Stability, Failure, and Measurements of Boreholes and Other Circular Openings (1993) / Chapter Skim
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5 Analytical and Numerical Modeling
5 Analytical and Numerical Modeling
Pages 51-72
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From page 51... ...
Unsupported Openings Most of the emoting work on borehole stability is based on perfectly elastic/plastic models that are calibrated with test data taken from conventional t~iamal compression embedments. Rupture is assigned to occur when the stresses reach the elastic limit that is usually set at the peak of the experimental stress-strain curve.
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From page 52... ...
Its magnitude affects the overall integrity of the borehole, and the principal stress tensor win be rotated in the neighborhood of the circular opening. Knowing the stress field associated with a particular wellbore configuration, various failure mecharusms can be assessed.
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From page 53... ...
There may be specific orientations, in 3-D space, where the pressures required for initiation and breakdown are maximized. From a practical viewpoint, there is sometimes a misconception that once the in-situ stress tensor is known and one is contemplating a horizonW hole, it suffices to drill this hole parallel to the minion horizontal stress component.
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From page 54... ...
To rationalize a marriage between initiation-related effects and propagation effects, e.g., represented by linear elastic finite elements, several minimum assumptions must be recognized, including scale conditions wherein the instantaneously initiated fracture is of sufficient let for a smooth transition between the two extreme disciplines of consideration Gngraffea, 1987~. Inelastic Analysis Despite the fact that the elastic approach is widely used in the design of circular openings, it is viewed as being insufficient to predict quantitatively failure and to describe various failure modes observed in underground excavations, as well as in instrumented hollow cylinder tests.
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From page 55... ...
Maury (1987) also specified plastic analysis for oil field operations, delineating various failure mechanisms as a function of mud weight, a wellbore pressure analog.
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From page 56... ...
considered borehole stability in a deep rock layer under a uniform stress field at infinity, a.,, as illustrated in Figure 10. Furthermore, they considered a deep section of Me borehole.
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From page 57... ...
Borehole stability in a deep rock layer under uniform stress at infinity.
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From page 58... ...
Other solutions can be easily compacted for more complicated constitutive models. · Warping of the borehole wall.
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From page 59... ...
Fo~ation of shear bands.
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From page 60... ...
analyzed borehole stability using the fate element method, determining the lowest stress at infinity that causes warping of the borehole. This theory suggests that the critical bifurcation stress corresponds to the short wavelength limit Mat is affecting a vanishingly narrow ring of material in the vicinity of the borehole wall.
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From page 61... ...
clearly Mow a progressive failure mechanism; the computed failure modes are in a good qualitative agreement with the laboratory and field observations. Also, the existence of an intends length in the constitutive equations enables one to model the existence of the scale effect in the problem; thus, small holes fail at higher external stresses than large holes.
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From page 62... ...
62 STABILITY OF BOREHOLES AND OTHER OPENINGS .,, ~ ,,. Figure 15.
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From page 63... ...
that linear elasticity inadequately predicted funnel convergence near failure. Using a power law variation for Young's modulus as a function of the confining stress for a vertical wellbore in an elastic medimn with isotropic horizontal stresses, a generalized representation of Hooke's law was presented.
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From page 64... ...
, substantial cooldown around a welt/bore can occur. Reservoir cooling will generate tensile stresses, which may stabilize or destabilize the near-wellbore region, depending on the interrelationship between the radial, the axial and the circumferential.
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From page 65... ...
Surface instability corresponds to the infinitesimally small wavelength limit with respect to the borehole radius, i.e., to a bifurcation solution that is affecting only an infinitesimal ring of material close to the borehole wall. The short wavelength limit is an accumulation point of bifurcation.
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From page 66... ...
Depending on the far-field stress tensor and the formation constitutive relations, the loading on the casing can be calculated with levels of accuracy parallel to those defined for openhole completions. Elastic Analysis As an approximation, oilfield calculations have often simplistically involved computing the stress concentration at the borehole wall, implementing these values as boundary loads on the cement sheath, and subsequently determining the loading applied to the casing as a thin-walled cylinder.
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From page 67... ...
, well-known in the ge ote chnic al do maw Intersections As a first approximation, the stability of perforations can be assessed by assuming their cross section to be circular. The problem is then similar to the openhole configuration discussed earlier, with the exception that the loading conditions are dependent on the depth of the perforation The perforation tunnel acts as a stress concentrator but in a stress field that is influenced by the borehole itself.
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From page 68... ...
viewed rock splitting near an opening an`1 rock bursting as a result of crack initiation and propagation associated with the existence of radial tensile stresses around the excavation. The existence of such stresses was predicted on the basis of a non-linear elasticity theory with second-order terms to account for shear induced volume expansion (Reiner, 1949~.
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From page 69... ...
These tensile stresses cause latent, surface-parallel cracks to open These opened tensile cracks magnify the effect of the diffuse bifurcation, since under a field of uniamal compressive stresses, parallel to the Griffith cracks, tensile stress concentrations are established at the crack tips. It is then assumed that this mechanism may result in an unstable growth of cracks and finally in splitting.
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From page 70... ...
Blot (1972) indicated first that in Fin apace, the ~e" intensity factor of a Griffith crack in a stress field parallel to its extent drops to zero for values of initial stress correppor~ing to surface instability.
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From page 71... ...
Applications of the discrete element method to slope stability (steeply dipping foliation planes) and mining problems are foments in Cun~aD (1987)
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From page 72... ...
Discontinuous Deformation Analysis This numerical approach is fi~nd~mentaBy different from the discrete element method in mat it couples a complete kinematic theory for block interactions with the eq,~ilibri~ and strain compatibility relations of continuum mechanics. The minimization of potential energy associated with internal deformations and interblock contacts leak to an implicit formulation like that of finite element analysis.
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