Reciprocity and cross coupling of two-phase flow in porous media from Onsager theory

The symmetry properties of the permeability matrix in the macroscopic trans port law for two-phase immiscible flow in porous media are investigated. Th e porous medium is treated as a single, closed thermodynamic system being f orced by piston reservoirs. This construction is used to relate the Darcy f luxes to the time derivatives of the piston motion, and to identify the flu xes and forces in the Onsager sense. When the surface-tension forces that d evelop on the fluid interface are linear in the interface displacement, Ons ager's theory is directly applicable and the permeability matrix must be sy mmetric. This argument is extended to show that reciprocity still holds whe n surfactants modify interface properties. [S1063-651X(99)08310-5].