The CO2–Brine Two-Phase Relative Permeability Model Considering the Effects of Pore Pressure and Displacement Rate

Accurate prediction of CO2–brine relative permeability is essential for evaluating CO2 migration and storage performance in saline aquifers. However, conventional empirical models rely heavily on fitted parameters, while existing fractal models generally provide limited descriptions of the effects of pore pressure and displacement rate on two-phase flow. To address these limitations, a pore-scale-based fractal relative permeability model is developed by coupling two-phase flow theory, fractal pore-size distribution, and numerical integration. The main innovation lies in incorporating pressure-dependent CO2 viscosity and a variable immobile water-film thickness governed by pore radius, driving pressure gradient, and brine viscosity into the effective flow radius. Compared with conventional models employing fixed water-film thickness or neglecting injection-condition effects, the proposed formulation provides a physically based representation of the responses of CO2–brine relative permeability to pore pressure and displacement rate. The model is evaluated using six displacement experiments conducted on four sandstone cores. The coefficients of determination (R2) range from 0.957 to 0.998 for the brine phase and from 0.869 to 0.955 for the CO2 phase, demonstrating good agreement between predictions and measurements. Sensitivity analyses indicate that increasing absolute permeability generally enhances the relative permeabilities of both phases. Increasing pore pressure from 10 to 55 MPa and displacement rate from 1 to 5.5 mL·min−1 generally increases two-phase relative permeability and maximum CO2 saturation while reducing residual brine saturation. The proposed model provides a physically informed approach for characterizing CO2–brine two-phase flow under varying injection conditions and supports relative permeability prediction for CO2 storage in water-wet sandstone saline aquifers.