Use of Single-Cutter Data in the Analysis of PDC Bit Designs: Part 1 - Development of a PDC Cutting Force Model
Authors: Glowka David A. 
Published: December 2007

Summary
A practical conceptual model of the rock drag cutting process is developed to provide a method for mathematically describing the process as it applies to polycrystalline-diamond-compact (PDC) drill bits. Laboratory test results obtained at atmospheric pressure with single PDC cutters are presented and analyzed to provide equations that relate cutter forces to rock type, cut depth, and cutter-wear state. Two distinct modes of wear are identified, and possible explanations for the differences are offered. The effects of interaction among closely spaced cutters are studied, and a model is developed that accounts for the effects on cutter forces. The effects of providing PDC cutters with water-jet assistance are also investigated and shown to be significant.

Introduction
Research has been conducted for several years at Sandia Natl. Laboratories to foster the development of PDC bits for geothermal drilling. This work has been directed toward the high-temperature, hard-rock drilling environment typically found near geothermal resources. The results, however, can be applied to drilling environments of interest to the petroleum industry as well.
Our previous experimental and theoretical studies suggest a strong dependence of the PDC cutter wear rate on the frictional temperature that develops at the cutter/rock interface.1,2 The results indicate that above a critical wear-flat temperature of approximately 662°F [350°C], wear mechanisms that greatly accelerate cutter wear become operative. These mechanisms include thermal softening of the tungsten-carbide/cobalt (WC/Co) substrate to which the PDC layer is bonded and adverse internal stresses that arise becausze of the severe thermal and mechanical loading imposed on the cutter. Such thermally accelerated water can reduce bit life by one or two orders of magnitude, generally to an unacceptable level.3
Below 662°F [350°C], PDC cutter wear is usually very low and is caused predominantly by abrasion, without any apparent thermal effects. Because of the effects of wear on cutter geometry, however, even minor wear can have a significant effect on cutter and bit performances.3 Abrasive wear is a strong function of the abrasiveness of the rock being cut and the stresses that develop at the cutter/rock interface.
Designing and operating PDC bits to perform effectively within the constraints suggested by these wear phenomena are the subjects of this paper. Part 1 presents laboratory work that provides insight and quantitative data on cutter/rock interaction. A cutter-interaction model based on the laboratory results is developed and shown to provide a means for predicting the effects of multiple cutters on a PDC bit face. In Part 2 (Ref. 4), this model is generalized and used to develop algorithms for a computer code (PDCWEAR) that predicts the performance and wear of PDC drill bits. General trends related to the effects of bit design and operation, as predicted by the code, are also identified and discussed.

Laboratory Single-Cutter Tests
We seek a model of the PDC cutting process that will allow us to determine the penetrating and drag forces acting on each cutter located on the bit face. The primary parameters that affect these forces include the rock type, cutter design and wear state, position on the bit, cutter interaction, cutting speed, rock stress state, and fluid environment (Fig. 1).
It is possible to duplicate many of these parameters in laboratory single-cutter tests. Most of the cutting conditions encountered by each cutter in full-scale, atmospheric-pressure, laboratory bit tests can be duplicated with a modified milling machine, relatively small rock samples, and single cutters. Similarly, deep-hole drilling conditions can, to a large degree, be duplicated in single-cutter tests in the laboratory with test cells that measure single-cutter forces under elevated hydrostatic, confining, and pore pressures.5–7* Typical downhole rock types, cutter configurations, and cutting speeds can also be duplicated with these test cells.
A more difficult simulation is the cutter interaction that occurs on full-scale bits, where cutting forces on each cutter are reduced by the presence of previous cuts made by adjacent cutters. We have found in unconfined rock tests at atmospheric pressure that interaction does not occur unless the previous cuts are close enough laterally that they actually remove rock that would otherwise be removed by the test cutter. The cross-sectional area of rock removed by each cutter, therefore, seems to be the parameter that characterizes cutter interaction and that controls cutter forces.