Page 220 - Applied Petroleum Geomechanics

In situ stress estimate 215

in a vertical well. The azimuth in the image log along the wellbore starts
from North, to East, South, West, and goes back to North. The drilling-
induced fractures are thin and long fractures parallel to the borehole axis
and can be identified from resistivity image (darker color) in the image log,
as shown in Fig. 6.14A.
Assuming that the downhole mud pressure is equal to the formation
initiation pressure when drilling-induced tensile fractures occur, Eq. (6.48)
can be used to calculate the maximum horizontal stress for the vertical
hydraulic fracture in a vertical well, i.e.,
(6.57)
s H ¼ 3s h p m p p þ T 0
where p m is the downhole mud pressure when drilling-induced tensile
fractures occur.
The other method is to assume that the tensile fractures are generated at
the wellbore wall when the minimum effective tangential stress (absolute
value, because tensile stress is a negative value) becomes less than the tensile
strength of the rock. Kirsch’s equation can be used to calculate the effective
tangential stress. The minimum effective tangential stresses at the wellbore
0
wall in a vertical well (s q ) can be obtained from Kirsch’s equation as
follows:
0
s ¼ 3s h s H p m ap p (6.58)
q
When vertical tensile fractures are generated in elastic, impermeable
rocks in a vertical wellbore, the following relation is satisfied: s þ T 0 0.
0
q
When the rock starts to fail, Biot’s coefficient can be assumed as a ¼ 1.
Therefore, Eq. (6.58) can be rewritten as:
(6.59)
s H 3s h p m p p þ T 0
where T 0 is the tensile strength of the rock to the horizontal tensile stress
(absolute value is used in the equation). Therefore, Eq. (6.59) is similar
to Eq. (6.57).
Plotting Eq. (6.59) in the stress polygon diagram and combining with
other methods (e.g., wellbore breakout), the maximum horizontal stress can
be constrained (refer to Section 6.4.4).
For an inclined borehole, the drilling-induced fractures are no longer
created along the borehole axial direction, but en echelon fractures
(Fig. 6.14B) are generated (e.g., Sun et al., 2017; Thorsen, 2011) because of
shear stress presence in the far field of the wellbore. Inversion methods of