VARIATIONAL-PRINCIPLES OF THE FILTRATION OF AN INCOMPRESSIBLE FLUID IN MEDIA WITH DUAL-POROSITY

Dual variational principles for the steady single-phase and two-phase filtration of an incompressible fluid in media with dual porosity are constructed. By a medium with dual porosity, we mean two media, which are embedded in one another, with different porosities and permeabilities and which are coupled by a fluid crossflow [1]. The principle of minimum energy dissipation [2, 3], which is also used to close the equations and to find the structure of generalized forces, is the basis for constructing the variational principles. These principles enable one to determine the pressure fields, crossflows and filtration rates in the media. For steady single-phase filtration, the variational principles completely define the solution of the problem while, in the case of two-phase filtration, they hold for fixed saturations.