Page 201 - Applied Petroleum Geomechanics

196 Applied Petroleum Geomechanics

acting on the fracture plane can be expressed in the following equation
(Klee et al., 2011):
1
2 2
S n;i ¼ S V cos a þ sin af½S Ho þ S ho þðdS H =dz þ dS h =dzÞz i Š
2 (6.17)
½S Ho þ S ho þðdS H =dz þ dS h =dzÞz i Šcos 2ðq q 1 Þg
where q and a are the strike and dip angles of the particular fracture plane at
depth z i ; S Ho and S ho are the principal horizontal stresses at the upper limit
of the investigated borehole section; the stress derivatives are the horizontal
principal stress gradients and q 1 is the orientation of S Ho with respect to
north. The equation includes six unknowns; the solution therefore requires
a minimum of six measurements of S n at various depths on fractures with
different orientations. This method is attractive because shut-in pressures
are easy to identify and are usually reliable (Klee et al., 2011). In addition,
no assumptions on pore pressure are required.
6.2.2 Leak-off tests in the reverse faulting stress regime

In a strong tectonic stress regime, particularly the reverse faulting stress
regime, vertical stress is the minimum stress and the injection-induced
fracture is horizontal, and the closure pressure is equal to vertical stress
s V , i.e.,

s V ¼ p c (6.18)
Therefore, the closure pressure measured from a hydraulic injection test
in the reverse faulting stress regime is not a true reflection of the minimum
horizontal stress. Alternative methods are needed; for instance, the mini-
mum horizontal stress can be interpreted from drilling-induced fractures
using Kirsch’s wellbore solution (refer to Section 6.4.2.2).

6.2.3 Minimum stress interpretations from leak-off tests
As stated in Eq. (6.15), s h is equal to the closure pressure (at the inflection
point) during the pressure decline in Fig. 6.4; however, this method can be
difficult to apply when the inflection point is less well-defined, as pointed
out by Jones and Sargeant (1993) and Desroches and Kurkjian (1999).One
approach to determine the minimum horizontal stress is to use the instan-
taneous shut-in pressure (p isip ). However, this is not an exact relationship.
Although p isip is an adequate approximation of closure stress, it is usually
difficult to determine accurately. If large amounts of fluid have been pumped