Voidage packed beds

TABLE 13.1 Packed Bed Voidage for Different Packing Arrangements... 

Hence, since the bed depth H, the water viscosity p and the packed bed voidage e may be assumed constant, then (—Ap) plotted against U should give a straight line of gradient... 

In order to obtain a value of U f from Equation (7.7) we need to know the voidage of the bed at incipient fluidization, e = emf- Taking mf as the voidage of the packed bed, we can obtain a crude LTmf- However, in practice voidage at the onset of fluidization may be considerably greater than the packed bed voidage. A typical often used value of ,f is 0.4. Using this value. Equation (7.7) becomes... 

Knowing the required pressure gradient, the packed bed voidage and the particle and gas properties. Equation (8.25) can be solved for Llrei, the magnitude of the relative gas velocity ... 

The total voidage i in a packed bed (outside and inside particles) is... 

The Rowe-Claxton empirical equation has been found to conform to many experimental studies of heat transfer in a packed bed, such as the reactor typically used in the catalytic processes described earlier. It is first necessary in this situation to define die voidage of the system, AV, where... 

Note that the abscissa in Figure 2.4 starts at a value of 0.4, which corresponds to the voidage of a randomly packed bed. Equation 2.44 is valid for the extremes of flow regimes but strictly requires correction for the intermediate case (Khan and Richardson, 1990 Di Felice, 1994). 

Fluidised beds have been used previously for the industrial-scale recovery of the antibiotics streptomycin and novobiocin.30 However, more recently, considerable interest has been shown in the use of fluidised beds for the direct extraction of proteins from whole fermentation broths.31 In a packed bed, the adsorbent particles are packed within the contactor. The voidage, that is, the inter-particle space, is minimal and thus feedstock clarification is mandatory to avoid clogging of the bed. In a fluidised/expanded bed, the adsorbent bed is allowed to expand by irrigation with feedstock. Bed voidage is increased, allowing the passage of particulates in the feed. The diameters of the adsorbent beads are exaggerated for illustrative clarity. 

Before the bed can become fluidized, however, the particles must dislodge from their packed state, which expands the bed. Thus, the porosity (s) in Eqs (14-5) and (14-9) is not the initial packed bed porosity but the expanded bed porosity at the point of minimum fluidization ( ml ), i.e., the minimum bed voidage in the bed just prior to fluidization. Actually, the values of C and C2 in Eq. (14-8) that give the best results for fluidized beds of uniform spherical particles have been found from empirical observations to be ... 

In a packed bed of unit volume, the volumes occupied by the voids and the solid particles are e and (1 — e) respectively where e is the voidage fraction or porosity of the bed. Let S0 be the surface area per unit volume of the solid material in the bed. Thus the total surface area in a packed bed of unit volume is (1 — e)S0. 

If n ranges from 2.4 to 4.8, there should be a point of inflexion in the curve occuring at values of e between 0.41 and 0.65, corresponding to very high concentrations (C = 0.59 to 0.35). It may be noted that the point of inflexion occurs at a value of voidage e below that at which the mass rate of sedimentation x/r is a maximum. For coarse particles (n 2.4), the point of inflexion is not of practical interest, since the concentration at which it occurs (C 0.59) usually corresponds to a packed bed rather than a suspension. 

Intraparticle porosity refers to the fraction of the particle volume which is occupied by internal pores most manufactured food particles are porous. However, it is important to distinguish this quantity from bed voidage. The interparticle voidage e is the fraction of the packed bed occupied by the void spaces between particles and is defined as... 

A 12-m length of pipe is packed with 1 m of 2-mm material, 9 m of 1-cm material, and 2 m of 4-mm material. Estimate the variance in the output C curve for a pulse input into this packed bed if the fluid takes 2 min to flow through the bed. Assume a constant bed voidage and a constant intensity of dispersion given by IMudp = 2. 

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