Importance of Considering Hysteresis in Macroscopic Models of Two-phase Flow in Porous Media

Considering hysteresis in the traditional Darcy equation-based models is necessary to accurately capture the two phase flow behavior when subsurface systems experience successive drainage and imbibition processes such as in the case of geological carbon storage (GCS). Numerical simulators solving two-phase flow equations must make reliable predictions of fluid distributions during injection and post-injection redistribution of CO2, which is essential for developing appropriate monitoring and assessment plans in order to minimize risks of leakage (e.g., through fractures and/or abandoned wells). Generally, existing numerical simulators of the two-phase flow either neglect the hysteresis or include hysteresis based on the empirical constitutive relationships, not suitably incorporating basic physics of capillary flow with entrapment. This study presents testing of new mathematical hysteretic capillary pressure - saturation - relative permeability models with the goal of more accurately predicting the post-injection distribution of the fluids. The developed macroscopic constitutive models are based on basic physics of two-phase capillary displacements at pore-scale and void volume fraction distribution and connectivity properties. To test the new models, a traditional two-phase flow model with the developed hysteretic functions as input is compared against some intermediate-scale flow cell experiments conducted under macroscopically homogeneous and heterogeneous conditions. The model testing results that will be presented demonstrate the importance of taking into account hysteresis in the constitutive models of the traditional two-phase flow models for more accurate prediction of post-injection plume distribution.