Flow of suspensions in a hydraulic fracture consisting of Herschel-Bulkley fluid and spherical particles

TL;DR

This study models the flow behavior of Herschel-Bulkley suspensions with spherical particles in a vertical channel, highlighting how non-Newtonian fluid rheology influences particle distribution, migration, and suspension dynamics under gravity and pressure gradients.

Contribution

It introduces a comprehensive model incorporating non-Newtonian rheology, particle migration, and slip effects to analyze suspension flow in hydraulic fractures.

Findings

Non-uniform particle distribution causes density variations and downward migration.

Fluid rheology significantly affects velocity profiles and particle fluxes.

Slip velocity and gravitational settling influence suspension stability and flow patterns.

Abstract

The purpose of this study is to develop a model for the flow of suspensions consisting of Herschel-Bulkley fluid mixed with spherical particles. In particular, the focus is to investigate the effect of non- Newtonian rheology of the carrying fluid on the flow behavior of a suspension. Two-dimensional steady flow problem in a vertical channel is considered, in which both the pressure gradient and gravity drive the suspension flow. Dependence of the velocity profile and particle concentration across the channel on the fluid rheology parameters and orientation of the pressure gradient is investigated. It is found that the non-uniform particle distribution in the flow across the channel leads to the non-uniform density of the suspension, which causes sinkage of the denser regions and promotes downward migration of the particles even without slip velocity. Particle and suspension fluxes are calculated for various fluid rheologies and pressure gradient orientations. The effect of slip velocity between the phases is added via filtration term that captures fluid flow once particles reach the maximum concentration and stall, and via the settling term that describes gravitational particle settling.