Seismic dispersion and attenuation in saturated porous rocks with aligned fractures of finite thickness: Theory and numerical simulations — Part 1: P-wave perpendicular to the fracture plane

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. WA49-WA62 ◽  
Author(s):  
Junxin Guo ◽  
J. Germán Rubino ◽  
Nicolás D. Barbosa ◽  
Stanislav Glubokovskikh ◽  
Boris Gurevich
Keyword(s):  
Numerical Simulations ◽  
Fluid Pressure ◽  
Theoretical Models ◽  
Seismic Attenuation ◽  
Fracture Plane ◽  
Fracture Density ◽  
High Fracture ◽  
Background Medium ◽  
Theoretical Predictions ◽  
Dispersion And Attenuation

When a seismic wave travels through a fluid-saturated porous reservoir containing aligned fractures, it induces oscillatory fluid flow between the fractures and the embedding background medium. Although there are numerous theoretical models for quantifying the associated seismic attenuation and velocity dispersion, they rely on certain assumptions, such as infinitesimal fracture thickness and dilute fracture concentration, which rarely hold in real reservoirs. The objective of this work is to overcome some of these limitations and, therefore, improve the applicability of the available theoretical models. To do so, we extend existing models to the finite fracture thickness case for P-waves propagating perpendicular to the fracture plane using the so-called branching function approach. We consider three types of fractures, namely, periodically and randomly spaced planar fractures, as well as penny-shaped cracks. The extended unified model is then tested by comparing with corresponding numerical simulations based on Biot’s theory of poroelasticity. We consider two cases of 2D rock samples with aligned elliptical fractures, one with low fracture density and the other with high fracture density. The results indicate that the influence of the finite fracture thickness on seismic dispersion and attenuation is small at low frequencies when the fluid pressure has enough time to equilibrate between the fractures and background medium. However, this effect is significant at high frequencies when there is not sufficient time for the fluid pressure equilibration. In addition, the theoretical predictions of the penny-shaped crack model are found to match the numerical simulation results very well, even under relatively high fracture density. Analyses of stress distributions suggest that the small discrepancies found between theoretical predictions and numerical simulations are probably due to fracture interactions. In a companion paper, we will extend the analysis for considering the full stiffness matrix and anisotropic properties of such rocks.

Seismic dispersion and attenuation in saturated porous rocks with aligned fractures of finite thickness: Theory and numerical simulations — Part 2: Frequency-dependent anisotropy

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. WA63-WA71 ◽  
Author(s):  
Junxin Guo ◽  
J. Germán Rubino ◽  
Nicolás D. Barbosa ◽  
Stanislav Glubokovskikh ◽  
Boris Gurevich
Keyword(s):  
Numerical Simulations ◽  
Stiffness Matrix ◽  
Relaxation Function ◽  
Fractured Reservoirs ◽  
Theoretical Models ◽  
Fracture Plane ◽  
Frequency Dependent ◽  
Theoretical Approaches ◽  
Dispersion And Attenuation ◽  
Good Agreement

Numerous theoretical models have been proposed for computing seismic wave dispersion and attenuation in rocks with aligned fractures due to wave-induced fluid flow between the fractures and the embedding background. However, all these models rely on certain assumptions, for example, infinitesimal fracture thickness or dilute fracture concentration, which rarely hold in real reservoirs and, thus, limit their applicability. To alleviate this issue, theoretical models for periodically or randomly spaced planar fractures and penny-shaped cracks were recently extended by the authors to the case of finite fracture thickness for P-waves propagating perpendicular to the fracture plane. Theoretical predictions under low and relatively high fracture density were then assessed by comparing with corresponding numerical simulations. However, the case of arbitrary incidence angles as well as the behaviors of S-waves remained unexplored. In this work, we therefore extended the prediction results to the full stiffness matrix through two theoretical approaches. The first approach uses an interpolation between the low- and high-frequency limits using a relaxation function obtained from the normal-incidence solution. The second approach is based on the linear slip theory with a frequency-dependent fracture compliance. Both derivations rely on the fact that all the stiffness coefficients are controlled by the same relaxation function. With the full stiffness matrix, anisotropic seismic properties can then be studied. P- and S-wave velocities and attenuations at different frequencies and incidence angles and also corresponding anisotropy parameters are calculated for one synthetic 2D rock sample. The results indicate that the predictions provided by the two theoretical approaches are in good agreement with each other and also indicate a good agreement with the corresponding numerical simulations. The extended theoretical models presented in this work are easy to apply and computationally much cheaper than numerical simulations and, hence, can be used in the seismic characterization of fractured reservoirs.

scholarly journals Seismic Imaging of Active and Ancient CO2 Pathways in the Little Grand Wash Fault

2021 ◽  
Author(s):  
Jonathan Yelton
Keyword(s):  
Seismic Velocity ◽  
Fluid Pressure ◽  
P Wave ◽  
Geochemical Data ◽  
Migration Behavior ◽  
High Porosity ◽  
Seismic Velocities ◽  
Fracture Density ◽  
High Fracture ◽  
Stress Changes

Understanding the migration behavior of carbon dioxide (CO2) during long-term geological storage is crucial to the success of carbon capture and sequestration technology. I explore p-wave and s-wave seismic properties across the Little Grand Wash fault in east-central Utah, a natural CO2 seep and analogue for a long-failed sequestration site. Travertines dated to at least 113,000 k.y. and geochemical surveys confirm both modern and ancient CO2 leakage along the fault. Outgassing is currently focused in damage zones where the total fluid pressure may reduce the minimum horizontal effective stress. Regional stress changes may be responsible for decadal- to millennial-scale changes in CO2 pathways. I identify subsurface geologic structure in the upper few hundred meters and relate surface CO2 outgassing zones to seismic reflection and first arrival tomography data. I tie my hammer seismic results to borehole logs, geology from outcrops, and geochemical data. I generate velocity tomograms that cross the fault zone and construct rock physics models. I identify high porosity and/or high fracture density zones from slow seismic velocity zones. These zones match mapped fault locations, are fully saturated, and are conduits for upward fluid/gas migration. Anomalously high seismic velocities at the fault are consistent with ancient CO2 flow pathways. Low CO2 flux regions show seismic velocities consistent with shallow unsaturated host rock. Studying the behavior of CO2 in this system can give insight of potential risks in future sequestration projects.

Seismic moduli dispersion and attenuation obtained using Digital Rock Physics

2021 ◽  
Author(s):  
Simón Lissa ◽  
Matthias Ruf ◽  
Holger Steeb ◽  
Beatriz Quintal
Keyword(s):  
Seismic Waves ◽  
Numerical Models ◽  
Fluid Pressure ◽  
Rock Physics ◽  
Viscous Friction ◽  
Seismic Attenuation ◽  
Rock Properties ◽  
Digital Rock Physics ◽  
Digital Rock ◽  
Dispersion And Attenuation

<p>Seismic waves are affected by rock properties such as porosity, permeability, grain material and by their heterogeneities as well as by the fluid properties saturating the rocks. Consequently, seismic methods are a valuable tool for the indirect characterization of rocks. For example, at the microscale, the presence of compliant pores (cracks or grain contacts) in fluid-saturated rocks can cause strong seismic attenuation and velocity dispersion. In this case, the deformation caused by a passing wave induces a fluid pressure gradient between compressed compliant pores and much less compressed pores (stiff isometric pores or cracks having a different orientation than the most compressed ones) if they are hydraulically connected. The consequent fluid pressure diffusion (FPD) dissipates seismic energy due to viscous friction in the fluid.</p><p>Digital rock physics (DRP) aims to reproduce experimental measurements using numerical simulation in models derived from high resolution rock images. We developed a DRP workflow to calculate the frequency dependent seismic moduli dispersion and attenuation in fluid-saturated models derived from micro X-Ray Computed Tomography (µXRCT) images. Filtering, segmentation and meshing procedures are applied on sub-volumes of different rock images to create 3D numerical models. We apply our workflow to calculate seismic moduli attenuation due to FPD at the microscale (squirt flow). We consider a µXRCT image of a cracked (through thermal treatment) Carrara marble sample. A detailed visualization of the fluid pressure as well as of the energy dissipation rate in the 3D model helps to understand the squirt flow attenuation process at different frequencies.</p>

Analyzing the Impacts of Meshing and Grid Alignment in Dual-Porosity Dual-Permeability Upscaling

2021 ◽  
pp. 1-20
Author(s):  
Ziming Xu ◽  
Juliana Y. Leung
Keyword(s):  
Fracture Network ◽  
Fracture Plane ◽  
Fracture Density ◽  
Shape Factors ◽  
Stimulated Reservoir Volume ◽  
Reservoir Volume ◽  
Multiple Length Scales ◽  
Fracture Intensity ◽  
Cumulative Production ◽  
The Difference

Summary The discrete fracture network (DFN) model is widely used to simulate and represent the complex fractures occurring over multiple length scales. However, computational constraints often necessitate that these DFN models be upscaled into a dual-porositydual-permeability (DPDK) model and discretized over a corner-point grid system, which is still commonly implemented in many commercial simulation packages. Many analytical upscaling techniques are applicable, provided that the fracture density is high, but this condition generally does not hold in most unconventional reservoir settings. A particular undesirable outcome is that connectivity between neighboring fracture cells could be erroneously removed if the fracture plane connecting the two cells is not aligned along the meshing direction. In this work, we propose a novel scheme to detect such misalignments and to adjust the DPDK fracture parameters locally, such that the proper fracture connectivity can be restored. A search subroutine is implemented to identify any diagonally adjacent cells of which the connectivity has been erroneously removed during the upscaling step. A correction scheme is implemented to facilitate a local adjustment to the shape factors in the vicinity of these two cells while ensuring the local fracture intensity remains unaffected. The results are assessed in terms of the stimulated reservoir volume calculations, and the sensitivity to fracture intensity is analyzed. The method is tested on a set of tight oil models constructed based on the Bakken Formation. Simulation results of the corrected, upscaled models are closer to those of DFN simulations. There is a noticeable improvement in the production after restoring the connectivity between those previously disconnected cells. The difference is most significant in cases with medium DFN density, where more fracture cells become disconnected after upscaling (this is also when most analytical upscaling techniques are no longer valid); in some 2D cases, up to a 22% difference in cumulative production is recorded. Ignoring the impacts of mesh discretization could result in an unintended reduction in the simulated fracture connectivity and a considerable underestimation of the cumulative production.

Transmission of Elegant Laguerre-Gaussian beams at a dielectric interface - numerical simulations

2009 ◽  
Vol 57 (2) ◽  
pp. 181-188 ◽  
Author(s):  
W. Szabelak ◽  
W. Nasalski
Keyword(s):  
Numerical Simulations ◽  
Total Internal Reflection ◽  
Polarization Effect ◽  
Internal Reflection ◽  
Gaussian Beams ◽  
Cross Polarization ◽  
Dielectric Interface ◽  
Theoretical Predictions ◽  
Critical Incidence

Transmission of Elegant Laguerre-Gaussian beams at a dielectric interface - numerical simulations Behaviour of Laguerre-Gaussian beams impinged at a dielectric interface under distinct angles is discussed. For different incident angles the beams interact with the interface differently. Two ranges of incident angles, specified by a position of a spectral cone of beam field and related to a cross-polarization effect, are analyzed. Boundary between these two ranges is defined. Cases of critical incidence and total internal reflection are also discussed. Paraxial beams near the lower paraxial limit are considered. Theoretical predictions are confirmed by numerical simulations.

scholarly journals The Close AGN Reference Survey (CARS)

2018 ◽  
Vol 618 ◽  
pp. A27 ◽  
Author(s):  
M. C. Powell ◽  
B. Husemann ◽  
G. R. Tremblay ◽  
M. Krumpe ◽  
T. Urrutia ◽  
...  
Keyword(s):  
Ambient Medium ◽  
Theoretical Models ◽  
Ionized Gas ◽  
X Ray ◽  
Gas Streams ◽  
Hot Gas ◽  
Upper Limits ◽  
Theoretical Predictions ◽  
Different Origins

Aims. We probe the radiatively-efficient, hot wind feedback mode in two nearby luminous unobscured (type 1) AGN from the Close AGN Reference Survey (CARS), which show intriguing kpc-scale arc-like features of extended [O III]ionized gas as mapped with VLT-MUSE. We aimed to detect hot gas bubbles that would indicate the existence of powerful, galaxy-scale outflows in our targets, HE 0227–0931 and HE 0351+0240, from deep (200 ks) Chandra observations. Methods. By measuring the spatial and spectral properties of the extended X-ray emission and comparing with the sub kpc-scale IFU data, we are able to constrain feedback scenarios and directly test if the ionized gas is due to a shocked wind. Results. No extended hot gas emission on kpc-scales was detected. Unless the ambient medium density is low (n H  ∼  1 cm−3 at 100 pc), the inferred upper limits on the extended X-ray luminosities are well below what is expected from theoretical models at matching AGN luminosities. Conclusions. We conclude that the highly-ionized gas structures on kpc scales are not inflated by a hot outflow in either target, and instead are likely caused by photoionization of pre-existing gas streams of different origins. Our nondetections suggest that extended X-ray emission from an AGN-driven wind is not universal, and may lead to conflicts with current theoretical predictions.

scholarly journals Initial effective stress controls the nature of earthquakes

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
François X. Passelègue ◽  
Michelle Almakari ◽  
Pierre Dublanchet ◽  
Fabian Barras ◽  
Jérôme Fortin ◽  
...  
Keyword(s):  
Effective Stress ◽  
Physical Mechanism ◽  
Fluid Pressure ◽  
Fault Slip ◽  
Rupture Velocity ◽  
Complete Spectrum ◽  
Available Energy ◽  
Different Types ◽  
Theoretical Predictions ◽  
Shallow Part

Abstract Modern geophysics highlights that the slip behaviour response of faults is variable in space and time and can result in slow or fast ruptures. However, the origin of this variation of the rupture velocity in nature as well as the physics behind it is still debated. Here, we first highlight how the different types of fault slip observed in nature appear to stem from the same physical mechanism. Second, we reproduce at the scale of the laboratory the complete spectrum of rupture velocities observed in nature. Our results show that the rupture velocity can range from a few millimetres to kilometres per second, depending on the available energy at the onset of slip, in agreement with theoretical predictions. This combined set of observations bring a new explanation of the dominance of slow rupture fronts in the shallow part of the crust or in areas suspected to present large fluid pressure.

scholarly journals Bioinspired aerofoil adaptations: the next steps for theoretical models

2019 ◽  
Vol 377 (2159) ◽  
pp. 20190070 ◽  
Author(s):  
Lorna J. Ayton
Keyword(s):  
Experimental Data ◽  
Theoretical Models ◽  
Theoretical Modelling ◽  
Experimental Measurements ◽  
Far Field ◽  
Acoustic Analogy ◽  
Trailing Edge ◽  
Trailing Edge Noise ◽  
Theoretical Predictions ◽  
Field Noise

The extended introduction in this paper reviews the theoretical modelling of leading- and trailing-edge noise, various bioinspired aerofoil adaptations to both the leading and trailing edges of blades, and how these adaptations aid in the reduction of aerofoil–turbulence interaction noise. Attention is given to the agreement between current theoretical predictions and experimental measurements, in particular, for turbulent interactions at the trailing edge of an aerofoil. Where there is a poor agreement between theoretical models and experimental data the features neglected from the theoretical models are discussed. Notably, it is known that theoretical predictions for porous trailing-edge adaptations do not agree well with experimental measurements. Previous works propose the reason for this: theoretical models do not account for surface roughness due to the porous material and thus omit a key noise source. The remainder of this paper, therefore, presents an analytical model, based upon the acoustic analogy, to predict the far-field noise due to a rough surface at the trailing edge of an aerofoil. Unlike previous roughness noise models which focus on roughness over an infinite wall, the model presented here includes diffraction by a sharp edge. The new results are seen to be in better agreement with experimental data than previous models which neglect diffraction by an edge. This new model could then be used to improve theoretical predictions for far-field noise generated by turbulent interactions with a (rough) porous trailing edge. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.

scholarly journals Numerical Simulations of Jets from Active Galactic Nuclei

Galaxies ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 24 ◽  
Author(s):  
José-María Martí
Keyword(s):  
Numerical Simulations ◽  
Active Galactic Nuclei ◽  
Galactic Nuclei ◽  
Theoretical Models ◽  
The Status ◽  
Hydrodynamical Description ◽  
Jet Plasma ◽  
The Impact ◽  
Continuous Injection ◽  
Double Radio Galaxies

Numerical simulations have been playing a crucial role in the understanding of jets from active galactic nuclei (AGN) since the advent of the first theoretical models for the inflation of giant double radio galaxies by continuous injection in the late 1970s. In the almost four decades of numerical jet research, the complexity and physical detail of simulations, based mainly on a hydrodynamical/magneto-hydrodynamical description of the jet plasma, have been increasing with the pace of the advance in theoretical models, computational tools and numerical methods. The present review summarizes the status of the numerical simulations of jets from AGNs, from the formation region in the neighborhood of the supermassive central black hole up to the impact point well beyond the galactic scales. Special attention is paid to discuss the achievements of present simulations in interpreting the phenomenology of jets as well as their current limitations and challenges.

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