A Model of Non-Newtonian Slurry Flow in a Flat Channel with Permeable Walls

A shear-thinning slurry flow in a flat channel is modeled. A diffusive flux modeling approach that accounts for particle migration to the channel center is employed. Fluid leakoff through permeable channel walls is also taken into account. A number of calculation examples are presented for Newtonian and power-law suspensions, and two examples are given for Herschel-Bulkley slurries. Evolution of the cross-sectional solids concentration distribution along the channel is studied at different slurry system parameters. The calculations show a significant effect of particle stratification on the pressure gradient. The results demonstrate the importance of transverse particle transport in narrow, flat channels, and, therefore, this phenomenon should be accounted for in the modeling of different technological processes, such as proppant transport in hydraulic fracturing.