Modeling and Investigation of the Velocity-Dependent Cutting Process with PDC Cutters Using the Discrete Element Method

Polycrystalline diamond compact (PDC) bits with multiple fixed cutters drill through deep formations and are used in oil and gas, geothermal, and mining industry. The bit-rock interaction excites drill string vibrations, which need to be mitigated to improve drilling performance. A velocity-weakening characteristic of the bit torque can cause severe self-excited high-frequency torsional oscillations (HFTO) of the bottom hole assembly (BHA). The dependency on velocity can be attributed to rate-sensitive rock cutting forces at each cutter. The purpose of this paper is to model the rate effect of cutting forces and determine influencing factors in the single-PDC cutting process. In this paper, a modified bonded-particle model (discrete element method, DEM) for rock in deep drilling environments is applied to the pressurized cutting process. Potential modification strategies considering rate indicators at different scales are compared and discussed to reproduce rate dependency in the particle contact model. Two specific models, incorporating cutting-speed-dependent bond strength or grain elastoplasticity, are implemented and verified. The relationship between rate-sensitive cutting forces and the causal rock failure mechanisms is then clarified by interpreting the results from a continuum perspective. Moreover, the influences of axial force and cutter wear state on the rate dependency are investigated. In cutting simulations at a constant depth of cut and various cutting speeds, both models result in rate-dependent cutting forces in good qualitative agreement with rock experiments: Significant hardening is reflected in the axial force component. The modification of contact models combined with a macroscopic rate indicator (i.e. cutting speed) has proven to be a feasible and effective way to reproduce the rate effects in the cutting simulations. In subsequent simulations with constant axial force, the steady-state tangential force decreases as the cutting speed increases, matching the reduction of torque on the bit with increasing RPM. Rate dependency intensifies at higher axial forces or with dull cutters, which agrees with laboratory full-scale bit tests in the literature. This study proposes a practical approach to integrating observed rate effects of downhole rock cutting processes into numerical rock models. The results enhance our understanding of the rock cutting process and have positive implications for the improvement of the cutter design against undesirable rate effects.