Summary The main purpose of this paper is to present our polycrystalline diamond compact (PDC) cutter model and its verification. The PDC cutter model we developed is focused on a PDC cutter cutting a rock in 3D space. The model studies the forces between a cutter and a rock and applies the theory of poroelasticity to calculate the stress state of the rock during the cutting process. Once the stress state of the rock is obtained, the model can then predict rock failure by the modified Lade criterion (Ewy 1999). This work also developed a trial-and-error procedure to predict cutting forces, and the stress state of a rock before cutting process is also considered. A complete verification of the cutter model is conducted. The model results (i.e., predicted cutting forces) are compared with measured cutting forces from cutter tests in multiple published articles. The major influencing factors on cutting forces—backrake angle, side-rake angle, depths of cut, worn depth (or wear flat area), and hydrostatic pressure—are all studied and verified. A good agreement between the model results and cutter test data is found, and the overall mean relative error is approximately 15%. The influence of inhomogeneous precut stress state of a rock is also studied. Overall, the cutter model in this paper is complete and accurate. It is ready to be integrated into a PDC bit model.

Summary In this paper, we integrated our polycrystalline diamond compact (PDC) cutter model (Chen et al. 2021) into a PDC bit model that can predict the weight on bit (WOB), torque on bit (TOB), and imbalanced side force on a bit under given drilling conditions. We first proposed a method to determine the actual cutting plane and depth of cut of each cutter on a PDC bit. Once the two parameters for each cutter are determined, the cutter model can then be applied to calculate the cutting force of each cutter. The final bit force and moment (i.e., WOB, TOB, and imbalanced side force) are calculated as the resultant force and moment of cutting forces of all cutters. The PDC bit model in this paper considers all bit design parameters, including bit matrix geometry, blade profile, cutter layout, and the inclination of each cutter. Furthermore, the bit model also considers some bottomhole assembly (BHA) parameters (e.g., bit tilt angle, location of first fulcrum point, and tool face/steering plane angle), which allows the bit model to simulate a bit under different drilling modes. The bit model is also validated by published test data and field applications. Finally, case studies are conducted, and the influence of bottomhole stresses, BHA parameters, and drilling modes on bit force and moment are discussed. A field application of the bit model is also provided. The bit model can be directly used for PDC bit design and simulation. In fact, this paper presents a general way to integrate a cutter model into a PDC bit model. Readers are also encouraged to apply this method to integrate their own cutter model into a PDC bit model.

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