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

Abstract

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.

A study on PDC drill bits quality

“…According to the abrasive destructive mode of drag bits, quality can be defined by two main parameters: materials wear rate and excavation performance. Wear rate calculus by Archard's model has been commonly used in several works to describe PDC/rock behavior [2]. Cutting efficiency evolution is closely linked to wear flat formation during friction and it is initially determined by the sample depth of cut.…”

Mathematical Modelling of the Mechanics of Core Drilling in Geomaterials

“…Notice the remarkable similarity between Equation (12) and Equation (7), obtained by Wojtanowicz and Kuru (1993) by means of empirical assumptions. The optimal rate of advancement h h depends on the base material by means of the indenters' penetration u.…”

“…Assumptions of the Model Wojtanowicz and Kuru (1993) derived a model for rock drilling, based on the static balance of the forces acting on a single cutter, assuming similarity between bit and cutter. Three equations constitute the mathematical model: torque, drilling velocity (or rate of penetration), and drill bit life.…”

“…In the model, u is the cutter penetration in the base material, h is the cutting angle, b is the back rake angle, k is the side rake angle, f n and f t are, respectively, the normal and tangential forces acting upon the indenter, f c is the cutting force (orthogonal to the cutting area), f w is the component of the normal force orthogonal to the wear-flat, f fw and f fc are the frictional forces acting respectively on the wear-flat area and on the cutting surface area. The bit life, drilling velocity, and bit torque equations are deduced from the balance of forces on a cutter moving with FIGURE 2 Geometrical and static assumptions according to Wojtanowicz and Kuru (1993): (a) axial view of the core bit; (b) lateral view of a cutter with back rake angle b < 0 .…”

A methodology for the optimization of PCD compact core drilling in basalt rock

“…The initial value is a function of rock strength as well as the process parameters. The gradual increase in the force and torque value is proportional to insert wear (e.g., [4,24]). Also observed is that force and torque rate increase is smaller in soft basalt than in hard basalt.…”