Nonlinear dynamic modeling and analysis of borehole propagation for directional drilling

Fahim Shakib (Corresponding author), Emmanuel Detournay, Nathan van de Wouw

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Boreholes with complex trajectories are drilled with the help of downhole rotary steerable systems. These robotic actuators, which are embedded in the drillstring, are used to steer the bit in the desired direction. This paper presents a dynamic non-smooth borehole propagation model for planar directional drilling. Essential nonlinearities, induced by the saturation of the bit tilt and by non-ideal (undergauged) stabilizers, are modeled using complementarity conditions, leading to a closed-form analytical description of the model in terms of a so-called delay complementarity system. The analytical form of the model allows for a comprehensive dynamic and parametric analysis. Firstly, (quasi-)stationary solutions generated by constant actuator forces are analyzed parametrically as a function of the actuation force. Secondly, an analysis of the local stability of these solutions shows the coexistence of multiple (stable and unstable) solutions and their dependency on key system parameters, such as the weight-on-bit and bit characteristics. Thirdly, a numerical simulation study shows the existence of steady-state oscillations, which are a consequence of the non-smooth characteristics of the bit tilt saturation and the stabilizers. Such limit cycles represent borehole rippling, which is the planar equivalent of the highly detrimental borehole spiraling observed in practice. The constructed model and the pursued analysis provide essential insights in the effects causing undesired borehole rippling. Herewith, the presented results can be used to support improved directional drilling system design and to form the basis for further work on automation techniques for the downhole robotic actuator to mitigate spiraled boreholes.
Originele taal-2Engels
Pagina's (van-tot)178-201
Aantal pagina's24
TijdschriftInternational Journal of Non-Linear Mechanics
Volume113
DOI's
StatusGepubliceerd - jul 2019

Vingerafdruk

Directional drilling
Nonlinear Modeling
Drilling
Dynamic Modeling
Boreholes
Nonlinear Analysis
Dynamic Analysis
Nonlinear Dynamics
Propagation
Actuator
Complementarity
Tilt
Saturation
Robotics
Actuators
Parametric Analysis
Stability of Solutions
Local Stability
Stationary Solutions
Coexistence

Trefwoorden

  • Directional drilling
  • Borehole spiraling
  • Linear complementarity problems
  • Delay complementarity systems

Citeer dit

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abstract = "Boreholes with complex trajectories are drilled with the help of downhole rotary steerable systems. These robotic actuators, which are embedded in the drillstring, are used to steer the bit in the desired direction. This paper presents a dynamic non-smooth borehole propagation model for planar directional drilling. Essential nonlinearities, induced by the saturation of the bit tilt and by non-ideal (undergauged) stabilizers, are modeled using complementarity conditions, leading to a closed-form analytical description of the model in terms of a so-called delay complementarity system. The analytical form of the model allows for a comprehensive dynamic and parametric analysis. Firstly, (quasi-)stationary solutions generated by constant actuator forces are analyzed parametrically as a function of the actuation force. Secondly, an analysis of the local stability of these solutions shows the coexistence of multiple (stable and unstable) solutions and their dependency on key system parameters, such as the weight-on-bit and bit characteristics. Thirdly, a numerical simulation study shows the existence of steady-state oscillations, which are a consequence of the non-smooth characteristics of the bit tilt saturation and the stabilizers. Such limit cycles represent borehole rippling, which is the planar equivalent of the highly detrimental borehole spiraling observed in practice. The constructed model and the pursued analysis provide essential insights in the effects causing undesired borehole rippling. Herewith, the presented results can be used to support improved directional drilling system design and to form the basis for further work on automation techniques for the downhole robotic actuator to mitigate spiraled boreholes.",
keywords = "Directional drilling, Borehole spiraling, Linear complementarity problems, Delay complementarity systems, Borehole spiraling, Delay complementarity systems, Directional drilling, Linear complementarity problems",
author = "Fahim Shakib and Emmanuel Detournay and {van de Wouw}, Nathan",
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Nonlinear dynamic modeling and analysis of borehole propagation for directional drilling. / Shakib, Fahim (Corresponding author); Detournay, Emmanuel; van de Wouw, Nathan.

In: International Journal of Non-Linear Mechanics, Vol. 113, 07.2019, blz. 178-201.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

T1 - Nonlinear dynamic modeling and analysis of borehole propagation for directional drilling

AU - Shakib, Fahim

AU - Detournay, Emmanuel

AU - van de Wouw, Nathan

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N2 - Boreholes with complex trajectories are drilled with the help of downhole rotary steerable systems. These robotic actuators, which are embedded in the drillstring, are used to steer the bit in the desired direction. This paper presents a dynamic non-smooth borehole propagation model for planar directional drilling. Essential nonlinearities, induced by the saturation of the bit tilt and by non-ideal (undergauged) stabilizers, are modeled using complementarity conditions, leading to a closed-form analytical description of the model in terms of a so-called delay complementarity system. The analytical form of the model allows for a comprehensive dynamic and parametric analysis. Firstly, (quasi-)stationary solutions generated by constant actuator forces are analyzed parametrically as a function of the actuation force. Secondly, an analysis of the local stability of these solutions shows the coexistence of multiple (stable and unstable) solutions and their dependency on key system parameters, such as the weight-on-bit and bit characteristics. Thirdly, a numerical simulation study shows the existence of steady-state oscillations, which are a consequence of the non-smooth characteristics of the bit tilt saturation and the stabilizers. Such limit cycles represent borehole rippling, which is the planar equivalent of the highly detrimental borehole spiraling observed in practice. The constructed model and the pursued analysis provide essential insights in the effects causing undesired borehole rippling. Herewith, the presented results can be used to support improved directional drilling system design and to form the basis for further work on automation techniques for the downhole robotic actuator to mitigate spiraled boreholes.

AB - Boreholes with complex trajectories are drilled with the help of downhole rotary steerable systems. These robotic actuators, which are embedded in the drillstring, are used to steer the bit in the desired direction. This paper presents a dynamic non-smooth borehole propagation model for planar directional drilling. Essential nonlinearities, induced by the saturation of the bit tilt and by non-ideal (undergauged) stabilizers, are modeled using complementarity conditions, leading to a closed-form analytical description of the model in terms of a so-called delay complementarity system. The analytical form of the model allows for a comprehensive dynamic and parametric analysis. Firstly, (quasi-)stationary solutions generated by constant actuator forces are analyzed parametrically as a function of the actuation force. Secondly, an analysis of the local stability of these solutions shows the coexistence of multiple (stable and unstable) solutions and their dependency on key system parameters, such as the weight-on-bit and bit characteristics. Thirdly, a numerical simulation study shows the existence of steady-state oscillations, which are a consequence of the non-smooth characteristics of the bit tilt saturation and the stabilizers. Such limit cycles represent borehole rippling, which is the planar equivalent of the highly detrimental borehole spiraling observed in practice. The constructed model and the pursued analysis provide essential insights in the effects causing undesired borehole rippling. Herewith, the presented results can be used to support improved directional drilling system design and to form the basis for further work on automation techniques for the downhole robotic actuator to mitigate spiraled boreholes.

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