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.

抽油杆抽油井可以是垂直的也可以是定向的。随着时间的流逝，对垂直井功能的研究工作导致了一套完善的数学模型和实用工具。但是，在定向井方面，尚未达成普遍共识，并且该话题仍在积极讨论中。本文回顾，扩展，实现和优化了一个最初于1995年设计的，被忽视的模型，该模型的计算复杂性导致处理时间长，阻碍了它的采用。该模型充分利用了杆柱的3D轨迹，允许使用两个粘性摩擦模型，并针对井下边界条件提出了自己的公式。考虑到杆-管环空内的流体流动，所得模型可用于有效模拟定向抽油杆抽油井的动态行为。我们基于显式有限差分方法，介绍并分析此CPU密集型模型的串行和并行软件实现。我们还将描述我们对原始模型和软件实现的准确性和性能的贡献。粗略估算出，如果我们要在现代处理器中运行旧版原始代码，则建议的串行版本比旧版原始代码快200倍左右。最重要的是，我们的并行实现达到了6.5 我们还将描述我们对原始模型和软件实现的准确性和性能的贡献。粗略估算出，如果我们要在现代处理器中运行旧版原始代码，则建议的串行版本比旧版原始代码快200倍左右。最重要的是，我们的并行实现达到了6.5 我们还将描述我们对原始模型和软件实现的准确性和性能的贡献。粗略估算出，如果我们要在现代处理器中运行旧版原始代码，则建议的串行版本比旧版原始代码快200倍左右。最重要的是，我们的并行实现达到了6.5\（\ times \）在共享内存系统中加速了串行版本，使其成为用于井设计和优化的合适工具。这项研究有助于对定向抽油杆抽油井的数学建模的讨论，并说明了以性能为中心的技术如何能够有效利用计算需求模型来促进进一步的改进和应用。