Transfer coefficient, cloud-emulsion

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.)... 

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... 

The mass transfer coefficient of gas between the cloud and the emulsion is... 

Here, CGS units are used. The mass transfer coefficient of the gas between cloud and emulsion is (eq. 3.545)... 

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). 

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... 

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

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... 

Kee Cloud-to-emulsion interchange coefficient for mass transfer... 

The mass transfer equation given in Eq. (67) can also be expressed in terms of cloud-to-emulsion gas interchange coefficient, Kqq as follows ... 

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