Analysis of the Motion of Deep-Water Drill Strings—Part 1: Forced Lateral Motion

Abstract

An equation of motion for a drill string, considering elastic, dynamic, and drag forces, is derived. This equation is then applied to two types of drill-string behavior; i.e., a beam having constant axial tension and a perfectly flexible cable under variable tension. A drill string is then synthesized by subdivision into short beam sections at the top and bottom, joined by a flexible cable in the center. The lateral deflection of the drill string is obtained by joining the beam and cable solutions, subject to boundary conditions at each junction. The drill string is considered built-in at the ocean floor and is displaced harmonically at the surface by the ship. An example is discussed and results are compared with experimentally measured values. The effect of roll will be considered in a subsequent paper; as the governing equations have been linearized, these solutions may be superimposed.