Effective poroelastic coefficients of isotropic oolitic rocks with micro and meso porosities

Abstract

The present work is devoted to the estimate of linear effective poroelastic properties of isotropic porous rocks characterized by an assemblage of porous grains (oolites), mesopores and solid grains. Examples of such type of microstructure may be found in oolitic limestones. Two distinct classes of pores are taken into account, micropores or intra oolitic pores and mesopores or inter oolitic pores. In the framework of Hashin Composite Sphere Assemblage (CSA, Hashin, 1962) and self-consistent models, a two step homogenization model is developed. At the first step, micropores are homogenized inside the oolites. At the second step, oolites, mesopores and solid grains are assembled by using the self consistent scheme. Levin’s theorem and transformation field analysis method are used to derive poroelastic coefficients (Biot coefficient and solid Biot modulus). Simple explicit formula are presented for effective poroelastic coefficients in the general case of double porosity media, under the assumption of spherical shape for all constituent particles and isotropic distribution. Finally comparisons between model and experimental data are presented for an oolitic limestone which includes micro-indentation results obtained at mesoscale and poromechanical results obtained at macroscale. Comparisons show that in the case of low macro stiffness, a degraded interfacial transition zone (ITZ) surrounding oolites, need to be introduced to fit the data