This paper presents a hybrid model to describe drill string dynamics for deep hole drilling. Generally, a typical rotary drill string has a length of several kilometers, but the diameter is less than half a meter. Due to the large ratio of length to diameter, a drill string is a very flexible system. Consequently, an operating drill string is always affected by axial, torsional and lateral vibrations, which potentially induce serious failures. In order to avoid fatal defects, simulations to forecast vibrations are necessary. The simulation should be capable to exhibit the complex dynamical phenomena, e.g. sick‐slip, forward whirl and backward whirl, and interactions between drill string and borehole. Usually, these simulations are very time‐consuming. In this work, a hybrid model consisting of lumped masses connected with weightless beam elements representing the drill string is developed. The interaction between the drill string and the borehole is implemented by unilateral constraints to describe the nonlinear contact behavior. It was shown that accuracy and simulating time were improved by this model with respect to classical finite‐element models. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
In drill string dynamics the Finite Element Method is usually applied to models of very long drill strings in a wellbore with arbitrary curvature. Taking account of geometrical constraint between the drill string and the wellbore, a high density of nodes is necessary. This density is much higher than the one needed to describe the natural vibrations properly, so this firstly leads to an extension of the computing time. A penalty function is frequently utilized to describe the contact problem between the drill string and the wellbore where the contact normal force acts only on the nodal points of the drill string. It was recognized that only node-to-surface contact models cannot fulfill this geometrical constraint, because the segment between two nodal points deeply penetrates the wellbore wall in some cases. A process with Gaussian points along the segment in time domain will be introduced, so that the drill string will be described according to this geometrical constraint with good accuracy but with a smaller density of nodes and less computing time.
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