CONSTRUCTION OF THE MATHEMATICAL MODEL OF THE DRILL PUMP UNIT FOR THE AUTOMATIC PRESSURE CONTROL SYSTEM AT ITS OUTPUT

Authors

• D. R. Kropyvnytskyi Institute of information technology, ІFNTUOG
• M. I. Gorbiychuk Institute of information technology, ІFNTUOG

Keywords:

математична модель, буровий насосний агрегат, автоматична система керування, тиск, передавальна функція

Abstract

The functional diagram of an optimal control system for the process of mechanical drilling, which has a hierarchical structure, has been considered. The lower level of the system includes a drilling pump unit, consisting of the "drive-drilling pump" system and a pneumatic compensator. The main task of the drilling pump unit is to provide a constant torque on the shaft, which allows maintaining a constant pressure of the flushing fluid at the well inlet. Analytical mathematical models for the drilling pump with an asynchronous drive and the pneumatic compensator have been developed. It has been shown that the developed mathematical models take the form of first-order differential equations and are nonlinear. It has been found that the developed mathematical models take the form of first-order differential equations and are nonlinear. To make them linear, the nonlinear dependencies were expanded into a Taylor series. The developed mathematical model of the pneumatic condenser includes the value of the air compressibility coefficient. The introduction of such a corrective coefficient is explained by the fact that the behavior of the gas differs from ideal under the operating pressure of supplying the drilling fluid into the well (from 14 MPa to 18 MPa). It has been determined that the air compressibility coefficient is a function of two arguments - pressure and temperature, which are variable quantities. This function was approximated by regressional polynomial of the second - order, and the coefficients values were computed by the method of least squares using the MatLab environment. To visualize the obtained results, a graph depicting the dependence of the compression coefficient on pressure and temperature was built, showing that the calculated coefficient values are appropriate to  the "experimental values" z with high accuracy. Laplace transforms were applied to the developed mathematical models, allowing to build of structural diagrams for the drilling pump unit and its components. Based on the obtained diagrams, an automatic control system for the drilling pump unit with an asynchronous drive was synthesized.

References

M. I. Horbiychuk, D. R. Kropyvnytskyi. Mathematical model of the process of deepening the well during drilling with screw downhole engines. Collection of scientific papers of Admiral Makarov National Shipbuilding University. 2021. No. 1 (484). P. 68-74. [in Ukrainian]

M. Horbiychuk, D. Kropyvnytskyi, V. Kropyvnytska. Improving empirical models of complex technological objects under conditions of uncertainty. Eastern-European Journal of Enterprise Technologies. 2023. No. 2 (122). P. 53-63.

Gorbiychuk M. I., Kropyvnytskyi D. R. Optimal control of the well deepening process taking into account the state of the bit arming. Bulletin of the Khmelnytskyi National University. 2023. Volume 1. No. 1, (317). P. 58-66. [in Ukrainian]

Kropyvnytska V. B. The well drilling process as a complex system with multi-criteria evaluation of processes. Quality control methods and devices. 2018. No. 2. P. 69-76. [in Ukrainian]

Kotskulich Ya.S., Orynchak M.I., Orynchak M.M. Drilling flushing fluids. Ivano-Frankivsk: "Fakel", 2008. 500 p. [in Ukrainian]

Making decisions when choosing bits and mode parameters of drilling depending on the nature of the initial information / G. M. Efendiev, S. A. Aliyev, M. D. Sarbopeeva [and others]. Geoinformatics, 2016. No. 3. P. 30–39. [in Ukrainian]

Ogorodnikov P.I., Svitlytskyi V.M., Ugryumov M.V. The influence of downhole drives on wave processes in the drill string. Oil and gas industry of Ukraine. 2020. No. 1. P. 3-7. [in Ukrainian]

T. V. Tabachnikova and L. V. Shvetskova. Results of mathematical modeling of the mud pump electric drive operation with the compensation unit in the circuit. IOP Conference Series Materials Science and Engineering. July, 2020. 012015. DOI:10.1088/1757-899X/860/1/012015

Zheng Zhou, Yuanbiao Hu, Baolin Liu, Kun Dai, Yudong Zhang. Development of Automatic Electric Drive Drilling System for Core Drilling. Applied Sciences, 2023. Volume 13, Issue 2. 1059 https://doi.org/10.3390/app13021059

Kaluzhnyi, B., & Malyar, A. Simulation of the start-up electric drive of a sucker rod pump installation. Electrotechnics and Computer Systems. 2019. Vol 66. P. 167-169.

Leonov, G.A.; Kuznetsov, N.V.; Kiseleva, M.A.; Solovyeva, E.P.; Zaretskiy, A.M. Hidden Oscillations in Mathematical Model of Drilling System Actuated by Induction Motor with a Wound Rotor. Nonlinear Dyn. 2014. Vol 77. P. 277–288.

Sementsov G.N., lagoyda A.I. Statistical identification of dynamic characteristics of boring pumping installations for optimization control. Modern engineering and innovative technologies. 2019. No. 2(09-02). P. 12-30. DOI: 10.30890/2567-5273.2019-09-02-006

Fundamentals of an electric drive [Text]: lecture notes / incl. V.V. Lyshuk, S.P. Litkovets. – Lutsk: Technical College of Lutsk National Technical University, 2020. 168 p. [in Ukrainian]

Fundamentals of an electric drive: a textbook / Yu.M. Lavrinenko, P.I. Savchenko, O.Yu. Sinyavskyi, D.G. Voytyuk, V.V. Savchenko, I.M. Hungry. K.: Lira-K Publishing House, 2017. 524 p. [in Ukrainian]

Kostinyuk L. D. Mathematical and structural models of asynchronous motors built on the basis of single-phase substitute circuits. Bulletin of the Lviv Polytechnic National University. 2008. No. 615: Electrical and electromechanical systems. P. 46-50. [in Ukrainian]

O. A. Pashchenko. The influence of hydrostatic pressure on energy consumption when drilling wells. Rock-destroying and metal-working instrument — technique and technology of its manufacture and application, 2016. Vol. 19. P. 107-112. [in Ukrainian]

Kovetsʹka YU.YU., Dmytrenko N.P., Skitsʹko O.I., Plakhotnya L.V. Teploobmin pry pryrodniy konvektsiyi hazu Van-der-Vaalʹsa. Teplofizyka ta teploenerhetyka. 2022, Vol.44. № 1. P. 5-12. [in Ukrainian].

Himmelblau David M., Riggs James B. Basic Principles and Calculations in Chemical Engineering: Eighth Edition. Prentice Hall, 2012. 857 p.

Andrew F. Hayes. Statistical methods for communication science. New Jersey, 2015. 507 p.

2023-06-13

How to Cite

Kropyvnytskyi, D. R., & Gorbiychuk, M. I. (2023). CONSTRUCTION OF THE MATHEMATICAL MODEL OF THE DRILL PUMP UNIT FOR THE AUTOMATIC PRESSURE CONTROL SYSTEM AT ITS OUTPUT. METHODS AND DEVICES OF QUALITY CONTROL, (1(50), 48–59. https://doi.org/10.31471/1993-9981-2023-1(50)-48-59

Section

AUTOMATION AND COMPUTER-INTEGRATED NON-DESTRUCTIVE TESTING TECHNOLOGIES