Experimental and Numerical Modeling of Convective Proppant Transport(includes associated papers 31036 and 31068 )
Authors: Barree R.D. , Conway M.W. 
Published: December 2007

Abstract
Slurry transport and settling experiments were conducted to improve current descriptions of proppant transport. Results of these experiments were used to formulate a new slurry transport model which was incorporated in a fully three-dimensional fracture simulator. The model was tested and verified against experimental observations of slurry transport in a 4 foot by 16 foot slot model. Results of the study indicate that proppant slurry transport can be accurately modeled when the effects of single particle settling, density driven flow, particle velocity profiles, and slurry rheology are accounted for.

Introduction
It has been a long-sought goal in hydraulic fracturing technology to accurately predict proppant slurry transport in non-Newtonian fluids. Numerous references exist in the petroleum literature describing various aspects of particle and slurry transport.
In the earliest studies relating to hydraulic fracturing applications, Kern and Perkins investigated sand transport in low viscosity fluids. They concluded that transport relies on high frontal velocity of the fluid and that rapid sedimentation of sand creates an immobile "dune" along the bottom of the fracture which restricts the fracture height open to flow. This leads to high local fluid velocities and establishment of an equilibrium sand bed height.
Other authors reported observing significant settling and less than perfect transport in both horizontal and vertical fractures. These studies, conducted in 1965-67, included the effects of particle size, drag coefficient, density, velocity, viscosity, and fluid yield point. The authors concluded that settling and particle segregation occur even in horizontal fractures and that the dense slurry accumulated on the bottom of the crack remains mobile but has a lower velocity than the average fluid speed.
In 1977, Novotny reported results of proppant transport studies conducted with non-Newtonian fluids. These observations showed that particles occupy different positions across the width of a vertical fracture at various shear rates and solids loadings. He also reported that particle settling rate is strongly influenced by fluid shear rate and the presence of the fracture walls.
In the same year Clark, et al, used a large scale slot flow model similar to that employed in this study to investigate proppant settling velocities after shut-in. These studies concluded that particle dusting can result in an increased settling velocity. The results presented were preliminary and did not address bulk slurry movement.
At about the same time Hannah, Harrington, and others utilized a cylindrical flow cell to study single particle settling rates in non-Newtonian fluids while under representative shear. They concluded that Stoke's Law can be applied, but may need to be modified by inclusion of an additional term to account for crosslinked fluid behavior.
These conclusions were partially supported by later work which indicated that single particle settling in crosslinked fluid depends on more complex parameters than just fluid viscosity.