scholarly journals Representative elementary volumes for evaluating effective seismic properties of heterogeneous poroelastic media

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. D169-D181 ◽  
Author(s):  
Marco Milani ◽  
J. Germán Rubino ◽  
Tobias M. Müller ◽  
Beatriz Quintal ◽  
Eva Caspari ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Velocity Dispersion ◽  
Fluid Pressure ◽  
Porous Rocks ◽  
Seismic Properties ◽  
Rock Samples ◽  
Periodic Distribution ◽  
Poroelastic Media ◽  
Synthetic Rock ◽  
Dispersion And Attenuation

Understanding and quantifying seismic energy dissipation in fluid-saturated porous rocks is of considerable interest because it offers the perspective of extracting information with regard to the elastic and hydraulic rock properties. An important, if not dominant, attenuation mechanism prevailing in the seismic frequency band is wave-induced fluid pressure diffusion in response to the contrasts in elastic stiffness in the mesoscopic-scale range. An effective way to estimate seismic velocity dispersion and attenuation related to this phenomenon is through the application of numerical upscaling procedures to synthetic rock samples of interest. However, the estimated seismic properties are meaningful only if the underlying sample volume is at least of the size of a representative elementary volume (REV). In the given context, the definition of an REV and the corresponding implications for the estimation of the effective seismic properties remain largely unexplored. To alleviate this problem, we have studied the characteristics of REVs for a set of idealized rock samples sharing high levels of velocity dispersion and attenuation. For periodically heterogeneous poroelastic media, the REV size was driven by boundary condition effects. Our results determined that boundary condition effects were absent for layered media and negligible in the presence of patchy saturation. Conversely, strong boundary condition effects arose in the presence of a periodic distribution of finite-length fractures, thus leading to large REV sizes. The results thus point to the importance of carefully determining the REV sizes of heterogeneous porous rocks for computing effective seismic properties, especially in the presence of strong dry frame stiffness contrasts.

Extended Gassmann Equation with Dynamic Volumetric Strain: Modeling Wave Dispersion and Attenuation of Heterogenous Porous Rocks

Geophysics ◽  
2021 ◽  
pp. 1-97
Author(s):  
Luanxiao Zhao ◽  
Yirong Wang ◽  
Qiuliang Yao ◽  
Jianhua Geng ◽  
Hui Li ◽  
...  
Keyword(s):  
Fluid Pressure ◽  
Volumetric Strain ◽  
Wave Dispersion ◽  
Heterogeneous Porous Media ◽  
Porous Rocks ◽  
Analytical Methodology ◽  
Heterogeneous Rocks ◽  
Rock Characterization ◽  
Wave Induced ◽  
Dispersion And Attenuation

Sedimentary rocks are often heterogeneous porous media inherently containing complex distributions of heterogeneities (e.g., fluid patches, cracks). Understanding and modeling their frequency-dependent elastic and adsorption behaviors is of great interest for subsurface rock characterization from multi-scale geophysical measurements. The physical parameter of dynamic volumetric strain (DVS) associated with wave-induced fluid flow is proposed to understand the common physics and connections behind known poroelastic models for modeling dispersion behaviors of heterogeneous rocks. We derive the theoretical formulations of DVS for patchy saturated rock at mesoscopic scale and cracked porous rock at microscopic grain scales, essentially embodying the wave-induced fluid pressure relaxation process. By incorporating the DVS into the classical Gassmann equation, a simple but practical “dynamic equivalent” modeling approach, extended Gassmann equation, is developed to characterize the dispersion and attenuation of complex heterogeneous rocks at non-zero frequencies. Using the extended Gassmann equation, the effect of microscopic or mesoscopic heterogeneities with complex distributions on the wave dispersion and attenuation signatures can be captured. The proposed theoretical framework provides a simple and straightforward analytical methodology to calculate wave dispersion and attenuation in porous rocks with multiple sets of heterogeneities exhibiting complex characteristics. We also demonstrate that, with the appropriate consideration of multiple crack sets and complex fluids patches distribution, the modeling results can better interpret the experimental data sets of dispersion and attenuation for heterogeneous porous rocks.

scholarly journals Seismic attenuation and dispersion in poroelastic media with fractures of variable aperture distributions

2019 ◽  
Author(s):  
Simón Lissa ◽  
Nicolás D. Barbosa ◽  
J. Germán Rubino ◽  
Beatriz Quintal
Keyword(s):  
Velocity Dispersion ◽  
Wave Attenuation ◽  
Fluid Pressure ◽  
Seismic Attenuation ◽  
Statistical Control ◽  
Geometrical Properties ◽  
Contact Areas ◽  
Poroelastic Media ◽  
Fracture Models ◽  
Variable Aperture

Abstract. Considering poroelastic media containing aligned periodic fractures, we numerically quantify the effects that fractures with variable aperture distributions have on seismic wave attenuation and velocity dispersion due to fluid pressure diffusion (FPD). To achieve this, realistic models of fractures are generated with a stratified percolation algorithm which provides statistical control over geometrical fracture properties such as density and distribution of contact areas. The results are sensitive to both geometrical properties, showing that an increase in the density of contact areas as well as a decrease in their correlation length, reduce the effective seismic attenuation and the corresponding velocity dispersion. Moreover, no FPD effects are observed in addition to the one occurring between the fractures and the background, in the analysed frequency range, by considering realistic fracture models. We demonstrated that if appropriate equivalent physical properties accounting for the effects of contact areas are employed, a simple planar fracture can be used to emulate the seismic response of fractures with realistic aperture distributions. The excellent agreement between their seismic responses is demonstrated for all incidence angles and wave modes.

Pore Aspect Ratio Spectrum Inversion from Ultrasonic Measurements and Its Application

2015 ◽  
Vol 23 (04) ◽  
pp. 1540009 ◽  
Author(s):  
Fuyong Yan ◽  
De-Hua Han ◽  
Xue-Lian Chen
Keyword(s):  
Aspect Ratio ◽  
Carbonate Rock ◽  
Velocity Dispersion ◽  
Rock Sample ◽  
Wave Dispersion ◽  
Ratio Spectrum ◽  
Poroelastic Media ◽  
Ultrasonic Measurements ◽  
Dispersion And Attenuation ◽  
Spectrum Inversion

We have conducted simultaneous ultrasonic velocity and pore volume change measurements on a carbonate rock sample. By including of pressure dependent porosity data, we have improved Cheng’s pore aspect ratio spectrum inversion methodology and made the inverted pore aspect ratio spectrum more realistic. Tang’s unified velocity dispersion and attenuation model is modified and extended to poroelastic media with complex pore structure under undrained condition. Using improved pore aspect ratio spectra inversion methodology and modified Tang’s model, we have explored the potential application of pore aspect ratio spectrum in prediction of seismic wave dispersion and attenuation.

scholarly journals Rigorous bounds for seismic dispersion and attenuation due to wave-induced fluid flow in porous rocks

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. L45-L51 ◽  
Author(s):  
Boris Gurevich ◽  
Dina Makarynska
Keyword(s):  
Bulk Modulus ◽  
Inviscid Fluid ◽  
Porous Rocks ◽  
Shear Moduli ◽  
Poroelastic Media ◽  
Viscous Shear ◽  
Rigorous Bounds ◽  
Shear Relaxation ◽  
Wave Induced ◽  
Dispersion And Attenuation

The Hashin-Shtrikman (HS) bounds define the range of bulk and shear moduli of an elastic composite, given the moduli of the constituents and their volume fractions. Recently, the HS bounds have been extended to the quasi-static moduli of composite viscoelastic media. Because viscoelastic moduli are complex, the viscoelastic bounds form a closed curve on the complex plane. We analyze these general viscoelastic bounds for a particular case of a porous solid saturated with a Newtonian fluid. In our analysis, for poroelastic media, the viscoelastic bounds for the bulk modulus are represented by a semicircle and a segment of the real axis, connecting formal HS bounds that are computed for an inviscid fluid. Importantly, viscoelastic bounds for poroelastic media turn out to be independent of frequency. However, because the bounds are quasi-static, the frequency must be much lower than Biot’s characteristic frequency. Furthermore, we find that the bounds for the bulk modulus are attainable (realizable). We also find that these viscoelastic bounds account for viscous shear relaxation and squirt-flow dispersion, but do not account for Biot’s global flow dispersion, because the latter strongly depends on inertial forces.

scholarly journals Impact of fracture clustering on the seismic signatures of porous rocks containing aligned fractures

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. MR295-MR308 ◽  
Author(s):  
Nicolás D. Barbosa ◽  
J. Germán Rubino ◽  
Eva Caspari ◽  
Klaus Holliger
Keyword(s):  
Fractured Reservoirs ◽  
Fluid Pressure ◽  
Fracture Network ◽  
Analytical Models ◽  
Porous Rocks ◽  
Seismic Properties ◽  
Velocity Anisotropy ◽  
Pressure Diffusion ◽  
Dispersion Regime ◽  
Attenuation Anisotropy

The presence of fractures in a reservoir can have a significant impact on its effective mechanical and hydraulic properties. Many researchers have explored the seismic response of fluid-saturated porous rocks containing aligned planar fractures through the use of analytical models. However, these approaches are limited to the extreme cases of regular and uniform random distributions of fractures. The purpose of this work is to consider more realistic distributions of fractures and to analyze whether and how the frequency-dependent anisotropic seismic properties of the medium can provide information on the characteristics of the fracture network. Particular focus is given to fracture clustering effects resulting from commonly observed fracture distributions. To do so, we have developed a novel hybrid methodology combining the advantages of 1D numerical oscillatory tests, which allows us to consider arbitrary distributions of fractures, and an analytical solution that permits extending these results to account for the effective anisotropy of the medium. A corresponding numerical analysis indicates that the presence of clusters of fractures produces an additional attenuation and velocity dispersion regime compared with that predicted by analytical models. The reason for this is that a fracture cluster behaves as an effective layer and the contrast with respect to the unfractured background produces an additional fluid pressure diffusion length scale. The characteristic frequency of these effects depends on the size and spacing between clusters, the latter being much larger than the typical spacing between individual fractures. Moreover, we find that the effects of fracture clustering are more pronounced in attenuation anisotropy than velocity anisotropy data. Our results indicate that fracture clustering effects on fluid pressure diffusion can be described by two-layer models. This, in turn, provides the basis for extending current analytical models to account for these effects in inversion schemes designed to characterize fractured reservoirs from seismic data.

scholarly journals Seismic attenuation and dispersion in poroelastic media with fractures of variable aperture distributions

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1321-1336 ◽  
Author(s):  
Simón Lissa ◽  
Nicolás D. Barbosa ◽  
J. Germán Rubino ◽  
Beatriz Quintal
Keyword(s):  
Velocity Dispersion ◽  
Wave Attenuation ◽  
Fluid Pressure ◽  
Seismic Attenuation ◽  
Statistical Control ◽  
Geometrical Properties ◽  
Contact Areas ◽  
Poroelastic Media ◽  
Pressure Diffusion ◽  
Variable Aperture

Abstract. Considering poroelastic media containing periodically distributed parallel fractures, we numerically quantify the effects that fractures with variable aperture distributions have on seismic wave attenuation and velocity dispersion due to fluid pressure diffusion (FPD). To achieve this, realistic models of fractures are generated with a stratified percolation algorithm which provides statistical control over geometrical fracture properties such as density and distribution of contact areas. The results are sensitive to both geometrical properties, showing that an increase in the density of contact areas as well as a decrease in their correlation length reduce the effective seismic attenuation and the corresponding velocity dispersion. Moreover, we demonstrate that if equivalent physical properties accounting for the effects of contact areas are employed, simple planar fractures can be used to emulate the seismic response of fractures with realistic aperture distributions. The excellent agreement between their seismic responses was verified for all wave incidence angles and wave modes.

A dynamic elastic model for squirt-flow effect and its application on fluid-viscosity-associated velocity dispersion in reservoir sandstones

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR201-MR212
Author(s):  
Zhi-Qiang Yang ◽  
Tao He ◽  
Chang-Chun Zou
Keyword(s):  
Velocity Dispersion ◽  
Pore Space ◽  
Pore Fluid ◽  
Quantitative Prediction ◽  
Elastic Model ◽  
Fluid Viscosity ◽  
Porous Rocks ◽  
S Wave ◽  
Flow Effect ◽  
Reservoir Sandstones

Velocity dispersion is a common phenomenon for fluid-charged porous rocks and carries important information on the pore structure and fluid in reservoir rocks. Previous ultrasonic experiments had measured more significant non-Biot velocity dispersion on saturated reservoir sandstones with increasing pore-fluid viscosity. Although wave-induced local squirt-flow effect could in theory cause most of the non-Biot velocity dispersion, its quantitative prediction remains a challenge. Several popular models were tested to predict the measured velocities under undrained conditions, but they either underestimated the squirt-flow effect or failed to simultaneously satisfy P- and S-wave velocity dispersions (especially for higher viscosity fluids). Based on the classic double-porosity theory that pore space is comprised of mainly stiff/Biot’s porosity and minor compliant porosity, an effective “wet frame” was hypothesized to account for the squirt-flow effect, whose compliant pores are filled with a hypothesized fluid with dynamic modulus. A new dynamic elastic model was then introduced by extending Biot theory to include the squirt-flow effect, after replacing the dry-frame bulk/shear moduli with their wet-frame counterparts. In addition to yielding better velocity predictions for P- and S-wave measurements of different fluid viscosities, the new model is also more applicable because its two key tuning parameters (i.e., the effective aspect ratio and porosity of compliant pores) at in situ reservoir pressure could be constrained with laboratory velocity measurements associated with pore-fluid viscosities.

Toward phenomenological universality of the mechanical behavior of arbitrarily anisotropic porous rocks

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA167-WA183 ◽  
Author(s):  
Patrick N. J. Rasolofosaon
Keyword(s):  
Mechanical Behavior ◽  
Empirical Relation ◽  
Fluid Pressure ◽  
Porous Rocks ◽  
Porous Network ◽  
Hooke’S Law ◽  
Fluid Content ◽  
Elastic Hysteresis ◽  
Hydraulic Hysteresis ◽  
Hooke's Law

The great diversity of the microstructures of rocks impedes the use of a universal rock physics model with idealized geometry to correctly describe the mechanical behavior of rocks. In this quest for universality, by ignoring the detailed description of the causes of the observed phenomenon and only focusing on the empirical relation between the cause (applied stress) and the effect (resulting strain), phenomenological models such as the linear elastic Hooke’s law roughly describe the mechanical behavior of rocks of contrasted microstructures. However, in detail, numerous laboratory experiments covering broad frequency and strain ranges (both typically more than eight orders of magnitude) on various types of rocks have also shown deviations from Hooke’s law due to anisotropy, frequency dependence, nonlinearity, possibly with the presence of hysteresis, and poroelasticity. A phenomenological model has been recently proposed that synthesizes all these behaviors in a single model, but unfortunately does not integrate the porous nature of rocks. The new model is based on a reformulation in modified spectral decomposition of the previous work using the 7D poroelastic tensor linking the dynamic parameters (i.e., the six stress components and fluid pressure) and the kinematic parameters (i.e., the six strain components and the local increase of fluid content ζ). In addition to the elastic hysteresis of the stress-strain curves, the model also predicts the existence of a second hysteresis, or hydraulic hysteresis, of the curve fluid pressure p versus fluid content ζ, qualitatively similar to the first one. Indeed, the elastic hysteresis is due to the opening and the closure of some compliant pores at different stress levels. These pores represent possible access radii for the saturating fluid; the hysteresis in the geometry of the porous network also induces the hydraulic hysteresis in the p-ζ curves.

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