Page 171 - Reservoir Geomechanics

154 Reservoir geomechanics

in Figure 5.2bwas taken just west of well C in Figure 5.8. Numerous earthquakes occur
in this region (shown by small dots), and are associated with slip on numerous reverse
and strike-slip faults throughout the area. The trends of active faults and fold axes are
shown on the map. The distribution of fractures and faults from analysis of ultrasonic
borehole televiewer data in wells A–D are presented in the four stereonets shown. The
direction of maximum horizontal compression in each well was determined from analy-
sis of wellbore breakouts (explained in Chapter 6) and is northeast–southwest compres-
sion(asindicatedbythearrowsonstereonets).Notethatwhilethedirectionofmaximum
horizontal compression is relatively uniform (and consistent with both the trend of the
active geologic structures and earthquake focal mechanisms in the region as discussed
later in this chapter), the distribution of faults and fractures in each of these wells is quite
different. The reason for this has to do with the geologic history of each site. The highly
idealized relationships between stress directions and Mode I fractures and conjugate
normal, reverse and strike-slip faults (illustrated in Figure 5.1) are not observed. Rather,
complex fault and fracture distributions are often seen which reflect not only the cur-
rent stress field, but deformational episodes that have occurred throughout the geologic
history of the formation. Thus, the ability to actually map the distribution of fractures
and faults using image logs is essential to actually knowing what features are present in
situ and thus which fracture and faults are important in controlling fluid flow at depth
(Chapter 11).

Three-dimensional Mohr diagrams

In a number of applications and case studies discussed in the chapters that follow it
will be necessary to calculate the shear and normal stress acting on arbitrarily oriented
faults in three dimensions. One classical way to do this is to utilize three-dimensional
Mohr diagrams as illustrated in Figure 5.9a (again see detailed discussions in Twiss
and Moores 1992 and Pollard and Fletcher 2005). As shown in the figure, the values
of the three principal stresses σ 1 , σ 2 and σ 3 are used to define three Mohr circles.
All planar features can be represented by a point, P, located in the space between the
two smaller Mohr circles (defined by the differences between σ 1 and σ 2 , and σ 2 and
σ 3 , respectively), and the big Mohr circle (defined by the difference between σ 1 and
σ 3 ). As in the case of two-dimensional Mohr circles (e.g. Figure 4.2), the position of
point P defines the shear and normal stress on the plane. The figure illustrates that
critically oriented faults (i.e. those capable of sliding in the ambient stress field) plot in
the region shown in Figure 5.9aas corresponding to coefficients of friction between 0.6
and 1.0.
Graphically, the position of point P in the three-dimensional Mohr circle is found
using two angles, β 1 and β 3 , that define the angles between the normal to the fault
and the S 1 and S 3 axes, respectively (Figure 5.9b). As shown in Figure 5.9a, to find the