A simulation model for dynamic behavior of directional sucker-rod pumping wells: implementation, analysis, and optimization

Abstract

Sucker-rod pumping wells can be either vertical or directional. Over time, research efforts on the functioning of vertical wells led to a well-established set of mathematical models and practical tools. When it comes to directional wells, however, no general agreement has been reached, and the topic remains in active discussion. This paper revisits, extends, implements and optimizes an overlooked model, initially devised in 1995, whose computational complexity resulted in long processing times that stymied its adoption. This model fully utilizes the 3D trajectory of the rod string, allowing for the use of two viscous friction models and proposing its own formulation for downhole boundary conditions. The resulting model can be used to efficiently simulate the dynamic behavior of directional sucker-rod pumping wells taking into account the fluid flow inside the rod-tubing annulus. We present and analyze a serial and a parallel software implementation of this CPU-intensive model based on an explicit finite-difference method. We also describe our contributions to the accuracy and performance of the original model and software implementation. A rough approximation shows that the proposed serial version is about 200 times faster than the legacy original code, if we were to run the latter in a modern processor. On top of that our parallel implementation achieved a 6.5$$\times $$ × speedup over the serial version in a shared-memory system, making it a suitable tool for well design and optimization. The research contributes to the discussions on mathematical modeling of directional sucker-rod pumping wells, and illustrates how performance-focused techniques can enable the effective use of computationally demanding models to facilitate further refinements and applications.

Ensuring the operational-technological characteristics of the new design solution of the sucker-rod pumping unit

“…According to the analysis of the current experience and modern literature related to this field, it is evident that the parameters of the rod pump's stuffing boxes, namely the applied releasable tension s [ ] and the increase in the power ratio of the drive mechanism, have the most significant impact on the application area of the newly designed pumping unit. These parameters reflect all the factors included in the three groups mentioned above and have a direct effect on the efficiency of the pumping unit [18][19][20].…”

Prediction of Sucker Rod-tubing Wear Depth in Surface Drive Screw Pump Production Wells

“…Han et al [5] measured the normal stress and eccentricity of the tubing string caused by the fluid through experiments, and proposed comprehensive measures to avoid local wear of the sucker rod. Based on the three-dimensional trajectory of sucker rod string, Araújo et al [6][7][8] proposed a new method for calculating the force of sucker rod string, deduced the mechanical analysis model of sucker rod string in three-dimensional directional well, and accurately analyzed the three-dimensional stress and dynamic state of downhole sucker rod string. Wu et al [9][10][11][12] established the dynamic model of sucker rod, and studied the deformation of tubing sucker rod caused by the eccentricity of screw pump rotor.…”