Dimensionless Methods for the Study of Particle Settling in Non-Newtonian Fluids
Authors: Jin Liang , Penny G.S. 
Published: December 2007

Summary
A systematic study of particle settling in polymer solutions and crosslinked gels used in the oil industry has been conducted. Friction factors obtained with failing sphere experiments and a newly developed direct drag force measurement technique are correlated to two dimensionless groups. One group is the Reynold's number, Re, defined by the steady shear rheogram of the test fluids. Another group, Nve, is defined by the viscoelastic parameters of the polymer systems. Unique methods of obtaining parameters for these two dimensionless groups are discussed and an algorithm for the prediction of particle settling is introduced.

Introduction

Definition of the Work
The transport and settling of particles in drilling and fracturing fluids are extremely important parameters to be considered in the successful completion of oil and gas wells. For that reason, many researchers have attempted to predict particle settling based on fluid properties provided by rheological models such as the power law model or the Bingham plastic model, where the rheological parameters are measured under steady shear conditions at moderate to high shear rates. Low shear viscosity as well as elasticity of borate crosslinked fluids in terms of G' has also been shown to correlate to static proppant settling. Recent work has shown that proppant transport can be accurately modeled when the effects of single particle settling, density driven flow, particle velocity profiles and slurry rheology are accounted for. The single particle setting velocity is important because it is used to predict the particle settling velocities in slurries based upon the shear rate and the volumetric solids loading. Single particle settling velocities are easily determined in clear time-independent fluids such as linear gels. However, when the fluid is crosslinked, the fluid changes with time making it difficult to obtain instantaneous settling velocities. de Kruijf et al. have shown settling velocities to vary by an order of magnitude depending upon the time after shearing and with exposed shear rate. Thus, a method of measuring properties to predict instantaneous settling velocities is needed to augment transport predictions.
The objectives of the work reported herein are threefold. The first objective is to systematically determine impact of viscous and elastic properties upon single particle settling. The second objective is to create a set of dimensionless relationships, which are capable of predicting settling over a broad range of fluid properties. Finally, the third objective is to provide a simple means of measuring fluid properties on shear history conditioned fluids in order to instantaneously predict settling behavior in time dependent fluids.
This paper begins with a discussion of dimensionless groups that relate the physical parameters involved in the settling process to the rheological properties of the test fluids. Experimental investigations are carried out to characterize the rheological properties of fluid systems with a range of viscous and elastic properties.