Determining the Theoretical Number of Stages not at Total Reflux

The McCabe Thiele Model is used to determine the theoretical number of stages when not at total reflux.

• Draw the equilibrium line on an x-y plot.

• Draw the y = x line.

• Plot the bottoms, feed, and distillate ethanol mole fractions along the y = x line.

• Plot the q-line (feed line) starting from the mole fraction of the feed extending through the equilibrium curve. The q-line is the moles of liquid produced per mole of feed. The feed is pure liquid therefore the q-line is 1 and should be at a 90 degree angle from the operating line.

• Plot the enriching operating line. The enriching operating line is calculated using the following equation:

R is the reflux ratio

x_D= mole fraction of desired product in the distillate

x_n is the composition leaving the nth stage.

y_n+1 =vapor composition entering the bottom of the column

• Plot the stripping operating line by extending a line from the bottoms mole fraction through the point where the enriching operating line intersects the q line.

• Draw a horizontal line from the distillate mole fraction on the operating line to the equilibrium line, followed by a vertical line drawn back down to the operating line. Repeat this until the desired bottoms composition is reached.

• Count the number of times the horizontal line hits the equilibrium line to determine the number of stages. Note: The last stage is the reboiler.