Hydrodynamic Models of Fluidization

A hydrodynamic model of fluidization attempts to account for several essential features of fluidization mixing and distribution of solids and fluid in a so-called emulsion region, the formation and motion of bubbles through the bed (the bubble region ), the nature of the bubbles (including their size) and how they affect particle motion/distribution, and the exchange of material between the bubbles (with little solid content) and the predominantly solid emulsion. Models fall into one of three classes (Yates, 1983, pp. 74-78)  

The discussion above suggests a hydrodynamic flow model based on two distinct regions in the fluidized bed a bubble region made up mostly of gas, but also containing solid 

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)  

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Schouten, J. C., and VandenBleek, C. M., Chaotic Behavior in the Hydrodynamic Model of a Fluidized Bed Reactor, Proc. llthlnt. Conf. on Fluidized Bed Comb., 1 459(1991)... 

Kuipers, J. A. M., Hoomans, B. P. B, and van Swaaij, W. P. M. Hydrodynamic Modeling of Gas-Fluidized Beds and their Role for Design and Operation of Fluidized Bed Chemical Reactors. Proceedings of the Fluidization IX conference, 15-30, Durango, USA (1998). 

The following analysis holds for Type B fluidization and for Type A bubbling fluidization, when the region of particulate fluidization is so small that it can be ignored. In the framework of the two-phase model (see the subsection Hydrodynamic modeling of bubbling fluidization), the bed expansion in terms of the fraction of the bed occupied by bubbles is... 

Hydrodynamic modeling of bubbling fluidization (type B fluidization)... 

Among the many mathematical models of fluidized bed reactors found in the literature the model of Werther (J ) has the advantage that the scale-dependent influence of the bed hydrodynamics on the reaction behaviour is taken into account. This model has been tested with industrial type gas distributors by means of RTD-measurements (3)and conversion measurements (4), respectively. In the latter investigation (4) a simple heterogeneous catalytic reaction i.e. the catalytic decomposition of ozone has been used. In the present paper the same modelling approach is applied to complex reaction systems. The reaction system chosen as an example of a complex fluid bed reaction is the synthesis of maleic anhydride (Figure 1). 

The chemistry component of the model is, in most aspects, identical to the chemistry of the classical models of fluidized bed gasification. A major difference between the classical reactor models and the present fluidized bed coal gasifier computer model is that the classical models require specification of the bed hydrodynamics, such as bubble size. The present model can predict bubble size and the associated solids mixing. Again it is expected that the two types of models are complimentary. The present model can be used to define the hydrodynamics in the hot reactive environment and these hydrodynamics (e.g., bubble size) can then be used as... 

Kuipers JAM, Hoomans BPB, van Swaaij WPM (1968) Hydrodynamic Models of Gas-Fluidized Beds and Their Role for Design and Operation of Fluidized Bed Chemical Reactors. In Fan L-S, Knowlton TM (eds) Proc of the Ninth Engineering Foundation Conference on Fluidization, Engineering Foundation, New York, ISBN/ISSN 0-939204-56-8... 

Liu X, Jiang Y, Liu C, Wang W, Li J Hydrodynamic modeling of gas—solid bubbling fluidization based on energy-minimization multiscale (EMMS) theory, Ind Eng Chem Res 53 2800-2810, 2014. 

The first commercial fluidized bed polyeth)4eue plant was constructed by Union Carbide in 1968. Modern units operate at 100°C and 32 MPa (300 psig). The bed is fluidized with ethylene at about 0.5 m/s and probably operates near the turbulent fluidization regime. The excellent mixing provided by the fluidized bed is necessary to prevent hot spots, since the unit is operated near the melting point of the product. A model of the reactor (Fig. 17-25) that coupes Iduetics to the hydrodynamics was given by Choi and Ray, Chem. Eng. ScL, 40, 2261, 1985. 

Another survey by Ibl (13) in 1963 listed 13 mass-transfer correlations established by the limiting-current method, only four of which were derived from quantitative considerations. At the time of writing the total number of publications is more than 200. The majority of these concern flow conditions under which theoretical predictions are, at best, qualitative. More recently, an increasing number of publications deal with model hydrodynamic studies of more complex situations, for example, packed and fluidized beds. 

A technique which can assist in the scale-up of commercial plants designs is the use of scale models. A scale model is an experimental model which is smaller than the hot commercial bed but which has identical hydrodynamic behavior. Usually the scale model is fluidized with air at ambient conditions and requires particles of a different size and density than those used in the commercial bed. The scale model relies on the theory of similitude, sometimes through use of Buckingham s pi theorem, to design a model which gives identical hydrodynamic behavior to the commercial bed. Such a method is used in the wind tunnel testing of small model aircraft or in the towing tank studies of naval vessels. 

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... 

Glicksman, L. R., Yule, T., Dymess, A., and Carson, R., Scaling the Hydrodynamics of Fluidized Bed Combustors with Cold Models ... 

After introducing some types of moving-particle reactors, their advantages and disadvantages, and examples of reactions conducted in them, we consider particular design features. These relate to fluid-particle interactions (extension of the treatment in Chapter 21) and to the complex flow pattern of fluid and solid particles. The latter requires development of a hydrodynamic model as a precursor to a reactor model. We describe these in detail only for particular types of fluidized-bed reactors. 

By converting the governing hydrodynamic equations for a particular system into nondi-mensional ones, Horio et al. (1986) and Glicksman (1988) derived the so-called scaling laws for fluidized beds. These laws should be seen as a guide to design small-scale, cold-flow models, which simulate the hydrodynamic behavior of the commercial units (Knowlton et al., 2005). 

Brue, E.. Moore, J., and Brown, R. C. Process Model Identification of Circulating Fluid Bed Hydrodynamics, in Circulating Fluidized Bed Technology IV (Amos A. Avidan, ed.), pp. 535-540. Somerset, Pennsylvania (1993). 

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