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Summary This paper describes a directional drilling model for calculating the equilibrium inclination of straight boreholes, considering a bottomhole assembly (BHA) with a “push-the-bit” rotary steerable system (RSS). The model yields closed-form expressions for the magnitude and orientation of the RSS pad force, which is required to maintain the inclination of the borehole. The explicit dependence of the RSS force on the positions of the stabilizers and the RSS, on the mechanical properties of the BHA, on the characteristics of the bit, and on the weight on bit enables the identification of particular cases of practical significance.

This paper uses a novel directional drilling model to explain seemingly anomalous behaviors of the evolving geometry of a borehole. The two cases of a BHA without and with a push-the-bit RSS are considered. The directional propagation of a borehole essentially depends on the bending of the BHA, which is constrained to deform within the borehole, and on the interaction between the drill bit and the rock formation. The directional model is used to illustrate, through theoretical examples, the consequence of the interrelation between these two elements of the problem. Also, a small set of dimensionless parameters governing the behavior of the directional drilling system is derived. They contrast properties of the bit/rock interface laws with those of the BHA.