Predicting the Mass Transfer Coefficient

Correlations based on dimensional analysis with the above variables in equation 3-10 would allow mass transfer rates to be easily predicted, e. g. in scaling-up lab results to full-scale or for changes in the liquid properties. However, no correlations have been developed with this complexity. 

Scale-up factors have been developed for changes in density, viscosity, surface tension and correlations using these factors have been successful for certain reactor geometries, i. e. stirred tank reactors, and well defined systems, i. e. air/water (Zlokamik, 1978)  

Similar factors have been developed for bubble columns, which includes the concept of gas hold-up eG, the fraction of the reactor liquid volume occupied by the gas dispersed in the liquid phase. The number of such factors can be reduced when comparing the mass transfer of just one compound in the same liquid/gas system, e. g. for oxygen or ozone transfer in clean water/air systems the above relationship reduces to the first three terms. 

Some useful correlations which can be used for a first approximation of the kLa s or c s in laboratory-scale ozone reactors can be found in Dudley (1995) for bubble columns, and Libra (1993) for STRs. Various correlations found in the literature, empirical as well as those based on theoretical or dimensional analysis, have been compared to results from their own experiments. Dudley concluded that correlations based on theoretical support performed better than those developed by curve-fitting. 

The disadvantages of using empirical correction factors, which lump many parameters together, becomes clear when one considers that a and 0 have been found to change depending on not only the concentration and type of contaminants, but also on the hydrodynamics of the system. Clearly, a better understanding of the relationship between physical properties and kLa and the quantification of these physical properties in (waste-)water is necessary, so that correlations based on dimensional analysis can be made. However, from the practical point of view, the empirical correction factors have proven their worth, when measured and used appropriately. 

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Equations 11 and 12 caimot be used to predict the mass transfer coefficients directly, because is usually not known. The theory, however, predicts a linear dependence of the mass transfer coefficient on diffusivity. 

A pulse of a racemic mixture (5 g each enantiomer) was carried out to check the adsorption model and to predict the mass transfer coefficient. The other model parameters used in simulation were = 0.4 and Pe = 1000. The mass transfer coefficient used to fit experimental and model predictions in the pulse experiment was k = 0.4 s k Model and experimental results are compared in Figs. 9-16 and 9-17. 

Mass transfer. It is not yet possible to predict the mass transfer coefficient with a high degree of accuracy because the mechanisms of solute transfer are but imperfectly understood as discussed Light and Conway(14), Coulson and Skinner(15) and Garner and Hale 16 1. In addition, the flow in spray towers is not strictly countercurrent due to recirculation of the continuous phase, and consequently the effective overall driving force for mass transfer is not the same as that for true countercurrent flow. 

Postulating that n is dependent on the turbulence in the system, Dobbins (1956) proposed that under sufficiently turbulent conditions, n approaches 0.5 (surface renewal or penetration theory), while under laminar or less turbulent conditions n approaches 1.0 (film theory). Thus, the selection of the value for n to predict the mass transfer coefficient should depend on the degree of turbulence in the system ... 

Mass-transfer coefficients. For spheres or crystals with a shape factor close to 1.0, Eq. (21.59) may be used to predict the mass-transfer coefficient As discussed on page 672, for suspended particles in an agitated system the coefficient will be... 

Prediction of Mass-Transfer Coefficients. Predict the mass-transfer coefficients... 

Theories of mass transfer try to predict the mass transfer coefficient k from a variety of process variables. What velocity dependence do they predict ... 

Predict the mass transfer coefficient in cm/sec for liquid n-butyl alcohol vaporizing into air at 80 °F and 1 atm. You know that the heat transfer coefficient in the same system in 56 Btu/hr ft °F. 

Experimental Mass Transfer Coefficients. Hundreds of papers have been pubHshed reporting mass transfer coefficients in packed columns. For some simple systems which have been studied quite extensively, mass transfer data may be obtained directiy from the Hterature (6). The situation with respect to the prediction of mass transfer coefficients for new systems is stiU poor. Despite the wealth of experimental and theoretical studies, no comprehensive theory has been developed, and most generalizations are based on empirical or semiempitical equations. 

Other correlations based partially on theoretical considerations but made to fit existing data also exist (71—75). A number of researchers have also attempted to separate from a by measuring the latter, sometimes in terms of the wetted area (76—78). Finally, a number of correlations for the mass transfer coefficient itself exist. These ate based on a mote fundamental theory of mass transfer in packed columns (79—82). Although certain predictions were verified by experimental evidence, these models often cannot serve as design basis because the equations contain the interfacial area as an independent variable. 

Prediction methods attempt to quantify the resistances to mass transfer in terms of the raffinate rate R and the extract rate E, per tower cross-sectional area Af, and the mass-transfer coefficient in the raffinate phase and the extract phase times the interfacial (droplet) mass-transfer area per volume of tower a [Eqs. (15-32) and (15-33)]. 

Many correlations have been published for predicting the height of a transfer unit, and the mass-transfer coefficients several are reviewed in Volume 2, Chapter 12. The two methods given in this section have been found to be reliable for preliminary design work, and, in the absence of practical values, can be used for the final design with a suitable factor of safety. 

Their correlations were based on a large amount of data on gas absorption and distillation with a variety of packings, which included Pall rings and Berl saddles. Their method for estimating the effective area of packing can also be used with experimentally determined values of the mass-transfer coefficients, and values predicted using other correlations. 

Numerous turbulent mass-transfer relationships are given in Eqs. (39)-(50), Table VII. Although the most important ones in practical applications are those for channels and tubes, several other configurations also have been investigated because of their hydrodynamic interest. Generally, it is not possible to predict mass-transfer rates quantitatively by recourse to turbulent flow theory. An exception to this is for the region of developing mass transfer, where a Leveque-type correlation between the mass-transfer coefficient and friction coefficient/can be established ... 

External mass transfer is the only process of the three involved in adsorption that can be predicted with reasonable accuracy from physical data. Mass transfer from the bulk gas to the particle surface can be considered by the film resistance approach. The rate of mass transfer is proportional to the external surface area of the adsorbent particles and the adsorbate concentration difference between the bulk gas and the particle external surface. The proportionality constant is the mass transfer coefficient, the reciprocal of the resistance to... 

Equation (35) predicts that the mass transfer coefficient increases with increases in the screw speed and the number of parallel channels on the screw. The explanation for this is rather simple and is related to the fact that each time the film on the barrel wall is regenerated and the surface of the nip is renewed, a uniform concentration profile is reestablished, which means that the driving force for mass transfer is maximized. Since the instantaneous mass transfer rate decreases with time, mass transfer rates can be maximized by keeping the exposure time as short as possible, and... 

The equations are also coupled by the mass transfer coefficient This is the standard mass transfer problem we encountered with catalytic reactions. As with catalytic reactors, processes are very often limited by mass transfer so that the kinetics become unimportant in predicting performance. 

The straight line for Ap = 0 represents diffusion in a stagnant medium [Eq. (3-44)]. In air spheres with diameters less than about 30 pm have transfer rates essentially equal to those in a stagnant medium, while in water the diameter for this to occur must be less than about 3 pm. In water the mass transfer coefficient is only weakly dependent on diameter, a prediction which has been verified experimentally (C2). For free fall in air, the transfer coefficient exhibits a larger decrease with diameter. The following expressions fit the predictions of Figs. 5.22 and 5.23 over the ranges indicated ... 

For particles with rough surfaces, e.g., with roughness elements of height less than 20% of d, the mass transfer coefficient is usually larger than predicted here (A5, J4, S3, S4), but at most by about 50%. Roughness is treated in more detail in Chapter 10. For a particle made up of a small number of particles in a cluster, the use of d in Eq. (6-35) gives good results (S4). 

The presence of container walls has a much smaller effect on Sherwood number than on drag since the mass transfer coefficient is only proportional to the one-third power of the surface vorticity. For a sphere with given settling on the axis of a cylindrical container, the Sherwood number decreases with 2, but it is still within 8% of the Sherwood number in an infinite fluid for 2 — 0.5. No data are available to test these predictions. 

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