Non-bubbling fluidization

Richardson and Zaki (1954) found the function /(e) which applied to both hindered settling and to non-bubbling fluidization. They found that in general, /(e) = e , where the exponent n was independent of particle Reynolds number at very low Reynolds numbers, when the drag force is independent of fluid density, and at high Reynolds number, when the drag force is independent of fluid viscosity, i.e. 

Khan and Richardson (1989) suggested the correlation given in Equation (3.25) (Chapter 3) which permits the determination of the exponent n at intermediate values of Reynolds number (although it is expressed in terms of the Archimedes number Ar there is a direct relationship between Rcp and Ar). This correlation also incorporates the effect of the vessel diameter on the exponent. Thus Equations (7.21), (7.22) and (7.23) in conjunction with Equation (3.25) permit calculation of the variation in bed voidage with fluid velocity beyond Umf-Knowledge of the bed voidage allows calculation of the fluidized bed height as illustrated below  

If packed bed depth (Hi) and voidage e ) are known, then if the mass remains constant the bed depth at any voidage can be determined  

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Mass transfer and axial mixing in non-bubbling fluidized beds have not been treated in this book. Indeed, to my knowledge not many data about these effects have been published in literature. Though these effects may not known quantitatively, all transport phenomena can be expected to be approximately linear processes (at low concentrations). The results about mass transfer, first order surface reaction and axial mixing presented in section 72.2,1 may be expected to apply here. 

The term three-phase fluidization, in this chapter, is taken as a system consisting of a gas, liquid, and solid phase, wherein the solid phase is in a non-stationary state, and includes three-phase slurry bubble columns, three-phase fluidized beds, and three-phase flotation columns, but excludes three-phase fixed bed systems. The individual phases in three-phase fluidization systems can be reactants, products, catalysts, or inert. For example, in the hydrotreating of light gas oils, the solid phase is catalyst, and the liquid and gas phases are either reactants or products in the bleaching of paper pulp, the solid phase is both reactant and product, and the gas phase is a reactant while the liquid phase is inert in anaerobic fermentation, the gas phase results from the biological activity, the liquid phase is product, and the solid is either a biological carrier or the microorganism itself. 

The cinephotographic method discussed above can be used only when the fluid in which the bubbles are formed is transparent. If the fluid is opaque, like some non-Newtonian fluids or fluidized beds, x-ray cinephotography has to be used. Rowe et al. (RIO, Rll) have used this technique for studying gas bubbles in fluidized beds. The column in which the bubbles are formed is placed between the x-ray tube and the cine camera (normally 35 mm). Photographs up to 50 frames per second have been obtained by Rowe and Partridge (RIO) with an exposure time per frame of the order of 0.01 sec. 

Minimum bubbling velocity timb is defined as the gas velocity at which bubbles first appear in aggregative fluidization. For coarse uniformly-sized particles, for example those in Geldart group B, it is usually the case that M i, = u /- However, very fine non-uniformly sized particles such as those in group A exhibit smooth bed expansion and no bubbling until a gas velocity considerably in excess of the minimum... 

A non-isothermal dynamic model has been developed for a shallow fulidized bed combustor, which can be used to predict, at least qualitatively, the transient and steady-state characteristics of such systems. Parametric studies have been conducted to examine the effects of excess air flow rate, bubble size and carbon feed rate. It has been shown that an appreciable carbon concentration gradient does exist in the bed. This explains why it is necessary to use multiple feed points in large fluidized bed combustors. A surprising result obtained is that the temperature iii the bed is essentially uniform under all conditions studied even though the carbon concentration is not uniform laterally. 

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