Stoneley-wave attenuation and dispersion in permeable formations

The tube wave, or low‐frequency manifestation of the Stoneley wave, has been modeled previously using the quasi‐static approximation; I extend this method to include the effect of the formation matrix compressibility, which tends to marginally increase the tube‐wave attenuation. Using the Biot theory of poroelasticity, I develop a fully dynamic description of the Stoneley wave. The dispersion relation derived from Biot’s equations reduces in the low‐frequency limit to the quasi‐static dispersion relation. Comparisons of the quasi‐static and dynamic theories for typical sandstones indicate the former to be a good approximation to at least 1 kHz for oil and water infiltration. At higher frequencies, usually between 5 and 20 kHz for the formations considered, a maximum in the Stoneley Q is predicted by the dynamic theory. This phenomenon cannot be explained by the quasi‐static approximation, which predicts a constantly increasing Q with frequency. Instead, the peak in Q may be understood as a transition from...

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