Abstract
We develop a dynamic model of a drill-string in a horizontal well having six Degrees-Of-Freedom, which accounts for longitudinal, lateral and torsional motions. In this model, nonlinearities that arise due to intermittent contacts of a drill-pipe with a borehole wall and complex interactions between a drill-bit and a rock formation are all considered. The lateral motions of the drill-bit are restricted and its interactions with a borehole generate an interlaced force being result of a friction and a cutting that has a regenerative effect. In the cutting process, a state-dependent time delay is introduced to couple the axial and torsional motions of the drill-bit. The dynamic model established in this article is tested where the friction and cutting effects are gradually switched on, which shows that the model is robust. Subsequently, the complex whirling of a horizontal drill-string is analyzed and a particular attention is given to the influence of driving rotation speed and dynamic friction coefficient. The study should help us to better understand nonlinear dynamic effects of drill-strings in horizontal wells, which will lay a foundation for optimizing drilling parameters.
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