Observation of the Biot slow wave in water‐saturated Nivelsteiner sandstone

Abstract

Acoustic signals are used extensively in the oil industry to determine the physical properties of reservoir rock. In the interpretation of these signals empirical laws play a major role. To obtain a more fundamental interpretation of the recorded wavetrains, the need for a comprehensive theory for acoustic wave propagation and damping in rocks is obvious. In this respect, Biot's (1956a,b) theory is a straightforward and effective two‐phase theory. In contrast to Biot, who derived the macroscopic equations for wave propagation in saturated poro‐elastic material by postulating definite positive‐energy density functions, Burridge and Keller (1981), Whitaker (1986a,b,c), and Pride et al. (1992) applied rigorous averaging techniques to derive the poro‐elastic equations from a microscale. De Vries (1989) and Geerits (1996) used the averaging techniques to derive macroscopic poro‐elastic equations for the nonviscous case. The fundamental feature of all these theoretical descriptions is the existence of both a fast and slow compressional wave, as well as a shear wave. For the fast compressional wave, the pore fluid and the porous matrix are compressed simultaneously, but for the slow compressional wave, the porous matrix relaxes while the pore fluid is compressed. The attenuation mechanism for these waves is based on viscous dissipation generated by the flow of the pore fluid relative to the porous matrix. For the slow wave, the viscous dissipation results in a strong, frequency‐dependent attenuation, which makes this wave very difficult to observe in fluid‐saturated rocks. However, because the slow compressional wave is especially sensitive to certain interesting properties of the permeable material, the detection of this slow compressional wave has been one of the major issues in the acoustics of fluid‐saturated permeable solids.