Taking a gas kick while drilling with a mud in which the kick cannot dissolve could be considered as a transient two-phase flow problem. "Driller's method" is the common industry practice to circulate the gas influx with a fixed bottom-hole pressure and a constant mud kill rate. Usually, the industry treats a gas kick as one single bubble. This assumption is suitable for design cases for kick tolerance and casing point selection, in which worst case pressures are considered. It, however, fails to address the complicated relationship between operational parameters and two-phase flow. In this work, we explore the potential to minimize the annulus surface pressure (aka, casing pressure) during gas kick circulation using two-phase flow considerations. This can be achieved by maximizing the hydrostatic losses in the annulus, which requires a decrease in average void fraction along the annulus. The study is limited to drilling with water-based muds.

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