scholarly journals Parameterization of elastic stress sensitivity in shales

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA147-WA155 ◽  
Author(s):  
Marina Pervukhina ◽  
Boris Gurevich ◽  
Pavel Golodoniuc ◽  
David N. Dewhurst
Keyword(s):  
Elastic Properties ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Bedding Plane ◽  
Stress Sensitivity ◽  
Crack Orientation ◽  
Fluid Identification ◽  
Orientation Anisotropy ◽  
Characteristic Pressure ◽  
Stress Dependency

Stress dependency and anisotropy of dynamic elastic properties of shales is important for a number of geophysical applications, including seismic interpretation, fluid identification, and 4D seismic monitoring. Using Sayers-Kachanov formalism, we developed a new model for transversely isotropic (TI) media that describes stress sensitivity behavior of all five elastic coefficients using four physically meaningful parameters. The model is used to parameterize elastic properties of about 20 shales obtained from laboratory measurements and the literature. The four fitting parameters, namely, specific tangential compliance of a single crack, ratio of normal to tangential compliances, characteristic pressure, and crack orientation anisotropy parameter, show moderate to good correlations with the depth from which the shale was extracted. With increasing depth, the tangential compliance exponentially decreases. The crack orientation anisotropy parameter broadly increases with depth for most of the shales, indicating that cracks are getting more aligned in the bedding plane. The ratio of normal to shear compliance and characteristic pressure decreases with depth to 2500 m and then increases below this to 3600 m. The suggested model allows us to evaluate the stress dependency of all five elastic compliances of a TI medium, even if only some of them are known. This may allow the reconstruction of the stress dependency of all five elastic compliances of a shale from log data, for example.

Relationships between the anisotropy parameters for transversely isotropic mudrocks

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. MR195-MR203
Author(s):  
Fuyong Yan ◽  
Lev Vernik ◽  
De-Hua Han
Keyword(s):  
Elastic Properties ◽  
Seismic Anisotropy ◽  
Measurement Data ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
The Other ◽  
Quality Analysis ◽  
Directional Bias ◽  
Empirical Relations ◽  
Anisotropy Parameters

Studying the empirical relations between seismic anisotropy parameters is important for the simplification and practical applications of seismic anisotropy. The elastic properties of mudrocks are often described by transverse isotropy. Knowing the elastic properties in the vertical and horizontal directions, a sole oblique anisotropy parameter determines the pattern of variation of the elastic properties of a transversely isotropic (TI) medium in all of the other directions. The oblique seismic anisotropy parameter [Formula: see text], which determines seismic reflection moveout behavior, is important in anisotropic seismic data processing and interpretation. Compared to the other anisotropy parameters, the oblique anisotropy parameter is more sensitive to the measurement error. Although, theoretically, only one oblique velocity is needed to determine the oblique anisotropy parameter, the uncertainty can be greatly reduced if multiple oblique velocities in different directions are measured. If a mudrock is not a perfect TI medium but it is expediently treated as one, then multiple oblique velocity measurements in different directions should lead to a more representative approximation of [Formula: see text] or [Formula: see text] because the directional bias can be reduced. Based on a data quality analysis of the laboratory seismic anisotropy measurement data from the literature, we found that there are strong correlations between the oblique anisotropy parameter and the principal anisotropy parameters when data points of more uncertainty are excluded. Examples of potential applications of these empirical relations are discussed.

scholarly journals Effective elastic properties of transversely isotropic materials with concave pores

2021 ◽  
Vol 153 ◽  
pp. 103665
Author(s):  
K. Du ◽  
L. Cheng ◽  
J.F. Barthélémy ◽  
I. Sevostianov ◽  
A. Giraud ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Transversely Isotropic ◽  
Effective Elastic Properties ◽  
Isotropic Materials ◽  
Transversely Isotropic Materials

scholarly journals The elastic properties of composites reinforced by a transversely isotropic random fibre-network

2019 ◽  
Vol 208 ◽  
pp. 33-44 ◽  
Author(s):  
Xiude Lin ◽  
Hanxing Zhu ◽  
Xiaoli Yuan ◽  
Zuobin Wang ◽  
Stephane Bordas
Keyword(s):  
Elastic Properties ◽  
Transversely Isotropic ◽  
Fibre Network ◽  
Random Fibre ◽  
Isotropic Random ◽  
Properties Of Composites

scholarly journals Stress Dependency of Shale Elastic Properties: Measurements, Modelling and Prediction

2010 ◽  
Vol 2010 (1) ◽  
pp. 1-4
Author(s):  
Marina Pervukhina ◽  
Boris Gurevich ◽  
David N. Dewhurst ◽  
Pavel Golodoniuc
Keyword(s):  
Elastic Properties ◽  
Stress Dependency

scholarly journals Transformation to zero offset in transversely isotropic media

Geophysics ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 947-963 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Ray Tracing ◽  
Impulse Response ◽  
Homogeneous Medium ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Amplitude Distribution ◽  
Isotropic Media ◽  
Zero Offset ◽  
Vertical Inhomogeneity

Nearly all dip‐moveout correction (DMO) implementations to date assume isotropic homogeneous media. Usually, this has been acceptable considering the tremendous cost savings of homogeneous isotropic DMO and considering the difficulty of obtaining the anisotropy parameters required for effective implementation. In the presence of typical anisotropy, however, ignoring the anisotropy can yield inadequate results. Since anisotropy may introduce large deviations from hyperbolic moveout, accurate transformation to zero‐offset in anisotropic media should address such nonhyperbolic moveout behavior of reflections. Artley and Hale’s v(z) ray‐tracing‐based DMO, developed for isotropic media, provides an attractive approach to treating such problems. By using a ray‐tracing procedure crafted for anisotropic media, I modify some aspects of their DMO so that it can work for v(z) anisotropic media. DMO impulse responses in typical transversely isotropic (TI) models (such as those associated with shales) deviate substantially from the familiar elliptical shape associated with responses in homogeneous isotropic media (to the extent that triplications arise even where the medium is homogeneous). Such deviations can exceed those caused by vertical inhomogeneity, thus emphasizing the importance of taking anisotropy into account in DMO processing. For isotropic or elliptically anisotropic media, the impulse response is an ellipse; but as the key anisotropy parameter η varies, the shape of the response differs substantially from elliptical. For typical η > 0, the impulse response in TI media tends to broaden compared to the response in an isotropic homogeneous medium, a behavior opposite to that encountered in typical v(z) isotropic media, where the response tends to be squeezed. Furthermore, the amplitude distribution along the DMO operator differs significantly from that for isotropic media. Application of this anisotropic DMO to data from offshore Africa resulted in a considerably better alignment of reflections from horizontal and dipping reflectors in common‐midpoint gather than that obtained using an isotropic DMO. Even the presence of vertical inhomogeneity in this medium could not eliminate the importance of considering the shale‐induced anisotropy.

Specimen Specific Multiscale Model for the Anisotropic Elastic Properties of Human Cortical Bone Tissue

2007 ◽  
Author(s):  
Justin M. Deuerling ◽  
Weimin Yue ◽  
Alejandro A. Espinoza ◽  
Ryan K. Roeder
Keyword(s):  
Cortical Bone ◽  
Elastic Properties ◽  
Structural Information ◽  
Transversely Isotropic ◽  
Longitudinal Axis ◽  
Orientation Distribution ◽  
Tissue Properties ◽  
Apatite Crystals ◽  
Micromechanical Models ◽  
Anisotropic Elastic

The elastic constants of cortical bone are orthotropic or transversely isotropic depending on the anatomic origin of the tissue. Micromechanical models have been developed to predict anisotropic elastic properties from structural information. Many have utilized microstructural features such as osteons, cement lines and Haversian canals to model the tissue properties [1]. Others have utilized nanoscale features to model the mineralized collagen fibril [2]. Quantitative texture analysis using x-ray diffraction techniques has shown that elongated apatite crystals exhibit a preferred orientation in the longitudinal axis of the bone [3]. The orientation distribution of apatite crystals provides fundamental information influencing the anisotropy of the extracellular matrix (ECM) but has not been utilized in existing micromechanical models.

A homogenization approach for modeling a propagating hydraulic fracture in a layered material

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. MR153-MR162 ◽  
Author(s):  
Egor V. Dontsov
Keyword(s):  
Elastic Properties ◽  
Hydraulic Fracture ◽  
Local Stress ◽  
Transversely Isotropic ◽  
Horizontal Stress ◽  
Layered Material ◽  
Elastic Response ◽  
Effective Parameters ◽  
Fine Mesh ◽  
Minimum Horizontal Stress

Shales are known to have a finely layered structure, which greatly influences the overall material’s response. Incorporating the effect of all these layers explicitly in a hydraulic fracture simulator would require a prohibitively fine mesh. To avoid such a scenario, a suitable homogenization, which would represent the effect of multiple layers in an average sense, should be performed. We consider a sample variation of elastic properties and minimum horizontal stress versus depth that has more than a hundred layers. We evaluate methodologies to homogenize the stress and the elastic properties. The elastic response of a layered material is found to be equivalent to that of a transversely isotropic material, and the explicit relations for the effective parameters are obtained. To illustrate the relevance of the homogenization procedure for hydraulic fracturing, the propagation of a plane strain hydraulic fracture in a finely layered shale is studied. To reduce the complexity of the numerical model, elastic layering is neglected and only the effect of the stress layers is analyzed. The results demonstrate the ability of the homogenized stress model to accurately capture the hydraulic fracture behavior using a relatively coarse mesh. This result is obtained by using a special asymptotic solution at the tip element that accounts for the local stress variation near the tip, which effectively treats the material at the tip element as nonhomogenized.

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