Estimating dry rock frame moduli of high-resolution 3D digital rock images using the contact-mechanics-based effective medium approach

Abstract

We have developed a method to estimate the dry frame elastic moduli of high-resolution 3D digital rock images using the contact-mechanics-based effective medium theory (EMT) model. The existing EMT models often are used to predict the effective dry frame elastic moduli of granular aggregates as a function of porosity, average number of contacts per grain, grain radius, contact radius, and contact stiffnesses of an elastic two-grain combination. But, it is almost impossible to measure the number of contacts per grain, contact radius distribution, or contact stiffness distribution in complex rocks. Therefore, explicit assumptions based on simplified microstructural geometries often are made to predict these contact properties in granular aggregates. As a result, the predictions of dry frame elastic moduli using EMT models may fail to match the observed properties because of numerous simplified assumptions, which can be violated in complex rocks. Our method uses the morphological contact properties (i.e., the grain-to-grain contact radius distribution, grain radius distribution, and coordination number distribution) directly extracted from 3D digital rock images to improve the prediction accuracy of dry frame elastic moduli using the EMT models. With integration of digital rocks technology, there is no longer a need to assume the size and shape of the grains, contact size, and number of contacts. The prediction accuracy of our method is validated on high-resolution 3D micro-CT digital rock images of miniplugs extracted from plugs with ultrasonic velocity measurements under dry conditions at different confining pressures. Image-computed dry frame elastic moduli using the EMT model are consistent with laboratory-measured moduli extrapolated to ambient conditions.