Derivation of the nonlinear dynamics of the interface between a kick gas fluid and mud system in a gas wellbore based on momentum conservation principle

In this paper, the dynamics of the interface between a kick gas fluid and drill mud in the annular space of a drill hole has been considered using momentum balance approah. In so doing an existing momentum balance equation for mixture flow in conduits has been used to derive an interfacial velocity equation for aparticular scenario of kick event, where mud circulation ceases after kick detection. The model shows that the interface dynamics is non-linear. The utility of the derived equation stems from the fact that all parameters required for computation of velocities can be obtained. Based on the interfacial velocity model, the flux equation for annular mud flow and the maximum interfacial velocity at well head have been derived. The relevance of the velocity equation to casing design and running has also been dicussed. The approach in this work is purely analytical.