Granular and Packed Beds

Flow through granular and packed beds occurs in reactors with sohd catalysts, adsorbers, ion exchangers, filters, and mass transfer equipment. The particles may be more or less rounded or may be shaped into rings, saddles, or other structures that provide a desirable ratio of surface and void volume. 

Natural porous media may be consolidated (solids with holes in them), or they may consist of unconsolidated, discrete particles. Passages through the beds may be characterized by the properties of porosity, permeability, tortuosity, and connectivity. The flow of underground water and the production of natural gas and crude oil, for example, are affected by these characteristics. The theory and properties of such structures is described, for instance, in the book of Dullien Porous Media, Fluid Transport and Pore Structure, Academic, New York, 1979). A few examples of porosity and permeability are in Table 6.9. Permeability is the proportionality constant k in the flow equation u = kip) dPjdL. 

Although consolidated porous media are of importance in chemical engineering, only unconsolidated porous media are incorporated in process equipment, so that further attention will be restricted to them. 

Granular beds may consist of mixtures of particles of several sizes. In flow problems, the mean surface diameter is the appropriate mean, given in terms of the weight fraction distribution, Xi, by 

When a particle is not spherical, its characteristic diameter is taken as that of a sphere with the same volume, so that 

Direct application of these equations in Example 6.14 is not successful, but if El is taken as the reciprocal of the given expression, a plausible result is obtained. 

Natural porous media may be consolidated (solids with holes in them), or they may consist of unconsolidated, discrete particles. Passages through the beds may be characterized by the properties of porosity, permeability, tortuosity, and 

TABLE 6.7. Two-Phase Flow Correlations of Pressure Drop 

Whalley, cited by G.F. Hewitt, 1982). 2. [Lockhart and Martinelli, Chem. Eng. Prog. 45,39-48 (1949) Chisholm, Int. J. Heat Mass Transfer 10,1767-1778 (1967)]. 3. [Chisholm, Int. J. Heat Mass Transfer 16,347-348 (1973) Baroczy, Chem. Eng. Prog. Symp. Ser. 62,217-225 (1965)]. 4. (Friedel, European Two Phase Flow Group Meeting, Ispra, Italy, Paper E2,1979, cited by G.F. Hewitt, 1982). 

A long-established correlation of the friction factor is that of Ergun (Chem. Eng. Prog. 48, 89-94, 1952). The average deviation from his line is said to be 20%. The friction factor is 

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Granular and Packed Beds 117 Single Phase Ruids 117 Two-Phase Flow 118... 

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 quahtative 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. 

Flow of Fluids Through Granular Beds and Packed Columns... 

FLOW OF FLUIDS THROUGH GRANULAR BEDS AND PACKED COLUMNS... 

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