Axial dispersion in bubble columns

Although the mixing patterns in bubble columns do not obviously correspond to simple axial dispersion, the dispersed plug flow model has been found to hold reasonably well in practice. For a two-phase gas-liquid system, the equation for gas-phase convection and dispersion (Chapter 2, equation 2.14) becomes  

Experimental measurements of dispersion coefficients 91 have shown that, unless the liquid velocity is unusually high, both gas and liquid phase dispersion coefficients 

Although the most realistic model for a bubble column reactor is that of dispersed plug-flow in both phases, this is also the most complicated model in view of the uncertainty of some of the quantities involved, such a degree of complication may not be warranted. Because the residence time of the liquid phase in the column 

To incorporate mixing by the dispersed plug flow mechanism into the model for the bubble column, we can make use of the equations developed in Chapter 2 for dispersed plug flow accompanied by a first-order chemical reaction. In the case of the very fast gas-liquid reaction, the reactant A is transferred and thus removed from the gas phase at a rate which is proportional to the concentration of A in the gas, i.e. as in a homogeneous first-order reaction. Applied to the two-phase bubble column for steady-state conditions, equation 2.38 becomes  

The first-order constant klG will now be expressed in terms of the rate constant kx of the reaction in the liquid phase. From equation 4.14, the rate of transfer of A per unit area of gas-liquid interface is l(kxDA) CAi i.e. in terms of an enhanced mass transfer coefficient k L = V(kxDA) this rate of transfer is k LCAi. The rate of transfer per unit volume of dispersion JA is thus  

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Information on gas holdup and axial dispersion in bubble-columns containing suspended solid particles is scarce reference will therefore also be made to significant studies of bubble-columns with no particles present, results obtained for these systems being probably of some relevance to the understanding of bubble-column slurry operations. 

Groen JS, Oldeman RGC, Mudde RE, van den Akker HEA (1996) Coherent Structures and Axial Dispersion in Bubble Column Reactors. Chem Eng Sci 51(10) 2511-2520... 

Field RW, Davidson JF. (1980) Axial dispersion in bubble columns. Trans. Ins. Chem. Eng. UK, 58 228-236. 

Field, R. W. and J. F. Davidson. Axial Dispersion in Bubble Columns. Trans. Instn. Chem. Engineers 58 (1980) 228. 

Groen JS, Oldeman RSGC, Mudde RF, Van den Akker HEA Coherent strucmres and axial dispersion in bubble column reactors, Chem Eng Sd 51 2511—2520, 1996. http //dx.doi. org/10.1016/0009-2509(96)00110-8. 

Two main types of models are in common use for describing axial mixing in bubble columns. The most commonly used model is the Dispersion Model. Here, a diffusion-like process is superimposed on piston or plug flow. The stirred tanks-in-series model has also been used to describe flow of liquids in bubble columns. Levenspiel (1 ) presents a number of models incorporating various combinations of mixed tanks to model stagnant regions and backflow. 

Axial Dispersion Backmixing in bubble columns has been extensively studied. An excellent review article by Shah et al. [AIChE... 

Wachi, S., Morikawa, H. and Ueyama, K., 1987. Gas hold-up and axial dispersion in gas-liquid concurrent bubble column. Journal of Chemical Engineering Japan, 20, 309-316. 

NGf gas flow number [= xl/(/img)], dimensionless NPe Peclet number for axial dispersion (uGd0/DeE for liquid vtH/De for solids), dimensionless NKc Reynolds number (= aid2p/p in stirred tank) (= uGdcpJpL in bubble columns), dimensionless... 

One common feature of the studies described above is that they all indicate that the axial dispersion in the liquid phase (and the same should be true for the gas phase) of a packed bubble-column is considerably smaller than that obtained in the liquid phase of an unpacked bubble-column under equivalent flow conditions. 

Some studies13,141 on the liquid-phase axial dispersion in horizontally-sectionalized bubble-columns have also been reported. In these studies, the bubble-column was sectionalized by a series of sieve plates with bubble caps. The data indicated that the axial dispersion in this type of column was considerably less than in an open bubble-column. There was no effect of length-to-diameter ratio up to a ratio of 24 on the axial dispersion. The axial dispersion increased with... 

Recommendations For a cylindrical packed bubble-column, the use of Eq. (7-23) for the calculation of axial dispersion coefficient in the liquid phase is recommended. The axial dispersion in the gas phase of large columns needs to be investigated. Future study on this subject should concentrate on the pulsed-flow regime and the hydrocarbon systems. 

A review of the gas-phase axial dispersion in a stirred and unstirred bubble-column in the absence of solid particles is given by Ostergaard.97... 

A review on earlier studies of liquid-phase axial dispersion in unstirred bubble-columns with no solids is given by Ostergaard.97 Van de Vusse138 has discussed the liquid-phase RTD in stirred slurry reactors. 

The effects of suspended solid particles on liquid-phase axial dispersion in a cocurrent-upflow system have been studied by Schiigerl123 and Michelsen and Ostergaard.82 They showed that, in a three-phase column, the axial dispersion increases with gas rate. Unlike in a gas-liquid bubble-column, the liquid-phase axial dispersion coefficient in a three-phase column depends upon the liquid velocity. The nature of the effect is, however, dependent upon the gas rate and solids particle size. Similarly, the nature of the effect of solid size on the axial dispersion depends on the gas and liquid flow rates. 

Tuppurainen, J.M.I., "Liquid Holdup and Axial Dispersion in an Unbaffled bubble Column," B. Eng. Thesis, University of Queensland (Australia), 1979. 

In bubble columns, the gas phase exists as the dispersed phase in the continuous liquid phase. The homogeneous regime is characterized by almost uniformly sized bubbles. Further, the concentration of bubbles is uniform, particularly in the transverse direction. Therefore, bulk liquid circulation is practicahy absent. If the gas is sparged uniformly at the column bottom, it remains uniformly distributed all over the column. All the bubbles rise virtuahy vertically with minor transverse and axial oscillations. For all... 

Axial dispersion in the bubble column is usually well expressed by the following one-dimensional diffusion model with respect to liquid concentration c ... 

In regard to axial dispersion in unbaffled bubble-flow equipment like liquid-liquid spray columns, gas bubble columns, or fluidized catalyst beds, a close similarity has been supposed as a result of bubble flow and of turbulence induced by bubbles (B3, M33). Baird and Rice (B3) have assumed that the Kolmogoroflf concept for eddy viscosity in isotropic turbulence is applicable to evaluate E in the unbaffled bubble column under turbulent conditions, concluding that Ezt >s 0.35 in cm-sec units,... 

Both solvent sublation and bubble fractionation are viable as continuous countercurrent processes for the removal of hydrophobic compounds from water. Both processes are primarily dependent on the size of air bubbles introduced into the column as well as the extent of axial dispersion in the aqueous phase. The fractional removal in solvent sublation is less dependent on the column diameter. 

Liquid mixing in bubble columns is a result of global convective re-circulation of the liquid phase and turbulent diffusion due to eddies generated by the rising bubbles. By structuring the gas and the liquid flow, HyperCat reduces the axial dispersion for both phases leading to a large reduction in axial dispersion coefficients (Dax)- The real benefit of this reduced dispersion is that it is not a function of the colunm diameter (Dc) as is the case with conventional bubble colunm reactors. 

Figure 3, Liquid phase axial dispersion in HyperCat and Bubble Columns...

This review deals mainly with the discussion of various macroscopic hydro-dynamic, heat, and mass transfer characteristics of bubble columns, with occasional reference to the analogous processes in modified versions of bubble columns with a variety of internals. The hydrodynamic considerations include determination of parameters like flow patterns, holdup, mixing, liquid circulation velocities, axial dispersion coefficient, etc., which all exert strong influence on the resulting rates of heat and mass transfer and chemical reactions carried out in bubble columns. Different correlations developed for estimating the aforementioned parameters are presented and discussed in this chapter. 

Baird and Rice first applied the isotropic turbulence theory to correlate the axial dispersion coefficient in Newtonian fluids [39]. Their successful approach has been widely quoted to predict design parameters in bubble columns (Kawase and Moo-Young [40]). It was extended to non-Newtonian fluids by Kawase and Moo-Young [32]. The resulting equation may be written as... 

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