Wellbore-Stability Predictions by Use of a Modified Lade Criterion
- R.T. Ewy (Chevron Petroleum Technology Co.)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- June 1999
- Document Type
- Journal Paper
- 85 - 91
- 1999. Society of Petroleum Engineers
- 1.6 Drilling Operations, 4.1.2 Separation and Treating, 5.1.10 Reservoir Geomechanics, 1.2.2 Geomechanics, 1.11.2 Drilling Fluid Selection and Formulation (Chemistry, Properties), 1.2.3 Rock properties
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The two most commonly used rock failure criteria in wellbore stability analyses are the Mohr-Coulomb criterion and the Drucker-Prager criterion. Neither of these is compatible with three-dimensional rock strength measurements that have explored the influence of the intermediate principal stress. This paper presents a modified Lade criterion which has the following desirable qualities: 1. it correctly describes the influence of the intermediate stress on rock strength, and therefore on wellbore stability, 2. it can be rearranged to give a closed-form solution for critical mud weight, for any wellbore orientation, and 3. only two rock strength parameters are required, such as cohesion and friction angle. The modified Lade criterion predicts critical mud weight values that are less conservative than those predicted by the Mohr-Coulomb criterion yet are not as unconservative as those predicted by the Drucker-Prager criterion. It also reveals that the required increase in mud weight when going from low hole angle to high hole angle is not as great as predicted by either the Mohr-Coulomb or Drucker-Prager criteria.
The two most commonly used rock failure criteria in wellbore stability analyses are the Mohr-Coulomb criterion and the Drucker-Prager criterion. There are many examples in the literature demonstrating the application of these two criteria to wellbore stability computations. McLean and Addis1,2 summarize several of these references, and also provide a useful explanation and comparison of the two criteria.
These two failure criteria represent the two extreme treatments of the intermediate principal stress. The Mohr-Coulomb criterion assumes that the intermediate principal stress has zero influence on rock strength. Conversely, the Drucker-Prager criterion (also sometimes referred to as a linear extended von Mises criterion) gives just as much weight to the intermediate principal stress as it does to the major and minor principal stresses. If the two criteria are both fit to the same set of triaxial compression (s1>s2=3) strength data, then the Drucker-Prager criterion will predict higher rock strength than the Mohr-Coulomb criterion for all stress states other than triaxial compression.
While it is true that the intermediate principal stress has a strengthening effect, which is ignored by the Mohr-Coulomb criterion, the strengthening effect is not as profound as that predicted by the Drucker-Prager criterion. The Mohr-Coulomb criterion underestimates rock strength for general stress situations (s1?s2?3) but the Drucker-Prager criterion overestimates rock strength for these general stress states and is especially in error under triaxial extension (s1=s2>3) conditions.3
When applied to the wellbore situation, which is a very general stress state, the Mohr-Coulomb criterion is too conservative, because it neglects the strengthening effect of the intermediate principal stress. The Drucker-Prager criterion, because it overestimates the intermediate stress effect, can be unconservative and can give nonsensical stability predictions.2
Several researchers have proposed three-dimensional rock failure criteria that predict the effect of the intermediate principal stress much more accurately than either the Mohr-Coulomb or the Drucker-Prager criteria.3-8 However, it is usually difficult in practice to apply these complex criteria to the wellbore stability problem. This is especially true when one is analyzing the general deviated well problem (a well not aligned with any principal stress axis) and one is trying to solve for the "critical mud weight" that will prevent instability.
This paper presents a three-dimensional rock failure criterion that is a modification of a criterion originally developed by Lade.9 The criterion proposed in this paper has the following desirable qualities: 1. it correctly describes the influence of the intermediate principal stress on rock strength, and therefore on wellbore stability, 2. it can be rearranged to give a closed-form solution for critical mud weight, for any wellbore orientation, and 3. only two rock strength parameters are required, such as cohesion and friction angle.
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