Elastic moduli of anisotropic clay

Abstract

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 ma-jority of published works, only isotropic moduli for in situ clays are reported. However, anisotropy is inherent in the clay elas-ticity. 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 usesa 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 approxi-mation (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 [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] (in GPa); and the density equals [Formula: see text]. The Thomsen parameters for the clay composite are [Formula: see text], [Formula: see text], and [Formula: see text]. 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.

Linking preferred orientations to elastic anisotropy in Muderong Shale, Australia

“…Elastic properties of shales have been of long-standing interest (e.g., Rundle and Schuler, 1981;Hornby et al, 1994;Sayers, 1994;Jakobsen et al, 2000;Draege et al, 2006;Bayuk et al, 2007). Vasin et al (2013) propose two models based on quantitative information about mineral composition, microstructure, and preferred orientations that could be used to describe experimentally measured elastic coefficients of Kimmeridge Shale (Hornby, 1998).…”

Parameterization of elastic stress sensitivity in shales

“…Using this model in combination with the SCA approach, Ulm and Abousleiman (2006) estimate elastic moduli of clay minerals from measurements of elastic properties of a number of shales. Bayuk et al (2007) use the general singular approximation effective media approach to estimate the elasticity tensor of clay minerals from experimentally measured elastic properties of the Greenhorn Shale used in Hornby's study (Hornby et al, 1994). The approach of Ulm and Abousleiman (2006) and Bayuk et al (2007) is further refined by Pervukhina et al (2008aPervukhina et al ( , 2008b, who suggested using a differential effective media approach as the most relevant for shale microstructure.…”

Upper and lower stiffness bounds for porous anisotropic rocks

“…Recall that all inclusions must have the same orientation and aspect ratio, and are chaotically distributed within the rock volume. Following Bayuk & Chesnokov (1998, 2007, 2008), we choose our comparison body to be a linear combination of matrix ( m ) and inclusion ( i ) properties, that is, …”