Flow of viscous fluids through a porous deformable matrix

A self-contained account of mixture theory is presented as a framework for describing the flow of fluids, liquids and gases, through a porous deformable matrix, incorporating both mechanical and thermal effects. The theory comprises the conservation laws of mass, momentum and energy for each constituent and the mixture properties which describe the interactions between constituents. Mass transfer between constituents which arises during phase change and chemical reactions influences both conservation laws and mixture properties. An analysis of discontinuity conditions at a singular surface is presented, which would be needed, for example, to describe an advancing phase-change front. Details are presented for the flow of viscous fluids through a thermoelastic matrix undergoing infinitesimal deformation, a common model for underground reservoirs. The interactions of immiscible and miscible fluids are discussed. An essential ingredient is the relation between partial physical variables defined as mean values over mixture elements, and intrinsic variables defined with respect to the constituent elements.