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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一般各向异性地层中套管井应力计算的一种解析方法

我们提出了一种显式分析方法，用于计算一般各向异性地层中圆形套管井眼周围的应力分布。这种方法是基于纯弹性套管井模型开发的，该模型可以包含多个被同质各向异性介质包围的胶合同心套管柱。最内层套管的壁在井筒内部流体压力的作用下，地层可承受任意远场应力。每个套管-水泥边界都被认为是焊接的，因此水泥-地层边界也是如此。所导出的解析解可以应用于任意各向异性地层中的任意井眼轨迹，并且还可以应用于简并各向同性地层。