Analysis of a downhole passive regulator in drilling: A distributed parameter modeling approach

This paper pursues a model-based investigation of the effect of a downhole passive regulator (AST) on the performance of a rotary drilling system. In this work, the drill-pipe is represented as a continuum model in the form of partial differential equations (PDEs), capturing all modes of axial and torsional dynamics; the bottom-hole-assembly (BHA) is described by a discrete model governed by ordinary differential equations (ODEs); and the evolution of the rock surface under the bit is characterized by another PDE. These sub-systems are assembled and form a coupled PDE–ODE–PDE system model. We perform simulation-based studies on the proposed model for cases without and with the AST, and analyze the drilling performance in terms of the nonlinear behavior of both drilling systems, particularly in terms of depth-of-cut (rate-of-penetration) and drilling efficiency in the rock cutting process (torque-on-bit). In addition, we also analyze the friction-induced loading on the drill-bit and the dynamic loading on the drill-string. These numerical studies show that the use of the AST regulator can assist to improve the drilling performance and to decrease both the frictional loading on the bit and the dynamic loading on the string.