# Investigation on the effect of changing rotary speed and weight bit on PCD cutter wear

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## Abstract

The research is to determine the optimum range of rotary speed and weight-on-bit value for interbedded formation to reduce PCD cutter wear rate. To simulate an interbedded formation, a combination of limestone as the soft formation and granite as the hard formation is selected. The research is conducted based on analysis of cutter-rock interaction model, wear model and simulation of PCD cutter using finite element analysis in ABAQUS software. The results show that the optimum range of weight on bit and rotary speed for limestone is between 1000 N, 21.4 RPM, and 4000 N, 85.6 RPM, while for granite it is between 1000 N, 21.4 RPM and 3000 N, 64.2 RPM.

## Keywords

Drilling Weight on bit Rotary speed PDC cutter wear rate PDC cutter Interbedded formation FEA Rock-cutter interaction model Wear model## Introduction

In oil and gas industry, it is desirable to drill to the intended depth at the shortest possible time. Such objective relies on several factors, among which are drill bit technology and drilling rate. From several available drill bit types, the polycrystalline diamond compact (PDC) bit is widely used due to its high drilling performance. Drilling rate is known as rate of penetration (ROP), and factors that optimize ROP are drilling main operation parameter such as weight on bit (WOB), drill bit rotary speed (RPM), bit hydraulics and cutter wear. PDC bit consists of multiple polycrystalline cutters (PCD) attached to a bit body, and it cuts through rock by shearing.

The project objective is to investigate the effect of changing rotary speed (RPM) and weight on bit (WOB) on PDC cutter wear as a means to improve ROP. It is assumed that reducing PDC cutter wear rate will lead to increase in bit life and drilling rate, thus improving drilling efficiency.

## Theoretical background

### PDC cutter wear

### Rotary speed

Rotational speed less than 100 RPM tends to produce bigger rock cuttings. These big cuttings might crush the diamond cutter and stick to cutter surface, especially when drilling in medium formation such as Carthage Marble (Majidi, Miska and Tammineni 2011). The sticked rock cuttings caused bit balling and initiated cutter wear and degraded cutting efficiency. Thus, high rotary speed above 100 rpm was preferable for soft and medium formations (Majidi, Miska and Tammineni 2011).

*T*is bit life in hours, a is the bit life coefficient with a value of 9.2937 × 10

^{9},

*b*,

*c*and

*d*are the regression coefficients related to bit type. The values of

*b*= −3.04063,

*c*= −1.24374 and

*d*= −0.01867 (Zhang et al. 2013).

Rock abrasiveness and drilling operation parameter gave huge effect to bit life, especially on the formation of wear of PDC cutter (Ortega and Glowka 1982) as they were dynamically reacted during drilling practice (Zhang et al. 2013).

### Weight on bit (WOB)

*R*

_{p}is the rock compressive strength,

*µ*is the coefficient of friction,

*A*

_{w}is the wear area, and

*α*is the rake angle.

*m*value of Indiana Limestone is steeper than that of Carthage Marble because medium hardness Carthage Marble formation needs higher weight on bit compared to soft hardness Indiana Limestone formation. It can be concluded that for normal drilling process, weight on bit acted at higher value in medium, abrasive or hard formations.

Previous research studied the effect of weight on bit on the penetration rate of PDC based on different rates of cutter wear when drilling through soft and medium hardness formations. The study compared the ROP of two new bits, one moderately worn bit and one severely worn bit which were used to drill similar depth of 1294 ft (394 m). The results show that for soft formation, higher weight on bit (WOB) on the moderately worn bit can produce drilling rate similar to the new bits, while the severely worn bit showed 70% less ROP compared to the new bits. For the medium hardness formation, both worn bits have lower ROP compared to the new bits but the moderately worn bit has better ROP compared to the severely worn bit (Warren and Armagost 1988).

### Wear model

*W*, \(k_{2} , V, \sigma ,\) are the wear value, constant of wear, deformed value, and Von Mises stress, respectively. V is equal to \(a_{2}\) Пd, where \(a_{2}\) is the contact radius and d is the thickness of the layer. The proportionality constant, k2V, for polycrystalline diamond (PDC) has a value of (1.5 × 10

^{−11}). The constant b value is 0.5, and

*n*′ is the cyclic strain-hardening coefficient (Tangena 1987). Von Mises stress was the input of the wear model, and the relationship between Von Mises stress and wear was directly proportional to each other.

## Methodology

### Define parameter

Constant variable: back rake angle, cutter shape, feed rate size, cutter material, and type of formation.

Independent variable: weight on bit (WOB) and rotary speed (RPM).

Dependent variable: cutter wear rate.

Constant design parameters for PDC cutter

PDC constant parameter | Variable for limestone | Variable for granite |
---|---|---|

Size of cutter | 16 mm | 16 mm |

Material of cutter | PDC & WC–Co | PDC & WC–Co |

Diamond carbide interface | Conventional | Conventional |

Side rake angle | 0° | 0° |

Back rake angle | 30° | 30° |

Shape of cutter | Beveled | Beveled |

Rock-cutter friction angle | 33°–40° | 31°–40° |

Surface area of cutting face, A | 3.1163 × 10 | 3.1163 × 10 |

Shear contact area, AS | 1.5582 × 10 | 1.5582 × 10 |

The list of WOB and RPM values

Run | Weight on bit | Rotary speed |
---|---|---|

1 | 1000 | 21.4 |

2 | 2000 | 42.9 |

3 | 3000 | 64.2 |

4 | 4000 | 85.6 |

5 | 5000 | 107.0 |

6 | 6000 | 128.4 |

7 | 7000 | 149.8 |

Model parameter of PDC and rock formation

Material Properties | Limestone | Granite | PDC |
---|---|---|---|

Unconfined compressive strength, UCS (MPa) | 50 | 300 | – |

Density, | 1580 | 26200 | 3510 |

Ultimate tensile strength, UTS (MPa) | 2.5 | 256 | – |

Shear yield stress (Mpa) | 5 | 132 | – |

Young’s modulus, | 3.2 | 70 | 890 |

Poisson ratio | 0.1447 | 0.30 | 0.07 |

Kinetic coefficient, μk | 0.6223 | 0.45 | – |

Strength parameter | -8.93 | 0.79 | 4000 |

Strength parameter | 0.012 | 1.60 | 500 |

Strength parameter | 1566.99 | 0.007 | 0.14 |

Damage parameter | 0.040 | 0.040 | 0.05 |

Damage parameter | 1 | 1 | 1.873 |

Damage parameter | – | – | − 2.272 |

Basically, the penetration rate of the cutter is directly proportional to the wear rate. Thus, the decrement of ROP value with increment of RPM and WOB will show the same result for wear rate of drill cutter. Therefore, in deciding independent variable, the value of WOB and RPM will be loaded increasingly on the cutter during simulation. The value of parameter is given in Table 2 as follows.

The simulation of drill cutter with rock formation is executed in ABAQUS software. The basic rock relation was managed by Johnson–Cook law, and plastic strain was applied to evaluate the rock breaking (Adzis et al. 2018). The parameters of WC–Co and rock formation are shown in Table 3.

#### Analytical model

Analytical method is executed based on mathematical formula of cutter-rock interaction model, where the calculation is analyzed based on cutting face force. Using Eq. (4), the weight on bit, \(F_{n }^{c }\) and velocity, V will be the input in order to generate the output such as intrinsic specific energy, horizontal force, axial and shear stress of cutter test formula.

#### FEA

## Results and discussion

Intrinsic specific energy and horizontal force for independent parameter of single cutter test for granite

Variable | Limestone | Granite | |||
---|---|---|---|---|---|

Weight on bit, \(F_{N}\) (N) | Rotary speed, | Intrinsic specific energy,\(R_{\text{eq}}\) (MPa) | Horizontal force,\(F_{H}\) (N) | Intrinsic specific energy (MPa) | Horizontal force (N) |

1000 | 21.4 | 13 | 511 | 14 | 550 |

2000 | 42.9 | 26 | 1022 | 28 | 1101 |

3000 | 64.2 | 39 | 1533 | 42 | 1651 |

4000 | 85.6 | 52 | 2044 | 56 | 2201 |

5000 | 107.0 | 65 | 2555 | 71 | 2791 |

6000 | 128.4 | 78 | 3066 | 85 | 3341 |

7000 | 149.8 | 91 | 3577 | 99 | 3891 |

The result in Table 4 shows that analytical stress, axial stress, shears stress and intrinsic specific energy values rise linearly with the increment of WOB and RPM, and the maximum stresses are generated at 7000 N of weight on bit and 149.8 rpm of rotary speed. Axial stress increases because of the rise of weight on bit while, the increment of shear stress and intrinsic specific energy occurs when the value of rotary speed and horizontal force are added from the first to the seventh step of the run.

The result shows that axial stress that acts on granite has same value with limestone, but for shear stress, its value is larger compared to shear stress in limestone. It happens because the horizontal force for granite is higher than that in limestone for each run. Thus, hard and abrasive formation such as granite is proven to generate higher shear and total stress than soft formation. In conclusion, the wear rate of PDC cutter in granite directly will be higher than that in limestone.

Calculated stresses for independent parameter of single cutter

Run | Variable | Limestone | Granite | Limestone | Granite |
---|---|---|---|---|---|

Weight on bit, \(F_{N}\) (N) | Analytical stress (MPa) | Analytical stress (MPa) | Simulated stress (MPa) | Simulated stress (MPa) | |

1 | 1000 | 6.49 | 6.74 | 2.557 | 5.111 |

2 | 2000 | 12.98 | 13.49 | 5.663 | 5.241 |

3 | 3000 | 19.46 | 20.22 | 10.850 | 11.010 |

4 | 4000 | 25.96 | 26.97 | 17.270 | 6.292 |

5 | 5000 | 32.44 | 33.95 | 9.5480 | 9.870 |

6 | 6000 | 38.93 | 40.69 | 11.300 | 4.153 |

7 | 7000 | 45.42 | 47.43 | 4.377 | 13.54 |

The stress increases in big scale at the first until the fourth run because at these times, horizontal forces are generated increasingly in order to cut the formation. Once the formation is cut, the generated energy will be lesser, and at the maximum point of simulated stress, the wear of cutter is produced. The output of the simulation for granite shows different patterns where the stress starts to increase from the first run to the third run. The stress increases slowly before it decreases from the fourth run to the seventh run.

Wear values of PDC cutter

Weight on bit, \(F_{N}\) (N) | Limestone | Limestone | Granite | Granite |
---|---|---|---|---|

Analytical wear (m | Simulated wear (m | Analytical wear (m | Simulated wear (m | |

1000 | 6.28 × 10 | 2.48 × 10 | 6.52 × 10 | 4.94 × 10 |

2000 | 1.26 × 10 | 5.48 × 10 | 1.31 × 10 | 5.07 × 10 |

3000 | 1.88 × 10 | 1.05 × 10 | 1.96 × 10 | 1.07 × 10 |

4000 | 2.51 × 10 | 1.67 × 10 | 2.61 × 10 | 6.09 × 10 |

5000 | 3.14 × 10 | 9.24 × 10 | 3.28 × 10 | 9.54 × 10 |

6000 | 3.76 × 10 | 1.09 × 10 | 3.94 × 10 | 4.02 × 10 |

7000 | 4.39 × 10 | 4.23 × 10 | 4.59 × 10 | 1.31 × 10 |

The wear area of PDC cutter from analytical method is increasing with the increment of analytical stress, while for simulation method the wear areas are not consistent for granite and limestone. It occurs because of the same drilling failures such as vibration and cutter bouncing where they are produced from the effect of slip–stick action, broken formation, and pump-off force. Comparing both formations, it can be seen that the wear rate of PDC cutter for granite is bigger than that for limestone. This is because the higher stress in granite had speeded up the rate of wear of PDC cutter.

## Conclusion and recommendation

From analytical analysis, high weight on bit and rotary speed produce high horizontal force, intrinsic specific energy and stress on PDC cutter, but in finite element analysis, the increment value of these parameter produces inconsistent value of horizontal force, intrinsic specific energy and stress on PDC cutter. The main cause is because of instability of PDC cutter from vibration during simulation. The excess unstable mode of cutter initiates bit whirl and drilling failures which can increase cutter wear rate. In investigating the wear of PDC cutter, both methods show that the maximum value of horizontal force, intrinsic specific energy and stress generates high wear rate on PDC cutter.

The difference of data occurs between limestone and granite formation because the output of data of analytical method and finite element analysis is affected by the physical properties of rock formation. The best range of weight on bit and rotary speed for limestone is between 1000 N, 21.4 rpm and 4000 N, 85.6 rpm, while for granite 1000 N, 21.4 rpm and 3000 N, 64.2 rpm. At these ranges, the wear rates generated were small.

The output of the data is produced from single PDC cutter simulations. Therefore, execution of cutter test and simulation with rotary PDC cutter and for whole PDC bit are recommended in future in order to get more accurate data.

## Notes

### Acknowledgements

The authors would like to acknowledge Y-UTP grant 0153AA-A66 for supporting this research.

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