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Mechanical Analyses of Casings in Boreholes, under Non-uniform Remote Crustal Stress Fields: Analytical & Numerical Methods

Fei Yin1, Deli Gao1

Key Lab of Petroleum Engineering in the Ministry of Education, China University of Petroleum-Beijing, Beijing 102249, China. Corresponding author: Deli GAO. E-mail:,

Computer Modeling in Engineering & Sciences 2012, 89(1), 25-38.


The methods to design the casings used in oilfields, are currently based on the assumptions that the remote crustal-stress-field is axially symmetric, in plane strain. However, most of the failures of the casings are caused by non-uniform and asymmetric far-field crustal stresses, so that it is necessary for a proper design of the casings, to investigate and understand the casing's behavior under non-uniform far-field crustal stresses. A mechanical model is first established for the system, consisting of the casing and formation, by using the plane strain theory of linear elasticity. The non-uniform crustal stress is resolved into a uniform stress field and a deviatoric stress field. The analytical formulae for the stress and deformation fields within the casing, under non-uniform remote crustal stresses, are obtained by analyzing the stress and deformation fields of the combined system separately under the two components of applied crustal remote stress fields and then combining by linear superposition. Furthermore, a finite element analysis is also used to simulate this problem numerically. The crustal stress data in some oilfield are used to compute the tractions exerted on the external surface of the casing by the crustal formation, as well as the detailed stress-field within the casing, as an example. The maximum relative differences between the analytical solutions and the numerical results are about 6.5%. Under non-uniform remote crustal stresses, the normal traction exerted on the casing has an oval distribution, and the circumferential stress at the inner wall of the casing has a peanut-like distribution. It can be predicted that the initial yield failure in the casing occurs in the direction of the minimum horizontal crustal stress. Both the analytical and numerical solutions obtained in this paper are useful for the design of casings under the non-uniform remote crustal-stresses in an oilfield.


Cite This Article

Yin, F., Gao, D. (2012). Mechanical Analyses of Casings in Boreholes, under Non-uniform Remote Crustal Stress Fields: Analytical & Numerical Methods. CMES-Computer Modeling in Engineering & Sciences, 89(1), 25–38.

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