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Development of a Cutting Force Model for a Single PDC Cutter Based on the Rock Stress State

  • Wei Li
  • Xin LingEmail author
  • Hui Pu
Original Paper
  • 3 Downloads

Abstract

Polycrystalline diamond compact (PDC) bits are currently the most widely used bits in the petroleum industry. However, the rock-breaking mechanisms of PDC bits are not well understood, especially in deep hard-rock drilling. By modifying the Nishimatsu model, a single PDC cutter force model based on in situ stress is developed in this study. By coupling the mechanical properties of rock and the technological measures of rock breaking, the model can accurately solve the cutting force and assess the rock drillability when applied to a PDC bit. The analysis of research findings shows that the vertical stress initially has a greater impact on the cutting force despite a larger horizontal stress relative to the vertical stress. Moreover, the optimal cutting angle of a PDC cutter is between 15° and 20°. The applicable conditions of the model are obtained experimentally. The model can predict cutting forces in non-expansive rocks well with 2% error. Furthermore, the mechanical-specific energy under low confining pressure has been theoretically demonstrated to increase more quickly than that under high confining pressure. The proposed model can analyse the influence of effective horizontal and vertical stresses and rock strength on the cutting force, which can lead to a better understanding of the rock-breaking mechanisms of PDC drill bits. The results of this work can be used to study PDC bit performance and provide guidelines for the application and design of PDC bits for specific rocks.

Keywords

PDC drill bits Cutter Rock-breaking mechanism In situ stress Rock drillability 

List of Symbols

FR*

The force provided by the cutter to rock

Ff

The friction force between cutter and rock in cutting process

FR

The cutting force to break rock provided by the cutter

F

The resultant force on the failure line

P

The resultant stress per unit length on the failure line

λ

The distance from any point on the failure line AB to point A

P0

The resultant stress coefficient

h

The depth of the cut

α

The angle between the fracture line and the horizontal plane

n

The coefficient related to the parameters of cutting teeth

θ

The cutting angle of the PDC cutter

PL

The maximum of resultant stress P

τn0

The component of maximum resultant stress PL along the failure line

σn0

The component of maximum resultant stress PL vertical to the failure line

φ

The angle between direction of resultant force PL at point A and the front edge of the PDC cutter

τm

The shear strength of rock

φk

The friction angle of rock

Fσ

The normal component of the resultant force F on the failure line AB

Fτ

The tangential component of the resultant force F on the failure line AB

σv

Overburden load

Ph

Fluid column pressure

Pp

Pore pressure

σ1

The horizontal stress of the bottom hole rock

σ3

The vertical stress of the bottom hole rock

αc

The angle of inclination

μ

Poisson’s ratio of rocks

α*

The horizontal structural coefficients

R

The average cutting stress per unit area

Pσ

The average internal force per unit area of the oblique section whose angle with the horizontal plane is also α

R1

The cutting stress per unit area contributed to overcome the effective horizontal stress σ1

R2

The cutting stress per unit area contributed to overcome the rock shear strength

R3

The cutting stress per unit area contributed to overcome the effective vertical stress σ3

ξ

The wear coefficient of the cutter

r

The radius of the PDC cutter

SFD

The areas of the fracture surface

SADB

The contact surface between the cutter and rock

FR1

The cutting force contributed to overcome the effective horizontal stress

FR2

The cutting force contributed to overcome the rock shear intensity

FR3

The cutting force contributed to overcome the effective vertical stress

Notes

Acknowledgements

The research is financially supported by Natural Science Foundation of China, under Award no. 51774093.

Compliance with Ethical Standards

Conflict of interest

The authors are aware of the ethical responsibilities and they declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Petroleum EngineeringNortheast Petroleum UniversityDaqingChina
  2. 2.Department of Petroleum EngineeringUniversity of North DakotaGrand ForksUSA

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