# Mathematical modeling and control of the process of drilling wells

## Keywords:

drilling of wells, flushing-out, drilling speed by rock bit, pressure, mathematical model, regression analysis## Abstract

This paper considers the process of drilling wells using mathematical modeling. Mathematical models of deepening and flushing-out of wells are used to describe the drilling process. Mechanical speed of drilling bedrock by drill bit is described by the equation proposed by M.G. Bingham [2]. Along with this there is considered a complete mathematical model of the mechanical speed of drilling in view of the hydraulic parameters obtained by applying the least squares method and regression analysis. There is designed computational algorithm for finding the coefficients of full parametric model of drilling, which allows calculating the mechanical speed of drilling for arbitrary data. A comparative analysis of the drilling experimental and computational data is conducted. The paper deals with a mathematical model of the hydraulic flushing of well, based on the total loss of drilling fluid pressure in individual sections of the well. Flushing of well designed, not only to clean the bottomhole from cuttings, but also serves to claying (strengthening) of the borehole walls, cooling and lubrication of the tool, which occur during the motion of liquor. There are explored the pressure losses at various sections of wells depending on the physical parameters.

## References

[2] Binghem M.G. Problemyi burimosti gornyih porod. OZL ser. "Burenie" , M: VNIIOENG, 1966.

[3] Bulatov A.I. Spravochnik inzhenera po bureniyu. T. 1. – M: Nedra, 1995. – S. 30-35.

[4] Tsuprikov A., Cherednichenko V. Matematicheskoe i kompyuternoe modelirovanie protsessa bureniya skvazhin. – Saarbryukken, Germaniya: LAP, 2014. – S. 50-55.

[5] Linnik Yu.V. Metod naimenshih kvadratov i osnovyi matematiko-statisticheskoy teorii obrabotki nablyudeniy. – M,: FIZMATLIT, 1958.

[6] Shashakov V.B. Prikladnoy Regressionnyiy Analiz (Mnogofaktornaya Regressiya). – Orenburg: – 2003. – S. 5-15.

[7] Gimatudinov Sh.K. Spravochnaya kniga po dobyiche nefti. – M: Nedra, 1983. – S. 319-325

[8] Sumbatova A.R. Poteri napora po dline truboprovoda pri ravnomernom ustanovivshemsya dvizhenii [Elektron. resurs]. – 2014. – URL: http://ars.gubkin.ru/lost.htm (data obrascheniya: 10.03.2016)

[9] Bloomer J.J. Practical fluid mechanics for engineering application // CRC Press, Sep 21, 1999. – P. 150-154.

## Published

## How to Cite

*Journal of Mathematics, Mechanics and Computer Science*,

*91*(3), 97–108. Retrieved from https://bm.kaznu.kz/index.php/kaznu/article/view/542