Quaternary Distillation Systems with Less than N− 1 Columns

3838

Ind. Eng. Chem. Res. 2004, 43, 3838-3846

Quaternary Distillation Systems with Less than N - 1 Columns Jeung Kun Kim and Phillip C. Wankat* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2050

The design and synthesis of distillation cascades using side-stream columns with less than N 1 columns (two or one) for separations of relatively ideal four-component mixtures are studied. Condenser and reboiler heat duties are used to compare operating costs of cascades with less than N - 1 columns to base cases with three columns. A dimensionless volume index, ∑(VjNj/ FT), is used to compare capital costs. Quaternary feeds containing four of the five components n-butane, n-pentane, n-hexane, n-heptane, and n-octane were simulated using the commercially available software package Aspen Plus version 11.1. Columns were operated at L/D ) 1.15(L/ D)min and with optimum feed and product withdrawal locations. For systems with low concentrations of one component in the feed, side-stream cascades often show significantly lower operating and capital costs compared to the base cases. Low purity requirements (sloppy separations) also favor side-stream cascades. Tentative heuristics are developed to predict which cascade will have the lowest energy consumption and capital cost. Introduction Distillation is a widely used separation process and is a very large consumer of energy. A large amount of research work has been done to improve the energy efficiency of distillation systems in terms of either the design of optimal distillation schemes or improving internal column efficiency. Still, the optimal design and synthesis of multicomponent distillation systems remains one of the most challenging problems in process engineering.1-11 Most research on complex distillation configurations has been restricted to ternary mixtures. Recently, there have been studies of configurations for feeds with four or more components.4-12 These studies have focused especially on the parametric performance of multicomponent distillation flowsheets. Most of the studies have focused on complete separation of Ncomponent mixtures using N - 1 distillation columns with a reboiler at the bottom and a condenser at the top of each column. Some of the recent studies of multieffect cascades may use more than N - 1 columns,7,11 or more than 2(N - 1) sections.12 One approach to finding good separation processes quickly is to use heuristics. These are guidelines based on experience that aid a designer to find the better solution. Many researchers1-4 proposed heuristics for the optimal design and synthesis of multicomponent distillation systems. Specifically, Seader and Westerberg2 suggested a reasonable set of commonly used heuristics for designing separation sequences. Tedder and Rudd3 first developed criteria for use of side streams for the separation of ternary mixtures that do not exhibit azeotropes and suggested taking a vapor as a side-stream product if the side stream is below the feed and a liquid product if the side stream is above the feed. Also, they developed heuristics of when a single column can be used for separation of ternary mixtures. They showed that the most volatile or least volatile component must be low concentrations in the feed (typically 0.05 mole fraction or less) for the side stream systems * To whom correspondence should be addressed. Tel.: (765) 494-7422. Fax: (765) 494-0805. E-mail: wankat@ ecn.purdue.edu.

to be most economical. However, cascades that use less than N - 1 columns for multicomponent distillation processes have not been extensively studied. Rooks et al.5 proposed three distillation processes for separation of four-component mixtures (acetaldehyde, methanol, ethanol, water) with three azeotropes. Proposed processes consisted of a total of five, four, or three columns. The distillation process with four columns and the side stream reduced the total vapor flow approximately 20% compared to the distillation process with five columns (base case) when the total number of stages used was the same. The distillation process with three columns and the side stream had fewer stages (∼7%) and a lower total vapor flow rate (∼24%) than the base case. In this paper, we study 11 distillation processes with less than N - 1 columns for separation of quaternary mixtures. Feeds are restricted to cases where one of the components is at or below 0.05 mole fraction. The results are compared to five base cases with three columns each. The heuristic rules proposed by Tedder and Rudd3 for ternary mixtures are tentatively extended to quaternary systems. Multieffect cascades (heat integration) were not included in this study, although they would probably reduce energy use.7,11,12 Systems with side strippers and side enrichers are also of interest; however, since they have N - 1 ) 6 sections, they were not investigated here. This paper is dedicated to Art Westerberg for his pioneering studies of process synthesis including distillation processes and for his highly valued friendship. Simulations for Quaternary Distillation We consider the almost ideal quaternary systems containing four of the five components n-butane, npentane, n-hexane, n-heptane, and n-octane with variable feed concentrations. The performance analysis is based on comparison of surrogates for the operating and capital costs. The sum of the heat duties of the condenser and reboiler (Qc, Qb) are surrogates for the operating cost that allow comparison of different distillation cascades. For packed columns capital cost is often proportional to the volume of the column. Thus, a

10.1021/ie030640l CCC: $27.50 © 2004 American Chemical Society Published on Web 04/02/2004

Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 3839 Table 1. Feed Mole Fractions and Purities of Design Examples Containing No n-Octanea feed component A feed component B feed component C feed component E product purities

n-butane n-pentane n-hexane n-heptane n-butane n-pentane n-hexane n-heptane

example 1

example 2

0.0500 0.2500 0.4000 0.3000 0.998 0.966 0.992 0.998

0.0256 0.2564 0.4103 0.3077 0.998 0.976 0.992 0.998

relative volatilities

a

example 3

example 4

example 5

example 6

example 10

0.3000 0.4000 0.2500 0.0500 0.998 0.992 0.968 0.995

0.3000 0.1500 0.5000 0.0500 0.998 0.993 0.983 0.997

0.0500 0.4500 0.4500 0.0500 0.995 0.990 0.974 0.997

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 690 899.87

1 769 412.44

110.94

-1 788 346.87

1 866 842.57

110.65

-1 702 255.53

1 780 811.74

112.51

-1 766 528.73

1 845 012.86

109.83

-1 559 235.95

1 637 938.69

117.61

0.0732 0.3000 0.2439 0.0300 0.3902 0.5500 0.2927 0.1200 0.998 0.999 0.956 0.968 0.992 0.988 0.998 0.997 RAB ≈ 2.28 RBC ≈ 2.69 RCE ≈ 2.19

All separations are of approximately equal difficulty.

Table 2. Design Results for Example 1 for Base Cases

Figure 1a Figure 1b Figure 1c Figure 1d Figure 1e

column

Rm

Nt

Qc,I (kcal/h)

Qb,I (kcal/h)

Vmax [(kg mol)/h]

NtVmax/Ft

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

8.80 2.80 2.00 8.80 1.20 2.40 1.10 1.90 3.70 1.10 7.10 2.30 2.20 3.70 2.00

21 24 39 21 39 25 38 26 21 38 21 26 28 21 38

-242 451.13 -617 078.19 -831 370.55 -242 451.13 -995 950.82 -549 944.92 -1 033 479.20 -554 200.40 -114 575.93 -1 033 479.20 -199 813.00 -533 236.53 -613 446.36 -114 578.81 -831 210.78

265 306.95 658 491.90 845 613.58 265 306.95 1 035 480.54 566 055.08 1 081 975.86 578 924.24 119 911.64 1 081 975.86 213 699.66 549 337.34 672 733.38 119 892.55 845 312.76

48.93 108.03 132.00 48.93 156.13 96.26 159.88 95.80 23.12 159.88 40.33 93.31 106.33 23.12 132.00

10.28 27.12 73.54 10.28 63.69 36.68 60.75 35.58 16.18 60.75 12.10 36.98 29.77 16.18 71.66

volume index,13 ∑(VjNj/FT), is used as a surrogate for capital cost. The summation ∑(VjNj/FT) is proportional to the total volume of distillation columns needed per mole of feed for a given distillation process. The Vj term represents the largest vapor flow rate in each column. This summation is a rough indicator, which does not include the effect of pressure and other variables. We chose not to include pressure since the effect of pressure on cost is complex. Note that this index also ignores plate efficiency. For screening purposes the index ∑(VjNj/FT) should be sufficient and is easily calculated during the simulations. The mole fractions for different feeds are shown in Tables 1, 7, 11, and 14. The averages of the geometric average relative volatilities are given in these tables to provide some idea of the relative difficulty of the separations in the different examples. The geometric average was calculated from the values of the relative volatilities calculated at the top and bottom of the columns using the K values calculated by Aspen. Note that these average relative volatilities were not used in the simulations. The mole fraction of 0.05 was shown to be a borderline value for use of side-stream columns for ternary separations.3 When a side-stream system has economics approximately equal to those of a base case, it will become more favorable with lower feed concentrations and less favorable with higher feed concentrations. The distillation systems shown in Figures 1-12 were simulated using the Aspen Plus RADFRAC routine that is based on a rigorous equilibrium staged model. Components in the mixture are ranked according to their relative volatility; that is, for feed mixture ABCE, A is the most volatile component and volatility decreases in successive order, with E being the least volatile. Parts a and c of Figure 1 are the direct and indirect systems, respec-

tively, with N - 1 ) 3 columns. The five base cases are used for comparison purposes to determine if the new configurations are superior. On the basis of the ternary study3, the side-stream configurations in Figures 2-6, which have liquid side streams withdrawn above the feed, may be desirable when the feed contains little A and significant amounts of B (Figures 2-4), little B and significant amounts of C (Figure 5), or little A plus B and significant amounts of C. The cascades shown in Figures 7-11, which have vapor side streams withdrawn below the feed, may be favorable when the feed contains little E and large amounts of C (Figures 7-9), little C and large amounts of B (Figure 10), or small amounts of C plus E and large amounts of B. The single column shown in Figure 12 is a special case that may be applicable when the feed contains little A and little E, but significant amounts of B and C. VLEs are calculated with the Peng-Robinson EOS. Operation of all columns was at 3.0 atm. For all columns the distillate and side-stream flow rates were set from the mass balances. The simulator was used to estimate the minimum external reflux ratios, (L/D)min, for all columns by simulating columns with N ) 100. The actual reflux ratio used for each column was L/D ) 1.15(L/D)min. Although the optimum reflux ratio will obviously be different, the resulting costs should not differ greatly from the optimum values. The feed flow rate is F ) 100 (kg mol)/h. Simulation Results For the mixtures listed in all examples, the respective configurations are evaluated on the basis of the summation of Qb, the summation of Qc, and the volume index. Table 2 shows simulation results of example 1 (Table 1) for configurations shown in Figure 1a-e.

3840 Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004

Figure 1. Base cases for quaternary distillation with N - 1 ) 3 columns: (a, top left) conventional direct split sequence; (b, top right) light-heavy binary sequence; (c, middle left) conventional indirect split sequence; (d, middle right) heavy-light binary sequence; (e, bottom) conventional symmetrical sequence.

Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 3841 Table 3. Side-Stream Column Design Results for Example 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 9 Figure 10 Figure 11

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 859 022.77 -1 757 411.75 -1 479 988.23 -25 622 469.13 -25 110 471.00 -301 739 365 -218 995 809.10 -22 914 548.40 -18 604 380.20

1 937 514.06 1 835 910.93 1 558 467.61 25 700 948.35 25 188 915.08 301 817 884.20 219 326 255.00 23 139 455.32 18 829 145.46

154.69 127.53 122.55 177.70 1572.50 20700.76 14431.97 1158.87 1377.98

Example 1 has little component A in the feed mixture, and the A-B, B-C, and C-E separations are of approximately equal difficulty. From the simulation result (Table 2) for example 1 the system shown in Figure 1e requires the least heating and cooling. The base case shown in Figure 1a is next and requires a significantly lower volume index. The purities of all products can be improved by adding more stages for both base cases. Table 3 shows the simulation results for example 1 for saturated liquid side-stream cascades and for saturated vapor side-stream cascades (Figures 2-6 and 7 and 9-11, respectively). Unlike the base case, it is difficult to increase the purity of the side stream product B or C since A or E is always present when it is withdrawn. Since there is little A in the feed, we expect the saturated liquid side-stream systems (Figures 2-6) to in general be better than saturated vapor side

Figure 4. Column with a liquid side stream above the feed removing B followed by a binary column separating C and E.

Figure 5. Removal of light component A followed by a column with a liquid side stream above the feed removing C as side withdrawal.

Figure 2. Column with a liquid side stream above the feed removing B and C followed by a binary column separating B and C.

Figure 6. Column with a liquid side stream above the feed removing C followed by a binary column separating A and B.

Figure 3. Removal of heavy component E followed by a column with a liquid side stream above the feed removing B as side withdrawal.

streams.3 The results confirm this. On the basis of the simulation results, the configuration shown in Figure 4 (separation sequence A/B/CE f C/E) is the best of the side-stream configurations. It requires significantly less heating and cooling than the base case (Figure 1), but capital costs are higher than for the base cases. Compared to the conventional symmetric sequence base case (Figure 1e), the configuration in Figure 4 uses 5.1% less cooling and 4.9% less heating, but has a volume index that is 4.2% higher. To investigate the regions of validity for saturated liquid side-stream cascades, we change the amount of

3842 Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 Table 4. Side-Stream Column Design Results for Examples 2-4 example 2 ∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

Figure 1a -1 719 541.51 1 787 Figure 1b -1 813 431.48 1 881 Figure 1c -1 665 137.30 1 733 Figure 1d -1 755 605.40 1 823 Figure 1e -1 562 456.12 1 630 Figure 2 -1 978 214.93 2 046 Figure 3 -1 689 316.00 1 757 Figure 4 -1 517 937.40 1 586 Figure 5 -24 546 723.09 24 614

648.76 585.84 334.95 744.99 745.45 389.83 500.69 112.79 920.0 9

example 3 ∑(NtVmax/Ft) 111.80 108.64 112.40 109.31 118.12 162.65 126.58 121.87 1580.4 7

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

-1 640 257.90 1 727 432.69 -1 773 926.70 1 861 077.60 -1 699 204.42 1 786 371.56 -1 751 434.33 1 838 565.54 -1 552 843.39 1 640 054.26 -1 955 952.68 2 043 083.55 -1 685 716.58 1 772 820.62 -1 504 596.40 1 591 782.79 -30 324 481.00 30 411 631.20

example 4 ∑(NtVmax/Ft) 112.82 109.27 109.12 107.81 117.08 152.57 121.03 123.93 1975.91

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/ Ft)

-1 532 739.50 1 650 107.59 114.13 -1 556 545.93 1 673 935.50 113.50 -1 853 636.51 1 971 010.56 110.57 -1 842 852.96 1 960 234.56 98.96 -1 510 397.95 1 627 756.34 130.79 -117 403 415.60 117 520 806.60 8762.22 -10 214 379.40 10 331 771.60 617.12 -9 306 373.19 9 423 755.42 531.92 -1 662 117.96 1 779 480.62 149.26

Table 5. Base Case and Vapor Side-Stream Column Design Results for Example 5 Figure 1a Figure 1b Figure 1c Figure 1d Figure 1e Figure 7 Figure 8 Figure 9 Figure 10

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 420 428.58 -1 635 365.15 -1 996 123.40 -1 873 606.50 -1 501 122.10 -2 181 542.68 -1 438 828.32 -1 561 666.03 -17 384 215.86

1 493 776.73 1 708 730.58 2 069 508.36 1 946 981.40 1 574 466.52 2 254 938.28 1 673 862.70 1 796 755.17 17 684 794.02

104.21 98.27 89.35 93.51 103.78 149.18 101.51 122.39 1075.53

the A component (examples 2 and 3) keeping the ratios of xB/ xC and xC/xE in the feed equal to those of example 1. Table 4 shows the simulation results for examples 2-4. On the basis of the simulation results the configuration shown in Figure 4 is the best of the side-stream configurations for examples 2 and 3. It requires less heating (2.7% for example 2 and 2.9% for example 3) and cooling (2.9% for example 2 and 3.1% for example 3) than the base case (Figure 1e), but capital costs are higher (3.2% for example 2 and 5.9% for example 3) than for the base cases. If we use the rule of thumb14 that operating and capital costs per year are approximately equal, then the configuration in Figure 4 is marginally better. However, the purity of the B product is better for the base case, and the base case is more flexible if the concentration of A in the feed increases. Thus, this example results in a toss-up between Figures 1e and 4, and a more detailed economic comparison would be justified. On the basis of the results of examples 1-3, it is clear that an upper side draw between the distillate product and feed should be taken as a liquid, and a lower side draw between the feed and bottom product should be a vapor. Example 4 (Table 1) has little middle component B in the feed mixture, and A-B, B-C, and C-E separations are of approximately equal difficulty. Using the ternary heuristics,3 the best side-stream configuration is that in Figure 5 (separation sequence A/BCE f B/C/ E). However, since this is a quaternary separation, the ternary heuristics may not accurately compare the sidestream systems to the base cases. Compared to the base cases (Figure 1a,e), the configuration in Figure 5 requires more heating and cooling and has a higher volume index (Table 4). Table 5 shows simulation results for example 5 (Table 1). Since there is very little component E in the feed mixtures, the base cases and the configurations in Figures 7-11 with saturated vapor side streams are examined. The direct sequence base case (Figure 1a) has the lowest heat duties (operating cost), while the indirect base case (Figure 1c) has the lowest capital cost. The configuration shown in Figure 8 has slightly greater

Figure 7. Column with a vapor side stream below the feed removing B and C followed by a binary column separating B and C.

Figure 8. Column with a vapor side stream below the feed removing C followed by a binary column separating A and B.

heat duties but slightly lower capital cost than the base case configuration in Figure 1a. The effects of the amount of middle components in the feed when there is very little E in the feed are explored by comparing examples 5 and 6 (results in Table 6). The direct configuration shown in Figure 1a has the lowest heat duties and close to the lowest volume index. Figure 8 shows the best side-stream configuration for example 6. Compared to the base case in Figure 1a, it uses 4.3% less cooling and 16.4% more heating and has a volume index that is 10.6% higher. Thus, for example 6 the base case in Figure 1a is again probably preferable. To explore the effect of the components in the feed, the n-heptane was replaced with n-octane (Table 7). This switch makes the C-E separation easier than the other separations. Table 8 shows simulation results for

Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 3843 Table 6. Base Case and Side-Stream Column Design Results for Example 6 Figure 1a Figure 1b Figure 1c Figure 1d Figure 1e Figure 8 Figure 9 Figure 10

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 474 376.20 -1 549 329.68 -1 786 452.70 -1 762 985.50 -1 483 269.40 -1 410 563.02 -1 550 430.10 -69 425 051.00

1 570 155.14 1 645 137.25 1 882 254.06 1 858 779.53 1 579 042.93 1 827 722.56 1 967 578.08 69 605 996.10

106.12 106.62 103.74 105.97 109.88 117.37 138.92 4330.90

Table 7. Feed Mole Fractions and Product Purities for Design Examples Containing No n-Heptanea example 7 Figure 9. Removal of light component A followed by a column with a vapor side stream below the feed removing C as side vapor withdrawal.

feed component A feed component B feed component C feed component E product purities

n-butane n-pentane n-hexane n-octane n-butane n-pentane n-hexane n-octane

relative volatilities

a

Figure 10. Removal of heavy component E followed by a column with a vapor side stream below the feed removing B as side vapor withdrawal.

Figure 11. Column with a vapor side stream below the feed removing B followed by a binary column separating C and E.

examples 7 and 8, which contain very little component A in the feed mixture. According to the simulation results, the configuration shown in Figure 4 is clearly the best of the side-stream configurations for example 7. Compared to the best base case (Figure 1e), the configuration in Figure 4 uses 8.6% less cooling and 7.8% less heating and has a volume index that is 3.5% lower. For example 8, which contains more B and less C, the configuration in Figure 4 uses 11% less cooling and 9.8% less heating but has a volume index that is 13.8% higher than that of the base case in Figure 1e.

example 8

0.05 0.03 0.25 0.55 0.40 0.12 0.30 0.30 0.997 0.998 0.962 0.988 0.992 0.993 0.999 0.999 RAB ≈ 2.27 RBC ≈ 2.58 RCE ≈ 4.76

example 9 0.30 0.40 0.25 0.05 0.998 0.992 0.968 0.992

The C-E separation is easiest.

Thus, example 8 requires more detailed economic analysis. Since example 9 (Table 7) has an easy C-E separation and small amounts of E, the vapor side-stream systems in Figures 7-9 are studied. Table 9 shows the simulation results. The configuration shown in Figure 9 has lower condenser and reboiler duties than the best base case (Figure 1a). The configuration shown in Figure 9 clearly has the lowest operating cost and capital cost. Compared to the base case in Figure 1a, the configuration in Figure 9 uses 15% less cooling and 2.0% less heating and has a volume index that is 5.5% lower. It is instructive to compare example 9 to example 5, which has the same feed mole fractions, but component E is n-hexane. The best side-stream configuration was that in Figure 8, but the base case in Figure 1a was best (Table 5). The easier separation in example 9 favors the side-stream system. The distillation process with a single column for separations of four-component mixtures (Figure 12) is included in the investigation of a feed with small amounts of both components A and E (example 10, Table 1). Table 10 shows simulation results for this example for the base cases (Figure 1), the liquid side streams (Figure 4), the vapor side streams (Figures 7-9), and the configuration shown in Figure 12. The configuration in Figure 12 has the largest capital cost. The configuration shown in Figure 8 has the lowest overall energy use although its volume index is approximately 10% higher than that of the base case in Figure 1b. The configuration in Figure 8 is probably the best configuration for this example. The effects of the difficulty of the A-B split are explored by comparing examples 11 and 12, which contain no n-pentane (Table 11), to example 1. There is little component A in both feed mixtures. Examples 11 and 12 differ in the required recovery fraction of n-octane (or equivalently in the n-heptane product purity). The A-B separation is quite easy compared to the other separations for both examples. Table 12

3844 Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 Table 8. Base Case and Liquid Side-Stream Column Design Results for Examples 7 and 8 example 7 Figure 1a Figure 1b Figure 1c Figure 1d Figure 1e Figure 3 Figure 4 Figure 5

example 8

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 401 866.00 -1 500 505.80 -1 440 709.20 -1 504 719.79 -1 271 077.80 -1 403 093.50 -1 161 573.60 -25 664 372.00

1 541 927.07 1 640 452.89 1 580 694.15 1 644 696.87 1 411 175.31 1 543 039.81 1 301 539.27 25 804 245.40

74.75 74.66 76.75 75.63 79.85 71.27 77.07 1125.81

-1 259 642.60 -1 527 586.22 -1 599 906.21 -1 440 120.04 -1 139 333.11 -1 335 484.69 -1 013 915.43

1 406 380.64 1 674 312.91 1 746 612.21 1 586 817.41 1 286 073.97 1 482 171.28 1 160 680.25

70.51 81.18 81.92 85.17 76.80 105.57 87.39

Table 9. Base Case and Vapor Side-Stream Column Design Results for Example 9 Figure 1a Figure 1b Figure 1c Figure 1d Figure 1e Figure 7 Figure 8 Figure 9

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 275 211.90 -1 480 996.10 -1 860 631.50 -1 738 078.67 -1 411 422.40 -1 257 811.06 -1 438 817.98 -1 084 662.19

1 360 996.89 1 566 868.38 1 946 481.86 1 823 930.54 1 497 212.85 1 341 785.83 1 688 587.30 1 334 453.44

77.74 78.78 74.31 78.48 75.92 88.28 85.22 73.51

Table 10. Base Case and Vapor Side-Stream Column Design Results for Example 10 Figure 1a Figure 1b Figure 1c Figure 1d Figure 1e Figure 4 Figure 7 Figure 8 Figure 9 Figure 12

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 583 453.89 -1 923 885.52 -1 776 114.70 -1 974 464.70 -1 558 478.90 -2 632 067.46 -2 784 591.50 -1 324 844.40 -1 726 914.21 -1 728 361.00

1 628 010.74 1 968 448.45 2 006 204.62 2 019 037.05 1 603 038.15 2 676 616.76 2 829 199.37 1 662 122.23 2 064 171.30 2 065 677.24

108.98 90.82 91.45 91.21 100.61 167.41 150.54 99.62 108.26 174.23

shows the simulation results for the base cases and for the configurations shown in Figures 2-4 and allows comparison of the two examples. From the results of the simulation, example 11 has lower heat duties and volume index than example 12. Thus, for these examples, the low recovery fraction (sloppy separation) is preferable for the n-octane. However, the base case configuration shown in Figure 1e is preferable since it has lower heat duties and volume index. Compared to example 1, the base case in Figure 1e has clearly become preferable compared to that in Figure 1a, while the best side-stream system is that in Figure 4 in all cases. Examples 13 and 14 (Table 11) have an easy A-B separation and small amounts of E and again differ on the basis of product purities. Example 13 is the sloppier separation. The base cases and the configurations in Figures 7-9 are studied (Table 13). For example 13, the configuration shown in Figure 9 has the lowest heat duties and a reasonable volume index. Compared to the base case in Figure 1a, the design in Figure 9 uses 16.3% less cooling and 2.0% less heating and has a volume index that is 10.9% lower. The configuration in Figure 1c has greater heat duties but the lowest volume index. Compared to example 5 with the same feed mole fractions but a more difficult A-B separation, the energy requirements on example 13 are lower and the base case in Figure 1a no longer has the lowest energy requirements. In example 14 the base case in Figure 1a clearly has the lowest energy requirements. The base case can produce a purer product (comparing examples 13 and 14) with a much smaller increase in

Figure 12. Single column removing B in a liquid side stream above the feed and removing C in a vapor side stream below the feed. Table 11. Feed Mole Fractions and Product Purities for Design Examples Containing No n-Pentanea example example example example 11 12 13 14 feed component A feed component B feed component C feed component E product puritie s

n-butane n-hexane n-heptane n-octane n-butane n-hexane n-heptane n-octane

0.05 0.25 0.40 0.30 0.997 0.982 0.928 0.997

relative volatilities

a

0.05 0.25 0.40 0.30 0.998 0.972 0.985 0.985 RAB ≈ 5.26 RBC ≈ 2.10 RCE ≈ 2.19

0.30 0.40 0.25 0.05 0.998 0.997 0.923 0.998

0.30 0.40 0.25 0.05 0.998 0.989 0.964 0.995

The A-B separation is easiest.

energy requirements than the side-stream system in Figure 9. In the results for examples 13 and 14, the heat duties and volume index increase as the recovery fraction of n-octane increases. On the basis of the results for examples 11 and 12 and for examples 13 and 14, the operating and capital costs decrease when the product purity specifications are relaxed, and sidestream systems are often favored for these sloppy separations. Example 15 (Table 14) contains no n-hexane, and thus, the B-C separation is quite easy. There is little component A in the feed mixture. Table 15 shows the simulation results for the base cases and for the configurations shown in Figures 2-4. The configurations shown in Figures 2-4 have greater heat duties (operating cost) and volume index (capital cost) than for the base cases (Figure 1). The heat duties and volume indexes are similar for the base cases. Thus, one of the base cases would be chosen. Since example 16 (Table 14) has an easy B-C separation and small amounts of E, the base cases and

Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 3845 Table 12. Base Case and Liquid Side-Stream Column Design Results for Examples 11 and 12 example 11 Figure 1a Figure 1b Figure 1c Figure 1d Figure 1e Figure 2 Figure 3 Figure 4

example 12

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 938 581.80 -2 054 369.90 -1 995 692.82 -2 028 731.04 -1 857.484.90 -1 979 325.47 -1 955 737.40 -1 893 432.90

2 047 655.14 2 163 508.66 2 104 860.02 2 137 915.74 1 966 598.06 2 088 373.64 2 064 722.31 2 002 491.57

110.95 114.01 111.96 113.21 110.84 143.24 133.27 126.31

-2 072 862.10 -2 234 096.64 -2 198 645.41 -2 236 216.01 -1 987 079.27 -2 298 722.68 -2 357 671.41 -2 014 228.26

2 182 337.91 2 343 551.09 2 308 011.24 2 345 611.88 2 096 500.93 2 408 175.52 2 467 145.15 2 123 652.18

121.40 121.42 116.23 118.75 124.04 171.69 146.98 139.2

Table 13. Base Case and Vapor Side-Stream Column Design Results for Examples 13 and 14 example 13 Figure 1a Figure 1b Figure 1c Figure 1d Figure 1e Figure 7 Figure 8 Figure 9

example 14

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 340 209.30 -1 533 928.96 -2 112 648.95 -1 875 145.52 -1 608 137.16 -1 354 463.80 -1 444 001.01 -1 121 470.60

1 504 192.14 1 697 934.07 2 276 937.40 2 039 281.31 1 772 433.72 1 518 323.51 1 797 346.84 1 474 774.53

116.32 111.71 81.77 104.24 95.53 114.46 87.20 103.62

-1 467 127.40 -1 805 862.53 -2 233 169.30 -2 089 440.00 -1 754 751.70

1 631 726.36 1 970 475.70 2 397 820.97 2 254 130.68 1 919 442.88

119.93 107.49 84.01 93.92 105.09

-2 120 443.38 -2 092 571.79

2 461 696.36 2 433 838.01

109.74 191.33

Table 14. Feed Mole Fractions and Purities for Design Examples Containing No n-Hexanea feed component A feed component B feed component C feed component E product purities

n-butane n-pentane n-heptane n-octane n-butane n-pentane n-heptane n-octane

relative volatilities

a

example 15

example 16

0.05 0.25 0.40 0.30 0.999 0.984 0.930 0.998 RAB ≈ 2.27 RBC ≈ 5.45 RCE ≈ 2.35

0.30 0.40 0.25 0.05 0.998 0.998 0.924 0.998

The B-C separation is easiest.

Table 15. Base Case and Liquid Side-Stream Column Design Results for Example 15 Figure 1a Figure 1b Figure 1c Figure 1d Figure 1e Figure 2 Figure 3 Figure 4

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 540 173.98 -1 678 294.86 -1 559 340.29 -1 614 884.89 -1 453 231.01 -2 268 314.69 -2 132 450.60 -1 947 565.30

1 712 540.81 1 850 742.76 1 731 729.74 1 787 291.59 1 625 604.95 2 440 666.34 2 304 861.00 2 119 974.82

83.00 79.62 77.75 78.57 90.32 150.48 127.83 121.69

Table 16. Base Case and Vapor Side-Stream Column Design Results for Example 16 Figure 1a Figure 1b Figure 1c Figure 1d Figure 1e Figure 7 Figure 8 Figure 9

∑Qc,i (kcal/h)

∑Qb,i (kcal/h)

∑(NtVmax/Ft)

-1 088 700.77 -1 363 819.18 -1 815 232.91 -1 623 443.01 -1 195 905.74 -1 109 584.56 -941 832.37 -812 656.51

1 226 362.32 1 501 553.28 1 952 949.65 1 761 123.11 1 328 308.81 1 247 279.89 1 268 631.95 1 139 481.84

84.91 74.08 82.45 70.84 94.46 76.04 64.71 60.74

the configurations shown in Figures 7-9 are studied (Table 16). The configuration shown in Figure 9 has the lowest heat duties (operating cost) and volume index (capital cost) and is the best. Compared to the base case in Figure 1a, it uses 25.4% less cooling and 7.1% less heating and has a volume index that is 28.5% lower.

Heuristics On the basis of the results in the previous sections, the following tentative heuristics are proposed for the use of side-stream columns to separate quaternary mixtures. (1) Consider a liquid side stream above the feed if there is a small amount (approximately 0.05 mole fraction or less) of the most volatile component in the feed to a specific column. Consider a vapor side stream below the feed if there is a small amount (approximately 0.05 mole fraction) of the least volatile component in the feed to this column. This agrees with the ternary heuristics.3 (2) If a product is required in low purity (sloppy separations), side-stream configurations that withdraw this product as a side stream are often favored, but heuristic 1 must be satisfied. (3) If all separations are of approximately equal difficulty and the feed contains very little of the most volatile component, consider the direct base case (Figure 1a), the conventional symmetrical sequence case (Figure 1e), and the liquid side-stream system with the sequence A/B/CE f C/E (Figure 4). If the feed contains very little of the next most volatile component, consider the direct base case (Figure 1a). If the feed contains very little of the least volatile component, consider the direct base case (Figure 1a), the conventional symmetrical sequence case (Figure 1e), and the AB/C/E f A/B side-stream cascade (Figure 8). If there is very little of both the most and the least volatile components, use the direct base case (Figure 1a), the conventional symmetrical sequence case (Figure 1e), or the configuration in Figure 8. (4) If the separation of the least volatile and next least volatile components is easiest and the feed contains little of the most volatile component, compare the liquid side-stream column with the A/B/CE f C/E sequence (Figure 4) to the symmetrical base case (Figure 1e). If the feed contains little of the least volatile component, compare the vapor side-stream cascade using the A/BCE f B/C/E sequence (Figure 9) to the direct base case in Figure 1a. (5) If the separation of the most volatile and the next most volatile components is easiest and the feed contains little of the most volatile component, use the

3846 Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004

symmetrical base case (Figure 1e). If the feed contains little of the least volatile component, the vapor sidestream cascades with the sequences A/BCE f B/C/E (Figure 9) and AB/C/E f A/B (Figure 8) are appropriate for sloppy separations while the direct base case (Figure 1a) is better for sharp separations. (6) If the separation of the middle components is easiest and if the feed contains little of the most volatile component, consider the direct base case (Figure 1a), the indirect base case (Figure 1c), and the conventional symmetric sequence case Figure 1e). If the feed contains little of the least volatile component, use the vapor sidestream system with the sequence A/BCE f B/C/E (Figure 9). Discussion and Conclusions Side-stream designs for cascades with less than N 1 columns are developed for the separation of fourcomponent mixtures. Since the base cases have three columns and six sections, it is reasonable that the twoand one-column systems should have less than six sections to be less expensive. This constraint was employed in designing the side-stream systems. Using less than N - 1 columns can be economical for certain feeds and design requirement. However, to produce a high-purity side stream, there must be small quantities of one of the components in the feed. Comparison of examples 1 and 7, both with small amounts of A, when the C-E separation is made easier, shows the side-stream system in Figure 4 has a significant decrease in energy requirements and becomes the best system. Comparison of example 5 and 9, both with small amounts of E, shows that when the C-E separation becomes easier, the configuration in Figure 9 becomes the best case instead of that in Figure 1a (best case in example 5). On the other hand, comparison of examples 5 and 14, both with small amounts of E, shows that when the A-B separation is made easier (example 14), there is no advantage for the side-stream columns for the same required purities. The configuration in Figure 1a remains the best configuration. Comparison of examples 1 and 12 (approximately the same purity), both with small amounts of A, shows that when the A-B separation is made easier (example 12), the configuration in Figure 1e remains the best configuration. Thus, making the separation of heavy components easier favors the side-stream systems. This is reflected in heuristics 4 and 5. Similar side-stream cascades can be developed for three- and four-component simulated moving bed (SMB) adsorptive separations.15 Surprisingly, the side withdrawal in the SMB can be purer than a side stream with a true moving bed. The idea for this distillation research came from this SMB research. Further research is needed on detailed parametric studies of cascades with less than N - 1 columns for separations of multicomponent mixtures to analyze the economic performance. This is particularly true for nonideal systems and for multieffect distillation cascades. Since other systems were not studied, the heuristics only apply to comparison of side-stream cascades with the base cases for relatively ideal systems. The heuristics must be considered tentative because they were not based on a detailed economic analysis and they have not been extensively tested.

Acknowledgment This research was partially supported by NSF Grant CTS-0211208 and the ERC for the Advanced Bioseparation Technology, KOSEF. The comments of the reviewers were very helpful in improving the paper. Nomenclature A, B, C, E ) components D ) distillate flow rate, (kg mol)/h F ) feed flow rate, (kg mol)/h L ) liquid flow rate, (kg mol)/h Nt ) total number of theoretical trays Qb ) heat duty of the reboiler, kcal/h Qc ) heat duty of the condenser, kcal/h Rmin ) minimum reflux ratio R ) actual reflux ratio Vmax ) maximum vapor flow rate in each column, (kg mol)/h x ) amount of a component, kg mol Subscripts b ) reboiler c ) condenser

Literature Cited (1) Thompson, R. W.; King, C. J. Systematic synthesis of separation systems. AIChE J. 1972, 18, 941. (2) Seader, J. D.; Westerberg, A. W. A combined heuristic and evolutionary strategy for synthesis of simple separation sequences. AIChE J. 1977, 23, 951. (3) Tedder, D. W.; Rudd, D. F. Parametric studies in industrial distillation: part 1. design comparisons. AIChE J. 1978, 24, 303315. (4) Westerberg, A. W. The synthesis of distillation-based separation systems. Comput. Chem. Eng. 1985, 9, 421-429. (5) Rooks, R. E.; Malone, M. F.; Doherty, M. F. A geometric design method for side-stream distillation columns. Ind. Eng. Chem. Res. 1996, 35, 3653-3664. (6) Agrawal, R. Thermally coupled distillation with reduced number of intercolumn vapor transfers. AIChE J. 2000, 46, 21982210. (7) Agrawal, R. Multieffect distillation for thermally coupled configurations. AIChE J. 2000, 46, 2211-2224. (8) Rong, B.-G.; Kraslawski, A.; Nystro¨m, L. The synthesis of thermally coupled distillation flowsheets for separations of fivecomponent mixtures. Comput. Chem. Eng. 2000, 24, 247-252. (9) Rong, B.-G.; Kraslawski, A.; Nystro¨m, L. Design and synthesis of multicomponent thermally coupled distillation flowsheets. Comput. Chem. Eng. 2001, 25, 807-820. (10) Rong, B.-G.; Kraslawski, A. Partially thermally coupled distillation systems for multicomponent separations. AIChE J. 2003, 49, 1340-1347. (11) Rong, B.-G.; Kraslawski, A.; Turunen, I. Synthesis of functionally distinct thermally coupled configurations for quaternary distillations. Ind. Eng. Chem. Res. 2003, 42, 1204-1214. (12) Rong, B.-G.; Kraslawski, A.; Turunen, I. Synthesis of heat integrated thermally coupled distillation systems for multicomponent separations. Ind. Eng. Chem. Res. 2003, 42, 43294339. (13) Wankat, P. C. Multieffect distillation processes. Ind. Eng. Chem. Res. 1993, 32, 894-905. (14) Keller, G. E. Separations: New directions for an old field. AIChE Monogr. Ser. 1987, 83. (15) Kim, J. K.; Zang, Y.; Wankat, P. C. Single-cascade simulated moving bed systems for separation of ternary mixtures. Ind. Eng. Chem. Res. 2003, 42, 4849-4860.

Received for review August 6, 2003 Revised manuscript received December 19, 2003 Accepted February 10, 2004 IE030640L