The viscous resuspension of particles in an inclined rectangular fracture

Abstract

It has recently been observed that in laminar shear flows settled particles within a suspension can be resuspended. This phenomena, known as “viscous resuspension”, if properly exploited can have a beneficial effect on the process of proppant placement within a hydraulic fracture. By taking advantage of viscous resuspension effects it is possible to entrain particles from a settled bed back into the bulk shear flow which will enable them to be convected deep into the fracture channel and thus avoid the possibility of fracture closure. In practice the sedimentation/resuspension processes usually consist of rigid spherical negatively buoyant particles, which are of approximately equal size and density and do not aggregate, settling at very small particle Reynolds numbers from a suspension comprised of an incompressible Newtonian fluid. In this paper the particle concentration equation is solved initially for a fully developed steady one-dimensional gravity-driven flow down an inclined channel. The problem is then developed by adding a pressure-driven flow across the inclined channel. The concentration, momentum and conservation of mass equations have been solved numerically under a wide variety of operating conditions and initial feed particle concentrations, and typical concentration and velocity profiles at various angles of inclination of the channel and strengths of cross flow are presented.