Macroscale equilibrium conditions for two-phase flow in porous media

Flow in porous media is typically modeled at a length scale, referred to as the macroscale, such that a point of the system encompasses tens to hundreds of pore diameters. For such a system description, thermodynamic equilibrium conditions involve equality of the temperatures and chemical potentials of the system components at a point as well as mechanical conditions expressing an equilibration of forces at interfaces between phases and at common lines where interfaces come together. These force balances must be expressed in terms of macroscale thermodynamic variables and are obtained here. In addition, perturbations from the equilibrium state involve changes in the macroscale variables describing the amount of volume of a phase, area of an interface, or length of common line per volume of the system. A variational analysis provides the expressions for independent variations of these quantities, important information for completion of a continuum mechanical description of the system physics involving exploitation of the entropy inequality.