Abstract: In the process of immiscible two-phase flow within subsurface reservoirs, the capillary pressure contrast between fractured media and heterogeneous porous media serves as a decisive factor in governing fluid migration pathways. Due to the inherent heterogeneity of pore structures across different lithologies, capillary pressure functions exhibit significant disparities, leading to a profound phenomenon where the saturation field manifests as distinctive jumps or discontinuities at the interface, even while the fundamental condition of capillary pressure continuity is maintained. The abrupt transitions in fluid distribution substantially intensify the nonlinearity and complexity of multiphase flow behavior in subsurface environments. To address these complexities, this study establishes a comprehensive numerical model for compressible gas-water two-phase flow that explicitly incorporates extended capillary pressure effects. The accuracy and robustness of the developed model are validated through detailed comparisons with benchmark solutions reported in the literature. Based on this validated framework, numerical simulations were conducted to evaluate CO₂ sequestration processes within both fractured aquifers and heterogeneous anisotropic porous aquifers. The simulation results indicate that in fractured aquifers, capillary pressure effects significantly dictate the dynamics of CO₂ retention and migration. Specifically, when the extended capillary pressure effects are considered, the trapped CO₂ increases substantially, thereby enhancing the overall sequestration efficiency and contributing to superior long-term storage stability. In the case of heterogeneous aquifers, the capillary pressure gradients within high-permeability zones facilitate localized CO₂ entrapment. During the late stages of the sequestration process, the total storage capacity is observed to increase by approximately 4.8%. Furthermore, the spatial distribution of the CO₂ plume exhibits a nonlinear response to the capillary pressure, revealing the complex interplay between media heterogeneity and interfacial dynamics. Overall, this research provides a more rigorous and accurate theoretical foundation for assessing CO₂ storage potential under complex geological conditions.