Comparative Analysis of Mathematical Models of Drilling in Heterogeneous Geological Sections
DOI:
https://doi.org/10.31643/2027/6445.18Keywords:
drilling, heterogeneous formations, mechanical-mathematical models, energy models, kinematic models, empirical models, stick–slip, digital drilling.Abstract
This paper presents a comparative analysis of four main types of well drilling models in heterogeneous geological sections: mechanical-mathematical, energy, kinematic, and empirical. It is shown that each group of models focuses on different aspects of the process: the physics of bit-rock interaction (mechanical-mathematical approach), the energy efficiency of rock mass destruction (energy), the trajectory and movement of the tool (kinematic), as well as statistical patterns and the prediction of complications (empirical). The interaction between the bit and the rock is considered depending on their physical and mechanical properties. A comparison of the rotation speed of the rotor and bit is provided depending on the rock hardness. Based on a review of modern publications and the practical experience of leading service companies (Equinor, Schlumberger, Halliburton), the strengths and weaknesses of each approach are identified, and the need for their integration is substantiated. It is established that the integrated use of models of different classes allows not only to describe and explain phenomena but also to manage the drilling process in conditions of high geological variability.
Downloads
References
Gavrilov I V, Ponomarev V V. Analysis of crushing using digital image processing and the empirical Kuz-Ram model: a comparative study. Mining Industry. 2022; 11:33-41.
Kiselev A S, Nechaev S V. Study of drilling mud absorption during oil field development using artificial intelligence methods. Innovative Science. 2024; 6:45-52.
Burievich TJ. The questions of the dynamics of drilling bit on the surface of well bottom. Arch. Min. Sci. 2016; 61(2):275-283. https://doi.org/10.1515/amsc-2016-0020
Zafarian H, et al. A novel mathematical model of rock–bit interaction considering in-situ stresses. Scientific Reports. 2024; 14(2):112–125.
Song W. Evaluation and optimization of drilling efficiency based on an improved rock-breaking specific energy model. Journal of Petroleum Science and Engineering. 2024; 235:109–121.
Detournay E, Defourny P. A phenomenological model for the drilling action of drag bits. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts. 1992; 29(1):13–23.
Teale R. The concept of specific energy in rock drilling. International Journal of Rock Mechanics and Mining Sciences. 1965; 2(1):57–73.
Soares C, et al. Real-time predictive capabilities of analytical and machine-learning ROP models. Proceedings of SPE/IADC Drilling Conference and Exhibition. The Hague: SPE. 2019; 10. Paper SPE-194125-MS.
Schlumberger. Real Time MSE Ratio Monitoring Enables Early Bit Failure Detection and Delivers Rapid Decision-Making Tool to Drive Drilling Performance. Tech Paper. 2023. https://www.slb.com/resource-library/technical-paper/di/real-time-mse-ratio-monitoring-enables-early-bit-failure-detection
Halliburton sets standard in digital operations with LOGIX™ automated geosteering. Halliburton. https://www.halliburton.com/en/well-construction/drilling/drilling-optimization-solutions/drillstring-design-optimization
Isaev V V, Rogov D S. Modern concepts of the dynamics of rock-cutting tools. Sphere Oil & Gas. 2024; 4:112-124.
Petrov A N, Gavrilyuk S V. Complex model of an adjustable electric drive of a drilling rig rotor. Problems of mechanical engineering and automation. 2023; 2:65-74.
Sidorov M A, Kuznetsov I L. Influence of the unstable rotation mode of the bit on the energy efficiency of the electric drive of the drilling rig rotor. Mining information and analytical bulletin. 2022; 8:118-125.
Akhmedov T Sh, Ibragimov K N. Combined application of attribute analysis of 3D data and well logging (WL) for solving structural and kinematic problems using the example of the Kyurovdag field. Vector of Geosciences. 2023; 2:55-64.
Raissi M, Perdikaris P, Karniadakis G. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics. 2019; 378:686–707.
Kalantari S, Hareland G, Husein M. Application of artificial neural networks for real-time prediction of rate of penetration. Journal of Petroleum Science and Engineering. 2018; 163:85–99.
Pavlov A A, Grigoriev S N. Fractional-energy models in forecasting the efficiency of drilling and blasting operations. Mining information and analytical bulletin. 2024; 12:118-134.
Toshov JB, Rabatuly M, Bogzhanova ZhK, Zheldikbayeva AT, Malikov ShR, Toshov BR, Ergashev OS, Influence of Radiation and Magnetic Pulse Treatment on The Wear Resistance of Carbide Tools. Kompleksnoe Ispolzovanie Mineralnogo Syra = Complex Use of Mineral Resources. 2026; 337(2):47-54. https://doi.org/10.31643/2026/6445.16
Barkov A V. Geomechanical principles of low-permeability reservoir development management: diss. … Cand. of Technical Sciences. Moscow: Institute for Problems in Mechanics, Russian Academy of Sciences. 2024, 250.
Bourgoyne A T, Young F S. A multiple regression approach to optimal drilling and abnormal pressure detection. Society of Petroleum Engineers Journal. 1974; 14(4):371–384.
Ershov M S, Komkov A N, Feoktistov E A. Complex model of an adjustable electric drive of a drilling rig rotor. Zapiski Gornogo Instituta. 2023; 261:339–348. https://doi.org/10.31897/PMI.2023.20
Alikulov Sh, Toshov J, Mussin R, Rabatuly M, Tolovkhan B, Bogzhanova Zh, Gabitova A. Study of rational solution parameters during in-situ uranium leaching. Mining of Mineral Deposits. 2025; 19(1):37-46. https://doi.org/10.33271/mining19.01.037
Maurer W C. The perfect-cleaning theory of rotary drilling. Journal of Petroleum Technology. 1962; 14(11):1270–1274.
Akhmedov T Sh, Ibragimov K N. Joint application of attribute analysis of 3D data and geophysical well logging (GIS) for solving structural and kinematic problems using the example of the Kyurovdag deposit. Vector of geosciences. 2023; 2:55-64.
Wildemans R, Aribowo A G, Detournay E, van de Wouw N. Modelling and dynamic analysis of an anti-stall tool in a drilling system including spatial friction. Nonlinear Dynamics. 2019; 98:2631–2650. https://doi.org/10.1007/s11071-019-05075-6
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 J.B. Toshov, D.I. Erkinov, B.N. Baratov, N.S. Malybaev, A.N. Yesendosova, A. Zheldikbayeva, M. Rabatuly
This work is licensed under a Creative Commons Attribution 4.0 International License.
