Page 225 - Applied Petroleum Geomechanics

220 Applied Petroleum Geomechanics

Figure 6.19 Effective tangential stress and total radial stress (mud pressure) along the
wellbore circumference in a horizontal well drilled in the minimum horizontal stress
direction and located in the reserve faulting stress regime.

generate horizontal fractures because a much larger tensile stress (absolute
value) is created at the wellbore wall (this can be found by comparing Eq.
(6.61) to Eq. (6.66)). It may imply that for hydraulic fracturing operations in
a vertical well, the vertical fractures may be initiated first; these vertical
fractures will rotate and eventually develop into horizontal fractures after
penetrating through the near-wellbore zone into the undisturbed formation
because s V is the minimum in situ stress.
Because the maximum horizontal stress is the largest in situ stress in the
reverse faulting stress regime, the tensile fractures (horizontal ones) will
initiate at the side of the horizontal well (as shown in Figs. 6.18 and 6.19).
However, when the horizontal wellbore is not aligned with a principal
horizontal stress direction, the shear stress at the wellbore wall is not zero.
The borehole wall subjected to the maximum tension is at an angle (g)to
the borehole axis, and en echelon fractures are generated, as shown in
Fig. 6.14B. At the wellbore wall the effective principal tensile stress is equal
to the minimum effective principal stress and can be obtained by the
following equations:
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
0
s þ s 0 s s 0 q
0
z
z
s 0 ¼ q þ s qz (6.67)
tmax
2 2

1 1 2s qz
g ¼ tan (6.68)
2 s s 0 q
0
z