Hydraulic Jetting - Some Theoretical and Experimental Results
Authors: Pekarek J.L. , Lowe D.K. , Huitt J.L. 
Published: December 2007

Abstract
In a theoretical study of hydraulic jetting, the velocity of the abrasive material relative to the velocity of the fluid in the jet stream is analyzed as the jet stream moves through the convergent and straight sections of the nozzle and the region between the nozzle exit and target. the results revealed that the abrasive material exits from the jet nozzle at a lower velocity than the fluid. The exit particle velocity can be increased by increasing either the density of the fluid or the length of the nozzle, and/or decreasing either the particle density or particle diameter. In the divergent jet stream, there exists a point after which the particle velocity exceeds that of the fluid. the relative velocities were considered in the derivation of an equation to predict cutting rate of a circumferential notch and maximum notch depth. Data of a general nature and data which substantiate the theoretical results were obtained experimentally.

Introduction
The use of a fluid containing an abrasive material has been an established technique for cleaning and cutting for many years. In the petroleum industry, the early effort to use this technique to perforate and/or to overcome wellbore damage met with only limited acceptance because of the short life of the jet nozzle. With the introduction of improved perforating techniques, and later, hydraulic fracturing, the use of hydraulic jetting as a well completion technique became even less appreciated. It was only in recent years that interest in hydraulic jetting was revived. Once this interest was revived, the results of surface tests stimulated the interest of the industry even more than the state of the technology probably warranted because many of the tests were not appropriate for down-hole conditions. However, because of the stimulated interest, the development of the jet nozzle progressed very rapidly to the point where the nozzle life was no longer a problem. With this accomplished, the use of hydraulic jetting in well completion became an accepted practice in a short time. The purpose of this paper is to present a theoretical analysis of the hydraulic jet stream as it passes through the nozzle and travels to its target. With a better understanding of the jet stream and the effects of various parameters, the performance of the process can be predicted more accurately. Equations are presented for cutting rate as applied to circumferential wellbore notching that relate the jet stream make-up, notch configuration and formation material. Also, experimental data are presented on some factors pertinent to hydraulic notching that are not theoretically analyzed.

RELATED STUDIES
Most of the studies reported in the recent literature have pertained to the more practical aspects of hydraulic jetting; i.e., the effects of certain parameters as interpreted from experimental results, and the application of hydraulic jetting in well completion. In reviewing the effects of various parameters, it is interesting to note the reported depths of penetration obtained under various imposed conditions. In general, the depths vary from a few inches to several feet; however, a depth of penetration of less than 6 in., as reported by Thompson, seems more realistic for the usual field practice of hydraulic jetting with sand in water for a period of 20 to 30 minutes. In addition to the practical aspects, the study of Brown and Loper included a theoretical approach to hydraulic jetting. Their study resulted in the development of a theoretical expression for the maximum depth of penetration if jetting were continued for an infinite time. An analysis of the equations presented reveals that the initial cutting rate is infinite. The equation expressing centerline velocity is that of Forstall and Gaylord, which is applicable for a jet stream exiting in a large stationary medium. Since practically all of the fluid pumped into a perforation (or cut) must flow back through the perforation prior to re-entering the wellbore, a description of the medium as finite and nonstationary seems more reasonable.
JPT
P. 101^