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A Wellbore Stability Model for a Deviated Well in a Transversely Isotropic Formation Considering Poroelastic Effects

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Abstract

To analyse wellbore stability phenomena when drilling through a transversely isotropic formation such as shale, a wellbore stability model is developed based on the coordinate transformation method and complex variable elasticity theory. In order to comprehensively consider the anisotropies in the transversely isotropic formation, the model includes the followings: 1. the elastic anisotropy due to the sedimentation effect and naturally developed fractures and 2. the strength anisotropy due to the poor cementation between bedding planes and natural fractures. The model is further generalized by accounting for an arbitrary wellbore trajectory under an arbitrary in situ stress orientation. Next, the model is used in a parametric study that includes factors such as elastic anisotropy, strength anisotropy, multiple weak planes, in situ stress anisotropy, and poroelastic anisotropy, all of which can have a great influence on wellbore stability. Finally, a correction for a frequently used failure criterion has been made to ensure that the newly developed model is comprehensive and accurate for wellbore stability analyses in highly heterogeneous formations.

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Abbreviations

σ H :

Maximum horizontal principal stress

σ h :

Minimum horizontal principal stress

σ v :

Overburden stress

E ∥ :

Elastic modulus in the bedding plane of isotropy

E ⊥ :

Elastic modulus normal to the isotropic plane

ν ∥ :

Poisson’s ratio in the bedding plane of isotropy (characterizing contraction in-plane)

ν ⊥ :

Poisson’s ratio normal to the isotropic plane (characterizing contraction out of plane)

G ∥ :

Shear modulus for planes parallel to the isotropic bedding plane

G ⊥ :

Shear modulus for planes normal to the isotropic bedding plane

S o :

Cohesion strength of rock intact body

u o :

Coefficient of friction of rock intact body

\(\alpha_{\text{bp}} + \frac{\pi }{2}\) :

Dip direction of bedding planes

β bp :

Dip angle of bedding planes

S bp :

Cohesion strength on bedding planes

u bp :

Coefficient of friction on bedding planes

\(\alpha_{\rm nf} + \frac{\pi }{2}\) :

Dip direction of natural fractures

β nf :

Dip angle of natural fractures

S nf :

Cohesion strength on natural fractures

u nf :

Coefficient of friction on natural fractures

k s :

Shear stiffness of natural fractures

k n :

Normal stiffness of natural fractures

ω :

Dilation angle of natural fractures

s :

Space distance between natural fractures

K s :

Grain modulus

p :

Formation pressure

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Acknowledgments

The authors are grateful for the financial support from China National Natural Science Funds for Distinguished Young Scientists Project ‘Petroleum related Rock Mechanics’ (No 51325402).

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Authors and Affiliations

  1. School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Ming Liu

  2. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, People’s Republic of China

    Yan Jin, Yunhu Lu, Mian Chen, Bing Hou, Wenyi Chen & Xin Wen

  3. Schlumberger, Tianjin, China

    Xiaoning Yu

Authors
  1. Ming Liu
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  2. Yan Jin
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  3. Yunhu Lu
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  4. Mian Chen
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  5. Bing Hou
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  6. Wenyi Chen
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  7. Xin Wen
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  8. Xiaoning Yu
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Correspondence to Yan Jin.

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Liu, M., Jin, Y., Lu, Y. et al. A Wellbore Stability Model for a Deviated Well in a Transversely Isotropic Formation Considering Poroelastic Effects. Rock Mech Rock Eng 49, 3671–3686 (2016). https://doi.org/10.1007/s00603-016-1019-8

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