Abstract: Three-dimensvonal vertical vibration of the sucker rod string,tubing and liquid column in the sucker rod beam pumping system has been comprehensively atudied in this paper,a new set of partial differential equations describing the movement regularity of sucker rod beam pumping system have been obtained,and numerical solution of the partial differential equations have been obtained with finite山fference technique in a manner of lineAR and non-linear analysis.This mathematical model is better theoretically than one-dimensional and two-dimensional models which take sucker rod string only or sucker rod string and liquid column(unanchored tubing) only into consideration,so it may give a powerful tool for predicting the dynamic parameters of a sucker rod pumping system and well site diagnosis can be also.

摘要： 本文综合考察抽油井中抽油秆、油管和液柱的三维纵向振动,得到一组描述其运动规律的新的偏微分方程,并分别接线性和非线性两种方式,用有限差分法求其数值解.该数学模型比只考虑抽油杆的一维振动数学模型以及只考虑抽油杆、液柱(油管不锚定)的二维振动数学模型理论上要更加完善,因而可以成为预测有杆泵系统的动参数及进行故障诊断的有力工具.

关键词: 数学模型, 抽油杆, 三维振动, 有杆泵抽油, 偏微分方程组, 抽油井, 油管, 故障诊断, 有限差分法, 非线性特征