Rock Anelasticity, Pore Geometry and the Biot–Gardner Effect

Abstract

The anelastic properties of porous rocks depend on the pore characteristics, specifically, the pore aspect ratio and the pore fraction (related to the soft porosity). At high frequencies, there is no fluid pressure communication throughout the pore space and the rock becomes stiffer than at low frequencies, where the pore pressure is fully equilibrated. The models considered here include explicit pore geometry information in determining the poroelastic parameters. They are extensions of the EIAS (equivalent inclusion-average stress) and CPEM (cracks and pores effective medium) models to the whole frequency range, based on the Zener model. Knowing the degree of stiffness dispersion between the low- and high-frequency limits, we fit experimental data in the whole frequency range and obtain the average crack aspect ratio and soft porosity as a function of effective pressure. Then, we compute the dispersion and quality factor of the bulk, shear and Young moduli, and the P- and S-wave seismic velocities and quality factors as a function of frequency. However, when measuring axial or volumetric motions along a cylindrical sample, there is fluid flow at the ends of the sample in the experiments considered here. This generates dispersion and attenuation due to axial flow of the pore fluid, which does not occur for a plane wave in unbounded media. This phenomenon is called “drained/undrained transition" Pimienta et al. (J Geophys Res Solid Earth; https://doi.org/10.1002/2017JB014645 , 2017). Actually, it is an axial version of the Biot–Gardner (BG) effect, and implies an “artificial" (mesoscopic) attenuation peak (and dispersion) due to the generation of slow (diffusion) Biot modes at the cylinder boundary, inducing a global flow at the scale of the sample. The classical BG effect is due to fluid flow along the radial direction, on the basis of open-pore conditions at the sides of the sample. In this case, the sides are sealed. To use the EIAS and CPEM models, the BG effect has to be removed to obtain the intrinsic Q of the rock. The models are applied here for measurements on sandstone. The axial BG effect is more evident if the intrinsic attenuation is weak or absent. An example is Lavoux limestone, which has a bimodal porosity distribution, with an equal proportion of intragranular microporosity and intergranular macroporosity (round pores). In this case, the attenuation and dispersion are related to the BG effect, since no squirt flow is detected due to the absence of cracks. We verified that the bulk and Young moduli obtained from the axial and hydrostatic oscillations are consistent with each other, and that the theoretical description of the axial BG effect shows some discrepancies with the data.