The operating curves (lines) for a McCabe-Thiele diagram come from mass and energy balances around the column. If you assume a constant molar overflow (meaning that heat effects arent large), the molar vapor rate in the column is constant, except for what is added in the feed. This then allows the operating curves to be straight.
Figure 4 shows a McCabe-Thiele diagram for an ideal mixture. At a feasible reflux ratio, the two operating lines cross. If you project the lines to the x-axis, then, when these two projections overlap, there is a feasible design. The part of the rectifying operating line (orange) and of the stripping operating line (red) beyond where they overlap are ignored, and you can count the number of equilibrium stages required for the separation. If the reflux ratio is changed, then the whole graph can be re-computed. At minimum reflux (Figure 5) and less-than-minimum reflux (Figure 6), the profiles either just touch or do not touch at all.
Figure 4. Several feed-tray locations are possible for this separation of an ideal mixture. (Click to enlarge)
Figure 5. At minimum reflux, separation would require an infinite number of stages. (Click to enlarge)
Figure 6. Diagram clearly indicates that this particular separation is not feasible. (Click to enlarge)
This can be extended to three-component systems (and, with some additional thought, to four and more components), where just the projected operating lines are plotted. Of course, instead of being merely straight lines, they are now curves in two dimensions due to the extra components. The approach, however, is the same (using a conceptual design tool, such as Aspen Split):
- Determine the feed composition (We will assume a saturated liquid feed).
- Start by picking two fractions (mole or mass) in the distillate or bottoms products.
- Choose one fraction in the bottoms or distillate product (This uses up the degrees of freedom on the mass balance).
- Compute concentrations of the other components from the information in No. 1, No. 2 and No. 3.
- Select a reflux or reboil ratio.
- Compute the rectifying and stripping operating lines.
- Locate the feed stage. If the operating lines cross, then the feed stage is at their intersection; the number of stages then can be counted above and below the feed stage. If they do not cross, look at how the curves traverse the composition space and then change the reflux ratio or product specifications to allow the curves to cross.
Applying the design technique
For the acetone/isopropanol/water example (Figure 7), a distillation boundary caused by the water/isopropanol azeotrope separates the water from isopropanol. Like most azeotropes, this one is minimum boiling. Lets apply the above design technique to this mixture.
Figure 7. Separation is not possible if the overhead contains only a small amount of water. (Click to enlarge)
Assume that we have a feed composition representing the outlet of an equilibrium reactor dehydrogenating an azeotropic mixture of water and isopropanol to make a mixture of water/acetone/isopropanol (and hydrogen). The feed to the distillation column is 75% acetone, 11.8% isopropanol and 13.2% water. We wish to remove the product acetone and some of the water introduced in the feed, to prevent accumulation in the process. The isopropanol will be recycled to the reactor.
Because there is no azeotrope between acetone and isopropanol, you might be tempted to opt for a direct split to remove water as the bottoms stream in a first distillation column, with the acetone and isopropanol separated in a second column. However, a residue curve map analysis will quickly show that the distillation boundary between acetone and the isopropanol/water azeotrope prohibits this separation.
A stage-to-stage calculation can be performed as previously described. We specify relatively pure water in the bottoms product and, using a mass balance, a small amount of water in the distillate. We also set the reflux ratio at a value of 3. The stage-to-stage calculations for these specifications appear in Figure 7. Notice how the operating lines (blue and magenta) do not cross. This indicates an infeasible separation.
If the distillate composition is changed to allow more water to go overhead (thus putting the distillate composition in the same distillation region as the feed and the bottoms product), we can repeat the calculations to show that the operating lines do cross (Figure 8). This indicates a feasible separation; there are 7.9 stages with the feed at stage 2.3.
Another possibility is to instead remove acetone as a pure distillate product and generate an acetone-free bottoms product (Figure 9). Water can then be taken out in a second distillation column and the isopropanol/water azeotrope recycled back to the reactor.
Residue curve maps can help you quickly determine what feed splits that distillation can perform. The technique of specifying product compositions and calculating the required number of stages is powerful it allows you to find by visual feedback what changes are likely to be required to achieve the desired separation, if it is possible. This technique can be used regardless of whether there are azeotropes and even for relatively ideal systems. This initial analysis provides information and insights for carrying out detailed design calculations with process simulation software.
Raymond E. Rooks is a senior research specialist for the Dow Chemical Co., South Charleston, W.Va. E-mail him at RERooks@Dow.com.
1. Doherty, M.F. and M.F. Malone, Conceptual Design of Distillation Systems, McGraw-Hill (2001).
2. Barnicki, S.D., Put your column on the map, Chemical Processing, 67 (9), p. 39 (Sept. 2004).