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