Binary separation in a single-entry separator with or without recycle

2 Binary separation in a single-entry separator with or without recycle 

2 and both are different from Xyt the single-entry separator has achieved some separation. How much separation has been attained can be estimated by suitable descriptors, indices of separation. The simplest of these indices bear the name of specific separation processes where they are extensively used the desalination ratio Dr the solute rejection R and the decontamination factor Df. 

Note that all three definitions involve elimination of solute from a solvent (species 1). Further, the solvent is supposed to concentrate in exiting stream 1 and solute (species 2) in exiting stream 2. If there is separation, both Dr and Df will have values greater than 1, wheretis R 1. It is also clear that 

All such indices therefore describe separation by indicating how different the exit stream 1 composition is from the feed stream with respect to the soiute species. A somewhat similar index is the equiiibrium ratio of species i (obtained under phase-equilibrium conditions), 

Further, if one defines the mole ratio Xy = (xj/(l - Xy)) for a binary system, then 

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