48 In situ stress
Figure 4.6 Hydraulic fracturing straddle packer system being lowered into a
borehole during stress measurement tests in Cornwall, UK.
In the calculation method shown in Fig. 4.5(b), it is assumed that the
stress concentration of a principal stress component around the borehole
in the horizontal plane shown has extreme values of -1 and 3. As shown,
the shut-in pressure, Ps, is assumed to be equal to the minor horizontal
principal stress, oh. The major horizontal principal stress, oH, is then found
from the breakdown pressure. In the formula in Fig. 4.5, the breakdown
pressure, PB, has to overcome the minor horizontal principal stress
(concentrated three times by the presence of the borehole) and overcome
the in situ tensile strength of the borehole rock; it is assisted by the tensile
component of the major principal horizontal stress. Note that when a
borehole is pressurized with water at a given pressure, a tensile stress
component of the same value is induced in the borehole periphery.
Moreover, we have also assumed that the crack has propagated in a
direction perpendicular to the minor principal stress.
All of these factors contain further tacit assumptions, in particular
that the elasticity theory is valid. For this to be true, and the stress
concentration factors of -1 and 3 around the circular borehole to be valid,
the material of the borehole wall must be continuous, homogeneous,
isotropic and linearly elastic. Furthermore, we have also assumed in this
basic analysis that the rock is impermeable, so that borehole water has not
penetrated the rock and affected the stress distribution.