Abstract
The dynamic mathematical models were greatly developed to describe the motion of the sucker-rod pumping system since 1960s and various mathematic models based on different assumptions were presented. This paper does a study in three sides. First, a mathematical model is presented to describe the sucker-rod string with longitudinal and transverse vibrations, and coupled with longitudinal vibration of the tubing and fluid columns in a deviated well. Second, the relations of several kinds of mathematical models in sucker-rod pumping systems are discussed, and the model made in this paper, when based on different assumptions, can become different models made by people these years, which are presented in important references. Third, a method of characteristics is used to transform the set of partial differential equations which describe the vibration of the sucker-rod string, and coupled with vibrations of tubing and liquid columns in the sucker-rod pumping system. Through the transformation, a diagonal partial differential equations set is obtained. Hence a relatively complex model is transformed into a reduced model which is easy to solve. This model has basic meaning for using the technique of pattern recognition to make automatic diagnosis of sucker rod pumping system.
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© 2004 Springer-Verlag Berlin Heidelberg
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Liu, L., Tong, C., Wang, J., Liu, R. (2004). A Uniform and Reduced Mathematical Model for Sucker Rod Pumping. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science - ICCS 2004. ICCS 2004. Lecture Notes in Computer Science, vol 3037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24687-9_47
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DOI: https://doi.org/10.1007/978-3-540-24687-9_47
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