# Simulation and Catastrophe Detection of Spontaneous Combustion Processes in Suffide Ores
## 1 Introduction  
Pyrite, the most reactive sulfide ore, is present in large quantities in metal mines [1; 2; 3]. However, the spontaneous combustion of sulfide ores, a process that is highly susceptible to occur in sulfide-bearing mines, is one of the most critical factors affecting the safety of the mining process [4; 5; 6] and is also the most severe hazard in sulfide-bearing mines [7]. During the mining process, the exposed sulfide ore reacts with oxygen in the air, releasing a small amount of heat, which builds up and heats the sulfide ore, releasing more heat. When the temperature of the sulfide ore reaches a specific value for spontaneous combustion, spontaneous combustion can occur [8; 9]. Compared to coal mine spontaneous combustion fires, spontaneous combustion fires of sulfide ores are rare, which has led to their dangers being somewhat overlooked. However, in reality, the spontaneous combustion of sulfide ores poses a significant threat to mine safety, and its safety issues urgently need to be addressed. Especially with the continuous development of the economy and society, the demand for non-coal mineral resources is increasing, and shallow resources are gradually depleting. Most non-coal mines have had to turn to deeper mining. Currently, the leading global mining depths range from 2500 to 4000 m, such as South Africa's Rand gold mine with a maximum mining depth of 4530 m, and India's Kolar gold mine on the Deccan Plateau, which reaches a depth of 3260 m. This trend inevitably highlights the issue of increased geothermal temperatures, and the rise in deep mine temperatures will significantly increase the probability of spontaneous combustion fires in sulfide ores. Therefore, the spontaneous combustion of sulfide ores is a critical issue that urgently needs to be addressed in metal mines [10; 11]. To address the issue of the spontaneous combustion of sulfide ores, numerous scholars have conducted extensive research, primarily focusing on the spontaneous combustion mechanism, spontaneous combustion propensity evaluation, spontaneous combustion prediction and forecast, and spontaneous combustion prevention technology [12; 13; 14; 15]. Regarding the mechanism of spontaneous combustion of sulfide ores, the academic community believes that various mechanical forces encountered during sulfide ore mining make their chemical properties more active, significantly increasing their susceptibility to spontaneous combustion [16]. To evaluate the tendency for spontaneous combustion and assess the associated risks, scholars have applied methods such as game theory, set pair analysis, comprehensive methods based on weights, Bayesian discriminant analysis, TOPSIS comprehensive evaluation method, and cloud models [17; 18; 19; 20]. Additionally, some experts have developed various chemical inhibitors [21; 22], including thermophilic agents [23], imidazole ionic liquids [24], and composite inhibitors [25], to prevent the spontaneous combustion of sulfide ores, but these solutions have not been entirely effective. Therefore, many scholars aim to identify potential locations of spontaneous combustion before any signs appear [26; 27]. Predictive methods used include empirical statistical forecasting [28; 29], mathematical modeling and numerical simulation [30; 31], and landmark gas analysis and temperature measurement [32; 33; 34]. However, predicting surface combustion alone is not accurate and fails to provide timely warnings of danger. Scholars generally regard the spontaneous combustion of sulfide ores as a nonlinear multi-parameter coupled evolution process [35; 36], which is simply divided into incubation, development, and approaching stages [4; 37; 38; 39; 40]. Currently, research on the entire process of the spontaneous combustion of sulfide ores is minimal, particularly under unsteady conditions. This research is crucial for accurately determining the timing and location of spontaneous combustion.