The dynamic interaction between a rigid porous structure (porosity ϕ) and its saturating fluid is studied. From the microscopic conservation laws and constitutive relations, macroscopic equations are derived. An averaging technique proposed and discussed by for example Lévy, Auriault and Burridge & Keller is used, from which we reformulate the theory by Johnson, Koplik & Dashen. The macroscopic equations then serve to describe the high-frequency behaviour of an oscillating fluid within a porous sample. This behaviour may be characterized by the length parameter Λ and by the tortuosity parameter α∞. It is shown that Λ and α∞, which describe an oscillatory flow behaviour, may be evaluated on the basis of steady potential flow theory. Numerical results are then presented for several pore geometries, and for these geometries, the steady-state permeability k0 is computed numerically also. The parameter 8α∞ k0/ϕΛ2, first introduced by Johnson et al., is then evaluated and appears to be weakly dependent on pore geometry. This implies that for many porous media the dynamic interaction is described by an approximate scaling function. New experimental data, concerning oscillating flows through several porous media, are presented. Within limits of accuracy, these data are in agreement with the approximate scaling function.

The influence of a small amount of gas within the saturating liquid of a porous medium on acoustic wave propagation is investigated. It is assumed that the gas volumes are spherical, homogeneously distributed, and that they are within a very narrow range of bubble sizes. It is shown that the compressibility of the saturating fluid is determined by viscous, thermal, and a newly introduced Biot-type damping of the oscillating gas bubbles, with mean gas bubble size and concentration as important parameters. Using a super-saturation technique, a homogeneous gas-liquid mixture within a porous test column is obtained. Gas bubble size and concentration are measured by means of compressibility experiments. Wave reflection and propagation experiments carried out in a vertical shock tube show pore pressure oscillations, which can be explained by incorporating a dynamic gas bubble behaviour in the linear Biot theory for plane wave propagation.

We study the wave properties at a fluid/porousmedium interface by using newly derived closed-form expressions for the reflection and transmission coefficients. We illustrate the usefulness of these relatively simple expressions by applying them to a water/porousmedium interface (with open-pore or sealed-pore boundary conditions), where the porous medium consists of (1) a water-saturated clay/silt layer, (2) a water-saturated sand layer, (3) an air-filled clay/silt layer, or (4) an airfilled sand layer. We observe in the frequency range 5 Hz-20 kHz that the fast P-wave and S-wave velocities in the four porous materials are indistinguishable from the corresponding frequency-independent ones calculated using Gassmann relations. Consequently, for these frequencies we would expect the reflection and transmission coefficients for the four water/porous-medium interfaces to be similar to the ones for corresponding interfaces between water and effective elastic media (described by Gassmann wave velocities). This expectation is not fulfilled in the case of an interface between water and an air-filled porous layer with open pores. A close examination of the expressions for the reflection and transmission coefficients shows that this unexpected result is because of the large density difference between water and air.

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.

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