Model parameters fluidized beds

Some aspects of fluidized-bed reactor performance are examined using the Kunii-Levenspiel model of fluidized-bed reactor behavior. An ammonia-oxidation system is modeled, and the conversion predicted is shown to approximate that observed experimentally. The model is used to predict the changes in conversion with parameter variation under the limiting conditions of reaction control and transport control, and the ammonia-oxidation system is seen to be an example of reaction control. Finally, it is shown that significant differences in the averaging techniques occur for height to diameter ratios in the range of 2 to 20. 

Just as with the gas holdup, gas-liquid interfacial area should also be divided into two parts. The literature, however, gives a unified correlation. The same is true for volumetric gas-liquid mass transfer coefficients and mixing parameters for both gas and liquid phases. The fundamental r.echanism for inter-phase mass transfer and mixing for large bubbles is expected to be different from the one for small bubbles. Future work should develop a two phase model for the bubble column analogous to the two phase model for fluidized beds. 

We will discuss the evaluation of some of these model parameters subsequently, but let us first examine a second example of modeling of fluidized beds. 

This model bears a familial resemblance to some that were discussed earlier in this chapter. When the dispersion terms are discarded and appropriate changes in the names and significance of some of the parameters are recognized, then we end up basically at the Davidson-Harrison model for fluidized beds. 

Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

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. 

Table 1 gives the values of design and operating parameters of a scale model fluidized with air at ambient conditions which simulates the dynamics of an atmospheric fluidized bed combustor operating at 850°C. Fortunately, the linear dimensions of the model are much smaller, roughly one quarter those of the combustor. The particle density in the model must be much higher than the particle density in the combustor to maintain a constant value of the gas-to-solid density ratio. Note that the superficial velocity of the model differs from that of the combustor along with the spatial and temporal variables. 

Fitzgerald et al. (1984) measured pressure fluctuations in an atmospheric fluidized bed combustor and a quarter-scale cold model. The full set of scaling parameters was matched between the beds. The autocorrelation function of the pressure fluctuations was similar for the two beds but not within the 95% confidence levels they had anticipated. The amplitude of the autocorrelation function for the hot combustor was significantly lower than that for the cold model. Also, the experimentally determined time-scaling factor differed from the theoretical value by 24%. They suggested that the differences could be due to electrostatic effects. Particle sphericity and size distribution were not discussed failure to match these could also have influenced the hydrodynamic similarity of the two beds. Bed pressure fluctuations were measured using a single pressure point which, as discussed previously, may not accurately represent the local hydrodynamics within the bed. Similar results were... 

The parameter C in Eq. (25) is a dimensionless parameter inversely proportional to the average residence time of single particles on the heat transfer surface. It is suggested that this parameter be treated as an empirical constant to be determined by comparison with actual data in fast fluidized beds. The lower two dash lines in Fig. 17 represent predictions by Martin s model, with C taken as 2.0 and 2.6. It is seen that an appropriate adjustment of this constant would achieve reasonable agreement between prediction and data. 

Lele, S. S., and Joshi, J. B., Modelling of Air-Lift Fluidized Bed Optimization of Mass Transfer with Respect to Design and Operational Parameters, Chem Eng. J., 49 89 (1992)... 

One of the strengths of the KTGF, although still under development, is that it can offer a very clear physical picture with respect to the key parameters (e.g., particle pressure, particle viscosity, and other transport coefficients) that are used in the TFMs. The TFMs based on KTGF requires less ad hoc adjustments compared to the other two types of models. Therefore, it is the most promising framework for modeling engineering-scale fluidized beds. 

This model can have as many as six parameters for its characterization Kbe, Pe Pec, and ratios of volumes of regions, of solid in the regions, and of fluid in the regions. The number can be reduced by assumptions such as PF for the bubble region (Pe, - ), all solid in the emulsion, and all fluid entering in the bubble region. Even with the reduction to three parameters, the model remains essentially empirical, and doesn t take more detailed knowledge of fluidized-bed behavior into account. 

A one-parameter model, termed the bubbling-bed model, is described by Kunii and Levenspiel (1991, pp. 144-149,156-159). The one parameter is the size of bubbles. This model endeavors to account for different bubble velocities and the different flow patterns of fluid and solid that result. Compared with the two-region model, the Kunii-Levenspiel (KL) model introduces two additional regions. The model establishes expressions for the distribution of the fluidized bed and of the solid particles in the various regions. These, together with expressions for coefficients for the exchange of gas between pairs of regions, form the hydrodynamic + mass transfer basis for a reactor model. 

The main model parameter, the mean bubble diameter, db, can be estimated using various correlations. It depends on the type of particle and the nature of the inlet distributor. For small, sand-like particles that are easily fluidized, an expression is given for db as a function of bed height x by Werther (Kunii and Levenspiel, 1991, p. 146) ... 

The rise velocity of bubbles is another important parameter in fluidized-bed models, but it can be related to bubble size (and bed diameter, D). For a single bubble, the rise... 

The methods most generally used for the calculation of activity coefficients at intermediate pressures are the Wilson (1964) and UNIQUAC (Abrams and Prausnitz, 1975) equations. Wilson s equation was used by Sato et al. (1985) to predict the composition of fhe condensate gas stripped from a packed bed fermenter at 30°C, whilst Beck and Bauer (1989) used the UNIQUAC equation, with temperature-dependent parameters given by Kolbe and Gmehling (1985), for their model of an anaerobic gas-solid fluidized bed fermenter at 36°C. In this case it was necessary to go beyond the temperature range of fhe source data down to 16°C in order to predict the composition of the fluidizing gas leaving the condenser. 

Figure 20.7 Two-phase model to represent the bubbling fluidized bed, with its six adjustable parameters, V, (D/uL), (DluL)2, K.

Models vary in complexity. One-parameter models seem adequate to represent packed beds or tubular vessels. On the other hand models involving up to six parameters have been proposed to represent fluidized beds. 

Fig. 26. General two-region model of a fluidized bed. Fluid is in dispersed plug flow in both regions. The six parameters of this model are m, x, Vi, vi, Di, and Dz (L13).

Table IV shows the restrictions which must be placed on this general model to obtain each of the special cases studied. Also shown are the number of parameters for each of the models. What is now needed is an evaluation of these models to find those models which fit the fluidized bed in its wide range of behavior, and then to select from these the simplest model of good fit. Practically every one of these models is flexible enough to correlate the data of any single investigation consequently a proper evaluation would require testing every model under the extremely wide variety of operating conditions of different investigators.

In the fluid-bed granulation process, moisture control is the key parameter that needs to be controlled. Faure et al. (133) have used process control for scale-up of a fluidized bed process. They used infra-red probes to monitor moisture. As there are normally large numbers of inter-related variables, they used computerized techniques for process control, such as fuzzy logic, neural networks, and models based on experimental techniques. 

Die Orcutt model is very simple, offering analytical solutions, and thus is a useful tool for a rough estimation of the effect of various parameters on the operation of fluidized beds (Grace, 1984). However, it should be used only for qualitative comparisons, since its predictions have often been inaccurate compared to the experimental values obtained. The sources of those failures are the predicted uniform concentration of gas in the dense phase, which is not the case in experiments, and the assumption of the absence of solids in the bubble phase, which results in underestimating the conversion in the case of fast reactions. 

Figure 1731. Fluidized bed reactor processes for the conversion of petroleum fractions, (a) Exxon Model IV fluid catalytic cracking (FCC) unit sketch and operating parameters. (Hetsroni, Handbook of Multiphase Systems, McGraw-Hill, New York, 1982). (b) A modem FCC unit utilizing active zeolite catalysts the reaction occurs primarily in the riser which can be as high as 45 m. (c) Fluidized bed hydroformer in which straight chain molecules are converted into branched ones in the presence of hydrogen at a pressure of 1500 atm. The process has been largely superseded by fixed bed units employing precious metal catalysts (Hetsroni, loc. cit.). (d) A fluidized bed coking process units have been built with capacities of 400-12,000 tons/day.

Fluidized reactors are the fifth type of primary reactor configuration. There is some debate as to whether or not the fluidized bed deserves distinction into this classification since operation of the bed can be approximated with combined models of the CSTR and the PFR. However, most models developed for fluidized beds have parameters that do not appear in any of the other primary reactor expressions. 

Although general treatments of the flow in fluidized beds of coarse particles, in view of the difficulty of the problem, will only evolve slowly, there have been some promising developments. These include the success achieved in correlating heat transfer data (7, 113., 114) and the development of scaling parameters that permit the use of cold flow models to study many of the characteristics of AFBC s (114%115). 

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