Modelling elastic properties of partially saturated porous rocks with aligned fractures

Abstract

SUMMARY A simple but rigorous extension to anisotropy of the isotropic theory for partially saturated rocks is developed to model the variations of the P-wave velocities with angle of incidence and water saturation in partially saturated fractured rocks. The theory is developed to match ultrasonic measurements on a synthetic sandstone samples with a regular distribution of aligned, penny-shaped fractures. The velocity anisotropy in the dry fractured sample is well described with a set of standard anisotropic effective medium theory for penny-shaped cracks. The saturation dependence of the velocities is modelled by a combination of four mechanisms (squirt flow, uniform saturation, patchy saturation and full water saturation) and described by four corresponding theoretical models (squirt-flow relaxation model, anisotropic Gassmann–Wood equations, Backus average and anisotropic Gassmann equations). At ultrasonic frequencies, this simple but rigorous combination of poroelastic models can describe angle and saturation dependency of velocities and moduli in a partially saturated fractured and porous rock reasonably well.