Modelling elastic properties of partially saturated porous rocks with aligned fractures

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.