Stick–Slip Characteristics of Drill Strings and the Related Drilling Parameters Optimization
Abstract
:1. Introduction
2. Drill String Stick–Slip Vibration and Drilling Parameter Optimization
2.1. The Multidimensional Drill String Torsional Vibration Model
- (1)
- The research object is a vertical well;
- (2)
- The drill string is simplified into lumped masses including the rotary table, m drill pipes, n drill collars, and the bit;
- (3)
- BHA is equivalent to springs and viscous damping;
- (4)
- Overall stick–slip behavior of the drill string is approximated by stick–slip at the bit.
2.2. Drilling Parameters Optimization Based on Drill String Stick–Slip Torsional Vibration
3. Stick–Slip Model Validation and Influencing Factors Analysis
3.1. Validation of Stick–Slip Vibration Model
3.2. Analysis of Stick–Slip Vibration Characteristics
3.3. Analysis of Influencing Factors
4. Case Study of the Stick–Slip-Model-Based Drilling Parameters Optimization
4.1. Drilling Parameter Optimization for Soft, Medium-Hard, and Hard Formations
4.2. Comparison of the Optimized Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Yigit, A.; Christoforou, A. Coupled torsional and bending vibrations of actively controlled drillstrings. J. Sound Vib. 2000, 234, 67–83. [Google Scholar] [CrossRef]
- Eronini, I.; Somerton, W.; Auslander, D. A dynamic model for rotary rock drilling. J. Energy Resour. Technol. 1982, 104, 108–120. [Google Scholar] [CrossRef]
- Richard, T.; Germay, C.; Detournay, E. Self-excited stick–slip oscillations of drill bits. Comptes Rendus Mécanique 2004, 332, 619–626. [Google Scholar] [CrossRef]
- Besselink, B.; Van De Wouw, N.; Nijmeijer, H. A semi-analytical study of stick-slip oscillations in drilling systems. J. Comput. Nonlinear Dyn. 2011, 6, 021006. [Google Scholar] [CrossRef]
- Khulief, Y.; Al-Sulaiman, F.; Bashmal, S. Vibration analysis of drillstrings with self-excited stick–slip oscillations. J. Sound Vib. 2007, 299, 540–558. [Google Scholar] [CrossRef]
- Germay, C.; Van De Wouw, N.; Nijmeijer, H.; Sepulchre, R. Nonlinear Drillstring Dynamics Analysis. SIAM J. Appl. Dyn. Syst. 2009, 8, 527–553. [Google Scholar] [CrossRef]
- Leine, R.; Van Campen, D.; Keultjes, W. Stick-slip whirl interaction in drillstring dynamics. J. Vib. Acoust. 2002, 124, 209–220. [Google Scholar] [CrossRef]
- Jansen, J.D.; Van Den Steen, L. Active damping of self-excited torsional vibrations in oil well drillstrings. J. Sound Vib. 1995, 179, 647–668. [Google Scholar] [CrossRef]
- Puebla, H.; Alvarez-Ramirez, J. Suppression of stick-slip in drillstrings: A control approach based on modeling error compensation. J. Sound Vib. 2008, 310, 881–901. [Google Scholar] [CrossRef]
- Navarro-Lopez, E.M.; Cortes, D. Sliding-Mode Control of a Multi-DOF Oilwell Drillstring with Stick-Slip Oscillations. In Proceedings of the 2007 American Control Conference, New York, NY, USA, 9–13 July 2007. [Google Scholar]
- Canudas-De-Wit, C.; Rubio, F.R.; Corchero, M.A. D-OSKIL: A New Mechanism for Controlling Stick-Slip Oscillations in Oil Well Drillstrings. IEEE Trans. Control Syst. Technol. 2008, 16, 1177–1191. [Google Scholar] [CrossRef]
- Navarro-López, E.M.; Cortés, D. Avoiding harmful oscillations in a drillstring through dynamical analysis. J. Sound Vib. 2007, 307, 152–171. [Google Scholar] [CrossRef]
- Zamanian, M.; Khadem, S.E.; Ghazavi, M. Stick-slip oscillations of drag bits by considering damping of drilling mud and active damping system. J. Pet. Sci. Eng. 2007, 59, 289–299. [Google Scholar] [CrossRef]
- Yigit, A.S.; Christoforou, A.P. Stick-slip and bit-bounce interaction in oil-well drillstrings. J. Energy Resour. Technol. 2006, 128, 268–274. [Google Scholar] [CrossRef]
- Lin, Y.-Q.; Wang, Y.-H. Stick-slip vibration of drill strings. J. Eng. Ind. 1991, 113, 38–43. [Google Scholar] [CrossRef]
- Richard, T.; Germay, C.; Detournay, E. A simplified model to explore the root cause of stick–slip vibrations in drilling systems with drag bits. J. Sound Vib. 2007, 305, 432–456. [Google Scholar] [CrossRef]
- Richard, T.; Detournay, E. Stick–slip motion in a friction oscillator with normal and tangential mode coupling. Comptes Rendus De L’Académie Des Sci.-Ser. IIB-Mech. 2000, 328, 671–678. [Google Scholar] [CrossRef]
- Navarro-López, E.M.; Licéaga-Castro, E. Non-desired transitions and sliding-mode control of a multi-DOF mechanical system with stick-slip oscillations. Chaos Solitons Fractals 2009, 41, 2035–2044. [Google Scholar] [CrossRef]
- Kyllingstad, Å.; Halsey, G. A study of slip/stick motion of the bit. SPE Drill. Eng. 1988, 3, 369–373. [Google Scholar] [CrossRef]
- Krama, A.; Gharib, M.; Refaat, S.S.; Sassi, S. Hybrid fuzzy sliding mode for stick-slip suppression in drill string systems. J. Mech. Sci. Technol. 2022, 36, 1089–1102. [Google Scholar] [CrossRef]
- Liu, J.; Wang, J.; Guo, X.; Dai, L.; Zhang, C.; Zhu, H. Investigation on axial-lateral-torsion nonlinear coupling vibration model and stick-slip characteristics of drilling string in ultra-HPHT curved wells. Appl. Math. Model. 2022, 107, 182–206. [Google Scholar] [CrossRef]
- MacLean, J.D.; Vaziri, V.; Aphale, S.S.; Wiercigroch, M. Suppressing stick–slip oscillations in drill-strings by Modified Integral Resonant Control. Int. J. Mech. Sci. 2022, 228, 107425. [Google Scholar] [CrossRef]
- Riane, R.; Doghmane, M.Z.; Kidouche, M.; Djezzar, S. Observer-Based H Controller Design for High Frequency Stick-Slip Vibrations Mitigation in Drill-String of Rotary Drilling Systems. Vibration 2022, 5, 264–289. [Google Scholar] [CrossRef]
- Taraghi Osguei, A.; Mohammad Alizadeh, B.; Dobakhti, A. Two-three degree of freedom model for Anti Stick-Slip Tool of Drill-string. Amirkabir J. Mech. Eng. 2023, 55, 4. [Google Scholar]
- Long, Y.; Wang, X.; Wang, P.; Zhang, F. A Method of Reducing Friction and Improving the Penetration Rate by Safely Vibrating the Drill-String at Surface. Processes 2023, 11, 1242. [Google Scholar] [CrossRef]
- Rill, G.; Schuderer, M. A Second Order Dynamic Friction Model Compared to Commercial Stick-Slip Models. Modelling 2023, 4, 366–381. [Google Scholar] [CrossRef]
- Guan, Z.; Chen, T.; Liao, H. Theory and Technology of Drilling Engineering; Springer: Berlin, Germany, 2021. [Google Scholar]
Parameter Description | Parameter Symbol | Parameter Value |
---|---|---|
turning inertia of the rotary | Jr | 930 kg·m2 |
turning inertia of the drill pipe | Jp | 2782.25 kg·m2 |
turning inertia of the drill collar | Jc | 750 kg·m2 |
turning inertia of the drill bit | Jb | 471.97 kg·m2 |
equivalent stiffness coefficient between the rotary and drill pipe | krp | 698.06 N·m/rad |
equivalent stiffness coefficient between the drill pipe and drill collar | kpc | 1080 N·m/rad |
equivalent stiffness coefficient between the drill collar and drill bit | kcb | 907.48 N·m/rad |
damping coefficient of rotary | cr | 425 N·m/rad |
equivalent damping coefficient between the rotary and drill pipe | crp | 139.61 N·m/rad |
equivalent damping coefficient between the drill pipe and drill collar | cpc | 190 N·m/rad |
equivalent damping coefficient between the drill collar and drill bit | ccb | 181.49 N·m/rad |
damping coefficient of drill bit | cb | 50 N·m/rad |
coefficient of coulomb frication | 0.5 | |
coefficient of static friction | 0.8 | |
constant of Stribeck | 0.9 | |
thickness of border stratum | Dv | 0.000001 rad/s |
radius of drill bit | Rb | 0.155 m |
WOB applied to the drill bit | Wob | 97,347 N |
rotating torque | Tm | 9400 Nm |
Parameter Description | Parameter Symbol | Soft Formation | Medium-Hard Formation | Hard Formation |
---|---|---|---|---|
threshold weight | M | 10 kN | 20 kN | 30 kN |
rotate speed index | 0.68 | 0.68 | 0.68 | |
tooth wear coefficient | C2 | 3.26 | 3.82 | 4.68 |
pressure difference influence coefficient | Cp | 1 | 1 | 1 |
water purification coefficient | Ch | 1 | 1 | 1 |
tooth wear | h | 0.7 | 0.75 | 0.8 |
formation drillability coefficient | KR | 0.0038 | 0.0020 | 0.0008 |
Torque (kN·m) | 3 | 3.3 | 3.6 | 3.9 | 4.2 | 4.5 | |
---|---|---|---|---|---|---|---|
WOB (kN) | |||||||
93 | stick–slip | stick–slip | stick–slip | stick–slip | 1.44 | 1.56 | |
86 | stick–slip | stick–slip | stick–slip | 1.26 | 1.36 | 1.46 | |
79 | stick–slip | stick–slip | stick–slip | 1.18 | 1.27 | 1.36 | |
72 | stick–slip | stick–slip | 1.01 | 1.09 | 1.17 | 1.25 | |
65 | stick–slip | 0.84 | 0.92 | 1.00 | 1.07 | 1.14 | |
58 | 0.69 | 0.76 | 0.83 | 0.89 | 0.96 | 1.01 |
Torque (kN·m) | 5.0 | 5.3 | 5.6 | 5.9 | 6.2 | 6.5 | |
---|---|---|---|---|---|---|---|
WOB (kN) | |||||||
93 | stick–slip | stick–slip | stick–slip | stick–slip | 0.57 | 0.61 | |
89 | stick–slip | stick–slip | stick–slip | stick–slip | 0.56 | 0.60 | |
85 | stick–slip | stick–slip | stick–slip | 0.50 | 0.54 | 0.58 | |
81 | stick–slip | stick–slip | 0.46 | 0.49 | 0.53 | 0.56 | |
77 | stick–slip | 0.41 | 0.44 | 0.48 | 0.51 | 0.54 | |
73 | 0.36 | 0.40 | 0.43 | 0.46 | 0.49 | 0.52 |
Torque (kN·m) | 6.0 | 6.3 | 6.6 | 6.9 | 7.2 | 7.5 | |
---|---|---|---|---|---|---|---|
WOB (kN) | |||||||
93 | stick–slip | stick–slip | stick–slip | stick–slip | 0.159 | 0.171 | |
89 | stick–slip | stick–slip | stick–slip | 0.144 | 0.157 | 0.168 | |
85 | stick–slip | stick–slip | stick–slip | 0.142 | 0.153 | 0.163 | |
81 | stick–slip | stick–slip | 0.128 | 0.138 | 0.148 | 0.157 | |
77 | stick–slip | 0.115 | 0.124 | 0.133 | 0.142 | 0.150 | |
73 | 0.102 | 0.111 | 0.119 | 0.127 | 0.135 | 0.142 |
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Wang, C.; Chen, W.; Wu, Z.; Li, J.; Liu, G. Stick–Slip Characteristics of Drill Strings and the Related Drilling Parameters Optimization. Processes 2023, 11, 2783. https://doi.org/10.3390/pr11092783
Wang C, Chen W, Wu Z, Li J, Liu G. Stick–Slip Characteristics of Drill Strings and the Related Drilling Parameters Optimization. Processes. 2023; 11(9):2783. https://doi.org/10.3390/pr11092783
Chicago/Turabian StyleWang, Chao, Wenbo Chen, Zhe Wu, Jun Li, and Gonghui Liu. 2023. "Stick–Slip Characteristics of Drill Strings and the Related Drilling Parameters Optimization" Processes 11, no. 9: 2783. https://doi.org/10.3390/pr11092783