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.

Numerical and analytical investigation of compressional wave propagation in saturated soils

“…Gurevich et al (1999) Arntsen and Carcione (2001) numerically proved the existence of the slow wave in water-saturated Nivelsteiner sandstone under ultrasonic-frequency loading by employing the finite difference method. Their results compared well with the experimental observations presented by Kelder and Smeulders (1997), where a test similar to Plona (1980) work was carried out. The discrete element method (e.g.…”

Computation of Wave Attenuation and Dispersion, by Using Quasi-Static Finite Difference Modeling Method in Frequency Domain

“…Wave propagation through such macroscopic heterogeneous media creates pressure gradient at wavelength scale, equilibration of this pressure gradient results into a loss in wave energy. Two compressional and one shear wave was predicted in Biot's theory, experimental results also validate the presence of slow P-wave [Plona 1980, Kelder et al 1997. Meanwhile, another promising feature in Biot's theory is the low-frequency limiting velocities are identical with Gassmann predicted velocities.…”

Frequency-dependent viscous flow in channels with fractal rough surfaces

“…The dynamic interaction between a flowing fluid and the solid constituents of a porous medium is a key issue controlling wave propagation in geological [1][2][3] , biological 4,5 , and engineered systems 6,7 . The general theory of wave propagation in porous media was developed in references [8][9][10][11][12] .…”