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208 Reservoir geomechanics

stress orientation and magnitude at depth. In fact, we illustrate below that when drilling-
inducedtensilefracturesarepresent,itispossibletomakeinferencesaboutrockstrength
in situ from the presence, or absence, of wellbore breakouts. Analysis of data obtained
from multiple wells (and different stratigraphic levels in each) allows a fairly compre-
hensive model of the stress field to be developed. While such models are only accurate
within certain limits (obviously, the more information used to derive a stress model at
depth, the better the model is likely to be), the way in which uncertainties in the stress
estimates affect wellbore stability calculations can be addressed using rigorous, prob-
abilistic methods (Ottesen, Zheng et al. 1999; Moos, Peska et al. 2003). This will be
illustrated through case studies applied to wellbore stability in Chapter 10.We conclude
this chapter by discussing estimation of the magnitude of S Hmax by modeling breakout
rotations associated with slip on faults (Shamir and Zoback 1992; Barton and Zoback
1994).

Hydraulic fracturing to determine S 3

In this section we consider two fundamental aspects of hydraulic fracture initiation and
propagation that were addressed in a classic paper by Hubbert and Willis (1957)– the
wayin which the stress concentration around a well affects the initiation of hydraulic
fractures at the wellbore wall and the manner in which the orientation of the minimum
principal stress away from the well controls the orientation of a hydraulic fracture
as it propagates. In Chapter 12,we briefly consider the use of hydraulic fracturing
for stimulating production from depleted low-permeability reservoirs. The problem of
inadvertent hydraulic fracturing of wells and problems associated with lost circulation
during drilling is discussed in Chapter 8.
Hubbert and Willis (1957) presented a compelling physical argument that hydraulic
fractures in the earth will always propagate perpendicular to the orientation of the least
principal stress, S 3 . Because the work done to open a Mode I fracture a given amount
is proportional to the product of the stress acting perpendicular to the fracture plane
times the amount of opening (i.e. work is equal to force times distance), hydraulic
fractures will always propagate perpendicular to the least principal stress because it is
the least energy configuration. They confirmed this with simple sand-box laboratory
tests (Figure 7.1) and pointed out that igneous dike propagation is also controlled by
the orientation of the least principal stress. This fundamental point is the basis for
using hydraulic fracturing to measure the magnitude of the least principal stress as
discussed below. In strike-slip and normal faulting environments where S 3 ≡ S hmin ,
hydraulic fracture (and dike) propagation will be in a vertical plane perpendicular to
S hmin (and parallel to S Hmax ). In reverse faulting environments where S 3 ≡ S v ,hydraulic
fracture propagation will be in a horizontal plane. At the time that the Hubbert and
Willis (1957) paper was written, their arguments put to rest a great deal of argument