Upper and lower stiffness bounds for porous anisotropic rocks

• DOI: 10.1111/j.1365-246x.2008.03925.x
• Publication Date: 2008-10-16T07:41:51Z
• Authors: Irina O. Bayuk; Juliana K. Gay; John M. Hooper; Evgeni M. Chesnokov
• Keywords: Orthorhombic crystal system; Ellipsoid

We derive double inequalities providing the bounds for components of effective stiffness tensor a two-phase, porous-cracked medium with aligned ellipsoidal inclusions. The are derived on basis Hashin-Shtrikman variational principle, and conditions positive semi-definiteness quadratic forms. Inequalities presented isotropic, cubic, hexagonal orthorhombic overall symmetries. results obtained symmetry valid general determination transport properties (effective permeability, thermal electrical conductivity). conclude that diagonal have form bounds, whereas in these do not exist off-diagonal components. One important implication this is Voigt-Reuss averages provide upper lower tensor, as sometimes assumed. also present numerical by modelling various shales transverse isotropic