Development of Mathematical Model for Controlling Drilling Parameters with Screw Downhole Motor

Document Type : Original Article


Department of Wells Drilling, Saint-Petersburg Mining University, Saint-Petersburg, Russian Federation


Present article results of study on possibility of increasing the efficiency of drilling directional straight sections of wells using screw downhole motors (SDM) with a combined method of drilling with rotation of drilling string (DS). Goal is to ensure steady-state operation of SDM with simultaneous rotation of DS by reducing the amplitude of oscillations with adjusting the parameters of drilling mode on the basis of mathematical modeling for SDM – DS system. Results of experimental study on determination of extreme distribution of lateral and axial oscillations of SDM frame depending on geometrical parameters of gerotor mechanism and modes ensuring stable operation are presented. Approaches to develop a mathematical model and methodology are conceptually outlined that allow determining the range of self-oscillations for SDM – DS system and boundaries of rotational and translational wave perturbations for a heterogeneous rod with an installed SDM at drilling directional straight sections of well. This mathematical model of SDM – DS system's dynamics makes it possible to predict optimal parameters of directional drilling mode that ensure stable operation of borehole assembly.


1. Nutskova, M.V., Kupavykh, K.S., Sidorov, D.A., Lundaev, V.A., «Research of oil-based drilling fluids to improve the quality of wells completion». IOP Conf. Series: Materials Science and Engineering, Vol. 666, No. 1, (2019). DOI: 10.1088/1757-899X/666/1/012065
2. Wang, H., Guan, Z.-C., Shi, Y.-C., Liu, Y.-W., Liang, D.-Y., «Drilling Trajectory Prediction Model for Push-the-bit Rotary Steerable Bottom Hole Assembly», International Journal of Engineering (IJE), TRANSACTIONS B: Applications Vol. 30, No. 11, (2017), 1800-1806. DOI: 10.5829/ije.2017.30.11b.23
3. Neskoromnykh, V.V., Popova, M.S., «Development of a drilling process control technique based on a comprehensive analysis of the criteria», Journal of Mining Institute, Vol. 240, (2019), 701-710. DOI: 10.31897/PMI.2019.6.701
4. Liu, X.H., Liu, Y.H., Feng, D., «Downhole Propulsion/Steering Mechanism for Wellbore Trajectory Control in Directional Drilling». Applied Mechanics and Materials, Vol. 318, (2013), 185-190. DOI: 10.4028/
5. Izadia, M., Tabatabaee Ghomi, M., Pircheraghib, G., «Mechanical Strength Improvement of Mud Motor’s Elastomer by Nano Clay and Prediction the Working Life via Strain Energy», International Journal of Engineering (IJE), Transactions B: Applications Vol. 32, No. 2, (2019), 338-245. DOI: 10.5829/ije.2019.32.02b.20
6. Simonyants, S.L, Al Taee, M., «Stimulation of the Drilling Process with the Top Driven Screw Downhole Motor», Journal of Mining Institute, Vol. 238, (2019), 438-442. DOI: 10.31897/PMI.2019.4.438
7. Leine, R.I., van Campen, D.H., Keultjes, W.J.G., «Stick-slip whirl interaction in drillstring dynamics». ASME Journal of Vibration and Acoustics, Vol. 124, No. 2, (2002), 209-220. DOI: 10.1007/1-4020-3268-4_27
8. Li, Z., Guo, B., «Analysis of longitudinal vibration of drillstring in air and gas drilling». Rocky Mountain Oil and Gas Technology Symposium, (2007). DOI: 10.2128/107697-MS
9. Lui, H., Irving, P. G., Jaspreet, S. D., «Identification and control of stick-slip vibrations using Kalman estimator in oil-well drill string», Journal of Petroleum Science and Engineering, Vol. 140, (2016), 119-127. DOI: 10.1016/j.petrol.2016.01.017
10. Khegai, V., Savich, V., Mihitarov, A., Determination of torsional resonant frequencies of a tree, IOP Conference Series: Earth and Environmental Science, 316, (2019). DOI: 10.1088/1755-1315/316/1/012020
11. Lyagov, I.A., Baldenko, F.D., Lyagov, A.V., Yamaliev, V.U., Lyagova, А.А. Methodology for calculating technical efficiency of power sections in small-sized screw downhole motors for the «Perfobur» system. Journal of Mining Institute, Vol. 240, (2019), 694-700. DOI: 10.31897/PMI.2019.6.694
12. Dvoynikov, M.V., «Technology of Drilling Oil and Gas Wells by Modernized Screw Downhole Motors», Doct. Techn. Sci. Diss., Tyumen', (2010), 54 p. Source link:
13. Dvoynikov, M.V., Syzrantsev, V., Syzrantseva, K., «Designing a High Resistant, High-torque Downhole Drilling Motor», International Journal of Engineering (IJE), Transactions A: Applications Vol. 30, No. 10, (2017), 1615-1621. DOI: 10.5829/ije.2017.30.10a.24
14. Tikhonov, V.S., Baldenko, F.D., Bukashkina, O.S., Liapidevskii V.Y., «Effect of hydrodynamics on axial and torsional oscillations of a drillstring with using a positive displacement motor», Journal of Petroleum Science and Engineering, Vol. 183, (2019). DOI: 10.1016/j.petrol.2019.106423
15. Huang, M., Wang, Y., Liu, B., Gao, M., Wang L., «Development of Downhole Motor Drilling Test Platform», Geological Engineering Drilling Technology Conference (IGEDTC), Procedia Engineering 73, (2014), 71-77. DOI: 10.1016/j.proeng.2014.06.172
16. Moradi, S.S.T., Nikolaev, N.I., Chudinova, I.V., Martel, A.S., «Geomechanical study of well stability in high-pressure, high-temperature conditions», Geomechanics and Engineering, Vol. 16, No. 3, 331-339. DOI: 10.12989/gae.2018.16.3.331
17 Gospodarikov, A.P., Zatsepin, M.A., «Mathematical modeling of boundary problems in geomechanics», Gornyi Zhurnal, No. 19, (2019). DOI: 10.17580/gzh.2019.12.03
18. Zhu, X., Liping, T., Qiming, Y., «A literature review of approaches for stick-slip vibration suppression in oil well drill string». Advances in Mechanical Engineering, (2014), No. 6. 1-17. DOI: 10.1155/2014/967952
19. Samuel, R., Robertson, J.E., «Vibration Analysis and Control with Hole-Enlarging Tools», Annual Technical Conference and Exhibition, (2010). DOI: 10.2118/134512-MS