Fixed bed voidage

It should be noted that in the material balances, the fluidized bed voidage should be used instead of fixed-bed voidage, and that the appropriate mass transfer correlations should be used for particulate fluidization. 

J. N. Papageorgiou, G. F. Froment 1995, (Simulation models accounting for radial voidage profiles in fixed-bed reactors), Chem. Eng. Sci. 50, 3043. 

A solvent contaminated with 0.03 kmol/m3 of a fatty acid is to be purified by passing it through a fixed bed of activated carbon which adsorbs the acid but not the solvent. If the operation is essentially isothermal and equilibrium is maintained between the liquid and the solid, calculate the length of a bed of 0.15 m in diameter which will allow operation for one hour when the fluid is fed at 1 x 10-4 m3/s. The bed is free of adsorbate initially and the intergranular voidage is 0.4. Use an equilibrium, fixed-bed theory to obtain the length for three types of isotherm ... 

If flow conditions within the bed are streamline, the relation between fluid velocity uc, pressure drop (—A P) and voidage e is given, for a fixed bed of spherical particles of diameter d, by the Carman-Kozeny equation (4.12a) which takes the form ... 

In fixed-beds, the space-time as defined above is the superficial space time, as it is based on the total volume of the bed. The real space-time for a bed of bed voidage e is... 

In the analysis above, the void volume of the fixed bed (sVR) is considered to be fully filled with the fluid phase, i.e. the fluid holdup based on the total volume of the bed he t is equal to the bed voidage e. While this is expected in the case of a gas as fluid, it is not always true in the case of a liquid, especially in the case of downflow operation. In the case of incomplete filling of the bed with the fluid phase, the active bed volume is lower, and thus a portion of the solid phase is not in contact with the fluid, or in other words, is inactive in terms of reaction. 

However, bed voidage depends on dji) (Dixon, 1988). It can be proved that for dji) values lower than 0.1, the bed voidage can be considered practically constant. Indeed, it is common practice to use ratios of dJD lower than 0.1, and therefore, the bed voidage can be actually considered the same for common fixed beds. For instance, a bed consisting of particles with 2 mm diameter should have a diameter greater that 2 cm, which leads to a dji) ratio with a value of 0.1 maximum. Consequently, the bed voidage is critical only in laboratory experiments. In Figure 3.39, Dixon s correlations are presented for spheres and cylinders, in the case of dji) < 0.4 (Dixon, 1988). For cylinders, dp is equal to the diameter of a sphere of equal volume. 

In a reactor completely filled with liquid, the wetting efficiency is 100% or, in other words, the external wetting of the catalyst is complete (Burghardt et al., 1995). While it is true that when a fixed bed is completely filled with liquid wetting is complete (wetting efficiency is unity), the opposite is not true in a trickle bed, a portion of the bed voids will be always occupied by the gas phase. Thus, while in a well-operated trickle bed the wetting efficiency could be unity, its total liquid holdup based on the void volume is always lower than the bed voidage, i.e. the bed is never completely filled with liquid. 

In this equation, Re is tlie particle Reynolds number based on the minimum superficial velocity for fluidization. Moreover, for fixed-beds, we can set = 1 and sf = s. The correlation is applicable for void fractions between 0.4 and 0.8 with particle density up to 480 lb/ft3. Note that by changing the Rep number, the fluidized bed voidage ef is changed. 

The pressure drop and bed expansion profiles shown in Figure 9 represent the different stages from fixed to bubbling fluidisation for a typical gas-solid system of fine particles. Knowing the bed height, the average bed voidage can be obtained ... 

The range of the voidage change extends from that for the single particle in an infinite volume of fluid, e = 1, to the lower limit for the fixed bed, e0. At this point, Eq. (2.1) would still be valid, although it possesses a different physical meaning Instead of particles suspended by the fluid, this relation now signifies a fixed bed with pressure drop less than that required to balance the particles in the suspended state ... 

In moving-bed transport, solid particles are in contiguous contact with one another and are pushed along by the transporting fluid more or less in plug flow, with a voidage equivalent to that of the loosest fixed bed. The velocity of solids movement can be varied from zero to any practical upper limit. 

SIE Small-Scale Testing of Catalysts for Fixed-Bed Processes VOIDAGE... 

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