Nicolás D. Barbosa

Numerical upscaling in 2-D heterogeneous poroelastic rocks: Anisotropic attenuation and dispersion of seismic waves

The presence of stiffness contrasts at scales larger than the typical pore sizes but smaller than the predominant seismic wavelengths, can produce seismic attenuation and velocity dispersion in fluid-saturated porous rocks. This energy dissipation mechanism is caused by wave-induced fluid-pressure diffusion among the different components of the probed geological formations. In many cases, heterogeneities have elongated shapes and preferential orientations, which implies that the overall response of the medium is anisotropic. In this work, we propose a numerical upscaling procedure that permits to quantify seismic attenuation and phase velocity considering fluid-pressure diffusion effects as well as generic anisotropy at the samples scale. The methodology is based on a set of three relaxation tests performed on a 2D synthetic rock sample representative of the medium of interest. It provides a complex-valued frequency-dependent equivalent stiffness matrix through a least-squares procedure. We also derive an approach for computing various poroelastic fields associated with the considered sample in response to the propagation of a seismic wave with arbitrary incidence angle. Using this approach, we provide an energy-based estimation of seismic attenuation. A comprehensive numerical analysis indicates that the methodology is suitable for handling complex media and different levels of overall anisotropy. Comparisons with the energy-based estimations demonstrate that the dynamic-equivalent viscoelastic medium assumption made by the numerical upscaling procedure is reasonable even in presence of high levels of overall anisotropy. This work also highlights the usefulness of poroelastic fields for the physical interpretation of seismic wave phenomena in strongly heterogeneous and complex media.

Fluid pressure diffusion effects on the seismic reflectivity of a single fracture

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 Gassmanns 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.

Extension of the classical linear slip model for fluid‐saturated fractures: Accounting for fluid pressure diffusion effects

We develop extended boundary conditions based on the linear slip model that account for the impact of wave-induced fluid pressure diffusion between a fracture and its embedding background on the stiffening effect of the fluid saturating the fracture. We include these poroelastic effects into the linear slip model through complex-valued and frequency-dependent parameters characterizing the mechanical and hydraulic coupling between the two regions. This new set of effective fracture parameters contains generalized normal and tangential compliances, analogous to those defined in the classical formulation of the linear slip model, and an additional parameter related to the coupling between horizontal and vertical deformation of the fracture. Comparisons of the extended and classical linear slip models with a poroelastic thin layer model show that the extended formulation always performs better when modeling the displacement fields induced by an incident P-wave as well as the scattering coefficients. We found that the contribution of the additional effective parameter involved in the proposed boundary conditions is significant at low frequencies with respect to the undrained frequency regime of the fracture and large angles of incidence. These extended boundary conditions can be readily incorporated into viscoelastic modeling algorithms simulating the response of a large-scale fluid-saturated fracture or multiple non-interacting fractures of this kind. The proposed model is expected not only to improve the estimation of mechanical characteristics of fractures in corresponding inversion schemes, but can also be used for extracting information with regard to other practically important parameters, such as, for example, the background permeability.

Attenuation mechanisms in fractured fluid-saturated porous rocks: a numerical modelling study: Attenuation in fractured rocks

Seismic attenuation mechanisms receive increasing attention for the characterization of fractured formations because of their inherent sensitivity to the hydraulic and elastic properties of the probed media. Attenuation has been successfully inferred from seismic data in the past, but linking these estimates to intrinsic rock physical properties remains challenging. A reason for these difficulties in fluid-saturated fractured porous media is that several mechanisms can cause attenuation and may interfere with each other. These mechanisms notably comprise pressure diffusion phenomena and dynamic effects, such as scattering, as well as Biot’s so-called intrinsic attenuation mechanism. Understanding the interplay between these mechanisms is therefore an essential step for estimating fracture properties from seismic measurements. In order to do this, we perform a comparative study involving wave propagation modelling in a transmission set-up based on Biot’s low-frequency dynamic equations and numerical upscaling based on Biot’s consolidation equations. The former captures all aforementioned attenuation mechanisms and their interference, whereas the latter only accounts for pressure diffusion phenomena. A comparison of the results from both methods therefore allows to distinguish between dynamic and pressure diffusion phenomena and to shed light on their interference. To this end, we consider a range of canonical models with randomly distributed vertical and/or horizontal fractures. We observe that scattering attenuation strongly interferes with pressure diffusion phenomena, since the latter affect the elastic contrasts between fractures and their embedding background. Our results also demonstrate that it is essential to account for amplitude reductions due to transmission losses to allow for an adequate estimation of the intrinsic attenuation of fractured media. The effects of Biot’s intrinsic mechanism are rather small for the models considered in this study.

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

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.