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

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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.

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Abbreviations

FR * :

The force provided by the cutter to rock

F f :

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

P 0 :

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

P L :

The maximum of resultant stress P

τ n0 :

The component of maximum resultant stress PL along the failure line

σ n0 :

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

τ m :

The shear strength of rock

φ k :

The friction angle of rock

F σ :

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

F τ :

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

σ v :

Overburden load

P h :

Fluid column pressure

P p :

Pore pressure

σ 1 :

The horizontal stress of the bottom hole rock

σ 3 :

The vertical stress of the bottom hole rock

α c :

The angle of inclination

μ :

Poisson’s ratio of rocks

α*:

The horizontal structural coefficients

R :

The average cutting stress per unit area

P σ :

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

R 1 :

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

R 2 :

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

R 3 :

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

S FD :

The areas of the fracture surface

S ADB :

The contact surface between the cutter and rock

FR 1 :

The cutting force contributed to overcome the effective horizontal stress

FR 2 :

The cutting force contributed to overcome the rock shear intensity

FR 3 :

The cutting force contributed to overcome the effective vertical stress

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Acknowledgements

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

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Authors and Affiliations

  1. School of Petroleum Engineering, Northeast Petroleum University, Daqing, 163318, China

    Wei Li & Xin Ling

  2. Department of Petroleum Engineering, University of North Dakota, Grand Forks, ND, 58202, USA

    Hui Pu

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  1. Wei Li
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  2. Xin Ling
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  3. Hui Pu
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Correspondence to Xin Ling.

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Li, W., Ling, X. & Pu, H. Development of a Cutting Force Model for a Single PDC Cutter Based on the Rock Stress State. Rock Mech Rock Eng 53, 185–200 (2020). https://doi.org/10.1007/s00603-019-01893-7

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