The Effect of Nozzle Size, Number, and Extension on the Pressure Distribution Under a Tricone Bit
Authors: Sutko A.A. , Myers G.M. 
Published: December 2007

Laboratory surveys of bottom-hole pressures under a tricone bit when one, two or three nozzles are used indicate that hole cleaning and drilling rate should improve as the number of nozzles is decreased. Tests also show that these should improve as the length of the nozzle is increased.

Introduction
Minimum-cost well drilling demands the best possible use of the time and energy involved. One place where much energy is expended is at the bit. As the mud flows through the nozzles, across the bottom of the hole, and starts back toward the surface, friction and turbulent mixing dissipate a large amount of energy. In any general attempt to cut drilling costs, this part of the operation must be considered important. part of the operation must be considered important. There is no universal agreement as to what are the most important factors at and below the bit. Present-day ideas on this subject have come to us either from jet hydraulics studies or indirectly from other studies such as of rock mechanics.
With regard to jet hydraulics studies, Kendall and Goins have outlined hydraulics programs for maximum jet velocity, maximum jet impact, and maximum jet horsepower. They did not define which of these has the greatest effect on drilling rate. Van Lingen found that drilling rates increased if the bit nozzles were extended toward the bottom of the hole. Feenstra and van Leeuwen showed that, for impermeable rock drilling, increasing the jet velocity influences drilling rate more than increasing the flow rate. Both of these laboratory studies were made with a full-size bit. Using a microbit and low-permeability rock, Eckel has shown that drilling rate is a function of a Reynolds number involving flow rate, nozzle diameter, and fluid density and viscosity. He has also concluded that for a given viscosity drilling rate is not related to the mud solids content or the fluid loss.
All of the studies mentioned thus far suggest that jet velocity plays an important role in establishing the drilling rate. Feenstra and van Leeuwen state "jet action" (a more inclusive term than jet velocity) keeps the bit teeth and hole bottom clean and overcomes the "chip hold down effect." In a more basic study, McLean measured the impact pressure and crossflow on a simulated hole bottom under a jet bit. Concluding that crossflow (velocity) was the more important, he determined the relationship between crossflow and vertical velocity distribution, kinetic energy flux, and shear stress. All of these, he says, may have an effect on the cleaning of the hole bottom and the bit teeth.
The works of Maurer and Myers show that bottom-hole pressure has an effect on drilling rate. They found pressure has an effect on drilling rate. They found that as the difference between the mud pressure and the formation pressure increases the bit tooth forms a smaller crater. From this it appears that drilling rates should decrease as this pressure difference increases. Field data indicate that this is not universally true.
Considering the evidence presented thus far, it is apparent that the fluid velocity through and beyond the nozzles and the pressures existing at and near the bottom of the hole both play important roles in the drilling process. Our goal, then, is to study the bottom-hole pressure distribution as it is affected by nozzle velocity and to demonstrate the influence of different nozzle sizes, extensions, and numbers.
JPT
P. 1299