基于热力学理论的水泥石热–力耦合本构模型和有限元分析

A thermal-mechanical constitutive model for cement rock based on thermodynamics and its finite element application

深层地热井中,水泥环在温度作用下的塑性和应力非线性对井下系统的封固性有重要影响。基于热力学理论,建立适用于水泥石的黏弹塑性热–力耦合本构模型。模型考虑了密度、弹性应变与温度之间的耦合关系以及弹性应变与耗散方程的耦合关系,能够模拟水泥石在等温试验中的诸多重要力学特性,以及在非等温试验中随温度升高而产生的强度和刚度衰减。在本构模型基础上开发瞬态传热的平面有限元程序,对中石油肯尼亚地热开发项目的套管–水泥环–围岩系统进行了温度和应力分析。研究发现,系统会在套管–水泥环界面和水泥环–围岩界面处产生应力集中,且界面处的温度附加应力在单调的温度荷载作用下呈现非单调性发展;能量耗散的考虑对于准确模拟水泥石的滞回特性和塑性变形发展十分重要。

The plasticity and stress non-linearity of cement sheaths under thermal loadings have significant influence on the integrity logging of deep geothermal well systems. A thermal-mechanical elasto-viscoplastic model based on the thermodynamics is established with the density and the elastic strains coupled with the temperature and the dissipative equations coupled with the elastic strains. The model is able to simulate many important properties of cement stones in isothermal tests and the degradation of strength and stiffness with the rising of temperature in non-isothermal tests. A finite element code with transient heat conduction is developed based on the constitutive model. The code is then applied for the temperature and stress analysis of a CNPC geothermal well in Kenya. Results show that the thermal-induced mechanical stresses, especially at interfaces, are non-monotonic during the monotonic thermal loading. The consideration of energy dissipation is essential for the reasonable estimations of hysteresis and plastic deformations of cement stones.