Mass 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]... 

Gas interchange takes place between the two phases. The overall mass interchange coefficient per unit volume of gas bubbles is given by... 

The above equation can be converted to. fiioT, the mass interchange coefficient per unit volume of bubble, based on the appropriate surface-to-volume ratio, i.e.. 

Lbe = the mass transfer coefficient between the bubble and emulsion phase (m3 gas interchange volume/m3 of reactor) (1/s) yb = the volume fraction of the bubble occupied by solids ( rh,vs) = the reaction rate in bubbles per unit volume of solids, based on the reactant... 

K = the mass-transfer coefficient based on the bubble volume, (m3 gas interchange volume/m3 of bubble) (1/s)... 

In order to permit sizing a tower, data must be available of the height of a transfer unit (HTU). This term often is used interchangeably with the height equivalent to a theoretical stage (HETS), but strictly they are equal only for dilute solutions when the ratio of the extract and raffinate flow rates, E/R, equals the distribution coefficient, K = xE/xR (Treybal, 1963, p. 350). Extractor performance also is expressible in terms of mass transfer coefficients, for instance, KEa, which is related to the number and height of transfer units by... 

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... 

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. 

The reason that kbOt, is higher than calculated from Eq. (6-12) may be explained qualitatively by three effects (1) splitting, coalescence, and rupture of bubbles (T18, T20) (2) direct contact of gas and particles in the transition zone from dense phase to dilute phase (F18) (3) the influence of the particle capacitance effect (M21, M22) as a result of a small steady interchange of particles between the bubble void and the emulsion. An example of this is the case where particles are raining through the bubble (D18, R8, Wl) and (4) asphericity of the bubbles (D18). If the particle capacitance effect (discussed in the next section) is responsible for high experimental values for kb b. such values should not be applied to the usual catalytic reactions, where m is on the order of unity and particle capacitance has little effect on kbOt,. For design purposes it is normally better to use experimental mass-transfer coefficients obtained by a properly sized fluid bed for the reaction system of interest. 

The differences between the profiles calculated with the two models, the GM and FOR models, are too small to be seen and, thus, the GR and the FOR models are interchangeable at St/Bi > 5. In the case illustrated in Figure 16.20, the St/Bi ratio is of the order of 100. The results of this work can be used to observe the relative intensity of the external and internal mass transfer resistances. The value of was equal to kgxt = 3.8 cm/min based on a Dm of 0.0017 cm /min. This value is a bulk property and can not be applied to the stagnant solution inside the pore to measure the internal mass transfer resistance. Assuming a Dm = 0.0001 cm /min an internal mass transfer coefficient, kj t = 0.076 cm/min is obtained. Thus the ratio of the external and internal mass transfer is of the order 50 meaning the external resistance can be neglected compared to the internal one. 

Interchange mass transfer coefficients are used to account for the mass transfer between the phases. 

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