Inversion for Biot-consistent material properties in subresonant oscillation experiments with fluid-saturated porous rock

Abstract

To quantitatively interpret the results of a subresonant laboratory or numerical experiment with wet porous rock, it is insufficient to merely state the measured frequency-dependent viscoelastic moduli and [Formula: see text]-factors. The measured properties are apparent, i.e., dependent on the experimental setup such as the length of the sample and boundary conditions for pore flows. To reveal the true properties of the material, all experimental factors need to be accurately modeled and corrected for. Here, such correction is performed by developing an effective Biot’s model for the material and using it to predict driven oscillations of a cylindrical rock specimen. The model explicitly describes elastic and inertial effects, Biot’s flows, and viscous internal friction within the solid frame and pore fluid, and it approximates squirt and other wave-induced flow effects. The model predicts the dynamic permeability of the specimen, fast (traveling) and slow (diffusive) P- and axial-deformation waves, and it allows accurate modeling of any other ultrasonic or seismic-frequency experiments with the same rock. To illustrate the approach, attenuation and dispersion data from two laboratory and numerical experiments with sandstones are inverted for effective, frequency-dependent moduli of drained sandstone. Several observations from this inversion may be useful for interpreting experiments with porous rock. First, Young’s moduli measured in a short rock cylinder differ from those in a traveling wave within an infinite rod. In particular, for the modeled 8 cm long rock specimen, modulus dispersion and attenuation ([Formula: see text]) are approximately 10 times greater than for a traveling wave. Second, P-wave moduli cannot be derived from the measured Young’s and shear moduli by using conventional (visco)elastic relations. Third, because of wavelengths comparable with the size of the specimen, slow waves contribute to its quasistatic and low-frequency behaviors. Similar observations should also apply to seismic waves traveling through approximately 10 cm layering in the field.