	Department of Chemical Engineering College of Engineering
Florida A&M University		Florida State University

Experiment 300: Distillation

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Introduction

To follow

Experimental Overview

There are essentially two parts to the theoretical background regarding the analysis of the distillation column in our laboratory. The first area of interest is predicting values of the bottoms and distillate ethanol mole fractions based on the number of theoretical stages measured at total reflux and the known feed, bottoms, reflux, and distillate flow rates for the various experimental runs.

The second area of interest is determining the theoretical minimum number of stages and minimum reflux ratio based on the measured values of the bottoms and distillate ethanol mole fractions, not at total reflux.

Theoretical Stages at Total Reflux.

The theoretical minimum number of stages is the number of stages needed to reach a desired separation. The theoretical number of stages at total reflux may be calculated using the Fenske Equation and the McCabe Thiele Model.

Fenske Equation

The Fenske equation may be used to calculate the theoretical minimum number of stages, N_m, at total reflux for a distillation column with a total condenser.

X_D=mole fraction of desired product in distillate

X_B= mole fraction of desired product in bottoms

a₁= relative volatility of the overhead vapor

a_w= relative volatility of the bottoms liquid

McCabe Thiele Model

The McCabe Thiele model may also be used to determine the number of theoretical stages at total reflux. The following steps will enable one to determine the number of stages:

Draw the equilibrium line on an x-y plot.
Draw the y=x line.
Plot the measured bottoms and distillate ethanol mole fractions along the y = x line. For total reflux this line will be your operating 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 get the number of stages. Note: The last stage is the reboiler.

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.