A composite sphere assemblage model for porous oolitic rocks

The present work is devoted to the determination of linear effective poroelastic properties of porous rocks characterized by an assemblage of grains (oolites) coated by a matrix. In the framework of Hashin composite sphere assemblage (CSA [1]) models, a two-step homogenization method is developed. Three porous materials are considered and assembled into a CSA: oolite (o) coated by an interfacial transition zone ITZ (i) and a matrix (m). The overall porosity is supposed connected and decomposed into oolite porosity, interphase porosity and matrix porosity. The three constitutive porous materials (o, i, m) are homogenized at the first step and a sensitive study is performed on the homogenization scheme by comparing self consistent SC, differential self consistent DSC, generalized self consistent GSC, iterative self consistent ISC and Mori Tanaka schemes. At the second step, the simple three-phase model [2] is firstly recalled and general relations for effective linear poroelastic coefficients are presented in the four-phase model case [3]. Mathematical analogy between linear thermoelasticity and linear poroelasticity is used to establish theoretical results in the context of CSA.

► Linear poroelastic properties of porous oolitic rocks are presented.
► Microstructure is characterized by grains (oolite) coated by ITZ and matrix.
► A two-step homogenization scheme is presented in Hashin-CSA model framework.
► SC, DSC, MT, GSC homogenization schemes are compared at first homogenization step.
► Numerical applications are presented to porous oolitic limestone rocks.