Abstract
Drill-string vibrations occur frequently during drilling. Stick–slip vibration, a common form of vibration, reduces the rate of penetration and leads to bit wear and drill-string failure. The positive-displacement motor (PDM), as an important downhole dynamic drilling tool, is increasingly widely used in the field of oil and gas drilling, using hydraulic energy to output torque and speed. Field data have demonstrated that the combined drilling method of a PDM and polycrystalline diamond compact (PDC) bits can effectively alleviate stick–slip vibration; however, the effect is uneven and no research has yet been conducted on the mechanism by which PDM suppresses stick–slip vibration. In this study, the research status of tools for suppressing downhole vibrations is reviewed. A dynamic model of a multi-degree-of-freedom drill-string system with PDM is established, and the structural parameters in the model are calculated. The Runge–Kutta method is used to solve the model, and the influence of the PDM on stick–slip vibration is analyzed. Research has indicated that the output parameters of the PDM have a positive role in suppressing stick–slip vibrations, and that there is a critical value for eliminating these vibrations. The critical value is influenced by the drilling and output parameters of the PDM: the greater weight on the bit (WOB) will lead to a higher critical value; the greater the output parameter of the PDM, the lower the critical value. In addition, the output parameters of the PDM significantly change the correlation between the response parameters of the bit, which is the key to eliminate stick–slip vibration.
Similar content being viewed by others
References
Hegde, C.; Millwater, H.; Gray, K.: Classification of drilling stick slip severity using machine learning. J. Petroleum Sci. Eng. 179, 1023–1036 (2019). https://doi.org/10.1016/j.petrol.2019.05.021
Yigit, A.S.; Christoforou, A.P.: Coupled torsional and bending vibrations of actively controlled drill strings. J. Sound Vib. 234(1), 67–83 (2000). https://doi.org/10.1006/jsvi.1999.2854
Brett, J.F.: The genesis of bit-induced torsional drillstring vibrations. SPE Drill. Eng. 7(3), 168–174 (1992). https://doi.org/10.2118/21943-PA
Henneuse, H.: Surface detection of vibrations and drilling optimization. In: SPE Drilling Conference, New Orleans, Louisiana (1992). https://doi.org/10.2118/23888-MS
Dufeyte, M.: Detection and monitoring of the slip-stick motion: field experiments. In: SPE Drilling Conference, Amsterdam, Netherlands (1991). https://doi.org/10.2118/21945-MS
Macpherson, J.D.: Application and analysis of simultaneous near bit and surface dynamics measurements. SPE Drill. Complet 16(4), 230–238 (2001). https://doi.org/10.2118/74718-PA
Staff, J.: Torsional resonance of drill collars with PDC bits in hard rock. J. Petroleum Technol. 51(2), 44–45 (1999). https://doi.org/10.2118/0299-0044-JPT
Patil, P.A.: Model development of torsional drillstring and investigating parametrically the stick-slips influencing factors. J. Energy Res. Technol. 135(1), 13101–13103 (2013). https://doi.org/10.1115/1.4007915
Kriesels, P.C.; Keultjes, W.J.G.: Cost Savings through an integrated approach to drillstring vibration control. In: SPE Middle East Drilling Technology, AE (1999). https://doi.org/10.2118/57555-MS
David C.K.: Integrated drilling dynamics system closes the model-measure-optimize loop in real time. In: SPE Drilling Conference, Amsterdam, Netherlands (2003). https://doi.org/10.2118/79888-MS
Sugiura, J.: The use of the near-bit vibration sensor while drilling leads to optimized rotary-steerable drilling in push- and point-the-bit configurations. In: SPE Asia Pacific Oil and Gas Conference and Exhibition, Perth, WA, Australia (2008). https://doi.org/10.2118/115572-MS
Sugiura, J.; Jones, S.: Integrated approach to rotary-steerable drilling optimization using concurrent real-time measurement of near-bit borehole caliper and near-bit vibration. In: Intelligent Energy Conference and Exhibition Amsterdam, Amsterdam, The Netherlands (2008). https://doi.org/10.2118/112163-MS
Lai, S.W.; Bloom, M.R.: Stick/Slip detection and friction-factor testing with surface-based torque and tension measurements. SPE Drill. Complet 31, 119–133 (2016). https://doi.org/10.2118/170624-PA
Hohl, A.; Tergeist, M.: Prediction and mitigation of torsional vibrations in drilling systems. In: Society of Petroleum Engineers, Fort Worth, Texas, USA (2016). https://doi.org/10.2118/178874-MS
Rasheed, W.: Extending the reach and capability of non-rotating BHAs by reducing axial friction. In: SPE Coiled Tubing Roundtable, Houston, Texas (2001). https://doi.org/10.2118/68505-MS
Jain, J.R.; Ledgerwood, L.W.: Mitigating torsional stick/slip vibrations in oilwell drilling through PDC-bit design: putting theories to the test. J. Petroleum Technol. 63(12), 79–80 (2011). https://doi.org/10.2118/1211-0079-JPT
Davis, R.; Baudouin, N.: Innovative dual-diameter PDC bit design provides unique solution to successful drilling of challenging volcanic interval. In: IADC/SPE Drilling Conference and Exhibition, Fort Worth, Texas, USA, (2014). https://doi.org/10.2118/168006-MS
Vromen, T.; Detournay, E.: Dynamics of drilling systems with an Antistall tool: effect on rate of penetration and mechanical specific energy. SPE J. 24(5), 1982–1996 (2019). https://doi.org/10.2118/194487-PA
Knut, S.: Drilling difficult formations efficiently with the use of an Antistall tool. SPE Drill. Complet 24(4), 531–536 (2009). https://doi.org/10.2118/111874-PA
Reimers, N.: Antistall tool reduces risk in drilling difficult formations. J. Petroleum Technol. 64(1), 26–29 (2012). https://doi.org/10.2118/0112-0026-JPT
Carpenter, C.: Faster rate of penetration in hard chalk: proving a new hypothesis for drilling dynamics. J. Petroleum Technol. 68(2), 59–60 (2016). https://doi.org/10.2118/0216-0059-JPT
Arjun, P.P.: Model development of torsional drillstring and investigating parametrically the stick-slips influencing factors. J. Energy Resour. Technol. 135(1), 013103(1-7) (2013). https://doi.org/10.1115/1.4007915
Samba, B.A.; Pushkarev, M.: Positive displacement motor modeling: skyrocketing the way we design, select, and operate mud motors. In: Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, UAE (2016). https://doi.org/10.2118/183298-MS
Nguyen, T.C.; Al-Safran, E.; Nguyen, V.: Theoretical modeling of Positive Displacement Motors performance. J. Petroleum Sci. Eng. 166, 188–197 (2018). https://doi.org/10.1016/j.petrol.2018.03.049
Akutsu, T.; Rødsjø M.: Faster ROP in hard chalk: proving a new hypothesis for drilling dynamics. In: SPE/IADC Drilling Conference and Exhibition London, England (2015). https://doi.org/10.2118/173068-MS
Reboul, S.; Al-Mulaifi M.: Improving the directional behavior of PDC bits affected by S-tick slip: a statistical approach. In: International Petroleum Technology Conference, Virtual (2021). https://doi.org/10.2523/IPTC-21200-MS
Mihajlovic, N.; Veggel, A.A.: Analysis of friction-induced limit cycling in an experimental drill-string system. J. Dyn. Syst. Meas. Control 126(4), 709–720 (2004). https://doi.org/10.1115/1.1850535
Navarro-López, E.M.: Non-desired transitions and sliding-mode control of a multi-DOF mechanical system with stick-slip oscillations. Chaos Soliton Fractals 41(4), 2035–2044 (2009). https://doi.org/10.1016/j.chaos.2008.08.008
Christoforou, A.P.: Fully coupled vibrations of actively controlled drillstrings. J. Sound Vib. 267(5), 1029–1045 (2003). https://doi.org/10.1016/S0022-460X(03)00359-6
Savi, M.A.: Drill-string vibration analysis considering an axial-torsional-lateral nonsmooth model. J. Sound Vib. 438, 220–237 (2019). https://doi.org/10.1016/j.jsv.2018.08.054
Divenyi, S.; Savi, M.A.: Drill-string vibration analysis using non-smooth dynamics approach. Nonlinear Dyn. 70(2), 1017–1035 (2012). https://doi.org/10.1007/s11071-012-0510-3
Choe, Y.; Jin, H.; Kim, G., et al.: Axial-torsional mode correlation analysis of a drill string system with non-smooth characteristics. J. Petroleum Sci. Eng. 218, 110870 (2022). https://doi.org/10.1016/j.petrol.2022.110870
Moharrami, M.J.: Nonlinear integrated dynamic analysis of drill strings under stick-slip vibration. Appl. Ocean Res. 108, 102521 (2021). https://doi.org/10.1016/j.apor.2020.102521
Spanos, P.D.; Sengupta, A.K.: Modeling of roller cone bit lift-off dynamics in rotary drilling. J. Energy Res. Technol. 117(3), 197–207 (1995). https://doi.org/10.1115/1.2835341
Navarro-Lopez, E.M.; Suarez, R.: Practical approach to modelling and controlling stick-slip oscillations in oilwell drillstrings. In: IEEE International Conference on Computer Science and Automation Engineering, Shanghai, China (2011). https://doi.org/10.2118/194117-MS
Armstrong-Hélouvry, B.; Dupont, P.: A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica 30(7), 1083–1138 (1994). https://doi.org/10.1016/0005-1098(94)90209-7
Tian, J.; Li, G.: Torsional vibrations and nonlinear dynamic characteristics of drill strings and stick-slip reduction mechanism. J. Comput. Nonlinear Dyn. 14(8), 081007 (2019). https://doi.org/10.1115/1.4043564
Yigit, A.S.; Christoforou, A.P.: Stick-slip and bit-bounce interaction in oil-well drillstrings. J. Energy Res. Technol. 128(4), 268–274 (2006). https://doi.org/10.1115/1.2358141
Rubio, F.R.: D-OSKIL: a new mechanism for controlling stick-slip oscillations in oil well drillstrings. IEEE Trans. Control Syst. Technol. 16(6), 1177–1191 (2008). https://doi.org/10.1109/TCST.2008.917873
Navarro-López, E.M.: Avoiding harmful oscillations in a drillstring through dynamical analysis. J. Sound Vib. 307(1), 152–171 (2007). https://doi.org/10.1016/j.jsv.2007.06.037
Deniz, E.: Drillstring mechanics model for surveillance, root cause analysis, and mitigation of torsional vibrations. SPE Drill. Complet 29(4), 405–417 (2014). https://doi.org/10.2118/163420-PA
Rodgers, J.L.; Nicewander, W.A.: Thirteen ways to look at the correlation coefficient. Am. Stat. 42(1), 59 (1988). https://doi.org/10.1080/00031305.1988.10475524
Taylor, R.: Interpretation of the correlation coefficient: a basic review. J. Diagn. Med. Sonogr. 6(1), 35–39 (1990). https://doi.org/10.1177/875647939000600106
Soletta, J.; Farfan, F.: Measuring spike train correlation with non-parametric statistics coefficient. IEEE Lat. Am. Trans. 13(12), 3743–3746 (2015). https://doi.org/10.1109/TLA.2015.7404902
Acknowledgements
The authors thank the PetroChina Co Ltd.—Southwest Petroleum University Innovation Consortium Project (No. 2020CX040103)—Optimization of drilling methods and speed up technology for complex formations in deep wells, for their contributions to this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Shi, X., Jiao, Y., Yang, X. et al. Establishment of Drill-String System Dynamic Model with PDM and Influence of PDM Parameters on Stick–Slip Vibration. Arab J Sci Eng (2024). https://doi.org/10.1007/s13369-023-08620-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13369-023-08620-z