The driving-force diagram for a binary mixture is obtained by plotting

versus

, where

and

are the liquid and vapor mole fractions of the light component. Indeed, the driving force is

, where

and

are the vapor-liquid equilibrium (VLE) constants. For example, VLE behavior of a binary mixture composed of pentane and dichloromethane is predicted by setting

and

.

The binary mixtures considered here present a positive azeotrope with a composition given by

. For this case, the driving-force diagram is composed of two concave curves that intersect at the azeotrope position.

Let us take a saturated liquid feed with a composition,

.

If the reflux ratio is equal to

, then the operating lines, shown in light blue, intersect at

. For

, the operating lines are depicted in blue. The slope of the operating lines in the driving-force diagram can be easily related to the reboil and reflux ratios.

This Demonstration plots the driving-force diagram and the operating lines for

and

. You can change the value of the VLE behavior of the mixture by changing the values of the VLE constants

and

. The McCabe–Thiele diagram is also given for both when

and

. Finally, the minimum reflux ratio is computed in the program by two methods: (1) using the intersection of the feed line and the equilibrium curve (this is the classical McCabe–Thiele method) and (2) using the slope of the light blue operating lines in the driving-force diagram. Both methods give the same result for the minimum reflux ratio. In the present Demonstration, it is assumed that distillate and bottom specifications are

mole and

mole %, respectively.

One of the snapshot shows interesting behavior: the number of equilibrium stages is very large (exactly 23 plates are needed). This is due to the presence of a tangent pinch. In such a case, the reflux ratio should be increased to avoid having an excessive number of stages. Caution should be exerted when using this method of determination of the minimum reflux ratio because of the possibility of the presence of a tangent pinch.

Here only the left part of the driving-force diagram has been used. It is straightforward to use the right part of this diagram by selecting a feed with a composition above

. The distillate would be an almost pure light component and the bottom specification would be a little above the azeotrope's composition.