Theoretical Model and Experimental Validation of Coalbed Methane Adsorption/Desorption Dynamics in Cylindrical and Spherical Coal Particles.

Coal, as a porous medium, exhibits a strong adsorption capacity for gas. The laws governing gas adsorption and transport are critical research topics for gas disaster prevention and control, as well as for coalbed methane (CBM) extraction. This study takes coal samples from the Guobei Mine as the research subject. Isothermal adsorption experiments under constant pressure conditions were conducted on coal particles of different sizes to investigate the influence of particle size and initial pressure on gas adsorption capacity and adsorption rate. Based on the density gradient diffusion theory, mathematical models for gas adsorption in both cylindrical and spherical coal particles were established. These models were nondimensionalized, solved using the finite difference method for simulation analysis, and subsequently validated against experimental results. The research indicates that under the same initial pressure, smaller coal particle sizes result in a larger cumulative adsorption capacity and a faster adsorption rate. For particles of the same size, a higher initial pressure leads to a greater saturated adsorption capacity and a shorter time to reach adsorption equilibrium. The cumulative gas adsorption capacity conforms to an empirical model where ″the reciprocal of adsorption capacity shows a linear relationship with 1/t0.65″. The simulation results for cylindrical and spherical particles show a high degree of agreement. Under different initial pressures, the nondimensional pressure for both shapes follows a consistent pattern: "rapid surface response → internal gradient transmission → overall trend toward equilibrium". The equilibrium nondimensional time is approximately 0.08982 at 4.0 MPa, and ranges between 0.3 and 0.45 at 0.5 MPa, with the radial pressure gradient decay rate being consistent. The initial slope, equilibrium time, and saturated adsorption capacity of the nondimensional cumulative adsorption curves are essentially identical. For 50-60 mesh coal samples at 2 MPa, the deviation in the adsorption cycle is less than 0.05 cm3/g, confirming that particle shape has no significant effect on gas adsorption and transport. The established model accurately captures the dynamic characteristics of gas transport. The fit between simulated and experimental values is excellent, with R 2 > 0.99 and an average relative error of only 3.2%. This work breaks through the limitation of the "single spherical particle" assumption, enhances the applicability of the density gradient diffusion theory, and provides reliable theoretical support for the optimization of CBM extraction and gas disaster prevention and control.