A New Model and Calculating Method for Pump Dynamograph Diagnosis of Sucker Rod Pumping Systems
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摘要: 通过对多级杆柱上的微元体进行动力学分析,对现有的Gibbs模型进行了改进,建立了一个新的有杆抽油泵功图诊断数学模型.采用隐式差分格式和变步长有限差分格式对模型进行求解,得到了接箍上、下分界面处和抽油杆均质段任意位置处的位移及载荷表达式,推导了等效阻尼系数的计算公式,建立了相应的迭代算法来计算井下泵功图.以某油井地面示功图为例,利用该模型进行了实例计算,与Gibbs方法对比结果表明,该模型及算法得到的泵功图更接近实际.Abstract: The existing Gibbs model was improved through analysis of the dynamic characteristics of the micro units out of hybrid sucker rods. A new pump dynamograph diagnosis mathematical model was established for sucker rod pumping systems. The model was solved with the methods of implicit difference scheme and variable step size finite difference scheme. The displacement and load expressions at the interface of the box coupling and at any position of the uniform sucker rod segments were obtained. The formula of equivalent damping coefficient was derived and calculated through the corresponding iterative algorithm. With a well surface dynamometer card as an example, the pump dynamograph was calculated by means of the new model, and the results were compared with those from the Gibbs method. The comparison indicates that the new model and algorithm is stable and reliable, and the resulting pump dynamograph fits the actual situation better than that from the Gibbs model.
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