Wave velocities and attenuation of shaley sandstones as a function of pore pressure and partial saturation

We obtain the wave velocities and quality factors of clay-bearing sandstones as a function of pore pressure, frequency and partial saturation. The model is based on a Biot-type three-phase theory that considers the coexistence of two solids (sand grains and clay particles) and a fluid mixture. Additional attenuation is described with the constant-Q model and viscodynamic functions to model the high-frequency behavior. We apply a uniform gas/fluid mixing law that satisfies the Wood and Voigt averages at low and high frequencies, respectively. Pressure effects are accounted for by using an effective stress law. By fitting a permeability model of the Kozeny-Carman type to core data, the model is able to predict wave velocity and attenuation from seismic to ultrasonic frequencies, including the effects of partial saturation. Testing of the model with laboratory data shows good agreement between predictions and measurements.