Modeling of Cutting Rock: From PDC Cutter to PDC Bit—Modeling of PDC Cutter

Abstract

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.

Study on vertical multifracture propagations in deep shale reservoir with natural fracture network

“…Under the condition of plane strain, the critical fracture energy $${G}_{{\rm{n}}}$$ of rock normal (type I fracture) can be determined by the critical maximum stress $${T}_{\max }$$ that the rock can bear 14,34 $$${G}_{{\rm{n}}}=\frac{{K}_{{\rm{n}}}^{2}}{E}(1-{\nu }^{2})=\frac{1}{2}{T}_{\max }{\delta }_{{\rm{n}}},$$$where E is the elastic modulus, $${\rm{\nu }}$$ is Poisson's ratio, and $${K}_{n}$$ is the type I fracture toughness. In the same way, the critical fracture energy corresponding to type II and III fractures can be calculated.…”

“…where δ n , δ s , and δ t are the normal, first, and second tangential damage displacements of the cohesive element during the damage, respectively. Under the condition of plane strain, the critical fracture energy G n of rock normal (type I fracture) can be determined by the critical maximum stress T max that the rock can bear 14,34…”

Experimental and theoretical analysis of rock failure characteristics by a single PDC cutter under downhole pressurized conditions

“…Meanwhile, a series of theoretical models have been developed to investigate the effects of different pressures on rock failure characteristics. Compared to commercial software, these models significantly simplify the problem and speed up the calculation by making some reasonable assumption (Detournay and Atkinson, 2000;Chen et al, 2018;Chen et al, 2021b;Xiong et al, 2021). During the analysis process, the effects of downhole conditions, such as the in-situ stress, the hydrostatic pressure, and the rock temperatures can be more easily and freely considered by employing different boundary setups and loading pre-stresses in rocks.…”

“…In these studies, the influences of downhole pressures and thermal stresses were analyzed by superimposing different stress fields. Additionally, Chen et al modeled the cutting process of a single cuter, two cutters, and the whole bit based on the theory of linear poroelasticity (Chen et al, 2019;Chen et al, 2021a;Chen et al, 2021b). In their models, the rock failure efficiency under different cutting parameters (cutting speed, back rake angles, etc.…”

“…Based on the cutter diameter and cutting depth in the present study, the average interaction width between the rock and the cutter can be determined. This simplification facilitates mathematical modeling and has negligible effects on the accuracy of theoretical model (Chen et al, 2021b).…”