Multiphase flow in a capillary porous medium

Based on the theory of porous media, a calculation concept for the multiphase flow in a capillary porous medium will be presented. We will exclusively investigate the rise of liquids in porous bodies due to the capillarity phenomenon. The field equations used consist of the mechanical balance equations and the physical constraint conditions. The treatment of the capillary problem, based on thermomechanical investigations, yields the result that the capillarity force is a volume interaction force and depends on the free Helmholtz energy functions of the phases and the density gradient of the liquid. With respect to the aforementioned outcome, further constitutive relations for the ternary model are developed. The aim of this investigation is the numerical simulation of the behavior of liquid and gas phases in a rigid porous body at rest. Therefore, the needed weak formulations of the governing field equations, i.e. the balance equations of mass and the balance equations of momentum of the liquid and gas phases, will be given. The usefulness of the proposed theory will be demonstrated with an example.