Fractional Flow Approach to Saturation Overshoot

Saturation overshoot is observed for 1D vertical infiltrations (liquid replacing gas) in many porous media. Aspects of these infiltrations are often described using the Richards equation, which assumes that the gas viscosity is negligible compared to the liquid viscosity. Here, we develop a multi-phase, fractional flow approach to describe the physics behind the displacement front that includes the viscosity of the gas. We show that an overshoot profile will draw in gas behind the overshoot tip. We compare the fractional flow solution to the Richards equation solution and to experimental data, and show that the air viscosity plays an observable role when the infiltrating flux is greater than 50% of the saturated conductivity.