Control of Drilling Vibrations: A Time-Delay System-Based Approach (original) (raw)
Related papers
Analysis of drilling vibrations: A time-delay system approach
2012
The main purpose of this study is the description of the qualitative dynamical response of a rotary drilling system with a drag bit, using a model that takes into consideration the axial and the torsional vibration modes of the bit. The studied model, based on the interface bit-rock, contains a couple of wave equations with boundary conditions consisting of the angular speed and the axial speed at the top additionally to the angular and axial acceleration at the bit whose contain a realistic frictional torque. Our analysis is based on the center manifold Theorem and Normal forms theory whose allow us to simplify the model.
Journal of Computational and Nonlinear Dynamics, 2020
Drill strings are subjected to complex coupled dynamics. Therefore, accurate dynamic modeling, which can represent the physical behavior of real drill strings, is of great importance for system analysis and control. The most widely used dynamic models for such systems are the lumped element models, which neglect the system distributed feature. In this paper, a dynamic model called neutral-type time delay model is modified to investigate the coupled axial–torsional vibrations in drill strings. This model is derived directly from the distributed parameter model by employing the d’Alembert method. Coupling of axial and torsional vibration modes occurs in the bit–rock interface. For the first time, the neutral-type time delay model is combined with a bit–rock interaction model that regards cutting process in addition to frictional contact. Moreover, mistakes made in some of the related previous studies are corrected. The resulting equations of motion are in terms of neutral-type delay differential equations with two constant delays, related to the oscillatory behavior of the system, and a state-dependent delay, induced by the bit–rock interaction. Illustrative simulation results are presented for a representative drill string, which demonstrates intense axial and torsional vibrations that may lead to system failure without a controller.
Multiple mode analysis of the self-excited vibrations of rotary drilling systems
Journal of Sound and Vibration, 2009
This paper extends the approach proposed by to analyze the axial and torsional vibrations of drilling systems that are excited by the particular boundary conditions at the drag bit-rock interface, by basing the formulation of the model on a continuum representation of the drillstring rather than on a characterization of the drilling structure by a two degree of freedom system. These boundary conditions account for both cutting and frictional contact at the interface. The cutting process combined with the quasi-helicoidal motion of the bit leads to a regenerative effect that introduces a coupling between the axial and torsional modes of vibrations and a state-dependent delay in the governing equations, while the frictional contact process is associated with discontinuities in the boundary conditions when the bit sticks in its axial and angular motion. The dynamic response of the drilling structure is computed using the finite element method. While the general tendencies of the system response predicted by the discrete model are confirmed by this computational model (for example that the occurence of stick-slip vibrations as well as the risk of bit bouncing are enhanced with an increase of the weight-on-bit or a decrease of the rotational speed), new features in the self-excited response of the drillstring can be detected. In particular, stickslip vibrations are predicted to occur at natural frequencies of the drillstring different from the fundamental one (as sometimes observed in field operations), depending on the operating parameters.
Active Control of Coupled Axial and Torsional Drill-String Vibrations
2005
Drilling operations for oil and gas wells requires the control of a very flexible structure subjected to complex boundary conditions. One of the most important causes of failure in drill-strings and drill-bits is the stick-slip phenomenon occurring at drill-bit/formation interface. Although several works on drill-string dynamics have been recently published in the literature, the effect of axial excitation on stick-slip phenomenon and, more importantly, on drilling performance is still an open question. Hence, the coupling between axial and torsional vibrations and its effects on the drilling performance are studied in the present work, using an axial-torsional finite element model. The drill-bit-formation interaction is modelled using a nonlinear regularized friction model which accounts for the dynamical behavior of the reaction force at bit-formation interface. Numerical results confirm that a standard PI control driving system leads to a fluctuating drill-bit angular velocity. Then, an alternative drilling condition using axial excitations at the top-drive, combined to an axial direct velocity feedback controller, to minimize rate-of-penetration oscillations is tested, showing satisfactory results.
Qualitative properties of a model of coupled drilling oscillations
2018 22nd International Conference on System Theory, Control and Computing (ICSTCC), 2018
The model of the axial and torsional vibrations for a drillstring with distributed parameters is obtained using the variational approach within the Hamiltonian Mechanics. Further there is considered the model of the axial vibrations which is a linear system with control and perturbation input signals. To the aforementioned equations of the model a system of equations with deviated argument is associated by integration along the characteristics. The system with deviated argument is of neutral type and allows construction of the basic theory but has its difference operator marginally (critically, not strongly) stable. This aspect is discussed finally and suggests the use of the methodology of the singular perturbations.
Suppressing axial-torsional coupled vibrations in oilwell drillstring
2013
In drilling operation, a wide variety of oscillations causing failures often arise. Torsional vibrations (stick-slip) are originated by the cutting device (bit) motion, these vibrations in turn excite axial oscillations causing a phenomenon known as bit-bouncing. This paper addresses two important challenges: the modeling of the coupled axial and torsional dynamics in a vertical oilwell drilling system and the design of an effective controller to reduce undesirable behaviors. Through the D'Alembert transformation, the distributed parameter model of the drillstring is reduced to a neutral-type time-delay equation which effectively describes the oscillatory behavior of the system. The Lyapunov theory allows to develop an efficient strategy for the control synthesis guaranteeing the elimination of the stick-slip and bit-bounce. This approach leads the "practical" stabilization of the closed loop system. All results can be easily generalized to any time-delay system subject to bounded disturbances. The effectiveness of the strategy is validated through simulations.
Suppressing Axial-Torsional Coupled Vibrations in Drillstrings
HAL (Le Centre pour la Communication Scientifique Directe), 2013
In drilling operation, a wide variety of oscillations causing failures often arise. Torsional vibrations (stick-slip) are originated by the cutting device (bit) motion, these vibrations in turn excite axial oscillations causing a phenomenon known as bit-bouncing. This paper addresses two important challenges: the modeling of the coupled axial and torsional dynamics in a vertical oilwell drilling system and the design of an effective controller to reduce undesirable behaviors. Through the D'Alembert transformation, the distributed parameter model of the drillstring is reduced to a neutral-type time-delay equation which effectively describes the oscillatory behavior of the system. The Lyapunov theory allows to develop an efficient strategy for the control synthesis guaranteeing the elimination of the stick-slip and bit-bounce. This approach leads the "practical" stabilization of the closed loop system. All results can be easily generalized to any time-delay system subject to bounded disturbances. The effectiveness of the strategy is validated through simulations.