Single-phase flow through a porous media revisited

The problem of the flow trough a porous media is formulated in terms of a pressure equation, based on arguments of volume conservation which state the mechanical equilibrium between the solid and the fluid phases. In the resulting governing equations, the conservation of mass is replaced by a transport-diffusion equation for the pressure field. When the deformation of the solid matrix is negligible, the pressure equation can be approximated by a non-linear diffusion equation. The behavior of the system of equations is tested under an oscillatory pressure gradient.