Non-darcian behavior of two-phase flow in a vertical fracture with tortuous

Research on non-darcian flow behavior in fractured media is fundamental to understanding the governing laws flows in natural fractured aquifers, which is especially relevant in geothermal reservoir modeling. Although the Darcy model is utilized to describe slow flows in these geometries, quantitative descriptions of two-phase flows involving non-darcian effects in rough vertical fractures have received little attention. In this study, the three-dimensional Navier-Stokes equation coupled with Cahn-Hilliard model were solved for the immiscible gas-water system with the fracture geometry satisfies the Gaussian distribution under different piezometric boundary conditions. We report significant non-darcian flow behavior for Reynolds numbers between 998 and 26,930, suggesting that the quadratic-velocity model explains Darcy deviation for high specific water discharges q_w. Additionally, we found that the water saturation index S_w had a nonlinear relationship with q_w, which allowed the definition of two regimes in which water displaced the gas phase. These findings help to modify the current methodologies for estimating the relative permeability of two-phase fluid system, allowing for the inclusion of non-Darcy effects in such estimations.