Review on the structure of random packed‐beds

Abstract

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.

Local Structure Effects on Heat Transfer in Very Low Tube-to-Particle Diameter Ratio Fixed Beds of Spheres

“…In a recent comprehensive review of random packed bed structure, von Seckendorff et al bring together much literature data for the radial void fraction profile in packings of spheres. 18 They compared both oscillating and exponential forms of correlations for the range N > 5 and noted the difficulty of getting the correct oscillation period. They also reviewed correlations and data for the bed average void fraction ε and presented plots of ε against N. They remarked on the presence of local extrema for specific values of N. In a further study, 19 von Seckendorff et al compiled ε values from their own computergenerated results, from the experiments of Pottbacker et al 20 and from the theoretical work of McGeary, 12 and presented a very revealing plot for the range 1 ≤ N ≤ 6.…”

“…In a recent comprehensive review of random packed bed structure, von Seckendorff et al bring together much literature data for the radial void fraction profile in packings of spheres . They compared both oscillating and exponential forms of correlations for the range N > 5 and noted the difficulty of getting the correct oscillation period.…”

Experiments and simulation of liquid drainage in oscillating packed beds under roll and heave motions

“…[11,34] Alternative porosity models are also available and thoroughly discussed in the recent review article by von Seckendorff and Hinrichsen. [35] To confront the model output to the wire-mesh liquid saturation measurements, the simulated total liquid holdup was converted into simulated reduced freedraining liquid saturation after subtracting the static liquid holdup, ε stat , estimated with the Saez and Carbonell correlation [36] :…”

Issue Highlights

“…Thus, effects induced by a confining wall; a short bed height; particles' shape, size, and material; and their packing and compaction methods are studied and expressed in variations of particles' contact number and distribution, void or porosity content and its distribution, and pore characteristics. [8]…”