Kunii-Levenspiel fluidization

For details beyond the scope of this subsection, reference should be made to Kunii and Levenspiel, Fluidization Engineering, 2d ed., But-terworth Heinemann, Boston, 1991 Pell, Gas Fluidization, Elsevier, New York, 1990 D. Geldart (ed.). Gas Fluidization Technology, Whey, New York, 1986 and the vast number of papers published in periodicals, transcripts of symposia, and the American Institute of Chemical Engineers symposium series. 

The bubble model (Kunii and Levenspiel, Fluidization Engineering, Wiley, New York, 1969 Fig. 17-14) assumes constant-sized bubbles (effective bubble size d ) rising through the suspension phase. Gas is transferred from the bubble void to the mantle and wake at... 

Daizo Kunii, Octave Levenspiel, Fluidization Engineering second edition, (1991). 

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. 

Extension of the Kunii-Levenspiel bubbling-bed model for first-order reactions to complex systems is of practical significance, since most of the processes conducted in fluidized-bed reactors involve such systems. Thus, the yield or selectivity to a desired product is a primary design issue which should be considered. As described in Chapter 5, reactions may occur in series or parallel, or a combination of both. Specific examples include the production of acrylonitrile from propylene, in which other nitriles may be formed, oxidation of butadiene and butene to produce maleic anhydride and other oxidation products, and the production of phthalic anhydride from naphthalene, in which phthalic anhydride may undergo further oxidation. 

Using the Kunii-Levenspiel bubbling-bed model of Section 23.4.1 for the fluidized-bed reactor in the SOHIO process for the production of acrylonitrile (C3H3N) by the ammoxidation... 

As in the fluidized beds analysis (Section 3.8.3), a similar simplification has been made in Kunii-Levenspiel model for the material balances in the emulsion phase, where again the corresponding derivatives have been omitted (eqs. (3.529) and (3.530)). As in the case of liquid flow in trickle beds, the flow of the gas in the emulsion phase is considered too small and so the superficial velocities can be neglected. Thus, in trickle beds, from eq. (3.367),... 

D. Kunii and O. Levenspiel, Fluidization Engineering, Butterworths, London, 1991. 

The two-phase theory of fluidization has been extensively used to describe fluidization (e.g., see Kunii and Levenspiel, Fluidization Engineering, 2d ed., Wiley, 1990). The fluidized bed is assumed to contain a bubble and an emulsion phase. The bubble phase may be modeled by a plug flow (or dispersion) model, and the emulsion phase is assumed to be well mixed and may be modeled as a CSTR. Correlations for the size of the bubbles and the heat and mass transport from the bubbles to the emulsion phase are available in Sec. 17 of this Handbook and in textbooks on the subject. Davidson and Harrison (Fluidization, 2d ed., Academic Press, 1985), Geldart (Gas Fluidization Technology, Wiley, 1986), Kunii and Levenspiel (Fluidization Engineering, Wiley, 1969), and Zenz (Fluidization and Fluid-Particle Systems, Pemm-Corp Publications, 1989) are good reference books. 

FIG. 17-14 Bubbling-bed model of Kunii and Levenspiel. dy = effective bubble diameter, Cai, = concentration of A in bnbble, Cjy, = concentration of A in cloud, = concentration of A in emulsion, q = volnmetric gas flow into or out of bubble, = mass-transfer coefiicient between bnbble and cloud, and k = mass-transfer coefficient between clond and emnlsion. (From Kunii and Levenspiel, Fluidization Engineering, Wiley, New York, 1969, and Krieger, Malabar, Fla., 1977.)... 

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. 

Figure 12-18 From Kunii and Levenspiel Fluidization Engineering, Copyright 1969, Robert E. Kneger Pub. Co. Reproduced by permission of the publisher.

We are going to use the Kunii-Levenspiel bubbling bed model to describe reactions in fluidized beds. In this model, the reactant gas enters the bottom of the bed, and flows up the reactor in the form of bubbles. 

In view of the importance of the Davidson, Kunii-Levenspiel and other models, we consider them at some length in Case Stndy 11.5. The groundwork for these models as well as the other important features of fluidization mentioned earlier are briefly outlined below. 

FIGURE CS5.1 Schematics of several fluidized-bed reactor models (a) Davidson model, (b) Kunii-Levenspiel model, (c) Miyauchi model, (d), (e) Fryer-Potter and Jayaraman-Kulkami-Doraiswamy models. 

The Kunii-Levenspiel model for fluidization is given on the CD-ROM along with a comprehensive example problem. The rale limiting transpon steps are also discussed. See Professional Reference Shelf R12.3. 

Kunii, Daizo, and Octave Levenspiel, Fluidization Engineering. 2nd Ed., Butterworth-Heinemann, Boston, 1991, pp. 80,81. 

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