Page 192 - Reservoir Geomechanics

174 Reservoir geomechanics

boundary between the zones where the stress concentration exceeds the strength (as
defined above) or does not.
To better visualize why breakouts and tensile fractures around a wellbore are such
good indicators of far-field stress directions, let us first simplify equations (6.1)–(6.3)
for the stresses acting right at the wellbore wall by substituting r = R.In this case, the
effective hoop stress and radial stress at the wellbore wall are given by the following
equation:

T
σ θθ = S hmin + S Hmax − 2(S Hmax − S hmin ) cos 2θ − 2P 0 −
P − σ (6.4)
σ rr =
P (6.5)

where
P is the difference between the wellbore pressure (mud weight, P m ) and the
pore pressure. The effective stress acting parallel to the wellbore axis is:
σ zz = S v − 2ν(S Hmax − S hmin ) cos 2θ − P 0 − σ
T (6.6)

where ν is Poisson’s ratio. At the point of minimum compression around the wellbore
◦
◦
(i.e. parallel to S hmin )at θ = 0 , 180 , equation (6.4) reduces to
σ min = 3S hmin − S − 2P 0 −
P − σ
T (6.7)
θθ Hmax
whereas at the point of maximum stress concentration around the wellbore (i.e. parallel
◦
◦
to S Hmax )at θ = 90 , 270 ,
max
σ θθ = 3S Hmax − S hmin − 2P 0 −
P − σ
T (6.8)
such that the difference between the two is
σ max − σ min = 4 (S Hmax − S hmin ) (6.9)
θθ θθ
which corresponds to the amplitude of the sinusoidal variation of hoop stress around the
wellbore shown in Figure 6.3a and helps explain why observations of wellbore failures
so effectively indicate far-field stress directions. Fundamentally, the variation of stress
around the wellbore wall amplifies the far-field stress concentration by a factor of 4.

Introduction to breakouts

To understand the zone of compressive failure (breakouts) that results from the stress
concentration around the wellbore (Figure 6.2), one simply has to consider the fact that
like in a rock mechanics experiment, the rock surrounding the wellbore is subject to
three principal stresses defined by equations (6.4)–(6.6). If these stresses exceed the
rock strength, the rock will fail. The stress state at the wellbore wall at the azimuth
of S hmin (where the stress concentration is most compressive), is shown in Figure 6.3b
using a three-dimensional Mohr diagram. This can then be compared to a failure law
defining the strength of the rock. For this example, a Mohr–Coulomb failure law was
used but, of course, any of the failure laws discussed in Chapter 4 could have been