Page 201 - Fundamentals of Gas Shale Reservoirs

WELLBORE INSTABILITY IN GAS SHALE RESERVOIRS 181
can then be calibrated against core test data if any is avail­ The minimum horizontal stress obtained from above for­
able. However, for VTI material, the following equation pre­ mulae can be calibrated against direct measurements of
sented by Wilson et al. (2007) should be used to calculate the extended leak‐off test (XLOT), a standard leak‐off test (LOT),
UCS of rocks relative to the bedding planes. or a mini‐frac test (Yamamoto, 2003; Zoback et al., 2003).

UCS UCS max (cos k 1 sin )(1 sincos ) 8.4.2.4 Mud Weight Window in VTI Condition Calculat­
k 4 (8.23) ing all of the parameters mentioned earlier including, elastic,
12 sincos 1 2 strength, and in situ stress parameters under VTI condition,
( 21 k ) )
1 mud weight can be estimated by different failure criteria. In
drilling engineering practice, a linear poroelasticity stress
Where UCS is the UCS at ϑ with consideration of bedding model in conjunction with a rock strength criterion is com­
ϑ
effect and ϑ is the angle between the stress concentration to monly used to determine the optimum mud pressure required
bedding (e.g., 0 represents loading perpendicular to bed­ to stabilize the wellbore. During drilling, borehole collapse
ding). UCS max is the maximum strength at any orientation and drilling‐induced fractures are the two main wellbore
and k and k are defined as: instability problems that often lead to the need for fishing,
1 2
stuck pipe, reaming operations, sidetracking, and loss of
q
k 1 II (8.24) circulation. These problems can often be eliminated by
q selecting a suitable mud weight. This is typically carried out
using a constitutive model to estimate the stresses around the
UCS
k 2 min (8.25) wellbore coupled with a failure criterion to predict the ulti­
UCS max mate strength of reservoirs rocks. Therefore, the main aspect
of wellbore stability analysis is the selection of an appro­
where q is the strength when the bedding is parallel to the priate rock strength criterion. Numerous simple, and now
II
sample axis, q is the strength when bedding is perpendic­ common, triaxial criteria have been proposed during the last
ular to the sample axis, and UCS is the minimum strength few decades in which intermediate and minor principal
min
at any orientation. stresses are equal (σ > σ = σ ) (Bieniawski, 1974; Fairhust,
2
1
3
1964; Franklin, 1971; Hobbs 1964; Hoek and Brown, 1980;
8.4.2.3 Estimation of In Situ Stresses in VTI Formation Johnston, 1985; Mohr, 1900; Murrel, 1965; Ramamurthy
Two equations are often used to estimate far‐field (?) effective et al., 1985; Sheorey et al., 1989; Yudhbir et al., 1983). The
horizontal stress magnitudes using effective overburden stress triaxial criteria show close agreement with results of triaxial
term (this stress is easily obtained by integrating formation tests and are frequently used in stability analyses of rock
bulk density from surface to depth). Traditional equations structures. However, they ignore the influence of intermediate
used to determine horizontal in situ stress magnitude assume principal stress on ultimate strength of rocks causing unreal­
an isotropic poroelastic medium (Fjaer et al., 1992): istic prediction of stability for structures. For instance,
Mohr–Coulomb strength criterion is the most commonly
v E sta used triaxial criterion used for the determination of rocks
y
p
h (1 v) ( v P ) P p (1 v ) ( x v ) (8.26)
2
strength. This criterion suffers from two major limitations:
(i) it ignores the nonlinearity of strength behavior and (ii) the
v E sta effect of intermediate principal stress is not considered in its
p
H (1 v) ( v P ) P p (1 v ) ( y v x ) conventional form. Thus, the criterion overestimates the
2

(8.27) minimum mud pressure because it neglects the effect of the
intermediate principal stress (McLean and Addis, 1990).
However, considering VTI behavior of reservoir rocks, Vernik and Zoback (1992) found that Mohr–Coulomb
magnitude of in situ stress should be obtained using the criterion is not able to provide realistic results to relate the
following equations (Higgins et al., 2008): borehole breakout dimension to the in situ stresses in
crystalline rocks. Thus, they recommended the use of a
E v E Ev strength criterion to consider the effect of the intermediate
11 31 ( P ) P 11 11 12
h v p p 2 h 2 2 H principal stress. Zhou (1994) developed a numerical model
E ( 1 v ) 1 ( v ) 1 ( v )
33
12
12
12
(8.28) to determine the borehole breakout dimensions based on
various rock failure criteria. He found that the Mohr–
Coulomb criterion tends to predict larger breakouts than are
E 11 v 31 E 11 Ev predicted by criteria that incorporate the effect of σ . Song
11 12
H E ( 1 v ) ( v P ) P p 1 ( v ) H 1 ( v ) h 2
p
2 2
2
33 12 12 12 and Haimson (1997) concluded that the Mohr–Coulomb
(8.29) criterion did a poor job in the prediction of breakout