A Dynamic Model of Percolating Gas in an Open Well-Bore

The two-phase dynamics of a gas-kick percolating up a vertical well, drilled using a partly evacuated riser, is described by two ordinary differential equations and algebraic relations. We model the gas as bubbles distributed with a distribution function along the well. The simplicity of the model makes it well suited for estimation purposes and controller design. We present simulation results where an unscented Kalman filter is used to estimate the current location of the gas, distribution of the gas, and rise-velocity. These estimates can be used to predict when the gas will pass the blowout preventer and reach the drilling rig.