P-wave dispersion and attenuation due to scattering by aligned fluid saturated fractures with finite thickness: theory and experiment

Abstract

Fractures often play an important role in controlling the fluid flow in hydrocarbon reservoirs. When the seismic wave propagates through media containing fracture corridors, significant scattering dispersion and attenuation can occur. In this work, we study the P-wave dispersion and attenuation due to the scattering caused by 2-D fluid-saturated aligned fractures with finite thickness, which are embedded in an isotropic elastic background medium. Using the Foldy approximation and the representation theorem, the P-wave dispersion and attenuation are related to the displacement discontinuities across the fractures. These fracture displacement discontinuities are obtained from the boundary conditions and the P-wave dispersion and attenuation can thus be calculated. A numerical example shows that the fracture thickness has significant influence on the dispersion and attenuation, especially in the low-frequency regime when the fracture size is smaller than the seismic wavelength. The effects of the fluid bulk modulus are also significant, which are opposite to those of the fracture thickness. However, the effect of the fluid viscosity is found to be negligible for the studied configurations. To validate the proposed model, the theoretical predictions are compared with ultrasonic measurements on fractured samples. The comparison shows overall good agreement between theory and experiment. This work reveals the important influence of fracture thickness and saturating fluid properties on the P-wave scattering dispersion and attenuation. Hence, it shows a potential to extract these parameters from seismic data.

Effects of Coupling Between Wave‐Induced Fluid Flow and Elastic Scattering on P‐Wave Dispersion and Attenuation in Rocks With Aligned Fractures

“…Hence, we can first calculate θ ( ξ ) through equation . It is not easy to solve equation analytically, but it can be solved numerically (e.g., Guo, Shuai, et al, ). In order to do so, we need to discretize equation as follows: where N is the number of discretized points, Δξ = a / N , z i = iΔξ , ξ j = jΔξ , and δ ij is the Kronecker's delta.…”

“…However, we can note that the characteristic frequency for FB‐WIFF is more sensitive to fracture radius than that for elastic scattering. This is because the characteristic frequency for the FB‐WIFF is approximately inversely proportional to the square of the fracture radius (e.g., Galvin & Gurevich, ), whereas that for the elastic scattering is only inversely proportional to the fracture radius itself (Guo, Shuai, et al, ). Therefore, in the cases where the characteristic frequencies of FB‐WIFF and elastic scattering are not far away from each other, varying the fracture radius may result in significant strengthening of the coupling between FB‐WIFF and elastic scattering.…”

“…The influence of the fracture thickness on the coupling between FB‐WIFF and elastic scattering is shown in Figure . As we only consider the cases with small fracture thickness, we restrict the largest fracture half‐thickness to 0.05 m. This corresponds to the largest fracture aspect ratio of 0.1 (e.g., Guo, Shuai, et al, ). Similar to the effects of facture radius, we can observe that with the increasing fracture thickness, characteristic frequencies for FB‐WIFF and elastic scattering both decrease.…”

“…The elastic scattering by a set of randomly distributed aligned dry fractures were then derived using Foldy (1945) approximation (e.g., Kawahara, 1992;Kikuchi, 1981;Zhang & Achenbach, 1991;Zhang & Gross, 1993a, 1993b. Based on this, the models for the elastic scattering by fluid-saturated fractures in the elastic nonporous background were further developed by several authors (e.g., Guo et al, 2018;Kawahara & Yamashita, 1992;Murai et al, 1995).…”

Coda and Intrinsic Attenuations From Ultrasonic Measurements in Tight Siltstones

“…However, the scattering effect is strong when the ultrasonic wavelength is comparable to the fabric, pore, and/or microcrack sizes (Wu & Aki, 1988). Recent studies of coda waves at ultrasonic frequencies have been undertaken (e.g., Guo & Fu, 2007; Guo, Shuai, et al, 2018; Wei & Fu, 2014). Guo et al (2009) analyzed the pore pressure dependence of the coda and intrinsic attenuations by using the single scattering model in sandstones and observed that attenuation increases with pore pressure.…”