Abstract
Abstract The generalized lumped-parameter model of the drill-string system is studied in this paper to provide a fundamental understanding of the torsional stick-slip vibrations in downhole drilling. Our investigation focuses on analysing the cause of three coexisting states: bit sticking, stick-slip vibration, and constant rotation. A critical region of multistability is identified based on the lumped-parameter model, and the conditions for switching between these multiple stable states are discussed. Special attention is given to the bifurcation structure of the considered drill-string model, which is obtained via path-following methods for nonsmooth dynamical systems. The bifurcation scenario is compared to the case when a longer drill-string is considered, which amounts to drilling deeper. It is found that the main features of the bifurcation picture persist under variation of the drill-string length, with certain numerical differences regarding for instance the window of multistability.
Highlights
The oil and gas energy sector provides non-renewable natural resources which have become crucial to everyday life
A deeper understanding of the observed stick-slip vibrations can be achieved via the application of path-following techniques for nonsmooth dynamical systems, as this allows us to carry out the numerical continuation of stick-slip solutions, a task that cannot be performed via standard continuation methods
In order to carry out a detailed investigation of the torsional stick-slip vibration and the multistability in the drill-string system shown in Fig. 2(b), we will apply numerical continuation methods for non-smooth dynamical systems, implemented via the continuation platform COCO [29]
Summary
The oil and gas energy sector provides non-renewable natural resources which have become crucial to everyday life. The drill-string model considered in the present work has followed closely the physical setting proposed and analyzed by Navarro-López [1,3,30,31] Her analysis has primarily focused on the study of friction-induced stick-slip vibrations, based on a simplified torsional lumped-parameter model of an oilwell drill-string with multiple degrees of freedom. A deeper understanding of the observed stick-slip vibrations can be achieved via the application of path-following techniques for nonsmooth dynamical systems, as this allows us to carry out the numerical continuation of stick-slip solutions, a task that cannot be performed via standard continuation methods In this way, we are able to classify the system dynamics in detail, when varying two main control parameters, that is, the control torque and the WOB.
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