Modeling and experiments for the time-dependent diffusion coefficient during methane desorption from coal

Abstract

Statistical analysis shows that in the coal matrix, the diffusion coefficient for methane is time-varying, and its integral satisfies the formula μtκ/(1 + βκ). Therefore, a so-called dynamic diffusion coefficient model (DDC model) is developed. To verify the suitability and accuracy of the DDC model, a series of gas diffusion experiments were conducted using coal particles of different sizes. The results show that the experimental data can be accurately described by the DDC and bidisperse models, but the fit to the DDC model is slightly better. For all coal samples, as time increases, the effective diffusion coefficient first shows a sudden drop, followed by a gradual decrease before stabilizing at longer times. The effective diffusion coefficient has a negative relationship with the size of the coal particle. Finally, the relationship between the constants of the DDC model and the effective diffusion coefficient is discussed. The constant α (μ/R2) denotes the effective coefficient at the initial time, and the constants κ and β control the attenuation characteristic of the effective diffusion coefficient.