Investigation of CO2 Transport Characteristics for a Time Variable-Order Fractional Derivative Model in Low-Permeability Reservoirs

Low-permeability reservoirs include well-developed fracture networks and significant variations in pore structure across multiple scales that are characterized by pronounced heterogeneity. The heterogeneity of the storage structure may evolve dynamically during CO2 flooding processes. Consequently, CO2 transport exhibits distinct anomalous diffusion behavior. Conventional advection-diffusion equation models fail to accurately capture this complex transport phenomenon. To fill this knowledge gap, the variable-order fractional derivative serves as a non-local operator expressed in a differential-integral form, which can effectively describe the global spatial correlation and temporal memory effects inherent in particle movement within heterogeneous media structures or complex flow fields. This study aims to investigate the mechanism of CO2 transport in low-permeability reservoirs using a variable-order fractional advection-diffusion equation (V-FADE) model. The finite difference method is well applied to numerically solve the variable-order fractional differential equation. Numerical experiments and field applications of the V-FADE model effectively capture the apparent positive skewness and the accelerating sub-diffusion phenomenon observed in gas breakthrough curves (BTCs). Furthermore, simulation studies demonstrate a strong correlation with experimental data reported in previous literature. The decrease in variable order leads to a heavier late-time tailing in BTCs. Notably, the time-dependent variable order alpha(t) serves as a key parameter that characterizes the temporal evolution of reservoir pore structure and microfracture connectivity during transport processes; meanwhile, the anomalous diffusion dynamics and the associated concentration tailing in BTCs are clearly explained. Therefore, aiming at the process and dynamic characteristics of CO2 transport in low-permeability reservoirs, an analysis of the influence of external environmental factors and pore-scale structural properties on oil displacement efficiency can provide valuable theoretical and technical guidance for reservoir production. This study not only aims to enhance oil recovery but also contributes to carbon storage and environmental protection.