Correlation for Mass-Transfer Coefficient

Mackay D, Yeun ATK (1983) Mass transfer coefficients correlations for volatilisation of organic solutes from water. Environ Sci Technol 17 211-233 Maier-Reimer E, Kriest I, Segschneider J, Wetzel P (2005) The UAMburg Ocean Carbon Cycle Model HAMOCC5.1 - Technical Description Release 1.1 -. MPI Reports on Earth System Science No. 14 1-57... 

Airlift reactors, 15 703-709, 726-727 gas-liquid volumetric mass transfer coefficient correlations for,... 

Gas-liquid volumetric mass transfer coefficient correlations, for airlift reactors, 15 704-705t Gas lubrication, 15 252 Gas mantles cerium in, 5 689 thorium in, 24 757 Gas masks, 5 832-835 Gas meter provers, liquid displacement, 11 652... 

Mackay, D. and Yeun, A.T.K. Mass transfer coefficient correlations for volatilization of organic solutes from water. Environ. Sci Technol, 17(4) 211-217, 1983. 

Mackay, D., Shiu, W.Y, Ma, K.C. (1995) Rlustrated Handbook of Physical-Chemical Properties and Environmental Fate for Organic Chemicals. Vol. 4, Oxygen, Nitrogen and Sulfur-Containing Compounds. Lewis Publishers/CRC Press, Boca Raton, Florida. Mackay, D., Yuen, T.K. (1983) Mass transfer coefficients correlations for volatilization of organic solutes from water. Environ. Sci. Technol. 17, 211-217. 

TABLE 8.2 Gas-Liquid Mass Transfer Coefficient Correlations for Airlift Bioreactors... 

Mackay, D., and A. T. K. Yeun. 1983. Mass Transfer Coefficient Correlations for Volatilization of Organic Solutes from Water, Environmental Science and Technology, vol. 17, pp. 211-217. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

Akita and Yoshida (1973) correlated the volumetric mass-transfer coefficient kLa for the absorption of oxygen in various aqueous solutions in bubble columns, as follows ... 

The correlations of Billet (66) and Onda et al. (187) are valid for various mixtures and packings and cover both absorption and distillation processes. The correlation of Kolev (133) is obtained for RA and certain random packings. In general, the mass transfer coefficient correlations need to be compared to one another and validated using experimental data. This shows, in particular, the way the mass transfer correlations influence the concentration prohles of the components and other relevant process characteristics. 

Equation 6.12 relates CP to flux (/) and the effective mass-transfer coefficient (kes) for retained solute. For a clean membrane keff = k, which is the boundary layer mass-transfer coefficient from Sherwood correlations [45, 46], However, for a membrane... 

Chrysikopoulos and Kim [70] developed time invariant, local mass transfer correlations for NAPL pool dissolution in saturated media based on numerically determined local mass transfer coefficients evaluated for interstitial fluid velocities of 0.1,0.5,0.7,0.85, and 1.0 m/day. It should be noted that solubility concentrations may occur at a NAPL-water interface when interstitial fluid velocities are less than 1.0 m/day [8]. Over 200 different rectangular pools with dimensions xx y in the range from 0.2 mx0.2 m to 10.0 mxlO.O m and approximately the same number of elliptic/circular pools with semiaxes axb in the range 0.1 mxO.l m to 5.0 mx5.0 m were examined. 

The results shown in Fig. 7 indicate that kLaL increases with pressure. On the other hand, for aqueous systems, Albal et al. (1983) showed both kLaL and kL to be independent of pressure. These investigators also showed that kLaL decreases with an increase in viscosity and increases with a decrease in surface tension. The mass-transfer coefficient data for oxygen-CMC-water and oxygen-water-Triton CF-32 were correlated by the dimensionless equation... 

Calculate the mass transfer coefficient, kL, for dissolution of oxygen from the air into 25°C water at 1 atm in a mixing vessel equipped with a flat-blade disk turbine and sparger. At those conditions, the diffusivity of oxygen in water, DAB, is 2.5 x 10 9 m2/s, the viscosity of water is 8.904 x 10-4 kg/(m-s), and the density of water is 997.08 kg/m3. Use Calderbank and Moo-Young s correlations (see Ref. 14). 

Figure 2. Comparison between experimental and model-predicted conversions for 2.5% Pd catalyst using the modified mass transfer coefficient correlations.

The mass transfer coefficient, jK, , for a sphere can be determined from the Sherwood number, Ns (= Q2Rq/Aib> where is the molecular diffusion coefficient of the solvent, species A, in the drying gas, species B), and the following engineering correlation [15] ... 

Exclusion of the dp/L and dp/D ratios from the correlations lead to gross errors up to 200% in the prediction of heat and mass transfer coefficients. Correlations of this form will be too particular to be useful for design. 

A systematic study of mass transfer in bubble columns by Mashelkar and Sharma (M8, M9, S23) is summarized in Fig. 23. Increasing the superficial gas velocity increases the gas holdup a, the volumetric mass-transfer coefficients, and the interfacial area per unit volume of dispersion, but not the true mass-transfer coefficients. Correlations proposed for ki, seem too specific to be extended to practical systems (H13, FI, A3). Sharma and Mashelkar (S21) found good agreement between their experimental values of and the values from Geddes stagnant sphere model equation (G3) ... 

Where is the overall mass transfer coefficient in m/s and Crs is the concentration of B in the sweep gas channel (mol/dm ). The overall mass transfer coefficient accounts for all resistances to transport the tube side resistance of the membrane, the membrane itself, and on the shell (sweep gas) side resistance. Further elaboration of the mass transfer coefficient and its correlations can be found in the literature and in Chapter 11. In general, this coefficient can be a function of the membrane and fluid properties, the fluid velocity, and the tube diameters. 

The film theory has an important drawback. Although, the value of 6 is not known, one should regard it as uniquely dete mined by the hydrodynamics of the liquid phase. On the basis, Eq.l2 would predict k to be proportional to the diffusivity D. Empiri cal mass transfer coefficient correlations available in the lit rature for a liquid in contact with a gas consistently indicate that in fact k is proportional to the square root of D. Therefore, analyses based on the film theory model are not expected to predict correctly the influence of diffusivity values on the enhancement factor I. Therefore, one is lead to a more complex model of the fluid mechanics involved, the penetration theory model. This model leads, in its several variations, to the correct prediction of the... 

A. Since there is no standardized set of mass-transfer equations and units, converting terms in different units is a common task. The first thing to do is to look for the defining equation used for mass transfer or at the form of the mass-transfer coefficient correlation. Treybal (1980) developed... 

The mass transfer outside catalyst particles was modelled with rigorous Maxwell-Ste n equations, along with simultaneous heat transfer [9]. The multicomponent mass transfer coefficient matrix was calculated by assuming a film model for mass transfer and estimating the jo factor for the packed bed [10], The mass transfer coefficient correlations were extended into multicomponent systems by approximate matrix function calculations [11]. 

To use all of these equations, the heights of the transfer units or the mass transfer coefficients and must be known. Transfer data for packed columns are often measured and reported direcdy in terms of and and correlated in this form against and... 

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. 

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