Numerical analysis of pressure-dependent characteristics of gas diffusion coefficient based on a bidisperse diffusion model

As a key parameter to describe the migration ability of gas in coal seam, the accuracy of gas diffusion coefficient has an important influence on the prediction and control of gas migration. In the existing bidisperse diffusion model, the gas diffusion coefficient is usually regarded as a constant, which ignores the change of gas diffusion coefficient with gas pressure in the complex pore structure of coal, resulting in the relationship between gas diffusion coefficient and gas pressure has not yet been clarified. In order to further explore the pressure-dependent characteristics of gas diffusion coefficient in coal, a combination of theoretical analysis and numerical simulation was used to carry out gas desorption experiments of coal particles with different particle sizes under different adsorption equilibrium pressures. By introducing the pressure-dependent diffusion coefficient, a pressure-dependent bidisperse diffusion model (EPBDM) was established, and particle swarm optimization algorithm was combined. The pressure-dependent diffusion coefficients of large and small holes are inverted; the pressure-dependent characteristics and spatio-temporal evolution of the diffusion coefficients are analyzed through numerical simulation and comparison with the model. The reliability and applicability of the model are further analyzed and discussed. The results show that: ① There is a positive correlation between the diffusion coefficients of large and small pores and the relative gas pressure; ② For the same particle size coal sample, the diffusion coefficient of large pores decreases with the increase of the initial equilibrium pressure, and the diffusion coefficient of small pores increases with the increase of the initial equilibrium pressure, and the change trend is opposite; At the same time, with the decrease of coal particle size, the diffusion coefficients of both large and micro-pores show a decreasing trend; ③ In terms of time and space scale, the diffusion coefficients of large pores and micropores in coal particles gradually decrease with the increase of desorption time, and the decreasing speed gradually slows down under the influence of pressure change, and the diffusion coefficients generally show non-uniform change characteristics; ④ Compared with the traditional bidisperse diffusion analytical model (CBDM), the simulation results of the pressure-dependent bidisperse diffusion model are highly consistent with the experimental data, and the fitting effect is obviously better, which can better reflect the real changes of the diffusion coefficients of large and small holes during the gas diffusion process. The research results can provide theoretical and methodological basis for further revealing the diffusion mechanism of coal gas.