MATHEMATICAL MODELLING AND SOLUTION PROCEDURE FOR THE BEHAVIOR OF SUCKER-ROD PUMPING SYSTEM

Abstract

This paper presents a simple and efficient approach for predicting the dynamic behavior of the sucker rod string. The dynamic behavior of the sucker rod string is an important factor for predicting the performance of a pumping system. Prediction of sucker-rod system behavior involves the solution of a boundary value problem. Such a problem includes a differential equation and a set of boundary conditions. For the sucker-rod problem, the wave equation is used, together with boundary conditions which describe the initial stress and velocity of the sucker rods, the motion of the polished rod and the operation of the downhole pump. Of these items, the wave equation, the polished rod motion condition and the down-hole pump conditions are of primary importance. Discussion of the mathematical model centers about these factors. In this study, the model consists of two analysis that are used to calculate the displacement and loads of the operation conditions of the sucker-rod pump. Practical usefulness of the proposed approach is shown by simple examples and tests. This study shows that the proposed approach is very efficient for predicting the performance of a sucker rod pumping system.