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

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.

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Plane-wave attenuation anisotropy in orthorhombic media

Geophysics ◽

10.1190/1.2387137 ◽

2007 ◽

Vol 72 (1) ◽

pp. D9-D19 ◽

Cited By ~ 44

Author(s):

Yaping Zhu ◽

Ilya Tsvankin

Keyword(s):

Attenuation Coefficient ◽

Wave Attenuation ◽

Fractured Reservoirs ◽

The Body ◽

P Wave ◽

Attenuation Coefficients ◽

Velocity Anisotropy ◽

Homogeneous Wave ◽

Anisotropy Parameters ◽

Attenuation Anisotropy

Orthorhombic models are often used in the interpretation of azimuthally varying seismic signatures recorded over fractured reservoirs. Here, we develop an analytic framework for describing the attenuation coefficients in orthorhombic media with orthorhombic attenuation (i.e., the symmetry of both the real and imaginary parts of the stiffness tensor is identical) under the assumption of homogeneous wave propagation. The analogous form of the Christoffel equation in the symmetry planes of orthorhombic and VTI (transversely isotropic with a vertical symmetry axis) media helps to obtain the symmetry-plane attenuation coefficients by adapting the existing VTI equations. To take full advantage of this equivalence with transverse isotropy, we introduce a parameter set similar to the VTI attenuation-anisotropy parameters [Formula: see text], [Formula: see text], and [Formula: see text]. This notation, based on the same principle as Tsvankin’s velocity-anisotropy parameters for orthorhombic media, leads to concise linearized equations for thesymmetry-plane attenuation coefficients of all three modes (P, [Formula: see text], and [Formula: see text]).The attenuation-anisotropy parameters also allow us to simplify the P-wave attenuation coefficient [Formula: see text] outside the symmetry planes under the assumptions of small attenuation and weak velocity and attenuation anisotropy. The approximate coefficient [Formula: see text] has the same form as the linearized P-wave phase-velocity function, with the velocity parameters [Formula: see text] and [Formula: see text] replaced by the attenuation parameters [Formula: see text] and [Formula: see text]. The exact attenuation coefficient, however, also depends on the velocity-anisotropy parameters, while the body-wave velocities are almost unperturbed by the presence of attenuation. The reduction in the number of parameters responsible for the P-wave attenuation and the simple approximation for the coefficient [Formula: see text] provide a basis for inverting P-wave attenuation measurements from orthorhombic media. The attenuation processing must be preceded by anisotropic velocity analysis that can be performed (in the absence of pronounced velocity dispersion) using existing algorithms for nonattenuative media.

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Fluid pressure diffusion effects on the excess compliance matrix of porous rocks containing aligned fractures

Geophysical Journal International ◽

10.1093/gji/ggaa197 ◽

2020 ◽

Vol 222 (1) ◽

pp. 715-733

Author(s):

Gabriel A Castromán ◽

Nicolás D Barbosa ◽

J Germán Rubino ◽

Fabio I Zyserman ◽

Klaus Holliger

Keyword(s):

Seismic Velocity ◽

Fractured Rock ◽

Finite Thickness ◽

Practical Importance ◽

Fluid Pressure ◽

Porous Rocks ◽

Compliance Matrix ◽

Pressure Diffusion ◽

Reservoir Permeability ◽

Wide Range

SUMMARY The presence of sets of open fractures is common in most reservoirs, and they exert important controls on the reservoir permeability as fractures act as preferential pathways for fluid flow. Therefore, the correct characterization of fracture sets in fluid-saturated rocks is of great practical importance. In this context, the inversion of fracture characteristics from seismic data is promising since their signatures are sensitive to a wide range of pertinent fracture parameters, such as density, orientation and fluid infill. The most commonly used inversion schemes are based on the classical linear slip theory (LST), in which the effects of the fractures are represented by a real-valued diagonal excess compliance matrix. To account for the effects of wave-induced fluid pressure diffusion (FPD) between fractures and their embedding background, several authors have shown that this matrix should be complex-valued and frequency-dependent. However, these approaches neglect the effects of FPD on the coupling between orthogonal deformations of the rock. With this motivation, we considered a fracture model based on a sequence of alternating poroelastic layers of finite thickness representing the background and the fractures, and derived analytical expressions for the corresponding excess compliance matrix. We evaluated this matrix for a wide range of background parameters to quantify the magnitude of its coefficients not accounted for by the classical LST and to determine how they are affected by FPD. We estimated the relative errors in the computation of anisotropic seismic velocity and attenuation associated with the LST approach. Our analysis showed that, in some cases, considering the simplified excess compliance matrix may lead to an incorrect representation of the anisotropic response of the probed fractured rock.

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

Geophysics ◽

10.1190/geo2015-0173.1 ◽

2016 ◽

Vol 81 (2) ◽

pp. D169-D181 ◽

Cited By ~ 11

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.

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Fracture connectivity can reduce the velocity anisotropy of seismic waves

Geophysical Journal International ◽

10.1093/gji/ggx159 ◽

2017 ◽

Vol 210 (1) ◽

pp. 223-227 ◽

Cited By ~ 11

Author(s):

J. Germán Rubino ◽

Eva Caspari ◽

Tobias M. Müller ◽

Klaus Holliger

Keyword(s):

Hydraulic Properties ◽

Seismic Waves ◽

Fractured Rock ◽

Fluid Pressure ◽

Fracture Networks ◽

Velocity Anisotropy ◽

Rock Formations ◽

Pressure Diffusion ◽

Static Elasticity ◽

Fracture Fluid

Abstract The degree of connectivity of fracture networks is a key parameter that controls the hydraulic properties of fractured rock formations. The current understanding is that this parameter does not alter the effective elastic properties of the probed medium and, hence, cannot be inferred from seismic data. However, this reasoning is based on static elasticity, which neglects dynamic effects related to wave-induced fluid pressure diffusion (FPD). Using a numerical upscaling procedure based on the theory of quasi-static poroelasticity, we provide the first evidence to suggest that fracture connectivity can reduce significantly velocity anisotropy in the seismic frequency band. Analyses of fluid pressure fields in response to the propagation of seismic waves demonstrate that this reduction of velocity anisotropy is not due to changes of the geometrical characteristics of the probed fracture networks, but rather related to variations of the stiffening effect of the fracture fluid in response to FPD. These results suggest that accounting for FPD effects may not only allow for improving estimations of geometrical and mechanical properties of fracture networks, but may also provide information with regard to the effective hydraulic properties.

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Anisotropic Porochemoelectroelastic Solution for an Inclined Wellbore Drilled in Shale

Journal of Applied Mechanics ◽

10.1115/1.4007925 ◽

2013 ◽

Vol 80 (2) ◽

Cited By ~ 9

Author(s):

Minh H. Tran ◽

Younane N. Abousleiman

Keyword(s):

Porous Media ◽

Fluid Pressure ◽

Transversely Isotropic ◽

Biological Tissues ◽

Analytical Models ◽

Combined Effects ◽

Saturated Porous Media ◽

Stress Distributions ◽

Shale Formations ◽

Electrically Charged

The porochemoelectroelastic analytical models have been used to describe the response of chemically active and electrically charged saturated porous media such as clay soils, shales, and biological tissues. However, existing studies have ignored the anisotropic nature commonly observed on these porous media. In this work, the anisotropic porochemoelectroelastic theory is presented. Then, the solution for an inclined wellbore drilled in transversely isotropic shale formations subjected to anisotropic far-field stresses with time-dependent down-hole fluid pressure and fluid activity is derived. Numerical examples illustrating the combined effects of porochemoelectroelastic behavior and anisotropy on wellbore responses are also included. The analysis shows that ignoring either the porochemoelectroelastic effects or the formation anisotropy leads to inaccurate prediction of the near-wellbore pore pressure and effective stress distributions. Finally, wellbore responses during a leak-off test conducted soon after drilling are analyzed to demonstrate the versatility of the solution in simulating complex down-hole conditions.

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Finite-Difference Modeling and Characteristics Analysis of Love Waves in Anisotropic-Viscoelastic Media

Bulletin of the Seismological Society of America ◽

10.1785/0120200372 ◽

2021 ◽

Author(s):

Shichuan Yuan ◽

Zhenguo Zhang ◽

Hengxin Ren ◽

Wei Zhang ◽

Xianhai Song ◽

...

Keyword(s):

Finite Difference ◽

Phase Velocity ◽

Velocity Dispersion ◽

Love Waves ◽

Velocity Anisotropy ◽

Viscoelastic Media ◽

Phase Velocities ◽

Phase Velocity Dispersion ◽

Anisotropic Elastic ◽

Attenuation Anisotropy

ABSTRACT In this study, the characteristics of Love waves in viscoelastic vertical transversely isotropic layered media are investigated by finite-difference numerical modeling. The accuracy of the modeling scheme is tested against the theoretical seismograms of isotropic-elastic and isotropic-viscoelastic media. The correctness of the modeling results is verified by the theoretical phase-velocity dispersion curves of Love waves in isotropic or anisotropic elastic or viscoelastic media. In two-layer half-space models, the effects of velocity anisotropy, viscoelasticity, and attenuation anisotropy of media on Love waves are studied in detail by comparing the modeling results obtained for anisotropic-elastic, isotropic-viscoelastic, and anisotropic-viscoelastic media with those obtained for isotropic-elastic media. Then, Love waves in three typical four-layer half-space models are simulated to further analyze the characteristics of Love waves in anisotropic-viscoelastic layered media. The results show that Love waves propagating in anisotropic-viscoelastic media are affected by both the anisotropy and viscoelasticity of media. The velocity anisotropy of media causes substantial changes in the values and distribution range of phase velocities of Love waves. The viscoelasticity of media leads to the amplitude attenuation and phase velocity dispersion of Love waves, and these effects increase with decreasing quality factors. The attenuation anisotropy of media indicates that the viscoelasticity degree of media is direction dependent. Comparisons of phase velocity ratios suggest that the change degree of Love-wave phase velocities due to viscoelasticity is much less than that caused by velocity anisotropy.

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Time Constraints on Seepage Through Fractured Regions on the Vestnesa Ridge off the W-Svalbard Coast

10.5194/egusphere-egu21-11489 ◽

2021 ◽

Author(s):

Hariharan Ramachandran ◽

Andreia Plaza-Faverola ◽

Hugh Daigle ◽

Stefan Buenz

Keyword(s):

Fluid Flow ◽

Effective Stress ◽

Gas Hydrate ◽

Fluid Pressure ◽

Fracture Network ◽

The Arctic ◽

Stability Zone ◽

Methane Seepage ◽

Carbonate Formation ◽

Hydrate Stability

Evidences of subsurface fluid flow-driven fractures (from seismic interpretation) are quite common at Vestnesa Ridge (around 79&#186;N in the Arctic Ocean), W-Svalbard margin. Ultimately, the fractured systems have led to the formation of pockmarks on the seafloor. At present day, the eastern segment of the ridge has active pockmarks with continuous methane seep observations in sonar data. The pockmarks in the western segment are considered inactive or to seep at a rate that is harder to identify. The ridge is at ~1200m water depth with the base of the gas hydrate stability zone (GHSZ) at ~200m below the seafloor. Considerable free gas zone is present below the hydrates. Besides the obvious concern of amount and rates of historic methane seeping into the ocean biosphere and its associated effects, significant gaps exist in the ability to model the processes of flow of methane through this faulted and fractured region. Our aim is to highlight the interactions between physical flow, geomechanics and geological control processes that govern the rates and timing of methane seepage.For this purpose, we performed numerical fluid flow simulations. We integrate fundamental mass and component conservation equations with a phase equilibrium approach accounting for hydrate phase boundary effects to simulate the transport of gas from the base of the GHSZ through rock matrix and interconnected fractures until the seafloor. The relation between effective stress and fluid pressure is considered and fractures are activated once the effective stress exceeds the tensile limit. We use field data (seismic, oedometer tests on calypso cores, pore fluid pressure and temperature) to constrain the range of validity of various flow and geomechanical parameters in the simulation (such as vertical stress, porosity, permeability, saturations).Preliminary results indicate fluid overpressure greater than 1.5 MPa is required to initiate fractures at the base of the gas hydrate stability zone for the investigated system. Focused fluid flow occurs through the narrow fracture networks and the gas reaches the seafloor within 1 day. The surrounding regions near the fracture network exhibit slower seepage towards the seafloor, but over a wider area. Advective flux through the less fractured surrounding regions, reaches the seafloor within 15 years and a diffusive flux reaches within 1200 years. These times are controlled by the permeability of the sediments and are retarded further due to considerable hydrate/carbonate formation during vertical migration. Next course of action includes constraining the methane availability at the base of the GHSZ and estimating its impact on seepage behavior.

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Analytical Models for Gravitating Radiating Systems

Advances in Mathematical Physics ◽

10.1155/2015/274251 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7 ◽

Cited By ~ 3

Author(s):

B. P. Brassel ◽

S. D. Maharaj ◽

G. Govender

Keyword(s):

Consistency Condition ◽

Fluid Pressure ◽

Nonlinear Ordinary Differential Equation ◽

Variable Coefficients ◽

Analytical Models ◽

Heat Conducting ◽

Elementary Functions ◽

Complex Transformation ◽

All Solutions ◽

Metric Functions

We analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. Several new classes of solutions are found to the governing equation by imposing various forms on one of the potentials. Interestingly, a complex transformation leads to an exact solution with only real metric functions. All solutions are written in terms of elementary functions. We demonstrate graphically that the fluid pressure, energy density, and heat flux are well behaved for the model, and the model is consistent with a core-envelope framework.

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A Sensitivity Analysis for Effective Parameters on 2D Fracture-Network Permeability

SPE Reservoir Evaluation & Engineering ◽

10.2118/113618-pa ◽

2009 ◽

Vol 12 (03) ◽

pp. 455-469 ◽

Cited By ~ 15

Author(s):

Alireza Jafari ◽

Tayfun Babadagli

Keyword(s):

Sensitivity Analysis ◽

Experimental Design ◽

Fractured Reservoirs ◽

Fracture Network ◽

Static Model ◽

Naturally Fractured Reservoirs ◽

Single Fracture ◽

Data Sets ◽

Fracture Networks ◽

Fractal Characteristics

Summary Fracture-network mapping and estimation of its permeability constitute two major steps in static-model preparation of naturally fractured reservoirs. Although several different analytical methods were proposed in the past for calculating fracture-network permeability (FNP), different approaches are still needed for practical use. We propose a new and practical approach to estimate FNP using statistical and fractal characteristics of fracture networks. We also provide a detailed sensitivity analysis to determine the relative importance of fracture-network parameters on the FNP in comparison to single-fracture conductivity using an experimental-design approach. The FNP is controlled by many different fracture-network parameters such as fracture length, density, orientation, aperture, and single-fracture connectivity. Five different 2D fracture data sets were generated for random and systematic orientations. In each data set, 20 different combinations of fracture density and length for different orientations were tested. For each combination, 10 different realizations were generated. The length was considered as constant and variable. This yielded a total of 1,000 trials. The FNPs were computed through a commercial discrete-fracture-network (DFN) modeling simulator for all cases. Then, we correlated different statistical and fractal characteristics of the networks to the measured FNPs using multivariable-regression analysis. Twelve fractal (sandbox, box counting, and scanline fractal dimensions) and statistical (average length, density, orientation, and connectivity index) parameters were tested against the measured FNP for synthetically generated fracture networks for a wide range of fracture properties. All cases were above the percolation threshold to obtain a percolating network, and the matrix effect was neglected. The correlation obtained through this analysis using four data sets was tested on the fifth one with known permeability for verification. High-quality match was obtained. Finally, we adopted an experimental-design approach to identify the most-critical parameters on the FNP for different fracture-network types. The results are presented as Pareto charts. It is believed that the new method and results presented in this paper will be useful for practitioners in static-model development of naturally fractured reservoirs and will shed light on further studies on modeling and understanding the transmissibility characteristics of fracture networks. It should be emphasized that this study was conducted on 2D fracture networks and could be extended to 3D models. This, however, requires further algorithm development to use 2D fractal characteristics for 3D systems and/or development of fractal measurement techniques for a 3D system. This study will provide a guideline for this type of research.

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Fracture network connectivity devolution monitoring using transdimensional data assimilation

10.5194/egusphere-egu21-8400 ◽

2021 ◽

Author(s):

Márk Somogyvári ◽

Mohammadreza Jalali ◽

Irina Engelhardt ◽

Sebastian Reich

Keyword(s):

Data Assimilation ◽

Weather Forecasting ◽

Fractured Reservoirs ◽

Fracture Network ◽

Model Parameters ◽

Fractured Aquifer ◽

Dynamic Changes ◽

Transport Pathways ◽

Fractured Aquifers ◽

Rock Characterization

In fractured aquifers, the permeability of open fractures could change over time due to precipitation effects and hydrothermal mineral growth. These processes could lead to the clogging of individual fractures and to the complete rearrangement of flow and transport pathways. Existing fractured rock characterization techniques often neglect this dynamicity and treat the reconstruction as a static inversion problem. The dynamic changes then later added to the model as an independent forward modeling task. In this research we provide a new data assimilation-based methodology to monitor and predict the dynamic changes of fractured aquifers due to mineralization in a quasi-real-time manner.We formulate the inverse problem as a dynamic &#8216;hidden Markov process&#8217; where the underlying model dynamicity is just partly known. Data assimilation methods are specifically designed to model such systems with strong uncertainties. A typical example for such problems is weather forecasting, where the combination of nonlinear processes and the partial observations make the forecasting challenging. To handle the strong random behavior, data assimilation approaches use stochastic algorithms. In this study we combine DFN-based stochastic aquifer reconstruction techniques with data assimilation algorithms to provide a dynamic inverse modelling framework for fractured reservoirs. We use the transdimensional DFN inversion of (Somogyv&#225;ri et al., 2017) to initialize the data assimilation. This method uses a transdimensional MCMC approach to identify the most probable DFN geometries given the observations. Because the method is transdimensional it can adjust the number of model parameters, the number of fractures within the DFN. We developed this idea further by enhancing a particle filter algorithm with transdimensional model updates, allowing us to infer DFN models with changing fracture numbers.We demonstrate the applicability of this new approach on outcrop-based synthetic fractured aquifer models. To create a dynamic DFN example, we simulate solute transport in a 2-D fracture network model using an advection-dispersion algorithm. We simulate fracture sealing in a stochastic way: we define a limit concentration above which the fractures could seal with a predefined probability at any timestep. At the initial timestep, a hydraulic tomography experiment is performed to capture the initial aquifer structure, which is then reconstructed by the transdimensional DFN inversion. At predefined timesteps hydraulic tests are performed at different parts of the aquifer, to obtain information about new state of the synthetic model. These observations are then processed by the data assimilation algorithm, which updates the underlying DFN models to better fit to the observations.

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