Page 178 - Applied Petroleum Geomechanics

172 Applied Petroleum Geomechanics

smaller coefficient of friction of the fault (m f ¼ 0.2). The stress polygon in
the shale is much smaller (Fig. 5.6).
5.3.2 Poisson’s ratioedependent stress polygon

Zhang and Zhang (2017) verified that the horizontal stress calculated from
the uniaxial strain method is the minimum value of the minimum hori-
zontal stress, which can be used as the lower bound horizontal stress to draw
LB
the stress polygon. This lower bound minimum horizontal stress (s ) can
h
be expressed in the following equation:
n
LB
s h ¼ ðs V ap p Þ þ ap p (5.15)
1 n
where n is Poisson’s ratio of the formation and can be obtained from the
compressional and shear velocities (V p and V s ) from Eq. (2.77).
UB
The upper bound of the maximum horizontal stress (s ) in strike-slip
h
and reverse faulting regimes can be obtained from the following equation:
s UB ¼ 1 n ðs V ap p Þþ ap p (5.16)
H
n
Based on Eqs. (5.15) and (5.16), the new stress polygon (Fig. 5.7) can be
drawn when Poisson’s ratio of the formation is available. Fig. 5.7 plots two

Figure 5.7 Poisson’s ratio dependent stress polygons and stress bounds calculated
from Eqs. (5.15) and (5.16) in a sandstone and a shale with a ¼ 1 and Poisson’s ratios
(PR) of 0.3 and 0.4, respectively.