Independent from their intended purpose, the understanding of structural characteristics of random packings of particles having defined shapes is important to understand and optimize fluid dynamic behaviour, heat, and mass transfer. The packing structure can be described by the coordination number, local porosity profiles, the average porosity, and pore characteristics, which are influenced by the wall and thickness effect; the material, shape, and size distribution of the packing particles; the packing and compaction mode; and the shape and material of the packing's containing walls. Therefore, existing knowledge on the structure of randomly packed mono-sized particles is reviewed to provide an updated selection of relevant parameters and their derived correlations obtained by experimental, numerical, and analytical means.packed-bed reactor, porosity, random particle packings, review, structure
| INTRODUCTIONRandom packings of particles having defined shapes are deployed in all kinds of industrial applications and come in all orders of magnitude. The most prominent examples comprise micro-sized particle beds as commonly used in chromatography packed columns, [1][2][3] packed-bed reactors filled with catalytic shaped bodies having millimetre size, [4,5] packed columns used in separation processes such as distillation incorporating particles in the lower centimetre range, [6,7] and the pebble-bed reactor, which is a gas-cooled nuclear reactor, moderated by a packing of graphite spheres. [8][9][10] In addition to those, numerous less-known applications of packed-beds exist, ranging from powder-bed 3D printers, [11] solar-energy storage systems, [12] earth science, [13] civil engineering, [14,15] and pharmaceutical processing, [16] to the pyrolysis of pelletized wood fuels, [17] to name but a few.Irrespective of its intended purpose, the extent of a packed-bed is limited by a confining wall of commonly cylindrical shape, though flat plates and other container geometries are possible. Despite its generally random nature, close to this confinement the particles' placement is naturally forced to align with the wall's geometry. This imposed order reaches a couple of particle diameters into the packing and is usually named the wall effect. Its influence on the overall packed-bed characteristics decreases with increasing tube-to-particle diameter ratio λ = D d p . While most applications operate in an only sparsely affected λ-range, this effect becomes dominant, for instance, in catalytic multitubular reactors, typically performing at λ = 4-7 [18] or a single-pellet-string reactor with a λ < 2. [19] Moreover, some packed-bed utilizations, especially chromatography columns, have very delicate requirements regarding bed homogeneity and its derived characteristics.Abbreviations: DEM, discrete element method; Erfc, error function; J 0 , Bessel function of first kind and zero order; MRJ, maximally random jammed; RCP, random close packing; RLP, random loose packing.