Comprehensive Modeling of a Vertical Oilwell Drilling System

Abstract

This chapter provides a comprehensive mathematical description of the system given by a set of partial differential equations which embeds individual submodels corresponding to the different levels of the drillstring. The upper extremity is accurately described by appropriate top boundary conditions including the actuators’ dynamics. Wave equation models involving viscous and viscoelastic Kelvin–Voigt internal damping are chosen to represent the axial and torsional propagating waves traveling along the drillstring; a distinction between the different sections composing the drilling rod, i.e., the series of drillpipes and the Bottom Hole Assembly (BHA), is made. The system trajectories at the bit level are characterized by the bottom boundary conditions involving a nonlinear term to represent the bit-rock contact from which undesirable vibrations arise. This chapter presents an accurate experience-based model of the frictional torque which considers the drilling surface characteristics and the bit geometry.