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Influence of Weight-on-Bit on Percussive Drilling Performance

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Abstract

A phenomenological model for percussive drilling systems is proposed in this paper to explain the experimentally demonstrated existence of an optimal weight-on-bit (WOB), for which the rate of penetration (ROP) is maximized. Several hypotheses have been previously proposed to explain this universal characteristic of percussive drilling, including increased wear of the bit, reduced indexing, and poor cleaning of debris under excessive WOB. Motivated by experimental evidence, we instead consider an increase of the pseudo-stiffness of the bit-rock interface (BRI) with increasing WOB, and investigate its effect on the impact energy transmitted to the rock. The 1D model approximates the dynamics underlying the drilling process by assuming that the impact of the hammer generates a longitudinal wave in the bit. It is shown that the BRI pseudo-stiffness influences the incident wave and associated energy transmitted from the bit to the rock. As a consequence, the drilling efficiency is affected by the dependence of the BRI stiffness on the WOB. The model indicates that there exist optimal conditions for the energy transfer from the bit to the rock in terms of the impedance ratio and the BRI stiffness/WOB. Thus it confirms that there is a sweet spot as seen in practice, which suggests that the root cause of the existence of a sweet spot in the ROP-WOB relationship lies in the nature of the BRI laws, rather than with issues related to bit indexing, bit wear, and/or cleaning of the debris.

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References

  • Ajibose OK, Wiercigroch M, Pavlovskaia E, Akisanya AR, Károlyi G (2012) Drifting impact oscillator with a new model of the progression phase. J Appl Mech 79(6)

  • Ajibose OK, Wiercigroch M, Pavlovskaia E, Akisanya AR (2010) Global and local dynamics of drifting oscillator for different contact force models. Int J Non-Linear Mech 45(9):850–858

    Article  Google Scholar 

  • Bruno MS (2005) Fundamental research on percussion drilling : improved rock mechanics analysis , advanced simulation technology , and full- scale laboratory investigations. Tech Rep 626, Terralog Technologies Inc

  • Cheetham WR, Inett E (1953) Factors affecting the performance of percussive drills. Trans Inst Min Metall Eng 63:45–74

    Google Scholar 

  • Chiang LE, Elías DA (2000) Modeling impact in down-the-hole rock drilling. Int J Rock Mech Min Sci 37(4):599–613. https://doi.org/10.1016/S1365-1609(99)00124-0

    Article  Google Scholar 

  • Depouhon A (2014) Integrated dynamical models of down-the-hole percussive drilling. PhD thesis, Université de Liège, Liège, Belgique

  • Depouhon A, Denoël V, Detournay E (2015) Numerical simulation of percussive drilling. Int J Numer Anal Meth Geomech 39(8):889–912. https://doi.org/10.1002/nag.2344

    Article  Google Scholar 

  • Fairhurst C (1961) Wave mechanics of percussive drilling. Mine Quarry Eng 122–130

  • Fourmeau M, Depouhon A, Kane A, Hoang H, Detournay E (2015) Influence of indexation and impact energy on bit/rock interface law in percussive drilling: an experimental study. In: 49th U.S. Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association, San Francisco, California

  • Franca LFP (2011) A bit-rock interaction model for rotary-percussive drilling. Int J Rock Mech Min Sci 48(5):827–835. https://doi.org/10.1016/j.ijrmms.2011.05.007

    Article  Google Scholar 

  • Ghosh R, Schunnesson H, Gustafson A (2017) Monitoring of drill system behavior for water-powered in-the-hole (ITH) drilling. Minerals 7(7):121. https://doi.org/10.3390/min7070121

    Article  Google Scholar 

  • Gnirk PF (1962) An experimental investigation of the indexing phenomenon for static single-tooth penetration in Indiana limestone. University of Minnesota School of Mines and Metallurgy, Minnesota

    Google Scholar 

  • Graff KF (1975) Wave motion in elastic solids. Dover books on physics series. Dover Publications, USA

    Google Scholar 

  • Haimson B (1966) High velocity, low velocity and static bit penetration characteristics in Tennessee Marble. Master’s thesis, University of Minnesota

  • Han G, Dusseault MB, Detournay E, Thomson BJ, Zacny K (2009) Principles of drilling and excavation, vol 2. Wiley, Hoboken, pp 31–140. https://doi.org/10.1002/9783527626625.ch2

    Book  Google Scholar 

  • Han G, Bruno M (2006) Lab investigations of percussion drilling from single impact to full scale fluid hammer. In: 41st US Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association, Golden, Colorado

  • Han G, Bruno M, Lao K, (2005) Percussion drilling in oil industry : review and rock failure modelling. In: AADE 2005 National Technical Conference and Exhibition, Houston, Texas

  • Hartman Howard L (1990) Drilling principles. In: Kennedy BA (ed) Surface mining, 2nd Edition, Society for Mining, Metallurgy, and Exploration, chap Mining Ope, pp 513–523

  • Hartman HL (1959) Basic studies of percussion drilling. Min Eng 11:68–75

    Google Scholar 

  • Hartman H (1962) Crater geometry relations in percussive drilling. Mine Quarry Eng 28(12):530–6

    Google Scholar 

  • Hartman HL (1966) The effectiveness of indexing in percussion and rotary drilling. Int J Rock Mech Min Sci 3:265–278

    Article  Google Scholar 

  • Haynes CD (1963) Constant energy-variable velocity effects in percussive drilling. PhD thesis, Pennsylvania State University

  • Hustrulid WA (1965) A study of energy transfer to rock and prediction of drilling rates in percussive drilling. Master’s thesis, University of Minnesota

  • Hustrulid WA (1968) Theoretical and experimental study of percussive drilling of rock. PhD thesis, University of Minnesota

  • Hustrulid WA, Fairhurst C (1971) A theoretical and experimental study of the percussive drilling of rock Part II-force-penetration and specific energy determinations. Int J Rock Mech Min Sci Geomech Abstracts 8(4):335–356. https://doi.org/10.1016/0148-9062(71)90046-5

    Article  Google Scholar 

  • Hustrulid WA, Fairhurst C (1972) A theoretical and experimental study of the percussive drilling of rock Part IV-application of the model to actual percussion drilling. Int J Rock Mech Min Sci Geomech Abstracts 9(3):431–442. https://doi.org/10.1016/0148-9062(72)90007-1

    Article  Google Scholar 

  • Izquierdo LE, Chiang LE (2004) A methodology for estimation of the specific rock energy index using corrected down-the-hole drill monitoring data. Min Technol 113(4):225–236. https://doi.org/10.1179/037178404225006218

    Article  Google Scholar 

  • Kivade S, Murthy CS, Vardhan H (2015) Experimental investigations on penetration rate of percussive drill. Procedia Earth Planetary Sci 11:89–99. https://doi.org/10.1016/j.proeps.2015.06.012

    Article  Google Scholar 

  • Kou S (1995) Some basic problems in rock breakage by blasting and by indentation. PhD thesis, Tekniska Högskolan i Luleå

  • Krivtsov AM, Wiercigroch M (2000) Penetration rate prediction for percussive drilling via dry friction model. Chaos Solitons Fractals 11(15):2479–2485

    Article  Google Scholar 

  • Lindqvist PA, Hai-hui L (1983) Behaviour of the Crushed Zone in rock indentation. Rock Mech Rock Eng 207:199–207

    Article  Google Scholar 

  • Lundberg B (1973) Energy transfer in percussive rock destruction-I: comparison of percussive methods. Int J Rock Mech Min Sci Geomech Abstracts 10(5):381–399. https://doi.org/10.1016/0148-9062(73)90024-7

    Article  Google Scholar 

  • Lundberg B (1982) Microcomputer simulation of stress wave energy transfer to rock in percussive drilling. Int J Rock Mech Min Sci Geomech Abstracts 19(5):229–239. https://doi.org/10.1016/0148-9062(82)90221-2

    Article  Google Scholar 

  • Lundberg B (1985) Microcomputer simulation of percussive drilling. Int J Rock Mech Min Sci Geomech Abstracts 22(4):237–249. https://doi.org/10.1016/0148-9062(85)92951-1

    Article  Google Scholar 

  • Lundberg B, Collet P (2010) Optimal wave with respect to efficiency in percussive drilling with integral drill steel. Int J Impact Eng 37(8):901–906. https://doi.org/10.1016/J.IJIMPENG.2010.02.001

    Article  Google Scholar 

  • Lundberg B, Okrouhlik M (2001) Influence of 3D effects on the efficiency of percussive rock drilling. Int J Impact Eng 25(4):345–360. https://doi.org/10.1016/S0734-743X(00)00053-1

    Article  Google Scholar 

  • Lundberg B, Okrouhlik M (2006) Efficiency of a percussive rock drilling process with consideration of wave energy radiation into the rock. Int J Impact Eng 32(10):1573–1583. https://doi.org/10.1016/J.IJIMPENG.2005.02.001

    Article  Google Scholar 

  • Lundquist RG (1968) Rock drilling characteristics of hemispherical insert bits. Master’s thesis, University of Minnesota

  • Maurer CW (1962) The “perfect–cleaning” theory of rotary drilling. J Petroleum Technol 14:1270–1274. https://doi.org/10.2118/408-PA

    Article  Google Scholar 

  • Muhammad A (1996) Control of ith percussive long hole drilling in hard rock. PhD thesis, McGill University

  • Nordlund E (1989) The effect of thrust on the performance of percussive rock drills. Int J Rock Mech Mining Sci Geomech Abstracts 26(1):51–59. https://doi.org/10.1016/0148-9062(89)90525-1

    Article  Google Scholar 

  • Paone J, Madson D, Bruce WE, States U, Mines B (1969) Drillability studies-laboratory percussive drilling. U.S. Dept. of the Interior, Bureau of Mines, Washington

    Google Scholar 

  • Pavlovskaia E, Wiercigroch M, Grebogi C (2001) Modeling of an impact system with a drift. Phys Rev E 64(5):056224

    Article  Google Scholar 

  • Pearse G (1985) Hydraulic rock drills. Min Magzines pp 220–231

  • Schunnesson H (1990) Drill process monitoring in percussive drilling—a multivariate approach to data analysis. PhD thesis, Luleå University of Technology

  • Shaw S (1965) Effects of farying degrees of rotation on rate of penetration of percussion drill bits. Unpublished Report

  • Simon R (1963) Energy balance in rock drilling. In: Texas drilling and rock mechamcs symposium, Society of Petroleum Engineers, https://doi.org/10.2118/499-PA

  • Simon R (1964) Transfer of the stress wave energy in the drill steel of a percussive drill to the rock. Int J Rock Mech Min Sci Geomech Abstracts 1(3):397–411. https://doi.org/10.1016/0148-9062(64)90006-3

    Article  Google Scholar 

  • Song X, Kane PA, Aamo OM, Detournay E (2020) A time scale regard on percussion drilling. Int J Impact Eng Submitted

  • Stephenson BR (1963) Measurement of dynamic force-penetration characteristics in Indiana limestone. Master’s thesis, University of Minnesota

  • Unger HF, Fumanti RR (1972) Percussive drilling with independent rotation. US Dept of Interior, Bureau of Mines

    Google Scholar 

  • Vanzant BW (1962) Dynamic rock penetration tests at atmospheric pressure. In: 5th Symposium on rock Mechanics, University of Minnesota

  • W Berry C (1959) Effect of varying bit shape on force-penetration characteristics in rock for impulsive loading. Master’s thesis, University of Minnesota

  • W Maurer C (1959) Impact crater formation in sandstone and granite. Master’s thesis, Colorado School of Mines

  • Worsley R (1960) Energy, impulse, and velocity effects in fracturing produced by chisel bits in limestone. PhD thesis, Colorado School of Mines

  • Wu C (1993) Influence of springy impact interface and curved drill rods on energy transfer in percussive rock drilling. PhD thesis, Luleå University of Technology

  • Wu C (1991) An analytical study of percussive energy transfer in hydraulic rock drills. Min Sci Technol 13(1):57–68. https://doi.org/10.1016/0167-9031(91)90254-A

    Article  Google Scholar 

  • Zou D (2017) Rock drilling. Theory and technology of rock excavation for civil engineering. Springer, Singapore, pp 49–103. https://doi.org/10.1007/978-981-10-1989-0

    Chapter  Google Scholar 

Download references

Acknowledgements

This study is a part of the research project INNO-Drill (Technology platform for research-based innovations in deep geothermal drilling) funded by The Research Council of Norway (Grant 254984) and industry partners (Epiroc, Enel Green Power, Lyng Drilling, NOV, Ravel, Robit, Rock Energy, Sandvik Mining and Construction, Tomax and Zaptec).

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A Appendix

A Appendix

1.1 A.1 Hammer-Bit Interface

The equation governing the evolution of the displacement of the HBI following impact is formulated by substituting the following expressions for the velocity and force at the HBI into Eq. (5)

$$\begin{aligned} V_{h}(t)= \,& {} \frac{\partial U}{\partial t}\left| _{x=0}\right. =cU'(ct), \end{aligned}$$
(18)
$$\begin{aligned} F(0,t)=\, & {} EA\frac{\partial U}{\partial x}\left| _{x=0}\right. =-EAU'(ct), \end{aligned}$$
(19)

which are obtained by setting \(x=0\) in Eqs. (3) and (4). Thus

$$\begin{aligned} \int _{0}^{t}U'(c\tau )d\tau =-\frac{m_{h}}{EA}\left( cU'(ct)-V_{0}\right) . \end{aligned}$$
(20)

After integrating the left term, this equation becomes

$$\begin{aligned} U'(ct)+\frac{EA}{m_{h}c^{2}}U(ct)=\frac{EA}{m_{h}c^{2}}U(0)+\frac{V_{0}}{c}, \end{aligned}$$
(21)

whose general solution is

$$\begin{aligned} U(ct)=De^{-\frac{EA}{m_{h}c}t}+U(0)+\frac{m_{h}c}{EA}V_{0}. \end{aligned}$$
(22)

After identifying the constant D using the initial condition \(U(0)=0\), the displacement of the HBI induced by the impact of the rigid hammer is is given by

$$\begin{aligned} U(ct)=\frac{m_{h}cV_{0}}{EA}\left[ 1-e^{-\frac{EA}{m_{h}c}t}\right] . \end{aligned}$$
(23)

The displacement increases from \(t=0\) to asympotically reach \(\frac{m_{h}cV_{0}}{EA}\) at large time provided that the elastic bit assembly is unbounded.

1.2 A.2 Bit-Rock Interface

Once the incident wave reaches the BRI, the force balance at the interface is given by

$$\begin{aligned} \begin{array}{cc} f_{t}=\kappa (u_{2}-u_{1}),&0\le \tau \le \tau _{p}\end{array}, \end{aligned}$$
(24)

where \(u_{1}\) and \(u_{2}\) represent the displacement at the BRI on the bit and rock side, respectively. Differentiating Eq. (24) with respect to time yields

$$\begin{aligned} \frac{df_{t}}{d\tau }=\kappa (v_{2}-v_{1}),0\le \tau \le \tau _{p}. \end{aligned}$$
(25)

Given the assumed semi-infinite and homogeneous nature of the rock, no wave reflection in the rock will occur. Hence, the velocity \(v_{1}\) and \(v_{2}\) on both sides of the interface can be expressed as

$$\begin{aligned} \left\{ \begin{array}{l} v_{1}=f_{t}-2f_{i}\\ v_{2}=-\lambda f_{t} \end{array}\right. ,0\le \tau \le \tau _{p}. \end{aligned}$$
(26)

Substituting Eq. (26) back into Eq. (25) yields the equation governing the evolution of the force applied by the bit on the rock

$$\begin{aligned} \frac{df_{t}}{d\tau }+\kappa \left( \lambda +1\right) f_{t}=2\kappa f_{i},\;0\le \tau \le \tau _{p}. \end{aligned}$$
(27)

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Song, X., Aamo, O.M., Kane, PA. et al. Influence of Weight-on-Bit on Percussive Drilling Performance. Rock Mech Rock Eng 54, 3491–3505 (2021). https://doi.org/10.1007/s00603-020-02232-x

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