model, providing new insights and methodologies for coal mine goaf disaster prevention and mitigation. To achieve this, a reaction pathway model was established to simulate TG and DTG experiments before and after hammer-drop impact, enabling a comprehensive analysis of how mechanical disturbances influence the pyrolysis and oxidation kinetics of coal [51,52,53]. By varying the drop height in our hammer-drop experiments, we simulated different dynamic load conditions, which allowed us to systematically investigate their effects on the oxidation kinetics of fragmented coal. These samples, along with untreated coal, were conducted using TG-DSC under inert (N₂) and oxidative atmospheres at three different heating rates (5 K/min, 10 K/min, and 15 K/min), allowing for a comparative analysis of characteristic temperature points and kinetics parameters under different impact conditions. Subsequently, an inverse modeling approach was applied using genetic algorithms (GA), utilizing heat release indicators from DSC to iteratively optimize and determine key kinetics parameters, including stoichiometric coefficients, pre-exponential factors, apparent activation energy, and reaction orders. This method accurately reconstructed a six-step coal–oxygen reaction pathway, consisting of one-step drying, two-step oxygen-free pyrolysis, and three–step heterogeneous oxidation reactions. This study not only pioneers the investigation into the effects of dynamic load on the oxidation kinetics of fragmented coal but also establishes a comprehensive kinetic model that could significantly enhance our ability to predict and mitigate coal spontaneous combustion risks in deep mining environments. Additionally, a comprehensive coal–oxygen reaction kinetic model and parameters set were developed, providing a valuable foundation for future numerical simulations.

This study employs long-flame coal samples to demonstrate the experimental and analytical methodology. Given the substantial variations in composition and chemical reactivity across different coal ranks, the characteristics of the investigated coal cannot fully represent other coal types. In principle, the proposed methodology can be adapted through minor modifications to assess the characteristics of diverse coals.

2. Experimental and Dynamic Model Construction

2.1. Basic Parameters of Experimental Samples

In this study, coal samples were obtained from the Xiwan open-pit coal mine in Shenmu County, Shaanxi Province, China. Due to the high proportion of long-flame coal and its strong tendency for spontaneous combustion, these samples were particularly well-suited for the study. The results of proximate analysis and ultimate analysis are summarized in

Table 1. Proximate analysis of coal samples.

	Mad (%)	Aad (%)	Vad (%)	FCad (%)
Samples	3.16	9.92	31.20	55.72

and

Table 2. Ultimate analysis of coal samples.

	C (%)	H (%)	O (%)	S (%)
Samples	89.39	4.82	4,27	0.51

. Before and after the experiments, our samples were sealed in dedicated airtight containers and stored in a cool, dark place to prevent pre-oxidation.

2.2. Preparation of Experimental Samples

The coal samples in Section 2.1 were separated into particles of 0.048 to 0.075 mm and collected as raw coal. In order to study the dynamic load of fragmented coal, a constant-height hammer-drop experiment system is used to simulate the impact of coal in the goaf. The height of the goaf in a longwall mining method is about 3 m. Therefore, hammer-drop heights up to 3 m are set to simulate the influence of different types of dynamic loads on broken coal in the goaf, such as roof caving. The hammer-drop experiment system, as shown in Figure 1, is composed of base, stent, glass cover, hammer, and sample cell. The glass cover with a diameter of 9.4 cm and a height of 3 m can control the falling height of the hammer according to its number. The hammer drop employed in this study utilized a 3 kg M1-class standard weight as the impact head, with precise cylindrical dimensions of 7.8 cm in diameter and 13 cm in height. The chrome-plated surface underwent mirror polishing to minimize friction effects. All impact tests were conducted under strictly controlled free-fall conditions, with the hammer released from stationary positions (zero initial velocity) to ensure consistent kinetic energy transfer. The values of drop heights of the hammer are shown in

Table 3. Values of hammer drop heights.

Sample	S1	S2	S3
Drop height	0 m	2 m	3 m

. Raw coal was named S1 in the blank control group, S2 crushed by hammer at a height of 2 m, and S3 at a height of 3 m. After the drop-hammer test, we used the same method to screen the coal powder to obtain particles of the same size as the raw coal (0.048~0.075 mm) for the TG experiment.

2.3. Thermal Analysis Test

Coal samples subjected to the hammer-drop experiment were further analyzed using simultaneous thermal analysis (STA), integrating thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) to characterize their pyrolysis and oxidation behavior under various thermal conditions. TG analysis tracks mass variation under controlled heats, providing insights into thermal stability and pyrolysis characteristics. DSC analysis characterizes the thermal effect of the material in different temperature ranges by measuring the heat flow difference between the sample and the inert reference material, and obtains the phase transition, enthalpy, and reaction thermodynamic parameters. The TG-DSC technique enables simultaneous acquisition of mass loss and heat flow data, offering a comprehensive dataset to elucidate coal pyrolysis and oxidation mechanisms. This approach is crucial for understanding the thermo-mass transfer and kinetics characteristics of fragmented coal under thermal conditions.

Before the TG-DSC experiments, coal samples underwent standardized pre-treatment, including grinding and sieving, and drying in a 333 K oven for 24 h completely removes the influence of moisture on the surface of the sample to ensure homogeneity and minimize experimental errors. Key parameters, such as heating rate and temperature range, were then set according to research objectives to accommodate different pyrolysis and oxidation conditions. After treatment, data underwent baseline correction, noise reduction, and smoothing to enhance signal quality and measurement reliability. Finally, analysis of heat flow and mass loss peaks provided thermodynamic parameters, elucidating the pyrolysis and reaction kinetics of the coal samples.

As shown in Figure 2, a Mettler-Toledo TGA/DSC 1/1600 simultaneous thermal analyzer (Mettler-Toledo GmbH, Greifensee, Switzerland) was used for TGA-DSC analysis.. The instrument provides high-precision measurements, with a mass resolution of 0.0001 mg and temperature accuracy within ±0.5 °C, ensuring data reliability. A 20 mg coal sample was accurately weighed and uniformly placed in an alumina crucible weighing 0.31 g to minimize thermal conduction inconsistencies.

Three heating rates (5 K/min, 10 K/min, and 15 K/min) were applied to systematically investigate coal pyrolysis and oxidation under various thermal conditions. The gas atmosphere control system, comprising high-purity N₂ and O₂ cylinders, was regulated in real-time by high-precision mass flow controllers (MFCs) to ensure stable and accurate oxygen concentration. Before entering the reaction chamber, N₂ and O₂ were thoroughly mixed to maintain a uniform gas environment. All experiments were conducted at a constant gas flow rate of 50 mL/min to ensure consistency and reproducibility.

2.4. GA and Reverse Modeling

In this study, the Genetic Algorithm (GA) was used for inverse modeling to estimate reaction kinetics parameters, a method that has been extensively validated in combustion kinetics research [54,55,56,57]. Building on the kinetic analysis methodology established by Rein and Huang for peat combustion [16], we incorporated thermogravimetric (TG) data obtained under varying hammer-drop heights. This kinetic analysis method was employed to characterize the reaction behaviors of the samples during pyrolysis and oxidation, resulting in the construction of a model comprising a six-step oxidation–pyrolysis pathway. The optimal reaction pathway parameters, accurately reflecting the oxidation-pyrolysis kinetics characteristics of coal, were determined through an optimized inverse calculation method using the Genetic Algorithm. The algorithm implementation followed a standardized process, as illustrated in Figure 3. First, a multi-step reaction model was constructed based on TG analysis data. The kinetics parameters derived from thermal analysis methods were used as the initial characteristic values. Next, the Genetic Algorithm was applied to perform inverse calculations, yielding the optimal parameter set. This set was then compared with the experimental results for validation. When the predicted values closely matched the experimental data, it indicated that the chosen reaction model accurately represented the reaction pathways of the samples.

In this study, TG data and the Arrhenius equation are employed to develop an initial reaction model based on the proposed stepwise reaction pathway. GA is then utilized to optimize and identify the best set of kinetics parameters for the model.

3. Results and Discussion

The oxidation kinetics of coal is a complex chemical process that involves two key stages: pyrolysis and oxidation. To accurately analyze these stages, two sets of experiments were designed. The first set focused on pyrolysis under a nitrogen atmosphere, while the second set examined oxidation under an air atmosphere.

3.1. Mass Loss and Thermal Behavior in an N₂ Atmosphere

3.1.1. Analysis of Pyrolysis Reaction Characteristics of Coal in Inert Gas

By exporting TGA data, the relationship between sample mass and temperature can be obtained. The first derivative of the TGA curve yields the mass loss rate (DTG curve), providing insights into decomposition kinetics.

Figure 4 shows the TG-DTG curves of different falling heights when the heating rate is 5 K/min in an N₂ atmosphere. The DTG curve exhibits three distinct reaction peaks, indicating that the sample undergoes three major pyrolysis stages. The peak temperatures are labeled as T₁, T₂, and T₃, corresponding to the following thermal events: Stage 1 (Dehydration Phase): the TGA curve shows a mass loss of approximately 3%, closely aligning with the moisture content (3.2%) from proximate analysis. This phase is primarily associated with the removal of free water, adsorbed water, and chemically bound water within the coal matrix. Stage 2 (Volatile Release Phase): Occurring between 500 and 800 K, this stage is characterized by endothermic reactions under a nitrogen atmosphere, resulting in a mass loss of about 22%. It is mainly attributed to the pyrolysis of long-flame coal, leading to the formation of volatile gases such as CO₂ and CH₄. These gases are carried away by the N₂ flow, accelerating mass loss and causing the DTG curve to reach its peak. However, compared to the volatile matter content (31.2%) from proximate analysis, this stage does not fully account for all volatile release. Stage 3 (Secondary Degassing Phase): This stage occurs between 800 and 1100 K, dominated by polycondensation reactions, with relatively minor mass loss. It mainly involves secondary degassing, which appears as net exothermic behavior in the DSC curve. At the end of this stage, approximately 60% of the initial mass remains, consistent with the fixed carbon and ash content from proximate analysis, indicating that the final pyrolysis products consist of ash and residual char. The TGA-DTG curves indicate that impact intensity influences the reaction stages of coal. Under dynamic load, an increase in hammer-drop height leads to an earlier and more pronounced DTG peak, suggesting that a higher impact force accelerates the attainment of characteristic temperatures and intensifies the reaction. The accelerated response can be attributed to several factors. Firstly, the formation of microcracks and increased pore structure caused by the impact force enhance heat transfer efficiency and increase the reactive surface area. Secondly, the improved pore connectivity facilitates the escape of pyrolysis gases, minimizing the inhibitory effects of volatile accumulation and leading to a more complete thermal decomposition.

At a heating rate of 5 K/min, the T₂ characteristic temperature appears approximately 18 K earlier for S2, and 29 K earlier for S3, compared to S1. Additionally, the proportion of residual pyrolysis products decreases after impact, indicating a more complete pyrolysis of the coal.

Experimental results indicate that the dehydration process for all three coal samples occurs primarily between room temperature and 443 K. As heating continues, volatile release begins at approximately 600 K, leading to the formation of semi-coke. With further increasing temperature, semi-coke undergoes polycondensation reactions, ultimately converting into char, with the process completing around 1000 K.

3.1.2. Pyrolysis Kinetics of Coal in Inert Gas

This study postulates a global reaction mechanism. The Arrhenius equation establishes a quantitative relationship between the reaction rate (ω) and temperature (T) in complex reaction systems, assuming pseudo-elementary reaction steps with an average reactant concentration [58]. This equation is based on the apparent kinetics assumption, the derived parameters represent equivalent kinetic descriptors that statistically characterize the macroscopic behavior of multi-step reactions. The kinetics parameters obtained from this model are applicable to the simplified reaction pathway of coal oxidation at the particle scale, as illustrated in Equation (1).

$$\omega ={\displaystyle \frac{\mathrm{d}\alpha }{\mathrm{d}T}}=A{\mathrm{e}}^{-{\displaystyle \frac{E_{\mathrm{a}}}{\mathrm{R}T}}}f(\alpha )$$

(1)

In this equation, A is the apparent pre-exponential factor, R is the molar gas constant, and E_a is the apparent activation energy of the substance in the units of kJ/mol and the function f(α) corresponds to the differential reaction model of the substance. Here, α refers to the conversion rate:

$$\alpha ={\displaystyle \frac{m_0-m}{m_0-m_{\infty }}}$$

(2)

Here, m represents the mass at the time of the reaction, m₀ is the initial mass, and m_∞ is the mass at the end of the reaction in mg units.

Using the Kissinger method [59], by differentiating both sides of Equation (1) and introducing the condition ${\displaystyle \frac{\mathrm{d}}{\mathrm{d}t}}{\displaystyle \frac{\mathrm{d}\alpha }{\mathrm{d}t}}=0$ at the peak of the reaction rate, the integral form of the reaction kinetics equation for the corresponding sample can be derived. This equation can be expressed as Equation (3).

$$\ln {\displaystyle \frac{\beta }{\mathrm{R}{T}^2}}=\ln {\displaystyle \frac{A\mathrm{R}}{E_{\mathrm{a}}}}-{\displaystyle \frac{E_{\mathrm{a}}}{\mathrm{R}}}{\displaystyle \frac{1}{T_{\mathrm{p}}}}$$

(3)

Here, β represents the heating rate, in units of K/min, and T_p is the temperature at the peak of the reaction rate, corresponding to the peak temperatures T₁, T₂, and T₃ in the previously mentioned DTG curves. Therefore, the apparent activation energy E_a and pre-exponential factor A can be determined by the linear relationship between ${\displaystyle \frac{1}{T_{\mathrm{p}}}}$ and $\ln {\displaystyle \frac{\beta }{\mathrm{R}{T}^2}}$, as shown in Figure 5.

Nine sets of thermogravimetric data from three samples were used in the Kissinger method to calculate the apparent activation energy and apparent pre-exponential factor A for the samples at different drop–hammer heights, as summarized in

Table 4. Kinetics parameters of the sample in an N₂ atmosphere.

Parameters	S1			S2			S3
	Stage 1	Stage 2	Stage 3	Stage 1	Stage 2	Stage 3	Stage 1	Stage 2	Stage 3
Ea/(KJ mol−1)	114.1512	345.7709	333.1087	64.7577	253.6768	280.8469	61.3986	202.6957	178.8092
ln(A)/ln(s−1)	14.1214	12.7739	13.3286	6.5058	15.2082	10.9504	7.1444	11.5825	6.3294
R2	0.9982	0.9945	0.9765	0.9609	0.9974	0.9822	0.9882	0.9745	0.9708

. As illustrated in the chart, the activation energies of coal samples are significantly reduced under the impact force of the drop hammer, with the effect being more pronounced at a drop height of 3 m compared to 2 m. Notably, the apparent activation energy during the devolatilization stage showed the greatest decrease, by approximately 41%. On the one hand, dynamic load can cause the fracture and degradation of aliphatic side chains (–CH₂–, –CH₃), leading to the formation of shorter hydrocarbon chains and free radicals, which are more prone to volatilization during pyrolysis and require less energy for removal [60]. On the other hand, the devolatilization stage predominantly involves the breaking of weak bonds, including aliphatic chains (–CH₂–, –CH₃), carboxyl groups (–COOH), and ether linkages (–O–) [61], which are particularly susceptible to damage under dynamic load. Compared to the more stable reactions during the semi-coke condensation stage, breaking these weak bonds requires relatively lower energy. As a result, the reduction in activation energy during the devolatilization stage is more significant.

3.1.3. Pyrolysis Reaction Pathway of Coal in Inert Gas

In the previous chapter, the basic sequence of pyrolysis reactions was identified using thermogravimetric data, and some of the relevant kinetics parameters were calculated. The multi-component accumulation model assumes that the solid reaction material is composed of x distinct components. During the pyrolysis process of the sample, each component decomposes independently without affecting the others. As a result, the overall decomposition process can be seen as the sum of the individual pyrolysis reactions of these components. For each component, its pyrolysis follows the mathematical framework of solid-state reaction kinetics, which is described by Equations (4) and (5). To make this clearer, the reaction rate (ω) for each step of the i-th component’s reaction is reformulated as follows [16]:

$${\omega }_i=A_i{e}^{-{\displaystyle \frac{E{\mathrm{a}}_i}{\mathrm{R}T}}}{y}_i^n{y}_{{\mathrm{O}}_2}^{n_{{\mathrm{O}}_2}}$$

(4)

where $y_i$ is the mass fraction of the solid reactant, $y_{O_2}$ is the mole fraction of oxygen, n is the reaction order of the solid reactant, and $n_{O_2}$ is that of oxygen. Therefore, in the pyrolysis reaction of long-flame coal, the rate of mass change for each component can be calculated from ω_i. When the experiment is conducted under an inert atmosphere, the values of both $n_{O_2}$ and $y_{O_2}$ are zero. Specifically, ${\dot{m}}_{\mathrm{w}}$ represents the mass change rate of water, ${\dot{m}}_{\mathrm{c}}$ denotes the mass change rate of coal, ${\dot{m}}_{\mathrm{s}}$ refers to the mass change rate of semi-coke, and ${\dot{m}}_{\mathrm{ch}}$ indicates the mass change rate of char.

$${\dot{m}}_{\mathrm{w}}=-{\omega }_1$$

$${\dot{m}}_{\mathrm{c}}=-{\omega }_2$$

$${\dot{m}}_{\mathrm{s}}={\omega }_2{v}_2-{\omega }_3$$

$${\dot{m}}_{\mathrm{ch}}={\omega }_3{v}_3$$

(5)

In this context, ω₁ refers to the reaction rate of the first step in pyrolysis, which involves the dehydration of coal. ω₂ is the reaction rate for the second step, where coal devolatilizes to form semi-coke. ω₃ represents the reaction rate for the third step, which is the polycondensation of semi-coke. The stoichiometric coefficients v₁, v₂, and v₃ correspond to the solid-phase products in each of these three reaction steps. These coefficients are calculated using the initial mass m₀, the mass after dehydration m₁, the mass after devolatilization m₂, and the mass after the semi-coke polycondensation m₃.

$$v_1=m_1/m_0$$

$$v_2=m_2/m_1$$

$$v_3=m_3/m_2$$

(6)

The expression for the mass change rate throughout the entire reaction process is given by

$$\dot{m}={\dot{m}}_{\mathrm{w}}+{\dot{m}}_{\mathrm{c}}+{\dot{m}}_{\mathrm{s}}+{\dot{m}}_{\mathrm{ch}}$$

(7)

The mass change throughout the entire pyrolysis reaction is expressed as

$$m_{\infty }=m_0-{\displaystyle \int \dot{m}\mathrm{d}\alpha }$$

(8)

In the previous section, the kinetics parameters and stoichiometric coefficients for x components were obtained. With this information, the equations outlined earlier can be used to derive the theoretical curve of the overall conversion rate of solid pyrolysis as it changes with time. By comparing this theoretical curve to the experimental data, the fit can be evaluated by calculating the deviation between them. The Genetic Algorithm (GA), an optimization method inspired by natural biological evolution, simulates processes such as natural selection, crossover, and mutation to search for the optimal solution to a problem. In this context, each individual in the population represents a potential solution. Through iterative processes of selection, crossover, and mutation, the population gradually converges toward a better solution. GA has gained significant attention for its broad applications in optimization, machine learning, and intelligent control. Its main advantage lies in its ability to directly manipulate the structure of solutions, while leveraging parallel computing to explore the entire solution space efficiently, thereby enhancing global search capabilities. In this study, GA is used to iteratively select suitable parameter values from an initial set within a defined solution space. These parameters are used to calculate the residual mass and mass loss rate of coal samples during a programmed heating process, which are then compared to experimental data (TG/DTG). When the deviation between the calculated and experimental values meets the predefined criteria of the objective function, the selected parameters are considered optimal. The objective function, φ, is defined as the ratio of the error between the calculated (cal) and experimental (exp) values to the experimental value.

$${\phi }_i={\displaystyle \frac{\left|{\dot{m}}_{\exp }-{\dot{m}}_{\mathrm{cal}}\right|}{{\dot{m}}_{\exp }}}·\gamma +{\displaystyle \frac{\left|m_{\exp }-m_{\mathrm{cal}}\right|}{m_{\exp }}}·(1-\gamma )$$

$$\phi ={\displaystyle \sum _{i=1}^N{\phi }_i}$$

(9)

Here, φ_i represents the objective function for each heating rate, while φ is the sum of the objective function values for all curves. γ and $(1-\gamma )$ are the weight coefficients for the mass loss rate and residual mass of each curve, respectively, both set to 0.5.

For each calculation, the number of iterations is set to 500, and the population size is set to 100. The results of each iteration are used as the initial values for the next calculation, and the process is repeated until the objective function stabilizes, ultimately yielding the most suitable kinetics parameters.

For selecting the initial values and search ranges in the genetic algorithm, the apparent activation energy E_a, pre-exponential factor A, and stoichiometric coefficients are based on the results obtained from thermogravimetric analysis. E_a and ln(A) are varied within 0.8 to 1.3 times their initial values, while the stoichiometric coefficients are adjusted within the range of 0.9 to 1.1 times the initial values, to define the search space for the genetic algorithm. The initial value for the reaction order n is set to 1, with the search range spanning from 0.1 to 6. The specific parameters and their search ranges are presented in

Table 5. Kinetics parameters of the sample in an air atmosphere.

Parameters	S1		S2		S3
	Stage 4	Stage 5	Stage 4	Stage 5	Stage 4	Stage 5
Ea/(KJ mol−1)	165.8584	197.6496	146.3496	187.0652	138.9377	147.9892
ln(A)/ln(s−1)	11.4256	10.8694	11.7822	10.4904	10.9027	8.4071
R2	0.9863	0.9972	0.9945	0.9608	0.9963	0.9950

. Other than the initial kinetics parameters, all other starting conditions align with those from the thermogravimetric experiments. A comparison between the calculated values obtained using the genetic algorithm and the experimental data is shown in Figure 6. The kinetics parameters obtained through the genetic algorithm effectively reconstruct the peak values and positions of all TG data. The φ values for the three samples shown in Figure 6 are 9.39%, 8.2%, and 8.4%, respectively. The initial moisture content of 3.1% is in close agreement with the proximate analysis.

3.2. Mass Loss and Thermal Behavior in an Air Atmosphere

3.2.1. Analysis of Coal Oxidative Pyrolysis Characteristics in an Air Atmosphere

The thermogravimetric results of the three samples in an air atmosphere (oxygen concentration of 21%) at a heating rate of 5 K/min are shown in Figure 7.

The TGA results clearly reveal that during the dehydration stage (room temperature to 450 K), the DTG peak in an air atmosphere closely corresponds to the mass loss observed in the TGA curve under a nitrogen atmosphere. This indicates that the dehydration process occurs independently of oxygen. However, within 400 to 600 K, the TG curve under an air atmosphere exhibits a distinct upward trend compared to that in nitrogen, suggesting that in addition to devolatilization, an oxygen uptake reaction also occurs, leading to a temporary increase in sample mass. The second DTG peak (600~850 K; this stage is defined as stage IV; the peak temperatures are labeled as T₄) is considerably sharper and more pronounced than that in nitrogen, with a narrower and taller profile. Notably, between 600 and 700 K, the right-hand side of the peak exhibits a distinct upward shift, overlapping with subsequent reactions to form a composite peak. Within the 600~850 K range, simultaneous pyrolysis and oxidation reactions occur, leading to the formation of semi-coke, char, and oxidation products. The final reaction stage (850–950 K; this stage is defined as stage V; the peak temperatures are labeled as T₅) appears in the DTG curve, and once it diminishes to zero, no further mass loss is detected, marking the completion of the reaction.

Figure 7 illustrates the influence of drop–hammer height on the reaction process. With increasing drop–hammer height, the DTG peak appears earlier and reaches a higher intensity, indicating that dynamic load accelerates the attainment of the characteristic temperature and intensifies the reaction process.

3.2.2. Oxidative Pyrolysis Reaction Pathway of Coal in Air

Based on the analysis in the previous section, the oxidative pathway of coal in an air atmosphere includes not only the three-step pyrolysis process observed in a nitrogen atmosphere, but also reactions between semi-coke and oxygen as well as char and oxygen. The overall reaction pathway is illustrated in Figure 8.

Similarly, the Kissinger method is employed to calculate the E_a and A for the three-step oxidation reactions as initial estimates. Unlike the fully separated stages observed in pure pyrolysis under a nitrogen atmosphere, the introduction of oxidation reactions under air leads to overlapping reaction stages. Specifically, both the direct oxidation of coal to char and the oxidation of semi-coke to char occur during Stage 4, within the temperature range of 600–850 K. These two steps cannot be clearly distinguished based on the current TG-DSC data alone. Therefore, the peak temperature T₄ is used to calculate the initial kinetics parameters for both steps, which will be further refined using a genetic algorithm in subsequent modeling. Additionally, the oxidation of char to ash corresponds to the T₅ peak temperatures, which are used to determine the parameters for Stage 5, as shown in Figure 9 and Table 5.

In addition to the previously established three-step pyrolysis reactions, the remaining oxidation reaction steps are as follows: ω₄ represents the reaction rate of direct coal oxidation to char; ω₅ corresponds to the oxidation rate of semi-coke to char; and ω₆ denotes the oxidation rate of char to ash. ${\dot{m}}_{\mathrm{as}}$ represents the mass change rate of ash, and the mass variations of the respective substances are as follows:

$${\dot{m}}_{\mathrm{w}}=-{\omega }_1$$

$${\dot{m}}_{\mathrm{c}}=-{\omega }_2-{\omega }_4$$

$${\dot{m}}_{\mathrm{s}}={\omega }_2{v}_2+{\omega }_4{v}_4-{\omega }_3-{\omega }_5$$

$${\dot{m}}_{\mathrm{ch}}={\omega }_3{v}_3+{\omega }_5{v}_5-{\omega }_6$$

$${\dot{m}}_{\mathrm{as}}={\omega }_6{v}_6$$

(10)

v₄, v₅, and v₆ represent the stoichiometric coefficients of the solid-phase products in the three oxidation reaction steps.

Thus, the mass change rate equation for the entire reaction process in an air atmosphere is expressed as follows:

$$\dot{m}={\dot{m}}_{\mathrm{w}}+{\dot{m}}_{\mathrm{c}}+{\dot{m}}_{\mathrm{s}}+{\dot{m}}_{ch}+{\dot{m}}_{\mathrm{as}}$$

(11)

The mass change throughout the pyrolysis reaction is expressed as

$$m_{\infty }=m_0-{\displaystyle \int \dot{m}\mathrm{d}\alpha }$$

(12)

The model parameters were rationally defined based on the characteristics of products in different reaction stages. For the direct oxidation reactions of coal and semi-coke, the formation of gaseous products is relatively limited, with most of the mass retained as solid char. Therefore, the initial value of the solid-phase yield coefficient in this stage was set to 0.8, with a search range of 0.6–1, to ensure that the majority of the mass is converted into char in the simulation. In contrast, for the oxidation of char, the reaction leaves only ash as residue, with nearly all of the mass released in the form of gaseous products. Thus, the initial value of the solid-phase yield coefficient for this stage was set to 0.05, with a search range of 0.01–0.1, to reflect the extremely low proportion of solid products during char oxidation. These settings ensure that the model parameters remain within physically meaningful limits while maintaining sufficient flexibility for optimization, thereby improving the accuracy and stability of reaction pathway simulations.

Following the establishment of the six-step reaction mass change model, the calculation method remains consistent with the pyrolysis reaction model. Figure 10 demonstrates the agreement between calculated results from the six-step model and experimental data. The fitting results of oxidation and pyrolysis for the three samples under different experimental conditions were compared. It was found that the fitting errors were smaller when considering the oxidation reaction, with φ of 5.1%, 4.7%, and 4.2%, while the thermodynamic parameters are listed in

Table 6. Six-step reaction kinetic parameters derived from TG/DTG data of samples S1, S2, and S3.

Reaction step	Parameters	Unit	S1	S2	S3
${\omega }_1:\mathrm{Coal}·{\mathrm{H}}_2\mathrm{O}\stackrel{{\mathrm{N}}_2}{\to }\mathrm{Coal}$ (Coal drying dehydration)	Ea	KJ/mol	105.7256	82.4857	63.4082
	ln(A)	ln(s−1)	12.3981	7.4659	8.4220
	n		3.3301	3.4213	3.1920
	v	kg kg−1	0.97	0.97	0.97
	nO2		0	0	0
${\omega }_2:\mathrm{Coal}\stackrel{{\mathrm{N}}_2}{\to }\mathrm{Semi}-\mathrm{coke}$ (Devolatilization)	Ea	KJ/mol	278.9330	248.2394	197.1206
	ln(A)	ln(s−1)	12.4859	15.9821	11.5672
	n		4.3317	4.6734	4.1026
	v	kg kg−1	0.7536	0.7497	0.7442
	nO2		0	0	0
${\omega }_3:\mathrm{Semi}-\mathrm{coke}\stackrel{{\mathrm{N}}_2}{\to }\mathrm{Char}$ (Semi-coke condensation to Char)	Ea	KJ/mol	310.3451	291.3772	210.4877
	ln(A)	ln(s−1)	13.2469	10.5918	6.2918
	n		2.5912	2.9148	2.5209
	v	kg kg−1	0.9021	0.9140	0.9098
	nO2		0	0	0
${\omega }_4:C\mathrm{oal}\stackrel{O_2}{\to }\mathrm{Char}$ (Oxidize to Char)	Ea	KJ/mol	181.1491	176.2140	159.8911
	ln(A)	ln(s−1)	12.3431	14.6920	11.9998
	n		3.1923	3.1095	3.7762
	v	kg kg−1	0.8266	0.8523	0.8014
	nO2		5.1945	5.9922	5.8971
${\omega }_5:\mathrm{Semi}-\mathrm{coal}\stackrel{O_2}{\to }\mathrm{Char}$ (Semi-coke oxidizes to Char)	Ea	KJ/mol	153.1941	142.1095	120.2851
	ln(A)	ln(s−1)	13.5491	11.5480	11.1249
	n		2.2143	2.1910	2.5091
	v	kg kg−1	0.8221	0.8022	0.7987
	nO2		5.9129	5.1284	5.7980
${\omega }_6:\mathrm{Char}\stackrel{O_2}{\to }\mathrm{Ash}$ (Char oxidizes to ash)	Ea	KJ/mol	178.1329	151.4910	131.5494
	ln(A)	ln(s−1)	9.1241	11.4871	7.1485
	n		1.2247	1.9471	1.0879
	v	kg kg−1	0.0923	0.0901	0.0894
	nO2		1.7549	2.1042	1.6282

.

4. Conclusions

A drop-hammer test was implemented in this study to simulate the collapse of a hard roof in a mined-out area, and the effects of different dynamic load intensities on the pyrolysis and oxidative decomposition behavior of coal, as well as its reaction kinetics, were systematically analyzed. The chemical kinetics of impact-treated coal exhibit significant changes during thermal analyses, which exhibit the following: shortened reaction duration, increased reaction intensity, and reduced apparent activation energy. As the impact intensity increases, these trends become more pronounced, with apparent activation energy decreasing by 13~41% at different stages relative to untreated coal, indicating that mechanical damage significantly lowers the energy barrier for oxidation reactions, suggesting that dynamic load significantly enhances coal pyrolysis.

A simplified kinetics model was first established, upon which the kinetics parameters were further optimized to simulate coal combustion behavior under different dynamic load conditions. The kinetics parameters are considered as the fundamental basis for chemical reaction simulations in numerical models. This study emphasizes the application of a kinetics model with a defined level of complexity to optimize a set of kinetics parameters, ensuring more accurate simulation of TG/DTG experiments under various heating rates and atmospheric conditions. This objective was successfully achieved through the effective integration of genetic algorithms (GA) and inverse modeling techniques for TG/DTG analysis. This model successfully captures the effects of dynamic load on coal pyrolysis and oxidation, as demonstrated by the close agreement between simulated and experimental TG/DTG data.

This microscale model provides a foundation for understanding and predicting macroscale coal spontaneous combustion behavior in practical mining scenarios, accounting for the effects of dynamic load at varying drop–hammer heights. The model, which includes three pyrolysis and three oxidation reactions, provides an accurate simulation of TG/DTG experimental data under different impact conditions. The reverse-engineered TG curves based on the kinetics parameters show a deviation of less than 10% from the experimental data. These results support the use of this model for more precise simulations of coal combustion and provide deeper insights into the pyrolysis and oxidation processes, which are crucial for predicting and preventing coal spontaneous combustion. Furthermore, the proposed six-step reaction model can be applied in future numerical simulations to improve simulation accuracy. By incorporating this model into computational frameworks, it is possible to more precisely simulate the thermochemical processes of coal under dynamic load conditions. These results support the use of this model for more precise simulations of coal combustion and provide deeper insights into the pyrolysis and oxidation processes, which are crucial for predicting and preventing coal spontaneous combustion. From the perspective of resource conservation, this study provides theoretical guidance for accurately predicting spontaneous combustion risks, thereby reducing coal loss and extending the service life of mines. From an environmental protection standpoint, mitigating the risk of spontaneous combustion reduces CO₂ emissions, optimizes control strategies, and lowers prevention costs, aligning with the principles of sustainability.