By Martha Belem Saldivar Márquez, Islam Boussaada, Hugues Mounier, Silviu-Iulian Niculescu

This e-book stories the result of exhaustive study paintings on modeling and keep an eye on of vertical oil good drilling platforms. it really is interested in the research of the system-dynamic reaction and the removing of the main destructive drill string vibration modes affecting total perforation functionality: stick-slip (torsional vibration) and bit-bounce (axial vibration). The textual content is prepared in 3 parts.

The first half, Modeling, offers lumped- and distributed-parameter types that permit the dynamic habit of the drill string to be characterised; a entire mathematical version making an allowance for mechanical and electrical parts of the general drilling procedure is usually supplied. The allotted nature of the procedure is accommodated by way of contemplating a procedure of wave equations topic to nonlinear boundary stipulations; this version is remodeled right into a pair of neutral-type time-delay equations which could triumph over the complexity fascinated by the research and simulation of the partial differential equation model.

The moment half, research, is dedicated to the research of the reaction of the process defined through the time-delay version; vital houses important for reading method balance are investigated and frequency- and time-domain strategies are reviewed.

Part III, regulate, matters the layout of stabilizing keep watch over legislation aimed toward getting rid of bad drilling vibrations; various keep watch over options in keeping with infinite--dimensional process representations are designed and evaluated. The keep an eye on proposals are proven to be potent in suppressing stick-slip and bit-bounce in order that a substantial development of the general drilling functionality should be achieved.

This self-contained booklet offers operational directions to prevent drilling vibrations. in addition, because the modeling and keep watch over options provided the following may be generalized to regard different engineering difficulties, it constitutes an invaluable source to researchers engaged on keep watch over and its engineering software in oil good drilling.

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Extra resources for Analysis and Control of Oilwell Drilling Vibrations: A Time-Delay Systems Approach

Example text

This portion of the curve gives a substantial destabilizing effect and it is usually considered as the source of the stickslip phenomenon in several mechanisms [11]. According to the Stribeck curve, the friction force, in practical applications, does not decrease discontinuously (as in Fig. 3), but is continuously dependent on the sliding velocity (see for example, the Karnopp friction model in Fig. 5). The Stribeck friction can be modeled as follows [222]: ⎧ if v = 0 ⎨ F(v) if v = 0 and |Fe | < Fs F = Fe ⎩ Fs sgn(Fe ) otherwise where F(v) is an arbitrary function which may take the form of the curve in Fig.

9). Tfb Tfb Tsb Tcb Tsb . Φb . Φb ≠ 0 Fig. 9 Coulomb and static friction Drillstring torque . 3 Dry Friction Plus Karnopp’s Model Another common model for Tfb (Φ˙ b (t)) is defined below ⎧ if Φ˙ b (t) < Dv , |Teb | Tsb ⎪ ⎪ Teb ⎪ ⎪ ⎪ (stick) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ if Φ˙ b (t) < Dv , |Teb | > Tsb ˙ Tfb (Φb (t)) = Tsb sgn(Teb ) ⎪ (stick-to-slip transition) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ Dv , if Φ˙ b (t) ⎪ ⎪ ⎩ Tcb sgn(Φ˙ b (t)) (slip) where Dv > 0 specifies a small enough neighborhood of Φ˙ b (t) = 0 and Teb is the applied external torque that must overcome the static friction torque Tsb to make the bit move.

A similar transformation of PDE boundary value problems to time-delay equations plays a significant role in a wide range of other biological, physical, and engineering problems. These include cardiovascular system dynamics [136], homeostatic mechanisms for maintaining blood pressure (the system model is presented in [223] and a bifurcation analysis in [265]), laser optical fibers, power transmission line networks [42], sonar/radar ranging technologies [25], and many other applications [134]. A different modeling method for describing structural waves propagating in a drill system is proposed in [129].

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