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

This booklet studies the result of exhaustive examine paintings on modeling and regulate of vertical oil good drilling structures. it's interested by 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 geared up in 3 parts.

The first half, Modeling, provides lumped- and distributed-parameter versions that let the dynamic habit of the drill string to be characterised; a finished mathematical version taking into consideration mechanical and electrical parts of the general drilling approach is usually supplied. The disbursed nature of the procedure is accommodated by way of contemplating a method of wave equations topic to nonlinear boundary stipulations; this version is remodeled right into a pair of neutral-type time-delay equations that may conquer the complexity thinking about the research and simulation of the partial differential equation model.

The moment half, research, is dedicated to the learn of the reaction of the procedure defined via the time-delay version; vital homes invaluable for examining approach balance are investigated and frequency- and time-domain strategies are reviewed.

Part III, keep watch over, issues the layout of stabilizing keep an eye on legislation aimed toward getting rid of bad drilling vibrations; different regulate thoughts in line with infinite--dimensional process 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 general drilling functionality might be achieved.

This self-contained publication presents operational guidance to prevent drilling vibrations. moreover, because the modeling and regulate ideas awarded right here might be generalized to regard different engineering difficulties, it constitutes an invaluable source to researchers engaged on regulate and its engineering program in oil good drilling.

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

**Sample text**

8). According to [49], the function ς0 g(v) + ς2 v is determined by the steady-state friction force at constant velocity. The Stribeck effect can be reproduced by taking: ς0 g(v) = FC + (Fs − FC ) e−(v/vσ ) , 2 where FC , Fs , and vσ are the Coulomb friction, the stiction force, and the Stribeck velocity, respectively. For steady-state motion, the relation between velocity and friction is defined by: Fss (v) = ς0 g(v)sgn(v) + ς2 v FC sgn(v) + (Fs − FC ) e−(v/vσ ) sgn(v) + ς2 v. 2 The LuGre friction model reproduces different phenomena such as the presliding displacement, the frictional lag, and the stick-slip motion.

7) with: fb (Φ˙ b (t)) = Wob Rb μb (Φ˙ b (t)) ˙ μb (Φ˙ b (t)) = μcb + (μsb − μcb )e−γb |Φb (t)| . 9) Simulation results presented in [252] validate the proposed model. Fig. 11 Karnopp’s model with a decaying friction term Tsb Tfb Tcb 2Dv . Φb -Tcb -Tsb 38 3 Bit-Rock Frictional Interface Fig. 12 Simplified torque on bit model proposed in [155] 1 -k T k . 6 Simplified Torque on Bit Model Is worth mentioning that the models presented above may be complicated for practical purposes. For this reason, the construction of a simplified model which captures their essential dynamic properties is of interest.

4). Consider an element of length l0 under the mean tension T0 . 7) where E 0 is the Young modulus, or elasticity factor under the tension T0 . This law only applies for a sufficiently small relative elongation dl/l0 . At time “t”, the segment (x, x +Δx) has a static length of l0 and takes the position (x +q(x, t), x +Δx +q(x + Δx, t)). Under a tension force, the segment length increases from l0 = Δx to l = l0 +dl = Δx +(∂q/∂ x)Δx, we then have dl/l0 = ∂q/∂ x. The elasticity law implies: T − T0 = E 0 σ0 ∂q .