Mechanistic Insights into CO₂ Transport in Fractal Porous Media via Wavelet-Assisted Damped Fractional Brownian Motion

Understanding CO₂ transport in fractal porous media requires models capable of capturing multi-scale structural variability and temporal correlations inherent to complex geological formations. In this work, we develop a mechanistic stochastic framework based on wavelet-assisted damped fractional Brownian motion (WA-DFBM) to describe CO₂ migration and diffusion across fractal pore structures. The method integrates multi-resolution wavelet decomposition with the long-range dependence and damping characteristics of fractional Brownian motion, enabling simultaneous representation of microscopic heterogeneity, temporal memory, and dissipative effects. The resulting WA-DFBM framework reproduces key transport signatures observed in porous media, including anomalous diffusion, non-stationary fluctuations, and scale-dependent variance evolution. Comparison with conventional Brownian-based models demonstrates that WA-DFBM provides enhanced capability for representing multi-scale pore heterogeneity and dynamic variability. This approach offers improved mechanistic insight into CO₂ transport behavior in fractal porous media and establishes a generalized modeling framework applicable to a wide range of subsurface flow and transport problems.