Design of Distillation Columns Ideal Mixtures

The feed that enters a distillation column can be a vapor, a partially vaporized liquid, a saturated liquid, or a subcooled liquid. Here we only derive the respective mass balances by assuming that the feed is a saturated liquid, and thus the composition of the feed equals precisely the composition of the liquid in the column at the feed supply. For other cases, the vapor and liquid portions have to be considered in the mass and heat balances, and we refer to textbooks that specialize in thermal operation units. 

The McCabe-Thiele approach for a binary mixture can be described as follows. First, we take the vapor-liquid equilibrium diagram y/x plot). Then we draw the operating lines based on the mass balance for the liquid and the vapor phase. There is one operating line for the stripping section and one for the top (rectification or enriching) section. The assumption of (in each case) constant molar flows of liquid and vapor ensures strictly straight operating lines. 

The reflux ratio R is defined as the ratio of the reflux flow to the distillate flow  

As shown by Eigure 3.3.11, this operating line is represented for a given desired top product composition (xA,d) and reflux ratio R by a line that intersects the diagonal line that splits the vapor-liquid equilibrium plot in half at a value of yA = XA.d, as required by Eq. (3.3.16) for xa = Xaa. The slope is R/(R+1) - see Eq. (3.3.16) - and the operating line of the rectification section intersects the y-axis (xa = 0) at yA = XA.dli + 1)- 

With the assumption that the feed enters the column as saturated liquid with a composition equal to the liquid at the feed supply (xA,feed = a). Eq. (3.3.17) can be rewritten for the lower-boiling compound A, and we obtain the equation for the operating line of the stripping section  

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