Analysis of DNAPL infiltration in a medium with a low-permeable lens

In this paper we study the infiltration of DNAPL in a porous medium containing a single low-permeable lens. Our aim is to determine whether DNAPL infiltrates into the lens, or not. A key role is played by the capillary pressure: DNAPL cannot infiltrate into the lens unless the capillary pressure exceeds the entry pressure of the lens. In the model this is reflected by an interface condition for the capillary pressure. Both a homogeneous medium and a medium with a lens are analyzed. For the homogeneous configuration we derive an estimate of the stationary DNAPL plume width as a function of depth, and an asymptotic solution for small saturations. For the configuration with a lens we assume that the lens is much larger than the width of the unperturbed DNAPL plume in the homogeneous medium. We show that DNAPL infiltrates into the lens if a critical inflow rate is exceeded. This inflow rate is determined explicitly. A numerical algorithm is presented in which the extended capillary pressure condition is incorporated. Good agreement is found between the numerical and analytical results.