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

Rubino, J. Germán; Caspari, Eva; Müller, Tobias M.; Milani, Marco; Barbosa, Nicolás D.; Holliger, Klaus

doi:10.1002/2016jb013165

Cited by 67 publications

(107 citation statements)

References 24 publications

Supporting

Mentioning

107

Contrasting

Order By: Relevance

“…Under plane strain conditions and assuming that the responses of the probed sample can be represented by an equivalent homogeneous anisotropic viscoelastic solid (Rubino et al, ), the average stress and strain components (equations and ) can be related through a complex‐valued, frequency‐dependent equivalent Voigt stiffness matrix

([], \begin{matrix} < σ_{11}^{k} > \\ < σ_{22}^{k} > \\ < σ_{12}^{k} > \end{matrix}) = ([], \begin{matrix} C_{11} (ω) & C_{12} (ω) & C_{16} (ω) \\ C_{12} (ω) & C_{22} (ω) & C_{26} (ω) \\ C_{16} (ω) & C_{26} (ω) & C_{66} (ω) \end{matrix}) \cdot ([], \begin{matrix} < ϵ_{11}^{k} > \\ < ϵ_{22}^{k} > \\ < 2 ϵ_{12}^{k} > \end{matrix}) .

…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

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

([], \begin{matrix} < σ_{11}^{k} > \\ < σ_{22}^{k} > \\ < σ_{12}^{k} > \end{matrix}) = ([], \begin{matrix} C_{11} (ω) & C_{12} (ω) & C_{16} (ω) \\ C_{12} (ω) & C_{22} (ω) & C_{26} (ω) \\ C_{16} (ω) & C_{26} (ω) & C_{66} (ω) \end{matrix}) \cdot ([], \begin{matrix} < ϵ_{11}^{k} > \\ < ϵ_{22}^{k} > \\ < 2 ϵ_{12}^{k} > \end{matrix}) .

…”

Section: Methodsmentioning

confidence: 99%

“…They observed very good agreement between the theoretical predictions and the values obtained from corresponding numerical simulations. Rubino et al () extended the numerical methodology of Rubino et al () to compute the seismic properties of a poroelastic sample in the presence of generic effective anisotropy.…”

Section: Introductionmentioning

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

show abstract

“…Readers are referred to the work of Rubino et al . () for the details of the numerical upscaling procedure.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Effects of fracture intersections on seismic dispersion: theoretical predictions versus numerical simulations

Guo

Rubino

Glubokovskikh

et al. 2016

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

The detection and characterisation of domains of intersecting fractures are important goals in several disciplines of current interest, including exploration and production of unconventional reservoirs, nuclear waste storage, CO2 sequestration, and groundwater hydrology, among others. The objective of this study is to propose a theoretical framework for quantifying the effects of fracture intersections on the frequency‐dependent elastic properties of fluid‐saturated porous and fractured rocks. Three characteristic frequency regimes for fluid pressure communication are identified. In the low‐frequency limit, fractures are in full pressure communication with the embedding porous matrix and with other fractures. Conversely, in the high‐frequency limit, fractures are hydraulically isolated from the matrix and from other fractures. At intermediate frequencies, fractures are hydraulically isolated from the matrix porosity but can be in hydraulic communication with each other, depending on whether fracture sets are intersecting. For each frequency regime, the effective stiffness coefficients are derived using the linear‐slip theory and anisotropic Gassmann equations. Explicit mathematical expressions for the two characteristic frequencies that separate the three frequency regimes are also determined. Theoretical predictions are then applied to two synthetic 2D samples, each containing two orthogonal fracture sets: one with and another without intersections. The resulting stiffness coefficients, Thomsen‐style anisotropy parameters, and the transition frequencies show good agreement with corresponding numerical simulations. The theoretical results are applicable not only to 2D but also to 3D fracture systems and are amenable to being employed in inversion schemes designed to characterise fracture systems.

show abstract

“…From the spatially averaged complex‐valued stress and strain fields of the three tests, we obtain a frequency‐dependent complex valued 2D stiffness matrix in Voigt notation by applying a least square procedure (Rubino et al . ). The following relation holds

(\begin{matrix} false⟨ σ_{11} (ω) false⟩ \\ false⟨ σ_{22} (ω) false⟩ \\ false⟨ σ_{12} (ω) false⟩ \end{matrix}) = (\begin{matrix} C_{11} & C_{12} & C_{16} \\ C_{12} & C_{22} & C_{26} \\ C_{16} & C_{26} & C_{66} \end{matrix}) (\begin{matrix} false⟨ ε_{11} (ω) false⟩ \\ false⟨ ε_{22} (ω) false⟩ \\ false⟨ 2 ε_{12} (ω) false⟩ \end{matrix}),

where the stiffness coefficients

C_{ij}

describe an effective anisotropic viscoelastic behaviour of the fractured poroelastic medium, provided that the sub‐sample has the size of a representative elementary volume (REV).…”

Section: Methodsmentioning

confidence: 97%

“…We apply the numerical upscaling scheme of Rubino et al . () for anisotropic 2D media in the frequency domain, which is based on a finite element solution of Biot's consolidation equations (Biot ). By neglecting all inertia‐related terms and transforming equations (–) into the space‐frequency domain, we obtain the following coupled system of the total stress equilibrium and Darcy's law expressed in displacements

\begin{matrix} true \\ right \nabla \cdot σ & = & left bold0, \end{matrix}

\begin{matrix} true \\ right - \nabla p & = & left i ω \frac{η}{κ_{o}} boldw . \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

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

Caspari

Новиков

Lisitsa

et al. 2018

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 67 publications

References 24 publications

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

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

Effects of fracture intersections on seismic dispersion: theoretical predictions versus numerical simulations

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

Contact Info

Product

Resources

About