Semi-Analytical Modeling of Rate-Dependent Relative Permeability in Heterogeneous Formations

Relative permeability (k_r) is an important property characterizing multi-phase flow in porous media, in particular considering applications of oil and gas production or CO₂ storage in subsurface formations. Coreflooding experiments are the most common method of determining k_r, usually conducted at a given total injection rate. However, k_r is known to be a rate dependent effective property due to capillary heterogeneity effects and therefore full characterization requires conducting experiments at different flow rates, a complex and time consuming process. This work presents a new approach for calculating rate dependent effective k_r curves based on a 1D semi-analytical solution for steady state flow. The method entails calibrating a 1D permeability structure to represent the 3D flow of coreflooding experiments. Then, the calibrated 1D model is used to estimate k_r curves at varying rates. We apply the method to three cases, two synthetic and one based on experimental data. Results show applicability for a wide range of flow rates.