BED PARTICLE SIZE DISTRIBUTION AND CYCLONE DESIGN

In a fluidized bed reactor, entrained particles leaving in a dilute phase stream are conventionally and desirably either partially or wholly condensed into a bulk stream and returned to the bed via a centrifugally driven cyclone system. At equilibrium, or when steady state operation is attained, any particle loss rate from the cyclones, as well as the remaining bed particle size distribution, are functions of (a) the rate of any particle attrition within the system and (b) the smallest particle size that the cyclone system was designed to completely collect (i.e., with 100% efficiency), or conversely the largest size which the system cannot recover. These two functions result in an interdependency between loss rate and bed particle size distribution, eventually leading to an equilibrium state (Zenz Smith, 1972 Zenz, 1981 Zenz Kelleher, 1980). 

Case A. To illustrate, consider a situation in which a reactor is charged with a catalyst having a size distribution ranging from 1 to 150 

Case B. Suppose, more realistically, that the catalyst undergoes a known, experimentally determined, rate of attrition as a function of particle size (Zenz, 1971 Zenz Kelleher, 1980). The particle loss rate from the cyclone system will now approach and finally equal the rate of production of 0 to 10 micron particles by attrition from all the larger sizes. To maintain reactor inventory, this loss rate will be replaced, at an equal rate, with fresh catalyst. Since the rate of attrition of any size particle depends on its concentration in the stream subjected to the attrition (as finer particles effectively cushion the coarser), and since the loss is replaced with fresh catalyst (containing the coarsest), the bed size distribution will reach a steady state between 10 and 150 microns in which the mean size, as well as all sizes smaller than the largest, will now be decreased from what would have prevailed under conditions of zero attrition. 

The choice of cyclone modification, from an operating point of view, becomes a balance of incremental profit from increased conversion, versus catalyst makeup charges, and from a capital cost point of view, the price of either of the cyclone modifications, which must be depreciated. In many instances, there is an additional background time element, involving ongoing development of more attrition resistant and/or active catalyst. 

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