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Ind. Eng. Chem. Res. 2010, 49, 3980–3982
Feed-Stage Multiplicity in Multicomponent Distillation William L. Luyben* Department of Chemical Engineering, Lehigh UniVersity, Bethlehem, PennsylVania 18015
Finding the optimum feed-stage location in distillation design usually is achieved by determining what location minimizes reboiler energy consumption. There is a minimum in a plot of energy versus feed stage in ideal distillation columns. However, in multicomponent systems, multiple steady states may occur as feed-stage location is varied. This note presents a numerical example of this phenomenon. 1. Introduction A common approach to distillation design is to evaluate the economics of energy and capital as a function of the total number of trays used in the column. Given feed conditions, specifications for both product streams and column pressure, a number of cases are explored with varying numbers of total trays. Typically, as more trays are used, reboiler energy consumption decreases, column diameter decreases, and heat exchanger area decreases (reboiler and condenser). Thus, energy costs go down as more trays are used. Capital costs may initially go down as more trays are used because the reduction column diameter and heat exchanger area may be more significant than the increase in column height. However, eventually column height becomes more dominant, and capital costs will increase as more trays are used. Total annual cost is often used as the economic objective function to be minimized in the trade-off between energy costs and annual capital costs. For each of the cases examined, the optimum stage on which the feed should be introduced must be found. This is usually accomplished by simply finding the feed stage that minimized reboiler heat input. The optimum feed stage is typically a stage with compositions that are similar to the composition of the feed. If we make a plot of feed-stage location versus reboiler heat input (or alternatively, reflux ratio), there is a minimum in the curve at the optimum. Feeding too high in the column requires more energy. Feeding too low in the column also requires more energy. This is the normal behavior expected. In the following sections, we consider two cases. The first is a simple binary separation with constant relative volatility. This system behaves as expected. The second is a multicomponent separation involving two azeotropes in which the feed-stage behavior is unexpected.
this system is 2.208, so the ratio of the actual reflux ratio to the minimum reflux ratio is 1.13, which a typical practical ratio for heuristic design. Figure 2 show how reflux ratio varies with feed tray location in this ideal system. The curve is monotonic and unique. It clearly shows that tray 10 is the optimum feed tray. Feeding on a tray other than optimum changes the McCabeThiele diagram and increases the reflux ratio required to achieve the specified separation. Figure 3 shows what happens if the feed is introduced lower in the column on tray 5. A higher reflux
Figure 1. McCabe-Thiele diagram; NF ) 10.
2. Ideal Binary Column A binary mixture of light and heavy components is fed as a saturated liquid into a distillation column with 20 ideal trays plus a partial reboiler and total condenser. Feed composition is 40 mol % light. The relative volatility is constant at 2. The distillate composition is specified to be 95 mol % light. The bottoms composition is specified to be 5 mol % light. Figure 1 shows the traditional McCabe-Thiele diagram for this system using 20 theoretical trays. The feed tray is specified to be tray 10 from the bottom with the partial reboiler providing one theoretical stage. Notice that the liquid composition on tray 10 is close to the feed composition. The required reflux ratio is 2.493 with this feed tray location. The minimum reflux ratio in * To whom correspondence should be addressed. E-mail: WLL0@ Lehigh.edu. Tel.: 610-758-4256. Fax: 610-758-5057.
Figure 2. Effect of feed tray on reflux ratio.
10.1021/ie1001108 2010 American Chemical Society Published on Web 03/17/2010
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Figure 6. Composition profiles; NF ) 21 when moving down column. Figure 3. McCabe-Thiele diagram; NF ) 5.
Figure 7. Composition profiles; NF ) 21 when moving up column.
Figure 4. McCabe-Thiele diagram; NF ) 15.
Figure 8. Temperature profiles.
Figure 5. Multiple steady states.
ratio is required to fit exactly 21 steps (20 trays plus partial reboiler) between the bottoms composition xB ) 0.05 and the distillate composition xD ) 0.95. Notice the pinch on the rectifying operating line above tray 5.
Figure 4 gives the McCabe-Thiele diagram when the feed is introduced higher in the column on tray 15. The effect is to again require a higher reflux ratio because of the pinch on the stripping operating line near the feed tray. These results are exactly what we would expect. In the next section, we look at a nonideal multicomponent system and demonstrate some unexpected results.
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Figure 9. Composition profiles.
3. Nonideal Multicomponent Column The feed to a column contains 24.54 mol % methyl acetate, 35.56 mol % methanol, 24.19 mol % butanol, and 15.71 mol % butyl acetate. The objective is to take the two light components (MeAc and MeOH) out the top and the two heavy components (BuOH and BuAc) out the bottom. The vapor-liquid phase equilibrium relationships are complicated by two minimum-boiling homogeneous azeotropes. Using NRTL physical properties in Aspen Plus (Version 2006.5, Aspen Technology, Burlington, MA), a methyl acetate/methanol azeotrope occurs at 1.1 atm pressure with a temperature of 329.2 K and a composition of 66.13 mol % methyl acetate. A butanol/butyl acetate azeotrope occurs at 1 atm pressure with a temperature of 389.9 K and a composition of 78.06 mol % butanol. The specifications for this column are somewhat unusual. The key components are not adjacent in terms of boiling points. The normal boiling points of methyl acetate, methanol, butanol, and butyl acetate are 330.1, 337.8, 390.8, and 399.3 K, respectively. So the separation in this column should be to keep butanol from going overhead and methanol from going out the bottom. But, simulation results showed that the concentration of butanol in the distillate is much lower than the concentration of butyl acetate. In the bottoms, the concentration of methanol is much lower than the concentration of methyl acetate. This odd behavior may be the result of the azeotropes. The specification for the distillate is 0.1 mol % butyl acetate. The specification for the bottoms is that the sum of the methanol and the methyl acetate is 0.1 mol %. For some values of parameters, the dominant impurity in the bottoms is methanol, but for other values of parameters, the dominant impurity in the bottoms is methyl acetate. The sum of the compositions is obtained in the Radfrac model in Aspen Plus by selecting both components as the “selected components” in the design spec feature. The distillation column operates at 1.2 atm and has 37 stages. Using Aspen Plus notation, the reflux drum is stage 1 and the reboiler is stage 37, so the column has 35 trays. We want to find the optimum feed stage. Figure 5 shows the result of an investigation of feed-stage location. We start with feed introduced on stage 16 in the upper part of this 37-stage column. The calculated reboiler duty is QR ) 3.472 MW. Moving the feed down in the column produces
small decreases in the QR until stage 22 is reached. Here, the reboiler heat input is 3.438 MW. But moving down to stage 23 produces a big jump in QR to 4.333 MW! Continuing to move down the column increases reboiler heat input. Now we turn around and move the feed back up the column. Returning to stage 22 yields a QR of 4.047 MW instead of the 3.438 MW we found before! It should be emphasized that the product specifications are exactly the same in these two cases. The distillate and bottoms products leaving the column are essentially the same with only slight changes in the methyl acetate and methanol impurities in the bottoms. Their sum is still 0.1 mol %. However, the temperature and composition profiles are drastically different. The region of multiple steady states is when the feed is introduced on stages 20, 21, or 22. Above and below these stages, results are consistent and unique. Figures 6 and 7 show the composition profiles for the two steady states. In Figure 6, the compositions of the light components (MeAc and MeOH) are small in the stripping section below the feed stage. In Figure 7, these light component compositions are much larger in the stripping section, particularly the methanol. Figure 8 compares the temperature profiles of the two steady states. The temperatures are lower when the compositions of the light components are larger. Figure 9 gives a direct comparison of the profiles for each of the individual components. The major difference is the larger methanol concentration in one of the steady states. This corresponds to smaller butanol concentrations. 4. Conclusion The occurrence of multiple steady states for feed tray location has been demonstrated. This phenomenon complicates the selection of the best feed tray location. Designers should be aware of this possibility. The cause of the multiplicity is a high degree of nonlinearity in the vapor-liquid phase equilibrium describing the azeotropic system. ReceiVed for reView January 17, 2010 ReVised manuscript receiVed March 1, 2010 Accepted March 5, 2010 IE1001108
