January 31, 2012  Tagged with: , , , , , , , ,

*Note: This article assumes you have rudimentary knowledge of how a simple distillation column operates.  Though much of the basics of the simple model for a distillation column will be covered below, it should not be considered as a stand alone reference.

# Introduction

While taking my separations and mass transfer operations course at UF, I took a particularly interesting exam where I was tasked with predicting the performance of a distillation column with two inputs.  This may be getting ahead of myself, as the problem’s information was written into the proof, but the problem was as follows:

## The Test Problem

Given a distillation column separating n-pentane and n-heptane, with a feed rate of 200 kgmol/hr of a 40 mol% n-pentane liquid at bubble point, a 95 mol% distillate stream, a 5 mol% bottoms stream, a 30 mol% side stream with a flow rate out equal to that of the bottoms leaving, a reflux ratio equal to twice that of the minimum, and a 50% average tray efficiency, use the McCabe-Thiele graphical method and the provided vapor-liquid equilibrium data to determine a) the flow rate and composition of all streams, b) the minimum reflux ratio, c) the number of theoretical plates required, and d) the optimum placement of the feed stream and side stream.

So, the information given so far is

• $F=200 kgmol/hr$
• $x_F=0.40$
• $q_F=1$
• $x_D=0.95$
• $x_W=0.05$
• $G=-W$ (negative sign due to opposite orientation)
• $x_G=0.30$
• $q_G=1$
• $R_D=2R_{min}$
• $\epsilon_a=0.50$