Stick-slip is a major problem in offshore drilling because it may cause damage to the drill bit as well as crushing or grinding the sediment layer, which is crucial problem in scientific drilling because the purpose of the scientific drilling is to recover core samples from the layers.

To mitigate stick-slip, first of all it is necessary to establish a model of the torsional motion of the drill bit and express the stick-slip phenomenon. Toward this end, the present study proposes a model of torsional waves propagating in a drillstring. An analytical model is developed and used to derive a neutral delay differential equation (NDDE), a special type of equation that requires time history, and an analytical model of stick-slip is derived for friction models between the drill bit and the layer as well as the rotation speed applied to the uppermost part of the drill string. In this study, the stick-slip model is numerically analyzed for several conditions and a time series of the bit motions is obtained. Based on the analytical results, the appearance of stick-slip and its severity are discussed.

A small-scale model experiment was conducted in a water tank to observe the stick-slip phenomenon, and the result is discussed with numerical analysis. In addition, utilizing surface drilling data acquired from the actual drilling operations of the scientific drillship Chikyu, occurrence of stick-slip phenomenon is discussed.

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