Multifractal Characterization of Methane Adsorption in Coal Pores

The present research on the complex and heterogeneous characterization of methane (CH₄) adsorption in coal pores has not yet been revealed. In this article, the multifractal theory is employed to explore the complexity and heterogeneity of CH₄ adsorption in coal pores. The results show that the generalized fractal dimension <i>D</i>(<i>q</i>) follows a monotonically decreasing inverse <i>S</i>-shape as <i>q</i> increases, and the multifractal singularity spectrum function <i>f</i>(α) displays a convex functional relationship with α, indicating the presence of multifractal characteristics of the CH₄ adsorption in coal pores. As the key multifractal parameters, the generalized dimension spectrum (<i>q</i> ∼ <i>D</i>(<i>q</i>)) and the multifractal singularity spectrum (α ∼ <i>f</i>(α)) of the CH₄ adsorption present a favorable quantitative relation with that of coal pores, including micropores (<2 nm), mesopores (2-50 nm), and macropores (>50 nm). This finding demonstrates that the multifractal pore structure has a controlled effect on the multifractal behavior of CH₄ adsorption. This study achieves a novel characterizing method on the complexity and heterogeneity of CH₄ adsorption in coal pores and reveals the mechanism of CH₄ adsorption in coal pores from the multifractal perspective. The derived results display potential theoretical and application values in the synthesis of coal-based materials based on a fractal design strategy.