This paper presents the development of a simplified two-phase well control computer model to simulate gas kicks. The paper identifies key factors in the prediction of kick behavior based on a comparison between a fully implicit dynamic two-phase model and a single-phase model. The model also analyzes kick responses for directional and horizontal slimholes and wells drilled with coiled tubing. Directional and horizontal wells consider multiple build-up rates. This paper highlights the effect of homogeneous or locally high pressured horizontal wells and the effect of reeled coiled tubing. This paper also examines theoretical kill sheets for several well trajectories from vertical to horizontal and for coiled tubing drilling. Theoretical kill sheets are compared with conventional kill sheets.

The simplified two-phase well control model developed in this study is reliable and stable. It can handle vertical, directional, and horizontal wells with multiple build-up rates and hold sections and does not have any numerical problems such as may occur with a dynamic two-phase well control model. For directional and horizontal wells with high build-up rates, choke pressure changes rapidly without much kick expansion because of vertical height change of the kick mixture as the kick moves through the curve.

A conventional kill sheet is good enough for a conventional large diameter vertical well with uniform well geometry. However, a theoretical kill sheet should be used with some amount of over-pressure for directional, and horizontal wells, especially when those are slimhole wells or are drilled with coiled tubing.

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