Bubble, rising, mass transfer

As the bubbles rise, mass transfer of the reactant gases takes place as they flow (diffuse) in and out of the bubble to contact the solid particles where the reaetion produet is formed. The product gases then flow back into a bubble and finally exit the bed when the bubble reaches the top of the bed. The rate at which the reaetants and products transfer in and out of the bubble affects the conversion, as does the time it takes for the bubble to pass through the bed. Consequently, we need to deseribe the veloeity at which the bubbles move through the eolumn and the rate of transport of gases in and out of the bubbles. The bed is to be operated at a superfieial veloeity Mq- To calculate these parameters we need to determine a number of fluid-mechanics parameters associated with idle fluidization proeess. Speeifieally, to detennine the velocity of the bubble through the bed we need to first ealeulate ... 

In a number of refining reactions where bubbles are formed by passing an inert gas through a liquid metal, the removal of impurities from the metal is accomplished by transfer across a boundary layer in the metal to the rising gas bubbles. The mass transfer coefficient can be calculated in this case by the use of the Calderbank equation (1968)... 

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. 

Recent publications on mass transfer from single bubbles include a theoretical study by Ruckenstein (R4) and theoretical and experimental studies by Lochiel and Calderbank (C4, L7). Bowman and Johnson (B8, J3) and Li et al. (L5) have studied mass transfer from streams of bubbles rising in water. 

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

A large deep bath contains molten steel, the surface of which is in contact with air. The oxygen concentration in the bulk of the molten steel is 0.03% by mass and the rate of transfer of oxygen from die ait is sufficiently high to maintain die surface layers saturated at a concentration of 0.16% by weight. The surface of die liquid is disrupted by gas bubbles rising to the surface at a frequency of 120 bubbles per in2 of surface per second, each bubble disrupts and mixes about 15 enr of the surface layer into the bulk. 

Ivey, H. J., 1967, Relationships between Bubble Frequency, Departure Diameter, and Rise Velocity in Nucleate Boiling, Int. J. Heat Mass Transfer 70 1023. (2)... 

Gas logging, the adherence of small bubbles to particles, causing them to rise to the surface in the reactor and form an inefficient packed bed with poor mass transfer properties, can be a problem in various fermentations and in wastewater treatment. A double entry fluidized bed reactor has been developed with simultaneous top (inverse) and bottom (conventional) inlets to overcome this problem (Gilson and Thomas, 1993). 

Tests have been carried out on the rate of extraction of benzoic acid from a dilute solution in benzene to water, in which the benzene phase was bubbled into the base of a 25 mm diameter column and the water fed to the top of the column. The rate of mass transfer was measured during the formation of the bubbles in the water phase and during the rise of the bubbles up the column. For conditions where the drop volume was 0.12 cm3 and the velocity of rise 12.5 cm/s, the value of Kw for the period of drop formation was 0.000075 kmol/s m2 (kmol/m3), and for the period of rise 0.000046 kmol/s m2 (kmol/s m3). 

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 rates at which drops and bubbles rise and fall are rather more sensitive to traces of surface-active materials than are the mass-transfer coeflScients 77a, 77b). Whereas, for example, the rate of fall of CCh drops... 

If we simply turn the drawing of the bubble column upside down, we have a spray tower reactor. Now we have dense liquid drops or solid particles in a less dense gas so we spray the liquid from the top and force the gas to rise. The same equations hold, but now the mass transfer resistance is usually within the hquid drop. 

In the previous problem the hydrogen bubbles are initially 0.1 cm in diameter, and they contain pure H2 gas at a concentration of 0.05 moles/cm (which does not change as the bubbles rise). Hydrogen is transferred from the bubbles to the liquid with a rate limited by mass transfer (k, = Dyi lR) in the liquid around the bubble with Dq, = 1 x 10 cm /sec. There is no reaction in the bubbles. 

Mass transfer during formation of drops or bubbles at an orifice can be a very significant fraction of the total mass transfer in industrial extraction or absorption operations. Transfer tends to be particularly favorable because of the exposure of fresh surface and because of vigorous internal circulation during the formation period. In discussing mass transfer in extraction, it has become conventional (H12) to distinguish four steps (1) formation, (2) release, (3) free rise or fall, (4) coalescence. Free rise or fall has been treated in previous chapters. Steps 1 and 2 are considered here. 

An oxygen bubble with a diameter of 0.4cm is rising in water at 20 °C with a constant velocity of 0.2 m s . Estimate the liquid phase mass transfer coefficient... 

---