Scaling relationships for fluidized beds

The equations of conservation of mass for gas and particle phases are given, respectively, by 

The relevant boundary conditions for this system are given as follows  

The dimensionless boundary conditions corresponding to Eqs. (5.372) through (5.377) can then be expressed as 

The nondimensionalized pressure term, pf/pU2, can be ignored when the gas velocity is low compared to the speed of sound or when the effects of pressure on the thermodynamic 

It should be noted that the coefficient fi is not an independent parameter it depends on the bed properties. In a fluidized bed, particles are closely spaced it is assumed that the Ergun equation can be applied to account for the pressure drop in the bed. Thus, from Eq. (5.358), we have 

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Glicksman, L. R., Hyre, M. R., and Woloshun, K., Simplified Scaling Relationships for Fluidized Beds, Powder Technol.,11 All (1993b)... 

Glicksman LR. Scaling relationships for fluidized beds. Chem Eng Sci 39 1373, 1984. 

Glicksman LR, Hyre MR, Woloshun K. Simplified scaling relationships for fluidized beds. Powder Technol 77 177, 1993b. 

Nicastro MT, Glicksman LR. Experimental verification of scaling relationships for fluidized bed. Chem Eng Sci 39 1381, 1984. 

Newby, R. A., and Keaims, D. L., Test of the Scaling Relationships for Fluid-bed Dynamics, Fluidization V, (K. Ostergaard and A. Sorensen, eds.), Engineering Foundation, New York (1986)... 

Newby RA, Keaims DL. Test of the scaling relationships for fluid-bed dynamics. In Ostergaard K, Sorensen A, eds. Fluidization V. New York Engineering Foundation, 1986. 

Several attempts have been made to determine proper scaling relationships for Group B fluidized beds. These early attempts, and a rigorous... 

Designing a model fluidized bed which simulates the hydrodynamics of a commercial bed requires accounting for all of the mechanical forces in the system. In some instances, convective heat transfer can also be scaled but, at present, proper scaling relationships for chemical reactions or hydromechanical effects, such as particle attrition or the rate of tube erosion, have not been established. 

Figure 30 shows the relationship of the catalyst-to-methanol ratio with the selectivity to Hght olefins. Compared with Fig. 21, it is interesting to note the quahtative agreement between the pilot-scale results and microscale results. F iure 30 can be used to optimize and control the catalyst circulation rate during the reaction, which on other side su ests that microscale fluidized bed reactor can be effectively used in scaling up the fluidized bed reactor with suitable methodology for analysis. 

In later sections, the use of the scaling relationships to design small scale models will be illustrated. For scaling to hold, all of the dimensionless parameters given in Eqs. (36), (37) or (39) must be identical in the scale model and the commercial bed under study. If the small scale model is fluidized with air at ambient conditions, then the fluid density and viscosity are fixed and it will be shown there is only one unique modeling condition which will allow complete similarity. In some cases this requires a model which is too large and unwieldy to simulate a large commercial bed. 

The simplified scaling relationships, Eq. (53), offer some flexibility in the model design since fewer parameters must be matched than with the full set of scaling relationships. When the fluidizing gas, the pressure and temperature of the scale model are chosen, the gas density and viscosity for the scale model are set. The model must still be geometrically similar to the commercial bed. There is still one free parameter. Generally this will be the linear scale of the model. For the simplified scaling relationships, the gas-to-solid density ratio must be maintained constant... 

Glicksman and Farrell (1995) constructed a scale model of the Tidd 70 MWe pressurized fluidized bed combustor. The scale model was fluidized with air at atmospheric pressure and temperature. They used the simplified set of scaling relationships to construct a one-quarter length scale model of a section of the Tidd combustor shown in Fig. 34. Based on the results of Glicksman and McAndrews (1985), the bubble characteristics within a bank of horizontal tubes should be independent of wall effects at locations at least three to five bubble diameters away from the wall. Low density polyurethane beads were used to obtain a close fit with the solid-to-gas density ratio for the combustor as well as the particle sphericity and particle size distribution (Table 6). 

Three-dimensional electrodes were mentioned in Section 5.1.1.2. Table 5.4 indicates a potential advantage, namely a high space-time yield. Such electrodes differ from their two-dimensional counterparts in the distribution of potential and current density in the matrix of the electrodes. Rigorous analysis would require evaluation of three-dimensional potential distributions. Fortunately this is often unnecessary one-dimensional approximate models or simplified two-dimensional models are sufficient. A comprehensive treatment of three-dimensional electrodes is beyond the scope of the present text (the reader has already been referred to the review in Ref. 5, particularly for information on fluidized bed electrodes. Further information can be found in Refs. 42-44.) We will concentrate on two limiting types of operation of packed-bed electrodes to illustrate the current distributions encountered and their relationship to scale-up. 

The vacuum fluidized bed technique is already being applied for drying, coating and granulating processes at laboratory size as well as for full production scale (Figure 13.2). Relationships and parameters, which have been determined in detailed experimental studies researches stay obtained while up-scaling to production scale [7]. 

Evaluation of the applicability of fluidized-bed-reactor modeling for the OCM reaction as a means of reactor simulation and scale-up. (It should be emphasized that the study of items (1) and (2) was not aimed at investigating the best possible catalyst from the point of view of maximizing selectivity or yield but to illustrate the general pattern of relationships and the methodology of modeling). 

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