In  we have developed a modified three-layer model for solid-liquid flow in horizontal pipes, 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. The steady-state model predictions show very good agreement with experimentally measured results in the literature.
In this paper we extend the steady-state three-layer model to annular geometries and apply it to the design of open-hole gravel packing operations, in the typical parameter ranges of gravel packing operations for alpha wave placements. Alpha wave design is a key factor for successful gravel packing, and the models typically used are either based on small-scale experiments or are not specifically developed for gravel packing, e.g. cuttings transport models. In gravel packing the hydraulic configuration is slightly different. We explain how bed height is selected via coupling between the inner and outer annuli and from the outer annulus hydraulics. We investigate the effects of important parameters such as the slurry flow rate, mean solids concentration, wash pipe diameter, etc. on gravel packing operations.