# The rock breaking and ROP increase mechanisms for single-tooth torsional impact cutting using DEM

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## Abstract

Torsional impact drilling is a new technology which has the advantages of high rock-breaking efficiency and a high rate of penetration (ROP). So far, there is no in-depth understanding of the rock-breaking mechanism for the ROP increase from torsional impact tools. Therefore, it has practical engineering significance to study the rock-breaking mechanism of torsional impact. In this paper, discrete element method (DEM) software (PFC2D) is used to compare granite breaking under the steady and torsional impacting conditions. Meanwhile, the energy consumption to break rock, microscopic crushing process and chip characteristics as well as the relationship among these three factors for granite under different impacting frequencies and amplitudes are discussed. It is found that the average cutting force is smaller in the case of torsional impact cutting (TIC) than that in the case of steady loading. The mechanical specific energy (MSE) and the ratio of brittle energy consumption to total energy are negatively correlated; rock-breaking efficiency is related to the mode of action between the cutting tooth and rock. Furthermore, the ROP increase mechanism of torsional impact drilling technology is that the ratio of brittle energy consumption under the TIC condition is larger than that under a steady load; the degree of repeated fragmentation of rock chips under the TIC condition is lower than that under the steady load, and the TIC load promotes the formation of a transverse cracking network near the free surface and inhibits the formation of a deep longitudinal cracking network.

## Keywords

Torsional impact rock breaking Mechanical specific energy Fractal dimension Microcrack DEM## 1 Introduction

Torsional impact drilling (TID) is a new drilling technology developed on the basis of rotary drilling (Sapinska-Sliwa et al. 2015). In the past 10 years, various torsional impact drilling tools have been developed and achieved good results (Gillis et al. 2004; Schen et al. 2005; Wu et al. 2010). Among them, the invention of the Tork Buster TID tool makes it possible for polycrystalline diamond compact (PDC) bits to drill into deeper and harder formations at a faster speed. This technology can effectively suppress or even eliminate the stick–slip vibration of bottom drilling tools and improve drilling efficiency and well quality (Ledgerwood et al. 2010; Clayton 2010; Zhu and Liu 2017; Deen et al. 2011). However, researchers have focused more on tool development, field testing and application of this technology. There is no in-depth understanding of the mechanism for the increase in ROP of rock breaking with the torsional impact tools, which makes the application of the technology limited to a certain extent (Zhu and Liu 2017).

In the last 10 years, a large number of scholars have carried out some studies related to rock breakage and torsional impact rock breaking. Zhang et al. (2011) had measured rock stress–strain behavior and rock deformation and strength characteristics under different rock conditions by triaxial stress tests. They showed that the initial fractures influenced the rock crushing effect and the compaction effect also influenced the rock mechanical properties. The influence of the drilling process on the bottom-hole pressure of the rock surface was studied by Akbari et al. (2011). It is pointed out that the rate of penetration (ROP) is a logarithmic function of the bottom-hole pressure. The rock fragmentation processes induced by double drill bits subjected to steady and dynamic loading were investigated using a numerical method by Wang et al. (2011). Wang et al. (2011) compared the effect of rock breaking when there were torsional impact load and no torsional impact load at the same torsion and weight of bit (WOB) by using their ANSYS model. Results showed that the torsional impact can reduce the accumulated energy storage in the drilling pipe, alleviate the stick–slip vibration, and greatly improve the working conditions of the PDC bit. Zhu et al. (2014) established a dynamic simulation model of full-scale PDC bits for dynamic rock breaking using a finite element model (FEM) to research high-frequency torsion impact. The conclusion is that the tensile stress and compressive stress are intersecting when drilling into a hard formation under high-frequency torsional impact, and the tensile stress is the main stress. Bagde and Karekal (2015) studied sandstone crushing under vibration loading through experiments and numerical simulations. It concluded that vibratory loading has benefits in fracturing rock at relatively lower load compared to conventional loading. Fan et al. (2015) used experimental data to establish a multi-fissured particle flow model with different dip angles, and the failure mode in the test process was reproduced by numerical simulation. Yang et al. (2015) presented an experimental investigation of the damage mechanisms of granites under uniaxial tension using a digital image correlation (DIC) method, and the experimental results showed that the damage was related to the strain as well as to the strain gradient. Li et al. (2016) experimentally investigated the fracture process of sandstone specimens containing a pre-cut hole under coupled static and dynamic loads, and the results show that the combined effects of stress concentration around the pre-cut hole and far-field strain generated by static loading promote rock impact damage. Liu et al. (2017) believed that it is feasible to improve the rock-breaking efficiency of an impact crushing device by increasing the impact frequency and rotating torque.

Using a single tooth to cut rock can reflect the local rock-breaking behavior of the drilling bit to a certain extent. There have been some investigations into single-tooth cutting (Lei and Kaitkay 2003; Su and Akcin 2011; Yadav et al. 2018; Zhu and Jia 2013), and some conclusions have been drawn. Therefore, the use of a single tooth instead of an integral drilling bit simplifies the problem to a large extent, but it is still possible to draw relatively accurate conclusions. Meanwhile, using the DEM can well reflect the internal defects and inhomogeneity of the rock.

Therefore, based on the background of above TID technology in this study, DEM software (PFC2D) is used to compare the rock-breaking behavior of granite under steady and torsional impacting conditions. At the same time, the energy consumption to break rock, microscopic crushing process and chip characteristics as well as the relationship among these three factors for granite under different impact frequencies and amplitudes are discussed. The purpose is to reveal the rock-breaking mechanism of torsional impact in detail and then provide some technical references for the design and work of downhole torsional impact rock-breaking tools.

## 2 Analysis of the rock-breaking process of TIC

- 1.
The impact action time is very short, the rotary motion of the drilling tooth in the rock-breaking process is simplified to a uniform linear motion, and the torsional impact mode is realized by applying an impact velocity with a very short duration of action.

- 2.
The stiffness of the PDC tooth is quite large relative to that of the rock, so the PDC tooth is simplified as a rigid body.

- 3.
The influence of the factors such as drilling fluid, formation pressure, geothermal and other factors affecting the internal energy change of rock are not considered.

### 2.1 Rock-breaking mode and fracture characteristics of chips

*a*and a cutting speed

*v*. Deterioration occurs in the area below the rock in contact with the tooth, forming a partially degraded area. Due to TIC of the PDC tooth, more or less chips may be generated directly below the PDC tooth, obliquely below the contacting zone of the PDC tooth and the rock, and in the movement direction of the PDC tooth. The generation of these chips will cause the cutters to cause repetitive crushing during the rock-breaking process. The degree of this repeated fragmentation will directly affect the rock-breaking efficiency.

For the above four modes of action, according to the scale of the repeated crushing rate and the total crushing efficiency of the rock after cutting, the crushing efficiency among them is ranked from high to low empirically as: ideal type > interference type > step type > standard type.

*V*(mm

^{3}) and the amount of debris whose volume exceeded

*V*is recorded as

*N*. So there is:

*N*is the number of chips whose volume exceeds

*V*(mm

^{3});

*x*is the particle size (mm) corresponding to volume

*V*;

*D*is the fractal dimension (Sahimi 1992; Xie and Pariseau 1993).

*D*is, the higher the degree of fragmentation of the chips is, i.e., the higher the repetitive breaking rate (RBR) of the rock during the cutting process (Matsui et al. 1982). Meanwhile, due to \(x \propto V^{1/3}\), there is:

*B*is an undetermined constant.

The fractal curve of ln*N*–ln*V* is made by counting the volume *V* and number *N* of the chips; then, the fractal dimension *D* of the debris can be obtained from the fractal curve. Thus, the relationship between the corresponding rock-breaking efficiency and the size of the debris as well as the RBR can be obtained.

### 2.2 TIC energy consumption

*W*is the total work (energy) consumed by the broken rock (mJ);

*V*is the broken volume of rock (mm

^{3}), and the smaller the MSE (mJ/mm

^{3}or MPa), the higher the rock-breaking efficiency will be.

*D*is the fractal dimension;

*x*

_{max}is the size of the largest piece of rock debris after cutting;

*MSE*is the mechanical specific work.

*c*microcracks are produced during the whole cutting process, the brittle energy consumed is as follows:

*δ*is the energy consumed by a microcrack is generated (mJ), supposing it is a constant;

*c*is the number of cracks;

*E*

_{B}is the brittle energy (mJ).

*k*is defined as follow:

*k*is BECC (1/J);

*E*is the energy provided by the drilling tooth (mJ);

*W*is the external work (mJ).

*E*

_{B}and the external energy

*E*, it can be concluded that the brittle energy consumption ratio (BECR) in the total energy used for rock breaking is:

*η*

_{B}is BECR.

PFC2D can neither determine the brittle energy for producing cracks nor accurately calculate the BECR *η*_{B} in the total energy of the broken rock. However, we can simply compare the relative energy consumption of brittle energy to total energy when cutting the same rock by the BECC *k*.

## 3 Rock parameter calibration and cutting model establishment

The particle flow code (PFC) is a micro-DEM, which is proposed by Cundall and Strack (1980) to simulate the motion and interaction of spherical particles. The Itasca Consulting Group has developed a PFC series of software with the same name based on this method, which is divided into two types: PFC2D and PFC3D.

UCT results of granite

Height | Diameter | Density | Poisson’s ratio | Elastic modulus | Compressive strength |
---|---|---|---|---|---|

50.05 | 24.96 | 2547.6 | 0.130 | 15,600.2 | 104.0 |

BST results of granite

Length | Diameter | Maximum load | Tensile strength |
---|---|---|---|

25.14 | 24.71 | 9.141 | 9.37 |

There are various contact models in PFC2D. This paper uses the flat-joint model, and the particles contacting with others cannot only transmit force, but also transmit torque. The flat-joint model can fit well to rock material with a large tensile compression limit ratio. The advantage of using the flat-joint model to simulate granite is that it can be used to simulate the properties of hard rock and it is easy to monitor the crack growth process. For detailed information on this contact model, please refer to the literature of Potyondy (2012a, b; 2013) and Potyondy and Cundall (2004).

### 3.1 Material calibration results

Calibration results of microparameters of granite

Density | Friction coefficient | Particle modulus | Particle contact modulus | Radius range | Radius multiplier |
---|---|---|---|---|---|

2547.6 | 0.577 | 14,000 | 14,000 | 0.1–0.2 | 1 |

Stiffness ratio | Normal bond strength \(\sigma_{\text{c}}^{*}\), MPa | Porosity | Contact stiffness ratio | Cohesive stress | Friction angle |
---|---|---|---|---|---|

2.5 | 20 | 0.1 | 2.5 | 40 | 30 |

Comparison of macroscopic parameters between numerical experiments and actual experiments

Elastic modulus | Compressive strength | Splitting strength | |
---|---|---|---|

Numerical simulation | 15,367.6 | 107.7 | 9.49 |

Actual experiment | 15,600.2 | 104.2 | 9.37 |

Relative percentile error, % | 1.49 | 3.36 | 1.28 |

### 3.2 Cutting model establishment

Fixed parameters for TIC model

Rake angle, degree | Cutting depth, mm | Steady load cutting velocity, m/s | Cutting stroke, mm | Single impacting time, ms |
---|---|---|---|---|

15 | 2 | 1 | 20 | 2 |

*v*

_{0}= 1 m/s. The loading type recorded for TIC is denoted by letter ‘T’, and the first number represents the impacting frequency, and the second number represents 10 times the impacting amplitude. For example, T3_2 indicates that during the cutting stroke, the torsional impacting frequency is three times and the impacting amplitude is 0.2, that is, the maximum impact velocity

*v*

_{max}is: \(v_{\rm{max} } = (1 + 0.2)v = 1.2\;{\text{m/s}}\). TIC loads are shown in Table 6.

Load application of TIC model

Impacting amplitude | Loading label at different impacting frequencies | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

0.1 | T1_1 | T2_1 | T3_1 | T4_1 |

0.2 | T1_2 | T2_2 | T3_2 | T4_2 |

0.3 | T1_3 | T2_3 | T3_3 | T4_3 |

## 4 Results analysis and discussion

### 4.1 Cutting force and MSE

*k*can be used to characterize the relative amount that the brittle energy consumption takes of the total energy consumption after the rock-breaking process. In order to reveal the influence of different impacting frequencies and impacting amplitudes on the MSE and brittleness energy consumption in the rock-breaking process, the BECC

*k*and MSE are performed in the same coordinate system, as shown in Fig. 11. From Fig. 11, it is known that the BECC

*k*and MSE show an inverse correlation and a symmetrical distribution. That is to say, at the same impacting frequency and impacting amplitude, the smaller the MSE is, the larger the BECC

*k*will be and vice versa. Therefore, the larger the proportion of brittleness to total energy consumption, the smaller the MSE of rock breaking and the higher the efficiency of rock breaking.

### 4.2 The mode of action between cutting tooth and rock and the fractal characteristics of chips

The fractal dimensions of each TIC load case

Loading label | Fractal dimension | Loading label | Fractal dimension | Loading label | Fractal dimension | Loading label | Fractal dimension |
---|---|---|---|---|---|---|---|

T1_1 | 1.6959 | T2_1 | 1.7846 | T3_1 | 1.4260 | T4_1 | 1.3923 |

T1_2 | 1.5219 | T2_2 | 1.8196 | T3_2 | 1.7848 | T4_2 | 1.5917 |

T1_3 | 1.5981 | T2_3 | 1.8003 | T3_3 | 1.8105 | T4_3 | 1.6951 |

In addition, in conjunction with Eq. (6) in Sect. 2.1, let \(a = \frac{4 - D}{{V_{\rm{max} }^{(4 - D)/3} }}\). The MSE and value *a* under each loading case are shown in Fig. 14b. Figure 14a, b have striking similarities. It can be seen from Fig. 14b that the MSE and the value *a* show a tendency to change synchronously under various loading cases. This proves the correctness of the formula for energy consumption of rock breaking proposed by Yan et al. (2008). This further shows that the RBR of rock in the TIC process is an important factor that affects the crushing efficiency of rock.

### 4.3 The crack propagation mode

As the cutting progresses, the cracks of the rock under steady load case develop toward the longitudinal direction of the rock, as shown in Fig. 16a; at the same time, a secondary crack develops on the basis of longitudinal cracks, such as Fig. 16b shows. In the case of TIC, although the longitudinal cracks also expand, the impact causes more cracks to propagate in the transverse direction to form transverse cracks, as shown in Fig. 16c. The laterally spreading cracks continue to expand toward the free surface and eventually form a cracking network near the free surface of the rock, as shown in Fig. 16d. The crack network near the free surface of rock can promote the formation of larger size rock chips, making the efficiency of rock-breaking relatively higher.

In terms of the properties of cracks produced under steady load and TIC cases, there are mainly two types: tensile cracks and shear cracks. Shear cracks are mainly distributed in the dense crack area where the cutter comes into contact with the rock, while tensile cracks are dominant in other places, as shown in Figs. 15, 16 and 17.

The ratio of number of shear cracks to total number of cracks under each TIC load case

Loading label | Ratio of number of shear cracks to total number of cracks, % | Loading label | Ratio of number of shear cracks to total number of cracks, % | Loading label | Ratio of number of shear cracks to total number of cracks, % | Loading label | Ratio of number of shear cracks to total number of cracks, % |
---|---|---|---|---|---|---|---|

T1_1 | 7.31 | T2_1 | 8.73 | T3_1 | 7.53 | T4_1 | 7.20 |

T1_2 | 6.05 | T2_2 | 9.51 | T3_2 | 7.86 | T4_2 | 7.90 |

T1_3 | 6.61 | T2_3 | 9.63 | T3_3 | 8.77 | T4_3 | 7.28 |

## 5 Conclusion

- 1.
The average cutting force is smaller in the case of torsional impact cutting than that in the case of steady loading. As the impacting frequency increases, there are optimal ranges of impacting frequency and impacting amplitude. In actual projects, the impacting frequency should not be too large.

- 2.
The MSE and the ratio of brittle energy consumption to total energy are negatively correlated: the larger the ratio of energy consumption of brittleness is, the smaller the MSE is, and the higher the rock-breaking efficiency will be.

- 3.
Four types of modes of action between the cutting tooth and rock are introduced. The rock-breaking efficiency is related to the mode of action between the cutting tooth and rock: the mode of action between the cutting tooth and rock at the optimal impacting frequency and amplitude range is the ideal type. Meanwhile, the rock-breaking efficiency is related to the repetitive breaking degree (fractal characteristics) of cutting chips: the greater the fractal dimension is, the higher the repetitive breaking rate of chips is, and the lower the rock fragmentation efficiency will be.

- 4.
The cracks in the interior of the rock, both under steady load and in TIC cases, are dominated by tensile cracks, and the shear cracks are mainly distributed in the zone where the cutter comes into contact with the rock.

- 5.
The reason why the rock-breaking efficiency under the TIC case is higher than that under the steady load case is the ratio of brittle energy consumption under the TIC condition is greater than that under the steady load; the degree of repeated fragmentation of rock chips under the TIC condition is lower than that under the steady load; and the torsional impact load promotes the formation of a transverse cracking network near the free surface and inhibits the formation of a deep longitudinal cracking network in the rock.

## Notes

### Acknowledgement

This study is supported by the National Natural Science Foundation of China (Grant No.51674214), International Cooperation Project of Sichuan Science and Technology Plan (2016HH0008), Youth Science and Technology Innovation Research Team of Sichuan Province (2017TD0014) and Applied Basic Research of Sichuan Province (Free Exploration-2019YJ0520). Such supports are greatly appreciated by the authors.

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