基于动力学缩比和传递矩阵法的水平井基频求解方法  

Method of solving fundamental frequency of horizontal well based on dynamic scaling and transfer matrix methods

作　　者：尹宜勇[1] 白翰钦 曲从锋 刘欢[1] 王国强 王通 朱文佳 YIN Yiyong;BAI Hanqin;QU Congfeng;LIU Huan;WANG Guoqiang;WANG Tong;ZHU Wenjia(College of Engineering, China Agricultural University, Beijing 100083, China;CNPC Engineering Technology R&D Company Limited, Beijing 102206, China)

机构地区：[1]中国农业大学工学院,北京100083 [2]中国石油集团工程技术研究院有限公司,北京102206

出　　处：《中国石油大学学报（自然科学版）》2022年第3期158-165,共8页Journal of China University of Petroleum(Edition of Natural Science)

基　　金：国家自然科学基金面上项目(52175126);中国石油科技创新基金研究项目(2019D-5007-0306)。

摘　　要：为提升振动固井技术的应用效果和固井效率,提出一种水平井套管柱基频的求解方法。基于动力学相似理论推导获得水平井套管柱基频的相似比,通过传递矩阵数值求解方法进行试验模型的基频计算,并通过试验对该方法进行正确性验证分析;依据基频相似比,结合传递矩阵计算方法实现原型水平井的基频计算。结果表明通过传递矩阵法,能够对水平井缩比模型基频进行求解,计算结果与缩比模型振动试验结果吻合较好,计算与试验误差小于10%;随着离散质量点数增加,求解精度大幅度增加,误差从114%、89.9%、44.1%缩小至2.3%;成熟的动力学相似理论与经过验证的传递矩阵法相结合,无需实体模型即可实现对原型井基频的求解,通过该方法可缩短技术周期,降低成本。In order to improve the application effect and cementing efficiency of the vibration cementing technology,a method to study the fundamental frequency of the casing string of horizontal well was presented.Firstly,based on the similarity theory in dynamics,the similarity ratio of the fundamental frequency of the casing string for the horizontal well was derived.Then,the fundamental frequency of the experimental model was calculated by the transfer matrix numerical solution method,and the correctness of the method was verified by experiments.Finally,based on the fundamental frequency similarity ratio and the transfer matrix method,the fundamental frequency of prototype horizontal well can be calculated.The results show that the fundamental frequency of the scaling model for the horizontal well can be solved by the transfer matrix method,and the margin of error between the calculated results and the experiment results is less than 10%,which demonstrates that the calculated results are in good agreement with the vibration testing results of the scaling model.With the increase of the discrete mass points,the accuracy of solution is greatly increased,and the error decreases from 114%,89.9%,and 44.1%to 2.3%.The mature similarity model theory combined with the verified transfer matrix method can be used to solve the fundamental frequency of the prototype well without building solid models.This method can shorten the technical cycle and reduce the cost.

关 键 词：水平井 相似理论 传递矩阵法 集中质量法 基频 

分 类 号：TE256[石油与天然气工程—油气井工程] O327[理学—一般力学与力学基础]