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Formation anisotropy—the directional variation of physical properties—can be the result of either of the following processes:
- Depositional processes (intrinsic)
- Tectonic processes (stress-induced)
Formation anisotropy is evidenced through variations in:
- Rock strength
- Borehole failure
Acoustic logging can provide insight on these variations that assist in anisotropy analysis.
In acoustic/seismic terms, intrinsic anisotropy is structural in nature and is commonly seen as transverse isotropy (TI or vertical transverse isotropy, VTI), in which properties differ in the vertical or horizontal planes, such as in shales or thinly bedded intervals. Stress-induced anisotropy is known as azimuthal anisotropy (or horizontal transverse isotropy, HTI), in which acoustic parameters in a vertical borehole vary with azimuthal orientation, such as the case of fractures parallel to the borehole.
Analyses of in-situ anisotropy (primarily stress induced) are made using direct or derived shear-wave velocity and provide the magnitude and azimuth of anisotropy (i.e., direction of the maximum and minimum horizontal stresses as well as an indication of their difference). Anisotropy analysis has been widely used in solid-earth seismology, geothermal studies, and more recently, in exploration geophysics (see summaries in Crampin and Chastin and Helbig and Thomsen).
In the petroleum industry, these results are used in well design and well placement:
- For optimum reservoir drainage
- To detect and characterize faults and fractures in openhole and cased hole
- To predict borehole instability and sand production,
- For optimizing the design and evaluation of well completions (perforations and hydraulic fracturing) [See section below on Crossed-dipole anisotropy analysis]
Compressional-, shear- and Stoneley-wave properties are each affected, to some degree, by the presence and type of formation anisotropy. While the shear-wave response to azimuthal anisotropy (see the section below on Crossed-dipole anisotropy analysis) and Stoneley waves to VTI anisotropy is well known, the effect on compressional-wave energy is less well characterized. In some situations, information from additional measurements, such as borehole images, dip logs, or both, may be necessary for relating the measured anisotropy to geological features.
Borehole acoustic azimuthal and VTI anisotropy analysis is an advance made possible by the recent introduction of new inversion methods. These methods use the crossed-dipole shear to derive azimuthal anisotropy and the Stoneley wave to derive TI anisotropy in slow formations, or a combination of these modes in deviated wells. A reasonable shear velocity can be derived using inversion techniques with low-frequency Stoneley-wave dispersion which is sensitive to the horizontal shear (in contrast to the dipole’s sensitivity to the vertical shear).
Several new applications have been made possible by anisotropy analysis:
- Identification of formation alteration using dipole-shear dispersion
- Stress estimation,
- Distinguishing between intrinsic and stress-induced anisotropy using dispersion crossover
Crossed-dipole anisotropy analysis
- Shear-wave splitting
- Shear-wave birefringence
- Shear-wave velocity anisotropy
The difference in fast and slow shear-wave slowness provides a measure of the magnitude of anisotropy. Shear-wave splitting is useful for evaluating:
- Bedding planes that intersect the borehole at an angle
- Unbalanced tectonic stresses perpendicular to the borehole
Because the flexural waves induced by dipole-acoustic sources have a directional component, the use of mutually perpendicular (crossed) pairs of dipole transmitters and receivers can detect and measure dipole shear-wave splitting. In isotropic formations, both receiver components (X and Y) will measure the same shear-wave arrival time. However, in an azimuthally anisotropic formation, the shear wave measured at the X-component of the receiver pair will be different from the one measured at the Y-component; one is called the fast shear component, the other, the slow shear component (Fig. 1). To measure the fast and slow shear-wave slowness, four components are measured (Fig. 2):
- Two inline components, X-X and Y-Y
- Two crossline components, XY and YX
Fig. 1 – Diagram illustrating the principle and configuration of crossed-dipole logging: two orthogonal dipole transmitter and receiver array systems. The tool acquires four array data sets, two in-line, XX and YY; two crossed-line, XY and YX, and uses the physics of shear-wave splitting in azimuthally anisotropic rocks to determine the fast-shear polarization azimuth (courtesy of Baker Atlas).
The dipole flexural shear mode is affected by a variety of factors including formation anisotropy. Significant borehole ellipticity (the result of borehole failure or breakouts) and high relative inclination between the borehole and formation may result in erroneous interpretation of dipole-derived anisotropy and must be accounted for during data processing. Additionally, the presence of shale anisotropy in high-angle and horizontal wells, can significantly influence compressional velocity, which must be corrected for this effect.
Initially, mathematical rotation methods originally developed for use in processing surface seismic data were used to determine the fast-wave direction together with the slowness values for the fast and slow shear wave. More recently, inversion methods are being applied to the four data sets to simultaneously determine the azimuth and magnitude of the anisotropy (Fig. 3).
An anisotropy map (Fig. 4) combines the derived average anisotropy and its azimuth to generate an azimuthal image. This display facilitates interpretation by allowing the analyst to quickly assess depth intervals of interest by looking at the brightness, direction, and continuation of the features on the map. The map also facilitates comparison with borehole-image logs. Rose diagrams (Track 3) provide an accurate indication of the fast shear azimuth over each labeled depth interval. The integration of monopole and dipole measurements yields improved estimates of:
- Magnitude of anisotropy
Horizontal stress and hydraulic fracturing
Fractures, both natural and hydraulically induced, develop in relation to regional or localized stress patterns and play a major role in optimizing production and reservoir drainage. An estimate of the magnitude and azimuth of the horizontal stresses surrounding a borehole is needed for accurately placing wells to take advantage of existing fracture patterns and for artificially inducing fracture patterns during well completion through hydraulic stimulation.
The stresses operating on a rock formation are described by a triaxial coordinate system that consists of:
- Two principal horizontal stresses, σx and σy
- A vertical stress component, σz, which is the overburden.
In a borehole, these downhole stresses are expressed as radial components at the borehole wall:
- The vertical component σz
- The radial component σr
- The tangential component σθ
- The (azimuthal) shear component, σrθ
Unbalanced-formation-stress components produce distortion around the borehole (stress-induced anisotropy) that results in shear-wave splitting. The azimuth of the fast-shear wave parallels the direction of maximum horizontal stress and the azimuth of the slow-shear wave parallels the direction of the minimum horizontal stress. Hydraulic-fracture azimuth is parallel to the direction of maximum horizontal stress.
Hydraulic well stimulation consists of perforating an interval, then packing and pressuring these perforations to create fractures behind casing to allow increased production. Crossed-dipole anisotropy logging can estimate the vertical extent of the formation-stress fracture along the borehole and its azimuth in the formation (Fig. 5).
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