Well control has always been a very important issue in the oil and gas exploitation business, since it involves money savings, people safety and environment threatening. The advancement of the exploration frontiers from onshore to offshore fields, particularly, deep and ultra-deep waters, has increased even more the relevance of kick control and blowout prevention during drilling operations. Widely used drilling practices have been optimized and re-evaluated, so have new technologies been developed to handle specific issues related to deepwater drilling operations, such as reliable and efficient well control practices. This effort has great importance to some countries like Brazil, which have most part of their oil and gas production (close to 75%) concentrated on offshore wells, about 70% of those reserves are located in deep waters. Regarding such scenario, this article presents a comprehensive and discussed literature review about well control in deep and ultra-deep waters, covering the evolution of the analytical and numerical kick models. A mathematical model has been developed to predict the pressure behavior inside the annulus during a gas-kick circulation out of the well in deep water scenarios. Considerations regarding the effects of wellbore geometry, frictional pressure losses, influx expansion, and two-phase flow models have been implemented in the present model. The analysis of the effect of some important parameters in well control in the surface pressure, such as the pit gain, water depth, mud density and pump flow rate are presented.

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