Elastic moduli of anisotropic clay

Clay minerals are important components in shales, controlling their elastic properties and anisotropy. The elasticity of crystalline clay minerals differs significantly from that of clay in situ because of the ability of clay particles to bind water. In the majority of published works, only isotropic moduli for in situ clays are reported. However, anisotropy is inherent in the clay elasticity. We develop an inversion technique for determination of the stiffness tensor of in situ clay from the shale's stiffness tensor. As an example, we obtain the stiffness tensor of a "water-clay" composite from the data on the water-saturated Greenhorn shale sample, whose clay composition consists of almost equal amounts of illite and smectite and comparable amounts of kaolinite and chlorite. The stiffness tensor of the water-clay composite is found for the Greenhorn shale with step-by-step inversion based upon an effective medium theory. The inversion uses a nonlinear optimization technique with bounds imposed on the estimated parameters. In the inversion, we apply different approaches of the effective medium theory using a published method referred to here as the generalized singular approximation (GSA). The GSA method makes it possible to take into account the microstructure of shales. The resulting elasticity constants of the anisotropic (transversely isotropic) in situ clay composite are C-11 = 23.7, C-33 = 8.5, C-44 = 0.8, C-66 = 5.7, and C-13 = 3.1 (in GPa); and the density equals 2.17 g/cm(3). The Thomsen parameters for the clay composite are epsilon = 0.89, gamma = 3.10, and delta = -0.34. The elasticity constants found for this clay composite can be used in the theoretical analysis of shales that have a similar composition of clay but with different mineral compositions. The inversion technique developed can be used for general shale water-clay composites when the mineral composition and orientation of the clay platelets are known.