The impact of flow displacement patterns on hydraulic tortuosity for unsaturated flow

Abstract

Hydraulic tortuosity is one of the key parameters used to characterize the fluid transport properties of porous media. One of the existing debates on hydraulic tortuosity is whether it is an intrinsic property or a correction factor to match the experimental data with a particular model. In this study, a series of immiscible displacement simulations with different capillary numbers and contact angles were established by using the phase field method based on three-dimensional micro-computed tomography images of porous media. Then, the vector-based tortuosity method based on the flow velocity field is used to predict the dynamic evolution of hydraulic tortuosity of unsaturated porous media. Interestingly, the transient hydraulic tortuosity at different flow displacement patterns shows different dynamic evolutions where the quasi-steady-state hydraulic tortuosity is related to both the fluid saturation and the characteristics of the trapped voids in the porous media. These phenomena can be explained by the complex and interesting pore-scale displacement events, including viscous self-correcting smoothing, noncooperative Haines jumps, capillary self-correcting smoothing, and corner flow.