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 6.5times 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.