Flow in non-saturated porous media with discontinuous hydraulic conductivity

Abstract

When studying the flow in an unsaturated porous medium from a point recharge, two phenomena are identified: In the first the residual soil retention conditions are negligible, the mass of water available to flow is constant in time, for So the dimensional analysis considering first order self similarity is sufficient to solve the known diffusion equation. Conversely, if residual soil retention is taken into account, the mass of water available to flow is variable over time because the capillary forces retain some of the water in the pores, so that the mass does not comply with a law Of conservation and the assumption of previous self similarity is not valid. Then another type of self-similar assumption is called the second order, in which the so-called anomalous exponents appear. Under these conditions the equation to be solved is nonlinear with discontinuous coefficient and is called the Baremblatt Equation. The dimensional analysis is not enough to obtain the complete solution one goes to other different techniques, in this case to solve a problem of self value. In the second part will present the numerical solution and the application of this problem