Bubble holdup, interfacial area

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 Miura (Y3) reported empirical correlations for average bubble diameter, interfacial area, gas holdup, and mass-transfer coefficients. The bubble diameter was calculated as... 

The correlations detailed in Sections 7.6.2.1-7.6.2.5 [17,18] are based on data for the turbulent regime with 4 bubble columns, up to 60 cm in diameter, and for 11 liquid-gas systems with varying physical properties. Unless otherwise stated, the gas holdup, interfacial area, and volumetric mass transfer coefficients in the correlations are defined per unit volume of aerated liquid, that is, for the liquid-gas mixture. 

In this dynamic situation the volume of the dispersed phase held up in the liquid pool is also variable, depending on the rate of rise of the bubbles and the volumetric feed rate. Statistical averages are used to characterize the system, since the holdup, interfacial area, and bubble diameter vary with time and with position in the vessel. 

In slurry systems, similar to fluidized beds, the overall rate of chemical transformation is governed by a series of reaction and mass-transfer steps that proceed simultaneously. Thus, we have mass transfer from the bubble phase to the gas-liquid interface, transport of the reactant into the bulk liquid and then to the catalyst, possible diffusion within the catalyst pore structure, adsorption and finally reaction. Then all of this goes the other way for product. Similar steps are to be considered for heat transfer, but because of small particle sizes and the heat capacity of the liquid phase, significant temperature gradients are not often encountered in slurry reactors. The most important factors in analysis and design are fluid holdups, interfacial area, bubble and catalyst particle sizes and size distribution, and the state of mixing of the liquid phase. ... 

Macrokinetic processes for slurry systems are sketched on Table 7. The main points are the characteristics of the three phase dispersion (fluid holdups, interfacial areas, bubbles and catalyst particles size distributions), the state of macromixing of fluids which can be defined through the concept of residence time distribution, the state of micromixing of fluids which for the gas phase shall determine the degree of coalescence of bubbles, the heat transfer between the reactor and the environment. 

In addition to scale-up difficulties, there are a number of problems related to the stable operation of a bubble column associated with hydrodynamics. For example, consider the important commercial application of bubble columns in hydroprocessing of petroleum resids, heavy oils and synthetic crudes. Hydrodynamic cold flow and hot flow studies on the Exxon Donor Solvent coal liquefaction process (Tarmy et al., 1984) showed that much of the literature correlations for the hydrodynamic parameters (holdup, interfacial area and dispersion coefficients) obtained with cold flow units, at ambient conditions, are not applicable for commercial units operating at relatively higher pressures. In addition, the flow pattern in commercial units was considerably different. In the hydroprocessing of petroleum residues by the H-Oil and LC-Fining processes, refinery operations have experienced problems with nonuniform distribution of gas and liquid reactants across the distributor, maintaining stable fluidization and preventing temperature excursions (Beaton et al., 1986, Fan, 1989 and Embaby, 1990). Catalyst addition, withdrawal and elutriation have also been identified as problems in these hydrotreaters. 

Region II, 0.02 < P < 2. Most of the reaction occurs in the bulk of the liquid. Both interfacial area and holdup of liquid should be high. Stirred tanks or bubble columns will be suitable. 

Region III, P < 0.02. Reaction is slow and occurs in the bulk hquid. Interfacial area and liquid holdup should be high, especially the latter. Bubble columns will be suitable. 

Auxiliary data are the sizes of bubbles and droplets. These data and the holdups of the two phases are measured by a variety of standard techniques. Interfacial area measurements utihze techniques of transmission or reflection of light. Data on and methods for finding sohi-bihties of gases or the relation between partial pressure and concentration in hquid are also well estabhshecT... 

Calderbank et al. (C1-C4), who worked with systems quite similar geometrically to that of Yoshida and Miura, found that the average bubble diameter for air in water at 15°C ranged from 3 to 5 mm. Westerterp et al. (W2-W4) found the range to be 1-5 mm for air in sodium sulfite solution at 30°C. In addition, they noted that any increase in interfacial area between the bubbles and the liquid was due primarily to the increase in gas holdup, and the average bubble diameter was essentially unaffected by the impeller speed and was approximately 4.5 mm (W3). 

Three main flow patterns exist at various points within the tube bubble, annular, and dispersed flow. In Section I, the importance of knowing the flow pattern and the difficulties involved in predicting the proper flow pattern for a given system were described for isothermal processes. Nonisother-mal systems may have the added complication that the same flow pattern does not exist over the entire tube length. The point of transition from one flow pattern to another must be known if the pressure drop, the holdups, and the interfacial area are to be predicted. In nonisothermal systems, the heat-transfer mechanism is dependent on the flow pattern. Further research on predicting flow patterns in isothermal systems needs to be undertaken... 

The use of floating bubble breakers has been used to increase the volumetric mass transfer coefficient in a three-phase fluidized bed of glass beads (Kang et al., 1991) perhaps a similar strategy would prove effective for a bed of low density beads. Static mixers have been shown to increase kxa for otherwise constant process conditions by increasing the gas holdup and, therefore, the interfacial area (Potthoff and Bohnet, 1993). 

The above equations for e and ky a are for nonelectrolyte solutions. For electrolyte solutions, it is suggested that e and k a be increased by approximately 25%. In electrolyte solutions the bubbles are smaller, the gas holdups are larger, and the interfacial areas larger than in nonelectrolyte solutions. 

The gas-liquid interfacial area per unit volume of gas-liquid mixture a (L 1. or L ), calculated by Equation 7.26 from the measured values of the fractional gas holdup and the volume-surface mean bubble diameter d, were correlated... 

Fermentation broths are suspensions of microbial cells in a culture media. Although we need not consider the enhancement factor E for respiration reactions (as noted above), the physical presence per se of microbial cells in the broth will affect the k a values in bubbling-type fermentors. The rates of oxygen absorption into aqueous suspensions of sterilized yeast cells were measured in (i) an unaerated stirred tank with a known free gas-liquid interfacial area (ii) a bubble column and (iii) an aerated stirred tank [6]. Data acquired with scheme (i) showed that the A l values were only minimally affected by the presence of cells, whereas for schemes (ii) and (iii), the gas holdup and k a values were decreased somewhat with increasing cell concentrations, because of smaller a due to increased bubble sizes. 

Mass transfer is essential in EL-ALRs. Smaller bubbles and a uniform gas holdup radial distribution increase the interfacial area and improve mass transfer. Intensified turbulence increases the surface renewal frequency and decreases bubble size. A novel internal to improve mass transfer and the hydrodynamic behavior in a gas-liquid system is reported. Experiments were carried out to study the effect of the internal on the bubble behavior and liquid velocity in an EL-ALR. 

A. Schumpe, W.D. Deckwer, Gas holdups, specific interfacial areas, and mass transfer coefficients of aerated carboxymethyl cellulose solutions in a bubble column, I EC Process Des. Develop. 21 (1982) 706-711. 

Power or energy dissipated in the aerated suspension has to be large enough (a) to suspend all solid particles and (b) to disperse the gas phase into small enough bubbles. It is essential to determine the power consumption of the stirrer in agitated slurry reactors, as this quantity is required in the prediction of parameters such as gas holdup, gas-liquid interfacial area, and mass- and heat-transfer coefficients. In the absence of gas bubbling, the power number Po, is defined as... 

Large interfacial area due to large gas holdup and to smaller-diameter bubbles, generated by the rotating disk... 

The physical technique just described directly measures the local surface area. The determination of the overall interfacial area in a gas-liquid or a liquid-liquid mechanically agitated vessel requires the application of this technique at various positions in the vessel because of variations in the local gas (or the dispersed-phase) holdup and/or the local Sauter mean diameter of bubbles or the dispersed phase. The accuracy of the average interfacial area for the entire volume of the vessel thus depends upon the homogeneity of the dispersion and the number of carefully chosen measurement locations within the vessel. 

Gas absorption is a function of the gas and liquid mass transfer coefficients, the interfacial area, and the enhancement due to chemical reaction. The gas-liquid interfacial area is related to the Sauter mean bubble diameter and the gas holdup fraction. The gas holdup fraction has been reported to vary with radial position (7-11) for column internal diameters up to 0.6 m. Koide et al" Tl2), however, found that the radial distribution of gas holdup was nearly constant for a column diameter of 5.5 m. Axial distribution of average gas holdup has been reported by Ueyama et al. (10). The average gas holdup... 

The gas interfacial area per unit volume of column is related to the gas holdup and Sauter mean bubble size. 

The radial distribution of interfacial area for a two-phase system is shown in Figure 11. As discussed earlier, the gas holdup fraction is a strong function of radial position, but the Sauter mean bubble size is a less pronounced function of radial position. Consequently, the radial distribution of interfacial area has a shape similar to the gas holdup radial profile. Therefore, the inter facial area is well described with a third order polynominal equation. 

The conductivity probe technique has been applied successfully to gas-phase measurements in a slurry bubble column. The presence of solids does not appreciably change the gas-phase characteristics for a volume fraction of solids less than 5 percent. The radial distribution functions of gas holdup and interfacial area increase significantly from the wall to the center of the column. The average Sauter mean bubble diameter is greater than the Sauter mean bubble diameter measured near the wall. 

---