A generalized Biot-Gassmann model for the acoustic properties of shaley sandstones

We obtain the wave velocities of clay-bearing sandstones as a function of c lay content, porosity and frequency. Unlike previous theories, based simply on slowness and/or moduli averaging or two-phase models, we use a Biot-typ e three-phase theory that considers the existence of two solids (sand grain s and clay particles) and a fluid. The theory, which is consistent with the critical porosity concept, uses three free parameters that determine the d ependence of the dry-rock moduli of the sand and clay matrices as a functio n of porosity and clay content. Testing of the model with laboratory data shows good agreement between pred ictions and measurements. In addition to a rock physics model that can be u seful for petrophysical interpretation of wave velocities obtained from wel l logs and surface seismic data, the model provides the differential equati on for computing synthetic seismograms in inhomogeneous media, from the sei smic to the ultrasonic frequency bands.