Analytical and numerical study of mean porosity variations in annular packed beds of spherical pellets

Abstract

Annular packed beds are used in pebble-bed nuclear reactors, annular membrane reactors for hydrogen production and annular chromatography columns, yet, unlike the cylindrical geometry, no validated model predicts their mean porosity across a wide range of confinement ratios, and the only available correlation was calibrated from a single experimental point. This study uses rigid-body simulation (RBS) to generate annular packed beds of spherical pellets at 52 confinement ratios between 2.25 and 15, with three independent realizations each and a fixed inner radius-to-particle diameter ratio of 2. The generation procedure is validated against annular experimental data comprising an unadjusted radial porosity profile and an independent mean porosity measurement. The mean porosity oscillates non-monotonically with a decaying amplitude, and the first extremum interval is markedly shorter than the subsequent ones. A layer-stacking analytical framework, previously developed for cylindrical beds, is extended to the annular geometry through circular monolayer, zig-zag monolayer and two-coupled-rows regimes, with the first transition located analytically at a confinement ratio of approximately 2.74. The model reproduces the simulated mean porosity within its domain and explains its largest deviation through a nesting threshold at $2+\sqrt{3}\approx 3.73$, the annular counterpart of the cylindrical threshold. Beyond this domain, an empirical correlation combining a damped oscillation with a quadratic decay envelope describes the full range with a coefficient of determination of 0.970, against 0.690 for the existing annular correlation. These models provide the mean porosity required by pressure drop and transport models for annular reactors and columns.