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

ISBN-10: 3319157469

ISBN-13: 9783319157467

ISBN-10: 3319157477

ISBN-13: 9783319157474

This e-book studies the result of exhaustive learn paintings on modeling and keep watch over of vertical oil good drilling structures. it really is concerned with 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 equipped 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 complete mathematical version making an allowance for mechanical and electrical parts of the final drilling procedure is additionally supplied. The disbursed nature of the process is accommodated by means of contemplating a process of wave equations topic to nonlinear boundary stipulations; this version is reworked right into a pair of neutral-type time-delay equations that could triumph over the complexity fascinated about 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; very important homes worthy for reading process balance are investigated and frequency- and time-domain suggestions are reviewed.

Part III, keep watch over, matters the layout of stabilizing regulate legislation geared toward putting off bad drilling vibrations; varied regulate recommendations according to infinite--dimensional procedure representations are designed and evaluated. The keep an eye on proposals are proven to be powerful 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 directions to prevent drilling vibrations. moreover, because the modeling and keep watch over ideas awarded right here might be generalized to regard assorted 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**

**Example text**

Most of the approaches include the Coulomb friction model and the model proposed by Karnopp. They consider the stiction and the Stribeck effects which entail the inclusion of decaying terms. A brief description of the different structures of the decaying terms is also presented. It is worth mentioning that to properly reproduce the drilling vibrations, the general system model must be subject to a suitable friction law; the present chapter provides the basic ideas to choose an accurate frictional torque model.

The Stribeck curve comprises four phases [13]: I. No sliding (zero velocity). II. Boundary lubrication, the velocity is not enough to entrain fluid lubricant into the junction, then the sliding occurs with solid-to-solid contact. III. Partial fluid lubrication, the velocity is adequate to entrain some fluid into the junction, but not enough to completely separate the surfaces. IV. Full fluid lubrication, the surfaces are completely separated by a fluid film. Negative viscous friction (Stribeck effect) Phase III.

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 [53], 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.

### Analysis and Control of Oilwell Drilling Vibrations: A Time-Delay Systems Approach by Martha Belem Saldivar Márquez, Islam Boussaada, Hugues Mounier, Silviu-Iulian Niculescu

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