Interchange coefficient

A realistic treatment of mass transfer between the gas and solid phases requires consideration of the bed structure comprising the bubble phase and the emulsion phase (see 9.4). Considering bubbles containing species A passing through a fluidized bed where species A is in depletion, the mass transfer, or the mass interchange coefficient from the bubble phase to the emulsion phase, K, can be related to the difference in the concentration of species A in the bubble phase, CAib, and that in the emulsion phase, CA,e, by [Kunii and Levenspiel, 1968]... 

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). 

Therefore, Eq. (12.77) gives the gas-to-emulsion phase interchange coefficient for mass transfer... 

Kbc Bubble-to-cloud interchange coefficient for mass transfer... 

It is assumed here that the size of the last compartment is determined from the difference between the cummulative compartments size and the height of the expanded bed. However, for consistency, gas interchange coefficients and the linear bubble phase gas velocity are based on a hypothetical bubble diameter predicted from Eqn. (12). The computational scheme also takes into consideration the possibility of only two phases in any compartment. 

The dependence of heat and mass transfer coefficientes on the scale factors dp/L and dp/D can also be rationalized in terms of gas bypassing through the bed in the form of bubbles. Since bubbles coalesce and grow as the rise from the distributor, a longer bed, big L/D values, will operate with larger bubbles in its upper part. This will lead to smaller values of the Sherwood and Nusselt numbers since the interchange coefficient between bubble and emulsion phase varies inversely with bubble diameter. 

Step response measurements with a tracer gas 26-28) were used to determine interchange coefficients in fluid beds. 

Figure 9.12 Gas interchange coefficients derived from kinetic tests and tracer tests. 

Use the simple two-phase model to calculate the gas interchange coefficients and compare with values in Figure 9.12. 

The interchange coefficient, kc, has been estimated from the response to pulse inputs of tracer gas [8,13], Patience and Chaouki [8] used sand in a 0.083-m riser and reported values (their k) that ranged from 0.03 to 0.08 m/sec. The values increased with gas velocity, but with considerable scatter in the data. White and coworkers [13] used sand and FCC catalyst in a 0.09-m riser and found k (their k values of 0.05-0.02 m/sec that decreased with gas velocity. The interchange coefficient kc is based on a unit coreannulus area and can be converted to a volumetric coefficient K for comparison with other models. For kc = 0.03 m/sec, AT 1.2 sec which seems the right order of magnitude based on the values shown in Figure 9.12. Flowever, if kc is independent of diameter, D, the volumetric coefficient K will vary inversely with D if rJR is constant. 

Partridge and Rowe [7] have derived an interchange coefficient between the ensemble of bubble plus interchange zone on one hand and the emulsion phase on the other. They used the analogy with mass transfer between a drop and a surrounding fluid for which experimental correlations are available ... 

In Eq. 13.4-5 and in the following relations for interchange coefficients the bubble diameter or the diameter of the bubble + interchange zone is a critical parameter. There are no generally valid correlations for this diameter to date. An estimate may be obtained from... 

The interchange coefficient between bubble and cloud is calculated from the appropriate equation given in Table 12.5. 

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

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