套管-水泥浆系统流固耦合振动特性研究

Study of fluid structure interaction vibration characteristics of casing filled and surrounded by slurry

已有文献在计算振动固井套管固有振动特性时,未充分考虑水泥浆和套管流固耦合的影响,难以准确地得出套管在水泥浆条件下的振动特性。本文进一步考虑了套管和水泥浆的耦合振动特性,基于Euler-Bernoulli梁柱理论及Hamilton变分原理推导了套管与水泥浆耦合振动控制方程,采用有限元方法计算了套管在水泥浆条件下的振动特性,综合分析了管内压力、水泥浆密度、套管长度、水泥浆阻尼等因素对耦合系统横向振动固有频率的影响。结果表明:套管-水泥浆系统的耦合特性不可忽略,随着水泥浆密度的增加,套管横向振动的固有频率降低;套管内流体压力、水泥浆的粘性阻尼和科氏阻尼对耦合系统的横向振动固有频率影响较小,可以忽略不计;随着套管长度的增加,套管横向振动固有频率减小。研究结果可为振动发生器的优化设计提供理论基础。

In the course of designing vibration cementation equipment, previous research did not take fluid-structure interaction(FSI) into account when analyzing the vibration characteristics of casing coupled with slurry. It is difficult to accurately calculate the vibration characteristics of casing. According to Euler-Bernoulli beam theory and extended Hamilton principle, the coupled vibration equation of casing and slurry has been established. Finite Element Method has been used to solve the governing equations and analyze the vibration characteristics of casing with different dimensions, inner pressures, densities and damping of slurry. Results show that the coupled characteristics of casing and slurry cannot be dismissed, since the natural frequency that taking FSI into account is much lower than that neglecting the slurry in casing, and the natural frequency will became lower with the increase of slurry density. The inner pressure of casing and the damping of slurry have slight influence on the transverse natural frequency of casing, so that the impact of inner pressure and the damping of slurry can be neglected. The transverse natural frequency will decrease with the increase of the length of casing. The paper provides a theoretical basis for the design of vibration excitation equipment.