Multicomponent pseudo-binary systems

A variety of conditions are possible with multicomponent systems in general. When one needs to separate partldes of one size from particles of all other sizes present in a suspension, or when particles of different sizes are to be separated from one another as well as from the medium of suspension, a multi-component separation problem exists. If a macromol-ecular substanire or solution Is to be fractionated, the nature of the description of the separation problem Is similar. Such problems are handled most conveniently by dealing with pseudo binary systems. We will come across such cases as we proceed further in this book, although binary systems will be encountered much more frequently. 

Like distillation, the McCabe-Thiele analysis is strictly valid only for a binary system. However, only two components are usually present at significant concentrations within each individual section of the coliunn (and, besides, in practice, the SMB process is essentially used to separate binary mixtrues). A preliminary analysis in which each section is considered as a pseudo binary McCabe-Thiele system can therefore provide useful guidance in the design of a multicomponent adsorption system. 

If we compare Eqs. 5.1.14 with the conservation equation (Eq. 5.1.2) for a binary system and the pseudo-Fick s law Eq. 5.1.15, with Eq. 3.1.1 then we can see that from the mathematical point of view these pseudomole fractions and pseudofluxes behave as though they were the corresponding variables of a real binary mixture with diffusion coefficient D-. The fact that the are real, positive, and invariant under changes of reference velocity strengthens the analogy. If the initial and boundary conditions can also be transformed to pseudocompositions and fluxes by the same similarity transformation, the uncoupled equations represent a set of independent binary-type problems, n - 1 in number. Solutions to binary diffusion problems are common in the literature (see, e.g.. Bird et al., 1960 Slattery, 1981 Crank, 1975). Thus, the solution to the corresponding multicomponent problem can be written down immediately in terms of the pseudomole fractions and fluxes. Specifically, if... 

In reactive flow analysis the Pick s law for binary systems (2.285) is frequently used as an extremely simple attempt to approximate the multicomponent molecular mass fluxes. This method is based on the hypothesis that the pseudo-binary mass flux approximations are fairly accurate for solute gas species in the particular cases when one of the species in the gas is in excess and acts as a solvent. However, this approach is generally not recommend-able for chemical reactor analysis because reactive mixtures are normally not sufficiently dilute. Nevertheless, many industrial reactor systems can be characterized as convection dominated reactive flows thus the Pickian diffusion model predictions might still look acceptable at first, but this interpretation is usually false because in reality the diffusive fluxes are then neglectable compared to the convective fluxes. 

The graphical-based shortcut methods for binary batch distillation may be applied to multicomponent distillation only when the separation is between two key components to produce one distillate product and the residue. In this case the calculations may be approximated by lumping the other components with either of the key components and treating the system as a pseudo-binary. 

Not aU possible applications of mass transfer theory have been discussed, and multicomponent systems have been treated as pseudo binary or ternary systems. To delve deeper, the reader should consult specialized books, some of which are listed in the References section. 

There are a number of other aspects of eutectic solidification, particularly the divorced eutectics," and the pseudo-binary eutectics which occur in multicomponent systems. These are both very specialised topics and will not be dealt with further here. 

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