套管-水泥环-地层耦合系统热应力理论解

Theoretical solution of thermal stress for casing-cement-formation coupling system

根据弹性力学和热力学理论,推导了套管-水泥环-地层耦合系统的热应力和热位移理论计算公式,分析了系统热应力和热位移径向分布规律,以及套管温升、弹性模量、热膨胀系数、壁厚、水泥环与地层弹性模量和泊松比等参数对套管热应力和热位移的影响。结果表明:随着离套管中心径向距离的增加,径向热位移和热应力先增大后减小,最大值分别位于地层和套管外壁,而套管上Von Mises应力值迅速下降,最大值位于套管内壁;随着套管温升和套管、水泥环、地层弹性模量与热膨胀系数的增加,套管内壁Von Mises应力和外壁径向压力增大,其中套管参数变化对计算结果影响更明显。在进行稠油热采井套管抗挤毁强度计算时,应考虑热膨胀在套管外壁产生的径向压应力的影响。

The formulas of thermal stress and displacement for casing-cement-formation coupling system were derived based on the elastic mechanics and thermodynamics. The thermal stress and radial thermal displacement distribution of the coupling system were calculated. The effects of parameters on casing thermal stress and displacement distribution were studied, including casing temperature increment, elastic modulus, coefficient of thermal expansion, wall thickness, elastic modulus and Poisson＇s ratio of cement and formation. The results show that the radial displacement and stress firstly increase and then decrease with the radial distance increasing from casing center, and the maximum values are located on formation and casing external wall respectively. While the casing Von Mises （VOM） stress declines rapidly with the radial distance increasing, and the maximum value is located on the casing internal wall. Meanwhile, VOM stress on the casing internal wall and external radial stress increase with the temperature increment, elastic modulus and coefficient of thermal expansion of casing-cement-formation coupling system increasing. The variation of casing parameters has a great effect on the computational solution. The radial thermal stress on casing external wall formed by thermal expansion should be considered for calculating casing collapse strength in steam injection wells.