One-phase flow in porous media with hysteresis

Abstract

This paper presents a numerical simulation of one phase flow through a porous medium showing a hysteretic relation between the capillary pressure and the saturation of the phase. The flow model used is based on mass conservation principle and Darcy's law. Boundary conditions of Neumann and Signorini type are imposed. The hysteretic relation between the capillary pressure and the saturation is described by a Preisach hysteresis operator. A numerical algorithm for the treatment of the arising system of equations is proposed. Results of numerical simulations are presented.