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OPTIMIZATION OF THE CURVILINEAR BOREHOLE TRAJECTORIES BY THE METHODS OF LINEAR AND NONLINEAR PROGRAMMING


ABSTRACT

Andrusenko E.N. Minimization of the cost of oil and gas borehole by the methods of linear and nonlinear programming. Visnyk National Transport University. Series «Economical sciences». Scientific and Technical Collection. - Kyiv: National Transport University, 2020. - Issue 2 (47).

The task is posed of constructing optimal trajectories of oil and gas wells by linear and nonlinear programming methods, as well as the theory of optimal control.

The object of study is the geometry of the axial line of deep directional, horizontal and branching trajectories of oil and gas wells.

The purpose of the work is to build the optimal trajectory of an oil or gas well, ensuring its minimum cost, minimum length and minimum values of its construction parameters.

A technique was developed for optimizing the geometry of the trajectory of an oil or gas well using the methods of optimal control theory. Cases of the formulation of the Lagrange, Mayer, and Boltz problems are considered under various (linear and nonlinear) constraints on the values of phase variables and control functions.

The simplest case is considered when the initial outline of the trajectory is close to optimal, then after linearizing the initial equations of the model, the optimization search problem can be reduced to a linear programming problem, and the simplex method is used to solve it.

KEYWORDS: OIL AND GAS WELL, MINIMUM COST, MINIMUM LENGTH, THE OPTIMIZATION THEORY.

REFERENCES

  1. Avriel, Mordecai (2003). Nonlinear Programming: Analysis and Methods. Dover Publishing.
  2. Bertsekas, Dimitri P. (2016). Nonlinear Programming ( Third ed.). Cambridge, Massachussets.: Athena Scientific.
  3. Betts, J.T. (2016). Practical Methods for Optimal Control Using Nonlinear Programming (2nd). Philadelphia, Pennsylvania: SIAM Press.
  4. David M. Himmelblau (1972). Applied Nonlinear Programming. The University of Texas, Austin, Texas. Mc Graw-Hill Book Company.
  5. Gulyayev, V.I., Bazhenov, V.A., Koshkin, V.L. (1988) Optimal Control of Mechanical Systems Motion. UMK VO, Kyiv (in Russian).
  6. Gulyayev, V., Glazunov, S., Glushakova, O., Vashchilina, E., Shevchuk, L., Shlyun, N., Andrusenko, E. (2019) Modelling Emergency Situations in the Drilling of Deep Boreholes. Cambridge Scholars Publishing.
  7. Jan Brinkhuis and Vladimir Tikhomirov (2005) Optimization: Insights and Applications, Princeton University Press.
  8. Luenberger, David G.; Ye, Yinyu (2008). Linear and Nonlinear Programming. International Series in Operations Research & Management Science. 116 (Third ed.) New York: Springer.
  9. Mokhtar S.Bazaraa (2013). Nonlinear Programming: Theory and Algorithms. (3 ed). Wiley Publishing.
  10. Richard E. Bellman. (2010) Dynamic Programming. Princeton Landmarks in Mathematics, Princeton.
  11. Ross, I.M. (2009). A Primer on Pontryagin's Principle in Optimal Control. Collegiate Publisher.
  12. Ruszczynski, Andrze (2006). Nonlinear Optimization. Princeton, NJ: Princeton University Press.

AUTHOR

Andrusenko Elena Nikolaevna, Ph.D., associate professor, National Transport University, associate professor department of high mathematics, e-mail: a.andrusenko@gmail.com , tel. +380672981387, Ukraine, 01010, Kiev, Boichuka str. 42, of. 511, orcid.org/0000-0001-9986-5888.

REVIEWER

Gaidaichuk V.V., Ph.D., Engineering (Dr.), professor, Kyiv National University of Structures and Architecture, Head of Department of Theoretical Mechanics, Kyiv, Ukraine.

Article language: Ukrainian

Open Access: http://publications.ntu.edu.ua/visnyk/47/003.pdf

Print date: 15.04.2020

Online publication date: 27.10.2020


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