Consider a distillation column with a partial reboiler and a total condenser. This column is used to separate three hypothetical components

,

, and

with relative volatilities

and

(i.e., the reference component is

) to be determined by the user. The calculation assumes that the reference component is the intermediate-boiling component,

, and that the lightest and heaviest components are

and

, respectively. The feed to the column has a thermal quality,

, also determined by the user. The feed composition is 40 mole%

, 30 mole%

, and 30 mole%

. The fractional recoveries in the distillate of components

and

are 98% and 95%, respectively. The fractional recovery in the bottom of component

is 95%. The distillate rate,

, can be computed from the equations

and

for

, where

stands for fractional recovery. One can use as a basis a feed flow rate equal to 100 kmol/hr. In such a case, the distillate rate

kmol/hr. The Demonstration applies the Underwood equations [1] in order to determine the minimum reflux ratio,

.

The relevant root (between

and 1) of the first Underwood equation is shown by the blue dot in the figure. The red curve is a plot of the function

Finally, the green region indicates where the appropriate root,

, of the first Underwood equation is expected.