Binary separation in a double-entry separator

The double-entry separator performance is often characterized for a two-component system by the equilibrium ratio Ki (definition (2.2. If)) as well as by the separation factor ajj (definition (2.2.2a)). Both definitions relate the two product stream compositions and are related to each other by (2.2.2i). The compositional differences between the light fraction and feed stream 1 may be indicated by a heads separation factor 

Similarly, the tails separation factor between feed stream 2 and the heavy fraction is 

Unlike that far a single-entry separator, where = aj X 0(2 by definition, here. 

The distribution ratio k u of species i between the two product streams 1 and 2 can be defined here in the same manner as in (2.2.19)  

For binary vapor-Uquid systems used in distillation (see Example 2.3.1) if vapor phase y = 1 and liquid phase j = 2, then, for species i, k u is equal to X, a parameter frequently used in distillation analysis (see Problem 2.2.1). We see further from (2.2.2a) that 

---