SUN Ren-yuan, ZHANG Yun-fei, FAN Kun-kun, WANG Jian, LIU Zhuo, LU Xue-jiao. A New Model and Calculating Method for Pump Dynamograph Diagnosis of Sucker Rod Pumping Systems[J]. Applied Mathematics and Mechanics, 2014, 35(4): 423-431. doi: 10.3879/j.issn.1000-0887.2014.04.008
 Citation: SUN Ren-yuan, ZHANG Yun-fei, FAN Kun-kun, WANG Jian, LIU Zhuo, LU Xue-jiao. A New Model and Calculating Method for Pump Dynamograph Diagnosis of Sucker Rod Pumping Systems[J]. Applied Mathematics and Mechanics, 2014, 35(4): 423-431.

# A New Model and Calculating Method for Pump Dynamograph Diagnosis of Sucker Rod Pumping Systems

##### doi: 10.3879/j.issn.1000-0887.2014.04.008
Funds:  The National Science and Technology Major Project of China(2011ZX05031-002-007HZ)
• Received Date: 2013-07-25
• Rev Recd Date: 2013-11-06
• Publish Date: 2014-04-15
• 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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