Study of Stick-Slip in a Torsional Drill bit Using Neutral Delay Differential Equations

Mudhangulla, Sridhar Babu (2017) Study of Stick-Slip in a Torsional Drill bit Using Neutral Delay Differential Equations. Masters thesis, Indian Institute of Technology Hyderabad.

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Abstract

St ick - slip is a major problem in scientific drilling because it may cause crushing or grinding to the sediment layer as well as damage to the drill bit. The main purpose of scientific drilling is to collect core samples from sedimentary layers for studying p ast climate changes, life history and long term crust transformation. In this study a model of the torsional motion of drill bit is established and stick - slip phenomenon is expressed. An analytical model is developed and used to derive a neutral delay diff erential equation (NDDE) which requires time history and an analytical model of stick - slip is derived for coulomb frictional model between drill bit and the sediment layer as well as the variable rotational speed at the top of the drill - string. The stick - s lip model is numerically analyzed for several conditions and analysis is done using three different methods to obtain the drill bit motion and discussed about the mitigation of stick - slip. Three different methods for solving the model are discussed and the ir results are compared.

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