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The wave-induced interlayer flow between mesoscopic-scale heterogeneities (i.e., larger than pore scale but smaller than the predominant wavelengths) is the most important cause of attenuation at frequencies below 1 kHz. According to the White's layered model ( White et al., 1975 ), the wave-induced flow at an interface is symmetrical in periodically layered porous media due to its symmetrical structure. However, in one-dimensional (1-D) randomly layered porous rocks, layers of various thicknesses lead to different types of the interlayer flow. The coexistence of various wave-induced interlayer flow patterns at different interfaces results in interactions. The numerical creep test and a volume average of White's analytical solution were used to analyse the interactions in the two kinds of models (i.e., representative elementary volumes and randomly layered models). One of the parameters used to build a randomly layered model is the standard deviation of the thickness of the water-saturated layer, which could control the interaction strength of the interlayer flow. The detailed characteristics of the interlayer flow interaction were demonstrated by analysing the relative fluid velocity, while the statistical characteristics of the interlayer flow interaction were demonstrated by analysing the average solid velocity. We investigated the effect of the interaction on the amplitude versus the deviation at the interface between a non-dispersive medium and a patchy-saturated dispersive medium in three types of reservoirs. These results are beneficial for describing the distribution of oil/gas patches based on the statistical seismic properties in a layered formation with random disorder. [ABSTRACT FROM AUTHOR]

Porosity, fluid type and rock texture significantly affect acoustic wave propagation, since velocity dispersion and attenuation in fluid saturated rocks are mainly caused by wave-induced local fluid flow between microcracks and intergranular pores. We analyze P-wave velocity dispersion as a function of porosity to obtain information about the rock microstructure. The P-wave velocities in water-saturated rocks are predicted from measurements in gas-saturated rocks, using the Gassmann fluid substitution equation (the relaxed state). The dispersion is estimated from the difference between this predicted velocity and the measured one, where the latter corresponds to the unrelaxed state. We evaluate the wave dispersion as a function of porosity for 112 carbonates, 128 sandstones and 56 volcanic rocks, including our measurements for 86 tight rocks, showing that dispersion increases with porosity in the low porosity range, but decreases in the high porosity range. The dispersion peak occurs at a porosity of approximately 15%. Double-porosity poroelasticity modeling based on the local fluid-flow mechanism confirms this behavior. The microcrack radius has a peak in the porosity range 15–19% for all the lithologies from our collection, while the behavior of microcrack porosity is less evident. The dispersion peak may reveal the characteristics of lithological units, in particular porosity, fluid type and rock microstructure. • Acoustic wave dispersion peaks at a characteristic porosity around 15% for the three lithologies. • Poroelasticity modeling shows microcrack radius and porosity peak in the porosity range of 15-19%. • Different lithologies can be discriminated in tight rocks by the relations between dispersion and porosity. [ABSTRACT FROM AUTHOR]

The double-porosity theory of wave propagation in rocks considers a single scale based on soft and stiff pores, and wave attenuation occurs by local fluid flow between these pores. However, rocks exhibit more complicated fabric structures, with heterogeneities presented at multiple scales, having a self-similar fractal nature as reported. We develop a poroelasticity model to describe wave anelasticity in a fluid-saturated medium consisting of infinite components, i.e., an infinituple-porosity medium. Numerical modeling is achieved with infinite iterations, where at each iteration one component is added (a porous inclusion embedded in a porous host), analogous to the differential effective medium (DEM) theory of solid composites. By considering the self-similar structure, the properties of each component (inclusions) are scale-dependent. The example shows that the P-wave velocity dependence on frequency depends on the fractal dimension. Application of the model to sandy sea-bottom sediments shows a good agreement, with fractal dimension of 2.88. [ABSTRACT FROM AUTHOR]

Wave propagation in rocks induces fluid pressure gradients and flow between stiff intergranular pores and compliant microfractures. This, in turn, leads to wave anelasticity, i.e., attenuation and velocity dispersion. Three known squirt-flow models attempt to explain this phenomenon. Based on these theories, we reformulate a new one, where we derive the dry-rock moduli on the assumption that the boundary fluid pressure is constant. The new model improves the predictions of the other models, e.g., a better description at high frequencies and the inclusion of permeability effects. The numerical example shows the response due to the characteristic squirt-flow length and fluid viscosity on wave propagation. The reformulated model is applied to experiments made on water-saturated tight sandstones, where the squirt-flow length is determined, showing that it increases with increasing permeability and porosity at full saturation. • A new squirt-flow model by deriving the dry-rock moduli on the assumption of the constant boundary fluid pressure. [ABSTRACT FROM AUTHOR]