Model of Kunii and Levenspiel

FIG. 17-14 Biihhling-hed model of Kunii and Levenspiel. dy = effective hiih-ble diameter, = concentration of A in hiihhle, = concentration of A in cloud, = concentration of A in emulsion, y = volumetric gas flow into or out of hiihhle, ky,- = mass-transfer coefficient between bubble and cloud, and k,. = mass-transfer coefficient between cloud and emulsion. (From Kunii and Leoen-spiel, Fluidization Engineering, Wiley, New York, 1.96.9, and Ktieger, Malahar, Fla., 1977.)... 

Bubbling bed model of Kunii and Levenspiel Rowe and Partidge (1962) also found out that each bubble of gas drags a substantial wake of solids up the bed. On the basis of these findings, Kunii and Levenspiel (1972) developed the bubbling bed model. The assumptions used in that model are the following ... 

In the bubbling bed model of Kunii and Levenspiel (K24), there are two transfer steps for the bubble mass transfer, namely, the transfer between bubble void and cloud-particle overlap region kbOb and that between the cloud-particle overlap region and the emulsion phase keOr,. They further assume that the cloud-particle overlap region and the bubble wake are mixed perfectly, and contact freely with the cloud gas. Their basic equations in the present notation are (for their case 2) ... 

The bubbling bed model of Kunii and Levenspiel (1969) provides the best overall representation of the experimental data in this study. Predicted bubble phase profiles tend gently to traverse the measured profiles, while dense phase profiles are in reasonable agreement over most of the bed depth. Overall conversions are well predicted. The success of the model can be mainly attributable to (1) the moderate global interphase mass transfer, (2) the negligible percolation rate in the dense phase, (3) the occurrence of reaction within the clouds and wakes assumed by the model, and (4) the use of average bubble properties to simulate the entire bed. 

Figure 7 Nomenclature used in developing the model of Kunii and Levenspiel. (From Kunii and Levenspiel, 1991.)...

The model of Kunii and Levenspiel also focuses on a single bubble, as shown... 

Figure 11.7 Single-bubble model of Kunii and Levenspiel (1969). (Reprinted from Fluidization Engineering, Wiley, by permission of John Wiley Sons, Inc.)...

Figure 11. Model of Kunii and Levenspiel (1) (level II model)...

Figure 23.9 illustrates the model and kinetics scheme for these conditions. We confine our analysis to a single first-order reaction, based on the development of Kunii and Levenspiel (1990 1991, pp. 300-302). However, extension to other reaction orders is straightforward. 

However, in many cases Eov and fb are unknown, so g cannot be determined in this way. For modeling purposes Kunii and Levenspiel [81] proposed some rough approximations. For beds of Geldart A solids, g mb, whereas... 

Details of the bubbling-bed reactor are explained in Case Study 11.5 along with a comparison and discussion of alternative models with varying degrees of complexity. The Miyanchi-Marooka model for the freebroad region (or the dilute phase) is among the models considered. Kunii and Levenspiel... 

Investigator Type of correlation Phases involved Model associated Kunii and Levenspiel [2] Particle-to-gas heat transfer coefficient Gas-solid Gas in plug flow through the bed... 

As a final word on this development of selectivity, and indeed the developments and illustrations provided throughout this discussion of fluidized beds, we must remember that good old Academic Reaction 1 was employed throughout. However, one should be able to insert any form of reaction kinetics desired with the expectation that the equations will become nonlinear. The concept of rate processes occurring in a series of steps is a core of these models, even though there is no strong a priori evidence to support this view. A different viewpoint, picturing mass transport from a solids-lean phase to a solids-rich, cloud-emulsion phase was reported to be superior in some respects to series models such as that of Kunii and Levenspiel [see J.J. Carberry, Trans. Inst. Chem. Eng., 59, 15 (1981) and A.A. Shaikh, Chem. Eng. TechnoL, 13, 273 (1990)]. 

The hydrodynamics in FBMRs consist of the behavior of the emulsion phase, i.e., the mixture of the sohd particles and the interstitial gas, along with the behavior of the gas bubbles. A complete overview of the characteristics and related models for fluidized beds is reported in the excellent book of Kunii and Levenspiel (1991). It is quite accepted that the most difficult FBR to be simulated is a bubbling fluidized bed, where the description of bubble behavior should be taken into account along with the description of soHd movement and reactions occurring on the solid surface. 

To apply the packet model, we first need to ealeulate some bubble charaeteristics, utilizing hydrodynamie theory. The neeessary equations ean be obtained from Chapter 3, or from the book of Kunii and Levenspiel (1991). First, to estimate the bubble diameter ([Pg.282]

Figure 35 Schematic representation of several multizone models (a) core-annulus-I-freeboard approach of Kunii and Levenspiel (1997) (b) four-zone approach of Neidel et al. (1995) (c) five-zone approach of Schoenfelder et al. (1994).

If ov and fb are known from experiments, e can be determined by this equation. However, in many cases Sov and fb are unknown, so cannot be determined in this way. For modeling purposes Kunii and Levenspiel [47] proposed some rough approximations. For beds of Geldart A solids, >= ,nb, whereas for beds of Geldart B and D solids, Sg m/. In the latter case, where g emf, the volume balance over the bed can be written as ... 

Cyclones. According to the model presented above, Eq. (24), a minimum loss rate due to cyclone attrition requires to avoid both high inlet velocities Ue and high solids mass fluxes mc m at the cyclone inlet. The latter requirement can be fulfilled by locating the cyclone inlet above the transport disengaging height (TDH) (Kunii and Levenspiel, 1991). In addition, an enlargement of the freeboard section will reduce the amount of particles that are entrained and thus the mass flux, mc in. 

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) ... 

Kunii and Levenspiel(1991, pp. 294-298) extend the bubbling-bed model to networks of first-order reactions and generate rather complex algebraic relations for the net reaction rates along various pathways. As an alternative, we focus on the development of the basic design equations, which can also be adapted for nonlinear kinetics, and numerical solution of the resulting system of algebraic and ordinary differential equations (with the E-Z Solve software). This is illustrated in Example 23-4 below. 

Several models have been proposed to account for reaction in the freeboard. Yates and Rowe (1977) developed a simple model based upon complete mixing of particles in the freeboard, coupled with either BMF or PF of the freeboard gas. Two model parameters are the rate of particle ejection from the bed, and the fraction of wake particles ejected. Kunii and Levenspiel (1990 1991, pp. 305-307) proposed a model of freeboard reaction which accounts for the contact efficiency of the gas with the solid, and the fraction of solid in the freeboard. A comprehensive freeboard entrainment model is... 

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