Equation Maxwell-Stefan diffusional

When more than two components are present, the efficiencies of each are not necessarily the same. The rigorous approach to handling multicomponent mixtures, outlined by Taylor and Krishna, uses the Maxwell-Stefan diffusional equations. Chan and Fair used the rigorous approach to compare multicomponent system separations with those predicted by the use of the equivalent pseudobinary systems. They found that if the dominant pair of components present in the mixture is used to determine efficiency for all of the components, the separation determined is quite close to that resulting from rigorous multicomponent procedures. 

Diffuslonal interaction methods. These calculate component efficiencies, but account for diffusional interactions. The calculation procedure is based on the Maxwell-Stefan diffusion equations, as developed by Krishna et al. (200,201). The equations are complex and are presented in the original reference. Lockett (12) has an excellent summary. For a ternary system, the steps below are followed (12) ... 

The modeling of RD processes is illustrated with the heterogenously catalyzed synthesis of methyl acetate and MTBE. The complex character of reactive distillation processes requires a detailed mathematical description of the interaction of mass transfer and chemical reaction and the dynamic column behavior. The most detailed model is based on a rigorous dynamic rate-based approach that takes into account diffusional interactions via the Maxwell-Stefan equations and overall reaction kinetics for the determination of the total conversion. All major influences of the column internals and the periphery can be considered by this approach. 

In dilute electrolyte systems, the diffusional interactions can usually be neglected, and the generalized Maxwell-Stefan equations are reduced to the Nemst-Planck equations (B3) ... 

In any event, we hope it is now well understood that mass transfer in multicomponent systems is described better by the full set of Maxwell-Stefan or generalized Fick s law equations than by a pseudobinary method. A pseudobinary method cannot be capable of superior predictions of efficiency. For a simpler method to provide consistently better predictions of efficiency than a more rigorous method could mean that an inappropriate model of point or tray efficiency is being employed. In addition, uncertainties in the estimation of the necessary transport and thermodynamic properties could easily mask more subtle diffusional interaction effects in the estimation of multicomponent tray efficiencies. It should also be borne in mind that a pseudobinary approach to the prediction of efficiency requires the a priori selection of the pair of components that are representative of the... 

For the q - - 1-component pseudo-mixture we may modify the formulation of the Maxwell-Stefan equation given in the last line of (2.298) and the generalized diffusional driving force expression (2.283). The dusty gas model, for s = 1,2,..., q+l, yields ... 

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