An energy-based approach to estimate seismic attenuation due to wave-induced fluid flow in heterogeneous poroelastic media

Solazzi, Santiago G.; Rubino, J. Germán; Müller, Tobias M.; Milani, Marco; Guarracino, Luis; Holliger, Klaus

doi:10.1093/gji/ggw302

Cited by 26 publications

(42 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…5, we observe excellent agreement between the results based on the energy-based approach and those obtained based on the viscoelastic assumption, which validates the use of the viscoelastic approach to upscale attenuation and dispersion characteristics from our heterogeneous medium described by the coupled LNS equations. For consistency, we do the same for the numerical scheme based on Biot's equations using the equations derived by Solazzi et al (2016) and, as these authors point out, the agreement is nearly perfect (Fig. 5).…”

Section: Interconnected Rectangular Cracksmentioning

confidence: 84%

Numerically quantifying energy loss caused by squirt flow

Quintal

Caspari

Holliger

et al. 2019

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

In interconnected microcracks, or in microcracks connected to spherical pores, the deformation associated with the passage of mechanical waves can induce fluid flow parallel to the crack walls, which is known as squirt flow. This phenomenon can also occur at larger scales in hydraulically interconnected mesoscopic cracks or fractures. The associated viscous friction causes the waves to experience attenuation and velocity dispersion. We present a simple hydromechanical numerical scheme, based on the interface‐coupled Lamé–Navier and Navier–Stokes equations, to simulate squirt flow in the frequency domain. The linearized, quasi‐static Navier–Stokes equations describe the laminar flow of a compressible viscous fluid in conduits embedded in a linear elastic solid background described by the quasi‐static Lamé–Navier equations. Assuming that the heterogeneous model behaves effectively like a homogeneous viscoelastic medium at a larger spatial scale, the resulting attenuation and stiffness modulus dispersion are computed from spatial averages of the complex‐valued, frequency‐dependent stress and strain fields. An energy‐based approach is implemented to calculate the local contributions to attenuation that, when integrated over the entire model, yield results that are identical to those based on the viscoelastic assumption. In addition to thus validating this assumption, the energy‐based approach allows for analyses of the spatial dissipation patterns in squirt flow models. We perform simulations for a series of numerical models to illustrate the viability and versatility of the proposed method. For a 3D model consisting of a spherical crack embedded in a solid background, the characteristic frequency of the resulting P‐wave attenuation agrees with that of a corresponding analytical solution, indicating that the dissipative viscous flow problem is appropriately handled in our numerical solution of the linearized, quasi‐static Navier–Stokes equations. For 2D models containing either interconnected cracks or cracks connected to a circular pore, the results are compared with those based on Biot's poroelastic equations of consolidation, which are solved through an equivalent approach. Overall, our numerical simulations and the associated analyses demonstrate the suitability of the coupled Lamé–Navier and Navier–Stokes equations and of Biot's equations for quantifying attenuation and dispersion for a range of squirt flow scenarios. These analyses also allow for delineating numerical and physical limitations associated with each set of equations.

show abstract

Section: Interconnected Rectangular Cracksmentioning

confidence: 84%

Numerically quantifying energy loss caused by squirt flow

Quintal

Caspari

Holliger

et al. 2019

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

show abstract

“…The same reasoning can be applied to the P wave attenuation at low fracture densities, although it does not explain the behavior at high fracture densities. Local contribution to the overall seismic attenuation per unit area (Solazzi et al, 2016) at the frequency of the second attenuation peak for (a, b) P waves and (c, d) S waves for a fracture network with a fracture density of 1.5% (Figures 10a and 10c) and a fracture density of 3.25% (Figures10b and 10d). A close inspection of the fluid pressure fields reveals certain areas with lower induced fluid pressures within the fractures than on average (orange ellipse in Figure 8i).…”

Section: Fracture-to-fracture Fpdmentioning

confidence: 99%

Seismic Attenuation and Stiffness Modulus Dispersion in Porous Rocks Containing Stochastic Fracture Networks

et al. 2018

Self Cite

View full text Add to dashboard Cite

Understanding seismic attenuation and modulus dispersion mechanisms in fractured rocks can result in significant advances for the indirect characterization of such environments. In this paper, we study attenuation and modulus dispersion of seismic waves caused by fluid pressure diffusion (FPD) in stochastic 2‐D fracture networks, allowing for a state‐of‐the‐art representation of natural fracture networks by a power law length distribution. To this end, we apply numerical upscaling experiments consisting of compression and shear tests to our samples of fractured rocks. The resulting P and S wave attenuation and modulus dispersion behavior is analyzed with respect to the density, the length distribution, and the connectivity of the fractures. We focus our analysis on two manifestations of FPD arising in fractured rocks, namely, fracture‐to‐background FPD at lower frequencies and fracture‐to‐fracture FPD at higher frequencies. Our results indicate that FPD is sensitive not only to the fracture density but also to the geometrical characteristics of the fracture length distributions. In particular, our study suggests that information about the local connectivity of a fracture network could be retrieved from seismic data. Conversely, information about the global connectivity, which is directly linked to the effective hydraulic conductivity of the probed volume, remains rather difficult to infer.

show abstract

“…To compute the inverse quality factor density for the relaxation tests, we follow the energy-based approach described in Solazzi et al (2016). By doing so, the local contribution to the inverse quality factor per unit area can be written as…”

Section: Appendix A: Inverse Quality Factor Densitymentioning

confidence: 99%

Sensitivity of Seismic Attenuation and Phase Velocity to Intrinsic Background Anisotropy in Fractured Porous Rocks: A Numerical Study

et al. 2017

Self Cite

View full text Add to dashboard Cite

Many researchers have analyzed seismic attenuation and velocity dispersion due to wave‐induced fluid flow (WIFF) related to the presence of fluid‐saturated fractures embedded in an isotropic porous background. Most fractured formations do, however, exhibit some degree of intrinsic elastic and hydraulic anisotropy of the background, and the impact of which on the effective seismic properties remains largely unexplored. In this work, we extend a numerical upscaling procedure to account for the potential intrinsic elastic and hydraulic anisotropy of the background. To do this, we represent the background of a representative sample of the fractured formation of interest with an anisotropic poroelastic medium and apply a set of relaxation experiments to compute the effective anisotropic seismic properties. A comprehensive numerical analysis allows us to observe that, for samples containing hydraulically connected fractures, the anisotropic behavior of both P and S waves differs significantly from that observed for an isotropic background. The anisotropy of the stiffness of the background plays a fundamental role for WIFF between the fractures and the background as well as for WIFF between connected fractures. Conversely, the anisotropy of the background permeability affects the characteristic frequency, the angle dependence, and the magnitude of the effects related to WIFF between fractures and background. In addition, different correlations between hydraulic and elastic background anisotropy lead to different degrees of effective seismic anisotropy. Our results therefore indicate that accounting for the effects of intrinsic background anisotropy on WIFF is crucial for a quantitative interpretation of seismic anisotropy measurements in fluid‐saturated fractured formations.

show abstract

An energy-based approach to estimate seismic attenuation due to wave-induced fluid flow in heterogeneous poroelastic media

Abstract: Whenever a seismic wave propagates through a fluid-saturated porous rock that contains heterogeneities in the mesoscopic scale range, that is, heterogeneities that are much larger than the typical pore size but much smaller than the predominant wavelengths, local

Cited by 26 publications

References 37 publications

Numerically quantifying energy loss caused by squirt flow

Numerically quantifying energy loss caused by squirt flow

Seismic Attenuation and Stiffness Modulus Dispersion in Porous Rocks Containing Stochastic Fracture Networks

Sensitivity of Seismic Attenuation and Phase Velocity to Intrinsic Background Anisotropy in Fractured Porous Rocks: A Numerical Study

Contact Info

Product

Resources

About