Multiple cracks in VTI rocks: Effective properties and fracture characterization

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. D81-D91 ◽  
Author(s):  
Vladimir Grechka
Keyword(s):  
Host Rock ◽  
Effective Properties ◽  
Crack Density ◽  
Transversely Isotropic ◽  
Multiple Cracks ◽  
Multiple Fracture ◽  
Fracture Characterization ◽  
Effective Media ◽  
Important Exception ◽  
Sonic Logs

The existing fracture-characterization techniques are based on assuming the unfractured host rock either to be isotropic or the magnitudes of both the background and crack-induced anisotropies to be small. I relax both assumptions and examine the effective media caused by fractures with realistic (not small) crack densities in a strongly anisotropic, primarily transversely isotropic (TI) host rock. The analysis of penny-shaped cracks in the noninteraction approximation (NIA) reveals the dependence of their excess fracture compliance tensors on the orientation of the background symmetry axis. As a result of this dependence, the excess fracture compliance tensor generally becomes rotationally noninvariant even when the cracks are circular. One of the consequences of this complication (compared to the background isotropy) is a reduction of symmetry from TI to monoclinic resulting from the presence of a single oriented fracture set. Verti–cal dry cracks in a vertically transversely isotropic (VTI) host constitute an important exception to this general rule.The effective symmetry for this arrangement is approximately orthorhombic (or orthotropic) even in the presence of multiple fracture sets that have arbitrary azimuths. I perform finite-element simulations on the so-called digital rocks to verify both the proximity of effective symmetry to orthotropy and the accuracy of the NIA up to the crack density of 0.15. Multiple sets of dry vertical cracks in a VTI host not only result in nearly orthorhombic effective symmetry but also their cumulative influence is equivalent to that of just two orthogonal (or principal) fracture sets. The possibility of replacing multiple fracture sets with two orthogonal ones paves the way for their characterization. The inverse problem of estimating the parameters of two orthogonal crack systems in a VTI background from the effective elasticity, however, is known to be nonunique. I suggest overcoming its ambiguity by combining 3D, wide-azimuth, multicomponent seismic data with sonic logs.

Feasibility of seismic characterization of multiple fracture sets

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1399-1407 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Host Rock ◽  
Fractured Reservoirs ◽  
Transversely Isotropic ◽  
Naturally Fractured Reservoirs ◽  
Multiple Fracture ◽  
Stiffness Tensor ◽  
Fracture Detection ◽  
Estimation Of Parameters ◽  
Fracture Characterization ◽  
Underlying Assumption

Estimation of parameters of multiple fracture sets is often required for successful exploration and development of naturally fractured reservoirs. The goal of this paper is to determine the maximum number of fracture sets of a certain rheological type which, in principle, can be resolved from seismic data. The main underlying assumption is that an estimate of the complete effective stiffness tensor has been obtained, for example, from multiazimuth, multicomponent surface seismic and vertical seismic profiling (VSP) data. Although typically only a subset of the stiffness elements (or some of their combinations) may be available, this study helps to establish the limits of seismic fracture‐detection algorithms. The number of uniquely resolvable fracture systems depends on the anisotropy of the host rock and the rheology and orientation of the fractures. Somewhat surprisingly, it is possible to characterize fewer vertical fracture sets than dipping ones, even though in the latter case the fracture dip has to be found from the data. For the simplest, rotationally invariant fractures embedded in either isotropic or transversely isotropic with a vertical symmetry axis (VTI) host rock, the stiffness tensor can be inverted for up to two vertical or four dipping fracture sets. In contrast, only one fracture set of the most general (microcorrugated) type, regardless of its orientation, is constrained by the effective stiffnesses. These results can be used to guide the development of seismic fracture‐characterization algorithms that should address important practical issues of data acquisition, processing, and inversion for particular fracture models.

Seismic inversion for the parameters of two orthogonal fracture sets in a VTI background medium

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 292-299 ◽  
Author(s):  
Andrey Bakulin ◽  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Seismic Data ◽  
Fractured Reservoirs ◽  
Crack Density ◽  
Transversely Isotropic ◽  
Seismic Inversion ◽  
Naturally Fractured Reservoirs ◽  
Multiple Fracture ◽  
Effective Parameters ◽  
Wide Range

Characterization of naturally fractured reservoirs often requires estimating parameters of multiple fracture sets that develop in an anisotropic background. Here, we discuss modeling and inversion of the effective parameters of orthorhombic models formed by two orthogonal vertical fracture sets embedded in a VTI (transversely isotropic with a vertical symmetry axis) background matrix. Although the number of the microstructural (physical) medium parameters is equal to the number of effective stiffness elements (nine), we show that for this model there is an additional relation (constraint) between the stiffnesses or Tsvankin's anisotropic coefficients. As a result, the same effective orthorhombic medium can be produced by a wide range of equivalent models with vastly different fracture weaknesses and background VTI parameters, and the inversion of seismic data for the microstructural parameters is nonunique without additional information. Reflection moveout of PP‐ and PS‐waves can still be used to find the fracture orientation and estimate (in combination with the vertical velocities) the differences between the normal and shear weaknesses of the fracture sets, as well as the background anellipticity parameter ηb. Since for penny‐shaped cracks the shear weakness is close to twice the crack density, seismic data can help to identify the dominant fracture set, although the crack densities cannot be resolved individually. If the VTI symmetry of the background is caused by intrinsic anisotropy (as is usually the case for shales), it may be possible to determine at least one background anisotropic coefficient from borehole or core measurements. Then seismic data can be inverted for the fracture weaknesses and the rest of the background parameters. Therefore, seismic characterization of reservoirs with multiple fracture sets and anisotropic background is expected to give ambiguous results, unless the input data include measurements made on different scales (surface seismic, borehole, cores).

Seismic characterization of multiple fracture sets: Does orthotropy suffice?

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. D93-D105 ◽  
Author(s):  
Vladimir Grechka ◽  
Mark Kachanov
Keyword(s):  
Finite Element ◽  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Multiple Fracture ◽  
P Waves ◽  
Fracture Characterization ◽  
Surface Reflection ◽  
Reflection Data ◽  
Effective Media ◽  
Independent Parameters

As geophysicists rely increasingly on effective media theories to characterize naturally fractured reservoirs, they become more and more interested in evaluating the accuracy of different theories, estimating their limits of applicability, and assessing their usefulness for practice. With this in mind, we compare two popular seismological theories of Hudson and Schoenberg with the theory of Kachanov developed in the context of mechanics of materials. By performing finite-element simulations of effective media for models that contain several sets of nonintersecting, circular, vertical fractures embedded in otherwise isotropic host rock, we examine the accuracy of these theories. Our numeric study reveals that predictions of both the first- and second-order Hudson's theories are typically inferior to those of others, especially when the fractures are dry. While, on average, the theories of Schoenberg and Kachanov fit finite-element computations with comparable accuracy, the latter appears to be more useful for fracture characterization. The reason is thatit correctly predicts the proximity of crack-induced anisotropy to orthotropy, whereas the other theories do not. Kachanov's results not only yield approximate effective orthotropy regardless of the number of fracture sets, their crack densities, and orientations, but they also lead to a substantially reduced number of independent parameters that govern the effective stiffnesses. This number is only four for dry cracks, compared to nine required for general orthorhombic media. These four quantities can be chosen as two Lamé constants of the isotropic background and two principal crack densities. If fractures are filled with a compressible fluid, the number of independent parameters increases. After numeric verification of the accuracy of crack-induced orthotropy, we invert the NMO ellipses and zero-offset traveltimes of P-waves and two split shear waves for the parameters characterizing multiple fracture sets. Our inversion reveals the fracture parameters that can be unambiguously estimated from multiazimuth, multicomponent surface reflection data.

Interpretation of borehole sonic measurements acquired in vertical transversely isotropic formations penetrated by vertical wells

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. D187-D202 ◽  
Author(s):  
Elsa Maalouf ◽  
Carlos Torres-Verdín
Keyword(s):  
Transversely Isotropic ◽  
Depth Interval ◽  
Bias Error ◽  
Layer By Layer ◽  
Spatial Averaging ◽  
Vertical Wells ◽  
Frequency Dependent ◽  
Sensitivity Functions ◽  
Stiffness Coefficients ◽  
Sonic Logs

Detecting vertical transversely isotropic (VTI) formations and quantifying the magnitude of anisotropy are fundamental for describing organic mudrocks. Methods used to estimate stiffness coefficients of VTI formations often provide discontinuous or spatially averaged results over depth intervals where formation layers are thinner than the receiver aperture of acoustic tools. We have developed an inversion-based method to estimate stiffness coefficients of VTI formations that are continuous over the examined depth interval and that are mitigated for spatial averaging effects. To estimate the coefficients, we use logs of frequency-dependent compressional, Stoneley, and quadrupole/flexural modes measured with wireline or logging-while-drilling (LWD) instruments in vertical wells penetrating horizontal layers. First, we calculate the axial sensitivity functions of borehole sonic modes to stiffness coefficients; next, we use the sensitivity functions to estimate the stiffness coefficients of VTI layers sequentially from frequency-dependent borehole sonic logs. Because sonic logs exhibit spatial averaging effects, we deaverage the logs by calculating layer-by-layer slownesses of formations prior to estimating stiffness coefficients. The method is verified with synthetic models of homogeneous and thinly bedded formations constructed from field examples of organic mudrocks. Results consist of layer-by-layer estimates of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. We observe three sources of error in the estimated coefficients: (1) bias error originating from deaveraging the sonic logs prior to the sequential inversion, (2) error propagated during the sequential inversion, and (3) error associated with noisy slowness logs. We found that the relative bias and uncertainty of the estimated coefficients are largest for [Formula: see text] and [Formula: see text] because borehole modes exhibit low sensitivity to these two coefficients. The main advantage of our method is that it mitigates spatial averaging effects of sonic logs, while at the same time it detects the presence of anisotropic layers and yields continuous estimations of stiffness coefficients along the depth interval of interest.

scholarly journals Precise inversion of logged slownesses for elastic parameters in a gas shale formation

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. B197-B206 ◽  
Author(s):  
Douglas E. Miller ◽  
Steve A. Horne ◽  
John Walsh
Keyword(s):  
Inclination Angle ◽  
Vertical Direction ◽  
Transversely Isotropic ◽  
Gas Shale ◽  
Elastic Parameters ◽  
Associated Production ◽  
Sonic Log ◽  
Inclination Angles ◽  
Shale Formation ◽  
Sonic Logs

Dipole sonic log data recorded in a vertical pilot well and the associated production well are analyzed over a [Formula: see text]-ft section of a North American gas shale formation. The combination of these two wells enables angular sampling in the vertical direction and over a range of inclination angles from 54° to 90°. Dipole sonic logs from these wells show that the formation’s average properties are, to a very good approximation, explained by a transversely isotropic medium with a vertical symmetry axis and with elastic parameters satisfying [Formula: see text], but inconsistent with the additional ANNIE relation ([Formula: see text]). More importantly, these data clearly show that, at least for fast anisotropic formations such as this gas shale, sonic logs measure group slownesses for propagation with the group angle equal to the borehole inclination angle. Conversely, the data are inconsistent with an interpretation that they measure phase slownesses for propagation with the phase angle equal to the borehole inclination angle.

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