Point Efficiency of Multicomponent Systems

For multicomponent systems the composition above the froth is given by Eq. 12.2.3 as 

The Murphree point efficiencies conventionally defined by Eq. 13.1.3 may be expressed in terms of the elements of the matrices [g]. For a ternary mixture there are two independent compositions and two independent efficiencies. Using Eq. 12.2.3 we can show that the component efficiencies and 91/2 given by 

The efficiency of component 3 can be expressed in terms of the efficiency of the other two components as 

Only when [g] is a diagonal matrix with all elements on the main diagonal equal to one another (i.e., [g] reduces to the form g[/]) will the three component efficiencies EQy2 ov2 have the same value. This will be the case in mixtures made up of components of a similar nature (e.g., close boiling hydrocarbons or mixtures of isomers). For mixtures made up of chemically dissimilar species, that is, mixtures with large differences between the binary pair diffusivities, we must except to have significant nondiagonal 

Examination of Eqs. 13.3.1-13.3.4 shows that the ratio of driving forces a = Ay lE/ yiE plays a key role in determining the relative magnitudes of the pQyy Now, in a multicomponent system, a may take any value in the range —00 to +00 (contrast this with a binary system for which Ayi/Ay2 = -1). Thus, the component EQy are unbounded and could exhibit values ranging anywhere from —00 to -Fool 

---