Models for Ground Water Flow: A Numerical Comparison Between Richards' Model and the Fractional Flow Model

In this paper we compare two models for flow in porous media. The first is the well known Richards' equation, which is based on the assumption that the air in the unsaturated zone has infinite mobility. This means that it models a single phase. In the second and more general full two-phase approach, the air is considered as a separate phase. Here, we use the fractional flow equation.We study the difference between the two models numerically by varying the relative contribution of the different physical terms (the gravity and the total velocity) in the fractional flow equation. Richards' equation is considered as the limit of the fractional flow approach when the mobility of the air-phase tends to infinity. In particular, we are interested in determining the parameter intervals where the two models differ significantly, and we will quantify the asymptotic behavior.The equations are studied in the two-dimensional (2D) case. The study is based on a relative permeability depending quadratically on the saturation, and a capillary pressure expressed by a cubic function of the saturation.