Sand Particle Transport in Perforated Casing
Authors: Haynes C.D. , Gray K.E. 
Published: December 2007

From the study reported here it was concluded that the sand-transporting efficiency of water increases (at a diminishing rate) with an increase in flow rate, but varies inversely with solids concentration and particle size over a wide range of flow rates. It was also concluded that transport efficiency is probably not affected by perforation pattern alone.

Introduction
The topic of formation sand control is known by all petroleum engineers, and the problems associated petroleum engineers, and the problems associated with the production of sand in oil, gas, and water wells have been studied extensively. Examples of approaches to these problems include work concerning the arching behavior of sand grains, consolidating chemicals, combustion techniques, and soil mechanics theory.An important aspect of sand control that has received inconsistent study is sand prepack operations, in which mixtures of sand and liquid are pumped down the well. Often, these sand grains must be transported through casing perforations (Fig. 1). Although the art of sand prepacking is a matter of routine in many oilfield operations, knowledge is scarce concerning the behavior of these sand grains in the fluid stream as they approach casing perforations. One reason for this scarcity of knowledge is that it is extremely difficult to apply a mathematical approach in expressing the behavior of solid particles in a liquid. The added difficulty of expressing fluid turbulence and the physical configuration of casing and perforations by mathematical models makes it almost perforations by mathematical models makes it almost impossible to completely solve the problem unless many simplifying assumptions are made. Particle trajectory studies have been made under these simplified conditions, but the results cannot be conveniently applied to specific down-hole configurations as encountered in petroleum operations. Experimental techniques may eliminate most of the problems associated with analytical treatment; but to simulate the field operation in a realistic manner, a considerable investment in laboratory equipment is required. Experimental techniques were deemed to have more direct application to this investigation, and were designed to minimize scale-up factors when applied to sand-pack operations.

Basic Considerations
The problem of determining whether a sand particle will be transported by the carrier fluid into the perforation or whether it will settle below the perforation or whether it will settle below the perforation essentially depends on the relative magnitudes of perforation essentially depends on the relative magnitudes of particle inertia and fluid drag. The inertia of the sand particle inertia and fluid drag. The inertia of the sand particle causes it to resist following the fluid paths particle causes it to resist following the fluid paths into the perforation. Fluid drag, however, tends to move the particle in the direction of flow. The shape of the particle and the turbulence level of the fluid determines the extent of extraneous particle movement along the primary direction of travel.Two extremes of particle transport are obvious by intuition:1. No sand particles are transported into the perforations at zero flow rate, since the fluid is not perforations at zero flow rate, since the fluid is not directed toward the perforations, and drag forces in the horizontal direction are zero.2. Nearly all particles are transported when the viscosity and flow rate are sufficiently high to prevent particle settling. High viscosity and high flow rate particle settling. High viscosity and high flow rate maximize the fluid drag and minimize particle inertia.
JPT
P. 80