Numerical Simulations of Water Penetration into Partially-saturated Sand

Abstract:

Gravity driven water flow into an initially dry porous medium can lead to a non-monotonic behaviour. Instead of a uniform flow front, water infiltrates in finger patterns, which has been observed experimentally. Fingering effect cannot be described by the Richards equation or standard two-phase flow system, unless some additional terms are incorporated. One of the most effective approaches to model the observed saturation and pressure overshoot is to include the so-called non-equilibrium capillarity effect. Besides it, capillary or relative permeability hysteresis between imbibition and drainage processes also plays a key role in the degree of nonmonotonicity and its pattern.

In this work, we investigated and compared different approaches for modelling non-monotonic saturation and pressure behaviours in fingering effect. Either hysteresis and/or dynamic capillarity was included. We showed different overshoot patterns in various models and discussed the main regime of these numerical models. Moreover, we employed our model to fit the experimental data conducted by S. Fritz (2012). Five different combinations of dynamic and hysteretic effects were done to investigate our ability to simulate the experimental data.