Anisotropy on relative permeability curve under the influence of gravity

The relative permeability–saturation (k_r–s) relationship is a macroscopic representation of microscale flow characteristics between multiphase immiscible fluids, governed by the interplay among capillary, viscous, and gravitational forces. Previous studies on two phase fluid flow have primarily derived the k_r–s relationship from horizontal core-flooding experiments while neglecting the influence of gravity. However, frequent advent of vertical flows caused by conditions such as macroscale heterogeneity, brine extraction, and CO₂ injection through horizontal well, emphasizes non-negligible gravitational effects varying with the direction of displacement. This study aims to provide experimental evidence of anisotropy on k_r–s relationship induced by gravitational forces, contributing to a deeper understanding of gravity’s role in multiphase flow systems. Steady-state relative permeability tests using a 1-meter acrylic column tightly packed with glass beads and two immiscible fluids were performed under various flow directions. In addition, several total flow rates and beads sizes were used to adjust dimensionless capillary and bond number, which indicate different interplays among three governing forces. Our experiments revealed the differences in the k_r–s relationship between upward and downward flow directions, suggesting that the isotropic k_r–s assumption may not fully capture these dynamics. Under conditions of higher bond number, such as in the finer glass beads, the anisotropy on k_r–s relationship were weaker, indicating the influence of gravitational forces on its anisotropy. This study underscores the need to account for anisotropy on k_r–s relationships under dynamic flow conditions.

Project Acknowledgement

This work was supported by Korea Institute of Energy Technology Evaluation Planning (KETEP) grant funded by the Korea government (MOTIE) (20212010200010, Technical development of enhancing CO2 injection efficiency and increase storage capacity)