Abstract: This paper presents a new mathematical model for a sucker-rod pumping system.in addition to the consideration of dynamics factors of the sucker-rod string,the new model also includes the compressible fluid equation which describes the dynamics of the fluid column.Four definite solution conditions suitable to field situation and a connecting condition for a tapered sucker-rod string are derived.The effect of fluid physical parameters,mechanical movement parameters and bottom-hole pump performance are considered in the model.A new mathematical method is used in the paper to solve the model.Both the theoretical analysis and field tests have shown the reliability and accuracy of the solution.The new model can be used to predict the condition of a pumping well at various patameters and the dynamographs of the polished rod and bottom-hole pump.

摘要： 本文提出了一个描述有杆抽油系统的新的数学模型。它与以前数学模型的不同之处是除了考虑了杆柱动力学因素以外,还包括了描述液柱动力学影响的可压缩流体方程,并建立了适应矿场情况的四种定解条件及描述多级组合杆柱的衔接条件。模型中考虑了液体物性参数、机械运动参数和井下设备工况的影响。本文采用一种新的数学方法对模型进行求解,理论分析和实际验证都说明该解法稳定性好,精确度高。新模型可用于预测抽油井在各种参数下的光杆和井下示功图及其各项工况指标。