Macroscopic description of multi-phase systems: A thermodynamic theory of flow in porous media

A systematic averaging technique was developed and used to derive multi-phase equations of mass, momentum, angular momentum, energy and entropy from the balance laws for a single continuum. The technique was systematized by requiring a single set of criteria to govern the averaging of all quantities and all equations. Next, a constitutive theory for solid-fluid systems was developed. Finally, the general form of constitutive assumptions for porous media was reduced using the Coleman and Noll method of exploitation of entropy inequality. The constitutive equations were then linearized and a set of field equations were obtained which provided nine equations to be solved for fluid density, porosity, fluid velocity vector, solid displacement vector and the medium temperature. Certain fluid flow cases were reviewed and appropriate equations of varying degrees of approximation were obtained.