Page 202 - Fundamentals of Gas Shale Reservoirs

182 GEOMECHANICS OF GAS SHALES

dimensions, while the criteria that consider the strength­ introduced a 3D failure criterion called Mogi–Coulomb
ening effect of intermediate principal stress were in much criterion. This failure criterion is a linear failure envelope in the
better agree ment with the experimental observations. Ewy Mogi domain containing two parameters that can be directly
(1999) concluded that the Mohr–Coulomb criterion is too and simply related to the two Coulomb strength parameters,
conservative in the prediction of minimum mud pressure the cohesion and the friction angle. The Mogi–Coulomb crite­
required to stabilize the wellbore. rion neither ignores the strengthening effect of intermediate
Hoek–Brown triaxial failure criterion is another well‐ stress, nor does it predict a strength as unrealistically high as
known criterion successfully applied to a wide range of rock does the other criteria. Figure 8.8 compares the results of three
for almost 30 years (Cai, 2010; Carter et al., 1991; Douglas, failure criteria namely Mohr–Coulomb, Hoek–Brown as well
2002). Zhang and Radha (2010) used the three‐dimensional as Mogi–Coulomb criteria in prediction of mud weight window
(3D) Hoek–Brown strength criterion developed by Zhang according to the VTI parameters obtained before.
and Zhu (2007) for wellbore stability analysis. Their study In this Figure 8.8, the first track is the depth and gamma
showed that the minimum mud pressures obtained were in ray log. In the second track the MWW is shown. The red pro­
better agreement with observed incidents than those obtained file to the left shows the mud weight corresponding to kick.
by the Mohr–Coulomb criterion. Despite successful applica­ The brown profile is the mud weight below which breakouts
tions of the Hoek–Brown criterion in a number of cases, it or shear failure will occur. On the other side, if the used mud
was indicated that the intermediate principal stress needs to weight exceeds the blue or green profiles, the model predicts
be included in the wellbore stability analysis (Al‐Ajmi and mud loss and induced fracture in the formation, respectively.
Zimmerman, 2006). For instance, Single et al. (1998) pointed Therefore, the white area in this track represents the safe
out the effect of σ in underground excavations applications MWW for drilling. As is seen from this figure, this window is
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and suggested a modification to the Hoek–Brown criteria changing as a function of depth and it is likely that it disap­
which is frequently used. Fjaer and Ruistuen (2002) devel­ pears at some depths meaning that there is practically no safe
oped a numerical model to simulate rock failure tests for a window to drill. In this case, the driller should take actions
granular material. Their simulations showed that σ has an such as excessive hole cleaning when drilling in this zone.
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influence on rock strength that is in rough agreement with From this figure, the important conclusion is prediction of
several previously published sets of experimental data. different safe MWW when applying different failure criteria.
In order to account for the effect of the intermediate prin­ In fact, a model which provides the most comparable predic­
ciple stress in rock failure response, many true‐triaxial or tion with reality is the most reliable model. The observation
polyaxial failure criteria such as those by Drucker and Prager regarding wellbore instability or failure during drilling is cap­
(1952), Mogi (1967, 1971), Lade and Duncan (1975), Zhou tured using caliper logs or image logs such as formation
(1994), Benz et al. (2008), and You (2009) have been devel­ micro imager (FMI). The caliper log (HCAL) corresponding
oped. The results obtained from these criteria have shown to this well is shown in the last track of Figure 8.8. As is seen
that the value of σ has a considerable effect on rock strength in this track, a 6‐inch bit was used to drill this section of the
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(Mogi, 2007). However, most of these criteria are mathemat­ well. Any change in caliper data from this size is an indica­
ically subject to some limitations and yield physically unrea­ tion of wellbore ovalisation or breakouts. From the caliper
sonable solutions. For instance, the Mogi criterion (Mogi, logs shown in this figure, severe breakouts are observed
1971) yields two values of σ at failure for the same value of within the intervals of 4306–4314 m and 4322–4358 m, as
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σ when it is used to predict the strength of some types of well as from 4400 to 4421 m. As is seen from this figure,
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rock (Colmenares and Zoback, 2002; You, 2009). Wiebols Mohr–Coulomb criterion overestimates the rock strength and
and Cook (1968) derived a failure criterion by calculating results in larger values for the lower bound of the safe mud
the shear strain energy associated with microcracks in the weight windows compared to the other two failure criteria.
material. This model predicts a strengthening effect of the This could be linked to the fact that in this criterion, the effect
intermediate stress, but it requires the knowledge of the coef­ of the intermediate stress is ignored. Although Hoek–Brown
ficient of sliding friction between crack surfaces—a param­ and Mogi–Coulomb criteria predict the breakouts observed
eter that cannot be determined experimentally. Furthermore, from caliper data more realistically, and the latter criterion
numerical methods are required for implementation of this appears to give a better match with the observed failures
criterion. Desai and Salami (1987) introduced a 3D failure from calipers. This can be related to the fact that the Mogi–
criterion that requires more than six input parameters, and Coulomb criterion considers the effect of the intermediate
Michelis (1987) proposed another criterion in which four stress in failure analysis which is happening in reality. It can
constants are involved (Hudson and Harrison, 1997; Pan and be concluded that Mogi–Coulomb criterion is a better failure
Hudson, 1988). In general, 3D failure criteria that contain criterion to determine the safe MWW. This can be related
numerous parameters or require numerical evaluation are to the fact that the Mogi–Coulomb criterion considers the
difficult to apply in practice, particularly for wellbore sta­ effect of the intermediate stress in failure analysis which is
bility problems. Recently, Al‐Ajmi and Zimmerman (2005) happening in reality.