Dynamic Experiments On Proppant Settling In Crosslinked Fracturing Fluids
Authors: Harrington Larry J. , Hannah Robert R. , Williams Dennis 
Published: December 2007

Abstract
This paper discusses a study of sand fall characteristics of crosslinked water-based fracturing fluids using a concentric cylinder transparent tester with the inner cylinder rotating and outer cylinder stationary. Fracturing fluids containing proppants screened to a 20–25 mesh tolerance (U.S. series screens) were crosslinked in the fluid and both were introduced into the annular gap between the rotor and stator. Variable shear rates were then imposed upon the fluid/proppant combination and the settling velocity observed. Various polymer concentration gels were used as well as two polymer concentration gels were used as well as two proppant densities as represented by ordinary frac proppant densities as represented by ordinary frac sand and sintered bauxite.
It has long been observed that most crosslinked gels, when at rest, will support proppants perfectly without separation. When pumped through transparent fracture models at low velocities no measurable proppant separation occurs. These observations have proppant separation occurs. These observations have led some to assume that these fluids perfectly supported the proppant throughout a fracturing treatment and the success of many designs rest on this assumption. This assumption rests on two observations:Proppant fall rates in these fluids do not follow Stokes law for a non-Newtonian fluidat rest.The apparent lack of separation during a veryshort residence time in a transparent model.
The authors, in a previous paper, presented data on proppant fall rates in simple gels while being sheared between concentric cylinders. This data seemed to verify that the non-Newtonian form of Stokes law was valid for these fluids. This problem has also been addressed by Novotny using a similar tester.
The experiments performed in the preparation of this paper showed that a slow but measurable fall rate is present using these fluids. In general, when the log of the proppant fall rates of these fluids is plotted as a function of the log of the non-Newtonian apparent viscosity, a straight line results. This line is parallel with a similar plot of Stokes law but is some 78 percent lower. For the particular crosslinked gel studied, then an empirical constant can be used to predict particle fall rate.

Introduction
Shortly after the determination that fractures were primarily vertical, questions concerning proppant placement arose. These questions were motivated by the placement arose. These questions were motivated by the understanding that gravity would cause the separation of the proppants from the fluid due to the action of gravity and would result in the building of a bank or dune of the proppant in the bottom portion of the fracture. Original studies of this phenomena were performed by Kern, et al, in a transparent vertical performed by Kern, et al, in a transparent vertical clear plastic fracture model. The results of these experiments confirmed that separation and banking of the proppant did occur. These tests were primarily performed using Newtonian oils as the proppant performed using Newtonian oils as the proppant transport medium.
Non-Newtonian fluids of the gelled water type were addressed by Babcock, et al, using an apparatus similar to the Kern tester and formulated a theory based on both Newtonian and non-Newtonian fluids. Wahl investigated proppant transport in horizontal fractures and established that the proppant formed dunes similar to that formed in river beds.
The above experimental work led to the development of mathematical models that would predict the final location of proppants, both that which had settled and that still suspended, at treatment completion.
The introduction of crosslinked gels in the mid to late 1960's brought about an era of highly viscous fracturing fluids capable of delivering high sand concentrations into the fracture. These fluids are made by hydrating a base polymer, introducing sand to this gel, and adding a metal-ion crosslinking chemical. The addition of the metal-ion results in a gross increase in viscosity and with the ability when static to support high proppant concentrations without separation.