- Email: [email protected]
Shale bedding planes control rock removal behaviors of PDC cutter: Single cutter experiment
Journal Pre-proof Shale bedding planes control rock removal behaviors of PDC cutter: Single cutter experiment Mao Sheng, Zhen Cheng, Shuyang Gao, Huaizhong Shi, Yanlong Zhang PII:
S0920-4105(19)31061-7
DOI:
https://doi.org/10.1016/j.petrol.2019.106640
Reference:
PETROL 106640
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 12 June 2019 Revised Date:
19 September 2019
Accepted Date: 31 October 2019
Please cite this article as: Sheng, M., Cheng, Z., Gao, S., Shi, H., Zhang, Y., Shale bedding planes control rock removal behaviors of PDC cutter: Single cutter experiment, Journal of Petroleum Science and Engineering (2019), doi: https://doi.org/10.1016/j.petrol.2019.106640. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1
Shale bedding planes control rock removal behaviors of PDC cutter: single
2
cutter experiment
3
Mao Shenga,b*, Zhen Chenga,b, Shuyang Gaoc, Huaizhong Shia,b, Yanlong Zhangd
4 5
a. State Key Laboratory of Petroleum Resources and Prospecting, (China University of Petroleum-Beijing), Beijing 102249, P.R. China
6
b. College of Petroleum Engineering, China University of Petroleum-Beijing, 102249, P.R. China
7
c. Sinopec Research Institute of Petroleum Engineering, Beijing, 10010, P.R. China
8
d. CNPC Engineering Technology R&D Company Limited, Beijing, 102200, China
9 10
* Correspondence to: Mao Sheng, E-mail: [email protected]
11 12 13
The highlight of this work can be presented as:
14
1) A parabolic correlation was observed between cutting force and bedding inclination.
15
2) Shear cracking along the weak bedding planes promotes chipping.
16
3) Bedding inclination controls the rock removal behaviors from crushing-dominate to
17
chipping-dominate.
18
1
19
Abstract
20
Shale bedding planes arise with the complexity of rock removal by the PDC cutters. A series of single
21
cutter experiments were conducted to understand the effects of bedding planes of shale on chip
22
formation behaviors. Six bedding inclinations were taken into account by recording the variation of
23
cutting force, cutting size, topography of debris, and high-speed images. Results demonstrate that the
24
average cutting force highly correlates with bedding inclination where a parabolic relation is observed.
25
The maximum value of cutting force is presented while perpendicular cutting to the bedding plane.
26
Crushing and chipping are approved to be two mechanisms of rock removal of the laminated shale.
27
Particularly, the bedding plane controls the chip formation behaviors. While the cutting force is
28
perpendicular to shale bedding, the crushing dominates the rock removal process in which more powder
29
debris are created. While the cutting force is parallel to shale bedding, the chipping dominates the rock
30
removal and more chunk-like cuttings are generated. Shear cracking along the weak bedding planes
31
promotes chipping that is controlled by the bedding inclination. In summary, the bedding plane
32
attributes to the variation of cutting force response, cutting size distribution, and even rock removal
33
mechanisms.
34 35
Keywords: shale, PDC, bedding plane, rock failure, chip formation
36
2
37
1 Introduction
38
Efficient drilling of Polycrystalline Diamond Compact (PDC) bit in shale formation recently attracts
39
much more attention since it is widely applicable in horizontal well drilling (Hanna, Douglas et al. 2011,
40
Soeder 2018, Zhai, Wang et al. 2018). Bedding plane is one nature of shale formation where the weak
41
strength and anisotropy mechanical properties fully exist. Figure 1 illustrates the contact relation of
42
PDC cutters and bedding planes with a contact angle. The contact angle would result in a more
43
complex shale drilling process. In order to offer basic guidelines for PDC cutter design and efficiency
44
improvement, influences of bedding planes on cutting force response and drilling efficiency should be
45
well recognized.
46 47
Fig. 1 Diagram of PDC bit drilling in bedding shale formation
48
Crushing and chipping are two widely accepted mechanisms of rock removal of the fixed cutters.
49
The crushing mode creates highly fractured and inelastically deformed rock, while major cracks initiate
50
and propagate to form big chips in chipping mode (Mishnaevsky 1995). However, the crushing and
51
chipping of rock is an extremely complex failure and cracking process that is controlled by two aspects:
52
rock properties and cutting situation. Cheatham and Daniels (Cheatham and Daniels 1979) investigated
53
the bit balling problems of clay shale drilling through single cutter experiments at atmospheric and
54
hydrostatic pressure conditions. They found that, the ductile and sticky nature of the clay shale were 3
55
two major contributors to the problems that the chip formation was similar to that of ductile metals
56
cutting. However, the cuttings generated under hydrostatic pressure were observed to be almost
57
identical to those achieved by cutting lead at atmospheric pressure. Finger (Finger 1984) developed a
58
linear cutting testbed and conducted a systematical rock cutting experiment on Berea sandstone and
59
Westerly granite. The large chips and a crushed powdery zone were identified by fluorescent dye. The
60
observations from experimental works were validated by Finite element and Discrete element
61
simulation (Huang, Detournay et al. 1999, Rojek, Onate et al. 2011, Jaime, Zhou et al. 2015). The
62
crushing failure and shear cracking mechanics were clarified through numerical analysis. Recently, Che
63
et al. (Che, Zhang et al. 2017) (Che and Ehmann 2014) proposed a comprehensive experimental scheme
64
to measure the force response and visualize chip formation process on Indiana limestone, Austin chalk,
65
and Berea sandstone. The chipping mode was found to highly correlate with the depth of cut, the rake
66
angle, and the rock types. Furthermore, they proposed a new cutting model by accounting for the
67
crushing zone and crack propagation behaviors from the observations of linear rock cutting (Che, Zhu
68
et al. 2016). The alternate sudden movements during chip formation was captured by high-speed
69
imaging and the crushing mode was found to occupy most of the time of an entire crushing and
70
chipping cycle (Cheng, Sheng et al. 2018). Moreover, the rake angle of the PDC cutter dramatically
71
affects the removal behaviors of crushed material where different cutting faces corresponds to specific
72
frictional angle and shear force on the rock failure plane. (Yahiaoui, Paris et al. 2016, Rostamsowlat,
73
Richard et al. 2018) Although the rock removal mechanisms have been illuminated so far from
74
numerical simulation and visualization experiments, yet most of studied rocks are relatively isotropic
75
and homogenous. The impacts of rock anisotropy, particularly weak bedding planes, are still required to
76
be recognized.
4
77
Many investigations attributed the anisotropy of rock mechanics and special failure behaviors to the
78
bedding planes of shale (Chenevert and Gatlin 1965, McLamore and Gray 1967, Niandou, Shao et al.
79
1997, Heng, Guo et al. 2015, Chen, Lan et al. 2018). The orientations of bedding planes determined the
80
failure mode since the weak strength is along the bedding planes. Moreover, the bedding plane slip was
81
identified to present a significant effect on borehole and casing stability. Special breakout patterns of the
82
laminated shale failure were found to be different from that of the isotropic formation and were
83
controlled by bedding inclination and in-situ stress conditions (Tien, Kuo et al. 2006, Labiouse and
84
Vietor 2014, Meier, Rybacki et al. 2015). Additionally, hydraulic fracture propagation was also
85
confirmed to be affected by bedding planes which promote the complexity of fracture network (Yushi,
86
Xinfang et al. 2016, Lin, He et al. 2017, Tang, Wu et al. 2018). In aspects of rock cutting, Ozcelik and
87
Yilmazkaya (Ozcelik and Yilmazkaya 2011) found the rock anisotropy, particularly the bedding
88
inclination to the cutting direction, was naturally sensitive to the cutting efficiency and force response
89
of diamond wire cutting. Gong and Liu (Gong, Zhao et al. 2005) (Liu, Xu et al. 2019) proposed a 2D
90
TBM cutting model to illustrate the joint orientation. They found the joint orientation could influence
91
the crack initiation and propagation as well as the fragmentation pattern. Though tremendous studies
92
demonstrate the importance of bedding planes on rock failure, wellbore stability, and hydraulic fracture
93
propagation, yet most of those studies did not discuss the effects of bedding plane on rock removal
94
mechanisms of PDC cutters, particularly for the cutting force response, chip formation process, and
95
complicated mechanisms.
96
In this paper, a series of single cutter experiments on laminated shale was conducted by considering
97
a wide range of bedding inclinations from 0° to 150°. The dynamic responses of cutting force, cutter
98
acceleration, and debris size distribution were obtained at different bedding inclinations. Extraordinary
5
99
crushing and chipping patterns were captured by high-speed imaging technique. Based on the observed
100
phenomena, a conceptual cutting model of laminated shale formation was proposed and further
101
mechanisms were discussed.
102
2 Materials and method
103
2.1 Linear rock cutting testbed
104
A linear rock cutting testbed was built based on a mechanical shaping machine as illustrated in Figure 2.
105
The testbed could precisely control the cutting speed (100~1200mm/min) and cutting depth (accuracy
106
of 0.01 mm). A cutter holder was particularly designed to fix single PDC cutter. The rake angle of cutter
107
was capable to adjust into five levels of negative 15, 20, 25, 30, 35, 40 degrees. A planar PDC cutter
108
with diameter of 13 mm and thickness of 25 mm, as a typical PDC bit cutter, was selected for this study.
109
The rock block was fixed by a specific holder to limit X and Y direction movement. In order to achieve
110
a linear cutting, the rock block was fed toward the cutter in x-direction while the cutter was kept
111
stationary.
112
Most importantly, the testbed was well equipped with a force measuring system, including a
113
single-component strain gauge (KYOWA KFWB-5-120-C1), which is close to the PDC cutter, a
114
unidirectional accelerator fixed at the cutter holder, and a data acquisition unit with a maximum
115
sampling rate of 100 Hz. Besides, a high-speed camera (Phantom V310) was used to visualize the chip
116
formation. The maximum resolution and recording speed of this high-speed camera are 1280 × 1024
117
and 50,000 fps.
6
118
Figure 2 Schematic diagram of (a) linear cutting testbed, (b)single PDC cutter scratching on shale block, and (c) Conceptual model of single PDC cutting on bedding shale 119
2.2 Rock specimen preparation
120
Organic-rich shale is our target material where these samples were collected from the outcrop of Lower
121
Silurian Longmaxi formation, which is located at south Sichuan basin in Changning, China. The
122
bedding plane is well rich in the Longmaxi Shale as shown in Figure 3. Mineralogical composition was
123
obtained from X-ray diffraction as listed in Table 1 and it can be seen that over 60% minerals belong to
124
brittle minerals. Particularly, the clay minerals mainly consist of illite without serious hydration
125
swelling problems. The mechanical properties were particularly measured in different bedding
126
inclinations, according to ISRM standard.
127
The specimens were cored from the same block and reshaped into the cubic blocks with side length of
128
200 mm by using a diamond-saw cutting machine. Fine polish was carried out to ensure the parallelism
129
of opposite surfaces of specimen was less than 100 µm. The sample can be reused after milling and
130
polishing cutting surface again. In total, six cubic blocks were prepared with six bedding inclinations of
131
0o, 30o, 60o, 90o, 120o, and 150o (Figure 3). The specimen was required to be dried in an oven at 100
132
for 48 hours before testing in order to remove the fluid influence.
7
133 134
Figure 3 Photographs of six cubic blocks with the bedding inclinations of 0o, 30o, 60o, 90o, 120o,
135
and 150o
136
Table 1. Mineral components and content of shale sample Minerals
Weight content (wt.%)
Quartz
22.2~35.1%
Clay
14.5~19.2%
Calcite
26.8~31.4%
Feldspar
1.2~2.6%
Pyrite
1.1~3.1%
Siderite
0.2~0.4%
Dolomite
11.6~30.2%
Total
100%
137 138
Table 2 Rock mechanical properties of shale sample Bedding inclination (°)
Rock density (g/cm3)
Young’s modulus (GPa)
Poisson ratio (1)
UCS (MPa)
36.04
0.145
189.65
30.74
0.153
107.96
60
36.54
0.131
79.66
90
42.15
0.231
142.25
0 30 2.53~2.59
8
139 140
2.3 Experimental design and procedures
141
A series of linear rock cutting tests were conducted on the cubic shale blocks. The variable parameter of
142
the experiment was bedding inclination. Except that, other cutting parameters including the cutting
143
depth, cutting speed, and rake angle were controlled as constant. Before each test, the PDC cutter was
144
first moved vertically to set a prescribing cutting depth at the edge of the specimen. Then the rock was
145
fed toward the cutter along horizontal direction at a given cutting speed. For each test, the horizontal
146
force and acceleration on the cutter holder, regarding as horizontal cutting force, were recorded through
147
a uniaxial strain gauge and accelerator with a sampling rate of 100 Hz. A high-speed camera captured
148
the chip formation process in the sample rate of 1000 frame per second. After test, the rock debris were
149
collected by brush clean and the sieve analysis was carried out to obtain five groups of size: 0/10mesh,
150
10/20mesh, 20/40mesh, 40/80mesh, and 80/
151
obtained to indicate the debris size distribution. The scratch profiles were finally imaged by 3D Laser
152
profile instrument and electrical microscope. In order to ensure the experimental repeatability, there are
153
three repeated tests in this study.
154
2.4 Force signal processing
155
Since the force and accelerator sensors were mounted on the cutter holder and kept stationary, there was
156
no signal while the stage moves without cutting. When the stage started to move at a constant cutting
157
speed, the PDC cutter will apply a cutting force on the shale sample. Meanwhile, system vibration and
158
discontinuously crushing and chipping process also led to dynamic acceleration change of the cutter.
159
The undesired noise originated from the system vibration usually belongs to a low frequency signal.
160
Hence, the low pass filter was used to ensure the noise-free force responses. The dynamic force
mesh. The weight percentage of each group was finally
9
161
responses that expose a strong oscillation with respect to time indeed reflect sufficient information on
162
the rock removal behaviors, such as crushing and chipping phenomenon. Unfortunately, the dynamic
163
force responses are difficult to be characterized in a simple way. Previous researchers proposed the use
164
of average force within a certain cutting distance or period of time and then study the change of the
165
average forces with respect to various process parameters. In this study, both average cutting force and
166
frequency analysis were used to identify the influences of bedding plane on rock removal mechanisms.
167
3. Results
168
3.1 Influence of shale bedding on cutting force responses
169
Force responses, as important indicator of the rock cutting processes, are capable of revealing the
170
intrinsic mechanisms of rock cutting in a quantitative way. As shown in Figure 4, continuous force data
171
indicates a fairly periodic fluctuation in a certain amplitude and frequency. The force response can be
172
divided into two groups according to the amplitude and frequency of cutting force. Firstly, a relatively
173
big amplitude but low frequency force was observed from the specimens with bedding inclinations of
174
0°, 30°, 120°, 150°. Secondly, a low amplitude but high frequency force is obvious for bedding
175
inclinations of 60°, 90°. Moreover, the macro and micro cracks were observed from the bottom and
176
edge of scratch profiles. Discontinuously crushing and chipping occurs at shale rock cutting inferred
177
from the fluctuation of cutting force and rough scratch surfaces.
10
178 179
Figure 4. Responses of horizontal cutting force of single PDC cutter on shale bedding
180 181
As shown in Figure 5, a strong correlation can be observed between the time-averaged force
182
responses and bedding inclination. It behaves a parabolic curve in which the cutting force achieves
183
maximum value of 3.15 KN at 90-degree orientation. Furthermore, the maximum force value at 90
184
degree is more than twice value of the minimum force at 0 degree. It is interested that the cutting force
185
at 120-degree orientation is only less than 60% cutting force at 60-degree orientation, though those two
186
orientations are angle complementarity. However, there exists little difference between the cutting
187
forces at 150-degree and 30-degree.
11
188 189
Figure 5 Average horizontal cutting force versus bedding angle
190 191
Figure 6 shows the time-dependent acceleration of PDC cutter when cutting through parallel or
192
perpendicular to the shale beddings and their probability density distributions. A phenomenon was
193
observed that the amount of strong acceleration while cutting perpendicular to the bedding plane was
194
almost twice of that while cutting parallel to the bedding plane. It can be inferred that the vibration
195
response of PDC cutter is highly related to the bedding inclination.
196 197
Figure 6 Response of accelerate of single PDC cutter on parallel and vertical bedding
198
12
199
3.2 Chip formation phenomena
200
Chip formation is a process of rock debris creating controlled by the rock removal mechanisms. As
201
shown in Figure 7, the chip formation process was observed when cutting perpendicular to the bedding
202
plane. The powder cuttings are initially created in the front of PDC cutter and following several
203
chunk-like cuttings ejected from shale matrix subsequently, which corresponds to the crushing and
204
chipping phenomena, respectively.
205 206
Figure 7 Chip formation process of single PDC cutter at the laminated shale, the parallel lines
207
denote the bedding inclination.
208 209
Chip formation photography of different bedding inclinations were compared as illustrated in Figure 8.
210
Both the crack propagation and the final shape of chips dramatically change with the bedding
211
inclination. For instance, the wedge-plate cuttings were present while cutting parallel to the bedding
212
plane, but the slim-rod cuttings appeared in perpendicular cutting.
13
213 214
Figure 8 Chipping phenomenon for different bedding inclinations, the parallel lines denote the
215
bedding inclination
216 217
The cutting size distributions and their photography at different bedding inclinations were plotted
218
in Figure 9. It can be seen that the weight percentages of the fine debris (more than 20 mesh) perform a
219
good agreement with the cutting force response to the bedding inclination. If cutting perpendicular to
220
the bedding plane, more fine debris and less chunk-like debris will be formed when compared with
221
other orientations. However, the amount of chunk-like debris would be increasing when the cutting
222
direction is parallel to the bedding plane.
223 14
224
Figure 9 (a) Cutting size distribution and (b) photography for different bedding inclinations
225 226
The topography of debris was reconstructed by 3D confocal microscope as shown in Figure 10.
227
The topography changes from wedge plate to slim rod with the increasing bedding inclination.
228
Moreover, the obvious shear planes can be found due to the results of shear failure from weak bedding
229
planes. In other words, the weak bedding planes change the trajectory of shearing cracking.
230 231
Figure 10 Photography and 3D laser profiles of cuttings for three typical bedding inclinations
232 233
4 Discussion
234
4.1 Bedding planes control chip formation behaviors
235
Our results confirm that the bedding plane performs a profound influence on chip formation in the shale
236
cutting process with a PDC cutter. There coexists powder and chunk-like cuttings from chip formation
237
process. Moreover, the occurrence of periodic fluctuation of cutting force causes from two reasons: the
238
increase of cutting force as the chip-boundary crack propagates through the rock ahead of the cutter,
239
and then decrease as the chip detaches and the cutter moves into the vacant space. Such observations
240
support that the crushing and chipping should be two primary rock removal mechanisms of laminated
241
shale. Particularly, the bedding inclination determines the domination of crushing and chipping in the
242
rock removal. More chunk-like cuttings produced indicates that the chipping dominates rock removal
15
243
when cutting parallel to the bedding plane. More powder cuttings created demonstrates the chipping
244
dominates rock removal when cutting perpendicular to bedding plane. The cutting force responses
245
consist of these two processes; the crushing-dominated removal which consumes more cutting force
246
while the chipping-dominated removal which consumes less. For practical drilling, it can be inferred
247
that the efficiency of parallel drilling to the bedding plane is lower than that of perpendicular drilling.
248
4.2 Mechanical influence of shale bedding on rock removal
249
The variations of average cutting force originate from the mechanical influence of shale bedding. As
250
illustrated in Figure 11, a conceptual model of PDC cutting on the laminated shale was proposed to
251
demonstrate the force loading on the bedding planes. With a decrease of bedding inclination, an
252
increase of shear force and decrease of normal force promotes shear crack generation, which is induced
253
from weak bedding planes. Consequently, more chunk-like cuttings would be produced at low bedding
254
inclination. However, with an increase of bedding inclination, it becomes harder for shear cracks to
255
initiate because of the increase of normal stress on the bedding plane. In this situation, the PDC cutter
256
should overcome the shear strength of rock matrix. Such mechanical analysis explains the cutting force
257
perpendicular to the bedding plane is almost twice of that while parallel cutting.
258
259 260
Figure 11 Conceptual model of PDC cutting on bedding shale with the rake angle of PDC cutter, α
261
and bedding inclination, θ. Horizontal cutting force can be decomposed into normal force and 16
262
shear force aligning with bedding plane.
263 264
5 Conclusions
265
Influences of bedding planes on rock removal behaviors were emphasized through a series of single
266
cutter experiments. A wide range of bedding inclinations from 0° to 150° were taken account. It can be
267
concluded that the bedding planes control the chip formation process of PDC cutter. The bedding plane
268
attributes to the variation of cutting force response, cutting size distribution, and even rock removal
269
mechanisms. Our observations support that the crushing and chipping are still two primary rock
270
removal mechanisms of laminated shale. The bedding inclination regulates which mechanism
271
dominates the rock removal behaviors. Finally, a mechanical model of PDC cutting which takes the
272
bedding planes into consideration was proposed to clarify the impacts of bedding planes on rock
273
fragmentation.
274
Acknowledgements
275
This work was financially supported by the National Natural Science Foundation of China (Grant
276
No.U1562212) and the PetroChina Innovation Foundation (Grant No. 2018D-5007-0308).
277 278
References
279
Che, D. and K. Ehmann (2014). "Experimental study of force responses in polycrystalline diamond face turning of
280
rock." International Journal of Rock Mechanics and Mining Sciences 72: 80-91.
281
Che, D., W. Zhang and K. Ehmann (2017). "Chip formation and force responses in linear rock cutting: An
282
experimental study." Journal of Manufacturing Science and Engineering 139(1): 011011.
283
Che, D., W.-L. Zhu and K. F. Ehmann (2016). "Chipping and crushing mechanisms in orthogonal rock cutting."
284
International Journal of Mechanical Sciences 119: 224-236.
285
Cheatham, J. J. B. and W. H. Daniels (1979). "A Study of Factors Influencing the Drillability of Shales:
286
Single-Cutter Experiments With STRATAPAX(T) Drill Blanks." Journal of Energy Resources Technology 101(3): 17
287
189-195.
288
Chen, J., H. Lan, R. Macciotta, Y. Wu, Q. Li and X. Zhao (2018). "Anisotropy rather than transverse isotropy in
289
Longmaxi shale and the potential role of tectonic stress." Engineering Geology 247: 38-47.
290
Chenevert, M. E. and C. Gatlin (1965). "Mechanical anisotropies of laminated sedimentary rocks." Society of
291
petroleum engineers journal 5(01): 67-77.
292
Cheng, Z., M. Sheng, G. Li, Z. Huang, X. Wu, Z. Zhu and J. Yang (2018). "Imaging the formation process of
293
cuttings: Characteristics of cuttings and mechanical specific energy in single PDC cutter tests." Journal of Petroleum
294
Science and Engineering 171: 854-862.
295
Finger, J. T. (1984). PDC Bit Research at Sandia National Laboratories.
296
Gong, Q.-M., J. Zhao and Y.-Y. Jiao (2005). "Numerical modeling of the effects of joint orientation on rock
297
fragmentation by TBM cutters." Tunnelling and underground space technology 20(2): 183-191.
298
Hanna, C., C. H. S. Douglas, H. Asr, B. Durairajan, M. Gerlero, L. Mueller, B. Pendse and C. Travers (2011).
299
Application Specific Steel Body PDC Bit Technology Reduces Drilling Costs in Unconventional North America
300
Shale Plays. SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA, Society of Petroleum
301
Engineers.
302
Heng, S., Y. Guo, C. Yang, J. J. Daemen and Z. Li (2015). "Experimental and theoretical study of the anisotropic
303
properties of shale." International Journal of Rock Mechanics and Mining Sciences 74: 58-68.
304
Huang, H., E. Detournay and B. Bellier (1999). "Discrete element modelling of rock cutting." Rock Mechanics for
305
Industry 1(1): 123-130.
306
Jaime, M. C., Y. Zhou, J.-S. Lin and I. K. Gamwo (2015). "Finite element modeling of rock cutting and its
307
fragmentation process." International Journal of Rock Mechanics and Mining Sciences 80: 137-146.
308
Labiouse, V. and T. Vietor (2014). "Laboratory and in situ simulation tests of the excavation damaged zone around
309
galleries in Opalinus Clay." Rock Mechanics and Rock Engineering 47(1): 57-70.
310
Lin, C., J. He, X. Li, X. Wan and B. Zheng (2017). "An experimental investigation into the effects of the anisotropy
311
of shale on hydraulic fracture propagation." Rock mechanics and rock engineering 50(3): 543-554.
312
Liu, X., M. Xu and P. Qin (2019). "Joints and confining stress influencing on rock fragmentation with double disc
313
cutters in the mixed ground." Tunnelling and Underground Space Technology 83: 461-474.
314
McLamore, R. and K. Gray (1967). "The mechanical behavior of anisotropic sedimentary rocks." Journal of
315
Engineering for Industry 89(1): 62-73.
316
Meier, T., E. Rybacki, T. Backers and G. Dresen (2015). "Influence of bedding angle on borehole stability: a 18
317
laboratory investigation of transverse isotropic oil shale." Rock Mechanics and Rock Engineering 48(4):
318
1535-1546.
319
Mishnaevsky, L. L. (1995). "Physical mechanisms of hard rock fragmentation under mechanical loading: A review."
320
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 32(8): 763-766.
321
Niandou, H., J. Shao, J. Henry and D. Fourmaintraux (1997). "Laboratory investigation of the mechanical behaviour
322
of Tournemire shale." International Journal of Rock Mechanics and Mining Sciences 34(1): 3-16.
323
Ozcelik, Y. and E. Yilmazkaya (2011). "The effect of the rock anisotropy on the efficiency of diamond wire cutting
324
machines." International Journal of Rock Mechanics and Mining Sciences 48(4): 626-636.
325
Rojek, J., E. Onate, C. Labra and H. Kargl (2011). "Discrete element simulation of rock cutting." International
326
Journal of Rock Mechanics and Mining Sciences 48(6): 996-1010.
327
Rostamsowlat, I., T. Richard and B. Evans (2018). "An experimental study of the effect of back rake angle in rock
328
cutting." International Journal of Rock Mechanics and Mining Sciences 107: 224-232.
329
Soeder, D. J. (2018). "The successful development of gas and oil resources from shales in North America." Journal
330
of Petroleum Science and Engineering 163: 399-420.
331
Tang, J., K. Wu, B. Zeng, H. Huang, X. Hu, X. Guo and L. Zuo (2018). "Investigate effects of weak bedding
332
interfaces on fracture geometry in unconventional reservoirs." Journal of Petroleum Science and Engineering 165:
333
992-1009.
334
Tien, Y. M., M. C. Kuo and C. H. Juang (2006). "An experimental investigation of the failure mechanism of
335
simulated transversely isotropic rocks." International Journal of Rock Mechanics and Mining Sciences 43(8):
336
1163-1181.
337
Yahiaoui, M., J. Y. Paris, K. Delbé, J. Denape, L. Gerbaud and A. Dourfaye (2016). "Independent analyses of cutting
338
and friction forces applied on a single polycrystalline diamond compact cutter." International Journal of Rock
339
Mechanics and Mining Sciences 85: 20-26.
340
Yushi, Z., M. Xinfang, Z. Shicheng, Z. Tong and L. Han (2016). "Numerical investigation into the influence of
341
bedding plane on hydraulic fracture network propagation in shale formations." Rock mechanics and rock
342
engineering 49(9): 3597-3614.
343
Zhai, G.-y., Y.-f. Wang, Z. Zhou, S.-f. Yu, X.-l. Chen and Y.-x. Zhang (2018). "Exploration and research progress of
344
shale gas in China." China Geology 1(2): 257-272.
345
19
S0920-4105(19)31061-7
DOI:
https://doi.org/10.1016/j.petrol.2019.106640
Reference:
PETROL 106640
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 12 June 2019 Revised Date:
19 September 2019
Accepted Date: 31 October 2019
Please cite this article as: Sheng, M., Cheng, Z., Gao, S., Shi, H., Zhang, Y., Shale bedding planes control rock removal behaviors of PDC cutter: Single cutter experiment, Journal of Petroleum Science and Engineering (2019), doi: https://doi.org/10.1016/j.petrol.2019.106640. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1
Shale bedding planes control rock removal behaviors of PDC cutter: single
2
cutter experiment
3
Mao Shenga,b*, Zhen Chenga,b, Shuyang Gaoc, Huaizhong Shia,b, Yanlong Zhangd
4 5
a. State Key Laboratory of Petroleum Resources and Prospecting, (China University of Petroleum-Beijing), Beijing 102249, P.R. China
6
b. College of Petroleum Engineering, China University of Petroleum-Beijing, 102249, P.R. China
7
c. Sinopec Research Institute of Petroleum Engineering, Beijing, 10010, P.R. China
8
d. CNPC Engineering Technology R&D Company Limited, Beijing, 102200, China
9 10
* Correspondence to: Mao Sheng, E-mail: [email protected]
11 12 13
The highlight of this work can be presented as:
14
1) A parabolic correlation was observed between cutting force and bedding inclination.
15
2) Shear cracking along the weak bedding planes promotes chipping.
16
3) Bedding inclination controls the rock removal behaviors from crushing-dominate to
17
chipping-dominate.
18
1
19
Abstract
20
Shale bedding planes arise with the complexity of rock removal by the PDC cutters. A series of single
21
cutter experiments were conducted to understand the effects of bedding planes of shale on chip
22
formation behaviors. Six bedding inclinations were taken into account by recording the variation of
23
cutting force, cutting size, topography of debris, and high-speed images. Results demonstrate that the
24
average cutting force highly correlates with bedding inclination where a parabolic relation is observed.
25
The maximum value of cutting force is presented while perpendicular cutting to the bedding plane.
26
Crushing and chipping are approved to be two mechanisms of rock removal of the laminated shale.
27
Particularly, the bedding plane controls the chip formation behaviors. While the cutting force is
28
perpendicular to shale bedding, the crushing dominates the rock removal process in which more powder
29
debris are created. While the cutting force is parallel to shale bedding, the chipping dominates the rock
30
removal and more chunk-like cuttings are generated. Shear cracking along the weak bedding planes
31
promotes chipping that is controlled by the bedding inclination. In summary, the bedding plane
32
attributes to the variation of cutting force response, cutting size distribution, and even rock removal
33
mechanisms.
34 35
Keywords: shale, PDC, bedding plane, rock failure, chip formation
36
2
37
1 Introduction
38
Efficient drilling of Polycrystalline Diamond Compact (PDC) bit in shale formation recently attracts
39
much more attention since it is widely applicable in horizontal well drilling (Hanna, Douglas et al. 2011,
40
Soeder 2018, Zhai, Wang et al. 2018). Bedding plane is one nature of shale formation where the weak
41
strength and anisotropy mechanical properties fully exist. Figure 1 illustrates the contact relation of
42
PDC cutters and bedding planes with a contact angle. The contact angle would result in a more
43
complex shale drilling process. In order to offer basic guidelines for PDC cutter design and efficiency
44
improvement, influences of bedding planes on cutting force response and drilling efficiency should be
45
well recognized.
46 47
Fig. 1 Diagram of PDC bit drilling in bedding shale formation
48
Crushing and chipping are two widely accepted mechanisms of rock removal of the fixed cutters.
49
The crushing mode creates highly fractured and inelastically deformed rock, while major cracks initiate
50
and propagate to form big chips in chipping mode (Mishnaevsky 1995). However, the crushing and
51
chipping of rock is an extremely complex failure and cracking process that is controlled by two aspects:
52
rock properties and cutting situation. Cheatham and Daniels (Cheatham and Daniels 1979) investigated
53
the bit balling problems of clay shale drilling through single cutter experiments at atmospheric and
54
hydrostatic pressure conditions. They found that, the ductile and sticky nature of the clay shale were 3
55
two major contributors to the problems that the chip formation was similar to that of ductile metals
56
cutting. However, the cuttings generated under hydrostatic pressure were observed to be almost
57
identical to those achieved by cutting lead at atmospheric pressure. Finger (Finger 1984) developed a
58
linear cutting testbed and conducted a systematical rock cutting experiment on Berea sandstone and
59
Westerly granite. The large chips and a crushed powdery zone were identified by fluorescent dye. The
60
observations from experimental works were validated by Finite element and Discrete element
61
simulation (Huang, Detournay et al. 1999, Rojek, Onate et al. 2011, Jaime, Zhou et al. 2015). The
62
crushing failure and shear cracking mechanics were clarified through numerical analysis. Recently, Che
63
et al. (Che, Zhang et al. 2017) (Che and Ehmann 2014) proposed a comprehensive experimental scheme
64
to measure the force response and visualize chip formation process on Indiana limestone, Austin chalk,
65
and Berea sandstone. The chipping mode was found to highly correlate with the depth of cut, the rake
66
angle, and the rock types. Furthermore, they proposed a new cutting model by accounting for the
67
crushing zone and crack propagation behaviors from the observations of linear rock cutting (Che, Zhu
68
et al. 2016). The alternate sudden movements during chip formation was captured by high-speed
69
imaging and the crushing mode was found to occupy most of the time of an entire crushing and
70
chipping cycle (Cheng, Sheng et al. 2018). Moreover, the rake angle of the PDC cutter dramatically
71
affects the removal behaviors of crushed material where different cutting faces corresponds to specific
72
frictional angle and shear force on the rock failure plane. (Yahiaoui, Paris et al. 2016, Rostamsowlat,
73
Richard et al. 2018) Although the rock removal mechanisms have been illuminated so far from
74
numerical simulation and visualization experiments, yet most of studied rocks are relatively isotropic
75
and homogenous. The impacts of rock anisotropy, particularly weak bedding planes, are still required to
76
be recognized.
4
77
Many investigations attributed the anisotropy of rock mechanics and special failure behaviors to the
78
bedding planes of shale (Chenevert and Gatlin 1965, McLamore and Gray 1967, Niandou, Shao et al.
79
1997, Heng, Guo et al. 2015, Chen, Lan et al. 2018). The orientations of bedding planes determined the
80
failure mode since the weak strength is along the bedding planes. Moreover, the bedding plane slip was
81
identified to present a significant effect on borehole and casing stability. Special breakout patterns of the
82
laminated shale failure were found to be different from that of the isotropic formation and were
83
controlled by bedding inclination and in-situ stress conditions (Tien, Kuo et al. 2006, Labiouse and
84
Vietor 2014, Meier, Rybacki et al. 2015). Additionally, hydraulic fracture propagation was also
85
confirmed to be affected by bedding planes which promote the complexity of fracture network (Yushi,
86
Xinfang et al. 2016, Lin, He et al. 2017, Tang, Wu et al. 2018). In aspects of rock cutting, Ozcelik and
87
Yilmazkaya (Ozcelik and Yilmazkaya 2011) found the rock anisotropy, particularly the bedding
88
inclination to the cutting direction, was naturally sensitive to the cutting efficiency and force response
89
of diamond wire cutting. Gong and Liu (Gong, Zhao et al. 2005) (Liu, Xu et al. 2019) proposed a 2D
90
TBM cutting model to illustrate the joint orientation. They found the joint orientation could influence
91
the crack initiation and propagation as well as the fragmentation pattern. Though tremendous studies
92
demonstrate the importance of bedding planes on rock failure, wellbore stability, and hydraulic fracture
93
propagation, yet most of those studies did not discuss the effects of bedding plane on rock removal
94
mechanisms of PDC cutters, particularly for the cutting force response, chip formation process, and
95
complicated mechanisms.
96
In this paper, a series of single cutter experiments on laminated shale was conducted by considering
97
a wide range of bedding inclinations from 0° to 150°. The dynamic responses of cutting force, cutter
98
acceleration, and debris size distribution were obtained at different bedding inclinations. Extraordinary
5
99
crushing and chipping patterns were captured by high-speed imaging technique. Based on the observed
100
phenomena, a conceptual cutting model of laminated shale formation was proposed and further
101
mechanisms were discussed.
102
2 Materials and method
103
2.1 Linear rock cutting testbed
104
A linear rock cutting testbed was built based on a mechanical shaping machine as illustrated in Figure 2.
105
The testbed could precisely control the cutting speed (100~1200mm/min) and cutting depth (accuracy
106
of 0.01 mm). A cutter holder was particularly designed to fix single PDC cutter. The rake angle of cutter
107
was capable to adjust into five levels of negative 15, 20, 25, 30, 35, 40 degrees. A planar PDC cutter
108
with diameter of 13 mm and thickness of 25 mm, as a typical PDC bit cutter, was selected for this study.
109
The rock block was fixed by a specific holder to limit X and Y direction movement. In order to achieve
110
a linear cutting, the rock block was fed toward the cutter in x-direction while the cutter was kept
111
stationary.
112
Most importantly, the testbed was well equipped with a force measuring system, including a
113
single-component strain gauge (KYOWA KFWB-5-120-C1), which is close to the PDC cutter, a
114
unidirectional accelerator fixed at the cutter holder, and a data acquisition unit with a maximum
115
sampling rate of 100 Hz. Besides, a high-speed camera (Phantom V310) was used to visualize the chip
116
formation. The maximum resolution and recording speed of this high-speed camera are 1280 × 1024
117
and 50,000 fps.
6
118
Figure 2 Schematic diagram of (a) linear cutting testbed, (b)single PDC cutter scratching on shale block, and (c) Conceptual model of single PDC cutting on bedding shale 119
2.2 Rock specimen preparation
120
Organic-rich shale is our target material where these samples were collected from the outcrop of Lower
121
Silurian Longmaxi formation, which is located at south Sichuan basin in Changning, China. The
122
bedding plane is well rich in the Longmaxi Shale as shown in Figure 3. Mineralogical composition was
123
obtained from X-ray diffraction as listed in Table 1 and it can be seen that over 60% minerals belong to
124
brittle minerals. Particularly, the clay minerals mainly consist of illite without serious hydration
125
swelling problems. The mechanical properties were particularly measured in different bedding
126
inclinations, according to ISRM standard.
127
The specimens were cored from the same block and reshaped into the cubic blocks with side length of
128
200 mm by using a diamond-saw cutting machine. Fine polish was carried out to ensure the parallelism
129
of opposite surfaces of specimen was less than 100 µm. The sample can be reused after milling and
130
polishing cutting surface again. In total, six cubic blocks were prepared with six bedding inclinations of
131
0o, 30o, 60o, 90o, 120o, and 150o (Figure 3). The specimen was required to be dried in an oven at 100
132
for 48 hours before testing in order to remove the fluid influence.
7
133 134
Figure 3 Photographs of six cubic blocks with the bedding inclinations of 0o, 30o, 60o, 90o, 120o,
135
and 150o
136
Table 1. Mineral components and content of shale sample Minerals
Weight content (wt.%)
Quartz
22.2~35.1%
Clay
14.5~19.2%
Calcite
26.8~31.4%
Feldspar
1.2~2.6%
Pyrite
1.1~3.1%
Siderite
0.2~0.4%
Dolomite
11.6~30.2%
Total
100%
137 138
Table 2 Rock mechanical properties of shale sample Bedding inclination (°)
Rock density (g/cm3)
Young’s modulus (GPa)
Poisson ratio (1)
UCS (MPa)
36.04
0.145
189.65
30.74
0.153
107.96
60
36.54
0.131
79.66
90
42.15
0.231
142.25
0 30 2.53~2.59
8
139 140
2.3 Experimental design and procedures
141
A series of linear rock cutting tests were conducted on the cubic shale blocks. The variable parameter of
142
the experiment was bedding inclination. Except that, other cutting parameters including the cutting
143
depth, cutting speed, and rake angle were controlled as constant. Before each test, the PDC cutter was
144
first moved vertically to set a prescribing cutting depth at the edge of the specimen. Then the rock was
145
fed toward the cutter along horizontal direction at a given cutting speed. For each test, the horizontal
146
force and acceleration on the cutter holder, regarding as horizontal cutting force, were recorded through
147
a uniaxial strain gauge and accelerator with a sampling rate of 100 Hz. A high-speed camera captured
148
the chip formation process in the sample rate of 1000 frame per second. After test, the rock debris were
149
collected by brush clean and the sieve analysis was carried out to obtain five groups of size: 0/10mesh,
150
10/20mesh, 20/40mesh, 40/80mesh, and 80/
151
obtained to indicate the debris size distribution. The scratch profiles were finally imaged by 3D Laser
152
profile instrument and electrical microscope. In order to ensure the experimental repeatability, there are
153
three repeated tests in this study.
154
2.4 Force signal processing
155
Since the force and accelerator sensors were mounted on the cutter holder and kept stationary, there was
156
no signal while the stage moves without cutting. When the stage started to move at a constant cutting
157
speed, the PDC cutter will apply a cutting force on the shale sample. Meanwhile, system vibration and
158
discontinuously crushing and chipping process also led to dynamic acceleration change of the cutter.
159
The undesired noise originated from the system vibration usually belongs to a low frequency signal.
160
Hence, the low pass filter was used to ensure the noise-free force responses. The dynamic force
mesh. The weight percentage of each group was finally
9
161
responses that expose a strong oscillation with respect to time indeed reflect sufficient information on
162
the rock removal behaviors, such as crushing and chipping phenomenon. Unfortunately, the dynamic
163
force responses are difficult to be characterized in a simple way. Previous researchers proposed the use
164
of average force within a certain cutting distance or period of time and then study the change of the
165
average forces with respect to various process parameters. In this study, both average cutting force and
166
frequency analysis were used to identify the influences of bedding plane on rock removal mechanisms.
167
3. Results
168
3.1 Influence of shale bedding on cutting force responses
169
Force responses, as important indicator of the rock cutting processes, are capable of revealing the
170
intrinsic mechanisms of rock cutting in a quantitative way. As shown in Figure 4, continuous force data
171
indicates a fairly periodic fluctuation in a certain amplitude and frequency. The force response can be
172
divided into two groups according to the amplitude and frequency of cutting force. Firstly, a relatively
173
big amplitude but low frequency force was observed from the specimens with bedding inclinations of
174
0°, 30°, 120°, 150°. Secondly, a low amplitude but high frequency force is obvious for bedding
175
inclinations of 60°, 90°. Moreover, the macro and micro cracks were observed from the bottom and
176
edge of scratch profiles. Discontinuously crushing and chipping occurs at shale rock cutting inferred
177
from the fluctuation of cutting force and rough scratch surfaces.
10
178 179
Figure 4. Responses of horizontal cutting force of single PDC cutter on shale bedding
180 181
As shown in Figure 5, a strong correlation can be observed between the time-averaged force
182
responses and bedding inclination. It behaves a parabolic curve in which the cutting force achieves
183
maximum value of 3.15 KN at 90-degree orientation. Furthermore, the maximum force value at 90
184
degree is more than twice value of the minimum force at 0 degree. It is interested that the cutting force
185
at 120-degree orientation is only less than 60% cutting force at 60-degree orientation, though those two
186
orientations are angle complementarity. However, there exists little difference between the cutting
187
forces at 150-degree and 30-degree.
11
188 189
Figure 5 Average horizontal cutting force versus bedding angle
190 191
Figure 6 shows the time-dependent acceleration of PDC cutter when cutting through parallel or
192
perpendicular to the shale beddings and their probability density distributions. A phenomenon was
193
observed that the amount of strong acceleration while cutting perpendicular to the bedding plane was
194
almost twice of that while cutting parallel to the bedding plane. It can be inferred that the vibration
195
response of PDC cutter is highly related to the bedding inclination.
196 197
Figure 6 Response of accelerate of single PDC cutter on parallel and vertical bedding
198
12
199
3.2 Chip formation phenomena
200
Chip formation is a process of rock debris creating controlled by the rock removal mechanisms. As
201
shown in Figure 7, the chip formation process was observed when cutting perpendicular to the bedding
202
plane. The powder cuttings are initially created in the front of PDC cutter and following several
203
chunk-like cuttings ejected from shale matrix subsequently, which corresponds to the crushing and
204
chipping phenomena, respectively.
205 206
Figure 7 Chip formation process of single PDC cutter at the laminated shale, the parallel lines
207
denote the bedding inclination.
208 209
Chip formation photography of different bedding inclinations were compared as illustrated in Figure 8.
210
Both the crack propagation and the final shape of chips dramatically change with the bedding
211
inclination. For instance, the wedge-plate cuttings were present while cutting parallel to the bedding
212
plane, but the slim-rod cuttings appeared in perpendicular cutting.
13
213 214
Figure 8 Chipping phenomenon for different bedding inclinations, the parallel lines denote the
215
bedding inclination
216 217
The cutting size distributions and their photography at different bedding inclinations were plotted
218
in Figure 9. It can be seen that the weight percentages of the fine debris (more than 20 mesh) perform a
219
good agreement with the cutting force response to the bedding inclination. If cutting perpendicular to
220
the bedding plane, more fine debris and less chunk-like debris will be formed when compared with
221
other orientations. However, the amount of chunk-like debris would be increasing when the cutting
222
direction is parallel to the bedding plane.
223 14
224
Figure 9 (a) Cutting size distribution and (b) photography for different bedding inclinations
225 226
The topography of debris was reconstructed by 3D confocal microscope as shown in Figure 10.
227
The topography changes from wedge plate to slim rod with the increasing bedding inclination.
228
Moreover, the obvious shear planes can be found due to the results of shear failure from weak bedding
229
planes. In other words, the weak bedding planes change the trajectory of shearing cracking.
230 231
Figure 10 Photography and 3D laser profiles of cuttings for three typical bedding inclinations
232 233
4 Discussion
234
4.1 Bedding planes control chip formation behaviors
235
Our results confirm that the bedding plane performs a profound influence on chip formation in the shale
236
cutting process with a PDC cutter. There coexists powder and chunk-like cuttings from chip formation
237
process. Moreover, the occurrence of periodic fluctuation of cutting force causes from two reasons: the
238
increase of cutting force as the chip-boundary crack propagates through the rock ahead of the cutter,
239
and then decrease as the chip detaches and the cutter moves into the vacant space. Such observations
240
support that the crushing and chipping should be two primary rock removal mechanisms of laminated
241
shale. Particularly, the bedding inclination determines the domination of crushing and chipping in the
242
rock removal. More chunk-like cuttings produced indicates that the chipping dominates rock removal
15
243
when cutting parallel to the bedding plane. More powder cuttings created demonstrates the chipping
244
dominates rock removal when cutting perpendicular to bedding plane. The cutting force responses
245
consist of these two processes; the crushing-dominated removal which consumes more cutting force
246
while the chipping-dominated removal which consumes less. For practical drilling, it can be inferred
247
that the efficiency of parallel drilling to the bedding plane is lower than that of perpendicular drilling.
248
4.2 Mechanical influence of shale bedding on rock removal
249
The variations of average cutting force originate from the mechanical influence of shale bedding. As
250
illustrated in Figure 11, a conceptual model of PDC cutting on the laminated shale was proposed to
251
demonstrate the force loading on the bedding planes. With a decrease of bedding inclination, an
252
increase of shear force and decrease of normal force promotes shear crack generation, which is induced
253
from weak bedding planes. Consequently, more chunk-like cuttings would be produced at low bedding
254
inclination. However, with an increase of bedding inclination, it becomes harder for shear cracks to
255
initiate because of the increase of normal stress on the bedding plane. In this situation, the PDC cutter
256
should overcome the shear strength of rock matrix. Such mechanical analysis explains the cutting force
257
perpendicular to the bedding plane is almost twice of that while parallel cutting.
258
259 260
Figure 11 Conceptual model of PDC cutting on bedding shale with the rake angle of PDC cutter, α
261
and bedding inclination, θ. Horizontal cutting force can be decomposed into normal force and 16
262
shear force aligning with bedding plane.
263 264
5 Conclusions
265
Influences of bedding planes on rock removal behaviors were emphasized through a series of single
266
cutter experiments. A wide range of bedding inclinations from 0° to 150° were taken account. It can be
267
concluded that the bedding planes control the chip formation process of PDC cutter. The bedding plane
268
attributes to the variation of cutting force response, cutting size distribution, and even rock removal
269
mechanisms. Our observations support that the crushing and chipping are still two primary rock
270
removal mechanisms of laminated shale. The bedding inclination regulates which mechanism
271
dominates the rock removal behaviors. Finally, a mechanical model of PDC cutting which takes the
272
bedding planes into consideration was proposed to clarify the impacts of bedding planes on rock
273
fragmentation.
274
Acknowledgements
275
This work was financially supported by the National Natural Science Foundation of China (Grant
276
No.U1562212) and the PetroChina Innovation Foundation (Grant No. 2018D-5007-0308).
277 278
References
279
Che, D. and K. Ehmann (2014). "Experimental study of force responses in polycrystalline diamond face turning of
280
rock." International Journal of Rock Mechanics and Mining Sciences 72: 80-91.
281
Che, D., W. Zhang and K. Ehmann (2017). "Chip formation and force responses in linear rock cutting: An
282
experimental study." Journal of Manufacturing Science and Engineering 139(1): 011011.
283
Che, D., W.-L. Zhu and K. F. Ehmann (2016). "Chipping and crushing mechanisms in orthogonal rock cutting."
284
International Journal of Mechanical Sciences 119: 224-236.
285
Cheatham, J. J. B. and W. H. Daniels (1979). "A Study of Factors Influencing the Drillability of Shales:
286
Single-Cutter Experiments With STRATAPAX(T) Drill Blanks." Journal of Energy Resources Technology 101(3): 17
287
189-195.
288
Chen, J., H. Lan, R. Macciotta, Y. Wu, Q. Li and X. Zhao (2018). "Anisotropy rather than transverse isotropy in
289
Longmaxi shale and the potential role of tectonic stress." Engineering Geology 247: 38-47.
290
Chenevert, M. E. and C. Gatlin (1965). "Mechanical anisotropies of laminated sedimentary rocks." Society of
291
petroleum engineers journal 5(01): 67-77.
292
Cheng, Z., M. Sheng, G. Li, Z. Huang, X. Wu, Z. Zhu and J. Yang (2018). "Imaging the formation process of
293
cuttings: Characteristics of cuttings and mechanical specific energy in single PDC cutter tests." Journal of Petroleum
294
Science and Engineering 171: 854-862.
295
Finger, J. T. (1984). PDC Bit Research at Sandia National Laboratories.
296
Gong, Q.-M., J. Zhao and Y.-Y. Jiao (2005). "Numerical modeling of the effects of joint orientation on rock
297
fragmentation by TBM cutters." Tunnelling and underground space technology 20(2): 183-191.
298
Hanna, C., C. H. S. Douglas, H. Asr, B. Durairajan, M. Gerlero, L. Mueller, B. Pendse and C. Travers (2011).
299
Application Specific Steel Body PDC Bit Technology Reduces Drilling Costs in Unconventional North America
300
Shale Plays. SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA, Society of Petroleum
301
Engineers.
302
Heng, S., Y. Guo, C. Yang, J. J. Daemen and Z. Li (2015). "Experimental and theoretical study of the anisotropic
303
properties of shale." International Journal of Rock Mechanics and Mining Sciences 74: 58-68.
304
Huang, H., E. Detournay and B. Bellier (1999). "Discrete element modelling of rock cutting." Rock Mechanics for
305
Industry 1(1): 123-130.
306
Jaime, M. C., Y. Zhou, J.-S. Lin and I. K. Gamwo (2015). "Finite element modeling of rock cutting and its
307
fragmentation process." International Journal of Rock Mechanics and Mining Sciences 80: 137-146.
308
Labiouse, V. and T. Vietor (2014). "Laboratory and in situ simulation tests of the excavation damaged zone around
309
galleries in Opalinus Clay." Rock Mechanics and Rock Engineering 47(1): 57-70.
310
Lin, C., J. He, X. Li, X. Wan and B. Zheng (2017). "An experimental investigation into the effects of the anisotropy
311
of shale on hydraulic fracture propagation." Rock mechanics and rock engineering 50(3): 543-554.
312
Liu, X., M. Xu and P. Qin (2019). "Joints and confining stress influencing on rock fragmentation with double disc
313
cutters in the mixed ground." Tunnelling and Underground Space Technology 83: 461-474.
314
McLamore, R. and K. Gray (1967). "The mechanical behavior of anisotropic sedimentary rocks." Journal of
315
Engineering for Industry 89(1): 62-73.
316
Meier, T., E. Rybacki, T. Backers and G. Dresen (2015). "Influence of bedding angle on borehole stability: a 18
317
laboratory investigation of transverse isotropic oil shale." Rock Mechanics and Rock Engineering 48(4):
318
1535-1546.
319
Mishnaevsky, L. L. (1995). "Physical mechanisms of hard rock fragmentation under mechanical loading: A review."
320
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 32(8): 763-766.
321
Niandou, H., J. Shao, J. Henry and D. Fourmaintraux (1997). "Laboratory investigation of the mechanical behaviour
322
of Tournemire shale." International Journal of Rock Mechanics and Mining Sciences 34(1): 3-16.
323
Ozcelik, Y. and E. Yilmazkaya (2011). "The effect of the rock anisotropy on the efficiency of diamond wire cutting
324
machines." International Journal of Rock Mechanics and Mining Sciences 48(4): 626-636.
325
Rojek, J., E. Onate, C. Labra and H. Kargl (2011). "Discrete element simulation of rock cutting." International
326
Journal of Rock Mechanics and Mining Sciences 48(6): 996-1010.
327
Rostamsowlat, I., T. Richard and B. Evans (2018). "An experimental study of the effect of back rake angle in rock
328
cutting." International Journal of Rock Mechanics and Mining Sciences 107: 224-232.
329
Soeder, D. J. (2018). "The successful development of gas and oil resources from shales in North America." Journal
330
of Petroleum Science and Engineering 163: 399-420.
331
Tang, J., K. Wu, B. Zeng, H. Huang, X. Hu, X. Guo and L. Zuo (2018). "Investigate effects of weak bedding
332
interfaces on fracture geometry in unconventional reservoirs." Journal of Petroleum Science and Engineering 165:
333
992-1009.
334
Tien, Y. M., M. C. Kuo and C. H. Juang (2006). "An experimental investigation of the failure mechanism of
335
simulated transversely isotropic rocks." International Journal of Rock Mechanics and Mining Sciences 43(8):
336
1163-1181.
337
Yahiaoui, M., J. Y. Paris, K. Delbé, J. Denape, L. Gerbaud and A. Dourfaye (2016). "Independent analyses of cutting
338
and friction forces applied on a single polycrystalline diamond compact cutter." International Journal of Rock
339
Mechanics and Mining Sciences 85: 20-26.
340
Yushi, Z., M. Xinfang, Z. Shicheng, Z. Tong and L. Han (2016). "Numerical investigation into the influence of
341
bedding plane on hydraulic fracture network propagation in shale formations." Rock mechanics and rock
342
engineering 49(9): 3597-3614.
343
Zhai, G.-y., Y.-f. Wang, Z. Zhou, S.-f. Yu, X.-l. Chen and Y.-x. Zhang (2018). "Exploration and research progress of
344
shale gas in China." China Geology 1(2): 257-272.
345
19