A revisit to the Lekhnitskii-Amadei solution for borehole stress calculation in tilted transversely isotropic media

Fang, Xinding

doi:10.1016/j.ijrmms.2018.02.001

Cited by 11 publications

(7 citation statements)

References 18 publications

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“…As mentioned above, the stress calculation was performed in the coordinate system proposed by Fang (2018). In-situ stresses and the material stiffness matrix were therefore transformed to the coordinate system by conducting three rotations: first to the global coordinate system; second to the traditional top-of-hole borehole coordinate system according to the well azimuth and inclination; third to the coordinate system proposed by Fang (2018). The third transformation is a rotation about the z-axis by an angle c , which is determined from the stiffness matrix.…”

Section: Amadei Solutionmentioning

confidence: 99%

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Anisotropic Wellbore Stability Analysis: Impact on Failure Prediction

Asaka

Holt

2020

Rock Mech Rock Eng

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Shale formations are the main source of borehole stability problems during drilling operations. Suboptimal predictions of borehole failure may partly be caused by neglecting the anisotropic nature of shales: Conventional wellbore stability analysis is based on borehole stresses computed from isotropic linear elasticity (Kirsch solution) with the assumption of no induced pore pressure. This is very convenient for a practical implementation but does not always work for shales. Here, anisotropic wellbore stability analysis was performed targeting an offshore gas field to investigate in particular the impact of elastic anisotropy on borehole failure predictions. Stress concentration around a circular borehole in anisotropic shale was calculated by the Amadei solutions, and induced pore pressure was obtained from the Skempton parameters based on anisotropic poroelasticity. Borehole failure regions and modes were then predicted using the effective stresses and those are apparently consistent with observations. A comparison with the conventional approach suggests the importance of accounting for elastic anisotropy: Predicted failure regions, modes, and also the associated mud weight limits can be completely different. This observation may have significant implications for other fields since shale often show strong elastic anisotropy.

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Section: Amadei Solutionmentioning

confidence: 99%

“…The third transformation is a rotation about the z-axis by an angle c , which is determined from the stiffness matrix. See Fang (2018) for the derivation of c . Verification of the stress calculation was performed by reproducing the results of Karpfinger et al (2011).…”

Section: Amadei Solutionmentioning

confidence: 99%

Anisotropic Wellbore Stability Analysis: Impact on Failure Prediction

Asaka

Holt

2020

Rock Mech Rock Eng

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“…We first investigate an isotropic model to demonstrate the applicability and stability 41 of the derived analytical solution for borehole stress calculation in isotropic formations. Properties of the model are listed in Table 1.…”

Section: Numerical Examplesmentioning

confidence: 99%

An analytical approach for cased borehole stress calculation in general anisotropic formations

Wang

Fang

Zhang

et al. 2020

Num Anal Meth Geomechanics

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We present an explicit analytical approach for calculating the distribution of stress around a circular cased borehole in a general anisotropic formation. This approach is developed based on a pure elastic cased borehole model, which can include multiple cemented concentric casing strings that are surrounded by a homogeneous anisotropic medium. The wall of the innermost casing is under the compression of borehole internal fluid pressure, and the formation can be subjected to arbitrary far-field stresses. Every casing-cement boundary is assumed to be welded, so as the cement-formation boundary. The derived analytical solution can be applied to an arbitrary wellbore trajectory in an arbitrary anisotropic formation and is also applicable to degenerate isotropic formations. Accuracy and robustness of the analytical solution is validated through comparing its results with those calculated from the classical Kirsch solution for an isotropic example that has identical elastic properties for all materials and from a finite element method for an anisotropic cased borehole example.

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“…Circular Hole in an Arbitrary TI Material. Fang [17] presented the explicit analytical solution for stress distribution around a circular hole in an arbitrary transversely isotropic medium subjected to boundary stresses and hole internal fluid pressure. In his derivation, a hole is assumed to be infinite and homogeneous in the axial direction so that the problem can be simplified based on the generalized plain strain assumption.…”

Section: Analytical Solution For Stress Distribution Around Amentioning

confidence: 99%

“…Fang [17] demonstrated that the explicit analytical expression for equation 4can be obtained and used for hole stress calculation in arbitrary transversely isotropic media regardless of the hole orientation relative to the material elasticity symmetry axis. Moreover, this solution is valid for degenerate isotropic cases.…”

Section: Analytical Solution For Stress Distribution Around Amentioning

confidence: 99%

An Approach for Stability Analysis of Gas/Fluid-Filled Cylindrical Hole in Laminated Materials

Leng

Hou

Duan

2020

Mathematical Problems in Engineering

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An explicit analytical workflow for cylindrical hole stability analyses in general laminated materials that possess transversely isotropic (TI) anisotropy is presented. In this approach, the calculation of the distribution of the stresses around a cylindrical hole and the failure evaluation at the hole wall consider the effects of both material elasticity anisotropy and strength anisotropy caused by material laminated structures. Material strength anisotropy is assumed to be caused by the sliding of preexisting weakness planes oriented parallel to the isotropic plane of the material. The effect of anisotropy on strength is modeled by combining a shear failure criterion for the intact matrix and a weak plane failure criterion for the planes of weakness. We derive critical pressure solutions for the stability of the intact matrix around a hole filled with gas or fluid based on the Mohr–Coulomb failure criterion and Drucker–Prager failure criterion; either one of them can be combined with the weak plane failure criterion to give the solution for hole wall shear failure pressure. The solution for hole wall fracture initiation pressure is derived based on the tensile failure criterion. This approach can be applied to holes of arbitrary orientation in general laminated materials.

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A revisit to the Lekhnitskii-Amadei solution for borehole stress calculation in tilted transversely isotropic media

Cited by 11 publications

References 18 publications

Anisotropic Wellbore Stability Analysis: Impact on Failure Prediction

Anisotropic Wellbore Stability Analysis: Impact on Failure Prediction

An analytical approach for cased borehole stress calculation in general anisotropic formations

An Approach for Stability Analysis of Gas/Fluid-Filled Cylindrical Hole in Laminated Materials

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