Transfer coefficient, bubble-cloud

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.)... 

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

Kce Mass transfer coefficient from cloud to bubble phase... 

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... 

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)... 

Mass transfer For the Kunii-Levenspiel model, the mass transfer coefficient of the gas between bubble and cloud is (eq. 3.544)... 

For the mass transfer coefficient between the bubble and its cloud due to diffusion, kbC, Davidson and Harrison (1963) also derived the following expression by assuming a spherical cap bubble with 0W = 50° (Problem 12.5)... 

Davidson and Harrison (1963) expressed the total interchange coefficient for mass transfer from the bubble to the emulsion, K, by using Eq. (12.84), which is reasonable for very fast bubbles with negligible cloud. For bubbles with a large cloud, the cloud-emulsion mass transfer coefficient, Kce, should also be considered, as indicated in Eq. (12.77). 

The mass transfer coefficient between a bubble and its cloud due to diffusion, k, given in Eq. (12.82) for a gas-solid fluidized bed can be derived on the basis of the mass... 

The Davidson and Harrison approach concentrates solely on the resistance at the bubble/cloud boundary (or bubble/dense phase boundary for a < 1). The transfer coefficient, referred to bubble surface area, is... 

For most practical conditions, a comparison of k and k from Equations (4) and (5) would suggest that the principal resistance to transfer resides at the outer cloud boundary. However, when (a), (b) and (c) are taken into account, this is no longer the case. In fact, experimental evidence (e.g. 30,31,32) indicates strongly that the principal resistance is at the bubble/ cloud interface. With this in mind, it is probably more sensible to include the cloud with the dense phase (as in the Orcutt (23, 27) models) rather than with the bubbles (as in the Partridge and Rowe (37) model) if a two-phase representation is to be adopted (see Figure 1). If three-phase models are used, then Equations (2) and (5) appear to be a poor basis for prediction. Fortunately the errors go in opposite directions. Equation (2) overpredicting the bubble/cloud transfer coefficient, while Equation (5) underestimates the cloud/emulsion transfer coefficient. This probably accounts for the fact that the Kunii and Levenspiel model (19) can give reasonable predictions in specific instances (e.g.20),... 

The overall mass and heat interphasc exchange coefficients can be obtained by summing the resistances from bubble to cloud and from cloud to emulsion (dense phase) in series. The overall bed to surface heat transfer coefficient is assumed to be mostly atuibuted to... 

Z eA Effective diffusivity of A through the grain solid product layer, P/t f Volume fraction of bubble phase kbc Mass transfer coefficient between bubble and cloud, t ... 

Pictures of bubbles and clouds have inspired some workers to develop reactor models based on the predicted behavior of individual bubbles [3,10]. In these models, the equations for gas interchange include a term for flow out of the bubble and a second term for mass transfer by molecular diffusion to the dense phase. In some models, the cloud is included as part of the bubble in others, diffusion from bubble to cloud and cloud to dense phase are treated as mass transfer steps in series. In these models, the mass transfer coefficient is assumed to vary with following the penetration theory, and the diffusion contribution is the major part of the predicted gas interchange rate. 

An important feature of fluidized-bed reactors is mass transfer between bubble and emulsion. Several models have been proposed for this exchange. The Davidson model assumes no cloud, so that only one mass transfer coefficient be (for direct bubble-emulsion exchange) is involved. On the other hand, the... 

K-L model is based on two successive mass transfer steps, leading to the coefficients febc for bubble-cloud exchange and for cloud-emulsion exchange. The equations for the K-L model are given in Table 12.5. 

Bubble-to-cloud, cloud-to emulsion, bubble-to-emulsion mass transfer coefficients, 1/s. 

Permeation flux through membrane Reaction rate constant for i-th reaction Bubble-to-cloud phase mass transfer coefficient for component I in cell n Bubble-to-emulsion phase mass transfer coefficient for component i in cell n Cloud-to-emulsion phase mass transfer coefficient for component i in cell n Adsorption constant for CO Equilibrium constant for y-th reaction... 

From these data, it is possible to calculate the transfer coefficients at the bubble interface with the cloud, he, using the following empirical equation (Equation 22.30) ... 

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