Mathematical Modeling of PDC Bit Drilling Process Based on a Single-Cutter Mechanics

An analytical development of a new mechanistic drilling model for polycrystalline diamond compact (PDC) bits is presented. The derivation accounts for static balance of forces acting on a single PDC cutter and is based on assumed similarity between bit and cutter. The model is fully explicit with physical meanings given to all constants and functions. Three equations constitute the mathematical model: torque, drilling rate, and bit life. The equations comprise cutter’s geometry, rock properties drilling parameters, and four empirical constants. The constants are used to match the model to a PDC drilling process. Also presented are qualitative and predictive verifications of the model. Qualitative verification shows that the model’s response to drilling process variables is similar to the behavior of full-size PDC bits. However, accuracy of the model’s predictions of PDC bit performance is limited primarily by imprecision of bit-dull evaluation. The verification study is based upon the reported laboratory drilling and field drilling tests as well as field data collected by the authors.