Mass transfer coefficient bubble diameter effect

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.)... 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

Yoshida and Akita (Yl) determined volumetric mass-transfer coefficients for the absorption of oxygen by aqueous sodium sulfite solutions in counter-current-ffow bubble-columns. Columns of various diameters (from 7.7 to 60.0 cm) and liquid heights (from 90 to 350 cm) were used in order to examine the effects of equipment size. The volumetric absorption coefficient reportedly increases with increasing gas velocity over the entire range investigated (up to approximately 30 cm/sec nominal velocity), and with increasing column diameter, but is independent of liquid height. These observations are somewhat at variance with those of other workers. 

This form is particularly appropriate when the gas is of low solubility in the liquid and "liquid film resistance" controls the rate of transfer. More complex forms which use an overall mass transfer coefficient which includes the effects of gas film resistance must be used otherwise. Also, if chemical reactions are involved, they are not rate limiting. The approach given here, however, illustrates the required calculation steps. The nature of the mixing or agitation primarily affects the interfacial area per unit volume, a. The liquid phase mass transfer coefficient, kL, is primarily a function of the physical properties of the fluid. The interfacial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dSM, which is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraction of the total fluid volume (gas plus liquid) which is occupied by gas bubbles. 

The effect on the liquid-phase mass transfer coefficient is most likely neutral to positive. Past experience has been that the liquid-phase mass transfer coefficient is only dependent on the phase data (Gestrich et al., 1978), but current research efforts have presented contradictory evidence (Han and Al-Dahhan, 2007), most likely due to the method used in calculating the liquid-phase mass transfer. It is probable that the effect is negligible at lower pressures due to the much more important changes in the bubble diameter and interfacial area however, the solubility dependence on pressure could be significant, especially at higher pressure (Kojima et al., 1997). 

Removing the heat of reaction necessitates an internal heat exchanger. This exchanger will also help to limit the bubble diameter. Take vertical tubes of 0.06 m outer diameter on a 0.14-m triangular pitch. This limits the effective diameter of the bubbles to 0.1 m. Note that this is a very crude way of determining the (average) bubble diameter, which is the main variable in the Kunii and Levenspiel model. Select the superficial velocity of the feed to be 1800 m/h. Calculate the mass transfer coefficients from (13.5.3-4) and (13.5.3-5) and use (13.5.3-13) to calculate the bed height. 

From the point of view of mass transfer, a fluidized bed without bubbles is very effective, since the volumetric mass transfer coefficient is as a rule very high (this is the product of the mass transfer coefficient at the particle surface, and the surface area of the particles in the bed). On the other hand, in bubbling beds the mass transfer between the fluid and the solid is usually limited by the mass transfer between the bubbles and the dense phase. This process can be described by another volumetric mass transfer coefficient, that is the product of the specific area of the bubbles, which is quite small due to the relatively large bubble diameters, and the mass transfer coefficient between the bubbles and the dense phase, which is relatively large, due to the effective interchange of gas in the bubbles and gas in the dense phase. The bubbles also contribute to a large residence time distribution of the fluid phase (compare section 7.2.4) and this reduces further the effectivity of the mass transfer between the fluid phase and the solid. In bubbling beds the fluid is usually a gas. 

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