Steady-state solutions of a propagating borehole: Helical trajectory

Deep boreholes with complex geometries are now drilled with the help of rotary steerable systems (RSS), which are downhole robots capable of steering the bit by either applying a force on the borehole walls (push-the-bit systems) or by tilting the bit (point-the-bit systems). This paper explores the existence of stationary borehole geometries in the form of vertical helical trajectories. These non-trivial solutions, which represent the equilibrium points of the dynamical equations governing the evolution of the borehole, correspond to situations where the deformed configuration of the bottomhole assembly (BHA) remains invariant during the propagation of the borehole, i.e., the BHA moves inside the created borehole as a rigid body. Formulation of the model yields a system of linear equations in terms of the radius and pitch of the helical boreholes. A parametric analysis of the solution for the idealized case of rigid BHA with one stabilizer shows the region of existence of helical trajectories and the dependence of the pitch and radius of the helix on the control parameters.