Graphical Representation of Binary Membrane Calculations

What is often called the McCabe-Thiele method for binary distillation calculations deploys a y-x (or y-x) diagram, say, for the more-volatile component, here designated the more-permeable component i. This furnishes substantiation that a separation can indeed be attained by the use of recycle or reflux in a multistage or cascade operation. 

A 45° diagonal is drawn across the figure, where y = x, and on this diagonal, the points are schematically located designating the composi-and Xg for the more-permeable component i. 

Operating lines and the intermediate behavior of the X locus or X line (or q line) are sketched in for a partitioning of the feedstream. Moreover, a few stage calculations are schematically shown at the more-permeable product end and for agreement between the feed and membrane 

A distinction is made, however, in that, in distillation, the temperature and phase equilibrium compositions vary. For membrane calculations, on the other hand, the relation between the reject and permeate 

The equilibrium curve, or IC-value, is for the most part represented by a straight line with slope K (or K,). Since this pertains to the more-permeable component, the slope is greater than unity. Furthermore, the K-value line lies above the 45° diagonal, albeit the actual determination is to a certain extent arbitrary, as per Example 3.1 of Chapter 3 that is, is it determined from a bubble-point, dew-point, or in-between type calculation on the feedstream composition  

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