Expansion of a Fluidized Bed

The expansion of a fluidized bed of resin is an important variable in determining how much resin will be held in a vessel. This property of a resin is measured very readily in a simple laboratory experiment. For uniform bead size, correlation of data can be done with the Richardson-Zaki equation expressed in the form... 

Assuming homogenous expansion of the fluidized-bed the collection efficiency Eg may be calculated as a function of process parameters, for example the size of the collector particle dp or the height of the fluidized-bed z as well as the effective single particle collection efficiency cp and the porosity of the fluidized-bed s ... 

Important criteria in the design of a fluidized-bed process are numerous and the most important are sorbent bead size and density, ligand accessibility for a given residence time, and stability of the solid phase. Upward speed is also critical and, with beads of a given density and particle size, is the result of a compromise between the maximum loading speed and the bed expansion factor. 

Figure 23 Effects of moisture content on the bed expansion in a fluidized bed.

Crucial to the design of a fluidized bed is a quantitative knowledge of the bed expansion as a function of the liquid superficial velocity, i.e., of either L or e [the two being interrelated by Eq. (13)] as a function of U. The chaotic behavior of a fluidized bed, in contrast, say, to viscous flow through an ordered (e.g., simple cubic) array of immobilized spheres, renders measurements from the former inherently less reproducible than from the latter. 

Results for single rising bubbles of a known volume were reported by Massimilla et al. [49]. The apparatus consisted of a fluidized bed column 3.5in I.D. Several types of particles were used - glass beads 0.79mm, 1.09mm - iron sand 0.2mm - silica sand 0.22mm. Water and air were employed as the liquid and gas phases, respectively. It was found that the relationship between the diameter of a single bubble and the bubble velocity was affected by the state of expansion of the liquid-solid bed and was almost independent of particle size and density. 

Gibilaro, L.G., Waldram, S.P. and Foscolo, P.U. (1984). A simple mechanistic description of the unsteady-state expansion of liquid-fluidized beds. Chem. Eng. Sci., 39, 607. 

The following section reports numerical solutions to the above equations, which relate to a two-dimensional slice of a fluidized bed of width equal to 0.2 m, and of sufficient height to allow for bed expansion -typically 0.4 m to accommodate an initial packed bed height of some 0.25 m. The system is restricted laterally by impermeable, rigid walls, and at the top and bottom by horizontal planes permeable for the fluid but not for the particles. Boundary conditions for each of the variables (uf, Up, Vf, Vp, p, and a) are imposed as follows ... 

Measurement of the expansion of a gas-liquid fluidized bed provides a measure of the holdup of solids or of the corresponding combined holdup of gas and liquid. From such measurements, the holdup of liquid may be calculated if the gas holdup has been determined independently. 

Abrahamson, A.R. and Geldart, D., Behaviour of gas-fluidized beds of fine powders part I. Homogeneous expansion. Powder Tech., 26 (1980) 35-46. 

Summarizing this short discussion it has to be stated, that up to now experiments providing absolute numbers of kf during protein adsorption in fluidized beds are not available, the interpretations are based on correlations derived for small ions. As ion exchange with fluidized resins is performed at much higher Reynolds numbers and mostly is not limited by particle side transport, the validity of the correlations for proteins has to be proven. Nevertheless, the influence of bed expansion at increased linear flow rate cannot be neglected and fluid side mass transport should be considered as a system parameter governing the sorption process in a fluidized bed under certain conditions. 

The functional progression dependency of the Sh-number on gas mass flow, expressed by the Re-number, is illustrated for experiment V-9 in Fig. 16.25. The curve has a maximum which is caused by the higher expansion (relative porosity) of the fluidized bed [66], In contrast to fixed beds, the energy input in fluidized beds is higher because of higher gas throughputs, and consequently the drying is faster. 

Rietema, K., The Effect of Interparticle Forces on the Expansion of a Homogeneous Gas-Fluidized Bed. Proc. Intern. Symp. Fluidization. Toulouse, pp. 28-40(1967). 

Yen and Yao [16] used a fin-type titanium cathodic current feeder (Fig. 2) in a fluidized-bed electrode to achieve enhanced copper recovery from dilute solutions. Copper particles served as the fluidized-bed cathode and platinized titanium screens were used as the anode, where oxygen evolution occurred. The feeder with the longer fin yielded higher current densities at increasing Reynolds numbers and larger bed expansions as compared with the short fin or the planar current feeder. The increased currents were due to the increased rate of copper deposition on the fluidized particles. 

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