The estimation of seismic properties of rocks with heterogeneous microstructures using a local cluster model — Preliminary results

Abstract

The estimation of physical properties for non-porous rocks has frequently been limited to considering the modal composition and orientation of the constituent grains. Studies of porous rocks indicate that the heterogeneity of microstructure can strongly influence the physical properties. Recently the increase in digital microstructural information has motivated the development of a local cluster model, which is sufficiently simple to be computationally fast and robust. The objective of this model is to be able to capture the microstructural sensitivity of physical properties. The stress distribution around an inclusion suggests that a first order elastic model needs only consider adjacent neighbours of a given point in the microstructure, this greatly simplifies the model.A preliminary set of model calculations were made on two rock types; a simulated water saturated porous sandstone composed of randomly oriented quartz grains and a polyphase non-porous gabbro with a strong crystal preferred orientation. The simulated isotropic sandstone provided a test case as analytical expressions for Voigt, Reuss and Hashin-Shtrikman bounds are known. The local cluster bounds for three microstructural models (random, layered and corner sharing) are within the Voigt, Reuss and Hashin-Shtrikman bounds. Further the local cluster bounds for the layered and corner sharing microstructural models are respectively 76% and 90% tighter than the Voigt-Reuss bounds, and 67% and 86% tighter than the Hashin-Shtrikman bounds. The local cluster lower bound was numerically unstable for a random microstructure due to the small values associated with the compliance of the pore fluid. The cluster model for the gabbro with experimentally measured grain orientation and spatial arrangement produced bounds that are 80% tighter than the Voigt-Reuss bounds, suggesting that microstructure in non-porous materials may be as important as in porous materials.