Procedia Engineering 73 ( 2014 ) 258 – 263

1877-7058 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of Geological Engineering Drilling Technologydoi: 10.1016/j.proeng.2014.06.196

ScienceDirectAvailable online at www.sciencedirect.com

Geological Engineering Drilling Technology Conference (IGEDTC), New International Convention Exposition Center Chengdu Century City on 23rd-25th May 2014

Experimental Study on Force of PDC Cutter Breaking Rock

Wang Jiajuna,* , Zou Deyonga, He Renqinga a China University of Petroleum(Huadong), Changjiang West Road.

Qingdao Economic and Technological Development Zone No. 66,Qingdao266580,China

Abstract

Because the anisotropy of shale formation should result in that wellbore deviations is unpredictable, the bit-rock interaction should be fully lucubrated in order to eliminate this problem. The impact of shale rock anisotropy and the cutting velocity on the load of PDC cutter wasn’t considered by the existing cutter-rock interaction models. On the basis of experiments of cutting shale with PDC cutter, using the stress tensor analysis theory, the relationship between the shale rock anisotropy and the cutter’s force is proposed in this paper. A new cutter-rock interaction model was established, and then a new bit-rock interaction model was set up. That applying these models to the ROP prediction of directional PDC bit can improve forecast accuracy is found. © 2014 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of Geological Engineering Drilling Technology.

Key words:PDC bits; shale formation; anisotropy; interaction model; cutting velocity

1. Introduction

The drill ability of shale formation is anisotropic, while the direction perpendicularto the formation layer is higher and the parallel direction is smaller [1-2]. As the PDC bit is always drilling to the direction which is easy to drill, while drilling shale formation, the drilling direction of PDC bit should change. Thus it is hard to control the direction wells trajectory, sometimes the spiral hole occurs, then drilling friction increasing, borehole cleaning ability decreasing, drill pipe bending and severely wearing of stabilizer[3].

* Corresponding author. Tel.: +8615588677613.

E-mail address: wangjiajun101@aliyun.com

© 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of Geological Engineering Drilling Technology

259 Wang Jiajun et al. / Procedia Engineering 73 ( 2014 ) 258 – 263

In the former models of ROP and force condition, the anisotropy index of formation was used to analyze the effect of formation anisotropy on ROP [4], The bit was simplified as hinge support beam fulcrum, and errors exist compared to the actual situation.

The purpose of this paper is to build the interaction model of PDC bit and shale formation based on full-Scale well drilling experiment in shale of kinds of formation dip, analyzing the effect of formation dip angle on the PDC bit steer ability, and provide theoretical basis for the special PDC bit design for direction wells[5].

2. Experiment on PDC Cutter Cutting Rock

2.1. The Test Equipment

The test equipment is the XY-2B drilling rig of China University of Petroleum [6], which comprises of adjustable speed motor, Kelly, bit, pressure device, sensors and data acquisition system. The bit of experiment is plotted as Fig.1. (b), it is a coring bit made up of three cutters.

(a) XY-2B drilling rig (b)Model of a PDC Bit

Fig.1ExperimentalEquipment

Fig.2Cutters Cutting Rock

Fig.3 Level diagram of PDC Cutters and Rock

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2.2. The Experimental Principle and Method

The rotational speed and torque is produced by the adjustable speed motor of drilling rig, the Kelly drives the bit to rotate and axial pressure device compresses on the bit, the sensor and data acquisition system can get the real-time bit weight, torque and displacement data, thus the normal pressure Fn and cutting force could be get[7-8].

A annular slot forms in the shale. As plotted in the Fig. 2, building the 3D coordinate system[9], in which the angle between the normal unit vector of formation layer and Z axis is the rock layer angle γ, the angle between the radial line in the center of PDC cutter and the X axis is the rotation angle.

The PDC cutter cuts the shale of kinds of formation layer angles, which the angle is 0 , 30 , 45 , 60 , 90 respectively. In the experiment, the bit weight is 3kN, 4kN, 5kN, 6kN, 7kN respectively, the rotating speed is 50r/min, 100r/min, 150r/min, 180r/min and the PDC diameter is 13mm, 16 mm, 19mm and the back rake angle is 5 , 10 , 15 , 20 , 25 .Each test of same condition is performed three times, and 1200 groups of data are acquired.

Tal.1 Rock Parameters

Rock Types

Drill ability /Kd

Hardness /MPa

Compressive Strength

/MPa

Tensile Strength

/MPa

Shale 5.0 944.5 67.34 5.58

Marble 5.7 1118.36 84.79 6.21

Granite 6.4 1490.8 94.18 7.02

Limestone 7 1785.4 103.54 7.87

2.3. The Analysis on Test Result

(1) The analysis of relationship between the cutting area and cutter force condition When the back rack angle, cutting velocity and rock drill ability is a constant, the force of cutters increases

linearly with the cutting area, shown in the fig.4. Because cutter area is the principal component influencing the force of cutters, the relationship between the force and cutting area can be expressed as a linearly function.

Fig.4The Relationship between Cutting Area and normal force Fn tangential force Fc (Back Rake Angle is 15 , Cutting Velocity is 0.28m/s)

(2) Analysis on the Relationship between Rock Drill ability and Cutter Load

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The rock drill ability Kd could reflect the drilling resistance of different rocks. When the back rack angle cutting velocity and cutting area is a constant, the force of cutter increases linearly with rock drill ability Kd, shown in the fig.5.

Fig.5 Relationships between Rock Drill ability and normal force Fn tangential force Fc (Back Rake Angle is 15 , Cutting Velocity is 0.28m/s)

(3) Analysis on the Relationship between PDC Cutter Back Rake Angle and Cutter Load When rock drill ability, cutting velocity and cutting area is a constant, it is a quadratic relationship between back

rake angle and the force of cutter, shown in the fig.6. When the back rake angle of cutter is over 10 , the normal force Fn, tangential force Fc increases with the back rake angle of cutter.

Fig.6Relationship between the Back Rake Angleω c and normal force Fn tangential force Fc (Cutting Area is 2.8 mm2, Cutting Velocity is 0.28m/s )

(4) Analysis on the Relationship between Cutting Velocity and Cutter Load When rock drill ability, back rake angle and cutting area is a constant, the normal force Fn, tangential force Fc

increases with the cutting velocity. It is a logarithmic relationship between cutting velocity and the force of cutter, shown in the figure 7.

0 1 2 3 4 5 6 7 8

Kd

A=1.4 A=2.8 A=4.2 A=5.6 A=7

0

1

2

3

4

Kd

A=1.4 A=2.8 A=4.2 A=5.6 A=7

262 Wang Jiajun et al. / Procedia Engineering 73 ( 2014 ) 258 – 263

Fig.7 Relationship between cutting velocity V and normal force Fn tangential force Fc back rake angle is 15°, shale

(5) Analysis on the Relationship between Rock Layer Angle and Cutter Load As the Figure 8 shows, when the rock layer angle is 45 , normal force Fn tangential force Fc have the same

trend as the angular position change. In the orthogonal isotropic rock, Req is called the coefficient of rock equivalent strength, it is sensitive to the rock layer angle, this can’t be observed in the isotropic formation, and it is the reason of the PDC bit lateral force.

Fig.8 Relationship between Angular Position and normal force Fn tangential force Fc Rock Layer Angel is 45°, back rake angle is 15°, Cutting Area is 2.8 mm2, shale

3. The Interaction Model of Cutters and Rock

The positive pressure Fn and cutting force Fc of a cutter is proportional to the cutting area A of a cutter, considering the nature of the rock and the cutting parameters of the cutter, the cutters and rock interaction model was established.

tan( )c eq

n c f eq

F R AF R A

(1)

Req is called the coefficient of rock equivalent strength, using Mohr - Coulomb criterion to calculate this value. For the isotropic rocks, Req is on the function of the cutter inclination ωc, hydrostatic pressure Pb, triangle angle θf of the chips, rock cohesion C, cutting velocity V and internal friction angle φ.

1 , , , , ,eq c b fR f P C V (2)

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For orthotropic rocks, Req also depend on the normal vector n of the rock level. As shown in Fig. 1, under the same force of the cutters, it is more easy to broke the rock in the combination a than in the combination b.

The rock material is assumed as a composite material, using orthogonal isotropic material failure criterion, the rock crushing yield function is:

22 21 2 3 4 0q T p N p

(3)

The parameters are:

12

13

3 ( ) :2

p Tr

q pI pI

N n nT n Nn

(4)

In this function, σ is the stress tensor, n is the unit normal vector of the rock level.

The rock cohesion C and internal friction angle φ is replaced by rockparameters 1 2 3 4, , , . For the isotropic rocks, Req is on the function of the cutter inclination ωc, hydrostatic pressure Pb, cutting velocity V, triangle angle θf

of the chips, rock parameters 1 2 3 4, , , .

2 1 2 3 4, , , , , , , ,eq c b fR f n P V (5)

4. Conclusions

(1) When rock drill ability, back rake angle and cutting area is a constant, it is a logarithmic relationship between cutting velocity and the force of cutter.

(2) When the back rack angle, cutting velocity and rock drill ability is a constant, the force of cutters increases linearly with the cutting area.

(3) When rock drill ability, cutting velocity and cutting area is a constant, it is a quadratic relationship between back rake angle and the force of cutter.

(4) In the isotropic orthogonal rock, the rock equivalent energy is sensitive to the layer angle of the formation.

References

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