Abstract

Drilling geometrically complex boreholes in the subsurface has been made possible with the development of downhole tools that steer the bit. This paper proposes a model of borehole propagation that can be used not only to predict the bit trajectory, here restricted to a vertical plane, but also to assess the conditions leading to abnormal situations. The model is formulated from considerations involving (a) a bit/rock interaction law that relates the force and moment on the bit to its penetration into the rock, (b) kinematic relationships that describe the local borehole geometry from the bit motion, and (c) a beam model of the bottom-hole assembly (BHA) that expresses the force and moment at the bit as functions of both the loads applied on the BHA and the geometrical constraints imposed by the stabilizers that center the BHA in the borehole. The coupling between the model components leads to the formulation of a delay differential equation that governs the evolution of the borehole inclination, with spa...

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