一种非均匀地应力下椭圆井眼套管-水泥环-地层力学特性半解析解

为研究井壁崩落形成椭圆形井眼后套管受力情况，在弹性力学理论的基础上，结合复变函数方法建立了非均匀地应力作用下椭圆形井眼内套管-水泥环-地层组合体应力模型，根据应力边界条件与位移单值条件得到了系统各界面处应力分布的半解析解；并探究了井眼椭圆度、水泥环弹性模量和泊松比对套管外壁径向应力与Mises 应力的影响。研究结果表明：与圆形井眼相比，椭圆形井眼能减小套管所受最大应力，降低应力非均匀度;高泊松比、低弹性模量水泥环也有利于减小套管受力。研究成果对井壁崩落段地层钻井液密度、套管规格选取和固井水泥性能设计具有重要的指导意义。

A Semi Analytical Solution for Mechanical Properties of Elliptical Borehole Casing-Cement- Stratum System in Non-Uniform in-Situ Stress Field

During drilling, wellbore collapsing will cause the wellbore to become elliptical. In order to study the stress of casing in elliptical wellbore, a stress model of casing-cement -formation system in elliptical wellbore under inhomogeneous in-situ stress was established on the basis of elastic mechanics theory and complex variable function method. The stress boundary condition and displacement single value condition were used to derive a set of linear equations that can get the stress potential function. On the basis of stress potential function, the analytical solutions of the stress distribution at all directions can be obtained. With that, the effects of hole ellipticity, cement sheath elastic modulus and Poisson''s ratio on the radial stress and Mises stress of casing outer wall are discussed. The results show that: compared with the circular hole, the elliptical hole can reduce the maximum stress and the stress non-uniformity; the cement sheath with high Poisson''s ratio and low elastic modulus can also reduce the casing stress. The results have important guiding significance for mud density and casing specification selection, cement performance design in the formation of wellbore caving section.