Fixed Beds of Granular Solids

Dp = average particle diameter, defined as the diameter of a sphere of the same volume as the particle e = void fraction 

Porous Media Packed beds of granular solids are one type of the general class referred to as porous media, which include geological formations such as petroleum reservoirs and aquifers, manufactured materials such as sintered metals and porous catalysts, burning coal or char particles, and textile fabrics, to name a few. Pressure drop for incompressible flow across a porous medium has the same qualitative behavior as that given by Leva s correlation in the preceding. At low Reynolds numbers, viscous forces dominate and pressure drop is proportional to fluid viscosity and superficial velocity, and at high Reynolds numbers, pressure drop is proportional to fluid density and to the square of superficial velocity. 

Creeping flow (Re 1) through porous media is often described in terms of the permeability k and Darcy s law  

For isotropic homogeneous porous media (uniform permeability and porosity), the pressure for creeping incompressible single phase-flow may be shown to satisfy the LaPlace equation  

For granular solids of mixed sizes the average particle diameter may be calculated as 

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Fixed Beds of Granular Solids Pressure-drop prediction is complicated by the variety of granular materials and of their packing arrangement. For flow of a single incompressible fluid through an... 

Among the unit operations, adsorption may be considered a prototype for all fluid-solid separation operations. When it is conducted under countercurrent conditions, the calculation methods required are entirely analogous to those for countercurrent absorption or extraction (H3). Often, however, it is most economical to conduct adsorption in a semi continuous arrangement, in which the solid phase is present as a fixed bed of granular particles. The fluid phase passes through the interstices of this bed at a constant flow rate and for an extended period of time. The concentration gradients in the fluid and solid phases display a transient or unsteady-state behavior, and their evolution depends upon the pertinent material balances, rates, and equilibria. 

The fixed beds of concern here are made up of catalyst particles in the range of 2-5 mm dia. Vessels that contain inert solids with the sole purpose of improving mass transfer between phases and developing plug flow behavior are not in this category. Other uses of inert packings are for purposes of heat transfer, as in pebble heaters and induction heated granular beds—these also are covered elsewhere. 

Sofnolime RG. This process, which is licensed by Molecular Products Ltd., UK, uses fixed beds of an alkaline granular solid called Sofnolime RG. The material is claimed to be a synergistic mixture of hydroxides that reacts with acid gases such as H2S, COS, CO2, SO2, and RSH. Typical reactions are... 

Deep bed or granular batch, for 0.01 to 50 J,m (see filter. Section 16.11.5.13). Fixed bar screen batch, grizzly (the filter cloth is made of rods and bars) removal of very coarse material of diameter >2 to 5 cm low concentration of solids <15 mg/L bars at 30 to 60° to the horizontal that can be cleaned manually or automatically. Microscreen (rotary drum or disk). Batch, removal of participles of diameter >20 jm 20 mg/L solids feed concentration. 

According to the previous chapters the reader may come to the conclusion that countercurrent columns are dominant as has been shown for mass transfer equipment used in the areas of rectification, absorption, and extraction. However, this is not true because the continuous transport of solid granular material is much more difficult in comparison to a fluid. Therefore, nearly all adsorbers are fixed beds which are operated batchwise. As a rule, at least two fixed beds are installed in continuously operated industrial processes. The first bed is used for the adsorption step whereas in the second the adsorbates is removed or desorbed at the same time. The duty of the two beds is changed when the adsorption capacity is exhausted. Sometimes several beds are arranged to cany out pressurization and depressurization steps. 

Kitagara ° nsed two commercial granular activated carbons for the adsorption of phenol, p.nitrophenol, and 2,4 dichlorophenol from aqueous solutions, and found that the adsorption data could be explained by the Freundlich isotherm equation. The adsorption at a given concentration decreased with increase in the temperature of adsorption, although the rate of adsorption increased with increase in the adsorption temperature. Scharifov derived a mathematical model for the adsorption of phenols by activated carbons from aqueous solutions and obtained an equation for the static adsorption isotherm, which could help in the calculation of adsorption of phenol at any concentration. Chakravorti and Weber used batch and fixed-bed systems for the removal of phenol from aqueous solutions by activated carbons. The pore-diffusion model and a homogenous solid model were used to explain the results. 

Knowing 0, the solid phase pressure and the solid phase bulk and shear viscosities can be calculated from formulae derived by Tun et al. [1984]. The granular temperature conductivity, k, has also been formulated by Tun et al. [1984]. y has been modeled in terms of 0 by Jenkins and Savage [1983]. For dense regimes, the interphase momentum transfer coefficient, / , can be calculated from the Ergun equation already encountered in Chapter 11 on fixed bed reactors [Gidaspow, 1994]. For dilute regimes, a correlation has been proposed by Wen and Yu [1966]. 

For process engineering purposes, the type of reactor needed for a specific reaction usually determines the shape and texture of catalytic solid materials, which in turn, may influence inter- and intra-particle transport phenomena effecting catalyst performance. Most frequently, packed-fixed-bed, fiuidized-bed, slurry-phase, and membrane reactors are used, which require different particle and pore sizes, shapes, specific surface areas, crushing and abrasion strengths (e.g. pellets, extrudates, spherical and granular particles, powders). Although these aspects play a vital role in the final preparation process for use of the catalysts in a pilot plant and later on in a commercial process plant, they are not discussed in this monograph, which focuses on the catalytic performance of a... 

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