Article

Received 20.08.2021

Revised 17.01.2022

Accepted 15.02.2022

Retrieved from Vol. 26, No. 1, 2022

Pages 127 -133

Gulyayev, V., & Shlyun, N. (2022). Optimal tracing of deep borehole trajectories by nonlinear programming methods. The National Transport University Bulletin, 26(1), 127-133. https://doi.org/10.33744/2308-6645-2022-1-51-127-133

Optimal tracing of deep borehole trajectories by nonlinear programming methods

Valerii Gulyayev Nataliia Shlyun

The issues of rational optimal trajectory of oil and gas wells are apparently one of the few areas of the oil and gas industry that still does not use optimal control and nonlinear programming methods. At the same time, the use of these methods makes it possible to design smoother and shorter trajectories with less risk of emergency situations occurring in them, leading to resonant vibrations of the system, buckling of the drill string and its sticking. In addition, in such columns, the conditions for the hydrodynamic and aerodynamic flow of the working fluid are improved, and the likelihood of the formation of blood clots and plugs is reduced. In this paper, a new approach for the optimal design of curved well trajectories based on the application of the anti-gradient descent method is proposed, resolving equations are formulated, algorithms for their solution are developed, a practical example is considered, and it is shown that solving this problem leads to a decrease in the total curvature of the well and its length.

 

deep borehole; borehole trajectory optimization; anti-gradient runing method; objective functions; nonlinear programming
  1. Gulyayev, V. I., Bazhenov, V. A., Koshkin, V. L. (1988). Optimal`noe upravlenie dvizheniem mekhanicheskikh sistem [Optimal Control of Mechanical Systems Motion]. Kyiv: UMK VO [in Russian].
  2. Bazaraa, Mokhtar S. (2013). Nonlinear Programming: Theory and Algorithms. 3rd ed. Wiley Publishing.
  3. Bertsekas, Dimitri P. (2016). Nonlinear Programming. Third ed. Cambridge, Massachussets: Athena Scientific.
  4. Betts, J. T. (2016). Practical Methods for Optimal Control Using Nonlinear Programming. 2nd ed. Philadelphia, Pennsylvania: SIAM Press.
  5. Gulyayev, V., Glazunov, S., Shlyun, N., et al. (2019). Modelling Emergency Situations in the Drilling of Deep Boreholes. Cambridge Scholars Publishing.
  6. Himmelblau, David M. (1972). Applied Nonlinear Programming. The University of Texas, Austin, Texas: Mc Graw-Hill Book Company.
  7. Korn, G. A., Korn, T. M. (2000). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulars for Reference and Reviews. General Publishing Company.
  8. Mordecai, A. (2003). Nonlinear Programming: Analysis and Methods. Dover Publishing.
  9. Ross, I. M. (2009). A Primer on Pontryagin’s Principle in Optimal Control. Collegiate Publisher.
  10. Ruszczynski Andrze (2006). Nonlinear Optimization. Princeton, NJ: Princeton University Press.
  11. Shlyun, N. V., Gulyayev, V. I. (2020). Buckling of a drill-string in two-sectional bore-holes. International Journal of Mechanical Sciences, 172, 105427.
  12. Stengel, R. F. (1994). Optimal Control and Estimation. New York: Dover (Courier). ISBN 0-486-68200-5.

https://doi.org/10.33744/2308-6645-2022-1-51-127-133