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Three-dimensional trajectory design for horizontal well based on optimal switching algorithms.

Xiang Wu1, Kanjian Zhang2

  • 1School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, PR China.

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|April 29, 2015
PubMed
Summary
This summary is machine-generated.

This study presents an efficient computational method for designing complex three-dimensional horizontal well trajectories. The approach effectively handles challenging constraints, ensuring accurate trajectory optimization for improved drilling operations.

Keywords:
Horizontal well trajectory designOptimal controlPenalty function methodSmoothing techniqueTime-scaling transformation

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Area of Science:

  • Engineering
  • Control Theory
  • Optimization

Background:

  • Designing three-dimensional (3D) trajectories for horizontal wells is complex.
  • Standard optimization techniques struggle with unknown switching instants and continuous state inequality constraints inherent in these problems.

Purpose of the Study:

  • To develop an efficient computational method for solving the 3D horizontal well trajectory design problem.
  • To address the challenges posed by complex constraints and unknown switching instants in optimal control problems of switched systems.

Main Methods:

  • A time-scaling transformation was employed to simplify the problem formulation.
  • A smoothing technique and a penalty function method were utilized to create an approximate problem.
  • Convergence analysis was performed to validate the proposed method.

Main Results:

  • The proposed method efficiently solves the 3D horizontal well trajectory design problem.
  • Convergence results demonstrate that solutions to the approximate problem are local optimal solutions to the original problem for large penalty parameters.
  • Two numerical examples confirmed the approach's effectiveness.

Conclusions:

  • The developed computational method offers an efficient solution for complex 3D horizontal well trajectory design.
  • The technique successfully overcomes limitations of standard optimization methods for switched systems with inequality constraints.
  • The approach provides a robust and accurate tool for trajectory optimization in horizontal well drilling.