Page 190 - Reservoir Geomechanics

172 Reservoir geomechanics

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strongly compressive to the north and south, the azimuth of S hmin ,or90 from the
direction of S Hmax . σ θθ decreases rapidly with distance from the wellbore wall at the
azimuth of S hmin (Figure 6.2c) as given by equation (6.2). Note that at a radial distance
equivalent to ∼1.5 wellbore radii, the value of σ θθ is about 50% greater than the far-field
value of σ Hmax (58.5 MPa), whereas it is almost three times this value at the wellbore
wall.
In marked contrast, at the azimuth of S Hmax the hoop stress is only slightly above
zero because of the relatively large difference between S Hmax and S hmin (equation 6.2).
Under such circumstances, the wellbore wall can go into tension which would lead
to the formation of drilling-induced tensile wall fractures (Aadnoy 1990; Moos and
Zoback 1990) because the tensile strength of rock is so low (Chapter 4). At the azimuth
of S Hmax , the hoop stress increases rapidly with distance from the wellbore wall. Note in
Figure 6.2b that at r = 1.5R, the value of σ θθ is slightly greater than the far-field value
of σ hmin which would be equivalent to S hmin − P p = 20 MPa (≡ 51.5 − 31.5MPa).
Hence, drilling-induced tensile wall fractures are restricted to being extremely close
(∼several mm to cm) to the wellbore (Brudy and Zoback 1999), unless the pressure in
the wellbore is sufficient to extend the fracture away from the wellbore as a hydrofrac
(see below).
Note that the stress components described in equations (6.1)–(6.3) are independent
of elastic moduli. For this reason, the manner in which stresses are concentrated does
not vary from formation to formation. Moreover, the stress concentration around a
wellbore is independent of R, the wellbore radius.
Because stresses are most highly concentrated at the wellbore wall, if either com-
pressive or tensile failure is going to occur, it will initiate there. Figure 6.3a shows the
variation of σ θθ , σ zz and σ rr at the wellbore wall for the same far field stresses used in
Figure 6.2. Note the extremely large variations in σ θθ with position around the well. σ zz
varies in a similar manner but the variations are much more subdued. The average value
of σ zz is the same as the far-field vertical effective stress of 56.7 MPa (88.2 − 31.5 MPa).
In Figures 6.2a and 6.3aitisobvious that compressive failure of the wellbore wall is
most likely to occur in the area of maximum compressive hoop stress (at the azimuth
of S hmin )if the stress concentration exceeds the rock strength (Bell and Gough 1979;
Zoback, Moos et al. 1985). The zone of compressive failure around the well is shown
in Figure 6.3c assuming a Mohr–Coulomb failure criterion and C 0 = 45 MPa, µ i = 1.0.
The stress concentration exceeds the rock strength everywhere within the contour lines
shown in Figure 6.3con opposite sides of the hole. The breakouts have a finite width,
w BO , the span of failed rock around the wellbore wall on one side, and initial depth,
both of which depend on rock strength for a given stress state (Zoback, Moos et al.
1985). The colors in Figure 6.3c indicate the value of rock strength required to pre-
vent failure. Hence, hot colors means it takes high strength to prevent failure (because
the stress concentration is high) whereas cold colors mean even a low-strength rock
will not fail (because the stress concentration is low). The contour line describes the