Find minimum number of stage if a column is operating at
total reflux (no product withdrawn).
The design composition of the distillate is 91.4 per cent, whereas
residue is 0.565 percent pure in more volatile component. These compositions are given on molar
basis. Equilibrium data is best
described by a fairly constant relative volatility value of 4.12.
Solution:
Steps involved are:
Calculate y as given by alpha x over (one plus (alpha minus
one) time x).
Draw a diagonal line.
Locate point 1 having coordinates (xW, xW).
Draw a vertical line from point 1 till it reaches
equilibrium curve.
Draw a horizontal line till it reaches the diagonal
line. This completes one stage.
Repeat this process till a horizontal line from the
equilibrium curve touches or passes condenser point (xD, xD)
Count the number of triangles thus formed. That represents the number of stages.
We may not a whole number.
There may be a fractional plate.
When the equilibrium data is generated using constant
relative volatility value (as in this case), the minimum number of stages can
be calculated by mathematical equation given by: log of (xD time (1
– xW) over (xW time (1 minus xD))) over log of
alphaWD
Please note that D stands for distillate, and W stands for
Waste (bottoms). AlphaWD is the average relative volatility between
the residue- and distillate sections.
The number of stages, calculated this way, includes ½ stage for
condenser and ½ for the reboiler.
Neither condenser nor reboiler is complete equilibrium stage.
Plugging in the values, minimum number of stages is found to
5.33.