A Fractal–Desorption Synergy Framework for Quantifying Gas Expansion Energy in Coal-and-Gas Outbursts
摘要
Coal-and-gas outbursts, which are catastrophic events in underground mining, are primarily governed by gas expansion energy released through rapid desorption. Current models, however, lack quantification of two critical parameters: equivalent diameter of outburst coal (dp) and size-dependent gas diffusion coefficient (Dc). To bridge this gap, we propose a diffusion-driven energy quantification framework integrating fractal size distribution theory with approximate solution of spherical gas diffusion. A desorption-controlled dp model is established, where dp is the fractal-weighted harmonic mean derived from methane desorption kinetics. Experimental validation via laser granulometry and desorption tests on size-fractionated tectonically deformed coals reveals that: (1) dp correlates solely with particle size distribution (PSD), independent of diffusion dynamics, and (2) the scale effect of desorption rates deviates from classic diffusion laws, originating from multi-matrix equivalence within single particles—a mechanism explaining the newly discovered Dc-size dependency. By incorporating matrix scale dp and Dc values, the refined model attributes 83.9–91.4% of gas expansion energy to desorption, surpassing transport work requirements. Validation across nine outburst cases demonstrates significant diameter discrepancies: mass-average (99.54 mm) > apparent dp (2.03 mm) > matrix scale dp (5.23 μm). We demonstrate, for the first time, that forward prediction of dp via desorption kinetics satisfies energy conservation, a paradigm shift from traditional inverse approaches relying on energy thresholds. This work provides a physics-based framework for outburst energy characterization and mechanism deciphering, with direct implications for real-time hazard warning.