Unified theory of flow and deformantion in double porous media

A more rigorous and unified treatment of the theory of flow and deformation in double porous media is presented. The governing differential equations based on the equations of equilibrium, the effective stress concept, Darcy's law and the conservation of fluid mass are derived. Using Betti's reciprocal law, a link is established between the matrix and pore volumetric deformations. In addition a link is established between the volumetric deformations of the two pore systems. Both links are considered essential for proper modelling of flow and deformation in a double porous medium. The governing equations derived are general in nature and reduce to all previously presented formulations in this area. It is shown that if the deformation link between the two pore systems is ignored, Aifantis (1977, 1979, 1980a and 1980b) theory of double porosity consolidation is obtained. When one of the pore spaces is reduced to zero the classical theory of single porosity consolidation (Biot, 1941) is obtained. Similarly, when the deformation of solid skeleton is neglected, Barenblatt's (1960) theory of double porosity is obtained.