Numerical simulation of experimental gravity-driven unstable flow in water repellent sand

Laboratory experiments related to gravity-driven unstable flows in water repellent porous media contained in two-dimensional chambers have been reported [Bauters, T.W.J., DiCarlo, D.A., Steenhuis, T.S., Parlange, J.-Y., 1998. Preferential flow in water-repellent sands. Soil Sci. Soc. Am. J. 62, 1185–1190]. These experiments demonstrate that water repellency has a significant impact on the stability of flow. As a follow up to these experiments, numerical solutions of the Richards equation for a two-dimensional domain are derived to examine the effect of water repellency on flow characteristics. Of particular interest is the development of gravity-driven unstable flow conditions caused by water repellency. The degree of water repellency of the porous medium is manifested in the water saturation—capillary pressure and water saturation—hydraulic conductivity relationships for the porous medium. To derive the numerical solutions, parameters closely representing the flow domain boundary conditions and the porous medium properties in the experiments of Bauters et al., were employed. In this paper we present the results of simulations for two cases: a water wettable sand and an extremely water repellent sand. The numerical solution for the water wettable sand led to a stable flow condition, while for the water-repellent sand the flow was unstable as manifested by the development of a single finger of flow. A new feature of these modeling results, in comparison to previous modeling results for gravity-driven unstable flow, is that the water pressure inside the finger core is positive. In testing the numerical solutions we compared the solution results to the laboratory results in terms of flow patterns, water pressure at a single reference point, and wetting front velocity. The degree of agreement between the laboratory results and the numerical solutions in terms of these measures is quite good.