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

This booklet experiences the result of exhaustive examine paintings on modeling and keep watch over of vertical oil good drilling platforms. it really is excited by the research of the system-dynamic reaction and the removal 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, provides lumped- and distributed-parameter types that let the dynamic habit of the drill string to be characterised; a entire mathematical version taking into consideration mechanical and electrical elements of the final drilling process can also be supplied. The allotted nature of the procedure is accommodated through contemplating a procedure of wave equations topic to nonlinear boundary stipulations; this version is reworked right into a pair of neutral-type time-delay equations which could conquer the complexity all in favour of the research and simulation of the partial differential equation model.

The moment half, research, is dedicated to the learn of the reaction of the method defined by means of the time-delay version; very important homes valuable for studying approach balance are investigated and frequency- and time-domain concepts are reviewed.

Part III, keep an eye on, issues the layout of stabilizing keep an eye on legislation geared toward casting off bad drilling vibrations; different keep watch over thoughts according to infinite--dimensional procedure 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 final drilling functionality may be achieved.

This self-contained booklet offers operational guidance to prevent drilling vibrations. moreover, because the modeling and keep watch over innovations offered right here should be generalized to regard different engineering difficulties, it constitutes an invaluable source to researchers engaged on regulate and its engineering software in oil good drilling.

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**Additional info for Analysis and Control of Oilwell Drilling Vibrations: A Time-Delay Systems Approach**

**Sample text**

8), we obtain: ρ0 which constitutes the wave equation with propagation speed: c = The normalized model can be written as: 2 ∂ 2q 2∂ q (x, t) = c ∂t 2 ∂x2 ∂q (0, t) = −u(t) ∂x q(x, 0) = q0 (x) √ E 0 σ0 /ρ0 . 11c) where x ∈ [0, 1]. 11c). ” The shear modulus and the second moment of area (also known as geometric moment of inertia) are denoted by G and J , respectively. The inertia I is such that I = ρa J , where ρa is the area density. A viscous damping γ 0 is assumed along the structure. Since most of the energy dissipation in drilling systems is taking place at the bit-rock interface, we may consider that the damping γ is null.

5 0 10 20 30 40 50 Time (s) Fig. 12) for T0 = 25 Nms rad−1 . a Bit angular velocity. 5 0 0 20 40 60 80 100 Time (s) −2 0 20 40 60 80 100 Time (s) Fig. 1. a Bit angular velocity. 9): T Φ˙ b (t) = cb Φ˙ b (t) + Wob Rb μb Φ˙ b (t) sgn Φ˙ b (t) . 14) The term cb Φ˙ b (t) represents the viscous damping torque at the bottom end and the expression Wob Rb μb Φ˙ b (t) sgn Φ˙ b (t) approximates the dry friction torque. Notations Rb and Wob stand for the bit radius and the weight on bit, respectively. 15) where μcb , μsb denote the Coulomb and static friction coefficients, the constant 0 < γb < 1 defines the velocity decrease rate.

The drillstring is regarded as a mass-spring-damper system which can be described by an ordinary differential equation. This finitedimensional system representation provides a rough description of the dynamics taking place at different levels of the string; it can be of one to several degrees of freedom. • Distributed parameter models. The drillstring is considered as a beam subject to axial and/or torsional efforts. A system of partial differential equations provides a characterization of the drilling variables in an infinite-dimensional setting.