Ind. Eng. Chem. Res. 1991,30,507-516
considered a guard bed protecting the carbon from Fe(CO)& The advantages of using the zeolite for Fe(CO)6removal include retention of capacity following thermal regeneration, higher bulk density than carbon, and that iron-laden zeolite is less combustible than iron-laden carbon. The active carbon located behind the zeolite would affect the required Ni(C0)4removal. Thermal treatment of the mixed bed in N2 at 120 O C is needed for satisfactory adsorbent regeneration.
Acknowledgment This work was supported by the Department of Energy under Contract No. DE-AC22-87PC90005. Registry No. Fe(CO)5, 13463-40-6; Ni(CO)4, 13463-39-3;
MeOH, 67-56-1; C, 7440-44-0.
Literature Cited Brief, R. S.; Blanchard, J. W.;Scala, R. A.; Blacker, J. H. Metal Carbonyls in Petroleum Industry. Arch. Environ. Health 1971, 23, 373-384. Brown, D. M.; Hsiung, T. H.; Rao, P.; Greene, M. I. Catalyst Activity and Life in Liquid Phase Methanol. Presented at the 10th Annual EPRI Clean Liquid and Solid Fuels Contractor’s Conference, Palo Alto, CA, April 1985. Dwyer, D. J.; Somorjai, G.A. Hydrogeneration of CO and C02Over Iron Foils. J. Catal. 1978, 52, 291-301.
507
Fisackerly, R. H.; Sundstrom, D. G. The DOW Syngae ProjectProject Overview and Status Report. Presented at the 6th Annual EPRI Conference on Coal Gasification, October 15-16, 1986. Hsiung, T. H. Air Products and Chemicals, Inc., unpublished information, 1987. Inouye, H.; DeVan, J. H. Formation of Iron Carboxyl Between a 1/2 Pet Mo Steel and High-pressure Gases Containing Carbon Monoxide. J. Mater. Energy Syst. 1979, 1, 52-60. Kuo, J. C. W. Tutorial Lecture on Indirect Coal Liquefaction at the 188th National Meeting of the American Chemical Society, Phildelphia, August 1984. Ludlum, K. H.; Eischens, R. P. Carbonyl Formation in Stainless Steel Infrared Cells. Surf. Sci. 1973, 40, 397-398. Markham, E. C.; Benton, A. F. The Adsorption of Gas Mixtures by Silica. J. Am. Chem. SOC.1931,53,497-503. Nagy, J. B.; Van Eunoo, M.; Derovane, E. G. Highly Dispersed Supported Iron Particles from the Decomposition of Iron Carbonyl on HY Zeolite. J. Catal. 1979,58, 230-237. Roberta, G.W.; Dicciani, N. K.; Kosek, J. The LPMEOH ProcessAn Efficient Route to Methanol from Coal. Presented at the Conference on Coal Gasification and Synthetic Fuels for Power Generation, San Francisco, CA, April 1985. Ross, L. W.; Haynie, F. H.; Hochman, R. T. Thermodynamic Functions of Nickel Carbonyl and Iron Pentacarbonyl. J. Chem. Eng. Data 1964, 9 (3), 339-340. Sirohi, V. P. Carbonyl Formation in Coal Gasification Plants. C. F. Braun & Co. report to ERDA under Contract No. E(49-18)-2240, 1974.
Receiued for review April 18, 1990 Revised manuscript received August 31, 1990 Accepted September 26,1990
Multicomponent Batch Distillation. 3. Shortcut Design of Batch Distillation Columns Mohommad S. Al-Tuwaim and William L. Luyben* Department of Chemical Engineering, Lehigh University, 111 Research Drive, Bethlehem, Pennsylvania 18015
As the trend to speciality chemicals continues to emphasize batch processing plants, the need for a quick, easy-to-use method for designing batch distillation columns becomes more important. Both the non-steady-state conditions and the nonlinearity of batch distillation make it difficult to derive analytical design formulas except for very basic and overly simplified systems. This paper presents a method for determining preliminary shortcut economic designs for both binary and ternary batch distillation columns. Design correlations are given that can be used to easily read off the optimum number of trays and the optimum reflux ratio for a given separation: specified relative volatilities, product purities, energy cost, and material of construction.
Introduction In many chemical plants, batch processes are becoming more important as the trend to speciality small-volume, high-value chemicals continues. The preference for batch over continuous processes is based on economic and operational criteria. Batch distillation columns play an important role in batch processes. Batch distillation provides outstanding flexibility: a single column can handle any number of components. To achieve the same result using a continuous distillation system, NC - 1 columns would typically be required for a system of NC components. The batch distillation process is characterized by unsteady-state conditions. This means that the compositions are functions of time. A large number of design and operating parameters must be optimized in order to design and operate the column. Furthermore, the policy of operating the column should be chqeen such that the process
* Author to whom correspondence should be addressed.
will be as simple as possible. Most of the work on batch distillation has been limited to binary systems. Luyben (1971), Bauerle and Sandal1 (1987), Coates and Pressburg (1961), Treybal(l970), Guy (1983), Kerkhof and Vissers (19771, and Featherstone (1976) all considered binary mixtures. On the other hand, ternary batch distillation was studied by Stewart et al. (1973), Van Dongen and Doherty (1985), and Luyben (1988). The work previously presented on the design of binary systems is usually with no tray holdup, an infinite number of trays (corresponding to minimum reflux), or a fixed number of trays. Moreover, previous work was carried out mainly to select an optimum policy of operating the column. Bauerle and Sandal1 (1987) presented analytical equations for the design of batch distillation columns (binary mixtures) with an infinite number of plates, neglecting any holdup in the column. Luyben (1971) showed that batch distillation can be significantly affected by design and operating parameters such as tray holdup, reflux drum holdup, and number of trays. He proposed a method to design batch distillation columns by using the
0888-5885 f 91f 263O-ObQ7$02.50f 0 Q 1991 American Chemical Society
508 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991
capacity factor concept and extended the work further (1988) to multicomponent systems. The objective of the work presented here is to develop shortcut design methods for batch distillation columns. Both binary and ternary systems are treated, and tray and reflux drum holdups are included in the model. Engineering economics have been used to determine the optimum number of trays. By defining the relative volatility of the system, product purities, energy costs, and the material of constructionof the column, the optimum reflux ratio along with the optimum number of trays can be specified. The reflux ratio is assumed to be constant in this study, and the optimum value of this fixed reflux ratio is determined as part of the design procedure. Coward (1966) showed that, for binary mixtures, little improvement can be achieved in going from a constant reflux ratio policy to a more complex constant composition, or even to the optimal control operation policy using Pontryagin's maximum principle. Furthermore, Luyben (1988) found similar results for ternary mixtures. Therefore a constant reflux policy is used in this work. The optimum reflux ratio for a given number of trays, relative volatility, and product purity is determined by maximizing the capacity factor. One limitation of this work should be pointed out: the effects of feed composition were not explored. All results assume the same feed composition: essentially equal fractions of all components. We believe that modest changes in the distribution of components in the fresh feed will have little effect on the results. However, drastically different feed compositions could significantly influence both the operation and the economics of batch distillation. For example, let us assume that the feed contains only 5 mol of one component. If the reflux drum holdup is 10 mol, the highest possible concentration of this component in the distillate is 50 mol %. If higher purities are required, the operation would have to be modified somehow, e.g., reduce reflux drum holdup or increase still pot charge.
Operation and System The design of a batch distillation column involves the determination of its diameter and number of theoretical separation stages. Incorporated in the calculation of these parameters is the determination of the optimum reflux ratio. The approach taken in this work is to find the optimum reflux ratios for columns with various numbers of trays and specified separation by maximizing the capacity factor proposed by Luyben (1971,1988). This part of the procedure is called the energy calculations. As more trays are used, the capacity factor increases and the optimum reflux ratio decreases. Thus,energy costa are reduced but capital costs are increased as the number of trays is increased. Then economic calculations are made for specific materials of construction and energy costs to find the optimum trade-off between capital and energy costa, i.e., the number of trays that minimizes total costs. The capacity factor (CAP) is defined as the total onspecification products produced per unit time. CAP is calculated by dividing the total on-specification products by the total time of the batch, tp, plus a 30-min period to empty and recharge the still pot. In general it can be expressed as NC
CAP
tF + 0.5 1'1
where Pi= total moles of the jth product collected during the batch. The specific expressions for both the binary and ternary systems will be given later in this paper. The total time of a batch includes the startup time at total reflux, the overhead products and slop cuta withdrawal time, and the final bottoms purification time. The system is optimized by maximizing CAP. An optimum reflux ratio will correspond to that maximum. CAP is used to calculate the vapor boilup required to meet the desired production rate. On the basis of the vapor boilup, the column diameter and the energy requirement of the system can be determined. The reboiler and condenser can then be designed. During the startup, the column operates at total reflux. Let us consider first a binary system. Product withdrawal begins at t = tE when the distillate composition ( X D ) reaches specification. At this point, distillate withdrawal is begun and is maintained at a constant rate throughout the rest of the batch. The overhead product withdrawal continues as long as its average composition meets specification. The average composition is calculated from the following equation:
When fD(t) drops to its specification value, the distillate flow is diverted to a slop cut tank, and the purification of the bottoms product starts. The purpose of the purification is to remove enough low reboiler from the column trays and still pot so that specification product will be attained when the column drains into the still pot. The average composition of the bottoms product f g ( t ) is calculated from the following equation: N HB(t)XB(t) + fB(t)
=
nil
HNXn(t)
N
(3)
n= 1
where H B and H N are the molar holdups of the still pot and individual column trays, respectively. For a binary separation only one slop cut will be produced. The slop cut is the distillate removed during the bottoms purification period before the bottoms product meets specification. For a binary system, the slop cut often has a composition similar to that of the fresh feed. Accordingly, it is recycled to the next batch and mixed with the fresh-feed charge. The operation cycle is similar for multicomponent systems except that multiple slop cuts can be produced. For example, a ternary system can have two slop cuts. The distillate is collected in a P1 tank until the average light-component composition (fDJin this tank drops to its specification. Then the distillate is diverted to a second tank where the S1 slop cut is collected. This first slop cut contains mainly the light and the intermediate components. When the purity of intermediate component composition in the distillate (xD2) reaches specification, the distillate is diverted to a third tank where the second product, P2, is collected. After that two events may occur: (1)fD2 drops below specification or (2) the average composition of the heavy component f m (in the still pot and on the trays in the column) rises above specification. If the first event takes place first, the distillate is diverted to the S2 slop tank and collected as the second slop cut until the second event occurs. Two slop cuta are formed if this is the sequence of events.
Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 SO9 Table I. Design Parameters Used for Both Binary and Ternary Mixtures A. Process Parameters parameter binary mixture ternary mixture 30/30/40mol I feed composition (Z) 50150 mol % 2.2511.611 relative volatility (a) 1.5,2,3, 4 41211 91311 number of trays (N) 10-100 10-100
B. Economic Parameters parameter description material of construction carbon steel, stainless steel, Monel type of trays valve energy cost $2.50, $5.00 depreciation period 5 yearsa
problem becomes more significant as the number of trays is increased. On the basis of the 100 Ib mol/h vapor rate, a still charge of at least 200 lb mol is needed to achieve the separation of a binary mixture for a column with a large number of trays and high level of purity. A still charge of at least 300 lb mol is required in the case of most ternary mixtures, but a still charge of 400 lb mol is needed in some cases for columns with high number of trays. The model describing the ternary batch distillation system is still pot (4) d ( H Bbj)~ = Rxlj - VyBj dt
2.5 years was used in one case.
If the second event is the first to take place, fDzis still above specification but the reflux drum composition may or may not meet specification. In this case, if the average composition of the mixture of the P2 product collected up to this time and the material in the reflux drum meets specification,the reflux drum is added to the P2 tank and there is no 52 slop cut. If the average composition does not meet specification, the material in the reflux drum is pumped into the 52 slop cut tank. The compositions of the two slop cuts are significantly different. The first slop cut contains mostly the light and intermediate components. The second slop cut contains mostly the intermediate and heavy components. Part 2 of this series of papers (Quintermo-Marmol and Luyben, 1990) discusses several alternative methods for handling these slop cuts. In this work we used the normal industrial strategy of simply recycling all of the slop cuts back to the initial still charge of the next batch. Several cycles are needed to build up to a pseudo-steady-state operation. Batch distillation of multicomponent mixtures of NC components could produce NC - 1slop cuts. Only binary and ternary systems are considered in this study, but the extension of the procedure to more components should be straightforward. The systems were simulated on a digital computer using fairly rigorous dynamic models. The simplifying assumptions include theoretical trays, equimolal overflow, constant relative volatilities, constant tray holdups (1lb mol), constant reflux drum holdup (10 lb mol), and total slop recycle. The number of trays was limited to a minimum of 10 and a maximum of 100 since it is unlikely that most batch plants would find it practical to install very tall columns. A 24-in.tray spacing was assumed, and only tray columns were considered. Modification of the procedure for packed columns (with their lower tray holdups) should be straightforward. For the ternary system it is assumed that the relative volatilities are the same between each adjacent component, e.g., 91311 or 4/2/1. The vapor boilup rate was set at 100 lb mol/h. This provides a convenient scaling factor for the energy consumption and the column diameter calculations required for any production rate. The tray and reflux drum holdups are realistic for typical columns with a 100 lb mol/h vapor flow rate and should scale up and down directly with the column vapor rate. The amount of material initially charged to the still pot has some effect on the capacity factor: the lower the initial charge, the higher the capacity factor. However, there is a lower limit for the initial still charge. There must be enough material remaining in the still pot at the end of the batch so that the reboiler can still function. This
k-1
Ynj
=
j = 1, 2
(5)
%XBk
ffjxnj
7j = l , 3 b-1
ffkxnk
I.-.
Nth tray
‘YjxNj
j=l,3
reflux drum
capacity factor binary system:
CAP =
ternary system: CAP =
HI30 -
Sl
tF + 0.5
HW
- Si - Sz
tF + 0.5
where HBo= initial still charge (lb mol): Sl= first slop cut (lb mol); Sz= second slop cut (lb mol). To design the system the following equipment must be specified: number of trays (column height), column diameter, condenser heat-transfer area, and reboiler heattransfer area. When the CAP is specified for a given system, the column diameter can be calculated. In addition, the heat-transfer areas of the condenser and the reboiler can be computed. Appendix A gives the equations used for these calculations.
510 Ind. Eng. Chem. Rea., Vol. 30, No, 3, 1991
Table 11. Energy Calculations for Binary Systems N RR CAP DIAD Aub Acb
4 N RR A. Relative Volatility of 1.5
CAP
DIAD
Aub
Acb
4
60 70 80 90 100
4.50 4.10 3.80 3.50 3.20
27.1 28.9 30.8 32.5 33.8
3.4 3.3 3.2 3.1 3.0
2022 1896 1779 1686 1621
2527 2370 2224 2107 2026
5.1 4.7 4.4 4.2 4.1
70 80 90 100
4.30 4.00 3.70 3.40
19.8 21.5 23.2 24.9
4.0 3.8 3.7 3.5
2767 2548 2362 2200
3459 3186 2952 2751
6.9 6.4 5.9 5.5
48.8 52.0 54.6 56.9 56.1
2.5 2.4 2.4 2.3 2.4
1122 1053 1003 963 976
1403 1317 1254 1203 1221
2.8 2.6 2.5 2.4 2.4
2.20 2.00 1.70 1.50 1.40
34.6 37.6 40.8 44.0 47.3
3.0 2.9 2.8 2.7 2.6
1583 1457 1343 1245 1158
1979 1821 1678 1556 1448
4.0 3.6 3.4 3.1 2.9
60 70 80 90 100
0.68 0.58 0.54 0.54 0.54
76.5 80.2 81.9 82.2 82.2
2.0 2.0 1.9 1.9 1.9
716 683 669 666 666
895 854 836 833 833
1.8 1.7 1.7 1.7 1.7
60 70 80 90 100
0.88 0.73 0.61 0.51 0.45
57.9 62.5 67.4 72.3 76.1
2.3 2.2 2.1 2.1 2.0
946 876 813 757 720
1183 1095 1016 947 900
2.4 2.2 2.0 1.9 1.8
D. Relative Volatility of 4 XD 95% 0.38 1031 2.1 50 920 1.8 60 0.30 1.7 70 0.27 863 815 1.6 80 0.27
88.7 92.6 94.5 94.3
1.9 1.8 1.8 1.8
617 591 579 581
772 739 724 726
1.5 1.5 1.4 1.5
74.1 79.4 85.1 88.6 88.7
2.0 2.0 1.9 1.9 1.9
739 690 643 618 617
924 862 804 773 772
1.8 1.7 1.6 1.5 1.5
10 20 30 40 50
10.10 6.30 5.90 5.40 5.00
9.8 18.2 21.3 23.4 25.2
5.6 4.1 3.8 3.6 3.5
5591 3010 2572 2341 2174
6989 3763 3215 2927 2718
14.0 7.5 6.4 5.9 5.4
20 30 40 50 60
8.70 6.50 5.90 5.30 4.70
10.2 13.0 15.0 16.6 18.2
5.5 4.9 4.5 4.3 4.1
5372 4215 3653 3301 3010
6715 5269 4566 4126 3763
13.4 10.5 9.1 8.3 7.5
XD
99%
10 20 30 40 50
3.50 3.10 2.80 2.50 2.20
29.4 35.9 39.8 42.8 45.8
3.2 2.9 2.8 2.7 2.6
1863 1526 1376 1280 1196
B. Relative Volatility of 2 XD = 95% 2329 4.7 60 1.90 1908 3.8 70 1.70 1721 3.4 80 1.50 1600 3.2 90 1.40 1495 3.0 100 1.40
10 20 30 40 50
5.30 3.60 3.20 2.90 2.60
16.6 22.6 26.3 29.2 31.8
4.3 3.7 3.4 3.3 3.1
3301 2424 2083 1876 1723
4126 3030 2604 2345 2154
XD =
99%
8.3 6.1 5.2 4.7 4.3
60 70 80 90 100
C. Relative Volatility of 3 XD = 95%
10 20 30 40 50
1.70 1.40 1.10 0.98 0.82
51.7 59.6 63.5 68.1 72.4
2.4 2.3 2.2 2.1 2.1
1059 919 862 804 756
1324 1149 1078 1005 946
2.6 2.3 2.2 2.0 1.9
10 20 30 40 50
2.10 1.70 1.60 1.50 1.20
33.6 40.1 45.5 49.7 53.6
3.0 2.8 2.6 2.5 2.4
1630 1366 1204 1102 1022
2038 1708 1505 1378 1277
4.1 3.4 3.0 2.8 2.6
XD
10 20 30 40
1.10 0.80 0.64 0.50
66.4 74.4 79.3 84.0
2.2 2.0 2.0 1.9
825 736 691 652
10 20 30 40 50
1.30 1.10 1.10 0.81 0.72
44.9 52.5 59.1 64.0 68.9
2.6 2.4 2.3 2.2 2.1
1220 1043 927 856 795
Xn
1525 1304 1159 1070 994
3.1" 2.6 2.3 2.1 2.0
99%
99% 60 70 80 90 100
0.53 0.34 0.23 0.17 0.17
OUnite: ft. bunits: ft2. eUnits: millions of Btu/h.
The study was carried out for the parameter values shown in Table I. Results A. Energy Calculations. The energy calculations are independent of the engineering economics calculations. A set of optimum reflux ratios (RRW) was obtained for each relative volatility, product purity, an? number of trays. Table I1 gives these results for the binary cases (four different relative volatilities and two product purities), and Table I11 gives reeulte for the ternary cases. As expected, the optimum reflux ratio decreases and the capacity factor increases as the number of trays increases for a given relative volatility and product purity. The column diameter (DIA)and the energy consumption (Q) were based on a production rate of 100 lb mol/h. This production rate can be scaled up or down to any desired
production rate without affecting the optimum reflux ratio. The other design parameters must be scaled by the appropriate factors. For example, the column diameter must be scaled by the square root of that factor. The capacity factor decreases as the product purity increases. For instance, a ternary system with relative volatility of 9/3/1,40-tray column, and product purity of 95% has a capacity factor of 45.94 lb mol/h. The same system with 99% product purity has a capacity factor of 31.02 lb mol/h. The decrease in the capacity factor is due to an increase in the batch time and an increase in the amount of slop cuts. The capacity factor also decreases as the relative volatility decreases (the difficulty of separation increases). The optimum reflux ratio as a function of relative volatility for different number of trays is plotted in Figure 1 for both binary and ternary systems with two different
Ind. Eng. Chem. Res., Vol. 30,No. 3,1991 511 Table 111. Energy Calculations for Ternary Systems N RR CAP DIA" ARb ACb Qc N RR A. Relative Volatilities of 2.25/1.5/1 %D = 95% 15612 10 9.30 3.5 9.4 19515 39.0 60 5.10 20 9.20 9.1 6048 7560 15.1 70 4.70 5.8 6244 30 7.50 11.0 5.3 12.5 80 4995 4.50 40 6.10 11.8 4632 5790 11.6 90d 4.90 5.1 50 5.60 4117 4.8 13.3 5146 100d 4.70 10.3 %D
20 30 40 50
13.90 10.70 9.40 8.40
4.4 6.1 6.1 7.6
8.4 7.1 7.1 6.4
12342 9028 8983 7248
15427 11285 11229 9060
A R ~ Acb
Q
4.6 4.4 4.3 4.4 4.2
3707 3488 3295 3401 3256
4634 4360 4119 4252 4070
9.3 8.7 8.2 8.5 8.1
8.2 8.9 9.4 10.0
6.1 5.9 5.7 5.6
6674 6178 5811 5480
8343 7722 7264 6850
16.7 15.4 14.5 13.7
CAP
DMa
14.8 15.7 16.6 16.1 16.8
= 99%
30.9 22.6 22.5 18.1
60 7od 80d 90"
7.50 7.90 7.30 6.70
B. Relative Volatilities of 4/2/1 %D = 95% 10 20 30 40 50
5.00 3.70 3.10 2.70 2.50
15.6 20.3 23.8 25.5 27.2
4.5 3.9 3.8 3.5 3.4
3519 2703 2303 2144 2013
4399 3379 2879 2681 2516
8.8 6.8 5.8 5.4 5.0
10 20 30 40 50
8.10 5.30 4.60 4.00 3.50
7.8 12.1 14.1 15.5 17.0
6.3 5.1 4.7 4.5 4.3
7052 4540 3900 3526 3227
8815 5675 4875 4407 4034
17.6 11.4 9.8 8.8 8.1
XD
60 70 80 90 l00d
2.30 2.20 2.10 2.00 2.20
28.9 30.5 31.9 33.4 32.3
3.3 3.2 3.1 3.0 3.1
1898 1798 1715 1642 1695
2373 2248 2144 2053 2118
4.7 4.5 4.3 4.1 4.2
60 70 80d 90d 100d
3.00 2.70 2.90 2.70 2.60
18.4 19.9 21.1 21.2 21.3
4.1 3.9 3.8 3.8 3.8
2975 2753 2597 2588 2573
3718 3442 3246 3235 3217
7.4 6.9 6.5 6.5 6.4
= 99%
C. Relative Volatilities of 9/3/1 XD
10 20 30 40 50
2.20 1.80 1.30 1.10 1.10
32.1 39.6 43.1 45.9 48.6
3.1 2.8 2.7 2.6 2.5
1705 1385 1270 1192 1128
2131 1731 1587 1491 1410
4.3 3.5 3.2 3.0 2.8
10 20 30 40 50
2.90 2.30 2.00 1.60 1.10
19.6 24.5 28.1 31.0 33.1
4.0 3.6 3.3 3.2 3.1
2791 2233 1952 1767 1654
3489 2792 2440 2208 2068
7.0 5.6 4.9 4.4 4.1
XD
a Unite:
ft.
Unite: ft2. e Units: millions of Btu/h.
95% 60 70 80 90 100
1.00 0.90 0.90 0.80 0.80
51.0 53.1 55.4 57.7 59.9
2.5 2.4 2.4 2.3 2.3
1075 1031 989 949 914
1344 1289 1236 1186 1143
2.7 2.6 2.5 2.4 2.3
60 70 80
1.10 1.10 0.90 1.10 1.10
36.6 41.3 43.6 43.1 44.8
2.9 2.7 2.7 2.7 2.6
1498 1326 1256 1272 1224
1872 1658 1571 1590 1530
3.7 3.3 3.1 3.2 3.1
= 99%
9od
l00d
Still charge of 400 mol used.
product purities. These reflux ratios maximize the capacity factor for the column with N given. In some cases a still holdup constraint was reached. A still charge of 400 lb mol was used in these cases instead of 300 lb mol. They usually occurred with N was large. It is worth noting that as the still charge was increased from 300 to 400 lb mol, the capacity factor decreased when the number of trays was held constant. Although the amount of the products and the batch time increased, the amount of the slop cut and the time used to form the slop cut increased. This had a negative effect on the capacity factor. The time used to form the slop cut represents approximately 24% and 30% of the total batch time for the 300 and 400 lb mol still charge cases,respectively. The cases shown in Table IV illustrate the effect of the slop cut period on the capacity factor. The increase in the slop cut period is due to the column holdup when the still charge is increased. By comparing the second product overhead composition of the two cases shown in Table I11 at the beginning of slop cut period, it can be seen that the overhead composition is lower for the case where a 400 lb mol of still charge is used. As a result, more time was needed to start the second product withdrawal. Since the liquid holdup on the trays had higher concentrations of light components while the still charge had high concentrations of heavy component, the separation was made more difficult.
Table IV. Effect of Still Charge on Capacity Factor (N = 80, RR = 1, X D 0.95, a = 9/3/1) He0 = 300 Hm 400 tE 0.5 0.5 p1 79.55 100.45 tPl 2.00 2.40 ZD1 0.64 0.72 xD2 0.36 0.28 xD3 0.00 0.00 S1 46.15 79.40 tS1 3.00 4.10 PP 57.45 75.25 tP2 4.11 5.55 s 2 0.00 0.00 p3 106.85 134.90 tF 4.11 5.55 CAP 55.00 53.04
It is also interesting to note that the optimum reflux ratio increased in some cases as the number of trays was increased as a result of the need to increase in the still charge. Figure 1B shows that the optimum reflux ratio of a 60-tray column for a relative volatility of 1.5 is 7.6 (point A), but it is 7.9 for a 70-tray column (point B). Another interesting phenomenon was observed in some cases. The use of total slop recycle produced a limit cycle. Figure 2 shows two cases that exhibit this behavior. Table V shows that it is due to the material in reflux drum. It is collected as a product in some cycles but discharged as a slop cut in others.
512 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 Table V. Limiting Cycle (N = 30, RR = 3.1, ID
0.95, a
4/2/1) cycle
HBO Xgol #Bo2
---
XRn?
tF
S1
SZ CAP
1 300 0.30 0.30 0.40 7.66 58.95 16.97 27.45
2 224.07 0.2740 0.4065 0.3194 8.65 51.76 10.00 22.86
3 209.12 0.2898 0.4230 0.2873 9.00 55.19 0.00 23.05
4 219.08 0.2982 0.4097 0.2921 8.93 53.02 10.00 22.57
5 212.83 0.2862 0.4238 0.2900 8.98 55.22 10.00 23.04
Table VI. Cases Used in the Engineering Economic Analysis case material of product energy no. construction purity, % costa 1 carbon steel 95 $2.50 2 $5.00 3 99 $2.50 4 $5.00 5 stainless steel 95 $2.50 6 $5.00 7 99 $2.50 8 $5.00 Monel 95 $2.50 9 10 $5.00 11 99 $2.50 12 $5.00 OPer lo00 lb of steam.
The results given in Tables I1 and I11 can be used for any set of economic bases and assumptions. B. Engineering Economic Analysis. The engineering economic analysis was performed with different materials of construction (carbon steel, stainless steel, and Monel) and using different energy costa ($2.50 and $5.00 per lo00 lb of steam). Table VI defines the various cases studied. The equations used to calculate the different costs are given in Appendix B. The diameter of the column decreases and the sizes of the reboiler and condenser decrease as the number of trays is increased. However, the height of the column increases rapidly, so total capital cost increases as the number of trays is increased. Energy consumption decreases as more trays are added to the column. The tradeoff calculations between capital and energy costs were used to determine the optimum number of trays. Table VI1 gives both capital and energy costs for binary separations with four different relative volatilities. The bases for the numbers in this table are 95% purities, $5/1000 lb of steam, and a stainless steel column. The optimum number of trays decreases from 100 to 60 as relative volatility increases from 1.51to 4. The total cost of the optimum is framed in the last column in Table VII. Table VI11 shows the effect of reducing energy cost to $2.50/ lo00 lb of steam for the relative volatility of 3. The optimum changes from a 70-tray column with total annual cost of $139000 to a 50-tray column with total annual cost of $98400. It is very important to note that these optima are quite flat. Therefore, from a practical engineering standpoint, it is not too important that the exact optimum column is designed. Table IX shows the effect of the payback period used. A 5-year payback period was assumed in the cases considered so far. Table IX shows that decreasing this to 2.5 years changes the optimum column from 70 trays to only 20 trays. These results are for the case with relative volatility of 3, product purity of 9690, and energy cost of
6 218.34 0.2988 0.4101 0.2911 8.94 53.12 10.00 22.54
7 212.85 0.2861 0.4239 0.2900 8.98 55.14 0.00 23.04
8 218.32 0.2988 0.4101 0.2911 8.94 53.12 10.00 22.54
9 212.88 0.2861 0.4239 0.2900 8.98 55.24 0.00 23.04
10
218.32 0.2988 0.4101 0.2911 8.94 53.12 10.00 22.54
Table VII. Costs for Binary SeJeparation(Carts" Calculated for a Stainless Steel Column, Product Purity of 96%, and Energy Cost of $S.OO/lOOO lb of Steam) reboiler condenser column capital steam total N cost cost cost cost cost cost A. a = 1.5 10 1.732 1.991 1.493 5.216 6.490 7.533 1.516 4.052 3.494 4.305 20 1.181 1.355 1.230 1.761 4.064 2.986 3.799 30 1.073 1.161 40 1.014 2.005 4.180 2.718 3.554 1.110 4.317 50 0.969 2.238 2.524 3.387 1.062 2.451 4.440 2.347 3.235 60 0.928 1.021 2.654 4.568 2.201 3.114 70 0.893 2.843 80 0.859 0.983 4.684 2.065 3.002 0.951 3.028 4.812 1.957 2.919 90 0.832 0.929 3.219 4.961 1.882 100 0.813
B. a 1 2 10 20 30 40 50 60 70 80 90 100
0.883 0.784 0.738 0.707 0.680 0.655 0.631 0.614 0.599 0.604
1.011 0.896 0.842 0.807 0.775 0.746 0.719 0.699 0.682 0.688
10 20 30 40 50 60 70 80 90 100
0.633 0.584 0.563 0.541 0.523 0.507 0.493 0.488 0.487 0.487
0.722 0.664 0.640 0.615 0.593 0.575 0.560 0.553 0.552 0.552
10 20 30 40 50 60 70 80
0.549 0.515 0.497 0.481 0.467 0.456 0.451 0.451
0.624 0.584 0.563 0.545 0.529 0.516 0.510 0.511
1.040 1.220 1.441 1.651 1.846 2.029 2.198 2.368 2.534 2.738
c. a = 3 0.878 1.047 1.252 1.435 1.608 1.772 1.931 2.097 2.270 2.442
2.934 2.900 3.021 3.165 3.301 3.430 3.549 3.680 3.815 4.030
2.163 1.772 1.598 1.486 1.389 1.303 1.223 1.165 1.118 1.134
2.750 2.352 2.202 2.119 2.049 1.989 1.933 1.901
2.233 2.295 2.454 2.591 2.724 2.854 2.984 3.138 3.309 3.481
1.230 1.067 1.002 0.934 0.878 0.831 0.793 0.777 0.774 0.774
1.677 1.526 1.492 1.452 1.423 1.402
1.990 2.081 2.233 2.376 2.511 2.649 2.802 2.976
0.958 0.855 0.802 0.757 0.717 0.687 0.673 0.674
1.940
WJ 1.404 1.435 1.470
D. a = 4 0.817 0.982 1.173 1.350 1.516 1.677 1.842 2.014
1.356 1.271 1.249 1.232 1.219
I m J 1.233 1.270
"All costa are in %1OOooO.
$5/1000 lb of steam. Figure 3 gives results for different relative volatilities. Table XA and Table XB illustrate results for two ternary cases with different product purities, but the same relative volatilities (9/3/1), energy cost ($2.50/1000 lb of steam), and materials of construction (stainless steel). The primary figure to use in the shortcut design procedure is Figure 4. The optimum number of trays is given for the various cases defined in Table VI. Both binary and ternary systems are given. For example, the optimum number of trays for the ternary system presented in case 9 (product purities of
Ind. Eng. Chem. Res., Vol. 30,No. 3,1991 513 I
'-
N-10
8 -
N-30
6 "50 '
4 -
"70
N-80
2 -
2
1
3
4
1
5
2
3
4
Rolillve Volillllly Rolitlvi Volitlllty
-INdo \
N-60
6
2
1
N-20
3
I\,
4
"70
3
2
4
Relallve Volatlllly
Relallve Volitlllty
Figure 1. Optimum reflux ratio ea a function of relative volatility for different number of trap. (A) Binary mixture with product purity of 95%. (B) Binary mixture with product purity of 99%. (C) Ternary mixture with product purity of 95%. (D)Ternary mixture with product purity of 99%.
\
N d O RR.l.1
100
95% Alphl-WJIl
8
-
80
I-
a
60
4
0
3 E
I
40
f0 N-30 RR.3.1
95% Alph#.C/2/1 20
10
O J
1
2
3
4
cyclrs
Figure 2. Limit cycles.
Rolitlve Volillllly
Figure 9. Effect of payback period on optimum number of trays.
514 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 Table VIII. Effect of Energy Costa on the Optimum Number of Trays (a= 3, ID 0.95) reboiler condenser column capital steam N cost cost cost cost cost Energy Cost = $2.50 10 0.633 0.722 0.878 2.233 0.615 20 0.584 0.664 1.047 2.295 0.534 30 0.563 0.640 1.252 2.454 0.501 40 0.541 0.615 1.435 2.591 0.467 50 0.523 0.593 1.608 2.724 0.439 60 0.507 0.575 1.772 2.854 0.416 70 0.493 0.560 1.931 2.984 0.397 80 0.488 0.553 2.097 3.138 0.388 90 0.487 0.552 2.270 3.309 0.387 100 0.487 0.552 2.442 3.481 0.387 10 20 30 40 50 60 70 80 90 100 a
0.633 0.584 0.563 0.541 0.523 0.507 0.493 0.488 0.487 0.487
Energy Cost = $5.00 0.722 0.878 2.233 0.664 1.047 2.295 0.640 1.252 2.454 0.615 1.435 2.591 0.593 1.608 2.724 0.575 1.772 2.854 0.560 1.931 2.984 0.553 2.097 3.138 0.552 2.270 3.309 0.552 2.442 3.481
total cost
-
100
43
9
1.062 0.993 0.992 0.985 0.986 0.993 1.016 1.049 1.083
80
-
60
-
1.677 1.526 1.492 1.452 1.423 1.402
3.7.12
2.6 1
-
40
11
-
20
1.230 1.067 1.002 0.934 0.878 0.831 0.793 0.777 0.774 0.774
1-8,lO-12
01
5,9,10
1
2
3
4
Relative Volatility
1.404 1.435 1.470
120
I
All costa are in $100OOO. 1.3,7
Table IX. Effect of Payback Period on Total Cost total costa N 5 vears 2.5 "vears 10 1.677 2.347 20 1.526 12.2151j 30 1.492 2.229 40 1.452 2.300 50 1.423 2.241 60 1.402 2.258 70 2.285 1.404 2.346 90 1.435 2.428 100 1.470 2.514
2,4,6,8,12
~~
10 5,ll
m -
In $100 OOO.
20
Table X. Costs for Ternary System (Coatsa for Stainless Steel Column, (I = 9/3/1, Energy Cost of $2.60/1000 lb of Steam) reboiler condenser column capital steam total N cost cost cost cgst coat cost A. Product Purities = 95% 10 0.838 0.958 1.012 2.808 0.990 1.551 20 0.771 0.881 1.210 2.862 0.861 1.433 30 0.706 0.805 1.408 2.920 0.741 1.325 40 0.680 0.775 1.617 3.072 0.694 1. 8 50 0.657 0.748 1.813 3.218 0.664 &I 60 0.639 0.728 2.002 3.369 0.624 1.298 70 0.623 0.710 2.184 3.517 0.598 1.301 80 0.609 0.693 2.358 3.659 0.574 1.306 90 0.595 0.677 2.523 3.794 0.551 1.310 100 0.582 0.662 2.684 3.928 0.531 1.316 10 20 30 40 50 60 70 80 90 100 a All
1.128 0.984 0.907 0.854 0.818 0.791 0.764 0.741 0.704 0.689
9
B. Product 1.293 1.127 1.038 0.976 0.934 0.903 0.872 0.846 0.804 0.785
Purities 1.181 1.375 1.608 1.827 2.039 2.245 2.437 2.621 2.764 2.939
= 99% 3.602 3.487 3.554 3.657 3.791 3.939 4.073 4.208 4.272 4.413
1.620 2.340 1.295 1.992 1.131 1.842 1.022 1.763 0.960 1.708 0.898 1.685 0.847 1,662 0.806 1.647 0.738 0.710 1.693
costa are in $100OOO.
95%, energy cost of $2.50/1000 lb of steam, and material of construction of Monelr is 70 if the relative volatilities
1
2
3
4
Roiativo Voiatlllty
Figure 4. Correlations for economic optimum batch distillation columns. (A) Binary system. (B) Ternary system. Table XI. Factors Used in Calculating Capital Costs for the Different Materials of Construction material of construction FM FTM FEX carbon steel 1.0 1.0 1.35 stainless steel 2.1 1.189 + 0.0577(DIA) 3.35 Monel 3.6 2.306 + 0.112O(DIA) 4.35
are 4/2/1. If the relative volatilities are 9/3/1, the optimum column has 30 trays. The optimum reflux ratios that correspond to these optimum designs can be read from Figure 1C. They are 2.2 and 1.6 for the two different relative volatilities.
Conclusion A quick, easy-to-use approximate design method is presented for batch distillation columns. It yields both the optimum number of trays and the optimum fixed reflux ratio for a given separation (product purities and relative volatilities) and given economic parameters (energy cost and materials of construction). The correlations presented in Figure 4 should be useful for obtaining shortcut designs for batch distillation systems.
Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 515 The specific numerical results clearly have limitations.
It is impractical to explore all possible parameters values. However, the ranges of parameters explored should be wide enough to make the results useful for approximate designs. The fact that the optima are quite flat should also help the general applicability of these results. In any event, a procedure is presented that is generic. The design engineer can follow the methods discussed in this paper for any specific numerical case and determine the optimum design if more precision is necessary. The effects of fresh feed composition have not yet been explored. Nomenclature Ac = condenser heat transfer area, ft2 AR = reboiler heat transfer area, ft2 CY. = relative volatility of component j dAP = capacity factor, lb mol of total product/h cb = cost of the shell as a function of shell weight, height, and diameter c b l = platform and ladder cost as a function of diameter D = distillate flow rate, lb mol/h DIA = column diameter, ft DIAmin= minimum diameter, ft F = production rate = 100 lb mol/h FEx = condenser or reboiler material of construction factor FM = material of construction factor (shell) FNT = cost factor for number of trays Fm = material of construction factor as a function of diameter (trays) Fm = cost factor for tray type HB = still pot holdup, lb mol Hm = initial still pot charge, lb mol HD = reflux drum holdup, lb mol HN = tray liquid holdup, lb mol H, = heat of vaporization, Btu/h H,' = molal heat of vaporization of the feed, Btu/(lb.mol) K, = empirical constant, ft/s for 24411. spacing L = tangent to tangent length, ft N = number of theoretical trays in the column NoPt= optimum number of theoretical trays Pl = amount of light product, lb mol ' P2 = amount of intermediate product, \b mol P3 = amount of heavy product, lb mol Q = energy consumption, Btu/h Q' = energy consumption, Btu/h R = flow rate of reflux, lb mol/h pL = liquid density, lb/ft3 pv = vapor density, lb/ft3 RR = reflux ratio RRoPt = optimum reflux ratio SC = steam cost per lo00 lb SI= amount of first slop cut, lb mol S2= amount of second slop cut, lb mol T = column total operating hours AT = temperature gradient, O F t = time, h t~ = startup or equilibrium time, h t p = time when batch is finished, h tp = on-specification product withdrawal time, h ts = slop cut withdrawal time, h U = overall heat-transfer coefficient, Btu/(h ft2 O F ) V = vapor boilup, mol/h V' = vapor flow rate required to produce F lb mol/ h of production rate, lb mol/h V , = maximum allowable superficial vapor velocity, ft/s 9.U = steam flow rate, lb/h W,= shell weight, lb XB = still pot composition, mole fraction RB = average still pot composition plus column trays, mole fraction low boiler
xBj = still pot composition, mole fraction of component j xB3 = heavy component product, mole fraction of component 3 x n = liquid composition on tray n,mole fraction of low boiler xnj.= liquid composition on tray n,mole fraction of component J
= reflux drum composition, mole fraction low boiler xDj = distillate composition, mole fraction of component j zD = average composition of distillate product, mole fraction yBj.= reboiler vapor composition, mole fraction of component J yNj = vapor composition from top tray, mole fraction of component j ynj = vapor composition from tray n,mole fraction of component j Zj = fresh feed composition, mole fraction component j XD
Appendix A. Energy Calculations Equations used in energy calculations: V'=
17F
Vl?
CAP
where V'= vapor flow rate required to produce F lb mol/h of production rate; V vapor boilup = 100 lb mol/h; F 3 production rate = 100 lb mol/h.
where DIAmin= minimum diameter (ft); MW vapor molecular weight; pv = vapor density = 0.16 lb/ft3; V , maximum allowable superficial vapor velocity (ft/s). Vm = Kv(
T PL - Pv ) 112
(A-3)
where K, = empirical constant = 0.3 ft/s for 24-in.spacing; pL = liquid density = 54 lb/ft3. The energy consumption was calculated as follows: Q'= V!H; (A-4) where Q'= energy consumption (Btu/h); H,' = molal heat of vaporization of the feed = 13 700 Btu/(lb mol). The steam flow rate was obtained using W = Q'/H, (A-5) where W = steam flow rate (lb/h); H, heat of vaporization of steam = 915.5 Btu/lb. The condenser heat-transfer area was obtained from Ac = q / U A T (A-6) where Ac = condenser heat-transfer area (ft2);q heattransfer rate (Btu/h) = V'(H,'); U overall heat-transfer coefficient = 100 Btu/(hr ft2OF); AT = temperature gradient = 20 O F . The reboiler heat-transfer area was similarly calculated except that U = 50 Btu/(hr ft2 O F ) and AT = 50 O F . Appendix B. Engineering Economic Calculations B.1. Capital Costs: B.1.1. Column Cost. The column cost was calculated as follows: where Cb = cost of the shell as a function of shell weight, height and diameter; FM material of construction factor (shell); NT = number of trays; Cbt = cost of trays as a function of diameter; FTM material of construction factor as a function of diameter (trays); FW cost factor for tray type (valve, grid, bubble cap, sieve); Fm = cost factor for number of trays; Cpl = platform and ladder cost as a function of diameter. The cost of trays as a function of diameter is given by f
516 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991
= 278.38 exp(O.l739(DIA)) If the number of trays (N)is below 40 C b = exp[6.329 + 0.18255(1n W,)+ 0.02297(1n WJ2] (B-2) C,I = 182.50(DIA)0~799sOL0*7MM (B-3) where W,3 shell weight (lbs); L = tangent to tangent length (ft). If N 1 40 Cb = exp[6.823 0.14178(1n W,) 0.02468(1n Wb2] (B-2’) C,I = 151.81(DIA)0.89S’6L0*m161(B-3’) cbt
The cost factor for number of trays is
(FNT)
Fm = 2.25/(1.0414)N
when N < 20 (B-4)
otherwise
= 1.0 (B-4’) The cost factor for tray type (Fm)= 1.0 for valve trays. Other factors are shown in Table XI. B.1.2. Condenser and Reboiler Capital Costs. The reboiler and condenser capital costs were calculated as follows: equipment cost = lp(0.73 + 0.064A0.66)Fm (B-5) where A E condenser or reboiler heat transfer area (ft2); Fm condenser or reboiler material of construction factor, All the capital costs are updated with cost indexes for the year 1987. B.2. Energy Cost. The energy cost was calculated as follows: FNT
energy cost = lUT(SC) (B-6) where W = steam flow rate (lb/h); T the column total operating hours (8500 h); SC steam cost per lo00 lb ($/lo00 lb of steam).
Literature Cited Bauerle, G. L.; Sandall, 0. C. Batch Dietillation of Binary Mixturea at Minimum Reflux. AZChE J. 1987,33,1034-1036. Coates, J.; Pressburg, B. S. How to Analyze the Calculations for Batch Rectification in Tray Columns. Chem. Eng. 1961, 68, 131-136. Coward, I. The Time-Optimal in Binary Batch Distillation. Chem. Eng. Sci. 1966,22,503-516. Featherstone, W. Rapid Method of Design for Batch Distillation. Processing 1976,22, 25-26. Guy, J. L. Modeling Batch Distillation in Multitray Columns. Chem. Eng. 1983,90,99-103. Kerkhof, L. H. J.; Vissers, H. J. M. On the Profit of Optimum Control in Batch Distillation. Chem. Eng. Sci. 1977, 33, 961-970. Luyben, W. L. Some Practical Aepecta of Optimal Batch Distillation Design. Znd. Eng. Chem. Process Des. Dev. 1971,10,54-59. Luyben, W. L. Multicomponent Batch Distillation: Part I-Ternary Systems with Slop Recycle. Znd. Eng. Chem. Process Des. Dev. 1988,27,642-647. Quintermo-Marmol, E.; Luyben, W. L. Multicomponent Batch Dietillation. 2. Comparison of Alternative Slop Handing and Og erating Strategies. Znd. Eng. Chem. Res. 1990, 29, 1915-1921. Stewart, R. R.;Weisman, E.; Goodwin, B. M.; Speight, C.E. Effect of Deaign Parameters in Multicomponent Batch Distillation. Znd. Eng. Chem. Process Des. Dev. 1973,12, 130-136. Treybal, R.E. A Simple Method for Batch Distillation. Chem. Eng. 1970, 77,9598. Van Dongen, D. B.; Doherty, M. F. On the Dynamice of Distillation Processes VI: Batch Distillation. Chem. Eng. Sci. 1985, 40, 2087-2093.
Received for review April 14, 1990 Revised manuscript received August 27, 1990 Accepted September 17,1990
