Computer Model Evaluates Oil Pumping Units in Inclined Wells

Abstract

Abstract The paper analyzes the dynamic behaviour of the sucker rod string in the inclined well. In this case, due to the curvature of the tubing the rod vibrates longitudinally as well as transversally. A mathematical model of the vibrating string consisting of two coupled differential equations was developed. The paper describes the fundamental assumptions and simplifications which can be used in the numerical analysis. The examples of the results are also presented. They include the effect of the distortion of the geometry of the rod string on the plunger load-displacement diagram and the diagram of the friction forces along the rod string. Introduction The evaluation of pumping units in the inclined wells has been a serious problem in engineering practice. The common practice at present is the application of the program developed for vertical wells to the analysis of deviated wells. This introduces substantial errors in the calculations of the stresses in the rod string and as regards the gearbox torques. Generally, the maximum torques calculated properly for the actual geometry of the slant hole pumping unit can be up to 40% larger than the corresponding values obtained from the calculations for vertical units. Besides, the application of the program for vertical wells to the evaluation of inclined, wells gives results in which all the friction forces from the rod string are concentrated at the plunger. This gives false prediction of high compressive forces at the bottom of the rod string and can be the reason for the wrong conclusions regarding the rod stability. The rod in the inclined well is under different static and dynamic forces than in the vertical one. It is supported by the tubing of wheeled couplings but it is also transversely loaded by its own weight. Therefore, the dynamic behaviour of the sucker rod in the deviated well is much more complicated and different from a vertical one. The differences are caused by the friction between the rod string and the tubing and the rod curvature. If the tubing is curved, the dynamically loaded rod string deforms and comes into contact with the wall of the tubing. The curvature causes the lateral displacements of the rod inside the tubing. It couples the longitudinal vibrations with the transverse vibrations. The axial compressive forces at the bottom of the well can buckle the rods. In this case, the problem becomes nonlinear and difficult to solve. The need to obtain a model for use in the evaluation of pumping units and downhole equipment in the inclined and deviated wells resulted in the development of an applicable design and optimization technique. SRPUMP computer program was developed a tool that allows a high level of expert knowledge to be applied daily in the field, dealing with problems of the inclined wells. Fundamental Assumptions An accurate prediction of the performance of the sucker rod string and the bottomhole equipment requires careful modelling of the dynamic behaviour of the rod.