Bubbling bed model

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. 

Figure 23.6 Bubbling-bed model representation of (a) a single bubble and (b) regions of a Auidized bed (schematic)...

In the following sections, we discuss reactor models for fine, intermediate, and large particles, based upon the Kunii-Levenspiel (KL) bubbling-bed model, restricting ourselves primarily to first-order kinetics. Performance for both simple and complex reactions is considered. Although the primary focus is on reactions within the bed, we conclude with a brief discussion of the consequences of reaction in the freeboard region and near the distributor. 

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. 

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. 

Figure 23.9 Schematic representation of regions of bubbling-bed model for intermediate-sized particles...

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... 

FIG. 17-15 Bubbling-bed model of Kunii and Levenspiel. db = effective bubble diameter, Cab = concentration of A in bubble, CAc = concentration of A in cloud, CM = concentration of A in emulsion, q = volumetric gas flow into or out of bubble, = mass-transfer coefficient between bubble and cloud, and kce = mass-transfer coefficient between cloud and emulsion. (From Kunii and Levenr spiel, Fluidization Engineering, Wiley, New York, 1969, and Krieger, Malabar, Fla., 1977.)... 

Thus we can safely use the bubbling bed model of this chapter. 

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 ... 

Following the bubbling bed model of Kunii-Levenspiel, the mass transfer coefficient of gas between the bubble and the cloud is (Levenspiel, 1972 Fogler, 1999)... 

Kunii-Levenspiel three-phase model (bubbling bed model)... 

The two-phase bubbling bed model is capable of many minor adjustments and has given numerous academics a lot of fun playing... 

The other end condition where the bubbling bed model is inappropriate is above the bed where there may be reaction in the free board region. With fine powders where there is appreciable elutriation gas and particles may remain in contact with further opportunity for reaction. This situation has not attracted the attention of many modellers but at least one model predicts that considerable reaction can continue under certain circumstances (20). 

Kunii, D., Levenspiel, 0., "Bubbling Bed Model for Kinetic Processes in Fluidized Bed-Gas-Solid Mass and Heat Transfer and Catalytic Reactions", lEC Proc. Des. Dev., 1968, J7,... 

Better models and design equations exist for fluidized-bed reactors and they should be used. One commonly used model is the bubbling bed model of Kimii and Levenspiel and is discussed in Chapter 12. 

The material that follows is based upon what is seemingly the best model of the fluidized-bed reactor developed thus far— the bubbling bed model of Kimii and Levenspiel. ... 

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. 

Descriptive Behavior of the Kurui-Levenspiel Bubbling Bed Model Mass Transfer in Fluidized Beds Reaction in a Fluidized Bed... 

CDP12-Kc Open-ended fluidization problem that requires critical thinking to compare the two-phase fluid models with the three-phase bubbling bed model. 

So far, the influence of bubble wake on mean bubble velocity i b relative to the column wall has not been mentioned, since Eq. (5-3) has been formulated on the basis of uy,o, which already includes the effect of the wake (although it lacks a correction for wake fraction). In bubbling-bed models (FIO, F12, K24, L5, S18) an upward flow of solid carried by the bubbles and bubble wakes leads to a downflow of solid (that has been assumed uniform) in the remainder of the bed. Then the bubble velocity b relative to bed wall should be smaller than the slip velocity of the bubble Ms relative to emulsion, since the bubble phase is retarded by downflow of... 

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 models show considerably different A or when s 1 sec". The bubble flow model (BFM) is for perfectly mixed emulsion, but a A or only slightly larger is obtained for BFM when the emulsicm is vertically unmixed. For the bubbling bed model (BBM)A or is fairly sensitive to different assumptions iorf an/w of about unity is recommended (FI 1, K24) to fit the reaction data available. The valued = 0.35 is taken from Rowe (D5) for 75-jU,m-diam. spherical particles. 

Two-phose consecutive model Bubbling bed model Bubble flow model (Ezs= Lewis-Gilliland-Glass ... 

Catalytic hydrogenation of ethylene by nickel- or copper-impregnated cracking catalyst is taken here for comparison. Figure 67 shows typical experimental A or values taken under a constant superficial gas velocity Uq by varying A ,. Curve LGG is based on the data by Lewis et al. (LI 2), GK by Gilliland and Knudsen (G7), and FKM those by Furusaki et al. (F18). The calculation ofA R will be explained later. The dotted curves are calculated by the two-phase consecutive model (TCM) and by the bubbling bed model (BBM) for Ug = 20 and 25 cm/sec, where the mean bubble size is 4.5 cm and the wake fracticm / = 1.0. 

Fig. 67, Overall rate constant k s for experimental ethylene hydrogenation runs by Ni-or Cu-impregnated cracking catalyst beds. Dotted curves were calculated by the two-phase consecutive model (TCM) and by the bubbling bed model (BBM). Full curves were calculated by the successive contact model.

Similarly the bubbling bed model may be visualized as a kind of direct contact model when is much greater than k r in Eq. (7-12), since the equation is now reduced to Eq. (7-9) with an apparent equality of/ eb = v under this extreme. Actually, however, the transfer of bubble gas to the cloud-wake region is limited by so that the amount of catalyst y Cb should be greater than v to account for the above data such a large/ Cb again seems unreasonable. 

Recently, Yates and Rowe (YIO) have observed, on the basis of their model for catalyst distribution in the freeboard region, that this region can usually exert a considerable influence on the course of the reaction. Their observation is essentially parallel with the concept of the successive contact mechanism. However, they use the bubbling bed model in calculating the reaction in the dense phase, so that the effect of directly contacting catalyst seems to be corrected two times, first partially in the dense phase and then in the freeboard region (see Section VII,A,3). 

In evaluating the transport properties in fluid catalyst beds during reaction, it is necessary to utilize reaction data obtained at relatively high reaction rate. The reactor models of different mechanisms have been reduced to the form of Eq. (7-35), as shown in Table VII, including the bubbling bed model when k a, ATor- Eq. (7-35) is equivalent to one developed by Lewis et al. (LI2) for their direct contact model of vertically unmixed emulsion (VUE). As a consequence, Eq. (7-35) is transformed (LI2) to ... 

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