Drilling–Equipment, Methods and Materials - Theory of Formation Cutting Using the Sand Erosion Process

The process of sand erosion has been harnessed to perform a useful function—the directed perforating of oilfield tubular goods and formation rock. In this process the sand is carried by a liquid medium and the resrrlting slurry is forced through a nozzle at an extren~ely high velocity. Upon impingement against casing or formation, the fast-moving sand particles erode a perforalion in the casing followed by cavity formation in the medium behind the casing. The many factors influencing the rate and extent of this penetration are inherently difficult to establish experimentally. Equations describing submerged jet behavior have been applied to these conditions. The following paper develops the equations for predicting the performance of the perforating jet. INTRODUCTION The cutting power of high-velocity sand has been well known in the petroleum industry for many years. Sand carried by a high-velocity gas stream causes severe erosion. This effect has been the cause of numerous production problems in certain areas. It was logical to expect that this phenomenon would one day be adapted to useful industrial applications. Development of mobile, high-pressure, high-horsepower pumping equipment in the last decade has made this possible. The sand erosion process involves pumping a fluid containing abrasive solids through a set of nozzles at a high differential pressure (2,000 to 4,000 psi). The pressure conversion into kinetic energy imparts high velocity to the sand particles which, upon impact with the formation face or casing wall, erode the material in an organized pattern. This paper attempts to establish the effects of the various parameters and to predict the performance and limitations of the process. The following factors will be considered: nozzle differential pressure, perforation size, sand concentration, nozzle stand-off distance and backpressure. In general, this discussion is presented along theoretical lines and is substantiated by field results and data where reliable field data exists. POWER EQUATIONS The penetration rate of a high-velocity hydraulic jet is proportional to the power or energy of the jet at the point in quesion. The power of the submerged jet will decrease with distance (or penetration) into the cavity created by the jet. As the cavity is extended into the formation, the power of the jet diminishes to a value equal to the threshold cutting power of the particular formation which is defiined as the lowest power level at which the formation will be abraded by the jet. Obviously, when this point is reached, no further cutting of the formation can occur. It is assumed that this power level for a particular formation is a function of the hardness of that formation. The following equation can be written for the hydraulic process of formation abrasion.