In this study, we propose a dynamic fractal dimension modeling (DFDM) framework that integrates image analysis, wavelet-based fractal methods, and structural fractal geometry to quantify the evolution of pore complexity. Unlike conventional static fractal approaches, our method captures time-dependent scaling laws and captures the spatiotemporal evolution of pore networks. The results demonstrate that dynamic fractal dimensions provide a robust descriptor of multi-scale heterogeneity, effectively bridging pore-scale processes with reservoir-scale behavior. This framework not only advances the theoretical understanding of fractal pore dynamics but also establishes a predictive tool with potential applications in unconventional hydrocarbon recovery, geological CO₂ sequestration, and multi-phase flow in porous media.

Predicting nonlinear flow in stress-sensitive porous media is critical for CO₂ displacement and storage performance. We develop a wavelet-based nonlinear partial differential equation (PDE) that explicitly captures localized pressure evolution and stress-permeability coupling beyond conventional Darcy flow. From this framework, three closure indicators are derived: the curvature \(\:\kappa\:\left(t\right)\), the scaling exponent \(\:n\left(t\right)\), and the inertial ratio \(\:R\left(t\right)\), which define a unified nonlinear criterion for regime transitions. Systematic displacement experiments reveal that these indicators robustly delineate three distinct flow regimes: nonlinear mixed-phase formation, quasi-Darcy displacement, and post-breakthrough inertial channelization. The measured transitions (\(\:{t}_{1}\),\(\:{t}_{2}\)) agree closely with theoretical predictions, confirming the robustness of the nonlinear PDE model. This integrated framework provides mechanistic insight into multi-phase transport under stress sensitivity and delivers quantitative tools for regime identification. The results offer direct guidance for optimizing injection strategies, predicting breakthrough, and mitigating channelization risks in CO₂-EOR and geological carbon storage.

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.

In this study, we propose a dynamic fractal dimension modeling (DFDM) framework that integrates image analysis, wavelet-based fractal methods, and structural fractal geometry to quantify the evolution of pore complexity. Unlike conventional static fractal approaches, our method captures time-dependent scaling laws and captures the spatiotemporal evolution of pore networks. The results demonstrate that dynamic fractal dimensions provide a robust descriptor of multi-scale heterogeneity, effectively bridging pore-scale processes with reservoir-scale behavior. This framework not only advances the theoretical understanding of fractal pore dynamics but also establishes a predictive tool with potential applications in unconventional hydrocarbon recovery, geological CO₂ sequestration, and multi-phase flow in porous media.

Accurately modeling CO₂ diffusion in low-permeability heterogeneous reservoirs is critical for optimizing enhanced oil recovery and carbon sequestration strategies. We present a novel stochastic time series model that integrates damping effects, fractional Brownian motion, and wavelet transforms to simulate CO₂ migration and diffusion behavior in complex porous media. Compared to traditional approaches, our model captures multi-scale heterogeneity and dynamic fluctuations more effectively, offering improved predictive accuracy at microscopic spatial and temporal scales. This approach provides a refined understanding of CO₂ transport mechanisms in tight reservoirs and supports the design of more efficient CO₂-EOR and CCUS operations.