New insights into the comparison of diffusion models and their impacts on gas extraction in coal seams

Diffusion is a crucial factor governing gas migration within coal seams. The particle method is mainly used to test the gas diffusion coefficient. However, selecting the appropriate particle size for diffusion coefficient determination remains challenging. Although various diffusion models have been proposed to fit experimental data accurately, their impact on gas extraction simulations is still unclear. In this study, gas diffusion experiments were conducted on nine samples with varying particle sizes, and parameters for four diffusion models were calculated by solving the inverse problem using numerical methods. Four numerical simulations of gas extraction were subsequently performed using these parameters. Finally, a calculation method for determining the time nodes to enhance gas extraction was proposed. Results showed that the gas desorption ratio initially decreased and then stabilized as particle size increased. The representative elementary volume size of coal particles for gas diffusion was 0.83–1.7 mm. Except for classical unipore diffusion model, other diffusion models could effectively fit the experimental data. Among these, time-dependent diffusion model is more suitable for predicting the gas pressure within coal seams and gas production. However, this requires establishing a quantitative relationship between laboratory test results and field-scale simulation parameters. The concept of equivalent extraction resistance was introduced to determine the time nodes for enhanced gas extraction, which were found to be necessary when daily production decreased to 14.47%–21.73% of the initial value. The research findings are of great significance for bridging laboratory results with practical field applications.