Drilling Systems: Stability and Hidden Oscillations
There are many mathematical models of drilling systems Despite, huge efforts in constructing models that would allow for precise analysis, drilling systems, still experience breakdowns. Due to complexity of systems, engineers mostly use numerical analysis
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Drilling Systems: Stability and Hidden Oscillations M.A. Kiseleva, N.V. Kuznetsov, G.A. Leonov, and P. Neittaanmäki
Abstract There are many mathematical models of drilling systems Despite, huge efforts in constructing models that would allow for precise analysis, drilling systems, still experience breakdowns. Due to complexity of systems, engineers mostly use numerical analysis, which may lead to unreliable results. Nowadays, advances in computer engineering allow for simulations of complex dynamical systems in order to obtain information on the behavior of their trajectories. However, this simple approach based on construction of trajectories using numerical integration of differential equations describing dynamical systems turned out to be quite limited for investigation of stability and oscillations of these systems. This issue is very crucial in applied research; for example, as stated in Lauvdal et al. (Proceedings of the IEEE control and decision conference, 1997) the following phrase: “Since stability in simulations does not imply stability of the physical control system (an example is the crash of the YF22) stronger theoretical understanding is required”. In this work, firstly a mathematical model of a drilling system developed by a group of scientists from the University of Eindhoven will be considered. Then a mathematical model of a drilling system with perfectly rigid drill-string actuated by induction motor will be analytically and numerically studied. A modification of the first two models will be considered and it will be shown that even in such simple models of drilling systems complex effects such as hidden oscillations may appear, which are hard to find by standard computational procedures. Keywords Drilling system • Induction motor • Hidden oscillation • Simulation
M.A. Kiseleva • N.V. Kuznetsov () • G.A. Leonov • P. Neittaanmäki University of Jyväskylä, Finland, Saint Petersburg State University, Russia e-mail: [email protected]; [email protected]; [email protected]; [email protected] J.A.T. Machado et al. (eds.), Discontinuity and Complexity in Nonlinear Physical Systems, Nonlinear Systems and Complexity 6, DOI 10.1007/978-3-319-01411-1__15, © Springer International Publishing Switzerland 2014
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Among the problems the drilling industry faces, drill string failure is of particular interest because of its frequency of occurrence. This issue suggests that the drill string was under a load which led to its break or operation cutoff. The costs derived from these failures are of such importance that finding solutions for reducing them has been a concern for industrial research for many years [8, 39]. For example, in 1985, among all the deep well drilling problems, 45% were related to drill string failures. In 1991, Shell Expro suffered exceptionally high losses due to drill string failures. These losses were estimated to be more than US $2MM in a two-month span and were caused by a specific drilling unit experiencing five failures within thi
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