A low-order two-phase dynamic flow model for drilling operations with gas kick is developed. The purpose is to enable fast and robust simulation of the behavior and propagation of influx gas in the bore hole, and the effects it has on the total flow dynamics. The model handles both open and closed wells, as well as the full range of pump rates and gas influx rates that are likely to occur in drilling operations. It incorporates equations for gas bubbles into a low-order liquid model in a new way. Some aspects of the gas are described in a mechanistic way, but with a new “dual-shape” bubble representation approach. Momentum is treated for the mixture as a whole, while conservation of mass is handled individually for each of the two phases. The result is a model consisting of a set of ordinary differential equations on explicit form, which makes it possible to couple it with control system- and estimation theory. A comparison with published data from four different sources shows that the model is able to qualitatively reproduce both steady state and transient responses in a handful quite different flow situations. In particular, we verified that the dominating effects that the gas has on compressibility, friction loss and hydrostatic pressure of the total mixture are satisfactory reproduced.

开发了一种低阶两相动流模型，用于气井钻探作业。目的是能够快速，可靠地模拟流入气体在钻孔中的行为和传播，以及其对总流动动力学的影响。该模型可处理裸眼和裸眼井，以及钻井作业中可能发生的全部抽水率和瓦斯涌入率。它以新的方式将气泡方程式合并到低阶液体模型中。气体的某些方面以机械方式进行描述，但采用了一种新的“双形”气泡表示方法。整体上对动量进行了处理，而对于两相中的每相，均单独处理了质量守恒。结果是一个模型，其中包含一组以显式形式表示的常微分方程，这使得将其与控制系统和估计理论结合起来成为可能。与来自四个不同来源的已发布数据的比较表明，该模型能够在少数完全不同的流动情况下定性地再现稳态和瞬态响应。特别地，我们证实了该气体对总混合物的可压缩性，摩擦损失和静水压力的主导作用得到了令人满意的再现。