Effect of fluids and frequencies on Poisson’s ratio of sandstone samples Available to Purchase

Poisson’s ratio $ν$ is an important parameter when interpreting measured geophysical and seismic data. For an isotropic medium, it directly relates to the ratio of P- and S-wave velocities. We have measured $ν$ as a function of pressure and frequency in fluid-saturated sandstones. The method of measuring $ν$ was first tested as a function of pressure and frequency using standard samples. The phase shift $φ$ between radial and axial strains was also measured. For all standard samples, such as the linear viscoelastic Plexiglas, the data indicated that $tan(φ)$ correlated with $ν$ and related to a dissipation on $ν$⁠. Then, $ν$ and $tan(φ)$ were measured as a function of pressure and frequency for two dry and fluid-saturated Fontainebleau sandstone samples. Under dry conditions, no frequency dependence and very small pressure dependence were observed. Unusual behaviors were observed under fluid-saturated conditions. In particular, $ν$ of one sample indicated a frequency-dependent bell-shaped dispersion under water and glycerin saturation that correlated with peaks in $tan(φ)$⁠. Plotting the measurements as a function of apparent frequency (i.e., normalizing by the fluid viscosity) indicated a good fit between the water- and glycerin-saturated measurements. The bell-shaped dispersion in $ν$ that was observed for one particular sandstone held for all effective pressures. These variations fully correlated with the peaks of $tan(φ)$ observed. Our results can be interpreted using fluid flow and effective medium theories in the case of a porous microcracked rock. Drained/undrained and relaxed/unrelaxed transitions have frequency and magnitude of variations that are consistent with the measurements. The rock sample microcrack density strongly affects this frequency dependence. The inferred $VP/VS$ ratio at low effective pressures also indicates a large frequency-dependent bell-shaped dispersion. The parameter $tan(φ)$ is a clear indicator of the frequency-dependent dissipation of $ν$ and relates to the attenuation of P- and S-waves.