有杆抽油系统通用数学模型研究

针对定向井有杆抽油系统,在井眼为平面曲线的情况下,给出了描述抽油杆柱横向和纵向振动以及管柱有纵向振动并耦合液柱振动的数学模型,讨论了有杆抽油系统几种主要数学模型间的关系。对于模型描述的杆柱、管柱、液柱振动的偏微分方程组给出了特征变换,转化成对角方程组,使问题的数值计算方法得到了简化,从而给出了有效解法。新的数学模型适用于有杆抽油系统的预测、设计以及抽油系统故障诊断的模式识别。

Study on a general mathematical model for suck and pumping system

A mathematical model was proposed for describing the longitudinal and transverse vibrations of sucker-rod string, longitudinal vibration of tubing string coupled with fluid columns vibration in the directional and horizontal well bore with plane curve. The relationships on several given mathematical models were discussed. Based on different assumptions, the characteristic transformation for a set of partial differential equations of the mathematical model was given, and a set of diagonal partial differential equations were obtained. The relatively complex model could be transformed into a reduced model that is easy to be solved. The generated model is suitable to prediction, design and fault diagnosis of suck and pumping system.