Single-phase flow through a porous media revisited

TL;DR

This paper revisits the modeling of single-phase flow in porous media using a pressure-based approach, deriving a nonlinear diffusion equation and analyzing system behavior under oscillatory pressure conditions.

Contribution

It introduces a pressure equation formulation based on volume conservation and mechanical equilibrium, providing a new perspective on flow modeling in porous media.

Findings

Pressure equation derived from volume conservation

Non-linear diffusion approximation for negligible solid deformation

System behavior analyzed under oscillatory pressure gradient

Abstract

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.