The distribution characteristics of adsorbed CH₄ across pores of various sizes underpin coal mine gas disaster prevention, resource assessment, and efficient coalbed methane (CBM) extraction. Utilizing Grand Canonical Monte Carlo (GCMC) simulations as a theoretical framework, this study establishes a mathematical model linking microscopic pore structure to macroscopic CH₄ adsorption thermodynamics in coal. Results reveal that micropores (0.38–1.5 nm) dominate pore structures in coal. For micropores (0.419–1.466 nm), CH₄ adsorption follows the Dubinin-Astakhov (DA) equation. The adsorption parameters change significantly as pore diameter increases, indicating that micropore size distribution predominantly governs CH₄ adsorption in coal. For larger pores (1.619–4.040 nm), Langmuir equation analysis reveals no significant changes in CH₄ adsorption parameters with increasing pore size, suggesting that the CH₄ adsorption behavior in pore structures larger than 1.5 nm is relatively consistent and does not vary substantially with respect to pore size. The accuracy of the mathematical model improves with coal rank, reducing prediction errors from 35.371% to 11.044%. Decomposed CH₄ adsorption isotherms reveal that while CH₄ adsorption capacity increases with equilibrium pressure for all pores, smaller pores achieve saturation at lower pressures. The proportion of total adsorption attributed to smaller pores peaks before declining with further pressure increases.

Coal and gas outburst disasters severely restrict the safe and sustainable development of deep coal resources. Outburst fluid migration is violent and highly nonlinear, posing significant challenges to its mathematical modeling. This paper presents a high-Mach-number compressible flow model for outburst fluid migration. By combining physical and numerical simulation methods, the spatiotemporal evolution characteristics of the outburst two-phase flow were revealed, and the influence of the turning angle on the migration law of the outburst fluid was analyzed. The results show that the impact pressure presents a strong–weak alternating distribution characteristic in the roadway. In the straight roadway, the impact pressure under the non-arc condition is generally higher than that under the arc condition. In the turning roadway, the impact pressure of arc and non-arc roadways increases sharply, especially in the non-arc roadway. The arc turning structures are helpful in promoting the passing ability of pulverized coal when compared with the non-arc turning structures. An arrangement of acute and right angles effectively reduces the disaster intensity of the dynamic pressure of airflow in the straight roadway but increases the disaster intensity after the turning roadway. An obtuse angle arrangement increases the disaster intensity of static pressure in the whole roadway.