Initial desorption law and expansion energy model of desorbed gas for crushed coal

Investigating the rapid initial desorption of gas from crushed coal is essential for accurately assessing the release of expansion energy during coal and gas outbursts. In this study, we developed an equivalent particle size model for gas desorption, based on the fractal particle size distribution of crushed coal. Through impact crushing experiments and gas desorption tests, we analyzed the relationship between the coal's firmness coefficient and equivalent particle size, and examined how particle size influences gas desorption volume. We also constructed an expansion energy model for the initially desorbed gas. The results show that the equivalent particle size for gas desorption increases with the firmness coefficient, reaching a plateau at approximately 0.5. The cumulative gas desorption volume decreases according to a power-law relationship with equivalent particle size across different time intervals, with fitting coefficients between 0 and 1 that approach zero over time. Among various single-pore diffusion models, the time-varying power-law diffusion model provided the best fit and most accurately predicted long-term desorption behavior. Notably, equivalent particle size has the greatest impact on the expansion energy of desorbed gas during outbursts. The expanison energy of desorbed gas increases gradually with the decrease in equivalent particle size, and then rises significantly once the equivalent particle size falls below 0.5 mm.