Analysis of Friction-Induced Limit Cycling in an Experimental Drill-String System

Abstract

In this paper, we aim for an improved understanding of the causes for torsional vibrations that appear in rotary drilling systems used for the exploration of oil and gas. For this purpose, an experimental drill-string setup is considered. In that system, torsional vibrations with and without stick-slip are observed in steady state. In order to obtain a predictive model, a discontinuous static friction model is proposed. The steady-state behavior of the drill-string system is analyzed both numerically and experimentally. A comparison of numerical and experimental bifurcation diagrams indicates the predictive quality of the model. Moreover, specific friction model characteristics can be linked to the existence of torsional vibrations with and without stick-slip.

Hidden Attractors in Dynamical Systems. From Hidden Oscillations in Hilbert–kolmogorov, Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits

“…Here, following [Kiseleva et al, 2012], on the examples of a two-mass model [de Bruin et al, 2009;Mihajlovic et al, 2004] of drilling system and its modified version, supplemented by equations of induction motor, we demonstrate that unique stable equilibrium state can coexist with a stable limit cycle (hidden oscillation) in both models. It is very possible that the breakdowns in real drilling systems happen due to the existence of hidden oscillations in such systems, which are difficult to find because of the limitation of the standard numerical procedure.…”

“…Below, the model studied in [de Bruin et al, 2009;Mihajlovic et al, 2004] will be considered. This model consists of an upper disc, actuated by a drive part, no-mass string, and lower disc.…”

Analyses of the robustness of the mathematical model with the laboratory prototype of the drilling process during simulation and vibration control experiments

“…Many different models were set up to analyze drill string vibrations including lateral vibrations (whirl) and mode coupling [3,9,10]. Other researchers have focused on models which represent torsional vibration and have attempted to suggest methods to avoid stick-slip behaviour [2,7]. Jansen [11] proposed an unbalanced mass model to represent a bend drill string section in which self excited vibrations were studied.…”

“…The performance of drill strings and their effect on drilling performance have been investigated and analyzed in a number of researches [1][2][3][4][5][6][7][8]. Many different models were set up to analyze drill string vibrations including lateral vibrations (whirl) and mode coupling [3,9,10].…”

Practical approach to modelling and controlling stick-slip oscillations in oilwell drillstrings

“…Most of them consider the drillstring as a torsional pendulum with different degrees of freedom, for instance: [12], [16], [28] propose singledegree-of-freedom models, [1], [3] propose two-degreeof-freedom models including a linear controller, and [9], [20], [27] present two-degree-of-freedom models for the mechanical part of the system plus the model for the rotary table electric motor system.…”