Two‐phase fluid flow through fractured porous media with deformable matrix

Abstract

The governing equations for a fully coupled analysis of two‐phase fluid flow through fractured porous media with deformable matrix are presented. Two porosities, three constitutes (one solid and two fluids), and five phases are identified. The porosities are referred to as pores and fractures, and the two fluid constitutes are taken as water and air. The governing equations are derived using a systematic macroscopic approach based on the theory of poroelasticity, the effective stress principle, and the balance equations of mass and momentum. Matrix displacement vector, pore air pressure, pore water pressure, fracture air pressure and fracture water pressure are introduced as primary variables. Special attention is given to cross‐coupling effects between the phases within the system. A general formulation is derived that reduces to all previously presented models in the field. When the pore air volume is reduced to zero, the fully coupled equations of flow and deformation for saturated double‐porosity media are recovered. Similarly, when the matrix deformation is neglected and full saturation is assumed, Barenblatt et al.'s (1960) classical theory of double porosity is obtained.