Kunii-Levenspiel fluidization model

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),... 

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 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. 

It is of interest to compare the efficiency of a fluidized bed in terms of the Kunii-Levenspiel model to that of a corresponding plug-flow reactor. We can do this by comparing the catalyst requirement in a PFR to that in the fluid-bed reactor (FBR) for the same conversion, which in general is the ratio of the effective... 

In this section, we will investigate three kinds of mass balances for a fluidized bed the plug flow, the CSTR, and the hydrodynamical Kunii-Levenspiel models [18]. The ideal models can be utilized only for rather crude, approximate calculations only the design of a fluidized bed should comprise a hydrodynamical model coupled with experiments on a pilot scale. 

The most advanced and realistic description of fluidized beds is the Kunii-Levenspiel model [18]. According to this model, the bubble phase is assumed to move in the reactor following the characteristics of a plug flow, while the gas flow in the emulsion phase is assumed to be negligible. The cloud and wake phases are presumed to possess similar chemical contents. The transport of the reacting gas from the bubble phase to the cloud and wake phases and vice versa prevails. The volume element, AV, therefore consists of three parts, as in Figure 5.34 ... 

FIGURE 5.34 Schematic structure of a fluidized bed according to the Kunii-Levenspiel model. (Data from Levenspiel, O., Chemical Reaction Engineering, 3rd Edition, Wiley, New York, 1999.)... 

As a summary, we can conclude that the Kunii-Levenspiel model for a fluidized bed consists of 3 AT N = number of components) molar balances (Equations 5.251 through 5.253) if all the components are utilized, or, 3 S (S = number of reactions) balances, if the key components are used as in Equations 5.251 through 5.253. The 3 - S balances comprise the model in case the extents of reactions are used in Equations 5.254 through 5.256. In the latter two cases, the concentrations of the components are related through Equations 5.248 through 5.250. 

In a general case of nonlinear kinetics, the fluidized bed model is solved numerically with an algorithm suitable for differential algebraic systems. The calculation procedure for fluidized beds with the Kunii-Levenspiel model involves numerous steps, as evidenced by the treatment. As a summary, the path from the minimum fluidization quantities (emf, Wfn() to the reactor model is presented in Table 5.6. The superficial velocity (wo) and the physical parameters are assumed to be constant. 

A catalytic oxidation process is going to be carried out in a fluidized bed with spherical catalyst particles. Calculate all the parameters of oxygen needed for the Kunii-Levenspiel model, starting from the physical data given below ... 

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... 

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. 

Matsui et compared experimental data on the steam gasification of coal char from a laboratory-scale fluidized-bed reactor with the Kunii and Levenspiel model. Good agreement was reported when the bubble diameter was treated as a fitted constant. 

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. 

The analysis of fluidized-bed reactors is based largely on the fluid mechanical model first described fully by Davidson and Harrison (1963) and modified later by a number of investigators (e.g., Jackson, 1963 Murray, 1965 Pyle and Rose, 1965 Kunii and Levenspiel, 1968a,b Rowe, 1971 Orcutt and Carpenter, 1971 Davidson and Harrison, 1971 Davidson et al., 1978 Van Swaaij, 1985). Our description of fluidized-bed reactor modeling will be based on the Kunii-Levenspiel adaptation (see Levenspiel, 1993). 

Botton R, Vergnes F, Bergougnou MA.Validation by means of industrial data of Kunii-Levenspiel type bubble models which can be used in the scale-up to commercial size of fluidized bed reactors. In Kunii D, Toei R, eds. Fluidization IV, Kashikojima, Japan. New York Engineering Foundation, 1983, pp 575-582. 

The simulation results of the one-dimensional model were found to be in fair agreement with the two-dimensional model considering the chemical conversion of the reactor, as is also utilized by the Kunii-Levenspiel type of modeis [85]. Moreover, with extended conductive fluxes, fair temperature profiles can be predicted with the one-dimensional model. On the other hand, the flow pattern, i.e., the phasic fractions and gas phase velocity, were associated with the largest uncertainty in the current model. However, the internal flow details did not have signiflcant influence on the chemical process performance. Thus, the current one-dimensional model was considered to have good potentials for further CEB model developments in order to study interconnected fluidized bed reactors with a dynamic solid flux transferred between the reactor units. 

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