Rock Physics in Complex Mineralogy: A Comparison of Shear Wave Prediction Models for Rock Physics

by Erik Alvarez and Jonathan Hall of Senergy Ltd.

Abstract

The most influential foundation work to rock physics has undoubtedly been the development of Gassman equations (1956); for its theoretical background and subsequent demonstration, it must be acknowledged pre-eminently. Despite the attractiveness of its scope and functional form, Gassman's model remains somewhat problematic to implement. This is because not all of the data required to implement the model are commonly available, and we require proxy methods to estimate them, such as effective medium models (Voigt, 1912, Reuss, 1929. etc.).

We review a number of published models including, Greenberg and Castagna, Xu and White and demonstrate their strength and limitations as shear wave prediction models and their impact when used as auxiliary models to Gassman’s equations. We present a new constitutive model, we call ‘total lambda, which is a new formulation of our previous model (Alvarez and Hall 2004) that predicts elastic properties between the Voigt and Reuss bounds as required, and the zero and critical porosity limits. The “total lambda” model can be used in isolation requiring no proxy secondary models, or as an auxiliary model to Gassman. It permits multimineral, multifluid, and fluid substitution modelling, and may be calibrated by readily available oilfield data, such as core measurements and logging data. Solving for the total lambda, total, response for a composite saturated porous medium is achieved by first determining the volumetric fractions of the matrix and fluid phases present, either directly from core descriptions and other measurements, such as X-ray diffraction or, indirectly from (calibrated) log data.

Erick Alvarez, CV

Erick Alvarez is a Geophysicist with 8 years in the industry, specialized in Rock Physics and Reservoir Characterisation, he has participated in reservoir characterisation studies from different parts of the world, like Mexico, Egypt, UAE, Argentina, West Africa, Russia (West Siberia), Malaysia and the North Sea. Erick Alvarez is currently part of the Reservoir Seismic Characterisation Group (RSC) in Senergy Limited and he is also part of the Edinburgh Time Lapse Project, of the Heriot-Watt university doing a research on 4D Seismic Characterisation.