Abstract
We measure the P-wave velocity in a clean medium sand subject to very low stress in a large-scale laboratory cross-hole experiment for frequencies less than 10 kHz. In dry sand the velocity is depth-, and therefore, stress-dependent according to a power law. The velocity in partially saturated sand is essentially the same as in dry sand, which confirms the analytical result of the Biot–Gassmann theory. At 100% saturation, the velocity largely exceeds that in dry and partially saturated sand, once again in accordance with the Biot–Gassmann theory. However, the theory under-predicts velocities by up to 12% in some cases at full saturation. The maximum attenuation determined from spectral analysis of the measured signals closely matches the characteristic frequency predicted by the Biot model.
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Notes
At higher velocities the error will be greater (smaller arrival time for the same data acquisition system resolution). However, for the highest velocities, a “smoothing” interpolation of the recorded waveform using a 3rd order polynomial enabled the error to be kept the same as at lower velocities.
σ′v is calculated assuming a perfectly saturated medium. i.e. \({\gamma^{\prime}=\gamma_{\rm sat}-\gamma_{\rm w}}.\)
This diagram helps to illustrate a point made in the conclusion: High accuracy velocity measurements are needed in order to predict with a meaningful resolution saturations below 99%.
Deaeration of water, use of carbon dioxide gas and application of a back-pressure.
Santamarina points out however that Biot’s characteristic frequency is not necessarily the central frequency of relaxation.
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Acknowledgments
The authors would like to thank Fugro France and in particular Alain Puech, project manager of COIMBRA. The COIMBRA project was backed by the Fonds de Soutien des Hydrocarbures. The advice and help of Michel Dietrich (LGIT) is greatly appreciated, as is the assistance of Michel Riondet (LEGI).
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Emerson, M., Foray, P. Laboratory P-wave measurements in dry and saturated sand. Acta Geotech. 1, 167–177 (2006). https://doi.org/10.1007/s11440-006-0015-7
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DOI: https://doi.org/10.1007/s11440-006-0015-7