# Analysis of the Influence of Downhole Drill String Vibration on Wellbore Stability

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model of the Influence of Drill String Vibration on Wellbore Stability

#### 2.1. Force Analysis Model of Wellbore under Drill String Vibration

- ${c}_{r}$—Recovery factor;
- ${\mu}_{r}$—Radial displacement of the center of mass of the drill string, m;
- ${c}_{f}$—Damping factor;
- ${v}_{r}$—Radial velocity of drill string center of mass, m/s;
- ${k}_{h}$—Wellbore stiffness, N/m;
- ${d}_{o}$—Wellbore diameter, m;
- ${d}_{i}$—Drill string diameter, m.

- ${v}_{1}$—Pre-crash velocity, m/s;
- ${v}_{2}$—Post-collision velocity, m/s.

- $\mu \left({v}_{s}\right)$—Coefficient of friction;
- ${v}_{s}$—Stick–slip speed, m/s.

#### 2.2. Solving Method for Wellbore Instability

- (1)
- The drilling tool collides with the wellbore, and the collision stress is large and exceeds the bearing capacity of the wellbore rock mass, resulting in the failure of the wellbore rock mass (indoor cyclic load test (marble)).
- (2)
- The drilling tool collides with the wellbore, and the collision stress is small and does not exceed the bearing capacity of the rock mass of the wellbore, but the multiple collisions between the drill string and the wellbore (the number of collisions exceeds 100 times) lead to a decrease in the strength of the rock mass of the wellbore and failure (thick-walled hollow cylinder cyclic loading (fatigue) test).
- (3)
- The collision stress between the drilling tool and the wellbore does not exceed the bearing capacity of the rock mass of the wellbore, but the multiple collisions between the drill string and the wellbore (the number of collisions exceeded 10,000 times) lead to a decrease in the strength of the rock mass of the wellbore and failure (cyclic load experiment (Buria sandstone)).

- $\left[\sigma \right]$—The rock strength of the wellbore, Pa;
- $S$—The contact area when the drill string collides with the wellbore, m
^{2}; - ${F}_{N}$—The minimum force required to destroy a rock, N.

- $\alpha $—Surrounding angle of drill string;
- $L$—Drill string length, m.

- $l$—The chord length of the arc corresponding to the central angle $\alpha $, m.

- $\delta $—Clay layer thickness, m;
- $\Delta $—The width of the ring gap, m.

- $n$—The instability evaluation coefficient of the wellbore;
- $F$—The maximum collision force per meter, N;
- ${F}_{N}$—The minimum force required to break the rock, N.

- $N$—Predict the number of collisions between drill string and wellbore per unit length;
- ${N}_{1}$—The number of collisions per unit time per unit contact area;
- $T$—The pure drilling time for drilling through the length of the BHA, s.

- ${N}_{2}$—The number of collisions between the drill string and the wellbore per unit length in the simulation time;
- ${T}_{1}$—Simulation time, s;
- $A$—The number of units per contact area;
- ${V}_{h}$—Mechanical drilling speed, m/s;
- ${l}_{1}$—The length of the BHA, m.

- ${S}_{1}$—Surface area of the inner wall of the wellbore per unit length, m
^{2}.

## 3. Establishment of Drill String Dynamic Model

#### 3.1. Basic Assumptions

- (1)
- The deformation of the drilling string is limited, and when the combination of drilling tools is deformed, it is guaranteed to have random nonlinear contact collision with the wellbore;
- (2)
- The geometric dimensions and material properties of drill pipes and collars remain constant;
- (3)
- The wellbore is a viscoelastic body, the axis of the wellbore and the axis of the drill pipe should coincide in the initial state, there is a ring gap between the wellbore and the drill string, and the wellbore cross-section is circular;
- (4)
- Treat the surrounding rock within 1 m of the drill string as a whole;
- (5)
- Ignore the influence of drilling fluid on the drill string.

#### 3.2. Establishing a Simulation Model

#### 3.3. Model Reliability Validation

## 4. Analysis of the Results

#### 4.1. Analysis of the Impact of Borehole Risk Assessment Instability under Drill String Vibration

#### 4.2. Influence of Drill String Vibration on Wellbore Stability under Different Drilling Tool Combinations

#### 4.2.1. Influence of Single Centralizer Placement on Wellbore Stability

#### 4.2.2. Effect of Single Centralizer Size on Wellbore Stability

#### 4.2.3. Comparative Analysis of the Influence of Single and Double Centralizers on the Stability of the Wellbore

## 5. Conclusions

- (1)
- When the single centralizer is placed close to the drill bit and the wellbore instability coefficient is low, the stability of the wellbore is improved compared with other situations;
- (2)
- When the packed hole centralizer is installed close to the drill bit, it will further reduce the borehole instability coefficient and improve the stability of the wellbore;
- (3)
- Compared to the double-centralizer drilling tool combination, the wellbore will be more stable with the single-centralizer drilling tool combination;
- (4)
- It is verified that this method can predict wellbore stability and optimize the drilling tool combination and drilling parameters according to the wellbore stability.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$A$ | The number of units per contact area |

${c}_{f}$ | Damping coefficient of drill string |

${c}_{r}$ | Recovery factor of drill string |

${d}_{i}$ | Drill string diameter, m |

${d}_{o}$ | Wellbore diameter, m |

$F$ | The maximum collision force per meter, N |

${F}_{N}$ | The minimum force required to destroy a rock, N |

${F}_{n}$ | The normal force of the collision of the drill string with the wellbore, N |

${F}_{z}$ | The friction resistance in the Z-axis direction when the drill string collides with the wellbore, N |

${k}_{h}$ | Wellbore stiffness, N/m |

$L$ | Drill string length, m |

$l$ | The chord length of the arc corresponding to central angle $\alpha $, m |

${l}_{1}$ | The length of the BHA, m |

${M}_{o}$ | The frictional moment of the drill string, N · m |

$N$ | Predict the number of collisions between drill string and wellbore per unit length |

${N}_{1}$ | The number of collisions per unit time per unit contact area |

${N}_{2}$ | The number of collisions between the drill string and the wellbore per unit length in the simulation time |

$n$ | The instability evaluation coefficient of the wellbore |

$S$ | The contact area when the drill string collides with the wellbore, m^{2} |

${S}_{1}$ | Surface area of the inner wall of the wellbore per unit length, m^{2} |

$T$ | The pure drilling time for drilling through the length of the BHA, s |

${T}_{1}$ | Simulation time, s |

${v}_{1}$ | The velocity before the drill string collides with the wellbore, m/s |

${v}_{2}$ | The velocity of the drill string after collision with the wellbore, m/s |

${V}_{h}$ | Mechanical drilling speed, m/s |

${v}_{r}$ | Radial velocity of drill string center of mass, m/s |

${v}_{s}$ | Stick–slip speed of the drill string, m/s |

$\alpha $ | Surrounding angle of drill string |

$\Delta $ | The width of the ring gap, m |

$\delta $ | Clay layer thickness, m |

${\mu}_{r}$ | Radial displacement of the center of mass of the drill string, m |

$\mu \left({v}_{s}\right)$ | Coefficient of friction of the drill string |

$[\sigma ]$ | The rock strength of the wellbore, Pa |

## References

- Chao, W.; Mian, C.; Yan, J. A prediction method of borehole stability based on seismic attribute technology. J. Pet. Sci. Eng.
**2009**, 65, 208–216. [Google Scholar] [CrossRef] - Zhang, J.; Lang, J.; Standifird, W. Stress, porosity, and failure-dependent compressional and shear velocity ratio and its application to wellbore stability. J. Pet. Sci. Eng.
**2009**, 69, 193–202. [Google Scholar] [CrossRef] - Wang, F.; Liu, X.; Jiang, B.; Zhuo, H.; Chen, W.; Chen, Y.; Li, X. Low-loading Pt nanoparticles combined with the atomically dispersed FeN4 sites supported by FeSA-NC for improved activity and stability towards oxygen reduction reaction/hydrogen evolution reaction in acid and alkaline media. J. Colloid Interface Sci.
**2023**, 635, 514–523. [Google Scholar] [CrossRef] [PubMed] - Li, Q.; Zhang, C.; Yang, Y.; Ansari, U.; Han, Y.; Li, X.; Cheng, Y. Preliminary experimental investigation on long-term fracture conductivity for evaluating the feasibility and efficiency of fracturing operation in offshore hydrate-bearing sediments. Ocean. Eng.
**2023**, 281, 114949. [Google Scholar] [CrossRef] - Pašić, B.; Gaurina-Međimurec, N.; Matanović, D. Wellbore instability: Causes and consequences nestabilnost kanala bušotine: Uzroci i posljedice. Rud.-Geološko-Naft. Zb.
**2007**, 19, 87–98. [Google Scholar] - Fam, M.A.; Dusseault, M.B.; Fooks, J.C. Drilling in mudrocks: Rock behavior issues. J. Pet. Sci. Eng.
**2003**, 38, 155–166. [Google Scholar] [CrossRef] - Van Oort, E. On the physical and chemical stability of shales. J. Pet. Sci. Eng.
**2003**, 38, 213–235. [Google Scholar] [CrossRef] - Yu, M.; Chenevert, M.E.; Sharma, M.M. Chemical–mechanical wellbore instability model for shales: Accounting for solute diffusion. J. Pet. Sci. Eng.
**2003**, 38, 131–143. [Google Scholar] [CrossRef] - Choi, S.K.; Tan, C.P.; Freij-Ayoub, R. A coupled mechanical-thermal-physico-chemical model for the study of time-dependent wellbore stability in shales. In Elsevier Geo-Engineering Book Series; Elsevier: Amsterdam, The Netherlands, 2004; Volume 2, pp. 581–586. [Google Scholar]
- Mohiuddin, M.; Khan, K.; Abdulraheem, A.; Al-Majed, A.; Awal, M. Analysis of wellbore instability in vertical, directional, and horizontal wells using field data. J. Pet. Sci. Eng.
**2007**, 55, 83–92. [Google Scholar] [CrossRef] - Diaz-Perez, A.; Cortes-Monroy, I.; Roegiers, J.C. The role of water/clay interaction in the shale characterization. J. Pet. Sci. Eng.
**2007**, 58, 83–98. [Google Scholar] [CrossRef] - Al-Bazali, T.; Zhang, J.; Chenevert, M.E.; Sharma, M.M. Experimental and numerical study on the impact of strain rate on failure characteristics of shales. J. Pet. Sci. Eng.
**2008**, 60, 194–204. [Google Scholar] [CrossRef] - Al-Bazali, T.; Zhang, J.; Chenevert, M.E.; Sharma, M.M. Factors controlling the compressive strength and acoustic properties of shales when interacting with water-based fluids. Int. J. Rock Mech. Min. Sci.
**2008**, 45, 729–738. [Google Scholar] [CrossRef] - Al-Bazali, T.M.; Al-Mudh′hi, S.; Chenevert, M.E. An experimental investigation of the impact of diffusion osmosis and chemical osmosis on the stability of shales. Pet. Sci. Technol.
**2011**, 29, 312–323. [Google Scholar] [CrossRef] - AL-Bazali, T.M. The consequences of using concentrated salt solutions for mitigating wellbore instability in shales. J. Pet. Sci. Eng.
**2011**, 80, 94–101. [Google Scholar] [CrossRef] - Sensoy, T.; Chenevert, M.E.; Sharma, M.M. Minimizing Water Invasion in Shale Using Nanoparticles. In Proceedings of the SPE Annual Technical Conference and Exhibition, New Orleans, LA, USA, 4–7 October 2009. [Google Scholar]
- Cai, J.; Chenevert, M.E.; Sharma, M.M.; Friedheim, J. Decreasing water invasion into Atoka shale using nonmodified silica nanoparticles. SPE Drill. Complet.
**2012**, 27, 103–112. [Google Scholar] [CrossRef] - Sharma, M.M.; Zhang, R.; Chenevert, M.E.; Ji, L.; Guo, Q.; Friedheim, J. A New Family of Nanoparticle Based Drilling Fluids. In Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 8–10 October 2012. [Google Scholar]
- Mcdonald, M.J. A Novel Potassium Silicate for Use in Drilling Fluids Targeting Unconventional Hydrocarbons. In Proceedings of the SPE Canadian Unconventional Resources Conference, Calgary, AB, Canada, 30 October 2012. [Google Scholar]
- Moroni, L.P.; Vickers, S.; Gray, C.; Davidson, M. Good Things Come In Little Packages: Nanotechnology for Reduction in Pore Pressure Transmission. In Proceedings of the SPE Annual Technical Conference and Exhibition, Amsterdam, The Netherlands, 27–29 October 2014. [Google Scholar]
- Dykstra, M.W.; Chen, D.; Warren, T.M.; Azar, J.J. Drillstring component mass imbalance: A major source of downhole vibrations. SPE Drill. Complet.
**1996**, 11, 234–241. [Google Scholar] [CrossRef] - Pla´ cido JC, R.; Santos HM, R.; Galeano, Y.D. Drillstring vibration and wellbore instability. J. Energy Resour. Technol.
**2002**, 124, 217–222. [Google Scholar] [CrossRef] - Field, D.J.; Swarbrick, A.J.; Haduch, G.A. Techniques for Successful Application of Dynamic Analysis in the Prevention of Field-induced Vibration Damage in MWD Tools. In Proceedings of the SPE/IADC Drilling Conference, Amsterdam, The Netherlands, 23–25February 1993. [Google Scholar]
- Melakhessou, H.; Berlioz, A.; Ferraris, G. A nonlinear well-drillstring interaction model. J. Vib. Acoust.
**2003**, 125, 46–52. [Google Scholar] [CrossRef] - Karkoub, M.; Abdel-Magid, Y.L.; Balachandran, B. Drill-string torsional vibration suppression using GA optimized controllers. J. Can. Pet. Technol.
**2009**, 48, 32–38. [Google Scholar] [CrossRef] - Liao, C.M.; Balachandran, B.; Karkoub, M.; Abdel-Magid, Y.L. Drill-string dynamics: Reduced-order models and experimental studies. J. Vib. Acoust.
**2011**, 133, 041008. [Google Scholar] [CrossRef] - Liao, C.M.; Vlajic, N.; Karki, H.; Balachandran, B. Parametric studies on drill-string motions. Int. J. Mech. Sci.
**2012**, 54, 260–268. [Google Scholar] [CrossRef] - Zhu, X.; Liu, W. The effects of drill string impacts on wellbore stability. J. Pet. Sci. Eng.
**2013**, 109, 217–229. [Google Scholar] [CrossRef] - Zhu, X.; Liu, W.; Liu, Q. The mechanism and law of wellbore instability due to drill string impact in air drilling. Int. J. Oil Gas Coal Technol.
**2014**, 8, 153–181. [Google Scholar] [CrossRef] - Vijayan, K.; Vlajic, N.; Friswell, M.I. Drillstring-borehole interaction: Backward whirl instabilities and axial loading. Meccanica
**2017**, 52, 2945–2957. [Google Scholar] [CrossRef] [Green Version] - Khaled, M.S. A New Approach for Predicting Drillstring Vibration Impact on Wellbore Stability. In Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 9–11 October 2017. [Google Scholar]
- Khaled, M.S.; Shokir, E.M. Effect of Drillstring Vibration Cyclic Loads on Wellbore Stability. In Proceedings of the SPE Middle East Oil & Gas Show and Conference, Manama, Bahrain, 6–9 March 2017. [Google Scholar]
- Kapitaniak, M.; Vaziri, V.; Chávez, J.P.; Wiercigroch, M. Experimental studies of forward and backward whirls of drill-string. Mech. Syst. Signal Process.
**2018**, 100, 454–465. [Google Scholar] [CrossRef] [Green Version] - Zheng, X.; Agarwal, V.; Liu, X.; Balachandran, B. Nonlinear instabilities and control of drill-string stick-slip vibrations with consideration of state-dependent delay. J. Sound Vib.
**2020**, 473, 115235. [Google Scholar] [CrossRef] - Li, Z.; Chen, L.; Zhong, Y.; Wang, L. Study on Sinusoidal Post-Buckling Deformation of Coiled Tubing in Horizontal Wells Based on the Separation Constant Method. Machines
**2023**, 11, 563. [Google Scholar] [CrossRef] - Makarenko, P.P.; Mande, A.R.; Gesackin, B.P.; Fu, Y. Determination of contact area between heavy drill pipe (УБT) and wellbore. Foreign Oilfield Eng.
**1997**, 13, 28. [Google Scholar]

**Figure 5.**Schematic diagram of drilling tool combination and installation of vibration measurement equipment.

**Figure 10.**Comparison of measured and simulated trajectory diagrams. (

**a**) Measured trajectory diagram. (

**b**) Simulated trajectory plot.

Part Name | Inner Diameter (mm) | Outside Diameter (mm) | Length (mm) | Material |
---|---|---|---|---|

Drill pipe | 129.9 | 149.2 | 500,000 | Steel |

Drill collars | 71.4 | 203.2 | 157,600 | Steel |

PDC bit | / | 330.2 | / | Steel |

Wellbore | 330.2 | / | 700,000 | Dacite |

Centralizer | / | 330.2 | 200 | Steel |

/ | 329.2 | |||

/ | 327.2 |

Constraint Name | Fixed Pair | Rotate the Pair |
---|---|---|

Added parts | Wellbore and ground | Drill pipe and wellbore |

Drill bits and drill pipes | ||

Drill pipe and drill collar |

Load | Apply Components | Direction | Specific Parameters |
---|---|---|---|

Gravity | Model as a whole | −Y | 9806.65 |

Contact force | Drill bits and boreholes | / | / |

Drill bits and bottom rock | |||

Drill string and wellbore | |||

Bushing force | Bottom rock and earth | / | / |

Unidirectional force | External node at the upper end of the drill pipe | Y | step (time, 0, 0, 0.5, $X$) |

Top driven | X-Z plane | step (time, 0, 0, 0.5, $Xd$) |

Stiffness | Force Index | Damping | Depth of Penetration | Static Friction Speed | Dynamic Friction Speed | Static Translation Speed | Friction Translation Speed | |
---|---|---|---|---|---|---|---|---|

Contact force | 2.0e^{5} | 1.3 | 10 | 0.1 | 0.3 | 0.1 | 100 | 1000 |

Serial Number | Name | Length (m) | Diameter (in) |
---|---|---|---|

1 | DC | 18 | 8 |

2 | Vibrator | 9 | 8 |

3 | DC | 99 | 8 |

4 | Vibration measurement equipment | 0.45 | 8 |

5 | DC | 30 | 8 × 1 + 9 × 2 |

6 | Torsion impactor | 0.75 | 9.6 |

7 | PDC drill bits | / | 13 |

Number of Experiments | Sensor Number | Sampling Frequency | Filter Frequency | Error |
---|---|---|---|---|

First trial | 1 | 100 | 10 | 1% |

2 | 1000 | 500 | 1% | |

3 | 1000 | 500 | 1% |

Lithology | Wellbore Site | Contact Area (m^{2}) | Collision Frequency (Times) | Damaging Force (N) |
---|---|---|---|---|

Dacite | Around the drill pipe | 7.31 × 10^{−4} | 0 | 49,640 |

100 | 42,790 | |||

10,000 | 34,748 | |||

Around the drill collar | 10.64 × 10^{−4} | 0 | 72,352 | |

100 | 62,367 | |||

10,000 | 50,646 |

Wellbore Lithology | Wellbore Stability Coefficient | Wellbore Status |
---|---|---|

Dacite | 0 < n < 1 | Safe |

n ≥ 1 | Dangerous |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shan, Y.; Xue, Q.; Wang, J.; Li, Y.; Wang, C.
Analysis of the Influence of Downhole Drill String Vibration on Wellbore Stability. *Machines* **2023**, *11*, 762.
https://doi.org/10.3390/machines11070762

**AMA Style**

Shan Y, Xue Q, Wang J, Li Y, Wang C.
Analysis of the Influence of Downhole Drill String Vibration on Wellbore Stability. *Machines*. 2023; 11(7):762.
https://doi.org/10.3390/machines11070762

**Chicago/Turabian Style**

Shan, Yonggang, Qilong Xue, Jin Wang, Yafeng Li, and Chong Wang.
2023. "Analysis of the Influence of Downhole Drill String Vibration on Wellbore Stability" *Machines* 11, no. 7: 762.
https://doi.org/10.3390/machines11070762