Penetration model multicomponent

In Chapter 7 we define mass transfer coefficients for binary and multicomponent systems. In subsequent chapters we develop mass transfer models to determine these coefficients. Many different models have been proposed over the years. The oldest and simplest model is the film model this is the most useful model for describing multicomponent mass transfer (Chapter 8). Empirical methods are also considered. Following our discussions of film theory, we describe the so-called surface renewal or penetration models of mass transfer (Chapter 9) and go on to develop turbulent eddy diffusivity based models (Chapter 10). Simultaneous mass and energy transport is considered in Chapter 11. 

Let us now turn our attention to multicomponent systems. An exact analytical solution of the multicomponent penetration model for ideal gas mixtures has been presented by Olivera-Fuentes and Pasquel-Guerra (1987). Their analysis, which, in many ways, is similar to the film model analysis of Section 8.3.5, is generalized below to any system described by constitutive relations of the form of Eqs. 2.2.9 or 3.2.5. 

In our analysis of the multicomponent penetration model we used the combined variable i = z/yfit. 

Equations 9.3.15 and 9.3.16 represent an exact analytical solution of the multicomponent penetration model. For two component systems, these results reduce to Eqs. 92.1. Unfortunately, the above results are of little practical use for computing the diffusion fluxes because they require an a priori knowledge of the composition profiles (cf. Section 8.3.5). Thus, a degree of trial and error over and above that normally encountered in multicomponent mass transfer calculations enters into their use. Indeed, Olivera-Fuentes and Pasquel-Guerra did not perform any numerical computations with this method and resorted to a numerical integration technique. 

Toor (1964) and Stewart and Prober (1964) did not use the method presented above they used the method described in Chapter 5. For the multicomponent penetration model, the following expression for the matrix of mass transfer coefficients is obtained (cf. Section 8.4.2) ... 

Extend the film-penetration model of mass transfer developed by Toor and Marchello (1958) to multicomponent mixtures. See also, Krishna (1978a). 

Krishna, R., A Note on the Film and Penetration Models for Multicomponent Mass Transfer, Chem. Eng. Sci., 33, 765-767 (1978a). 

Olivera-Fuentes, C. G. and Pasquel-Guerra, J., The Exact Penetration Model of Diffusion in Multicomponent Ideal Gas Mixtures. Analytical and Numerical Solutions, Chem. Eng. Commun., 51, 71-88 (1987). 

These values are within 5% of the values calculated with the penetration theory correction factor matrix and support our earlier suggestion that it is sufficient to use the simpler film model correction factor matrix in multicomponent mass transfer calculations at high mass transfer rates. ... 

The following three multicomponent transport models have been used to explain the depression of the permeability of a component in a mixture relative to its pure component value (Fig. 21) the Petropoulos model and the competitive sorption model, both of which assume that direct competition for diflfiisive pathways within the glass is negligible, and a more general permeability model in which direct competition can occur between penetrant molecules for both sorption sites and diffusion pathways. All three of the models presented here are based upon the framework of the dual-mode model. It is worth mentioning that the site-distribution model has recently been extended to accoimt for diffusion (98) and that free volume models exist for transport in glassy polymers (99). 

Equation 27 represents the basic equation for the NELF model based on the Sanchez and Lacombe lattice fluid theory it provides the explicit dependence of the chemical potential of each penetrant species of a multicomponent mixture on temperature, volume and composition. In view of equation 12 and equation 14 at given temperature, volume and composition this equation is valid for any pressure... 

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