Page 226 - Applied Petroleum Geomechanics

In situ stress estimate 221

0 0
where s t max is the effective principal tensile stress at the wellbore wall; s z
0
and s q are the effective axial and tangential stresses at the wellbore wall,
respectively; s qz is the shear stress at the wellbore wall (refer to Kirsch’s
equation in Chapter 10); g is the angle between borehole axis and the ten-
sile fractures.

6.4.3 Maximum horizontal stress from wellbore breakouts
When stress concentration around a wellbore exceeds rock compressive
strength, breakouts are induced around the wellbore. Barton et al. (1988)
presented the following equation to determine the maximum horizontal
stress utilizing observations of breakout width in a vertical well:

UCS þ p p þ p m s h ð1 þ 2 cos 2 qÞ
s H ¼ (6.69)
1 2 cos 2 q

where UCS is the uniaxial compressive strength of the rock; (180 -2q)is
the wellbore breakout angle.
In the above equation, Barton et al. (1988) assumed the wellbore
breakout occurs when the maximum tangential compressive stress is equal
to the uniaxial compressive strength. This assumption may be over-
simplified. Failure criteria should be applied to analyze wellbore shear
failure (breakout) and calculate the maximum horizontal stress.
Using the MohreCoulomb failure criterion, the following equation can
be obtained for calculating the maximum horizontal stress in a vertical well
(refer to Chapter 10, Section 10.5 for derivations):
UCS aðq 1Þp p þðq þ 1Þp m ð1 2 cos 2 b Þs h
b
s H ¼ (6.70)
1 þ 2 cos 2 b b

where 2b b is the wellbore breakout angle (degrees); 2b b ¼ 180 2q; q ¼
(1þ sin4)/(1 sin4); 4 is the angle of internal friction of the rock.
If the wellbore is in uniaxial loading condition, then q ¼ 0, and Eq.
(6.70) is simplified to Eq. (6.69). For borehole breakouts in inclined
boreholes, in situ stresses can be obtained from inversion of borehole
breakout data (e.g., Zajac and Stock, 1997).
6.4.4 Maximum horizontal stress from breakouts and
drilling-induced fractures
When both borehole breakouts and drilling-induced tensile fractures
(DITFs) occur in a vertical well, a stress polygon combined with wellbore
failure data can be used to determine the minimum and maximum