Page 282 - Reservoir Geomechanics

263 Wellbore failure and stress determination in deviated wells

The true fast direction is most closely approximated by the apparent fast direction
when the formation axis is close to being perpendicular to the borehole. This corre-
sponds to the results of Sinha, Norris et al.(1994) showing the amount of anisotropy
will also be at a maximum when the formation axis is normal to the borehole.
After applying quality control measures to the dipole sonic data collected in the
SAFOD boreholes, Boness and Zoback (2006) computed the mean fast direction of
the shear waves over 3 m intervals using Bingham statistics (Fisher, Lewis et al. 1987)
because the fast directions are of unit amplitude (i.e. they are not vectors). The nor-
malized eigenvalues give a measure of the relative concentration of orientations about
the mean and we discard any mean fast direction over a 3 m interval with a normalized
eigenvalue of less than 0.9. In the granite at depths shallower than 1920 m in both the
pilot hole and main hole the faults and fractures observed on the image logs show no
preferential orientation. However, there is an excellent correlation between fast direc-
tions in granite section and the direction of S Hmax from a wellbore failure analysis in
the pilot hole (Hickman and Zoback 2004) (Figure 8.19). The fact that the fast shear
waves were found by Boness and Zoback (2006)tobe polarized parallel to the stress
in the shear zones encountered in the two boreholes indicates that this is not structural
anisotropy but is instead directly related to perturbations in the stress state. Active fault
zones are often frequently associated with a localized rotation of S Hmax and a localized
absence of breakouts (see Chapter 11).
Boness (2006) analyzed the electrical image log from 2000 m to 3000 m in discrete
intervals of 10 m to compute the mean bed orientation using Fisher vector distribution
statistics (Fisher, Lewis et al. 1987)to compute the mean bed orientations. We can then
use the theoretical formulation presented above to compute the apparent fast direc-
tion for each discrete 10 m interval that would be observed in the SAFOD borehole
if the shear waves were being polarized with a fast direction parallel to the bedding
planes. Between 2000 m and 3000 m the borehole has an average azimuth and devi-
◦
ation from vertical of 35 and 54 .Within the massively bedded sandstones (2170 m
◦
to 2550 m), Figure 8.19 shows that the sonic log exhibits a northeast fast polarization
direction consistent with observations in the granite at shallower depths, but that do not
correlate with the theoretical fast directions if bedding planes were polarizing the shear
waves (Figure 8.19). However, in the finely laminated, clay-rich shale and siltstone
units below 2550 m the northwest fast direction of the sonic shear waves generally cor-
relates well with the theoretical fast directions for structural anisotropy. We interpret
the seismic anisotropy within these finely bedded stratigraphic layers to be controlled
by the alignment of clay and mica platelets in the strike direction of the bedding planes.
The electrical image log indicates that the bedding within most of the sandstone units
is spaced at much larger intervals on the order of 0.5 m to 2 m. The spacing of these
bedding planes is comparable to the 1.5 m wavelength of the sonic waves at the low
frequencies of interest, which explains why we only observe structural anisotropy