Page 258 - Reservoir Geomechanics

239 Wellbore failure and stress determination in deviated wells

Note that there is a change of sign in equation (8.7) that corrects an error in Peska
and Zoback (1995). The principal effective stresses around the wellbore are given
by
1
$ 2 2
σ tmax = σ zz + σ θθ + (σ zz − σ θθ ) + 4τ θz
2
(8.8)
1
$ 2
2
σ tmax = σ zz + σ θθ − (σ zz − σ θθ ) + 4τ θz
2

Failure of arbitrarily deviated wells

To evaluate the stability of wells of any orientation we use a lower hemisphere diagram
as illustrated in Figure 8.1d, where each point represents a well of a given azimuth and
deviation. Vertical wells correspond to a point in the center, horizontal wells correspond
to a point on the periphery at the appropriate azimuth and deviated wells are plotted at
the appropriate azimuth and radial distance. Figure 8.2 shows the relative stability of
wells of various orientations for normal, strike-slip and reverse faulting environments.
The principal stresses are in vertical and horizontal planes although Figure 8.2 also
could have been calculated for any arbitrary stress field (Peska and Zoback 1996). The
stress magnitudes, pore pressure and mud weight assumed for each set of calculations
are shown in each figure. The stresses and pore pressure correspond to a depth of
3.2 km and hydrostatic pore pressure. The mud weight is assumed to be equal to the
pore pressure, for simplicity. The color shown in each figure represents the rock strength
required to prevent the initiation of breakouts.A Mohr–Coulomb failure criterion was
utilized in these calculations, but any of the failure criteria discussed in Chapter 4
could have been used in the calculations. Red colors represent relatively unstable well
orientations as higher rock strength is required to prevent breakout initiation whereas
dark blue represents relatively stable well orientations as failure is prevented by much
lower rock strength.
Note that in normal faulting environments, breakout initiation is more likely to occur
in wells that are highly deviated in the direction of maximum horizontal stress than for
vertical wells. Conversely, wells that are highly deviated in the S hmin direction are more
stable than vertical wells. This is easy to understand for the case of horizontal wells.
Those drilled parallel to S Hmax have a trajectory that results in the greatest principal
stress, S v , pushing down on the well and the minimum principal stress, S hmin , acting in
a horizontal direction normal to the well path. This yields the maximum possible stress
concentration at the wellbore wall. For horizontal wells drilled parallel to S hmin , S v still
pushes down on the well, but S Hmax (which is only slightly below the value of S v ) acts
in a horizontal plane normal to the well path, resulting in a lesser stress concentration
(and much less stress anisotropy) on the wellbore wall. Note that the color patterns in