Cloud-wake phase

The remaining incoming gas combines with the emulsion gas to provide the gas for the cloud/wake phase, part of which constitutes the exit gas along with the bnbble-phase gas, and the rest constitutes the downflowing emulsion gas. 

Mass transfer from the bubble to the cloud-wake phase. There is a possible chemical reaction in the bubble phase, but this will be small since the amount of catalyst in the bubble phase is also small. 

Mass transfer of reactant into the cloud-wake phase from the bubble phase, and from there into the emulsion phase. There is chemical reaction in the cloud-wake phase. 

Ki,c,K e overall mass transfer coefficients, bubble to cloud/wake phase and cloud/wake to emulsion phase, respectively, time ... 

Damkohler number for cloud/wake phase = kf/Khc) Damkohler number for emulsion phase = kr/Kce) liquid phase Damkohler number = rik/k ) overall Damkohler number see equation (8-124)... 

The bubbling bed model proposed by Kunii and Levenspiel (1969) can be considered a modified version of the two-phase model where, in addition to the bubble and the emulsion phases, a cloud-wake phase is also considered. The model represents a group of models often referred to as backmixing or dense phase flow reversal models (see also Van Deem ter, 1961 Latham et al., 1968 Fryer and Potter, 1972). A key difference between this model and the rest of the two-phase models is that the interphase mass transfer considers two distinct resistances, one from the bubble phase to the cloud-wake phase, and the other from the cloud-wake phase to the emulsion phase. 

An alternative model for slugging fluidized bed reactors was proposed by Raghuraman and Potter (48). This Is an extension of their three-phase (bubbles, cloud-wake phase, emulsion phase) countercurrent backmlxlng model (21) which accounts for gas downflow In the dense-phase, said to occur for slugging beds when U > 2.5 U f Agreement with experimental results Is said (48,49) to be somewhat better for this model than for the Hovmand-... 

The bulk density of solids in the cloud and wake phases is given by ... 

Now let us calculate the fraction of solids dispersed in the bubble, cloud/wake, and emulsion phases per unit volume of bubble in the bed ... 

Similarly, the interchange coefficient between cloud/wake and emulsion phases is calculated as... 

In a closer study of the hydrodynamics of the fluidized bed, we discover that the gas bubbles have a certain special structure illustrated in Figure 5.33. A cloud phase is found around the bubble. At the lower end of the bubble, a particle-rich area is present a wake phase. The catalytic reactions proceed everywhere across the bed, on the surfaces, and in the pores of the solid particles— in the emulsion, bubble, cloud, and wake phases. The reaction velocities in the emulsion and the wake phases are higher than that in the bubble phase. This... 

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 ... 

Equation 5.238 illustrates the contributions of reactions proceeding in the bubble, cloud, and emulsion phases, respectively. If the reactions in the cloud and wake phases—or in the bubble phase—are negligible, the corresponding terms disappear from the balance Equation 5.238. 

For the cloud, wake, and emulsion phases, the modified extents of reactions are defined as follows ... 

Equation 5.243 is valid for both cloud and wake phases, whereas Equation 5.244 is restricted to the emulsion phase. Inserting the extent of reaction, b> into Equation 5.240 and taking into account that rbi = Vii b> ei = Vii e> and Vd = ViRc, we obtain... 

The volume fractions W/Vb (cloud and wake/bubble) and Ve/Vb (emulsion/bubble) are of considerable importance in the design of fluidized beds. They can be obtained from the fractions in the bubbles in the cloud and wake phases as well as in the emulsion phase. Levenspiel [18] has derived the following expressions for the volume fractions ... 

However, the concentrations in the cloud and wake phases, Cd, have to be calculated. We have... 

Complete mixing 1) Cloud-wake is treated as a separate phase and is in plug flow... 

The bubble model (Kunii and Levenspiel, Fluidization Engineering, Wiley, New York, 1969 Fig. 17-15) assumes constant-sized bubbles (effective bubble size db) rising through the suspension phase. Gas is transferred from the bubble void to the cloud and wake at mass-transfer coefficient /v, and from the mantle and wake to the emulsion... 

Focusing on the bubbles, it should be mentioned that they are not exactly spherical. They contain very small amounts of solids and have an approximately hemispherical top and a pushed-in bottom. Each bubble of gas has a wake that contains a significant amount of solids. These characteristics are illustrated in Figure 3.58. Consequently, during their journey in the reactor, the bubbles carry an amount of solids. The net flow of the solids in the emulsion phase must therefore be downward. The gas within a particular bubble remains largely within that bubble and only a small part of it penetrates a short distance into the surrounding emulsion phase, forming the so-called cloud. 

Applying the appropriate material balances for the solids and the gas, the fraction of the bed occupied by the bubbles and wakes can be estimated using the Kunii-Levenspiel model. The fraction of the bed occupied by that part of the bubbles which does not include the wake, is represented by the parameter d, whereas the volume of the wake per volume of the bubble is represented by a. Consequently, the bed fraction in the wakes is a and the bed fraction in the emulsion phase (which includes the clouds) is 1 — <5 — ot<5. Then (Fogler, 1999)... 

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