Assessment of the effective parameters of dual porosity deformable media

• Micro-macro physical analysis of double porosity deformable media.
• Methodology for combining homogenization and self-consistent approaches.
• Analytical estimates of effective parameters of double porosity deformable media.
• Quantification of effective viscoelastic effect.
• Influence of material morphology and parametric analysis.

This paper deals with the estimation of the effective parameters of double porosity isotropic deformable media paying particular attention to the effective viscoelastic effect. In this type of media two fluid-saturated pore networks of very different permeabilities are interconnected. This situation leads to a transient and inhomogeneous pressure diffusion state in the micropores that gives rise to effective viscoelastic properties at the macroscopic scale. The study is conducted in three steps. First, a methodology is developed that allows to reformulate the results previously obtained by homogenization within a self-consistent framework that enables the analytical estimation of the effective parameters. Then, the developed approach is applied to two basic double porosity morphologies, i.e. large pores embedded in a microporous domain and a microporous domain with a small amount of highly permeable fractures. In both cases the effective bulk and shear moduli, compressibility, and pressure-deformation coupling factor are determined. A parametric study of the analytical results follows. This leads to identify, for each effective parameter, the expected magnitude of the viscoelastic effect and the corresponding characteristic frequency according to (i) the type of morphology, (ii) the porosity and characteristic dimension of the Representative Elementary Volume, and (iii) the values of the physical parameters of the solid and fluid constituents.