Mass transfer coefficients models for

Mass-transfer coefficient models for the vapor and liquid coefficients are of the general form... 

Figure 4.58 Interphase mass-transfer coefficient obtained for a reaction engineering model [94. Reactor model...

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... 

If the DMS inventory in Salt Pond is at steady state in summer (5), production should approximately balance removal. Tidal removal of DMS to Vineyard Sound is minimal. Outflow from Salt Pond is thought to be primarily surface water, and using a maximum tidal range of 0-0.2 m/d and a mean surface water concentration of 10 nmol/L, we calculate an export rate of less than 2 /imol/m2/d. The water-air flux of DMS may be calculated using the two film model of liss and Slater (22 flux = -ki C, ). With the same surface water DMS concentration (C ) and an estimated mass transfer coefficient (ki) for DMS of 1.5 cm/h, the projected flux of DMS from the pond into the atmosphere would be 4 /unol/m2/d. This compares with the range of estimated emissions from the ocean of 5-12 /imol/m2/d (1). 

The mass-transfer efficiencies of various MHF contactors have been studied by many researchers. Dahuron and Cussler [AlChE 34(1), pp. 130-136 (1988)] developed a membrane mass-transfer coefficient model (k ) Yang and Cussler [AIChE /., 32(11), pp. 1910-1916 (1986)] developed a shell-side mass-transfer coefficient model (ks) for flow directed radially into the fibers and Prasad and Sirkar [AIChE /., 34(2), pp. 177-188 (1988)] developed a tube-side mass-transfer coefficient model (k,). Additional studies have been published by Prasad and Sirkar [ Membrane-Based Solvent Extraction, in Membrane Handbook, Ho and Sirkar, eds. (Chapman Hall, 1992)] by Reed, Semmens, and Cussler [ Membrane Contactors, Membrane Separations Technology Principle. and Applications, Noble and Stern, eds. (Elsevier, 1995)] by Qin and Cabral [MChE 43(8), pp. 1975-1988 (1997)] by Baudot, Floury, and Smorenburg [AIChE ]., 47(8), pp. 1780-1793 (2001)] by GonzSlez-Munoz et al. [/. Memhane Sci., 213(1-2), pp. 181-193 (2003) and J. Membrane Sci., 255(1-2), pp. 133-140 (2005)] by Saikia, Dutta, and Dass [/. Membrane Sci., 225(1-2), pp. 1-13 (2003)] by Bocquet et al. [AIChE... 

Having completed the formal development of an expression for the evaluation of the interfacial fluxes we turn to the actual evaluation of the zero-flux mass transfer coefficient k for some specific models of turbulence. It is usual in such developments to define the Stanton number... 

For heat transfer the film theory is the most commonly used model, and the physical picture of a laminar film in which the whole temperature difference is situated leads to a result analogous to the mass transfer coefficient model [5]. After integrating Fourier s law over the film, a comparison with the heat transfer coefficient model (5.126) yields ... 

An important feature of fluidized-bed reactors is mass transfer between bubble and emulsion. Several models have been proposed for this exchange. The Davidson model assumes no cloud, so that only one mass transfer coefficient be (for direct bubble-emulsion exchange) is involved. On the other hand, the... 

Table 2 summarizes the mass transfer coefficients determined for this model for batch tubes, stirred batch, and flowthrough reactor coi gurations and shows that the diffusive mass transfer coefficient kd increases in this order of reactor type. However, one would expect the mass transfer coefficient to follow such a pattern as flow is increased. On the other hand, although the rate constants for conventional models based on only chemical reaction can also be fit to data from these three reactor types, rate constants for these models should only depend on temperature, and these variations would not be expect. Thus, coupling mass transfer to reaction appears to provide a more meaningful explanation for the effects of flow on performance, but further work is needed to Mly develop and evaluate this approach. 

We need a pertinent reactor model (see Chapter 4), including a reaction model (see Section 3.2) for the chemistry at the working electrode. Strictly speaking, there should be a model for the anode reaction so that the potential drop at the anode can be calculated for each current density. Allowance for the drop has been made by simply doubling the cathode potential. This will suffice for an illustrative example but is not recommended in practice. As we have seen in Section 3.2, to use the reaction model we need values for the kinetic constants and mass transfer coefficient, and for the energy balance we need the enthalpies of reaction for the major reactions in the cell. 

As already mentioned foe mass transfer coefficients used for calculations in chemical engineeting are rather parameters in foe calculation model than physical values. That is diy speaking of methods for determination of these coefficients we should distinguish methods for determination of foe mass transfer coefficients for foe piston flow model and for foe diffusion model. Since for foe latter model foese coefficients are connected with foe axial mixing coefficients in gas and liquid phase, foe methods for their determination are discussed after foe mefoods for determination of foe axial mixing coefficients. 

The models, di ussol in Chapter 1, of fee elementary act of tiie mass transfer processes are able to pr ct fee mass transfer coefficient only for a limited circle of hydrorfynamic regimes and types of interfece, which are usually far away fiom tiie cor htions of fee industrial packed bed coluitms. Nevertheless, feey dlow tracing fee ways for creation of new, more effective packings. 

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. 

The main conclusion to be drawn from these studies is that for most practical purposes the linear rate model provides an adequate approximation and the use of the more cumbersome and computationally time consuming diffusing models is generally not necessary. The Glueckauf approximation provides the required estimate of the effective mass transfer coefficient for a diffusion controlled system. More detailed analysis shows that when more than one mass transfer resistance is significant the overall rate coefficient may be estimated simply from the sum of the resistances (7) ... 

The enhanced rate expressions for regimes 3 and 4 have been presented (48) and can be appHed (49,50) when one phase consists of a pure reactant, for example in the saponification of an ester. However, it should be noted that in the more general case where component C in equation 19 is transferred from one inert solvent (A) to another (B), an enhancement of the mass-transfer coefficient in the B-rich phase has the effect of moving the controlling mass-transfer resistance to the A-rich phase, in accordance with equation 17. Resistance in both Hquid phases is taken into account in a detailed model (51) which is apphcable to the reversible reactions involved in metal extraction. This model, which can accommodate the case of interfacial reaction, has been successfully compared with rate data from the Hterature (51). 

To model convection drying both the heat transfer to the coated web and the mass transfer (qv) from the coatiag must be considered. The heat-transfer coefficient can be taken as proportional to the 0.78 power of the air velocity or to the 0.39 power of the pressure difference between the air in the plenum and the ambient pressure at the coatiag. The improvement in heat-transfer coefficients in dryers since the 1900s is shown in Figure 20. The mass-transfer coefficient for solvent to the air stream is proportional to the heat-transfer coefficient and is related to it by the Clulton-Colbum analogy... 

The Shei wood-number relation for gas-phase mass-transfer coefficients as represented by the film diffusion model in Eq. (5-286) can be rearrangecTas follows ... 

Mass-transfer coefficients are derived from models. They must be employed in a similar model. For example, if an arithmetic concentration difference was used to determine k, that k should only be used in a mass-transfer expression with an arithmetic concentration difference. 

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