Received 07.08.2025
Revised 29.10.2025
Accepted 15.12.2025
Retrieved from Iss. 118, P. 2, 2025
Pages 47 -62
Abstract
This article examines the process of deformation of the drill string, during which it bends and comes into contact with the walls of an oil and gas well, continuing to change its shape under the influence of increasing axial force, distributed contact load, and torque. The purpose of the work is to construct nonlinear differential equations describing the contact interaction of the drill string pipe with the well wall, to propose a method for their numerical solution, and to present the results of computer modeling. Research methods are theoretical and experimental. This study develops a mathematical model to describe the mechanical interactions of a drill string with the wellbore during drilling, lowering, and raising operations. The model is based on the theory of curvilinear flexible rods and accounts for internal and external force factors, including contact and friction forces, gravity, and drilling fluid effects. A system of nonlinear differential equations is formulated to describe the stress-strain state of the drill string, incorporating geometric imperfections in the borehole trajectory. Computational simulations assess the impact of various borehole curvature conditions on drill string behavior, revealing significant influences on bending moments, frictional forces, and potential drill string seizure zones. The practical application of the obtained results lies in improving methods for predicting emergency situations related to drill string sticking and developing recommendations for selecting optimal drilling parameters. The obtained results make it possible to assess the likelihood of emergency situations, optimize drilling modes to enhance process efficiency, minimize equipment wear, and reduce the risks of accidents during the development of oil and gas fields.
Keywords:
curvilinear drilling, borehole, geometrical imperfections, internal and external forces, direct and inverse problemsKang, Z., Qin, H., Zhang, Y., Hao, X., Chen, G. & Hou, B. (2023). Coil optimization of ultra-deep azimuthal electromagnetic resistivity logging while drilling tool based on numerical simulation. Journal of Petroleum Exploration and Production Technology, (13), 787–801. DOI: 10.1007/s13202-022-01575-1.
Xu, Y., Wang, L., Chen, X. & Fan, Y. (2022). Improvement of drilling quality using precision directional drilling technology. Journal of Petroleum Exploration and Production Technology, (12), 1239–1250. DOI: 10.1007/s13202-022-01510-4.
Leśniak, G., Brunner, D.J. & Topór, T. (2022). Application of long-reach directional drilling boreholes for gas drainage of adjacent seams in coal mines with severe geological conditions. International Journal of Coal Science & Technology, (9). DOI: 10.1007/s40789-022-00553-6.
Liu, C., Zhang, D. & Zhao, H. (2022). Experimental study on hydraulic fracturing properties of elliptical boreholes. Bulletin of Engineering Geology and the Environment, (81). DOI: 10.1007/s10064-021-02531-9.
Zhou, J., Zhang, Y., Liu, H., Zhang, X. & Lin, X. (2021). Analysis of drillstring buckling in complex wellbores considering the effect of wellbore curvature. Journal of Petroleum Science and Engineering, (196). DOI: 10.1016/j.petrol.2020.107680.
Cunha, Jr A., Soize, C. & Sampaio, R. (2021). Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings. arXiv preprint. URL: https://arxiv.org/abs/2105.13454
Liu, F., Li, Q. & Fang, J. (2024). Key technology and practice of deep borehole pneumatic directional drilling in broken-soft coal seam in Yangquan mining area. Coal Geology & Exploration, (52). DOI: 10.12363/issn.1001-1986.24.04.0226.
Chudyk, I., Grydzhuk, Ja., Velychkovych, A. & Andrusyak, A. (2019). Analytical evaluation of inercial properties of the range of the drill string in its rotation. Eastern-European Journal of Enterprise Technologies, 7(97), 6–14.
Levkivska, L. V. & Gorbunovich, I. V. (2020). Komp’yuterne vyznachennya zony prykhvatu burylnoyi kolony u kryvoliniyniy sverdlovyni [Computerized determination of the stuck zone of a drill string in a curvature well]. Tekhnolohiyi, instrumenty ta stratehiyi realizatsiyi naukovykh doslidzhen: proceedings of the international scientific conference (Vol. 1), April 10, Lutsk, 91–93. [in Ukrainian].
Levkivska, L. V. & Gorbunovich, I. V. (2020). Doslidzhennya obertovoho y pozdovzhnoho rukhiv naddovhoho stryzhnya v pokhylykh porozhnynakh [Investigation of rotational and longitudinal motions of a super long rod in inclined bore-holes]. Bulletin of the National Transport University. “Technical Sciences”, 1(46), 92–102. [in Ukrainian].
Haydaychuk, V. V., Lazareva, M. V. & Levkivska, L. V. (2023). Prohnozuvannya zakrytychnoyi povedinky burylnykh kolon u horyzontalnykh sverdlovynakh [Forecasting supercritical behavior of drill strings in horizontal wells]. Strength of Materials and Theory of Structures, 110, 118–130. [in Ukrainian].
Levkivska, L. V. (2024). Pruzhne zakrytychne zhynannya burylnykh kolon u tsylindrychnykh porozhnynakh nafto-hazovykh sverdlovyn [Elastic supercritical bending of drill strings in cylindrical cavities of oil and gas wells]. Bulletin of the National Transport University. “Technical Sciences”, 1(59), 104–114. DOI: 10.33744/2308-6645-2024-1-58-104-114.