Settling of spherical particles in unbounded and confined surfactant-based shear thinning viscoelastic fluids: An experimental study Sahil Malhotra n , Mukul M. Sharma Petroleum & Geosystems Engineering, 1 University Station C0300, CPE 5.118, The University of Texas at Austin, Austin, TX 78712-0228, United States HIGHLIGHTS c Settling velocities of spheres in shear thinning viscoelastic fluids are measured. c Drag reduction at lower Weissenberg numbers (We) is observed. c This is followed by a transition to drag increase at higher We. c Elasticity is observed to reduce the effect of confining parallel walls. c New correlations to quantify settling velocities are presented. article info Article history: Received 26 March 2012 Received in revised form 10 September 2012 Accepted 17 September 2012 Available online 25 September 2012 Keywords: Settling velocity Shear-thinning Viscoelastic Weissenberg number Wall factor Reynolds number abstract An experimental study is performed to understand and quantify settling velocity of spherical particles in unbounded and confined surfactant-based shear thinning viscoelastic fluids. Experimental data is presented to show that elastic effects can increase or decrease the settling velocity of particles, even in the creeping flow regime. Experimental data shows that a significant drag reduction occurs with increase in Weissenberg number. This is followed by a transition to increasing drag at higher Weissenberg numbers. A new correlation is presented for the sphere settling velocity in unbounded viscoelastic fluids as a function of the fluid rheology and the proppant properties. The wall factors for sphere settling velocities in viscoelastic fluids confined between solid parallel plates are calculated from experimental measurements made on these fluids over a range of Weissenberg numbers. Results indicate that elasticity reduces the effect of the confining walls and this reduction is more pronounced at higher ratios of the particle diameter to spacing between the walls. Shear thinning behavior of fluids is observed to reduce the retardation effect of the confining walls. A new empirical correlation for wall factors for spheres settling in a viscoelastic fluid confined between two parallel walls is presented. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction and past work The free settling velocity of particles suspended in liquids is of importance in a wide variety of industrial applications. Slurries of solids suspended in fluids are widely used in applications ranging from semi-conductor processing to pharmaceutical manufacturing. In the oil industry, viscoelastic fracturing fluids are used to suspend proppants (typically sand) in hydraulic fractures. The proppants keep the created fracture open upon cessation of pumping. Settling of proppants is governed by the properties of proppants, rheology and density of fluid and the retardation effect of confining fracture walls. The settling velocity of single spherical particle in a Newtonian fluid in the creeping flow regime was first derived by Stokes in 1851, which is commonly referred to as the Stokes equation. Subsequent researchers studied settling at higher Reynolds numbers and presented expressions to calculate the drag force (Clift et al., 1978; Khan and Richardson, 1987; Zapryanov and Tabakova, 1999; Michaelides, 2002, 2003). The confining walls exert a retardation effect and reduce the settling velocities of particles. This effect is quantified in terms of a wall factor, F w , which is defined as the ratio of the settling velocity in the presence of confining walls to the unbounded settling velocity in the same fluid. Faxen (1922) pointed out that for Newtonian fluids, in the creeping flow regime, the wall factor depends only on the ratio of the particle diameter to the slot width, irrespective Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ces Chemical Engineering Science 0009-2509/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2012.09.010 n Corresponding author. Tel.: þ1 512 905 2837. E-mail addresses: sahilm@utexas.edu (S. Malhotra), msharma@mail.utexas.edu (M.M. Sharma). Chemical Engineering Science 84 (2012) 646–655