Two Applications of Flow in Porous Media with Threshold Gradient

Abstract

The theory of flow in porous media has been developed on the basis of the experimental Darcy's equation. Observations from engineering practice and laboratory studies suggest that in certain cases it is necessary to fundamentally reconsider this theory. This paper analyzes experimental data collected to date demonstrating that in certain fluid-porous media systems the flow may be described by a seepage law with a threshold gradient: no flow occurs until the hydraulic head gradient exceeds the threshold value, then the flow velocity follows Darcy's equation. Using this flow equation, the paper presents solutions to two practical problems that have not been previously reported. First, the paper studies the problem of refraction of flow lines at the interface of two homogeneous and isotropic saturated porous media with different conductivities and derives a generalized “tangent law.” Second, the problem of unsteady infiltration is studied with a numerical solution to the flow equation for the one-dimensional case. The predicted behavior differs from the known classical results for Richards' equation.