Microstructural Characterization of Oolitic Rocks and Numerical Evaluation of their Effective Elastic Properties

The present work focuses on the characterization of the geometry of the microstructure of porous oolitic rocks. These rocks are constituted by an assemblage of porous grains (oolites), pores and inter-granular crystals. X ray 3D Computed Tomography is used to identify the different components of these rocks by applying an algorithm based on grayscale values. This analytical method allows the characterization of the porous network (size, spatial distribution, and volume fraction), oolites and inter-oolitic crystals. The microstructure of these porous rocks has a significant effect on their macroscopic behavior. This micro-macroscopic relationship is taken into account in micromechanical models developed within the framework of the homogenization theory (e.g., Maxwell scheme) of random heterogeneous media. X ray tomography images showed that pores have irregular shapes, so the micromechanical modeling based on analytical solution is not relevant. Then, pores are approximated by ellipsoids using principal components analysis (PCA) method, which allows us to obtain the geometrical properties such as length of semi-axes and orientation of ellipsoids. To validate mechanically this approximation, we compared the contribution of irregularly shaped 3D pores and ellipsoidal pores to the effective elastic properties. The relative error due to this ellipsoidal approximation is then estimated. The compliance contribution tensors of irregular 3D pores are evaluated numerically using finite element method while those of approximated ellipsoidal pores are obtained analytically and numerically. The same procedure of approximation is applied on oolites. Shape and spatial parameters, such as the volume, radius and center of each oolite are also determined. The sphericity of the approximated oolites is calculated. The obtained values are close to 1, so oolites can be reasonably approximated by spheres.