By Martha Belem Saldivar Márquez, Islam Boussaada, Hugues Mounier, Silviu-Iulian Niculescu
This booklet stories the result of exhaustive learn paintings on modeling and keep an eye on of vertical oil good drilling platforms. it's excited about the research of the system-dynamic reaction and the removing of the main harmful drill string vibration modes affecting total perforation functionality: stick-slip (torsional vibration) and bit-bounce (axial vibration). The textual content is geared up in 3 parts.
The first half, Modeling, offers lumped- and distributed-parameter versions that let the dynamic habit of the drill string to be characterised; a entire mathematical version taking into consideration mechanical and electrical parts of the general drilling method can be supplied. The dispensed nature of the process is accommodated via 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 that could conquer the complexity concerned with 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 by means of the time-delay version; very important houses worthy for examining procedure balance are investigated and frequency- and time-domain strategies are reviewed.
Part III, keep watch over, matters the layout of stabilizing keep watch over legislation geared toward getting rid of bad drilling vibrations; assorted keep watch over innovations in accordance with infinite--dimensional approach representations are designed and evaluated. The regulate proposals are proven to be potent in suppressing stick-slip and bit-bounce in order that a substantial development of the final drilling functionality should be achieved.
This self-contained e-book presents operational instructions to prevent drilling vibrations. moreover, because the modeling and keep watch over ideas offered right here will be generalized to regard various 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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Additional info for Analysis and Control of Oilwell Drilling Vibrations: A Time-Delay Systems Approach
The next chapter presents a comprehensive model that considers such differences; furthermore, a frictional ToB model that comprises the bit geometry and the drilling surface characteristics is reviewed. Chapter 4 Comprehensive Modeling of a Vertical Oilwell Drilling System Classical models of the drillstring and different modeling approaches to approximate the frictional interface at the bit level were presented in preceding chapters. As previously explained, series pipe sections and the BHA (consisting of drill collars and the bit) constituting the drillstring are commonly regarded as a single flexible beam under the action of external forces at both extremities.
Several equations have been proposed to describe the dynamics taking place at the upper and lower ends of the drillstring; the main ones are presented in the sequel. 1 Kinematic Boundary Conditions In , the following boundary conditions are considered: Φ(0, t) = Ωt, GJ ∂Φ ∂ 2Φ ∂Φ (L , t) + I B 2 (L , t) = −T (L , t) . 14b) A lumped inertia I B is chosen to represent the assembly at the bottom hole. It is assumed that the speed at the surface (s = 0) is restricted to a constant value Ω, the other extremity (s = L), is subject to a torque T, which is a function of the bit speed.
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. 15) is shown in Fig. 15.