An Experimental Study of Indexed Dull Bit-Tooth Penetration Into Dry Rock Under Confining Pressure
Authors: Gnirk P.F. , Musselman J.A. 
Published: December 2007

Abstract
A study was made of indexed penetrations by a single dull bit tooth under statically applied loads into rock subjected to confining pressures from atmospheric to 5,000 psi and atmospheric pore pressure. Experimental results obtained with a 45 degrees wedge tooth over the above range of pressures are presented for two limestones and a sandstone, a variety of indexing distances and two degrees of tooth dullness. The optimum distance between successive bit-tooth penetrations required for maximum rock damage and chip formation decreases substantially with increasing confining pressure above the brittle-to-ductile transition pressure of a particular rock. However, the distance remains approximately constant for a variation in confining pressure below the transition pressure. At a given confining pressure, the bit-tooth force required for chip formation is constant for indexing distances greater than optimum, but generally decreases linearly with decreasing indexing distance for distances less than optimum. The chip-formation force data obtained at confining pressures for which the chip-generation mechanism is macroscopically of a pseudo plastic nature compare favorably with previous theoretical results for indexed dull bit-tooth penetration into an idealized, rigid, perfectly plastic rock.

Introduction
To study the cutting action of a roller-cone bit, the interaction of a penetrating bit tooth with craters formed in a rock surface by the passage of previous bit teeth must be considered. Current knowledge of the basic mechanics of bit tooth-rock interaction under simulated borehole environmental conditions has been extensively reviewed. Particularly of current interest are the effects of bit-tooth shape, distance between successive penetrations and differential pressure at the rock surface on the extent of the interaction. Pertinent to this paper are results of an experimental investigation of the interaction between successive penetrations by sharp, wedge-shaped bit teeth. It was demonstrated that both bit-tooth angle and differential pressure influence the extent of rock damage between successive bit-tooth penetrations. Specifically, the optimum or minimum distance between successive penetrations required for maximum interaction or chip generation tends to decrease with decreasing bit-tooth angle and increasing differential pressure. In addition, at differential pressures on the order of 2,000 psi for four varieties of limestones and sandstones, the macroscopic mechanism of chip formation exhibits a transition from brittle to ductile. In this paper, experimental consideration is given to successive or indexed penetrations by wedge-shaped bit teeth. Since pore pressure in a rock sample is maintained at atmospheric pressure, the differential pressure at the fluid-rock interface is equal to the confining pressure. The degrees of bit-tooth dullness include teeth with flat and round apexes (Fig. 1). Of primary concern in this paper are the bit-tooth forces required for chip formation, the macroscopic mechanism of chip formation and the minimum distance between successive penetrations, i.e., optimum indexing distance required for maximum rock damage as functions of differential pressure. Of further interest is a comparison of actual bit-tooth chip formation forces at elevated differential pressures with calculated forces from previous theoretical results for indexed dull bit tooth penetration into a rigid-plastic rock.

EXPERIMENTAL APPARATUS AND PROCEDURE
The experimental apparatus consists of a pressure vessel equipped with a piston through the side of the vessel (Fig. 2). A single bit tooth inserted in the lower end of the piston is forced at a desired rate into the rock when the ram pressure chamber is pressurized. Electrical instrumentation incorporated into the apparatus yields a graphical plot of force on the piston as a function of bit-tooth penetration or displacement into the rock. Since the piston and ram assembly are in force equilibrium for a constant, confining pressure in the main vessel, the fluid volume in the vessel remains constant during bit-tooth penetration.