定向井有杆抽油系统动态性能分析方法

由于杆管间库仑摩擦的影响,定向井有杆泵抽油系统动态参数预测模型是一个非线性的偏微分方程,求解复杂。鉴于此,提出了一种新的分析方法。该方法以定向井有杆抽油系统中的抽油杆柱作为研究对象,根据三次样条插值模拟得到的定向井的井眼轨迹,利用静力有限元法计算出了油管对抽油杆柱的支反力,进而得出了杆柱与油管之间的库仑摩擦力;给出了杆柱单元的受力分析;建立了有限元形式的杆柱系统动力学方程并利用状态空间法对其进行了数值求解,获得了悬点示功图。文末给出了两口油井的预测实例,并将预测结果与实测结果进行了对比。对比结果表明本文所提的分析方法是正确和有效的。

An analytical method for dynamic performance of sucker-rod pumping system of directional well

Because of the Coulomb friction between the rod and pipe,the prediction model of dynamic characteristics of sucker-rod pumping system in directional well is a nonlinear partial differential equation,whose solution is difficult and complex.In order to simplify the model,a novel analytical method is put forward.Firstly,based on the well trajectory fitted by using the cubic spline interpolation method,the support reaction between rod string and pipe in directional well is calculated according to the finite element method for static load.Secondly,using the calculated support reaction,the Coulomb friction force between rod string and pipe is computed.Thirdly,the loads analysis of rod element is performed and dynamic equations of rod element are derived.Assembling all element dynamic equations,the system dynamic equation of rod string is obtained.Finally,the state space method is employed to solve the established system dynamic equation with time-varying coefficients.In the end,two prediction examples are given,where a comparison between the predicted and the measured dynamometer cards is made to show that the presented analytical method is correct and effective.