ABSTRACT
Mechanical waves, which are commonly employed for the noninvasive characterization of fluid-saturated porous media, tend to induce pore-scale fluid pressure gradients. The corresponding fluid pressure relaxation process is commonly referred to as squirt flow and the associated viscous dissipation can significantly affect the waves' amplitudes and velocities. This, in turn, implies that corresponding measurements contain key information about flow-related properties of the probed medium. In many natural and applied scenarios, pore fluids are effectively non-Newtonian, for which squirt flow processes have, as of yet, not been analyzed. In this work, we present a numerical approach to model the attenuation and modulus dispersion of compressional waves due to squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids. In particular, we explore the effective response of a medium comprising an elastic background with interconnected cracks saturated with a Maxwell-type non-Newtonian fluid. Our results show that wave signatures strongly depend on the Deborah number, defined as the relationship between the classic Newtonian squirt flow characteristic frequency and the intrinsic relaxation frequency of the non-Newtonian Maxwell fluid. With larger Deborah numbers, attenuation increases and its maximum is shifted towards higher frequencies. Although the effective plane-wave modulus of the probed medium generally increases with increasing Deborah numbers, it may, however, also decrease within a restricted region of the frequency spectrum.
ABSTRACT
When seismic waves travel through a fluid-saturated porous medium containing a fracture, fluid pressure gradients are induced between the compliant fracture and the stiffer embedding background. The resulting equilibration through fluid pressure diffusion (FPD) produces a frequency dependence of the stiffening effect of the fluid saturating the fracture. As the reflectivity of a fracture is mainly controlled by the stiffness contrast with respect to the background, these frequency-dependent effects are expected to affect the fracture reflectivity. The present work explores the P- and S-wave reflectivity of a fracture modeled as a thin porous layer separating two half-spaces. Assuming planar wave propagation and P-wave incidence, this article analyzes the FPD effects on the reflection coefficients through comparisons with a low-frequency approximation of the underlying poroelastic model and an elastic model based on Gassmann's equations. The results indicate that, while the impact of global flow on fracture reflectivity is rather small, FPD effects can be significant, especially for P-waves and low incidence angles. These effects get particularly strong for very thin and compliant, liquid-saturated fractures and embedded in a high-permeability background. In particular, this study suggests that in common environments and typical seismic experiments FPD effects can significantly increase the seismic visibility of fractures.
ABSTRACT
Oscillatory fluid movements in heterogeneous porous rocks induced by seismic waves cause dissipation of wave field energy. The resulting seismic signature depends not only on the rock compressibility distribution, but also on a statistically averaged permeability. This so-called equivalent seismic permeability does not, however, coincide with the respective equivalent flow permeability. While this issue has been analyzed for one-dimensional (1D) media, the corresponding two-dimensional (2D) and three-dimensional (3D) cases remain unexplored. In this work, this topic is analyzed for 2D random medium realizations having strong permeability fluctuations. With this objective, oscillatory compressibility simulations based on the quasi-static poroelasticity equations are performed. Numerical analysis shows that strong permeability fluctuations diminish the magnitude of attenuation and velocity dispersion due to fluid flow, while the frequency range where these effects are significant gets broader. By comparing the acoustic responses obtained using different permeability averages, it is also shown that at very low frequencies the equivalent seismic permeability is similar to the equivalent flow permeability, while for very high frequencies this parameter approaches the arithmetic average of the permeability field. These seemingly generic findings have potentially important implications with regard to the estimation of equivalent flow permeability from seismic data.
