Proceedings World Geothermal Congress 2020

Reykjavik, Iceland, April 26 – May 2, 2020

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Numerical Analyses of the Granite Fragmentation in Rotary-Percussive Drilling with the

Consideration of Pre-Existing Fracture

Zhaosheng Ji, Huaizhong Shi, Gensheng Li

School of Petroleum Engineering, China University of Petroleum(Beijing), Beijing 163318, China

jzs448@163.com

Keywords: Rotary-Percussive drilling, Geothermal drilling, Distinct element method, Pre-existing fractures

ABSTRACT

Rotary-Percussive drilling technique is an efficient rock breaking method and well-suited for geothermal drilling. Taking typical

granite as research object, the fragmentation mechanism of rock was investigated using the distinct element method with the

consideration of pre-existing fractures. The investigation begins by establishing a cutter-rock interaction model to simulate the rotary-

percussion drilling into the rock. In the model, discrete fracture network (DFN) was used to better reflect the complex behavior of

rock materials and its parameters, such as fracture size, distribution and intensity, are obtained by statistics and calculation of fractures

in outcrops. Bonded Block Model (BBM) was used to simulate the initiation of cracks that can coalesce and propagate to fracture the

rock. The macroscopic physical parameters of rocks and fractures were obtained through a series of trial calculations by continuously

adjusting the microscopic contact parameters. As a dynamic problem, the damping effect of the rock was introduced into our model

by fitting it to the laboratory tests. Finally, two cases were studied: 1. Rock fragmentation only under impact load; 2. Rock

fragmentation under the coupling of impact load and lateral movement. The results represented the fragmentation process of rock

under the cutter indentation and the coupling of impact load and lateral movement. Both typical fracture system under the indentation

of cutter and the skip-slip phenomenon are obtained. When the dip angle of cutter takes the value of 45 degrees and the impact

amplitude take the value of 280 kN, the specific energy gets the minimum value which shows a high rock breaking efficiency. With

the increase of dip angle of cutter, the intensity of skip-slip effect is increased, which is bad for drilling. The impact amplitude has

no effect on the skip-slip effect, but the particle size is higher when the impact amplitude is higher. The research done by this paper

is of great significance to guide the application of Rotary-Percussive drilling and to reduce the cost of the development of geothermal

resources.

1. INTRODUCTION

Geothermal energy has increased its value as a clean, secure, alternative energy source (Conforti and Giampietro, 1997; Liu et al.,

2011; Tester et al., 2007; York, 2012). Its development requires to drill a lot of wells deep into the target formations, which accounts

for 30% to 50% of the cost of the hydrothermal geothermal electricity project and more than half of the total cost of Enhanced

Geothermal Systems (EGS) (Glowka, 1997; Yost et al., 2015). It is necessary to develop an efficient drilling method to reduce the

time and cost (Miyazaki et al., 2019). Rotary-Percussive drilling (RPD) is such a dominating method making holes in hard rocks, and

is well-suited for geothermal drilling (Finger and Blankenship, 2010; Lundberg and Okrouhlik, 2006). It can provide economic

benefits by reducing drilling time and drilling cost by combing the rotary drilling and percussive drilling (Patil and Teodoriu, 2013;

Zhong, 2016). In this drilling method, impact load induced by impactor and upper string is imposed on the conventional rotary bit to

penetrate into and crush the rock (Chiang and Elias, 2008). A sound understanding of bit-rock interaction and rock fragmentation

mechanisms under the impact load and rotary movement is essential to design down-hole tools, such as drill bits and impactors, and

optimize the drilling parameters.

Numerical simulation is a key approach to study the rock fragmentation mechanism in RPD (Che et al., 2012a; Che et al., 2012b;

Gonze and Tshibangu, 2017). A cutting model using the distinct element method (DEM) was established by Akbari et al. (2011).

They observed the failure and post failure of rock under bit clearly and found that the impact loads applied to rotary bit in RPD has

a positive effect on the drilling performance. A fitting equation of ROP as a function of bottom-hole pressure showed that ROP drops

rapidly with the increases of bottom-hole pressure. Block and Jin ( 2009) presented two kinds of failure mode of rock, namely brittle

and ductile failure mode, and they also studied the relationship between these two modes with parameters, such as confined pressure

and down-hole pressure. Carabaos et al. (2014) used DEM to simulate single cutter experiments to study the effects of cutting depth,

cutter friction and geometry on drilling efficiency. Besides DEM, finite-difference methods (Bilgesu et al., 2008), finite element

method (Dong and Chen, 2018; Kuang et al., 2016) are also used to study rock damage characteristics. In these studies, drilling

performance of different rock properties and operation parameters are evaluated. However, no matter what kinds of numerical method

were used, they all considered rock as an intact medium which is not a realistic situation. Rocks encountered in engineering practice

are quite often discontinuous and full of weak planes, such as fissures, fractures, and faults.

This paper focused on bit-rock interaction and rock fragmentation in RPD with the consideration of pre-exciting fractures. A cutting

model is established using DEM. Distribution and identity parameters of pre-exciting fractures are obtained by statistics and

calculation of cracks in outcrops. The macroscopic parameters of intact rocks and fractures are obtained by continuously adjusting

the microscopic contact parameters of the model and conducting tests. Two cases are studied:1. Rock fragmentation under only

impact load; 2. Rock fragmentation under the coupling of impact load and rotary movement. Finally, penetration displacement,

fracture number, fragment volume, specific energy and particles size distribution are used to evaluate the effect of dip angle of cutter

and amplitude of impact load on the rock fragmentation.

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2. CUTTER-ROCK INTERACTION MODEL

2.1 Principle of interaction model

Typical RPD schematic is shown in Fig. 1a. The drill bit indents into the rock under the action of the impactor and then cutting the

fractured rock under the action of the rotation (Rostamsowlat et al., 2018; Saksala, 2016). Considering the large computational costs,

this study only takes out one PDC cutter for 2D analysis. The cutter is simplified as a small declining rectangle (Akbari et al., 2011),

and the rock formation under the action of the cutter is full of discrete fractures as shown in Fig. 1b. The lower end of the cutter forms

an acute dip angle α with the rock. The upper end of the rock formation has a free boundary and the left and the right end faces have

a roller boundary to restraints horizontal displacements. In order to eliminate the influence of the boundary, the lateral dimension of

the rock is taken to be ten times greater than the diameter of the cutter. The rotation is replaced by a lateral velocity V in the two-

dimensional analysis (Menezes et al., 2014) while the impact loads are simplified as dynamic sine-shape load )cos(1 tF pulsed to

static load level 0F (Liu et al., 2017).To better demonstrate the rock breaking mechanism of the RPD, this study has two cases: 1.

the fractured rock is fragmented under only impact loads; 2. the fractured rock is fragmented under the cooping action of impact load

and lateral movement. It should be noted that the effects of drilling fluid are neglect and the rock heterogeneity is not considered (Liu

et al., 2008).

Figure 1: (a) schematic of RPD; (b) the principle of bit-rock interaction model

2.2 Intact rock specimen generation

The fractured rock model consists two key components, intact rock and the discrete fracture network (DFN). The intact rock is

simulated by the bounded particle model (BPM) using commercial code PFC (Itasca Consulting Group, 2019), which has a rectangle

geometry with length L and height H. BPM uses a large number of separate particles bounded together to represent the intact rock

behavior. Flat-joint model is used as the contact model between two particles and the particle geometry parameters are shown in

Table 1. For two study cases, the only impact load has a deeper penetration and shorter transverse affected distance while coupling

action has the opposite situation. So, two sets geometry parameters are applied to these two study cases, respectively.

Table 1: Geometry parameters for intact rock

Parameter Length L of rock

(mm)

Height H of rock

(mm)

Particle radius

(mm)

Particle density

（kg/m3） Porosity

Values Case 1 300 Case 1 100

0.25-0.5 2500 0.1 Case 2 400 Case 2 60

2.3 DFN generation

DFN is used to represent the pre-exciting fractures in rock, behaviors are generated by using smooth-joint model in contacts lying on

the weak plane (Itasca Consulting Group, 2019). It is difficult to get the structures and characters of fractures in formations. So we

chose an outcrop to quantify the DFN parameters, such as fracture size, orientations and density. FracPaQ (Healy et al., 2017) is one

efficient tool to quantify fracture patterns from 2D images. The outcrop used are shown in Fig. 2a (Palmstrom, 2005) and mapped

traces of fractures is show in Fig. 2b. The results are shown in Fig. 3. Maximum likelihood estimators (MLE) analysis is used to

calculate the fitting power law, exponential and log-normal scaling distributions for the segment lengths. We find that the log-normal

distributions has the best fitting performance as shown in Fig. 3a. Considering self-similar and scale effect of rock fractures (Barton

and Zoback, 1992), the fracture lengths obtained from the outcrop is applied to the model after being multiplied by a size factor η:

ououHL

LH (1)

where ouL and ouH are the values of the length and the height of evaluated outcrop zone, respectively. In this study, their values are

2.15 and 2.55, respectively. Fig. 3b demonstrates the distribution of the fracture strike and we can find there are four sets of fractures

which have average strike angle of 0°，45°，90° and 135°. Intensity of fractures (P21) (Dershowitz and Herda, 1992) is

estimated in Fig. 3c and the final average intensity is calculated to be 13.39 m-1. This intensity is divided into four set of fractures

with different strike angle according to their share.

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Figure 1: (a)Outcrop zone and (b)mapped traces of DFN in outcrop

Figure 2: DFN parameters: (a) Maximum-likelihood-estimators analysis for segment lengths with applied upper and lower

cut-offs, of 5%; (b) An equal area rose diagram color-coded by segment strike; (c) map of estimated intensity of

segments (P21, m-1)

2.4 Parameter setup

Table 2: Microscopic parameters used in this model

Model microscopic

parameters Value

Model microscopic

parameters Value

Effective

modulus,emod(GPa) 142 Damping coefficient 0.8

Normal-to-shear stiffness

ratio,kratio 8.4 NF normal stiffness(GPa) 625

Tensile strength,fj_ten(MPa) 20 NF shear stiffness

(GPa) 310

Cohesion,fj_coh(MPa) 125 NF fraction coefficient 0.4

Friction angle,fj_fa(degrees) 12.0 NF cohesion

(MPa) 0

Friction coefficient ,fj_fric 0.1 NF friction angle 0

According to the working principle of PFC, the macroscopic parameters from the target rock cannot be used as a model input

parameter. Rather, it is necessary to constantly adjust the microscopic parameters to make the model conform to the macroscopic

deformation and strength law. And then, these microscopic parameters are applied to the simulation model. Based on the calibration

procedure as shown in Fig. 4 (Wang and Cai, 2019), a series of trial-and-error tests are conducted to setup the microphysical

parameters to match the granite specimen (Bauer et al., 2016; Ye and Ghassemi, 2018). Unconfined compressive strength tests are

conducted to match the Poisson’s ratio and Young’s modulus of target granite by adjusting effective modulus and normal-to-shear

stiffness ratio while direct tension tests are conducted to match the tension strength. Then triaxle compressive strength tests are

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conducted to match the strength parameters, such as the cohesion strength and friction angle. RPD is a transient dynamic process for

which damping is a very important character. So, we also conduct cyclic compressive tests to match the damping characteristic of

granite. The test results have a good agreement with the experimental results (Li et al., 2005). Table 2 list the target and model value

of macroscopic strength and deformable parameter of the granite. Table 3 list the final macroscopic parameters used in this model.

Table 3: Macroscopic parameters used in this model

Intact rock

Parameter Target value Model value Fracture Parameter Target value Model value

Young

modulus(GPa) 67 63.37

Normal

Stiffness(GPa/m) 500 501.528

Poisson’s ratio 0.32 0.32 Shear

Stiffness(Gpa/m) 100 96.5

Tensile

stresngth(MPa) 11 10.97

Fracture Friction

angel 20 20.49

Unconfined

compressive

strength(MPa)

150 150.896

Internal friction

angel(degrees) 46 44.516

Figure 4: Calibration procedures of microscopic parameters for contacts in model

3. INTENTION UNDER IMPACT LOAD

A cutter is pressed into a rock under the drilling pressure. This is the first step for a bit to break rock. (Chiaia, 2001; Cook et al., 1984;

Kou et al., 2004; Mishnaevsky, 1995; Swain and Lawn, 1976). For a brittle hard rock, four stages are observed in the fragmentation

process of this step. Those stages are stress field building up, formation of crushed zone, surface chipping, and formation of subsurface

cracks. On the other hand, there are only three stages for plastic hard rock (Mishnaevsky, 1995). Under the cutter, the damage of

brittle rock can be roughly divided into two parts: crushing zone and crack system. Crack system consists of radial cracks and side

cracks. The side cracks initiate from the crush zone and propagate to the surface to form chips. Radial cracks propagate deep beneath

the indenter to weaken the rock strength. The general fragmentation picture of the rock is summarized in Fig. 5.

The simulation results show a good agreement with the studies by Paul and Gangal (1969) and a typical crack system of generate as

shown in Fig. 6. It can be easily seen that initial radial cracks are exceptionally developed because of the pre-existing fractuses nearby.

Significant differences caused by pre-exciting fractures are also shown in Table 4. In this table, parameters of drilling, such as

penetration displacement of cutter, fracgture number and fragment volume of rock, and rocks with and without pre-existing fractures

are presented. All of penetration displacement, fracture number and fragment volume by drilling into rock with pre-existing fracture

show a great increase than that of drilling into rock without pre-existing fractur. The increase percentages are 7.32%,20.27% and

14.83%,respectialy. There is also a certain reduction in specific energy, which refers to the energy required to break a unit rock, and

is often used to evaluate the efficiency of rock breaking (Akbari and Miska, 2017):

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frag

t

iytiytiyt

speV

FDD

E

01)(

(2)

where iytD and

iytF are the displacement of cutter and cutter-rock contact force at time it in the vertically downward direction, and

fragV is the fragment volume of rock.

Figure 5: Schematic diagram of fracture mode under the action of indenter (Paul and Gangal, 1969)

Both the increase and reduction show the important influence of pre-existing fractures on the fragmentation effect of rock under an

impact load, indicating the significance of introducing pre-existing fractures into bit-rock interaction research.

Figure 6. Fracture system under cutter with pre-exciting fracture

Table 4: parameters of drilling into rock with and without pre-existing fracture

Penetration

displacement /mm Fracture number /1000

Fragment volume /10-

3 m3

Specific energy

/106 J‧m-3

Without pre-exciting

fracture 16.67 12.926 9.37 1.02193

With pre-exciting

fracture 17.89 15.546 10.76 1.01787

Growth percentage 7.32% 20.27% 14.83% -0.4%

3.1 Dynamic fragmentation process

Sine-shape impact loads are used in our studies. Because the load cannot be applied to the model directly, we use the fish language

to program the servo function to control the dynamic velocity of the cutter to generate the target contact force between the cutter and

rock. The target and monitored contact force are as shown in Fig. 7 which also includes the observation parameters, such as the

fracture number, the fragment volume, and the penetration displacement of cutter. It can be seen from the picture that the crack

initiation, the increase of the fragment volume and the vertical footage increase occur only when the contact force increases to a

certain extent, which indicates the necessity of a certain level of static force. Fragmentation schematic at different time are shown in

Fig. 8. The rock first forms a crushed zone below the cutter under the impact. In this zone, the particles of rock debris are relatively

fine. Radial and lateral micro-cracks are produced at the edges of the crushed zone. As the pressure continues to increase, the finer

broken particles will be squeezed into the newly created micro-cracks or pre-existing cracks. The cracks open under the action of the

squeezing particles and continue to expand. The transverse cracks extend to the rock surface to form rock chips.

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Figure 7: Evaluated parameters vs time with a frequency of 100Hz, an impact amplitude of 250 kN, a static level of 800 kN

and dip angle of cutter of 45 deg.

Figure 8: Fragment schematic under impact load at different time with a frequency of 100Hz, an impact amplitude of 250

kN, a static level of 800 kN and dip angle of cutter of 45 deg.

3.2 Sensitivity analysis for indentation

The influence of cutter dip angle and amplitude load of impact on the crushing effect were studied by taking the penetration

displacement, fracture number, fragment volume, and specific energy as evaluation indexes.

3.2.1 Effect of dip angle on indentation

The effects of dip angle of cutter on intention are presented in Fig.9. All the penetration displacement, fracture number and fragment

volume decrease by the increase of dip angle while the specific energy decrease first then increase. Specific energy has the lowest

value when the dip angle is 45 deg. Fig. 9b shows the average broken particle size increases as the dip angle increases. And the

distribution of the particle sizes is smaller, which means the ratio of the small size cuttings is higher.

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Figure 9: (a) Evaluation parameters and (b) Particles size distribution of different dip angle with a frequency of 100Hz, an

impact amplitude of 250 kN and a static level of 800 kN.

3.2.2 Effect of impact amplitude on indentation

Figure 10: (a)Target applied force and (b) evaluated parameters of different impact amplitude with a frequency of 100Hz, a

static level of 800 kN and dip angle of cutter of 45 deg.

Different amplitude of impact loads as shown in Fig. 10a are applied to the cutter to evaluate their intention behaviors. We can find

from Fig. 10b that the fragment volume and penetration displacement have a similar trend with the increase of impact amplitude,

which increases first and then decreases. The specific energy has an opposite trend with the penetration displacement and fragment

volume. The highest penetration displacement, fragment volume, and the lowest specific energy are achieved when the impact

amplitude take the value of 280kN.

4. ROCK FRAGMENTATION UNDER COUPLING OF IMPACT LOAD AND ROTARY MOVEMENT

4.1 Dynamic fragmentation process

The actual RPD drilling is a coupling of impact and lateral motion. Under the impact load, the cutter is pressed into the rock to

produce a crushed zone and a crack system which reduces the strength of the rock. Then the chips are generated along the lateral

crack under the action of the transverse cutting motion as shown in Fig.11.

Figure 11: Fragment schematic under coupling of impact load and lateral movement at different time with a frequency of

100Hz, an impact amplitude of 250 kN, a static level of 800 kN , lateral velocity of 1.2 m/s and dip angle of cutter of 45

deg.

4.2 Sensitivity analysis for fragmentation

4.2.1 Effect of dip angle on fragment

Cutters with different dip angles give different drilling performance as shown in Fig. 12. Fracture number and penetration

displacement show the same trend as a function of dip angle of cutter. They increase as the dip angle increase from 25 degrees to 55

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degrees and then decrease. The fragment volume presents a shape that approximates W and the maximum fragment volume values

are taken at 25 degrees and 45 degrees. The optimal dip angle need future work to be determined with specific energy. Fig. 12b shows

a fluctuation of the lateral contact force which is the classic stick-slip phenomenon. In addition to the different average values, we

can see that the fluctuation amplitude is also different, that is, the strength of the stick-slip effect is different. The effect of stick-slip

grows strong with the increase of dip angle.

Figure 12: (a) Evaluated parameters and (b) lateral contact force of different dip angle of cutter with a frequency of 100Hz,

an impact amplitude of 250 kN, a static level of 800 kN and a lateral velocity of 1.2 m/s.

4.2.2 Effect of impact amplitude on fragment

Figure 13: (a) Evaluated parameters, (b) lateral contact force and (c) particle size distribution of different dip angle of cutter

The trend of penetration displacement, fracture number and fragment as a function of impact amplitude presents an approximate V

shape as shown in Fig.13a. All of them decrease first to a certain point and then increase. This point is the same as the penetration

displacement and fracture number which is about 250 kN. On the other hand, for fragment volume, it is a little smaller than 220 kN.

Fig. 13b shows little difference between intensity of skip -slip effect with different impact amplitude. The particle size distribution

of cuttings presents a phenomenon of secondary differentiation as shown in Fig. 13c. Most particles drop into two size group while

there are a few particles drop into the size group between them. The ratio of small size particles is higher when the impact amplitude

is smaller.

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5. CONCLUSION

A cutting model with the consideration of pre-existing fractures was established using DEM. In this model, the size, density and

distribution parameters of pre-existing fractures were counted and calculated from an outcrop. The macroscopic physical parameters

of rocks and fractures were obtained through a series of trial calculations by continuously adjusting the microscopic contact

parameters. As a dynamic problem, the damping effect of the rock was introduced into our model by fitting it to the laboratory tests.

Finally, two cases were studied: 1. Rock fragmentation only under impact load; 2. Rock fragmentation under the coupling of impact

load and lateral movement.

The results represented the fragment process of rock under the cutter indentation and lateral movement. Typical fracture system under

the indentation of cutter and the skip-slip phenomenon are obtained. When the dip angle of cutter takes the value of 45 degrees and

the impact amplitude take the value of 280 kN, the specific energy gets the minimum value that shows a high rock breaking efficiency.

With the increase of dip angle of cutter, the intensity of skip-slip effect increased, which is not ideal for drilling. The impact amplitude

has no effect on the skip-slip effect, but the particle size is higher when the impact amplitude is higher.

The research of this paper shows the great significance for deepening the understanding of rock breaking mechanism and optimize

drilling parameters in RPD, which leads to the development of geothermal resources.

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