Study on the Diffusion Dynamics of Coal Bed Gas Injected with Carbon Dioxide: Fickian Diffusion–Relaxation Phenomenon

The diffusion coefficient is a bridge for predicting gas diffusion processes. Accurately determining the diffusion coefficient of coalbed methane (CBM) when injecting carbon dioxide is crucial for improving CBM recovery and carbon dioxide storage. Current models often overlook how carbon dioxide and methane adsorption affect coal expansion, leading to disputed accuracy. The analysis revealed that unidirectional and bidirectional diffusion models (UM and BM), controlled only by concentration gradients, can seriously affect the accuracy of calculating the diffusion coefficients of CBM injected with CO2. Furthermore, there have been no publicly reported studies on accurately calculating CBM diffusion coefficients under conditions of carbon dioxide injection. This paper proposes a Diffusion–Relaxation (DR) model to study methane diffusion kinetics under conditions of carbon dioxide injection, originally developed for diffusion in polymer powder. The accuracy of the DR model was validated through carbon dioxide displacement methane diffusion experiments, and the limitations of the UM and BM models were discussed, revealing the diffusion mechanism of CBM injected with carbon dioxide. Therefore, this paper considers the diffusion process of methane injected into CO2 coalbeds to comprise two stages: an initial stage dominated by Fick diffusion over a short period and a subsequent relaxation diffusion stage. The diffusion mechanism of methane in CO2 injected coalbeds should be described as the superposition of Fick diffusion and diffusion relaxation caused by coal matrix adsorption expansion. Finally, this paper thoroughly examines the variances between Fickian diffusion and Fickian diffusion–relaxation at various stages, delving into the methane diffusion mechanisms in coal seams with and without CO2 injection in detail. This study offers a novel perspective on the replacement of CBM with carbon dioxide and its sequestration.