J.
G.
LOWENSTEIN
DISTILLATION COLUMN DESIGNING A new grnph Paper s2mplzJeeS stepping-oJ theoretical stages rn the pinched Zones of McCabe-Thiele diagrams.
Only one diagram is needed for the entire concentration range
mce McCabe and Thiele published their celebrated graphical design of fractionating columns in 1925 (3), engineers and chemists have attempted to devise more accurate methods of using the equilibrium diagram (X-Y diagram). Even at the beginning, McCabe and Thiele recognized that the diagram would have to be “opened up” when either the distillate or residue has to he nearly free of the second component, or when the equilibrium curve pinches-Le., approaches the 45’ (X-Y) line at a very shallow angle. These authors used two methods: one was to expand the X axis relative to the Y axis by a factor of 5 or 10; the second was to take the extreme ends of the diagram, say from 0 to 0.1 mole fraction and 0.9 to 1.0, and enlarge them to show smaller increments. Later workers in the field added such refinements as a graphical-analytical method where plates did not have to be stepped off but were calculated from the geometry of the equilibrium envelope ( 5 ) . Also, logarithmic scales were used to enlarge the diagram (4). This latter method has been favorably received because commercial logarithmic paper is available, eliminating the need for secondary calculations, and also because this arrangement enlarges the critical zone of the diagram, but only in the extremely dilute region of the more volatile (product) component. By adding decades as required, the user can go to dilutions of lo-”. However, in the concentrated region this system is not applicable and actually works against you, because it is well known that the distance between 0.9 and 1.0 is the smallest of the major (log) steps! An effective method has been described by Horvath and Schubert ( 2 ) which essentially overcomes this deficiency. For the concentrated regions inverted log paper is used, with major axes labeled 0.9, 0.99, 0.999, etc., instead of the usual O.OOl,O.Ol, 0.1. In this manner a McCabe-Thiele diagram can be drawn for the concentrated region which is exactly analogous to that drawn for the dilute region. However, the method still has the disadvantage that in order to cover the entire X-Y diagram three complete sets of curves must be drawn: one from lo-” to 0.1, one from 0.1 to 0.9, and a
S‘paper on the
