Dispersion coefficient bubble columns

AV reciprocating tachycardia, 5 108 Axial dispersion coefficient, 10 762 Axial dispersion/mixing, 10 762-763 in adsorption columns, 2 604 in bubble tray absorbers, 2 88-89 chromatographic adsorption, 2 610 in packed column absorbers, 2 61-65 Axial dissolved oxygen profiles, 25 707-708 Axial filtration, 22 385-386 Axial-flow angular-momentum flowmeter, 22 672-673... 

As has been analyzed, the basic model for bubble column assumes complete mixed flow for the liquid phase and plug flow for the gas phase. The Deckwer el al. correlation (3.202) for the liquid phase and the Field and Davidson equation (3.206) for the gas phase can be used for the estimation of the dispersion coefficient. The resulting coefficients are Dll = 0.09 m2/s and DLG = 0.49 m2/s. 

Mechanism of mass transfer from bubbles in dispersions Part II Mass transfer coefficients in stirred gas-liquid reactor and bubble column... 

Axial mixing in the liquid, induced by the upflow of the gas bubbles, can be substantial in commercial-scale bubble columns, especially in the chum turbulent regime. Due to typically small particle size, the axial dispersion of the solid catalyst in slurry bubble columns is expected to follow closely that of the liquid exceptions are high-density particles. The liquid axial mixing can be represented by an axial dispersion coefficient, which typically has the form... 

Cova (3 ) measured the solid concentration profiles of a Raney nickel catalyst with an average diameter of 15.7 ym in a h.6 cm id reactor, using water and acetone as the liquids. He developed a sedimentation diffusion model, assuming solid and liquid dispersion coefficients were equal, and slurry settling velocities were independent of solid concentration. The model was then applied to data for Raney nickel in 6.35 and kk.J cm id bubble columns, in both cocurrent and countercurrent flow. 

Kato, et al (5 ) measured solid concentration profiles, solid dispersion coefficients and terminal settling velocities for glass spheres in water, using 6.6, 12.2 and 21.k cm bubble columns. They developed a dimensionless, empirical correlation for the solid dispersion coefficients which agreed with their observed values to within 20%. 

Commercial reactors are non isothermal and often adiabatic. In a noniso-thermal gas-liquid reactor, along with the mass dispersions in each phase, the corresponding heat dispersions are also required. Normally, the gas and liquid at any given axial position are assumed to be at the same temperature. Thus, in contrast to the case of mass, only a single heat-balance equation (and corresponding heat-dispersion coefficient) is needed. Under turbulent flow conditions (such as in the bubble-column reactor) the Peclet number for the heat dispersion is often assumed to be approximately equal to the Peclet number for the mass dispersion in a slow-moving liquid phase. 

Stiegel and Shah35 found that the Peclet number was somewhat dependent upon the bed height. Unlike the unpacked bubble-column, the above correlation indicates that the axial dispersion coefficient in a packed bubble-column is dependent upon the liquid velocity. 

The above results indicate that, just as in the case of a cylindrical column, the axial dispersion coefficient in a packed rectangular bubble-column depends on the liquid flow rate. The most interesting aspect of this study was that, under... 

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. 

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. 

Farkas and Leblond30 used the axial distribution of solids to calculate the values of the axial dispersion coefficient. The data were, however, not correlated to gas and liquid velocities. A method for characterizing the age distribution of suspended particles in a continuous bubble-column is given by Yamanaka et al.146... 

In the homogeneous bubble flow regime, the gas phase is generally assumed to move in plug flow and the liquid phase axial mixing is characterized by the axial dispersion coefficient. The axial dispersion coefficient is dependent upon gas velocity and column diameter according to (26,41,42)... 

The determination of volumetric mass transfer coefficients, kLa, usually requires additional knowledge on the residence time distribution of the phases. Only in large diameter columns the assumption is justified that both phases are completely mixed. In tall and smaller diameter bubble columns the determination of kLa should be based on concentration profiles measured along the length of the column and evaluated with the axial dispersed plug flow model ( 5,. ... 

A useful description of mixing in bubble columns is provided by the dispersion model. The global mixing effects are generally characterized by the dispersion coefficients El and Eq of the two phases which are defined in analogy to Fick s law for diffusive transport. Dispersion in bubble columns has been the subject of many investigations which have recently been reviewed by Shah et al. (45). Particularly, plenty of data are available for liquid-phase dispersion. 

Bubble columns are convenient for catalytic slurry reactions also (67). It is therefore important to know how the hydrodynamic properties of the gas-in-liquid dispersion is influenced by the presence of suspended solid particles. In the slurry reactor absorption enhancement due to chemical reaction cannot be expected. However, if particle sizes are very small, say less than 5 yum, and if, in addition, the catalytic reaction rate is high a small absorption enhancement can occur ( 8). Usually the reaction is in the slow reaction regime of mass transfer theory. Hence, it is sufficient to know the volumetric mass transfer coefficient, kj a, and there is no need to separate k a into the individual values. 

Due to density differences the particles have the tendency to settle. Thus, solid concentration profiles result which can be described on the basis of the sedimentation-dispersion model (78,79,80). This model involves two parameters, namely, the solids dispersion coefficient, E3, and the mean settling velocity, U5, of the particles in the swarm. Among others Kato et al. (81) determined 3 and U3 in bubble columns for glass beads 75 and 163 yum in diameter. The authors propose correlations for both parameters, E3 and U3. The equation for E3 almost completely agrees with the correlation of Kato and Nishiwaki (51) for the liquid phase dispersion coefficient. 

In the previous section, stability criteria were obtained for gas-hquid bubble columns, gas-solid fluidized beds, liquid-sohd fluidized beds, and three-phase fluidized beds. Before we begin the review of previous work, let us summarize the parameters that are important for the fluid mechanical description of multiphase systems. The first and foremost is the dispersion coefficient. During the derivation of equations of continuity and motion for multiphase turbulent dispersions, correlation terms such as esv appeared [Eqs. (3) and (10)]. These terms were modeled according to the Boussinesq hypothesis [Eq. (4)], and thus the dispersion coefficients for the sohd phase and hquid phase appear in the final forms of equation of continuity and motion [Eqs. (5), (6), (14), and (15)]. However, for the creeping flow regime, the dispersion term is obviously not important. 

Various model parameters involved in the derivation of the stability criterion need to be specified in order to use the stability criterion for quantitative predictions. Model parameters essential for this purpose include the slip velocity, the virtual mass coefficient, and the dispersion coefficient. The procedure for estimation of these parameters is given for gas-solid (and solid-liquid) fluidized beds and bubble columns. 

In the previous section, it was pointed out that the critical gas hold-up is very sensitive to the d -v oo relationship and the values of m, Cy, and a. It was thought desirable to calculate the value of a for all the experimental points shown in Table V. For each point, four values of m (1, 1.4, 1.9 and 2.4) and three levels of Cy were considered. The values of a are given in Table VI. The average value works out to be 3.14. Table V also gives the comparison between the experimental critical gas hold-up and the critical gas hold-up predicted using the transition criterion [Eq. (25)] with dispersion coefficient equal to 3. The comparison between predicted and experimental gas hold-up for bubble columns is shown in Fig. 30. It can be seen... 

The most important parameter governing stability is the dispersion coefficient of the dispersed phase such as bubbles, drops, and particles. The published information is not sufficient. A comprehensive research program is needed for the measurement of dispersion in all multiphase reactors over a wide range of terminal velocities, column diameters, column heights, sparger designs, phase velocities, and continuous-phase physical properties. 

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