A preliminary study of coalbed methane adsorption at fractal interfaces

The adsorption and desorption mechanisms of coalbed methane (CBM) are foundational for revealing CBM accumulation mechanisms and achieving efficient CBM exploitation. Studies have indicated that coal reservoirs exhibit complex pore structures with fractal features, significantly influencing CBM adsorption at pore-solid interfaces. Based on a comparative analysis of several common adsorption models for gas-solid interfaces and a summary of their characteristics and applicable conditions, this study suggests that all these adsorption models still rely on the stationary assumption of adsorption selectivity for the description and application of CBM adsorption behavior at fractal interfaces while overlooking the scale invariance of the adsorption thickness. The fractal topography theory can effectively calibrate the scale invariance of fractal objects, providing theoretical support for the equivalent characterization of fractal interfaces. Hence, in combination with the description of CBM adsorption behavior at gas-solid interfaces in the above models, together with the fractal topography theory, this study proposed related hypotheses and control mechanisms of fractal adsorption behavior at pore-solid interfaces in coal reservoirs. Furthermore, it constructed an adsorption topography-based monolayer adsorption model, obtaining adsorption isotherms under different combinations of adsorption topological parameters. The analysis reveals that as the adsorption pressure increased, the adsorption coverage exhibited three distinct growth trends: exponential, linear, and logarithmic, while the adsorption heat displayed a trend of logarithmic decrease. The results of this study show that different combinations of adsorption topological parameters can yield different adsorption isotherms, making up for the deficiency that the Langmuir equation can merely describe a single type of adsorption isotherms. To verify the applicability of the model constructed, this study compared the actual adsorption isotherms with the simulated ones using the liquid nitrogen adsorption data of organic-rich argillaceous shale samples from the Wuxiang block of the Qinshui Basin. The finding indicates that adjusting the combinations of adsorption topological parameters can align the trends of simulated adsorption isotherms with those of actual ones. Finally, this study explored the research direction of the adsorption and desorption mechanisms and proposed the adsorption layer concept through analogy with the electron layer, emphasizing that developing fractal dynamics description models is essential for illuminating CBM adsorption and desorption regularities.