A three layer model for solids transport in pipes

Abstract

A modified three-layer model for solid-liquid flow in inclined pipes is developed, which overcomes the limitations of previous mechanistic models. The steady-state model predicts the pressure loss, critical velocity, concentration profile in the heterogeneous layer, mean heterogeneous layer and moving bed layer velocities, and bed layer heights for each set of parameters. We propose a new correlation for the turbulent solids diffusivity, and include appropriate closures for forces and stresses attributed to the solids and liquid phases in the different layers. The proposed turbulent solids diffusivity correlation and the steady-state model predictions show a good agreement with experimentally measured results in the literature: for concentration profiles in the heterogeneous layer, pressure losses and critical (deposition) velocity, both over a wide range of parameters and for different regimes. We also define a critical Péclet number based on which, a transition boundary between bed-load and heterogeneous regimes can be found. This boundary implicitly represents the critical velocity. In turbulent flow, the pressure loss vs mean velocity curve shows a characteristic minimum just before the critical velocity is attained, in agreement with published research.