Synthesis of Heat-Integrated Thermally Coupled Distillation Systems

Aug 12, 2003 - the traditional simple column configurations as well as the systems ... to look for the optimal distillation systems for multicomponent...
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Ind. Eng. Chem. Res. 2003, 42, 4329-4339

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Synthesis of Heat-Integrated Thermally Coupled Distillation Systems for Multicomponent Separations Ben-Guang Rong,* Andrzej Kraslawski, and Ilkka Turunen Department of Chemical Technology, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland

This paper presents the synthesis of heat-integrated thermally coupled distillation systems for multicomponent separations. The synthesized new distillation systems employ the thermal coupling and heat-integration principles simultaneously. As a consequence, they have the potential to significantly reduce both the energy and capital costs to a bigger magnitude than the traditional simple column configurations as well as the systems employing either heat integration or thermal coupling alone. First, a subspace of the possible heat-integrated partially coupled (HIPC) configurations with sharp splits has been identified for a multicomponent distillation. A formula is derived to calculate the number of possible HIPC configurations for any n-component mixture. A simple procedure is given to obtain the practical HIPC configurations for an n-component mixture. Then, the possible thermodynamically equivalent structures of the identified HIPC configurations are presented. The other possible heat-integrated thermally coupled distillation systems involving sloppy splits for an n-component mixture are also discussed. These heat-integrated thermally coupled distillation systems constitute a specific search space to look for the optimal distillation systems for multicomponent separations. 1. Introduction The classical design of a distillation system for a multicomponent separation uses only the simple columns. Each of the simple columns in a multicomponent distillation configuration receives a feed and performs a sharp split between two adjacent components of the feed mixture. Meanwhile, each of the simple columns produces a top product with a condenser and a bottom product with a reboiler. Thus, in any case of the simple column configuration for an n-component mixture, it needs n - 1 simple columns with n - 1 condensers and n - 1 reboilers.1,2 The simple column configurations for multicomponent distillation are simple and easy to design and operate. Because the number of separation sequences increases dramatically when the number of components in the feed mixture increases, a considerable number of works have been conducted on optimal synthesis of simple column configurations for an ncomponent distillation.1-5 The classical designs of simple column configurations for a multicomponent distillation suffer from the highenergy consumption and large capital investment. Therefore, the synthesis and design of economically efficient distillation systems for a multicomponent separation is ever becoming an important research problem in process engineering. Specifically, a large number of works have been done for the synthesis of the optimal heatintegrated simple column configurations since the work by Rathore et al.6 The task for the design of a heatintegrated simple column configuration consists of searching for the possible heat matches among all of the condensers and reboilers of the simple columns. This is usually done by increasing the pressure of a simple column to make its condenser work as a heat source of a reboiler of another column. Thus, in a heat-integrated * To whom correspondence should be addressed. Tel.: +358 5 6216113. Fax: +358 5 6212199. E-mail: [email protected].

simple column configuration, heat supplied to one column can be used by other columns at a different temperature level. In certain cases, the total heat demand of the whole distillation system can be significantly reduced by such heat integrations. Five or more component mixtures are the typical examples in the studies of optimal synthesis of heat-integrated distillation sequences.6-12 It should be indicated that, although it usually gives energy savings in a heat-integrated simple column configuration, its capital cost is very often higher than that of the corresponding traditional simple column configuration. This is because the heat integration in the traditional simple column configuration is for the enhancement of the heat transfer. However, the mass transfer of the system is usually deteriorated because of the decreases of the relative volatilities between the feed components by the pressure increments.12 To substantially reduce both energy and capital costs for a multicomponent distillation, the mass and heat transfers within a distillation system must be simultaneously enhanced. According to Petlyuk et al.,13 the separation inefficiency in the conventional simple configurations for a multicomponent distillation is due to the thermodynamic irreversibility during the mixing of streams at both the feed locations and the ends of the columns. This separation inefficiency can be improved by using thermal couplings within a multicomponent distillation system. Such thermally coupled multicomponent distillation systems have the potential to significantly reduce both energy consumption and capital costs when compared to the conventional simple column configurations. Specifically, a large number of research works have contributed to thermally coupled distillation systems for ternary mixtures, among which the thermally coupled dividing-wall column14,15 has been successfully used in many industrial separations for ter-

10.1021/ie030302k CCC: $25.00 © 2003 American Chemical Society Published on Web 08/12/2003

4330 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003

nary mixtures, where 30-50% savings on both energy and capital costs have been achieved.16,17 In industrial processes, the mixtures to be separated often contain four or more components. Recently, research on the design and synthesis of thermally coupled schemes for four or more component mixtures has received considerable effort. Sargent and Gaminibandara18 presented a Petlyuk-type fully thermally coupled (FC) scheme for a four-component mixture. Kaibel19 and Christiansen et al.20 have introduced distillation columns with vertical partitions for multicomponent separations. Agrawal21 presented some satellite column arrangements of fully coupled schemes for four or more component mixtures. Agrawal22 also illustrated some thermodynamically equivalent FC schemes for a specific known FC configuration for four and five component mixtures. Some specific thermally coupled configurations of four or more component mixtures have been parametrically studied.23-28 The recent studies have shown that the known four or more component thermally coupled schemes are useful in specific cases.20,23 Recently, some new results on the systematic synthesis of thermally coupled column configurations based on the identification of distinct separation sequences for four or more component mixtures have been presented.29-32 It can be said that the available works on the synthesis of thermally coupled distillation configurations for four or more component mixtures have created a large amount of feasible alternatives to look for promising distillation systems for a specific multicomponent distillation. In the previous works, we illustrated that a complete subspace of partially thermally coupled (PC) configurations for any n-component mixture can be exactly mapped from the traditional simple column configurations.29,30 In terms of tradeoff between economics and operability, the PC configurations have several advantages compared to the FC configurations when the number of components in the feed mixture increases (e.g., five or more components).29,30 A systematic case study for a five-component mixture has fully demonstrated the significant advantages of the PC configurations over the traditional simple column configurations for both energy and capital costs.29 In any PC configuration of a multicomponent distillation, there is elimination of n - 2 condensers and/or reboilers, which are associated with submixtures of two or more components in its corresponding traditional simple column configuration; the remaining n condensers and reboilers in the PC configuration are associated with the n pure products. These n heat exchangers need external utilities at the corresponding condensers and reboilers. It is observed that, among all of the PC configurations for a multicomponent distillation, the most volatile component must be captured in a rectifying section with a condenser and the least volatile component must be captured in a stripping section with a reboiler. However, the middle component(s) are flexible to be captured either in a rectifying section with a condenser or in a stripping section with a reboiler. It is known that all of the thermally linked columns are operated at roughly the same nominal pressure in a thermally coupled configuration in order to facilitate the vapor transfers between the columns.33 For ternary mixtures, Linnhoff et al.34 have concluded that the same nominal pressure of the two thermally linked columns would prohibit the heat integration of the columns with the background

process. However, for four or more component mixtures, such a nominal pressure will certainly provide the opportunities for heat integrations between the condensers and reboilers of the middle components within some of the PC configurations. It will produce the heatintegrated partially coupled configurations (HIPC). These HIPC configurations take the advantages of both thermal coupling and heat integration for a multicomponent distillation. Therefore, they have the potential to have bigger savings on both energy and capital costs than either thermally coupled configurations or heatintegrated simple column configurations. It will be illustrated in the next section that, for a four-component mixture, there is only one such HIPC scheme, while for five or more component mixtures, a subspace of the HIPC configurations can be formulated. It will produce a specific search space of the heat-integrated thermally coupled alternatives for the optimal design of distillation systems for multicomponent separations. The main objective of this paper is to systematically synthesize the heat-integrated thermally coupled systems for multicomponent distillations. First, the generation of the heat-integrated thermally coupled configurations (HITCs) with sharp splits for an n-component mixture is presented. A formula is derived to calculate the number of possible HIPC configurations for an n-component mixture. A simple and easy-to-use procedure is presented to obtain the practical HIPC configurations for any n-component mixture. Then, the thermodynamically equivalent structures of the HIPC configurations are formulated. Finally, the other possible HITCs involving sloppy splits for a multicomponent distillation are discussed. 2. Generation of the HIPC Configurations for a Multicomponent Distillation Let us first analyze the PC configurations for a ternary mixture ABC. For ternary separations, there are two simple column sequences called direct sequence (DS) and indirect sequence (IS). The corresponding partially coupled schemes for DS and IS are shown in parts a and b of Figure 1, respectively.30 It is seen that while the most volatile component A and the least volatile component C are produced from the corresponding rectifying section with condenser A and the stripping section with reboiler C in both PC configurations, the middle component B is produced from the rectifying section with condenser B in Figure 1a and the stripping section with reboiler B in Figure 1b. This means that we have the freedom to conduct the separation of the middle component(s) in different ways among the possible configurations for a multicomponent distillation. This observation gives us the inspiration to deal with the middle components for four or more component mixtures that can produce the HITCs. For four or more component mixtures, there are two or more middle components. Thus, one can conduct the lighter middle component(s) (LMC) being captured in stripping sections with reboiler(s) in some columns and the heavier middle component(s) (HMC) captured in rectifying sections with condenser(s) in other columns within a PC configuration. It will create opportunities for heat integrations among the heat exchangers associated with intermediate volatility products. Such an opportunity first appears for a quaternary mixture PC configuration, as shown in Figure 1c.

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Figure 1. (a and b) Partially coupled configurations for ternary mixtures. (c) HIPC for quaternary mixtures.

For a four-component mixture ABCD, there are two middle components, B and C. There are five PC configurations corresponding to the five simple column sequences,29-32 each of them having three column units. In each PC configuration for a four-component mixture ABCD, a rectifying section with condenser A and a stripping section with reboiler D must be used to produce the lightest component product A and the heaviest component product D; the two middle component products B and C can be produced with either two condensers or two reboilers or a condenser and a reboiler, respectively. There is a unique PC configuration in which the LMC B is produced from the stripping section with reboiler B of one column and the HMC C is produced from the rectifying section with a condenser C of another column. Because the thermally linked columns have the same nominal pressure, the temperature of condenser C is certainly higher than that of reboiler B. Thus, reboiler B can be heat integrated with condenser C for further energy savings of the original PC configuration, as shown in Figure 1c. Such a HIPC configuration for a four-component mixture had once been discussed as the analogue of Kaibel’s19 vertical partition column by Christiansen et al.35 A special case of a thermally coupled scheme had also been mentioned by Carlberg and Westerberg33 that was considered as an aggregate of a side stripper and a side enricher. However, research on the systematic synthesis of HIPC configurations for any n-component mixture (e.g., n g 5) is not available in the published literature. For five or more component mixtures, there are three or more middle components. Thus, more opportunities can be created for heat integrations among the heat exchangers associated with intermediate volatility products. The opportunity of heat integration appears if there simultaneously exist LMC(s) reboiler(s) and HMC(s) condenser(s) between different columns within a PC configuration. For five or more component mixtures, there are a certain number of such PC configurations in which the opportunities for heat integration among heat exchangers of intermediate volatility products exist. In the following section, a systematic approach is presented to synthesize these HIPC configurations for any n-component mixture. For an n-component mixture (n g 4), to identify all of its possible HIPC configurations, except the most volatile component and the least volatile component, all of the other components are called middle components. Thus, for an n-component mixture, there are n - 2 middle components. To generate the feasible separation sequences for a multicomponent distillation, it is im-

portant to determine the first split for the feed mixture.31,32 It was seen that there are n - 1 different first splits for an n-component mixture when only sharp splits are considered.32 Among the n - 1 first splits, there is always one that first separates the most volatile component of the feed mixture, which is called the direct first split. Similarly, there is always one that first separates the least volatile component of the feed mixture, which is called the indirect first split. Then, there are n - 3 first splits left, each of them will perform a split between two adjacent middle components, which are defined as the middle first splits. For each of the middle first splits, there will be two subgroups produced: one is associated with the most volatile component and another with the least volatile component. Simultaneously, the middle components of the feed mixture are sharply split into these two subgroups. The middle components involved in the subgroup with the most volatile component are called the LMCs, and those involved in the subgroup with the least volatile component are called the HMCs. It was illustrated that each of the n - 1 first splits will designate a branch for the generation of the feasible separation sequences for a multicomponent distillation.31,32 This means that simultaneously each of the n - 1 first splits will designate a branch for the generation of the feasible partially thermally coupled configurations.29,30 The partially thermally coupled configurations generated from the direct first split will always separate the most volatile component first and are called the direct partially coupled configurations (DPC). Similarly, the partially thermally coupled configurations generated from the indirect first split will always separate the least volatile component first and are called the indirect partially coupled configurations (IPC). The partially thermally coupled configurations generated from the middle first splits will always split the feed mixture between two adjacent middle components first and are called the middle partially coupled configurations (MPC). It is observed that, for each of the MPC configurations, there is always at least one LMC product produced from a reboiler in one column and always at least one HMC product produced from a condenser of another column. The reboiler with a LMC and the condenser with a HMC will provide the opportunity for heat integration between their associated columns because all of the columns in a partially coupled configuration have the same nominal pressure. This means that among those MPC configurations there is always the opportunity for heat integration among the heat exchangers associated with middle component products. Thus, one can con-

4332 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 Table 1. PC Configurations and HIPC Configurations for a Five-Component Mixture first splits

no. of PC schemes

no. of HIPC schemes

A/BCDE AB/CDE ABC/DE ABCD/E

5 2 2 5 total: 14

1 2 2 1 total: 6

clude that each of the MPC configurations will generate a HIPC. There is derived a formula for the calculation of the number of MPC configurations for an n-component mixture, eq 1 (see Appendix). n-3

∑ j)1

Cn )

(

(2j)!

[2(n - j - 2)]!

j!(j + 1)! (n - j - 1)!(n - j - 2)!

)

(1)

where n - 3 designates those n - 3 middle first splits and Cn is the number of HIPC configurations generated from the MPC configurations of the n - 3 middle first splits. The number of DPCs (IPCs) for an n-component mixture is equal to the number of PC configurations for an n - 1 component mixture. Thus, the number of HIPC configurations generated from the DPC (IPC) for an n-component mixture will be equal to the number of HIPC configurations generated for an n - 1 component mixture. Finally, the total number of the HIPC configurations for an n-component mixture can be calculated by the following formula of eq 2: n-3

Pn )

∑ j)1

(

(2j)!

[2(n - j - 2)]!

j!(j + 1)! (n - j - 1)!(n - j - 2)!

)

+ 2Pn-1 (2)

where Pn-1 represents the number of HIPC configurations for an n - 1 component mixture (P3 ) 0) and Pn represents the number of HIPC configurations for an n-component mixture (n g 4). For a five-component mixture, 14 PC configurations and 6 HIPC configurations in total can be generated, as illustrated in Table 1. The corresponding HIPC configurations in Table 1 for a five-component mixture are drawn in Figure 2. In a five-component PC configuration, except the condenser for the product of the most volatile component A and the reboiler for the product of the least volatile component E, there are three heat exchangers associated with three intermediate volatility products of B, C, and D. Thus, heat integration(s) in the corresponding PC configurations are implemented among the three intermediate product heat exchangers. In parts b and f of Figure 2, the heat integration is between the LMC reboiler B and the HMC condenser C of two different columns. In parts a and d of Figure 2, the heat integration is between the LMC reboiler C and the HMC condenser D of two different columns. There are two configurations of parts c and e of Figure 2 where the three intermediate volatility product heat exchangers can be simultaneously heat integrated. They are produced from MPC configurations, as shown in Table 1. In part e of Figure 2, the heat integrations are between two LMC reboilers B and C and one HMC condenser D among three different columns, and in part c, they are between one LMC reboiler B and two HMC condensers C and D among three different columns. It is interesting to note that, after heat integrations, each of the two configurations of parts c and e of Figure 2 has only two

heat exchangers with external utilities: a condenser for the most volatile component A and a reboiler for the least volatile component E. We define them as fully HITCs. These fully HITCs have features similar to those of fully thermally coupled configurations for a multicomponent distillation in which there are only two heat exchangers with external utilities: a condenser for the most volatile component and a reboiler for the least volatile component of the feed mixture. It is also seen that in parts a and f of Figure 2, except the first column unit for the first split of the feed mixture, the other three column units have the same structural features as the HIPC configuration for a four-component mixture, as shown in Figure 1c. We define these HIPC configurations of Figure 2 as the original HIPC configurations because the connections of the column units in the HIPC configurations are similar to the connections of the column units in their corresponding simple column configurations. We will show in the next section that this definition of the original HIPC configuration can distinguish it from other possible thermodynamically equivalent structures. That is the same purpose of the thermodynamically equivalent structures for the functionally distinct thermally coupled configurations for a multicomponent distillation.32 It is seen that an essential feature of these HIPC configurations is that they do not need any changes to the column sections and temperature levels of the original thermally coupled configurations. Moreover, the heat integrations are implemented among the existing heat exchangers in the original thermally coupled configurations. It can be expected that the energy savings of the HIPC configurations will depend on the relative volatilities between the feed components, as well as the compositions of the feed mixture. To have some impression on the additional benefits of the HIPC configurations over the PC configurations, a simple calculation of the HIPC configurations for a five-component mixture is performed. In our previous works,29,30 a five-component mixture in ref 7 has been used to compare the economic performance of the 14 PC configurations with those 14 SC configurations. The PC configuration corresponding to the separation sequence in Figure 2c (i.e., AB/CDE f A/B f C/DE f D/E) has been found to be the best one among the 14 PC configurations.29 It was also found that the simple column configuration corresponding to the separation sequence in Figure 2c (i.e., AB/CDE f A/B f C/DE f D/E) is the best one among the 14 SC configurations.29 The energy information for the heat exchangers in the PC configuration corresponding to Figure 2c is presented in Table 2 (from Table 7 of ref 30). It is seen that the temperature difference between condenser C and reboiler B is ∆TCB ) 9.2 °C and that between condenser D and reboiler B is ∆TDB ) 23.5 °C. Thus, it is practical for the heat integrations between reboiler B and condensers C and D, and heat duties of both condensers C and D can be used by reboiler B in the HIPC configuration of Figure 2c. The comparison of the total energy demand of HIPC of Figure 2c with those of PC and SC configurations is presented in Table 3. It is seen that a reduction of 30% total energy demand has been achieved in the HIPC configuration of Figure 2c compared to the original PC configuration. This means that, for the same five-component separation, a further 30% energy savings has been achieved in the HIPC configuration of Figure 2c compared to the

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Figure 2. Heat-integrated partially coupled systems for five-component mixtures: (a) DS; (b-e) middle sequences; (f) IS. Table 2. Energy Information of Heat Exchangers for the PC Configuration Corresponding to Figure 2c

Table 4. PC and HIPC Configurations for a Six-Component Mixture

heat exchanger

temperature (°C)

heat duty (106 kcal/h)

first splits

no. of PC schemes

no. of HIPC schemes

condenser A reboiler B condenser C condenser D reboiler E

77.05 98.24 107.48 121.75 140.09

20.40 12.57 6.54 2.03 15.64

A/BCDEF AB/CDEF ABC/DEF ABCD/EF ABCDE/F

14 5 4 5 14 total: 42

6 5 4 5 6 total: 26

Table 3. Comparison of the Total Energy Demand of HIPC of Figure 2c with Its PC and SC

scheme

total duty of the reboilers (106 kcal/h)

total duty of the condensers (106 kcal/h)

total energy demand (106 kcal/h)

SC30 PC30 HIPC

34.0 28.2 19.6

34.7 29.0 20.4

68.7 57.2 40.0

optimal PC configuration obtained in previous studies.29,30 Compared to the optimal SC configuration in previous studies for the same five-component separation,29,30 a reduction of 42% total energy demand has been achieved in the HIPC configuration of Figure 2c. Thus, substantial improvement of systems’ economic performance can be obtained by simultaneously employing thermal coupling and heat integration in the HIPC configurations for multicomponent distillations. For six or more component mixtures, there are many more possible combinations among the heat exchangers of middle components to produce the HIPC configurations. Even though it is easy to use the above equation (2) to calculate the number of all of the HIPC configurations for any n-component mixture, it is not straight-

forward to recognize the actual heat integrations among the middle component heat exchangers for all of the HIPC configurations when six or more components appear in the feed mixture. Here, a simple procedure is presented, with which it becomes a much easier task to identify the actual heat integrations for all of the HIPC configurations for a feed mixture with six or more components. Step 1. Identify the first splits for the feed mixture. This will produce n - 1 first splits with sharp splits, one direct first split, one indirect first split, and n - 3 middle first splits. Step 2. For each of the first splits, generate the corresponding PC configurations, like in Table 1 for a five-component mixture. Then, the number of corresponding HIPC configurations is obtained. For example, for a six-component mixture, 26 HIPC configurations in total are obtained, as illustrated in Table 4. Step 3. List all of the separation sequences for the identified HIPC configurations in step 2. For example, 26 separation sequences corresponding to the 26 HIPC configurations for a six-component mixture are presented in Table 5.

4334 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 Table 5. Separation Sequences of the HIPC Configurations for a Six-Component Mixture no.

separation sequence

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

A/BCDEF f B/CDEF f CD/EF f C/D f E/F A/BCDEF f BC/DEF f B/C f DE/F f D/E A/BCDEF f BC/DEF f B/C f D/EF f E/F A/BCDEF f BCD/EF f E/F f B/CD f C/D A/BCDEF f BCD/EF f E/F f BC/D f B/C A/BCDEF f BCDE/F f BC/DE f B/C f D/E AB/CDEF f A/B f C/DEF f D/EF f E/F AB/CDEF f A/B f C/DEF f DE/F f D/E AB/CDEF f A/B f CD/EF f C/D f E/F AB/CDEF f A/B f CDE/F f C/DE f D/E AB/CDEF f A/B f CDE/F f CD/E f C/D ABC/DEF f A/BC f D/EF f B/C f E/F ABC/DEF f A/BC f DE/F f B/C f D/E ABC/DEF f AB/C f DE/F f A/B f D/E ABC/DEF f AB/C f D/EF f A/B f E/F ABCD/EF f E/F f A/BCD f B/CD f C/D ABCD/EF f E/F f A/BCD f BC/D f B/C ABCD/EF f E/F f AB/CD f A/B f C/D ABCD/EF f E/F f ABC/D f A/BC f B/C ABCD/EF f E/F f ABC/D f AB/C f A/B ABCDE/F f A/BCDE f BC/DE f B/C f D/E ABCDE/F f AB/CDE f A/B f CD/E f C/D ABCDE/F f AB/CDE f A/B f C/DE f D/E ABCDE/F f ABC/DE f D/E f A/BC f B/C ABCDE/F f ABC/DE f D/E f AB/C f A/B ABCDE/F f ABCD/E f AB/CD f A/B f C/D

Table 6. Heat Exchangers Information of the HIPC Configurations for a Six-Component Mixturea no.

A

B

C

D

E

F

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond cond

cond cond cond cond cond cond reb reb reb reb reb cond cond reb reb cond cond reb cond reb cond reb reb cond reb reb

cond reb reb cond reb reb cond cond cond cond cond reb reb reb reb cond reb cond reb reb reb cond cond reb reb cond

reb cond cond reb reb cond cond cond reb cond reb cond cond cond cond reb reb reb reb reb cond reb cond cond cond reb

cond reb cond cond cond reb cond reb cond reb reb cond reb reb cond cond cond cond cond cond reb reb reb reb reb reb

reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb reb

a cond ) condenser. reb ) reboiler. The boldface italics stands for heat integrations.

Step 4. For each of the HIPC configurations in step 3, the heat exchangers information of condensers and reboilers about the n heat exchangers for the n products is indicated, and a table of heat exchangers information is formulated about all of the identified HIPC configurations. The heat exchangers information for condensers and reboilers of all 26 HIPC configurations for a sixcomponent mixture is presented in Table 6. Step 5. For each of the HIPC configurations in the heat exchangers information table (e.g., Table 6), identify the LMC(s) reboiler(s) and the HMC(s) condenser(s) and then the practical heat integrations in the HIPC configurations are clear. For example, the bold heat

exchangers in Table 6 are the identified condenser(s) and reboiler(s) for heat integrations in corresponding HIPC configurations for a six-component mixture. Among the 26 HIPC configurations for a six-component mixture, the first six HIPC configurations are produced from the direct first split of A/BCDEF for the feed mixture. As discussed above, this number is equal to the number of HIPC configurations for a fivecomponent mixture. In other words, these six configurations are produced from the subgroup of BCDEF from the first split, where the most volatile component is B and the least volatile component F, and C, D, and E are the middle components. Moreover, except for the first column unit for the first split of the feed mixture, the other four column units in each of the six HIPC configurations have exactly the same structural connections (including heat integrations) as the corresponding configurations in Figure 2 for a five-component mixture, whereby the feed stream in each of the configurations in Figure 2 is replaced with the two-way thermal coupling streams that are connected with the bottom of the first split column. The first split column has the feed mixture ABCDEF and a top condenser A. The same observation can be obtained for the last six HIPC configurations that are produced from the indirect first split of ABCDE/F for the feed mixture. The other 14 HIPC configurations are produced from the MPC configurations corresponding to the middle first splits, as shown in Table 4. There are five HIPC configurations (7, 9, 15, 18, and 20 in Table 6) produced from the MPC configurations for which, after heat integrations, each of them uses only two heat exchangers with external utilities: a condenser for the most volatile component A and a reboiler for the least volatile component F. They have features similar to those of the configurations in parts c and e of Figure 2 for a fivecomponent mixture and are defined as fully HITCs. It is interesting to note that if we implement the corresponding heat integrations among the heat exchangers of middle components inside a column shell with two or more individual splits, some of the HIPC configurations can use less than n - 1 column units for the whole separation task of an n-component distillation. Figure 3 presents three such HIPC configurations (9, 15, and 18 in Table 6), for which each of them uses only three column units for a six-component distillation. Again, the heat integrations in the systems of Figure 3 take advantage of the same column sections and energy resources of the original thermally coupled configurations. The same exercise can be done for four- or fivecomponent HIPC configurations, as illustrated in Figures 1c and 2 to reduce the number of column units in the HIPC systems. For these arrangements of column units, some special considerations can be given to column equipment designs in order to facilitate the heat exchanges at heat-integrated locations in the column shell, as Christiansen et al.35 discussed for Kaibel’s column19 implementation. Christiansen et al.35 also indicated that the start-up and operations for these kinds of column unit arrangements are relatively easy for a quaternary distillation system. 3. Thermodynamically Equivalent Structures of HIPC Configurations It is well-known that a thermally coupled configuration can produce thermodynamically equivalent structures by rearrangements of its column sections among

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Figure 3. Fully HIPC configurations for a six-component mixture.

the column units. Even though the thermodynamically equivalent structures of a thermally coupled configuration have the same nominal total vapor flow rate, there are differences in capital costs among the thermodynamically equivalent structures.28,29 Furthermore, some thermodynamically equivalent structures could be more operable than others with respect to the vapor transfers between the columns.22 In a recent study,36 we observed that there are a certain number of structural degrees of freedom in an original thermally coupled configuration that can produce a certain number of thermodynamically equivalent structures. The number of structural degrees of freedom in an original thermally coupled configuration is equal to the number of thermal couplings introduced into its traditional distillation configuration. The structural degrees of freedom in a thermally coupled configuration are related to those movable column sections designated by the introduced thermal couplings. For a PC configuration with n - 2 thermal couplings introduced, there are n - 2 structural degrees of freedom. These n - 2 structural degrees of freedom will designate n - 2 column sections that are movable among the column units in a PC configuration. The n - 2 movable column sections will produce 2n-2 thermodynamically equivalent structures for any PC configuration of an n-component distillation. It is interesting to note that these n - 2 movable column sections in a PC configuration are also movable in its HIPC configuration. Thus, the same number of thermodynamically equivalent structures can be produced for the HIPC configuration. For example, for a five-component PC configuration corresponding to its HIPC configuration in Figure 2c, there are three thermal couplings introduced corresponding to three submixtures of AB, CDE, and DE. The eliminations of the condenser AB and reboilers CDE and DE of the simple column configuration will make the column sections 3, 6, and 8 of the PC configuration movable among the column units. These three movable column sections of 3, 6, and 8 are also movable in the HIPC configuration of Figure 2c. Thus, eight thermodynamically equivalent structures in total can be generated by movement of the three movable column sections in different ways for a HIPC configuration. The HIPC configuration of Figure 2c has no movement of the movable column sections and was called the original HIPC configuration. The other seven thermodynamically equivalent structures for the HIPC configuration of Figure 2c are drawn in Figure 4.

Parts a-c of Figure 4 are produced by once moving one column section of 3, 6, or 8 of the HIPC configuration of Figure 2c, respectively. Parts d-f of Figure 4 are produced by once moving two column sections of (3, 6), (3, 8), or (6, 8) of the HIPC configuration of Figure 2c, respectively. The scheme of Figure 4g is produced by simultaneously moving all of the three column sections of 3, 6, and 8. Furthermore, for these thermodynamically equivalent structures, the combination of column units such as the systems in Figure 3 can also be implemented to reduce the number of column units of the thermodynamically equivalent systems. It is clear that, for each of the HIPC configurations of an n-component mixture, one can produce 2n-2 thermodynamically equivalent structures. Thus, the total thermodynamically equivalent HIPCs (TEHIPC) for an n-component mixture (Tn) can be calculated by the following formula of eq 3:

[( n-3

Tn )

∑ j)1

(2j)!

[2(n - j - 2)]!

) ]

j!(j + 1)! (n - j - 1)!(n - j - 2)!

+

2Pn-1 × 2n-2 (3) Table 7 illustrates the number of the HIPC configurations as well as the number of TEHIPC configurations in terms of the number of components in the feed mixture. Obviously, the HIPCs, together with their thermodynamically equivalent structures, constitute a specific search space for the optimal design of distillation systems for multicomponent separations. 4. HITCs Involving Sloppy Splits The HITCs for a multicomponent distillation discussed so far are produced from those thermally coupled configurations with only sharp splits. Thermally coupled configurations with only sharp splits have the same separation sequences as the corresponding conventional simple column configurations. Thus, they have the same number of n - 1 column units as the conventional simple column configurations for an n-component distillation. Simultaneously, they have the same number of 2(n - 1) column sections as the conventional simple column configurations, that is, the minimum number of column sections for a multicomponent distillation. It is known that one can generate feasible multicomponent distillation configurations by introducing sloppy splits

4336 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003

Figure 4. Thermodynamically equivalent structures of the HIPC configuration of Figure 2c. Table 7. Number of HITC Schemes Generated from the Simple Column Configurations for an n-Component Mixture no. of components

simple column configurations

original PC configurations

original HIPC configurations

thermodynamically equivalent HIPC configurations

4 5 6 7 8 9 10 11

5 14 42 132 429 1430 4862 16796

5 14 42 132 429 1430 4862 16796

1 6 26 100 365 1302 4606 16284

4 48 416 3 200 23 360 166 656 1 179 136 8 337 408

for the middle components of a multicomponent mixture. Multicomponent distillation column configurations involving sloppy splits will have more than 2(n - 1) column sections. However, through combination of the two-section columns, the thermally coupled configurations involving sloppy splits can have the same number

of column units as those configurations with only sharp splits (e.g., n - 1 column units), where some of the column units have more than two column sections.31,32 This makes them also attractive compared to the conventional simple column configurations on savings of both energy and capital costs.

Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 4337

Figure 5. Feasible HITCs involving sloppy splits for a five-component mixture.

It is seen that the HITCs can also be produced from the thermally coupled configurations involving sloppy splits for an n-component distillation. For an n-component distillation, n(n - 1)/2 first splits in total can be generated for the feed mixture when sharp and sloppy splits are simultaneously considered.31,32 Thus, apart from n - 1 first sharp splits, there are (n - 1)(n - 2)/2 first sloppy splits for the feed mixture. In a previous study, all of the functionally distinct thermally coupled configurations for quaternary mixtures have been synthesized.32 It was observed that the configuration shown in Figure 1c is the only HITC among all of the functionally distinct thermally coupled configurations for quaternary mixtures. However, for five or more component mixtures, we can generate the possible HITCs from each of the (n - 1)(n - 2)/2 first sloppy splits of the feed mixture. For example, for a five-component mixture, there are six first sloppy splits for the feed mixture, i.e., ABCDE, ABCDE, ABCDE, ABCDE, ABCDE, and ABCDE, with the underline designating the distributed middle component(s) of a sloppy split.32 An example HITC for each of the above six first sloppy splits for a five-component mixture is illustrated in parts a-f of Figure 5, respectively. The exercise for implementation of the heat integrations in the corresponding column units in Figure 5 has been done the same way as in the configurations of Figure 3. It is clear that, among all of the possible functionally distinct thermally coupled configurations for an ncomponent distillation, the HITC configurations can

always be generated from those thermally coupled configurations in which there simultaneously exist LMC reboiler(s) and HMC condenser(s) between different columns. Moreover, as long as the HITCs are defined for an n-component distillation, their thermodynamically equivalent structures can be easily generated by identifying the movable column sections in the corresponding original thermally coupled configurations. Synthesis of such HITC configurations involving sloppy splits will depend on the synthesis of all of the functionally distinct thermally coupled configurations for a multicomponent mixture. A method has been presented for the synthesis of all of the functionally distinct thermally coupled configurations for a multicomponent distillation, where all of the functionally distinct separation sequences for a multicomponent distillation are first generated on the basis of identification of all of the distinct sets of intended individual splits for a multicomponent distillation.31,32 5. Conclusions Multicomponent distillation systems employ multiple column units for multiple individual separation tasks. The final performance of a multicomponent distillation system will depend on the optimum synergy of the multiple individual tasks within the distillation system. It is understood that the optimum synergy of the multiple individual tasks within a multicomponent

4338 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003

distillation system is through simultaneous enhancement of both mass and heat transfers. In this paper, such a strategy for simultaneous enhancement of both mass and heat transfers within a multicomponent distillation system is presented by simultaneously employing both thermal coupling and heat-integration principles. The simultaneous employment of thermal coupling and heat integration allows us to design HITC distillation systems for multicomponent separations. The replacement of the heat exchangers associated with submixtures of binary or more components in traditional multicomponent distillation configurations with thermal coupling streams will produce thermally coupled configurations. The same nominal pressure among the column units within the thermally coupled configurations provides the opportunity for heat integrations among the remaining heat exchangers in the thermally coupled configurations. The opportunity of heat integrations appears if there simultaneously exist LMC(s) reboiler(s) and HMC(s) condenser(s) between different columns within a thermally coupled configuration. A significant feature of the HITCs for a multicomponent distillation is that they do not change the temperature levels of the external utilities of the original thermally coupled configurations. Moreover, these HITC configurations have exactly the same column sections as the original thermally coupled configurations. Thus, the new HITC distillation systems have the potential to significantly reduce both the energy and capital costs in comparison to the systems with either heat integration or thermal coupling alone. The synthesis of HITC distillation systems for an n-component separation is presented. A subspace of the possible HIPC configurations with sharp splits has been identified for a multicomponent distillation. A formula is derived to calculate the number of the possible HIPC configurations for any n-component mixture. A simple calculation of the HIPC configurations for a fivecomponent mixture fully demonstrated the advantages in energy savings of the HIPC configurations over the original thermally coupled configurations. These HITCs can produce the thermodynamically equivalent structures by rearrangements of the movable column sections among the column units. Moreover, the other possible HITC distillation systems involving sloppy splits for an n-component mixture are also discussed. These HITC distillation systems, together with the possible thermodynamically equivalent structures, constitute a specific search space to look for the optimal distillation systems for multicomponent separations. Acknowledgment The financial support from the Academy of Finland (Suomen Akatemia) and the National Technology Agency of Finland (TEKES) is gratefully acknowledged. Appendix. Calculation of the Number of HIPC Configurations Generated from the MPCs For an n-component mixture, the components in the mixture are ranked according to their relative volatilities. The first component is the most volatile component, and volatility decreases in successive order; the last component is the least volatile component. The components between the most volatile component and the

least volatile one are called middle components. There are n - 2 middle components for an n-component mixture. There are n - 1 different first splits for an n-component mixture when only sharp splits are considered. The one that first separates the most volatile component of the feed mixture is called the direct first split, and the one that first separates the least volatile component of the feed mixture is called the indirect first split. The remaining n - 3 first splits are called the middle first splits. Each of the n - 3 middle first splits will perform a split between two adjacent middle components. Each of the n - 1 first splits for the feed mixture will produce two subgroups. Let us define the subgroup with the most volatile component as the light subgroup (LS) and another with the least volatile component as the heavy subgroup (HS). Obviously, for the direct (indirect) first split, the number of components in the LS is 1 (n - 1) and the number of components in the HS is n - 1 (1). For a middle first split, the number of components in the LS will depend on which are the two adjacent middle components where the middle first split is performed. According to Thompson and King,1 the number of simple column separation sequences for an m-component mixture (Sm) is calculated as eq A1. For the n - 3

Sm )

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

(A1)

middle first splits of an n-component mixture, let j represent the order of the n - 3 middle first splits, i.e., j ) 1, n - 3. The first middle first split is between the first middle component and the second one. Thus, the number of components of the LS from the number j middle first split is j + 1, and the number of components of the HS from the number j middle first split is n - j - 1. Therefore, the number of separation sequences for the LS of the number j middle first split (Sj+1) can be calculated by eq A2 (j + 1 instead of m in eq A1).

Sj+1 )

(2j)! j!(j + 1)!

(A2)

Similarly, the number of separation sequences for the HS of the number j middle first split (Sn-j-1) can be calculated by eq A3 (n - j - 1 instead of m in eq A1).

Sn-j-1 )

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

(A3)

Therefore, the total number of separation sequences generated from the number j middle first split (MCj) can be calculated by eq A4. Finally, the total number of MPC

MCj ) Sj+1Sn-j-1 )

[2(n - j - 2)]! (2j)! j!(j + 1)! (n - j - 1)!(n - j - 2)! (A4)

configurations for all of the n - 3 middle first splits (j ) 1, n - 3) is calculated by eq A5. This is also the n-3

Cn )

∑ j)1

(

(2j)!

[2(n - j - 2)]!

j!(j + 1)! (n - j - 1)!(n - j - 2)!

)

(A5)

number of HIPC configurations generated from the MPCs.

Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 4339

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Received for review April 7, 2003 Revised manuscript received June 27, 2003 Accepted July 7, 2003 IE030302K