Bulk modulus dispersion and attenuation in sandstones

ABSTRACT We report experimental data on the frequency dependence of bulk elastic modulus in porous sandstones. A new methodology was developed to investigate the dispersion/attenuation phenomena on a rock’s bulk modulus K for varying confining pressures in the range of 1–50 MPa and fluids of varying viscosities (i.e., air, glycerin, and water). This methodology combined (1) ultrasonic (i.e., f∼0.5 MHz) P- and S-wave velocity measurements, leading to the high-frequency (HF) KHF, (2) stress-strain measurements from forced periodic oscillations of confining pressure at low-frequency (LF) ranges (i.e., f∈4 10-3;4 10-1 Hz), leading to KLF and QK−1, and (3) pore-pressure measurement to document the induced fluid-flow in the LF range (i.e., f∈4 10-3;4 10-1 Hz). The stress-strain method was first checked using three standard samples: glass, gypsum, and Plexiglas samples. Over the frequency and pressure range of the apparatus KLF was stable and accurate and the lowest measurable LF attenuation was QK−1∼0.01. The methodology was applied to investigate Fontainebleau sandstone samples of 7% and 9% porosity. The KLF and QK-1 exhibited correlated variations, which also correlated with an experimental evidence of frequency-dependent fluid-flow out of the sample. Attenuation peaks as high as QK-1∼0.15 and QK-1∼0.25 are measured. The attenuation/dispersion measured under glycerin saturation was compared to Biot-Gassmann predictions. The overall behavior of one sample was consistent with a dispersion/attenuation characteristic of the drained/undrained transition. On the reverse, the other sample exhibited exotic behaviors as the measurements were underestimated by the drained/undrained transition and indicated a direct transition from drained to unrelaxed domain. These different behaviors were consistent with the values of the critical frequencies expected for the drained/undrained (i.e., f1) and relaxed/unrelaxed (i.e., f2) transitions.