Oscillations and Stability of Drilling Systems: Analytical and Numerical Methods

Abstract

This work is devoted to study of electromechanical models of the drilling systems actuated by an induction motor. This subject is up-to-date due to the fact that failures of the drilling equipment cause significant time and expenditure losses for the drilling companies. Although there are many papers devoted to the investigation of the drilling systems, the equipment failures still occur in the drilling industry. In this study, we continue investigations started by researchers from Eindhoven University of Technology who introduced an experimental model of a drilling system. The model consists of two discs connected with each other by a steel string which may experience torsional deformation only. The upper disc which represents the upper part of the drill-string is connected to the driving part. The lower disc, which represents the end of the drill-string, experiences friction torque caused mainly by interaction with a shale. The key idea of the present study, that expands and refines the experimental model, was to introduce more complex equations of the driving part and, particularly, to consider the induction motor. Towards this end, two new mathematical models are considered. The first model is a simplified one. Its prototype is an electric hand drill. It can be assumed that the drill-string is absolutely rigid. Also, another model of a friction torque acting on the lower part of the drill-string is implemented. It is assumed that the friction torque has asymmetric characteristics of the Coulomb type. The qualitative analysis of this model made it possible to obtain conditions on permissible loads (i.e., permissible values of the friction torque) in case when the system remains in operational mode after the shale’s type changes. With the help of computer modeling, a particular case when there is a sudden load appearance (i.e., when the drill was idle before the transient process) was also studied. The second mathematical model takes into account the torsional deformation of the drill. For the friction torque with an asymmetric characteristic of the Coulomb type, local analysis of the system is provided. In the case of the friction model offered by the researchers from Eindhoven, the computer modeling of the system was carried out by the author. In the context of this modeling, an interesting effect represented by hidden oscillations of the stick-slip type was found. The results of the study have been published in 10 papers (three of which are indexed in Scopus).