Minimum Number of Stages, Total Reflux:  It is very useful to get an idea of minimum number of stages required to achieve a desired separation.  This can be achieved by using the diagonal line as the operating line.  The top- and bottom-operating lines merge when the column is operating under total reflux conditions.  No product is withdrawn. 

We can draw the number of steps as follows:

1. Draw a vertical line from point (x_W, x_W) till it touches the equilibrium curve.

2. Draw a horizontal line till it touches the diagonal line.

3. Repeat the steps (1) and (2) till we reach point (x_D, x_D).

4. The number of triangles represents the number of stages.

We may not get a whole number.

If relative volatility is fairly constant, then minimum number of stages can be calculated as

Where the subscript m, W, and D stand for minimum, waste, and distillate, respectively.  And α_WD is average relative volatility between the residue- and distillate-sections.  The number of stages computed in this way includes 1/2 stage for condenser and 1/2 reboiler.

The minimum number of stages above the feed point can also be calculated by replacing x_W with x_F in the above equation as follows:

Where the subscript m, F, and D stand for minimum, feed, and distillate, respectively.  And α_FD is average relative volatility between the feed- and distillate-sections.

A ratio of N_mWD/N_mFD gives a measure of the percentage of rectification section above the feed location.