Abstract The interface failure (micro-annulus and de-bonding) at the first interface between cement sheath and formation, or at the second interface between cement sheath and casing can be easily caused by alternating change of internal pressure and temperature in the casing during large-scale multistage hydraulic fracturing in shale-gas well. It is likely to have a great impact on casing stress and pose a potential threat to casing failure, especially the casing under non-uniform in-situ stress (NUS). Hence, based on the generation mechanism of micro-annulus in the first and second interface, the mechanical model coupling the casing and cement sheath as well as formation under non-uniform in-situ stress is presented with due consideration of the effect of interface failure status on casing stress. In the model, the failure interface with micro-annulus is considered by adopting boundary conditions of smooth contact, and the interface without micro-annulus is considered by adopting boundary conditions of ideal complete contact. The stress and displacement equations are derived by the semi analytical method, and the linear algebra equations and analytical solution of the equations are obtained based on the different contact status. The associated calculating program to calculate stress distribution of casing and cement sheath is developed and programmed. The effects of physical parameter and geometrical parameters of formation, cement sheath and casing, contact status of cement sheath boundary and non-uniformity of in-situ stress on casing stress have been systematically investigated.

中文翻译：

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非均匀地应力下套管与水泥环界面破坏对套管应力影响研究

摘要 水泥环与地层第一界面或水泥环与套管第二界面的界面破坏（微环空和脱胶）很容易由于套管内压力和温度的交替变化而引起。页岩气井多级水力压裂。它很可能对套管应力产生很大影响，并对套管失效构成潜在威胁，尤其是在非均匀地应力（NUS）下的套管。因此，基于第一和第二界面微环空的产生机制，提出了套管和水泥环以及地层非均匀地应力下的耦合力学模型，并适当考虑了界面破坏的影响。套管应力状态。在模型中，有微环的破坏界面采用光滑接触的边界条件，无微环的界面采用理想完全接触的边界条件。采用半解析方法推导出应力位移方程，并根据不同的接触状态得到方程的线性代数方程和解析解。开发并编写了计算套管和水泥环应力分布的相关计算程序。系统地研究了地层、水泥环和套管的物理参数和几何参数、水泥环边界的接触状态和地应力的不均匀性对套管应力的影响。无微环的界面采用理想完全接触的边界条件考虑。采用半解析方法推导出应力位移方程，并根据不同的接触状态得到方程的线性代数方程和解析解。开发并编写了计算套管和水泥环应力分布的相关计算程序。系统地研究了地层、水泥环和套管的物理参数和几何参数、水泥环边界的接触状态和地应力的不均匀性对套管应力的影响。无微环的界面采用理想完全接触的边界条件考虑。采用半解析方法推导出应力位移方程，并根据不同的接触状态得到方程的线性代数方程和解析解。开发并编写了计算套管和水泥环应力分布的相关计算程序。系统地研究了地层、水泥环和套管的物理参数和几何参数、水泥环边界的接触状态和地应力的不均匀性对套管应力的影响。采用半解析方法推导出应力位移方程，并根据不同的接触状态得到方程的线性代数方程和解析解。开发并编写了计算套管和水泥环应力分布的相关计算程序。系统地研究了地层、水泥环和套管的物理参数和几何参数、水泥环边界的接触状态和地应力的不均匀性对套管应力的影响。采用半解析方法推导出应力位移方程，并根据不同的接触状态得到方程的线性代数方程和解析解。开发并编写了计算套管和水泥环应力分布的相关计算程序。系统地研究了地层、水泥环和套管的物理参数和几何参数、水泥环边界的接触状态和地应力的不均匀性对套管应力的影响。