Velocities, Kinetic Energy and Shear in Crossflow Under Three-Cone Jet Bits
Authors: McLean R.H. 
Published: December 2007

Abstract
Velocity, kinetic energy and shear in crossflow beneath three-cone jet bits may influence cleaning of the bottom of the borehole and the teeth of the bit. Laboratory investigation shows that each of these parameters is a function of the diameter of the borehole and the product of the volume rate of flow and velocity through the nozzles (QVn). Increasing QVn or decreasing the diameter of the borehole increases each parameter. These functions provide means of predicting the magnitude of each parameter and of scaling the cleaning forces.
Introduction
In drilling operations using conventional jet-type rock bits, the impinging jets create an important flow mechanism. Called crossflow, this flow mechanism originates in the impact area of the jets, spreads across the bottom of the hole and supplies the principal source of energy to clean the teeth of the bit and most of the bottom. Besides providing the means of cleaning cuttings from the bit and the hole bottom, crossflow may also have other, less direct, effects on the rate of penetration. The shear stress generated on the bottom by crossflow will influence the thickness and permeability of any fitter cake of mud solids or crushed material which forms on the bottom. These factors may affect the rate of penetration. A previous publication introduced some fundamental concepts of crossflow. Crossflow was shown to occur in a thin layer adjacent to the bottom, and to cover the bottom completely. The maximum velocity in the crossflow above any position on the bottom was found to be directly proportional to the square root of the product of the volume rate of flow and velocity through the nozzles the jet QVn and inversely proportional to the diameter of the borehole. This information indicated that the effectiveness of crossflow in scavenging the bottom can be improved by maximizing the jet QVn. The investigation reported herein amplifies the definition of crossflow. Complete velocity profile data above a representative position on the bottom are analyzed. These data better illustrate control of the capacity of crossflow to scavenge the bottom, and also relate shear stress on the bottom to known, controllable parameters. The conclusion reached in the previous publication that maximization of the jet QVn produces the maximum cleaning beneath current jet bits is unchanged by these new data; rather, it is strengthened. Data presented here show that the kinetic energy flux above a representative position on the bottom is maximized by maximizing the jet QVn. The shear stress on the bottom will also be shown to be maximized in the same manner. Since the functions relating the jet QVn to velocity, shear stress and kinetic energy also involve the diameter of the borehole, means of equating, or scaling, these quantities in different sizes of boreholes will be illustrated.
EXPERIMENTAL EQUIPMENT AND TECHNIQUE
JET BIT MODEL
Data were recorded from the same laboratory model as used in the aforementioned investigation of the flow around a jet bit. The model consisted of a 4 3/4-in. three-cone, jet-type rock bit in a smooth, flat-bottomed borehole constructed of lucite. The bit had a shape and nozzle placement closely resembling larger three-cone jet bits commonly used in field operations. Fig. 1 illustrates the impact area on the bottom of a jet from this bit. Details of the orientation of the jets may be found in the previous publication.
TECHNIQUE OF MEASUREMENT
Measurements of the crossflow were made by inserting a very small Pitot tube through the bottom of the simulated borehole. Extreme thinness of the layer of crossflow necessitated accurate measurements of the height of the Pitot tube above the bottom to achieve close definition of the velocity profile. A cathetometer, which could be read to the nearest 0.005 cm, was used to make this measurement.
JPT
P. 1443ˆ