Optimal Design of Distillation Flowsheets with a Lower Number of

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Ind. Eng. Chem. Res. 2002, 41, 5716-5726

Optimal Design of Distillation Flowsheets with a Lower Number of Thermal Couplings for Multicomponent Separations Ben-Guang Rong* and Andrzej Kraslawski Department of Chemical Technology, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland

The thermally coupled distillation flowsheets for multicomponent separations are discussed on the basis of the intended individual splits. Then, the generation of the thermally coupled distillation flowsheets with a lower number of thermal couplings than the partially coupled scheme is presented. A formula is presented to calculate the number of feasible schemes with a lower number of thermal couplings. An integrated framework is formulated for parametric design and synthesis of the optimal thermally coupled distillation flowsheets for multicomponent separations. Based on the results of the calculations, significant insights have been made which are very helpful to the design and synthesis of the optimal thermally coupled distillation schemes for multicomponent separations. It has been found that a thermally coupled scheme with a lower number of thermal couplings could be more advantageous than one with thermal couplings introduced for all of its internal submixtures for a specific simple column configuration. 1. Introduction Distillation is the widely used separation method, and it is the largest energy consumer among process units. Improvement of the energy efficiency in distillation systems is still an active research field. Among the issues concerned with the improvement of the energy efficiency of distillation systems, the optimal design and synthesis of multicomponent distillation flowsheets is still one of the most challenging problems. The thermally coupled distillation scheme is considered to be one of the most promising systems because of its savings on both energy and capital costs.1,2 There have been conducted numerous research works on thermally coupled distillation schemes aiming at the steady-state and dynamic performance analysis, especially for ternary mixtures.1-14 A few interesting observations have been concluded. For example, for ternary mixtures the energy savings in the fully thermally coupled configuration (FC) can be less than 30% compared with those of traditional schemes.3,5,8 Among the three thermally coupled systems for ternary mixtures, over a wide range of relative volatilities and feed compositions, the side rectifier (SR) and the side stripper (SS) configurations tend to provide the most thermodynamically efficient designs more often than does the FC configuration.10 For ternary mixtures, there was an identified search space of the alternative schemes,3,5,15 and numerous efforts have been made to understand the advantages and disadvantages of the proposed schemes. Those works have contributed a lot to help engineers look for the optimal configuration for ternary distillation separations. Recently, Agrawal and Fidkowski14,16 have presented some new schemes for ternary separations aiming at the improvement of the thermodynamic efficiency and operability. Though an extended search space for the optimal design of distillation schemes for ternary mixtures has been presented on the basis of the * To whom correspondence should be addressed. Tel: +358 5 621 6113. Fax: +358 5 621 2199. E-mail: [email protected].

superstructure concept, the completeness of the proposed set of column configurations has never been proven.16 For mixtures with four or more components, the combinatorial problem makes it even more difficult to construct a superstructure in which all of the possible schemes are embedded. There have been conducted several works to find the possible thermally coupled distillation schemes for four and more component mixtures,4,17-19 and some specific structures of thermally coupled schemes for multicomponent separations have been identified. Recently, we have parametrically studied some of the thermally coupled distillation flowsheets for five-component mixtures20,21 from the viewpoint of economic evaluation and optimal synthesis of the multicomponent thermally coupled distillation flowsheets. Still, there are two major research issues concerned with the optimal design of thermally coupled distillation flowsheets for four or more component separations which are challenging and need much research efforts. The first one is to determine how many possible thermally coupled schemes exist for the separations of multicomponent mixtures. The answer will help to construct a complete search space of thermally coupled schemes for multicomponent separations. The second issue is to determine how to manage the search space for synthesis of the optimal multicomponent thermally coupled distillation flowsheets. It will help engineers to find applications of these new distillation schemes for specific industrial problems. At the moment, these two issues are also the two major obstacles for engineers to consider the use of the multicomponent thermally coupled distillation schemes. In this paper, we shall demonstrate how we generate, represent, and manage the search space for the optimal design of the thermally coupled distillation flowsheets for multicomponent separations. On this basis, an integrated framework is developed with which the engineers can consider the use of the thermally coupled schemes for multicomponent distillation separations.

10.1021/ie0107136 CCC: $22.00 © 2002 American Chemical Society Published on Web 10/09/2002

Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002 5717

Figure 1. Conventional sharp and sloppy separation schemes for ternary mixtures.

2. Alternative Space of Thermally Coupled Distillation Configurations 2.1. Generation of Thermally Coupled Distillation Schemes for Ternary Mixtures. The different types of thermally coupled distillation schemes for multicomponent separations can be generated by removing condenser(s) and (or) reboiler(s) of the simple column configurations.18,22 There are two ways to introduce thermal couplings in a simple column configuration: one is by sharp separation of feed or submixtures with more than binary components; another is by sloppy separation of feed or submixtures with three or more components. The former produces the partially thermally coupled distillation flowsheets (PC), and the latter gives the fully thermally coupled schemes (FC). For example, for separations of ternary mixtures ABC, there are two simple column sequences called direct sequence (DS) and indirect sequence (IS), as shown in parts a and b of Figure 1, respectively. These two simple column sequences are based on the sharp splits between the two adjacent components. There is also a prefractionator scheme (PF), shown in Figure 1c, which is based on the sloppy separation of feed ABC into two subgroups of AB and BC. It is interesting to note that there is a different number of individual splits between the sharp separation schemes and the sloppy separation one. For DS and IS schemes, each of them has two

individual splits, i.e., A/BC and B/C for DS and AB/C and A/B for IS, while for the PF scheme, there exist three individual splits of AB/BC, A/B, and B/C. However, for all of the schemes of DS, IS, and PF, each individual split has only two column sections, i.e., the rectifying section and the stripping one. For the PF scheme, this can be clearly visualized by the individual split configuration, as shown in Figure 1d. For an ideal or near-ideal ternary mixture, each separation unit in a configuration of Figure 1 has an intended split, either a sharp or a sloppy one. This results in the fact that each column section in a separation unit is enriched in either an individual component (desired product) or a submixture with two or more components (internal subgroups). For a column section enriched with a submixture of two or more components, there exists a prefractionation to the submixture. However, this prefractionation is disturbed by the condenser for supplying the needed reflux or the reboiler for supplying the boilup in that separation unit. Thus, an apparent remixing has existed for each of such column sections in a simple column configuration.2,4,8 As a consequence, it greatly diminished the separation efficiency of the separation process. However, the remixing can be avoided by eliminating the condenser or the reboiler in the corresponding rectifying or stripping column section. Then the vapor stream from the rectify-

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Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002

Figure 2. Thermally coupled sharp and sloppy distillation configurations of Figure 1.

ing section or the liquid stream from the stripping section can be directly introduced into its subsequent separation unit. Meanwhile, a liquid flow or a vapor flow is withdrawn from its subsequent unit at the same location of the vapor or liquid stream introduced from the prior column. The withdrawn stream is used as the needed liquid reflux or vapor boilup for the rectifying or stripping section of the prior column. It can produce the thermally coupled schemes. For each of the simple column configurations of Figure 1a-c, its corresponding thermally coupled configuration is shown in parts a-c of Figure 2, respectively. It can be seen from Figure 2 that the vapor flows of the thermally linked stripping column sections are from the same reboiler and that the liquid flows of the thermally linked rectifying sections are from the same condenser. Thus, by flexible combination of the thermally linked stripping column sections and the thermally linked rectifying column sections, the thermodynamically equivalent thermally coupled schemes can be produced. In Figure 3a there is such a thermodynamically equivalent scheme of Figure 2a. It is produced by combining the two stripping sections of the two separation units and leaving the rectifying column section 3 with a condenser as stand-alone; this is the so-called SR column. Similarly, when the two rectifying sections of Figure 2b are combined and the stripping column section 4 with a reboiler is left as stand-alone, the thermodynamically equivalent thermally coupled scheme of Figure 2b is produced, as shown in Figure 3b. It is the so-called SS column. For Figure 2c, the thermally linked stripping sections and rectifying sections can be combined either simultaneously or separately; thus, three thermodynamically equivalent thermally coupled schemes are produced, as shown in Figure 3d-f. Moreover, for Figure 2c, the two separation units can be implemented in a single-shell equipment, and a further thermodynamically equivalent thermally coupled scheme is produced, as shown in Figure 3c. It is the so-called dividing wall column (DWC).8,23 The flexibility of the combination of the thermally linked column sections makes it possible to generate topologically different thermodynamically equivalent thermally coupled schemes for multicomponent separations. However, each column section in the equivalent arrangements has the same function as the corresponding column section in the original conventional config-

uration. This observation can help us to understand the different thermally coupled schemes by identifying their column section counterparts. A column section counterpart is defined as a combination of a rectifying section with a stripping one that is specified for an intended individual split, either a sharp or a sloppy one. These column section counterparts are determined by the predefined individual splits in the simple column configurations. As discussed earlier, there are two individual sharp splits in DS and IS of parts a and b of Figure 1. Thus, each of them has two column section counterparts. For DS, the counterpart of sections 1 and 2 is for the intended sharp split A/BC, and the counterpart of sections 3 and 4 is for the split B/C. For IS, the counterpart (1, 2) is for the split AB/C and the counterpart (3, 4) is for the split A/B. Similarly, for the FC configuration, there are three column section counterparts corresponding to three individual splits, the counterpart (1, 2) for AB/BC, the counterpart (3, 4) for A/B, and the counterpart (5, 6) for B/C. It is interesting to note that the column section counterparts are not changed among the different arrangements of the thermodynamically equivalent schemes, because the predefined individual splits for the conventional configurations are not changed in the different thermodynamically equivalent systems. The importance of identifying the individual splits and the corresponding column section counterparts in a multicomponent flowsheet is not only for the generation of more feasible arrangements but also for the practicability of the parametric design of these complex distillation flowsheets. It is due to the fact that the practical design procedures are indispensable for engineers to use these economically attractive but more complex distillation systems. The design procedures should have two main purposes. The first is to help engineers to identify the promising arrangements among a large number of feasible configurations, and the second is to parametrically optimize the identified flowsheets and to present the optimal operating and equipment parameters by the given utilities and process constraints. 2.2. Possible Thermally Coupled Schemes for Four or More Component Mixtures. The understanding of the generation of the feasible thermally coupled distillation schemes shown above for ternary mixtures can be easily extended to the mixtures with


Figure 3. Thermodynamically equivalent thermally coupled configurations of Figure 2.

four or more components. It is expected that for four or more component mixtures the number of feasible thermally coupled schemes will increase sharply. Thus, for four or more component mixtures, there is a further threshold that the engineers must stride across. They must first identify the optimal or nearoptimal schemes for their problems among a large number of possible thermally coupled schemes. Then, the same as for ternary mixtures, they have to make a parametric study and optimize the identified promising schemes. There are several works on finding the possible arrangements of the thermally coupled schemes for more than three component mixtures. Sargent and Gaminibandara17 presented a superstructure for a fourcomponent fully coupled scheme. Kaibel4 illustrated some distillation columns with vertical partitions for multicomponent separations. Agrawal18 presented some satellite column arrangements of fully coupled schemes for four or more component mixtures. However, among the work of deriving a general superstructure which incorporates all other configurations as substructures, neither detailed analysis nor computational results are presented.19,21 Thus, design tools and available knowledge for supporting the utilization of these multicomponent schemes are very limited. It is obvious that the fully thermally coupled distillation schemes for four or more component mixtures are more complexity and difficulties in controllability and

operability because they have much more thermal coupling streams in the systems. Thus, we can expect that the partially thermally coupled schemes for four or more component mixtures are more promising. There are several reasons. First, they are more efficient than the conventional systems in terms of both energy and capital costs. Second, they are simple because of the lower number of thermal couplings as well as the lower number of column sections. In consequence, they are more amenable to control and operations. Third, there exists industrial experience, for example, in crude oil refinery and other applications.24 Finally, it is feasible to develop practical design procedures for the partially coupled schemes. In the following parts of this work, there are first generated the feasible multicomponent thermally coupled distillation schemes in terms of the intended individual splits, based on which a space of the alternative schemes with a lower number of thermal couplings is identified. Next, the thermally coupled schemes are arranged to the equivalent schemes in terms of the column section counterparts, in which each intended split is implemented by one of the basic separation units. Finally, an integrated framework is formulated on the basis of the design and synthesis for the alternatives included in the identified search space. Thus, there is presented a systematic procedure for designing and optimizing the thermally coupled distillation flowsheets for the separations of four or more component mixtures.

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Figure 4. Five-component simple column sequence and its partially thermally coupled scheme.

3. Alternative Space of Thermally Coupled Schemes with a Lower Number of Thermal Couplings In this chapter, we will demonstrate the generation of the thermally coupled alternatives that are simpler than the fully coupled schemes and more energyefficient than the conventional configurations. As indicated earlier, the submixture (including the feed) with three or more components can be separated into two subgroups by either a sharp or a sloppy split. If a subgroup from an individual split has two or more components, then it needs a successive individual split. Moreover, when the condenser or the reboiler corresponding to this subgroup is eliminated, a thermal coupling can be introduced with respect to this subgroup. In this way, a thermally coupled distillation flowsheet can be generated by the intended individual splits for all of the possible submixtures with two or more components. There is presented a procedure for the generation of all of the thermally coupled schemes from the conventional simple column configurations which formulates a subspace of the partially thermally coupled alternatives for multicomponent distillations.22 There is a unique partially thermally coupled scheme corresponding to a simple column configuration for a multicomponent separation with regard to the intended individual splits. Thus, the total number of partially thermally coupled schemes for an n-component mixture can be calculated by the formula of Thompson and King25 for simple column sequences.

Sn )

[2(n - 1)]! n!(n - 1)!

(1)

D/E, as shown in Figure 4a, then there is a unique corresponding partially thermally coupled flowsheet for it, as shown in Figure 4b.22 It is seen from Figure 4a that there are three column sections whose products are internal submixtures with two or three components. Column 1 has a condenser AB and a reboiler CDE, and column 3 has a reboiler DE. When the condenser(s) and reboiler(s) with the internal submixtures are eliminated, the partially thermally coupled scheme is produced as in Figure 4b. Its network representation is shown in Figure 5a.21 However, if the thermal coupling is not introduced simultaneously for all of the internal submixtures, then it can produce multicomponent thermally coupled distillation flowsheets with different numbers of thermal couplings. For the configuration of Figure 4a, we can introduce two thermal couplings simultaneously for submixtures AB and CDE, for AB and DE, or for CDE and DE. Then it produces three thermally coupled configurations with two thermal couplings as shown in parts b-d of Figure 5. Similarly, we can introduce only one thermal coupling for submixture AB, CDE, or DE. Then it produces three thermally coupled configurations with one thermal coupling, as shown in parts e-g of Figure 5. Following the discussion above, for each of the simple column sequences, one can generate all of the feasible thermally coupled distillation flowsheets with a lower number of thermal couplings than the partially coupled schemes for any multicomponent mixtures with four or more components. The following formula is derived for the calculation of the number of thermally coupled distillation schemes for an n-component simple column sequence. n-3

It must be indicated that it is not necessary to introduce the thermal coupling for every internal subgroup with binary or more components in a multicomponent separation system. Then, the number of feasible thermally coupled configurations for multicomponent separations is much higher than the known number of partially thermally coupled schemes. For example, for a five-component mixture, if the synthesized optimal simple column sequence is AB/CDE f A/B f C/DE f

Cn )

(n - 2)!

+1 ∑ j)1 j!(n - 2 - j)!

(2)

where Cn is the total number of thermally coupled distillation schemes generated from a simple column n-3 configuration. For n ) 3, Cn ) 1. The term ∑j)1 (n 2)!/j!(n - 2 - j)! represents the number of thermally coupled schemes with a lower number of thermal couplings than the partially coupled one.


Figure 5. Thermally coupled configurations for a five-component simple column sequence of Figure 4a. Table 1. Number of Thermally Coupled Schemes Generated from the Simple Column Sequences for an n-Component Mixture

no. of components

simple column sequences

partially thermally coupled schemes

3 4 5 6 7 8 9 10 11

2 5 14 42 132 429 1430 4862 16796

2 5 14 42 132 429 1430 4862 16796

totally generated thermally coupled schemes 2 15 98 630 4092 27027 181610 1239810 8582756

Thus, the total number of thermally coupled schemes for all of the simple column sequences of an n-component mixture can be calculated from the following formula:

Pn ) SnCn )

[

[2(n - 1)]! n!(n - 1)!

n-3

(n - 2)!

]

+1 ∑ j)1 j!(n - 2 - j)!

(3)

Table 1 illustrates the number of the partially coupled schemes, as well as the number of the totally thermally coupled schemes generated from the simple column configurations for mixtures with different numbers of components. Obviously, the generated thermally coupled schemes have formulated an alternative space for the optimal design of the thermally coupled distillation flowsheets with a lower number of thermal couplings for multicomponent separations. 4. Integrated Design Support Framework It is clear that, for multicomponent thermally coupled distillation flowsheets, if there are no available design procedures, it would be very difficult for designers to consider the applications of these flowsheets in the real industrial problems. For example, for a partially thermally coupled configuration for a five-component separation in Figure 4b, there are 16 design variables. As a consequence, it is impossible to give a set of reasonable initial values for these design variables using trial-anderror methods. Moreover, these design variables are strongly coupled because of the intercolumn thermally

linked transferring streams. Thus, any further simulation and optimization are related to the design procedures which can predict the initial values for these design variables. In our previous work, a shortcut design procedure has been developed for the design of any type of thermally coupled distillation flowsheets with sharp splits.21 With the developed design procedure, a computer representation of the flowsheets has been proposed based on the abstraction of the structural information of the generated flowsheets. Then, all of the configured systems can be included in a flowsheet base. A synthesis algorithm is developed which can simultaneously synthesize and compare all of the configurations in the flowsheet base in terms of the different objective functions. This methodology is more advantageous than the traditional superstructure approach for process synthesis, because the purpose of the flowsheet base is not only to store all of the possible configurations as the superstructure approach does. The flowsheet base is created for the parametric study and optimization of all of the stored configurations. Based on the above analysis, an integrated framework is formulated for the optimal design of the thermally coupled distillation flowsheets for multicomponent separations, as shown in Figure 6. It must be emphasized that this framework is developed based on the considerations of the concerns of the engineers for the applications of these simpler, more energy-efficient distillation systems. For this purpose, the design paradigm with the support of the integrated framework is the combination of the insight-based approach and the algorithmic methods for solving design problems. It emphasizes the interaction of the engineers with the support framework and allows them to control the design process by managing the search space and getting insights into the design problems. This is realized by the flexibility in utilizing of this design support framework. The flexibility means that the users and engineers can explore the search space of the design problems in different ways by the support of the design framework. For example, the designers can calculate only a specific scheme once, they can calculate and analyze a group of the identified schemes together, or they can synthesize and compare all of the identified schemes for a specific multicomponent mixture. The following examples illustrated the applicability of this integrated framework in the design and synthesis of the optimal thermally coupled schemes.

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Figure 6. Integrated framework for the optimal design of multicomponent thermally coupled distillation flowsheets. Table 2. Feed Components and Mole Fractions of the Example component

mole fraction

Tbp(bp), K

∆Tbp, K

A, ethanol B, 2-propanol C, n-propanol D, isobutyl alcohol E, n-butanol

0.25 0.15 0.35 0.10 0.15

351.5 355.4 370.4 381.0 390.9

3.9 15.0 10.6 9.9

5. Examples For thermally coupled distillation configurations, the introduced intercolumn thermally coupled streams are perceived to be the source of operating problems.14 Thus, for the design of the optimal thermally coupled distil-

lation flowsheets for multicomponent separations, among the feasible thermally coupled distillation configurations with similar economic performance, the one which has a lower number of thermal couplings is regarded as the optimal flowsheet. In our previous study,22 a fivecomponent mixture shown in Table 2 has been used to compare the steady-state performance of the 14 partially thermally coupled flowsheets with those 14 simple column configurations. The feed flow rate is 500.4 kmol/ h, and the recovery for each key component is 0.98. The obtained first two best simple column sequences are the sequence of AB/CDE f A/B f C/DE f D/E (sequence 9) and the sequence of AB/CDE f A/B f CD/E f C/D (sequence 8). The partially coupled scheme corresponding to sequence 9 is the best one among the 14 partially thermally coupled flowsheets. For sequence 9, there are six feasible thermally coupled configurations of Figure 5b-g which have a lower number of thermal couplings than the partially coupled scheme of Figure 5a. Similarly, there are also six feasible thermally coupled configurations for sequence 8 (Figure 7b-g), which have a lower number of thermal couplings than its corresponding partially coupled scheme of Figure 7a. With the developed integrated framework, the design results of the thermally coupled flowsheets with a lower number of thermal couplings for the simple column sequences 9 and 8 are presented in Tables 3 and 4, respectively. For comparison, the calculation results for the simple column sequence and its corresponding partially thermally coupled configuration are also included in Tables 3 and 4. The detailed information concerning the example and the calculation can be found in Rong et al.20,21 To understand the influence of the thermal couplings introduced for the different internal submixtures of the simple column configuration on the system’s economic performance, the thermal couplings introduced for the internal submixtures in Figures 5 and 7 are presented in Tables 5 and 6, respectively. From Tables 3 and 4, we can see that the values of the total annual costs are very different for the thermally coupled schemes with different numbers of thermal couplings for a specific simple column sequence. From Table 3, for sequence 9, the partially thermally coupled scheme (Figure 5a) with couplings introduced for all of its internal submixtures AB, CDE, and DE is the best coupled scheme in terms of the total annual costs among all of the thermally coupled schemes in

Figure 7. Thermally coupled configurations for the five-component simple column sequence 8.

Ind. Eng. Chem. Res., Vol. 41, No. 23, 2002 5723 Table 3. Design Results for Sequence 9 and Its Thermally Coupled Schemes in Figure 5

scheme

total duty of the reboilers (106 kcal/h)

total duty of the condensers (106 kcal/h)

annual capital cost (104 $/p.a.)

annual operating cost (104 $/p.a.)

total annual cost (104 $/p.a.)

sequence 9 a (PC) b c d e f g

34.0 28.2 30.4 29.7 30.6 31.6 32.9 32.1

34.7 29.0 31.1 30.4 31.4 32.3 33.6 32.8

78.9 75.2 74.6 74.1 79.1 72.4 75.2 77.4

405.3 352.6 382.5 373.2 378.4 399.1 409.3 379.3

484.2 427.8 457.1 447.3 457.5 471.5 484.5 456.7

Table 4. Design Results for Sequence 8 and Its Thermally Coupled Schemes in Figure 7

scheme

total duty of the reboilers (106 kcal/h)

total duty of the condensers (106 kcal/h)

annual capital cost (104 $/p.a.)

annual operating cost (104 $/p.a.)

total annual cost (104 $/p.a.)

sequence 8 a (PC) b c d e f g

36.0 29.8 32.7 30.6 32.2 33.6 35.0 33.0

36.8 30.7 33.5 31.5 33.0 34.4 35.8 33.8

81.6 79.1 78.4 77.8 78.2 75.0 78.1 81.3

412.4 374.9 394.3 373.9 388.5 406.2 419.2 380.5

494.0 454.0 472.7 451.7 466.7 481.2 497.3 461.8

Table 5. Introduced Thermal Coupling(s) for Submixture(s) in Schemes of Figure 5 scheme

thermal coupling submixture(s)

a b c d

AB, CDE, DE AB, CDE AB, DE CDE, DE

scheme


e f g

AB CDE DE

Table 6. Introduced Thermal Coupling(s) for Submixture(s) in Schemes of Figure 7 scheme


a b c d

AB, CDE, CD AB, CDE AB, CD CDE, CD

scheme


e f g

AB CDE CD

Figure 5. This partially coupled scheme is also the best one among all of the 14 partially coupled schemes for this example problem.22 For the three thermally coupled schemes with two thermal couplings introduced for its internal submixtures (Figure 5b-d), the best one is the scheme of Figure 5c with submixtures AB and DE as thermal couplings. The other two schemes of parts b and d of Figure 5 have very close total annual costs. All of these three schemes with two thermal couplings are advantageous in comparison to the simple column configuration and worse than the partially coupled scheme. For the three thermally coupled schemes with only one thermal coupling introduced for its internal submixtures (Figure 5e-g), the best one is the scheme of Figure 5g with submixture DE as the thermal coupling. It is interesting to note that for scheme of Figure 5g introducing one thermal coupling for the internal submixture DE can save 5.7% of the total annual cost compared with the simple column configuration of Figure 4a. However, for scheme Figure 5f, by introduction of one thermal coupling for the internal submixture CDE, the total annual cost of this thermally coupled scheme is higher than the simple column configuration. Thus, it is very important to design and synthesize the optimal thermally coupled distillation schemes by available design procedures on the basis of the specific multicomponent mixture to be separated.

The best scheme of Figure 5g with one thermal coupling for subgroup DE is justified based on the following considerations. First, a simple column is used to separate the feed mixture ABCDE as two subgroups of AB and CDE, which is based on the heuristic which favors 50/50 split.26 Then, the second simple column is used to separate the difficult split A/B, which is based on the heuristic which performs difficult separations last.26 Finally, a SR is used to separate subgroup CDE, which corresponds to the fact that there are similar relative volatilities for the two splits of C/D and D/E, while the amount of the middle component D is lower than the light component C and the heavy component E. From Table 4 for sequence 8, a counterintuitive fact is observed that the scheme of Figure 7c, with two thermal couplings introduced for the internal submixtures AB and CD, is better than the partially coupled scheme of Figure 7a, with the three thermal couplings introduced for all of its internal submixtures of AB, CDE, and CD. This is because in Figure 7c, by the two thermal couplings of AB and CD, the system is structured with two SSs. The first, with feed ABCDE, has A, B, and CDE as the top, side, and bottom products, respectively. The second, with feed CDE, has C, D, and E as the top, side, and bottom products, respectively. These two SSs are operated at the decoupled pressures and temperatures because of the reboiler CDE, while for Figure 7a, all of its separation units are coupled together because of the thermal couplings introduced for all of its internal submixtures. This results in two distinct features in Figure 7a compared with the scheme of Figure 7c. First, a much bigger main column is used in the scheme of Figure 7a; this makes the capital cost of the scheme of Figure 7a a little higher than the scheme of Figure 7c. Second, reboiler D in Figure 7a is operated at a higher temperature than reboiler D in Figure 7c because of the completely thermally linked column units in Figure 7a. This makes reboiler D in Figure 7a use a more expensive steam than reboiler D in Figure 7c. Thus, the operating cost of Figure 7a is a little higher than that of Figure 7c. This observation means that the improper introduction of thermal couplings into the simple column configurations not only makes the economic performance worse but also in-

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Table 7. Design Parameters for Flowsheets of Figures 4b and 8a-c for the Example Design Parameters for Flowsheets of Figures 4b and 8a for the Example flowsheet of Figure 4b parameter

column 1

D B Tdi Tbi Pdi Pbi Rm R/Rm Nt Nrt Qci Qri ΣV ΣQc ΣQr

123.82 74.54 77.05 140.09 1.00 2.07 13.87 1.2 138 64 20.40 15.64

column 2 0.00 78.09 88.34 98.24 1.46 1.83 50 50 0.00 12.57 3109.3 29.0 28.2

flowsheet of Figure 8a

column 3

column 4

column 1

170.96 0.00 107.48 117.57 1.50 1.71 2.59 1.2 26 0 6.54 0.00

52.99 0.00 121.75 131.33 1.65 1.85 2.65 1.2 25 0 2.03 0.00

123.82 298.49 77.05 117.57 1.00 1.71 13.87 1.2 90 16 20.40 7.17

column 2 0.00 78.09 88.34 98.24 1.46 1.83 50 50 0.00 12.57 3240.0 30.4 29.7

column 3

column 4

170.96 74.54 95.93 130.46 1.00 1.56 3.10 1.2 70 44 7.72 9.97

52.99 0.00 110.68 121.00 1.16 1.35 3.05 1.2 24 0 2.32 0.00

Design Parameters for Flowsheets of Figure 8b,c for the Example flowsheet of Figure 8b

flowsheet of Figure 8c

parameter

column 1

column 2

column 3

column 4

column 1

column 2

column 3

column 4

D B Tdi Tbi Pdi Pbi Rm R/Rm Nt Nrt Qci Qri ΣV ΣQc ΣQr

201.91 298.49 78.20 107.69 1.00 1.24 2.21 1.2 28 15 6.85 7.03

123.82 78.09 77.05 98.32 1.00 1.84 10.64 1.2 111 49 15.92 15.13 3497.0 32.8 32.1

170.96 74.54 95.94 130.46 1.00 1.56 3.10 1.2 70 44 7.72 9.97

52.99 0.00 110.63 120.95 1.16 1.34 3.05 1.2 24 0 2.32 0.00

123.82 298.49 77.05 117.57 1.00 1.71 13.87 1.2 90 16 20.40 7.17

0.00 78.09 88.34 98.24 1.46 1.83 ----50 50 0.00 12.57 3327.6 31.5 30.6

170.94 74.56 89.54 126.67 0.80 1.38 4.74 1.2 74 21 11.06 6.79

0.00 52.99 97.91 109.60 1.00 1.12 ----16 16 0.00 4.05

creases the difficulties in controllability and operability. Moreover, the scheme of Figure 7f with one thermal coupling for the internal submixture CDE is worse than the conventional simple column configuration of sequence 8. It is understood that for the scheme of Figure 7f a SR is first used to separate the feed ABCDE as three subgroups of AB, CD, and E. Next, two simple columns are used to separate the submixtures of AB and CD, respectively. In the SR, there is the highest amount (45%) of the side product of submixture CD compared with the top product AB (40%) and the bottom product E (15%). From the calculations for schemes of Figures 5e-g and 7e-g, it is concluded that side-column systems can reduce energy consumption very significantly where the amount of middle product is relatively small.2 Thus, it is very important to properly introduce thermal couplings for multicomponent distillation configurations. Based on the calculation results, when considering the tradeoffs between economic performance, controllability, and operability in terms of the different numbers of thermal couplings, for this specific multicomponent mixture, the preferred optimal alternatives are recommended as the schemes of Figure 5a,c,g and 7c. The scheme of Figure 5a was illustrated in Figure 4b, and Figure 8a-c illustrated the flowsheets of the preferred alternatives of Figures 5c,g and 7c, respectively. The detail parameters for these preferred schemes are presented in Table 7. The flowsheet of Figure 4b has the biggest savings on the total annual cost comparedwith the simple column configuration. The four columns are interlinked by the three thermal couplings. This

results in the fact that the pressures of the four columns cannot be independently determined; thus, its design and operability are more difficult. For the flowsheet in Figure 8a, because of the elimination of one thermal coupling in the first column, the system is decoupled into two side-column units, SS and SR, which can be designed separately; this makes it more operable than the scheme of Figure 4b. The same merits exist for the flowsheet of Figure 8c. As for the flowsheet of Figure 8b, the system is decoupled into three independent units: column 1, column 2, and a SR through the eliminations of the two thermal couplings in the first column. This makes it more flexible in terms of design and operability. However, the relative advantages of the dynamic performance of the four schemes can only be justified by a detail analysis according to the works of Knott27 and Jimenez et al.28 Another observation is that the thermally coupled schemes generated from the best simple column configuration of sequence 9 are more advantageous than the corresponding thermally coupled schemes generated from the second best simple column configuration of sequence 8. As we discussed earlier, the best partially coupled scheme was generated from the best simple column sequence.22 Here, from the calculation results in Tables 3 and 4, it is seen that the best thermally coupled scheme with a lower number of thermal coupling(s) than the partially coupled scheme is also generated from the best simple column configuration of sequence 9.


Figure 8. Flowsheets of the preferred alternatives of Figures 5c,g and 7c.

6. Conclusions Thermally coupled distillation flowsheets for multicomponent distillations have advantages on both the energy savings and the capital savings compared with the conventional simple column sequences. However, among the feasible alternatives with similar economic performance, the alternatives with a lower number of thermal couplings have very significant benefits for controllability and operability. In this work, the thermally coupled distillation flowsheets for multicomponent separations are discussed on the basis of the intended individual splits. Then, the generation of the thermally coupled distillation flowsheets with a lower number of thermal couplings than the partially coupled scheme is presented. These two aspects can help engineers to generate a feasible design alternative space through understanding and characterization of the separation problems at hand. A formula is presented to calculate the number of thermally coupled distillation flowsheets with a lower number of thermal couplings than the partially coupled schemes for an n-component mixture. An integrated framework is developed for the parametric design and synthesis of optimal thermally coupled distillation flowsheets for multicomponent separations. This integrated framework is very flexible and can be used to explore and to synthesize the optimal thermally coupled distillation flowsheets for practical multicomponent separation problems. The example has demonstrated its applicability in finding the simple and more energy-efficient thermally coupled schemes for multicomponent distillations. Based on the calculation results, some insights have been obtained which are very helpful to the design and synthesis of optimal thermally coupled distillation schemes for multicomponent separations. For example, there is an observation that a thermally coupled scheme with a lower number of thermal couplings could be more advantageous than the one with thermal couplings introduced for all of its internal submixtures for a specific simple column configuration. This insight could motivate the designers to look for the optimal thermally coupled distillation flowsheets with a lower number of

thermal couplings in terms of both economic performance and dynamic performance for multicomponent distillations. Acknowledgment The financial support from the Academy of Finland is greatly acknowledged. Nomenclature B ) bottom product flow rate, kmol/h Cn ) number of thermally coupled schemes for a simple column sequence D ) column distillate flow rate, kmol/h n ) number of components in a mixture Nt ) total number of theoretical trays Nrt ) tray number of the stripping section Pb ) column bottom pressure, atm Pd ) column top pressure, atm Pn ) number of thermally coupled schemes for an ncomponent mixture Qc ) heat duty of the condenser, 106 kcal/h Qr ) heat duty of the reboiler, 106 kcal/h R ) operating reflux ratio of a column unit Rm ) minimum reflux ratio of a column unit Sn ) number of simple column sequences for an ncomponent mixture Tb ) column bottoms temperature, °C Tbp ) normal boiling temperature of a component Td ) column top temperature, °C V ) vapor flow rate of columns, kmol/h

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Received for review August 28, 2001 Revised manuscript received August 22, 2002 Accepted August 28, 2002 IE0107136

Optimal Design of Distillation Flowsheets with a Lower Number of

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