Heuristic Optimization

There are two widely used heuristics for optimum distillation design. We will discuss both of them in this section and compare the designs that result from applying each. It should be emphasized that they cannot both be used simultaneously for rigorous design because fixing one of the two completely specifies the design of the column.

4.1.1 Set Total Trays to Twice Minimum Number of Trays

We discussed the use of the Fenske equation to find the minimum number of trays in Chapter 2 for constant-relative-volatility systems. We found the minimum number of trays more rigorously in Chapter 3 by using the simulator to find the number of stages where the required reflux ratio became very large. In the numerical example, the

Distillation Design and Control Using Aspen™ Simulation, By William L. Luyben Copyright © 2006 John Wiley & Sons, Inc.

minimum number of trays is 15. Taking twice this number and adding two stages for the reflux drum and reboiler give a 32-stage column, which is the column we designed in Chapter 3.

It is interesting to compare this rigorous number with what the Fenske equation predicts for the same system. The first issue is to find an appropriate value for the relative volatility for the propane/isobutane system at the operating pressure of the column (16.8 atm). The usual approach is to find the relative volatility at the temperature at the top of the column (stage 2 temperature is 325.6 K) and at the temperature in the reboiler (stage 32 temperature is 366.1 K).

By definition, relative volatility aLH is the ratio of the vapor and liquid compositions of component L divided by the same ratio of component H. The propane and isobutane compositions on the top tray (stage 2) can be seen in the subitem Profiles under the column C1 block in the Data Browser window:

Of course, in this binary system, the isobutane compositions are simply 1 minus the propane mole fractions. Therefore the relative volatility between propane and isobutane on the top tray is

= yc3 /xc3 _ 0.98/0.96356322 _ Œ yiCi/xiCi (1 - 0.98)/(1 - 0.96356322) :

Repeating this calculation for conditions in the reboiler gives

= yc3 /xc3 _ 0.01715812/0.01 _ 1 " y,C4/x;c4 (1 - 0.01715812)/(1 - 0.01) .

The geometric average of these relative volatilities is aaverage = 7(1-.8529)(1.7633) = 1.8076

The distillate and bottoms propane compositions are xD = 0.98 and xB = 0.01. Substituting these values in the Fenske equation gives the minimum number of trays N^n log