Elastic properties of rocks with multiple sets of fractures

Nichols, David E.; Muir, Francis; Schoenberg, Michael

doi:10.1190/1.1889682

Cited by 45 publications

(27 citation statements)

References 5 publications

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“…Additional difficulty occurs when one fracture is cut by another fracture. Nichols et al (1989) described the problem of modeling rocks with multiple sets of fractures based on the theory outlined by Schoenberg and Muir (1989). They also showed explicitly how to obtain the resultant compliance tensor for an orthogonal fracture set embedded in an isotropic medium.…”

Section: Modeling Discrete Fracturesmentioning

confidence: 99%

“…For multiple sets of non-orthogonal vertical fractures (Figure 3), Nichols et al (1989) show that the compliance matrix for the equivalent medium is…”

Section: Multiple Sets Of Non-orthogonal Vertical Fracturesmentioning

confidence: 99%

“…This long-wavelength equivalent medium theory was used by Schoenberg and Muir (1989) to derive the effective properties of a finely layered medium.…”

Section: Modeling Discrete Fracturesmentioning

confidence: 99%

“…To accurately model the response of seismic waves through boundaries in an elastic solid, Muir et al (1992) used the idea of Schoenberg and Muir (1989) to represent stiffness (or compliance) coefficients in a grid cell traversed by a fracture that is in some way the 'average' of a stack of parallel layers. Later yet, used the same idea together with a linear slip model for the boundary to implement discrete or single fracture(s) in a finite difference scheme.…”

Section: Modeling Discrete Fracturesmentioning

confidence: 99%

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Characterization of in-Situ Stress and Permeability in Fractured Reservoirs

Burns¹,

Toksoz²

2005

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During the past six months we have adapted our 3-D elastic, anisotropic finite difference code by implementing the rotated staggered grid (RSG) method to more accurately represent large contrasts of elastic moduli between the fractures and surrounding formation, and applying the perfectly matched layer (PML) absorbing boundary condition to minimize boundary reflections. Two approaches for estimating fracture spacing from scattered seismic energy were developed. The first relates notches in the amplitude spectra of the scattered wavefield to the dominant fracture spacing that caused the scattering. The second uses conventional FK filtering to isolate the backscattered signals and then recovers an estimate of the fracture spacing from the dominant wavelength of those signals. Both methods were tested on synthetic data and then applied to the Emilio field data. The spectral notch method estimated the Emilio fracture spacing to be about 30 to 40 m, while the FK method found fracture spacing of about 48 to 53 m. We continue to work on two field data sets from fractured carbonate reservoirs provided by our industry sponsors-the offshore Emilio Field data (provided by ENI-AGIP), and an onshore reservoir from the Middle East (provided by Shell). Calibration data in the form of well logs and previous fracture studies are available for both data sets. In previous reports we showed the spatial distribution fractures in the Emilio Field based on our calculated scattering index values. To improve these results we performed a map migration of all the scattering indices. The results of this migration process show a very strong correlation between the spatial distribution and orientation of our estimated fracture distribution and the fault system in the field. We observe that the scattering index clusters tend to congregate around the fault zones, particularly near multiple faults and at fault tips. We have also processed a swath of data from the second data set (the onshore carbonate field). FMI data are available from a number of wells for comparison to our seismic scattering analysis results. The agreement is very good, providing confidence that these methods can be applied to land seismic data that do not have the ideal azimuthal coverage. I. Executive SummaryThe purpose of this project is to develop and implement large-scale numerical models to quantify the effects of fracture parameter variations on seismic reflection signals and in-situ stress variations on flexural modes in boreholes. These models will be used as the basis of data analysis and inversion routines for estimating the heterogeneous fracture distribution in fractured reservoirs from seismic and borehole field data.Fracture property distributions estimated from seismic data will be used to estimate the permeability tensor in the reservoir for input to reservoir simulators.During the past six months we have adapted our 3-D elastic, anisotropic finite difference code in two ways. First, we implemented the rotated staggered grid (RSG) method to more ac...

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Section: Modeling Discrete Fracturesmentioning

confidence: 99%

“…For multiple sets of non-orthogonal vertical fractures (Figure 3), Nichols et al (1989) show that the compliance matrix for the equivalent medium is…”

Section: Multiple Sets Of Non-orthogonal Vertical Fracturesmentioning

confidence: 99%

“…This long-wavelength equivalent medium theory was used by Schoenberg and Muir (1989) to derive the effective properties of a finely layered medium.…”

Section: Modeling Discrete Fracturesmentioning

confidence: 99%

Section: Modeling Discrete Fracturesmentioning

confidence: 99%

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Characterization of in-Situ Stress and Permeability in Fractured Reservoirs

Burns¹,

Toksoz²

2005

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“…A vertical and a horizontal fracture, with the same fracture compliances as in the previous example, are considered within the closed surface in Figure 2(a). We use the effective medium theory (Nichols et al, 1989) to represent the intersection point of two fractures. Figure 5 the non-linear term, and using non-linear imaging condition, respectively.…”

Section: Intersecting Orthogonal Fracturesmentioning

confidence: 99%

Non-linear imaging condition to image fractures as non-welded interfaces

Minato

Ghose

2014

SEG Technical Program Expanded Abstracts 2014

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SUMMARYHydraulic properties of a fractured reservoir are often controlled by large fractures. In order to seismically detect and characterize them, a high-resolution imaging method is necessary. We apply a non-linear imaging condition to image fractures, considered as non-welded interfaces. We derive the imaging condition from the general correlation-type representation theorem, assuming compliances to be real-valued functions. We investigate the P-wave image due to P-wave sources and the effect of source illumination. We present here numerical modeling results for (1) a single dry fracture, (2) orthogonally intersecting fractures, and (3) deviated multiple fractures in a multi-layered subsurface. Our results show that the nonlinear terms in the imaging condition help to cancel the artefacts appearing in case of conventional imaging condition, and improve the resolution of the final image. For a multi-layered model, the one-sided source illumination from the earth's surface can image the multiple fractures. However, an incomplete source illumination restricts the removal of all the artefacts. In this case, installing additional borehole sources can greatly improve the resolution of the fracture distribution.

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Isolating Fracture-Induced Anisotropy From Background Anisotropy

Hood

Mignogna

1993

Review of Progress in Quantitative Nondestructive Evaluation

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Elastic properties of rocks with multiple sets of fractures

Cited by 45 publications

References 5 publications

Characterization of in-Situ Stress and Permeability in Fractured Reservoirs

Characterization of in-Situ Stress and Permeability in Fractured Reservoirs

Non-linear imaging condition to image fractures as non-welded interfaces

Isolating Fracture-Induced Anisotropy From Background Anisotropy

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