A bit–rock interaction model for rotary–percussive drilling

A bit–rock interaction model for rotary–percussive drilling

International Journal of Rock Mechanics & Mining Sciences 48 (2011) 827–835 Contents lists available at ScienceDirect International Journal of Rock ...

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International Journal of Rock Mechanics & Mining Sciences 48 (2011) 827–835

Contents lists available at ScienceDirect

International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms

A bit–rock interaction model for rotary–percussive drilling Luiz F.P. Franca CSIRO, 26 Dick Perry Ave, Perth 6102 WA, Australia

a r t i c l e i n f o

abstract

Article history: Received 26 July 2010 Received in revised form 9 March 2011 Accepted 18 May 2011

Rotary–percussive drilling is considered a promising approach to improve drilling performance in hard rock formations. Different from percussive drilling, it is a hybrid form of drilling, since the weight-onbit and the angular velocity are still acting as in conventional rotary drilling. This paper deals with a bit–rock interaction model for bits under rotary and percussive actions and a methodology to evaluate rotary–percussive drilling performance. First, experimental drilling data from laboratory tests conducted with an in-house designed drilling rig are investigated. Next, a phenomenological model for the drilling action is proposed, assuming that the interface laws are rate-independent and that the state of variables are averaged over at least one revolution of the bit. Within the framework of the proposed model, quantitative information from drilling data related to rock properties, bit conditions and drilling efficiency can be extracted. Furthermore, the effectiveness of the percussive action is captured by a single number, l ¼ e=c, which corresponds to the intrinsic specific energy ratio. The similarity between the experimental results and the theoretical predictions are encouraging in regard to the use of this model to investigate rotary–percussive drilling response. The results have also shown that rotary– percussive drilling technique has potential application as an alternative method for drilling highly deviated wells or horizontal wells, where the limitations of weight-on-bit can be compensated by percussive action. & 2011 Elsevier Ltd. All rights reserved.

Keywords: Rotary–percussive drilling Bit–rock interface laws

1. Introduction Rotary drilling is widely used in the oil and gas drilling, while percussive or hammer drilling is extensively employed in the mining industry for exploration and blaster holes. Despite the fact that rotary drilling is the only method that can currently drill holes up to 10,000 m deep in almost all formations, it suffers from low penetration rate, high values of weight-on-bit (W) and excessive bit wear, principally, in hard rock formations. Percussive drilling, on the other hand, has the advantages of high performance in hard formations, light W for straighter holes and low cost per meter. Its major drawbacks are therefore related to low penetration in shale and other soft formations and poor steerability [1]. Taking into account that the limitations of the rotary drilling technique can be overcome by percussive drilling and vice-versa, a combined rotary and percussive or a hybrid drilling technique could result in a fast drilling at a low level of W. In this regard, rotary–percussive drilling (RPD) has been considered a promising approach to improve drilling performance in hard rock formations, offering economic benefits in terms of reducing drilling time and cost [2–6].

E-mail address: [email protected] 1365-1609/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2011.05.007

Several downhole hydraulic hammers have already been deployed and tested for RPD [2,4,7]. Such hammers convert a portion of the drilling fluid power into mechanical impacts directly upon the drill bit. The stress wave energy generated during the impact is propagated in direction of the bit–rock interface. Part of the energy is transmitted to the rock and transformed into useful work. The major feature of the percussive action is to increase the zone of damaged rock directly beneath the area of impact, facilitating the rotary action. To date, laboratory and field tests with hydraulic hammers have shown improvements on the penetration rate by a factor of two or three in certain rock formations, even when combined with roller-cone bits [2,4,6,7]. Although these hammers have led a considerable increase of the penetration rate, they are not extensively used by the drilling industry because of two main reasons: inconsistent overall results and mechanical failure [5,8]. However, these negative effects can be mitigated through a fundamental study of the rock fragmentation process associated with combined rotary and percussion actions. This paper deals with a bit–rock interface model for bits under both percussive and rotary actions and a methodology to assess the RPD performance. First, drilling data from laboratory tests at atmospheric pressure conducted with an in-house designed drilling rig are investigated. Taking into account that the interface laws are rate-independent and that the state of variables are averaged

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over at least one revolution of the bit, a phenomenological model for the drilling action is proposed, i.e. a set of relations between (W), torque-on-bit (T), impact energy per blow (H), blow frequency (oÞ, rate-of-penetration (V), and angular velocity or rotary speed (OÞ, assuming that. By postulating that the penetration per revolution (d) is a combination of the rotary and the percussive penetrations per revolution, d ¼ dr þdp , a linear relation is obtained between the specific energy (E), the hammering strength (P) and the drilling strength (S), which are, respectively, proportional to T, H and W and inversely proportional to d. Within the framework of the model, the efficiency of the percussive action can be investigated through a single number l ¼ e=c, which corresponds to the intrinsic specific energy ratio. Moreover, quantitative information from drilling data related to rock properties, bit conditions and drilling efficiency can be extracted.

rate-independent process, the rotary drilling response can be described by relations involving three state variables W, T and dr, T ¼ T~ ðdr Þ

~ ðdr Þ: W ¼W

and

ð2Þ

Using the same logic established for rotary drilling in percussive drilling, in which the parameters or state variables are averaged over at least one revolution of the bit and the drilling process is rate-independent, the percussive drilling response can be described by relations involving two state variables, H (the impact energy per blow) and the percussive penetration per revolution (dp), ~ p Þ, H ¼ Hðd

ð3Þ

where dp ¼ 2pVp =O and Vp is the percussive penetration rate. 2.2. Basic variables t, $, w and d It is convenient for the purpose of developing drilling response model to establish new state variables. A scaled torque t and weight $ are defined as

2. Background 2.1. Rate-independent drilling process The rotary drilling response model consists of a set of relationships between four quantities: W, T, V and O. Assuming that these variables are averaged over at least one revolution of the bit, the interface laws that relate the dynamic to the kinematic variables are generally of the form W ¼ WðV, OÞ

and

T ¼ TðV, OÞ,

ð1Þ

where the dynamic variables, W and T, depend only on the kinematic variables, V and O. Nevertheless, experiments under kinematic control (V imposted) conducted at CSIRO have revealed that T depends only on the ratio V=O for a given bit and rock [9]. Fig. 1 presents a drilling test conducted in Savonnie re limestone with a roller-cone bit (IADC 531 of 63.5 mm in diameter) at constant rotary penetration per revolution dr ¼ 2pVr =O ¼ 1 mm=rev. (Vr is the rotary penetration rate) In this test, both O and Vr were increased linearly with time, so to maintain a constant rotary penetration per revolution dr (constant ratio Vr =OÞ. We can clearly observe that T is constant regardless of the rotary speed O, suggesting that the processes that are acting at the bit–rock interface are rate-independent. The same observation is reported by Detournay et al. [10] in tests conducted with drag bits. As a



2T a2

and



W , a

ð4Þ

where a is the bit radius. The scaled quantities t and $ have dimension [F][L]  1 and can conveniently be interpreted as the normal and shear force per unit length. Notice that the introduction of t and $ removes the influence of the bit dimension from the drilling response. In the case of percussive drilling, a scaled impact number w [F][L]  1 is defined as



2Gf , a2

ð5Þ

where G ¼ ZH is the impact energy expended to fragment the rock, Z is the hammer-bit energy transfer coefficient and f ¼ o=O is the number of blows per revolution of the bit. As the rotary and the percussive actions are independent, the total penetration rate of the bit V can be assumed as a combination of the rotary and the percussive penetration rates, V ¼ Vr þ Vp . A total or rotary–percussive penetration per revolution d can be thus described as d ¼ dr þ dp ¼

2p

O

ðVr þ Vp Þ ¼

2pV

O

:

ð6Þ

3. Experimental setup

30 dr = 1 mm/rev

Savonnière

Torque [N.m]

25 20 15 10 5 0 0

20

40

60

80

100

120

Rotary speed [RPM] Fig. 1. Drilling data conducted in Savonnie re limestone at atmospheric pressure with a roller-cone bit (IADC 531 of 2 12 inÞ. The penetration per revolution is controlled and maintained constant, dr ¼ 1 mm/rev, after [9].

A series of laboratory tests at atmospheric pressure conducted with an in-house designed drilling rig was carried at CSIRO in Perth (Australia). Fig. 2 shows an isometric perspective of the drilling rig, which consists basically of four components: upper assembly, hammer system, bit assembly and core drive mechanism. The upper assembly is composed of a geared brushless servomotor and a linear actuator mounted on the top of the frame. Designed to perform tests under kinematic control (V-imposed), the upper assembly has a load capacity of 40 kN and can provide a precise rate of penetration from 0.01 to 100 mm/s. Two different hammer systems are used: a vibro-impact oscillator and a pneumatic knocker (Singold-k80). The vibro-impact oscillator can supply an impact energy within the range of 7.5–12 J and impact frequency o of 4.7 Hz. The pneumatic knocker supplies a constant impact energy of 50 J at an impact frequency of 1.5 Hz. The bit assembly consists of a roller-cone bit (IADC 531 of 63.5 mm in diameter), a shaft and an short anvil. Although designed to spin, the bit assembly is blocked by a beam load cell, which is used to measure T. Located at the bottom part of the frame, the core drive mechanism consists of a geared brushless

L.F.P. Franca / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 827–835

829

V

upper assembly

load cell

beam load cell

W

hammer system

T

bit assembly

Ω

core drive mechanism Fig. 2. Experimental drilling rig (Frank Jr.).

servo-motor and a lathe chuck assembly. Different from conventional drilling rig, the core mechanism drives the rock sample at a controlled angular velocity O. Any rotary speed within the range 10–400 RPM can be imposed as well as ramp profiles. The core mechanism has a torque capacity of 200 N m. A circulation system composed of a dust collector and compressed air is used to clean the bit.

Table 1 Mechanical properties of the rocks, where q is the uniaxial compressive strength, r the density, E the Young’s Modulus and n the Poisson ratio.

4. Experimental results

and indentation. In this regime, the bit behaves incrementally as a sharp bit and, consequently, the drilling efficiency increases with d. Regime III (d 4 dn Þ is associated to different rock failure mechanisms and/or with a change in the ratio of the indentation over the cutting actions during the drilling process. This regime is characterised by a small variations of W and T with d. Large variations of W and T with d can also be observed in regime III. However, it is caused by a poor cleaning condition (the production of cutting exceeds what can be removed by the drilling fluid). More information regarding the bit– rock interface laws for conventional rotary drilling is presented later.

4.1. Conventional rotary drilling (d ¼ dr and w ¼ 0Þ A series of experiments was conducted in two rocks: Castlegate sandstone and Charmot limestones. The mechanical properties of both rocks are shown in Table 1. For these tests, the bit angular velocity O is maintained constant at 2ps1 (60 RPM) and a continuous variation of d is applied to the bit, i.e. an constant acceleration, V_ ¼ V_ r ¼ 0:04 mm=s2 , is imposed through the upper assembly. The drilling parameters (W,T) are recorded during each test. The drilling response for Castlegate sandstone illustrated in the $2d and t2d spaces are shown in Fig. 3. Notice that the drilling response in both spaces can be approximated by a straight line at least for d Z d0 , where, in this case, d0 ¼ 0.5 mm/rev. The results for Charmot in the $2d and t2d spaces are shown in Fig. 4. The same observations of Fig. 3 apply here. Again, the drilling data can be approximated by a straight line but, in this case, for d Z0:25 mm=rev, i.e. d0 ¼0.25 mm/rev. Franca [9] proposed a drilling response model for roller-cone bits, which is composed of three drilling regimes. A conceptual drilling response in the W–d or T–d spaces is shown in Fig. 8. Within the framework of this model, the drilling response for 0 o d o d0 mm=rev corresponds to regime I, which is dominated by an increase of contact area between the bit and the rock with d. For d0 rd r dn mm=rev (regime II), the contact area is fully mobilised and any change of W or T is assumed by both drilling actions, cutting

Rock

q (MPa)

r (g/cm3)

E (GPa)

n

Castlegate sandstone Charmot limestone

14 53

2.0 2.36

10.55 11.0

0.23 0.12

4.2. Rotary–percussive drilling (RPD) (d ¼ dr þ dp and w a 0Þ For all tests conducted with RPD, the scaled impact number w and the depth of cut per revolution d are imposed while W and T are recorded during each test. As the maximum H provided by the vibro-impact hammer is 12 J and by the pneumatic knocker is 50 J, the vibro-impact hammer was used in tests conducted in Castlegate sandstone and the pneumatic knocker for tests in Charmot limestone. Independently of the hammer system, H is constant and w can only be changed by varying the number of blows per revolution f. Although f is varying, the penetration per revolution d is maintained constant, i.e. V and O are kinematically controlled to maintain a constant ratio V=O. The drilling response for Castlegate sandstone in the $2w and t2w spaces for d¼ 0.8 and 1.3 mm/rev is shown in Fig. 5. First, it is worth noting the decreases of $ and t with increasing w. Next, the drilling responses are practically the same with the shift being due to

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250

60

I

II

150

[N/mm]

200 [N/mm]

II

I

50 55

1

100

40 15

30

1

20 50

10

0 0.0

0.5

1.0

1.5 2.0 d [mm/rev]

2.5

3.0

0 0.0

3.5

0.5

1.0

1.5 2.0 d [mm/rev]

2.5

3.0

3.5

Fig. 3. Experiments conducted in Castlegate for O ¼ 2ps1 (60 RPM): (a) $2d diagram and (b) t2d diagram.

600

150 II

I

120 215

400

[N/mm]

[N/mm]

500

1

300 200

90

58

60

1

30

100 0 0.0

0.5

1.0 1.5 d [mm/rev]

2.0

0 0.0

2.5

0.5

1.0 1.5 d [mm/rev]

2.0

2.5

Fig. 4. Experiments conducted in Charmot for O ¼ 2ps1 (60 RPM): (a) $2d diagram and (b) t2d diagram.

120

30 Rotary Drilling d = 1.3 mm/rev

100

Rotary drilling d = 1.3 mm/rev

25 d = 0.8 mm/rev

80

20

60

15

40

10

20

d = 0.8 mm/rev

5

d = 0.8 mm/rev d = 1.3 mm/rev

0

d = 0.8 mm/rev d = 1.3 mm/rev

0 0

0

20

40

60

80

100

0

20

0

40

60

80

100

Fig. 5. Experiments conducted in Castlegate for d¼ 0.8 and 1.3 mm/rev: (a) $2w diagram and (b) t2w diagram.

60

300 Rotary drilling d = 1.0 mm/rev

250

50

200

40 d = 0.5 mm/rev

150

d = 0.5 mm/rev d = 1.0 mm/rev

30 20

100 50

10

d = 0.5 mm/rev d = 1.0 mm/rev

0

0 0

10 0

20

30

40

50

60

0

10

20

30

40

0

Fig. 6. Experiments conducted in Charmot for d¼ 0.5 and 1.0 mm/rev: (a) $2w diagram and (b) t2w diagram.

50

60

L.F.P. Franca / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 827–835

Torque or Weight

different values of d. Also, the results can be approximated by a straight line at least for w Z 5.5 N/mm, suggesting that there is a threshold value for w, w0 , beyond which a linear constraint between $, t and w seems to be valid. It is interesting to stress that the value of w0 can be easily identified through the space $2w but the same cannot be said using the space t2w. The spaces t2w and $2w for tests conducted in Charmot limestone for d ¼0.5 and 1.0 mm/rev are shown in Fig. 6. The same observations of Fig. 5 apply here, i.e. $ and t decrease with increasing w and the drilling response can be approximated by a straight line for w Z w0 . In this particular case, the linear constraint between $, t and w is only valid for w Z10 N=mm.

831

II

I

III

[mm/rev]

5. Conceptual model 5.1. Linear constraint on the drilling response

Fig. 8. Conceptual drilling response for roller-cone bits in the space Td or Wd, after [9].

The drilling responses conducted with rotary drilling suggest that there is a linear constraint between $, t and d for d Zd0 . A linear constraint between $, t and w is also observed on the drilling responses conducted with RPD for w Z w0 . Hence, it is convenient to define two new variables

associated with different rock failure mechanisms and/or with a change in the ratio indentation/cutting actions [9]. Taking into account only regime II, the energy dissipation at the interface can be decomposed in two parts, that reflect two independent processes, namely rock fragmentation and frictional contact,

d~ r ¼ dr d0

t ¼ td ðd~ r Þ þ tf

and

w~ ¼ ww0 :

ð7Þ

A conceptual drilling response in the space $2w~ 2d is shown in Fig. 7. The plane P corresponds a linear constraint on the response in terms of three variables, $, w~ and d. The response of the bit under a constant d is represented by the P2R line, where the point P corresponds to the condition of pure percussive drilling ($ ¼ 0Þ, the point R the condition of conventional rotary drilling (w~ ¼ 0Þ and the point M a combination of both drilling methods. It is showed geometrically that, although the point M can move along the P2R line, the drilling response is always a linear combination of dr and dp. 5.2. Rotary drilling Franca [9] proposed a bit–rock interface laws for rotary drilling with roller-cone bits, which is based on the phenomenological approach initially developed by Detournay and Defourny [11] and Detournay et al. [10] for drag bits. The conceptual drilling response is shown in Fig. 8, where three drilling regimes are defined: Regime I is characterised by the increase of the contact area between the bit and the rock with load; regime II corresponds to a condition where there is a linear constraint between $, t and dr, and regime III is

and

$ ¼ $d ðd~ r Þ þ $f ,

ð8Þ

where ( )d denotes the rock fragmentation components and ( )f the frictional contact components. The rock fragmentation components td and $d are explicitly given by [9–11]

td ¼ ed~ r and $d ¼ zed~ r ,

ð9Þ

where e is the intrinsic specific energy (the amount of energy required to remove a unit volume of rock) and z is a dimensionless number, which is typically within the range [0.5–0.8] for drag bits and [2.0–5.0] for roller-cone bits [9,10]. The frictional contact components tf and $f are assumed to be constrained by a frictional relation [9–11]

tf ¼ mg$f ,

ð10Þ

where m is the coefficient of friction at the wear flat-rock interface and g is a number within the range [0.6–1.2] for drag bits, and g ¼ 1 for roller-cone bits [9,11]. Combining Eqs. (8)–(10), the complete model for the rotary drilling response is obtained as

t ¼ ed~ r þ mg$f $ ¼ zed~ r þ $f :

ð11Þ

5.3. Percussive drilling In the case of percussive drilling, the main research works started in the 1970s. To date, a considerable effort has been devoted to bit– rock interface laws for percussive drilling [12–17]. Many investigations regarding the bit–rock interaction are concerned mostly with the prediction of the penetration rate and the optimum thrust. Experimental results with wedge-shaped cutter percussive bits have shown that the bit–rock interaction can be modelled by two linear relationships between the force F and the penetration u, see Fig. 9 [13,18,19]. Hustrulid and Fairhust [12] proposed the following phenomenological model for the percussive penetration rate Vp: Vp ¼

Fig. 7. Linear constraint between $, w~ and d on the drilling response.

Go , pa2 c

ð12Þ

where c is the intrinsic specific energy in percussion drilling. It is worth mentioning that this model does not consider dissipation of

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L.F.P. Franca / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 827–835

provided to the bit is used into the rock fragmentation process. In this case, the drilling response will be located on the drilling line. Otherwise, if an increase of the overall contact is taken place, the state points will move away form the drilling line and the drilling efficiency will decrease. A bit efficiency x can be thus defined as

F

1 k

1 k/α



Γ up

force–penetration

curve

um

during percussive

action,

after

1

λη

E[MPa]

ε μγ

1

1

ζ

1

η

P [MPa]

ζε

ζλη

0

S

]

Pa

[M

Fig. 10. Schematic E–P–S diagram.

energy by frictional contact. However, it takes into account that part of the hammer energy is dissipated at the hammer-bit interface, i.e. G ¼ ZH, where Z stands for the hammer-bit energy transfer coefficient. More information regarding the energy transfer coefficient Z is presented in detail in the appendix. Once the variables are averaged over at least one revolution of the bit, a linear constraint on the drilling response can be established using the basic variables w~ and dp,

w~ ¼ cdp :

ð13Þ

5.4. Rotary–percussive drilling Combining Eqs. (11) and (13), and considering that d~ ¼ d~ r þ dp , a complete drilling response for RPD is obtained as

t þ lw~ ¼ ed~ þ mg$f , $ þ zlw~ ¼ zed~ þ $f ,

ð14Þ

where l ¼ e=c corresponds to the intrinsic specific energy ratio. In fact, the proposed model accounts for the two components of the intrinsic specific energy, e and c, which allows us to objectively measure the relative efficiency of both, the conventional rotary drilling and the percussive drilling. Originally introduced by Detournay and Defourny [11] for drilling response of drag bits, another representation of Eq. (14) can be obtained by scaling t, $ and w by the penetration per revolution d: E þð1bÞlP ¼ E0 þ mgS,

ð16Þ

u

Drilling line

ψ

:

αL

0 Fig. 9. Idealised [13,18,19].

e E þ lP

ð15Þ

where b ¼ mgz, E0 ¼ ð1bÞe, E ¼ t=d~ is defined as the specific energy, P ¼ w~ =d~ is the impact strength and S ¼ $=d~ is the drilling strength. It should be noted that E, P and S have dimension [F][L]  2 and an convenient unit is N/mm2 (MPa). A conceptual sketch of the E–P–S diagram is shown in Fig. 10. If the drilling response corresponds to an ideal condition or maximum efficiency, all the energy

6. Model parameters identification The rotary drilling responses (Figs. 3 and 4) are now investigated within the framework of the model. All the model parameters identified for Castlegate and Charmot are summarised in Table 2. The identified values of the intrinsic specific energy e, the slope in the t2d space, are close to the measured uniaxial compressive strength q of the rocks, see Table 1. This result suggests that there is a correlation between e and q in tests conducted at atmospheric pressure. A few authors have reported a similar correlation [9,23,24]. We can also observe that z is independent of the rock type and that m is different for each rock tested. In this case, z depends only on the bit design and m is correlated with the rock properties. The model parameters identified for RPD are summarised in Table 3. It is interesting to stress that l is C 0:19 for tests conducted in Castlegate, suggesting that the effectiveness of percussive action is low. In the case of Charmot limestone, the identified value of l is C 0:92, meaning that the percussive action is more effective, due to the fact that both intrinsic specific energies e and c are practically the same. These results suggest that the performance of the RPD is probably correlated to different failure modes, ductile and brittle, of both indentation and cutting processes. Understanding the factors controlling the transition between these regimes will require a careful analysis of the dependence of the drilling response on the bit design and on the rock formation. We can also observe that the identified values of z are almost the same, independently of the rock formation and the drilling method used, see Tables 2 and 3. The values identified of m, on the other hand, are varying with the rock type and the drilling method, meaning that m is intimately linked with both the rock properties and the drilling process. The same drilling responses as those of Figs. 5 and 6 illustrated in the E-P-S diagram are shown in Figs. 11 and 12, respectively. Here we can observe that Table 2 Bit–rock interaction parameters identified for Castlegate sandstone and Charmot limestone for rotary drilling. Material

Castlegate Charmot

e

ze

$f

m$f

(MPa)

(MPa)

(N/mm)

(N/mm)

15 58

55 215

47 36

10 0

z

m

3.7 3.7

0.2 0.07

Table 3 Bit–rock interaction parameters identified for Castlegate sandstone and Charmot limestone for RPD. Material

Castelgate Charmot

l

0.19 0.92

zlZ

0.74 3.50

$f

m$f

(N/mm)

(N/mm)

108 175

30 37

z

Z

m

3.9 3.8

0.120 0.044

0.27 0.21

L.F.P. Franca / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 827–835

833

d = 0.8 mm/rev d = 1.3 mm/rev

30 25 E [MPa]

20 15 10 100 5

80 60

0 90

80

70

40 60

50 P [MP

40

30

a]

S

20 20

10

0

]

Pa

[M

0

Fig. 11. Experiments conducted in Castlegate for d ¼ 0.8 and 1.3 mm/rev in the E–P–S diagram.

d = 0.5 mm/rev d = 1.0 mm/rev

60

E [MPa]

50 40 30 20 300

10 250 0

200 150

60 45

100 30 P [MP

a]

50

15 0

S

]

Pa

[M

0

Fig. 12. Experiments conducted in Charmot limestone for d¼ 0.5 and 1.0 mm/rev in the E–P–S diagram.

all responses are contained in the drilling plane and that the drilling efficiency x increases with d~ in both rocks.

7. Conclusions This paper presents several laboratory drilling data and a complete model to evaluate the responses of rotary–percussive drilling. This drilling method, which makes use of a downhole hydraulic hammer mounted onto a conventional rotary drilling assembly, is considered a promising technique to improve drilling performance in hard rock formations. Four basic scaled variables are initially defined, $, t, w and d, assuming that the interface laws between the bit and the rock are rate-independent and that the state of variables are averaged over at least one revolution of the bit. Next, drilling tests conducted in two rocks, Castlegate sandstone and Charmot limestones, at atmospheric pressure with an in-house designed drilling rig are investigated.

The drilling responses obtained with both drilling methods, rotary and rotary–percussive, suggest that there are linear constraints between $, t and d for d Zd0 and between w, $, t and d for w Z w0 . Also, the rotary and the percussive actions are independent processes and d always corresponds to a linear combination of d~ r and dp, d ¼ d~ r þdp . A method to evaluate the drilling response of rotary–percussive drilling is thus proposed, i.e. a set of relations between $, t, w and d, considering that drilling response is composed by two independent processes, rock fragmentation and frictional contact. A linear relation is also obtained between the specific energy E, the impact strength P and the drilling strength S, which are, respectively, proportional to t, w and $ and inversely proportional to d. The E–P–S diagram can be used as a drilling efficiency indicator. Moreover, the effectiveness of the percussive action can be captured by a single number l ¼ e=c, which corresponds to the intrinsic specific energy ratio. Within the framework of the model, the identified values of e are close to the measured uniaxial compressive strength q,

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suggesting that there is a correlation between e and q in tests conducted at atmospheric pressure. The results also suggest that z does not depend on the rock type and the drilling method used and that m is different for each rock and drilling process. The percussive action is more effective in Charmot limestone due probably to the brittle mode of failure induced by percussive action. The poor percussive performance in Castlegate sandstone is therefore caused by the ductile mode of failure of both indentation and cutting processes. Although the percussive action is inefficient in Castlegate sandstone in terms of energy consumption, much less W and T are really needed, depending on the percussive load imposed. Consequently, this hybrid drilling method has potential application for drilling highly deviated wells or horizontal wells, in which the limitations of W and T can be compensated by impulsive loads.

describe the bit axial compliance, a mass–spring–dashpot system is used. Combining this model with the force–penetration relationship, a system commonly referred to as the Zener model is obtained, see Fig. 13. The dimensionless equation of motion of this system is give by [20]     k ^ 00 k ^ 000 0 y^ þ y þðk1Þy^ þ y ¼ 0, ð19Þ 2B 2B 0 where y^ ¼ y=y0 , y0 ¼ W=k is the static penetration, y^ ¼ dðyÞ=dt, t~ ¼ o0 t, k ¼ ðk þkb Þ=kb is the connecting spring stiffness pffiffiffiffiffiffiffiffiffi(ffi k Z0Þ, pffiffiffiffiffiffiffiffiffiffiffiffiffi B ¼ c=2 mb o0 is a convenient damping ratio, o0 ¼ k=m is the natural frequency of the system and mb is the bit mass. ^ t~ n Þ is the maximum penetration, where Considering that y^ n ¼ yð t~ n is identified for y^ 0 ðt~ n Þ ¼ 0, the Eq. (18) can be rewritten as 2

ð1gÞy^ n



rn

,

ð20Þ

Acknowledgements

where rn ¼ mb =mh . It is important to point out that the mass ratio rn has to be small for a better energy transfer, i.e. mh Z mb .

The author wishes to thank CSIRO for financial support and for permission to publish this paper, E. Detournay and T. Richard for their helpful discussions and suggestions; to K. Mahjoob, R. Nematollahi and R. Aguiar for their assistance in the collection of drilling data; to Greg Lupton for the rig design and to Roy Ledgerwood from Hughes Christensen Co. for supplying the crossover sub used in the bit assembly.

The effect of the damping ratio of the bit on the energy transfer coefficient Z for k ¼ 1 (rigid bit), k ¼ 3 (medium to hard bit) and k ¼ 8 (soft bit) is shown in Fig. 14. Notice that Z deceases by increasing the damping ratio B and Z increases by decreasing k.

Appendix A. The energy transfer coefficient – g The force–penetration curve of an indentor into rock is normally used to estimate the energy expended to fragment the rock during a single indentation event, see Fig. 9 [13,18,19]. The penetration resistance kA ð0,1Þ and the unloading parameter a A ð0,1Þ characterise the bit–rock interface. In this model, the output work (GÞ supplied to the process of rock fragmentation is given by Z um Z um 1 2 G¼ Fu ðuÞ du Fl ðuÞ du ¼ ð1aÞkum , ð17Þ 2 0 up

A.2. Parameters identification Different approaches were used to identify the hammer before impact velocity Vh. In the case of the vibro-impact oscillator, the parameters of the system (stiffness, viscous damping) were identified and the hammer (mass) displacement measured for different conditions of amplitude of excitation and gap between

H

,

kb c κk u k

k Rock

ð18Þ

where H ¼ mh Vh2 =2, mh is the hammer mass and Vh the hammer impact velocity. If H and the unloading parameter a are known, 2 the efficiency is completely determined by kum performed during the loading phase. Also, because of the linearity of the equations governing this phase, the force kum and the penetration um are both proportional to the impact velocity Vh. As H is proportional to Vh as well, the efficiency Z is independent of the impact velocity Vh. In the case of this hybrid drilling technique, W maintains the bit always in contact with the rock and, consequently, the effect of W on Z can be neglected. The relationship between Z and W, in percussive drilling, has been extensively explored by several authors [12,21,22].

Fig. 13. Bit–rock indentation during loading (Zener model).

1.0 0.8

/(1- )

G

y

x c

where um is the maximum penetration and up is the final depth of penetration. The impact system efficiency or the energy transfer coefficient (ZÞ is defined as the ratio of G to the input kinetic energy (H) supplied by the hammer, i.e.



mb

mb

0.6 0.4

=1 =3

0.2

=8

A.1. Roller-cone bit compliance Roller-cone bits are characterised by moving parts or roller cones supported by bearings, which cause a relatively high axial compliance. Consequently, only part of the impact energy is really transmitted to the rock during percussive action. In order to

0.0 0.0

0.5

1.0

1.5

Fig. 14. Coefficient of energy transfer Z for k ¼ 1, 3 and 8.

2.0

L.F.P. Franca / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 827–835

Due to large values of B and rn (mb b mh Þ only a small portion of the impact energy is indeed transmitted to the rock, decreasing significantly the energy transfer from hammer to rock. A new hammer design, where mb 5 mh , and bits with fixed cutter can therefore be used to increase Z.

20

Force [kN]

15

bit Charmot Castlegate

References

1

10 kb = 12.8 5

0 0.0

0.3

835

0.6 0.9 1.2 Penetration [mm]

1.5

1.8

Fig. 15. Bit stiffness and static force–penetration curves for Castlegate and Charmot.

Table 4 Bit/rock parameters identified for Castlegate and Charmot. Rock

Z

k

a

B

rn

yðt~ n Þ (mm)

Castlegate Charmot

0.120 0.044

1.25 1.33

0.47 0.58

0.96 0.93

4.17 (vibro-impact) 8.57 (knocker)

1.96 2.62

the head of the hammer and the anvil. Next, Vh is estimated fitting the numerical solution with the experimental result. In the case of the pneumatic knocker, a quartz force sensor was used to measure the impact force and the time of impact. Once the hammer (moving mass) and the stroke are known, Vh can be easily estimated. In order to obtain the bit stiffness kb, the bit is pushed against a rigid block of metal. The same procedure, but against the two rocks, is conducted with the objective to obtain the penetration stiffness k. Fig. 15 shows the bit stiffness and the static force– penetration curves measured for both rocks. Using a linear fit during the loading phase, the bit stiffness and the penetration resistance are identified: kb I12:8 kN=mm; kI3:3 kN=mm for Castlegate and kI4:2 kN=mm for Charmot. During the unloading phase, we can observe that the upper two-thirds can also be approximately by a straight linear. However, the other one-thirds is still elastic but nonlinear, characterising a combination of friction and elastic deformation of the rock. The damping ratio B and the energy transfer coefficient Z are obtained using the pneumatic knocker. The idea is to measure the maximum penetration during one knocker blow. As the yðtn Þ and k are known, B is obtained solving Eq. (19). The knocker generates an impact velocity of Vh ¼6.45 m/s, which causes an initial bit velocity of 2.18 m/s. The overall hammer and bit parameters identified are shown in Table 4.

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