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., f0.5MHz) 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[410-3;410-1]Hz), leading to KLF and QK1, and (3) pore-pressure measurement to document the induced fluid-flow in the LF range (i.e., f[410-3;410-1]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 QK10.01. 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-10.15 and QK-10.25 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.

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