Effective elastic properties of weakly cemented sandstone considering grain lateral displacement

Abstract

Predicting shear-wave velocities in weakly cemented sandstones remains challenging. The widely used contact cement theory (CCT) often overestimates shear-wave velocities even when P-wave velocities are well predicted. To address this issue, the CCT is revisited. It is found that the effects of grain lateral displacement on shear-wave velocities are neglected in the CCT. Because grain lateral displacement couples with the tangential displacement of cement, it can strongly affect shear-wave velocities. This effect is captured by solving a system of coupled integral equations that link the two types of displacements. The resulting formulation enables more accurate estimation of the tangential stiffness of grain–cement assemblies and, consequently, of the shear moduli and shear-wave velocities. Application of the proposed approach to weakly cemented sandstones shows that grain lateral displacement markedly reduces tangential stiffness, leading to lower shear moduli and shear-wave velocities, and thus an increased VP / VS ratio. Comparisons with ultrasonic measurements on synthetic shaly sandstone samples demonstrate that incorporating grain lateral displacement significantly improves agreement with the experimental results. The present formulation is primarily applicable to dry, weakly cemented, quartz-dominated sandstones with small grain–cement contact regions, for which the low grain Poisson's ratio and elastic half-space approximation are appropriate. Within these applicable conditions, the proposed approach offers considerable potential for improving the seismic characterization of weakly cemented sandstone reservoirs.