Synthesis of Distillation Column Configurations for a Multicomponent

Ind. Eng. Chem. Res. 1996, 35, 1059-1071

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Synthesis of Distillation Column Configurations for a Multicomponent Separation Rakesh Agrawal Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, Pennsylvania 18195-1501

Thermally linked distillation column configurations to separate near-ideal multicomponent mixtures containing four or more components are discussed. It is shown that for sharp separation of an n-component mixture using only one reboiler and one condenser the minimum number of rectifying and stripping sections needed is 4n - 6. A stepwise procedure is proposed to obtain such distillation configurations, and a series of observations are presented which make the task of generating these configurations a little easier. It is found that, for n g 4, some of these distillation configurations are missing from the known superstructures in the literature. An alternative method is proposed to obtain an n-component superstructure. The resulting superstructure has all the earlier known configurations embedded within it and contains the substructures incorporating the missing configurations. This provides a more complete superstructure for the optimization task. Introduction Separation of a multicomponent feed into separate streams each enriched in one of the constituents of the feed stream is a common distillation problem. Column sequences to separate near-ideal multicomponent mixtures using simple distillation columns are fairly wellknown. Thompson and King (1972) presented an equation to calculate the number of such possible sequences for the separation of an n-component mixture into single-component product streams. When the number of components in the feed stream is greater than 3, the possible arrangements of distillation columns to produce n product streams, each enriched in one of the components, are fairly large. A large number of reboilers and condensers are often associated with these arrangements. Since the capital cost of reboilers and condensers represent significant components of the cost of the overall arrangement, it may be desirable to construct energy-efficient schemes which use fewer reboilers and condensers. One method to reduce the number of reboilers and condensers is to use thermally linked columns (Glinos, 1985). One particular thermally linked arrangement is that of Petlyuk et al. (1965). A noteworthy feature of the Petlyuk column arrangement is that the entire distillation can be performed by using only one reboiler and one condenser, independent of the number of components to be separated. While a number of studies have analyzed the Petlyuk column arrangement for a three-component mixture, only a little information is available for mixtures containing more than three components (Fidkowski and Kro´likowski, 1987; Carlberg and Westerberg, 1989; Triantafyllou and Smith, 1992). In the generalization of the three-component Petlyuk column to four or more components, it has been suggested that the number of sections required for separating an n-component mixture is equal to n(n - 1) (Petlyuk et al., 1965; Sargent and Gaminibandara, 1976). For n g 4, this is considerably more than the 2(n - 1) sections needed in conventional schemes utilizing multiple reboilers and condensers (Freshwater and Henry, 1975). Using a large number of distillation column sections adds considerably to the capital cost of the process. Both the liquid and vapor may have to be redistributed as they enter each column section. Such distributors add not only their own cost but also 0888-5885/96/2635-1059$12.00/0

additional height to the distillation columns, which further increases their cost. The total number of column sections used is also indicative of the amount of computational work required to design the scheme (Hohmann et al., 1982); it may also have an impact on the operability. One major objective of this paper is to find the minimum number of rectifying and stripping sections needed for a sharp separation of an n-component mixture using one reboiler and one condenser. A method is also suggested to draw all such possible schemes. The overall objective of a distillation-based synthesis problem is to find the column arrangement which will provide the best scheme in terms of cost and operability. When the feed contains more than three components, however, the task of synthesizing the optimal distillation column sequence presents a formidable combinatorial problem (Hendry and Hughes, 1972; Rodrigo and Seader, 1975). The number of possible distillation column configurations can become quite large. To make the problem more tractable, strategies based on heuristics and evolutionary methods have been suggested (Seader and Westerberg, 1977). Westerberg (1985) provided a good review of the methods available for the synthesis of distillation-based separation systems. As an alternative to combinatorial techniques, Sargent and Gaminibandra suggested the use of a “superstructure” configuration (1976). This superstructure has a large number of possible configurations embedded in it, and any particular configuration may be obtained by eliminating some column sections, reboilers, condensers, or interconnecting streams from the superstructure. The use of superstructures to find optimum distillation configurations seems to be receiving renewed attention (Hu et al., 1991; Novak et al., 1994). If a superstructure is to be used to find the optimum configuration, it is necessary that virtually all known configurations be substructures of the superstructure. In the later part of this paper, a new superstructure is proposed which contains the superstructure of Sargent and Gaminibandara as a substructure. Distillation Column Configurations Requiring Only One Reboiler and One Condenser In this part of the paper we will consider separation of a mixture containing four or more components into © 1996 American Chemical Society

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Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996

Figure 1. Network representation of five configurations available for the separation of mixture ABCD into pure products.

its constituents. Only mixtures with near-ideal vaporliquid equilibrium relationships are considered. The first objective is to find the minimum number of column sections needed to distill an n-component mixture using only one reboiler and one condenser. A column section is defined to be a portion of a distillation column which is not interrupted by entering or exiting streams or heat flows (Hohmann et al., 1982). After developing a method to determine the minimum number of column sections, a stepwise procedure is proposed to draw all column configurations containing this minimum number of sections. It is known that the separation of an n-component mixture into pure products requires at least n - 1 simple distillation columns (Freshwater and Henry, 1975). Each distillation column has one feed and produces an overhead and a bottom product stream. There is a rectifying and a stripping section in each of these columns. This means that the total number of column sections is 2(n - 1). Generally, this is also the minimum number of sections required to separate an n-component mixture in n pure product streams. One can use one reboiler with each stripping section and one condenser with each rectifying section. This would lead to a total of 2(n - 1) reboilers and condensers. By using thermally linked columns (side stripper or side rectifier), however, the vapor and liquid flows from one section of a column can be shared with another column (rectifying section of a column with the side stripper column and vice versa). This means that the condenser can also provide the condensing duty for the side stripping column, and the reboiler can provide the boiling duty for the side rectifying column. This implies that, for any two sections associated with a component of intermediate volatility, only one reboiler or one condenser would be needed. A condenser will always be needed for the lightest (the most volatile) component and a reboiler for the heaviest component. Therefore, the minimum number of reboilers and condensers needed for a distillation scheme which uses the minimum number of distillation column sections is equal to the number of components in the feed mixture. Let us illustrate the above point for a four-component mixture ABCD (n ) 4). Throughout this paper, components in a mixture are ranked according to their relative volatility; i.e., for feed mixture ABCD, A is the most volatile component and volatility decreases in successive order, with D being the least volatile. Three (n - 1) distillation columns are required to separate ABCD, in five feasible configurations (Thompson and King, 1972; Henley and Seader, 1981). Network representations of all five configurations are shown in Figure 1. In any given network, the feed mixture

Figure 2. Separation of a four-component mixture using six sections according to configuration III: (a) no thermal linking, (b) thermally linked columns.

represents a root node. The root and the intermediate nodes represent distinct separation tasks, and the terminal nodes represent the final desired products. A mixture at an intermediate node is a feasible subgroup from the feed; its presence at a node indicates that it is transferred from a section of a distillation column to another distillation column to be further separated into two subgroups. A line connecting a node with a successive node represents a section of a distillation column. All the configurations in Figure 1 have six (2(n - 1)) lines connecting different nodes, and therefore, in each of these separation configurations, six distillation column sections are needed to achieve the desired separation. For each of these configurations, a schematic with three (n - 1) distillation columns is given by Henley and Seader (1981). If a bottom reboiler and a top condenser is used with each of the distillation columns, then a total of six (2(n - 1)) reboilers and condensers will be needed. As an example, configuration III with six reboilers and condensers is shown in Figure 2a. However, as discussed above, by thermal linking this total number can be reduced to four (n). This can be done for any of the five configurations. Figure 2b shows an example of thermally linked columns for configuration III of Figure 1. Two reboilers and two condensers are used in this case. Once the minimum number of column sections and the associated minimum number of reboilers and condensers have been determined, it is possible to eliminate a reboiler or a condenser associated with a component of intermediate volatility by adding two more distillation sections. This can be done if the reboiler associated with the heaviest component and the condenser associated with the lightest component are both retained to provide boilup and reflux for the system. An example where a condenser is eliminated from configuration III is shown in Figure 3. The section above the feed in the rectifying section of the main column is split into two sections, and a stripping section is added to the side column producing C. The total number of sections in this modified scheme has increased to eight. Similarly, the other intermediate reboiler associated with component B can be eliminated to provide the configuration shown in Figure 4. The scheme in Figure 4 uses ten column sections. It is worth noting that the application of thermal linking and the elimination of intermediate reboilers and condensers to other configurations in Figure 1 also lead to the configuration with ten column sections. While configurations I and II lead to the scheme in Figure 4, each of the configurations IV and

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Figure 3. Separation of a four-component mixture using a column arrangement with eight sections, one condenser, and two reboilers.

Figure 4. Four-component distillation configuration with one reboiler and one condenser, using the minimum number of column sections.

V leads to a different scheme, which is discussed later in this paper. More column sections could, of course, be used to perform the separation, however, the minimum number of column sections needed for a fourcomponent feed mixture with only one reboiler and one condenser is ten. The result can be easily generalized for an n-component feed mixture. As discussed earlier, with 2(n - 1) column sections, the minimum total number of reboilers and condensers needed is n. When the n - 2 reboilers and condensers associated with components of intermediate volatility are removed, the number of additional column sections needed is 2(n - 2). Therefore, the minimum number of column sections needed with one reboiler and one condenser is 2(n - 1) + 2(n - 2) ) 4n - 6. The generalized system proposed by Sargent and Gaminibandra uses n(n - 1) column sections (1976). Their scheme for a four-component mixture using only one reboiler and one condenser is shown in Figure 5a. For n g 4, n(n - 1) is always greater than 4n - 6. For n ) 3, both n(n - 1) and 4n - 6 give six column sections, which is identical to the number used in the Petlyuk column configuration. It is interesting to note that the configuration in Figure 4 cannot be derived from the one in Figure 5a by simple elimination of column sections or stream flows. This point is easily observed by attempting to redraw the configuration of Figure 4 in a sequential column arrangement as shown in Figure 5b. While Figures 4 and 5b are identical, the configuration in Figure 5b is topologically different from the one in Figure 5a so that this configuration cannot be derived from that of Figure 5a. Even though the configuration in Figure 4 cannot be derived from Figure 5a, it is possible to derive other configurations containing ten column sections from Figure 5a. For example, setting the vapor and liquid

Figure 5. (a) Four-component separation scheme proposed by Sargent and Gaminibandara (1976); (b) configuration of Figure 4 redrawn for comparison.

traffic to zero in the section immediately below the withdrawal point of liquid stream BC from the second column to zero (and thereby eliminating this section) gives a column configuration with ten sections. It is clear that, for a given mixture with n g 4, there are multiple column configurations which use 4n - 6 sections and require only one reboiler and one condenser. The issue at hand is how to develop a systematic procedure so all such possible configurations could be drawn a priori. The first step is to calculate the number of nodes (or subgroups including both feed and products) which are used in a network representation to yield configurations with 4n - 6 sections. In order to obtain the minimum number of sections, the minimum number of subgroups should be transferred from one section to another; i.e., for any component of intermediate volatility only one subgroup should be transferred to provide rectification and only one subgroup should be transferred for stripping. This means that, for the n - 2 components of intermediate volatility, the number of required subgroups is 2(n - 2). The lightest (most volatile) and the heaviest (least volatile) components do not need additional subgroups as each of them shares a subgroup with its neighboring component. The condenser provides reflux for the most volatile component and the reboiler provides boilup for the least volatile component. Thus, the number of intermediate subgroups or nodes used in such a configuration is 2(n - 2). When the feed and the product components are also counted as subgroups, the total number of subgroups is 3n - 3. Any

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Figure 6. Generalization of the four-component configuration of Figure 4 to five- and six-component mixtures.

configuration with one reboiler, one condenser, and 4n - 6 sections will always use a total of 3n - 3 subgroups. The next step is to generalize the four-component scheme of Figure 4 for n > 4. Figure 6 shows network representations for five- and six-component mixtures. In this generalization, n-component mixtures are first separated into two mixtures, each with n - 1 components. The lightest and the heaviest components are separated from each other. In the subsequent steps of separation, the lighter mixture along the upper main branch produces sharp splits, with the heaviest component of the corresponding subgroup produced directly at each step. Similarly, the heavier mixture along the lower main branch produces sharp splits, with the lightest component of the corresponding subgroup produced directly at each step. Only two binary mixtures are transferred from one section to another. One of the binary mixtures is composed of the two most volatile components, and the other binary consists of the two least volatile components. As a matter of fact, the upper main branch consists of all feasible subgroups containing the most volatile component A and the lower main branch consists of all feasible subgroups containing the least volatile component. Subgroups composed of only the components of intermediate volatility are not transferred from one section to another (or from one column to another column). Notice that the total number of subgroups used is 3n - 3. In order to draw other configurations, subgroups containing only the components of intermediate volatility need to be generated at internal nodes which are not on the upper and lower main branches. The subgroups at these internal nodes can be readily identified. For example, in Figure 6a the subgroups at the internal nodes are found by inspection to be BCD, BC, and CD. All the feasible subgroups can be easily rank listed for any feed mixture (Rathore et al., 1974). The total number of different subgroups, including the feed, is given by n(n + 1)/2 (Henley and Seader, 1981). Therefore, the total number of subgroups containing only the components of intermediate volatilities is given by (n - 2)(n - 3)/2. The largest such internal subgroup

contains n - 2 components. The number of such internal subgroups containing n - l - 1 components is l, where l varies from 1 to n - 3. Once the subgroups at the internal nodes have been identified, other configurations with 4n - 6 sections can be drawn in a systematic manner. This is first illustrated for a five-component mixture. A convenient way is to start with the configuration shown in Figure 6a. A desired subgroup is inserted at the appropriate internal node, and then the final configuration is created by generating other necessary internal subgroups and eliminating some of the subgroups from each of the main branches. For example, let us start by using internal subgroup BCD. Now one of the four-component subgroups from either the upper or the lower main branch will have to be eliminated (Figure 7a-f). This is required to keep the total number of subgroups at 3n 3. In Figure 7a-c, BCD is generated from ABCD and subgroup BCDE is eliminated, while in Figure 7df, BCD is generated from BCDE and ABCD is eliminated. Internal subgroup BCD can be further separated into individual components through three possible schemes: (1) BCD to B and CD followed by CD to C and D (parts a and d of Figure 7); (2) BCD to BC and D followed by BC to B and C (parts b and e of Figure 7); (3) BCD to BC and CD followed by each binary to product components (parts c and f of Figure 7). After BCD has been separated by any of these schemes, the missing rectifying or stripping sections for components B-D are provided by the appropriate subgroups on the lower or upper main branches. Thus, in Figure 7a, B is connected to AB, C to ABC, and D to DE. All other subgroups, such as BCDE and CDE which do not serve any purpose, are eliminated. Similarly, the configurations in Figure 7b-f are drawn with 4n - 6 sections. This completes all possibilities using subgroup BCD. For a five-component mixture, the next internal subgroup to be tried is BC. This subgroup can be created from either ABC or BCDE. Figure 7g gives the configuration for creating BC from ABC. If BC were to be created from BCDE, more than fourteen sections would be required, so this configuration is discarded. Notice that BC need not be created again from BCD, since all configurations with BCD have already been accounted for. Similarly, Figure 7h shows the configuration when internal subgroup CD is used. Finally, parts i-k of Figure 7 give configurations when both internal binary mixtures BC and CD are used. In Figure 7i, BC is still created from ABC and CD from CDE. It is interesting to observe that when both BC and CD are used, it is possible to generate both from either the lower main branch (Figure 7j) or the upper main branch (Figure 7k). Together with Figure 6a, this gives a total of twelve for a five-component mixture. A similar exercise for a four-component mixture yields two additional configurations in addition to the one shown in Figure 4 (see inset figures of the later Figure 13). The procedure just outlined for a five-component mixture can be easily generalized for an n-component mixture. A configuration similar to the one shown in Figure 6 is easily drawn where, in the first step of separation, the feed is separated into two subgroups each containing n - 1 components. Besides providing the first configuration with 4n - 6 sections, this helps in the identification of all the (n - 2)(n - 3)/2 internal subgroups. These internal subgroups can also be found


Figure 7. Five-component configurations containing fourteen sections.

from the network representation of Sargent and Gaminibandra’s scheme (Hu et al., 1991). In order to generate configurations with internal subgroups, it is suitable to start with the internal (n - 2)-component subgroup. Then pick one of the (n - 1)-component subgroups on either the upper or the lower main branch. Configurations corresponding to each of the possible sequences of the internal (n - 2)-component subgroups producing pure products are thus generated. For a j-component subgroup the total number of sequences Rj producing pure products is given by (Appendix 1): j-1 j-1

Rj )

∑ ∑Rj-kRi

(1)

k)1i)k

The above equation is used with R1 and R2 each equal to 1. In the final step for each of the configurations, the missing rectifying or stripping duty for any of the product streams is provided by a subgroup from the lower or the upper main branch. Any of the resulting schemes with more than 4n - 6 sections or more than 3n - 3 total subgroups are discarded. The same procedure is then repeated with the (n - 1)-component subgroup on the other main branch. This will complete all the possible configurations using an internal (n 2)-component subgroup. This procedure may then be repeated to draw configurations with the missing internal (n - 3)-component subgroups. There are two internal (n - 3)-component subgroups. First the configurations are drawn using each internal (n - 3)component subgroup alone, and then both are used together. While generating these configurations, the internal (n - 2)-component subgroup is not to be used. The procedure is repeated with the next internal subgroup containing n - 4 components and so on. The number of internal subgroups containing n - l - 1 components is l. The configurations corresponding to each internal subgroup alone and all its possible combinations with other internal subgroups of the same size should be drawn. The total number of such combina-

l l tions is given by ∑i)1 Ci where:

l

Ci )

l! i!(l - i)!

(2)

While drawing configurations for all the internal (n - l - 1)-component subgroups, other internal subgroups with larger numbers of components are not to be used. The above procedure is repeated until configurations corresponding to internal binary mixtures (l ) n - 3) are generated. This stepwise procedure will ensure that all configurations with 4n - 6 sections are generated. The above procedure is quite tedious; however, from an exercise of generating these configurations for higher values of n, some trends can be observed and generalized. The following nine such generalized observations can make the task of generating schemes with 4n - 6 sections, one reboiler, and one condenser a little easier: 1. There is always one binary mixture on each of the upper and the lower main branches. 2. Any subgroup containing more than three components should not be sharp-split into two subgroups each containing two or more components. This would require the use of an additional reboiler or condenser. 3. With the exceptions of the feed and product streams, each subgroup has three line segments associated with it: One line segment corresponds to the creation of the subgroup, and the other two line segments represent the subgroups or products it splits into (corresponding to a rectifying and a stripping section). If a subgroup has four lines associated with it, then more than 4n - 6 sections must be used. 4. In a given configuration, all feasible subgroups containing n - j components cannot exist together for the values of j such that n - 2 < j < 1. Otherwise, it ensures that at a given depth of separation the components are present in more than two subgroups, leading to extra sections for separations. A depth of separation is defined by Hu et al. (1991). The feed node has depth of 1. For an n-component feed, at jth depth all subgroups have n - j + 1 components. For example, in

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Figure 6a, nodes at a depth of 3 include all feasible ternary mixtures: ABC, BCD, and CDE. A corollary of this observation is that, for any depth of separation, the feasible subgroups are chosen such that a component cannot be present in more than two subgroups. 5. Whenever any j-component subgroup in a configuration is separated such that each of the two separated subgroups have j - 1 components and, therefore, j - 2 components are common between these two separated subgroups, it is required that each subgroup immediately start producing the corresponding j - 2 components directly by sharp splits. The more volatile (j 1)-component subgroup should produce components by sharp split starting from the heaviest component in the subgroup. Similarly, the heavier (j - 1)-component subgroup should produce components by sharp split starting with the most volatile component in this subgroup. This observation is a generalization of the method used to generate the configurations of Figure 6, where it was applied to the feed subgroup. 6. The desired 4n - 6 sections are always obtained when a mixture with more than two components is separated along a separation sequence such that each subgroup is separated into two streams, with only one component being common to the two separated streams. In this sequence, a component of intermediate volatility is chosen, and all components lighter than this component are distilled into the light distillate and all components heavier than the chosen component are distilled into the heavy distillate. The chosen component divides itself between the distillate streams. For a five-component mixture, examples of the configurations which can be drawn according to this method are given in parts c, f, i, j, and k of Figure 7. It is apparent from these examples that this method when applied to every mixture which is generated along the separation sequence leads to the generation of all feasible binary mixtures. These binary mixtures are fed to a distillation column to produce the individual components of the feed mixture. All of these configurations can be easily derived by eliminating certain sections from the generalized scheme proposed by Sargent and Gaminibandra (1976). 7. Whenever a mixture is separated into two streams, such that more than one component is distributed between the two streams (but the lightest component is separated from the heaviest), then depending on the number of common components between the two streams, some final components must be produced directly by sharp splits in the next few steps in order to achieve the minimum number of sections (4n - 6). While the “next few steps” need not be the immediate next few steps for both of the separated subgroups (see observation no. 8), for simplicity consider the case when these sharp splits are done in the steps which do follow immediately. If m is the number of components which are common between the two streams, then in the next m - 1 steps of separation, the lighter mixture of the separation produces sharp splits, with the heaviest component produced in each successive step. Similarly, the heavier mixture produces sharp splits for the next m - 1 steps, with one lightest component produced in each step. If after these m - 1 steps the leftover mixtures have more than two components, then the final products can be obtained from them by following a suitable sequence of separation. For a five-component mixture, parts a, e, g, and h of Figure 7 give examples of configurations where the method discussed in obser-

vation no. 6 is used in conjunction with observation no. 7 for the case of multiple component overlap between the two separated subgroups. If only the methods suggested by observation no. 7 with immediate sharp splits and observation no. 6 are used either alone or in conjunction to generate the total sequence, then a recursive formula for the total number of such possible configurations Sn for an n-component mixture can be easily derived (Appendix 2): n-1 j-1

Sn )

∑ ∑ Sj-(m-1)Sn+1-j j)2 m)1

(3)

The above equation is only valid for n g 3 and should be used with S2 ) 1. For n ) 3, it gives S3 ) 1, which is the well-known Petlyuk configuration. As expected, the possible number of configurations increases rapidly with the increase in the number of components in the mixture; some other values are S4 ) 3, S5 ) 10, S6 ) 36, and S7 ) 137. For a five-component mixture, all the configurations in Figures 6a and 7 except for the ones in parts b and d of Figure 7 can be drawn by using this suggested method. This recursive formula gives a feel for the large number of configurations which exist using 4n - 6 sections, but it is not inclusive of all possible configurations. The following observation provides more explanation. 8. For a five-component mixture, the recursive formula given in observation no. 7 does not include configurations in parts b and d of Figure 7 because the required sharp splits from the subgroup ABCD in Figure 7b and from the subgroup BCDE in Figure 7d are delayed and instead subgroup BCD is generated which subsequently provides the required sharp split. This leads to an addendum to observation no. 7: when a feed or a subgroup is separated into two unequal size subgroups, such that more than one component is common between these subgroups, then the smaller size subgroup must immediately produce the required products by sharp splits. For the larger subgroup, however, it is possible to delay the formation of products by sharp splits for the next few steps, until the size of this subgroup is reduced to that of the original smaller size subgroup. Consider a case where a subgroup is separated into an i-component subgroup and another (i + j)-component subgroup, with m components being common between the two subgroups. The i-component subgroup should produce the required component product streams by sharp splits in the immediate next m 1 steps. The sharp split step for the (i + j)-component subgroup can be delayed until an i-component subgroup containing the desired component to be produced by sharp split is created. At the maximum, this sharp split step can be delayed for j steps. In this case, after j steps the size of the subgroup will be equal to i. Similarly the next sharp split step can be delayed until an (i 1)-component subgroup containing the required component to be sharp split is created. This means that the maximum number of steps for which this sharp split can be delayed is j + 1. This is continued until all m 1 sharp splits are completed within the maximum of j + m - 1 steps. Note that, of the two i-component and (i + j)-component subgroups, the more volatile one has to produce the heavier components by sharp split and the heavier subgroup has to produce the lighter components. Configurations in parts b and d of Figure 7 can be easily derived from this observation. Figure 8 gives four more examples using this observation. In


Figure 8. Some examples of configurations for six- and seven-component mixtures using 4n - 6 sections.

Figure 8a, while DEF produces D directly, the sharp split to E from ABCDE is delayed for two steps until CDE is formed. In Figure 8b, sharp split to E does not immediately follow the sharp split to F and subgroup CDE is created first. 9. If the separation sequence required by a step conflicts with the requirements of earlier steps, then that step must be eliminated. For example, consider the configurations shown in parts c and d of Figure 8. Feed ABCDEF is separated into two subgroups ABCDE and DEF with two components common between these subgroups. According to observation no. 8, component E must be produced by sharp split, and the smallest subgroup from which it can be produced is CDE. ABCDE is further separated into ABC and BCDE; this again requires that B be produced by sharp split, and the smallest subgroup from which it can be produced is BCD. However, the formation of both B and E cannot be delayed because, when BCDE is separated into BCD and CDE, observation no. 4 is violated, as all ternary groups would coexist. Furthermore, from observation no. 5 it follows that BCD should immediately produce D by sharp split and CDE should do the same for C; which contrasts with the earlier need to produce B first from BCD and E first from CDE. Therefore, for this case, the only manner in which BCDE can be further split is according to configurations shown in parts c and d of Figure 8. This completes a rather long discussion on the method and the observations which provide some guidance for drawing n-component configurations containing 4n 6 sections with one reboiler and one condenser. An Example. At this point it may be worthwhile to find if the new sequences (such as the one shown in Figure 4) are of any value and how they compare with the alternate configurations already available in the literature (such as the one in Figure 5a). This will be illustrated with respect to an example from the cryogenic distillation of air. The primary constituents of air are nitrogen, argon, and oxygen, with nitrogen being the most volatile and

oxygen the least. A standard-grade oxygen produced by a conventional process has about 99.5% oxygen and 0.5% argon; and a standard-grade nitrogen contains about 1-10 ppm oxygen and 0.1-0.5% argon. However, air has several trace components which are present in part per million by volume (ppm) range. Some of these show up in the ppm concentration range as contaminants in the standard-grade products. While the standard-grade products have historically been suitable for a large range of applications, they are definitely not suitable for the fast-growing electronic industry. The acceptable level of heavy impurities in ultrahigh purity (UHP) oxygen is less than 10 parts per billion by volume (ppb), and similarly the light impurities in electronicgrade nitrogen may need to be less than 10 ppb. It is clear that the conventional process for air separation is not suited for the production of electronic-grade oxygen and nitrogen; additional processing is required. For the purpose of this paper, air may be treated as a fivecomponent mixture. A detailed listing of air’s components can be found in Isalski (1989). Methane, which is the lightest of all the trace components heavier than oxygen, is taken as the representative of the heavy components. Similarly, neon, which is the heaviest of all the trace components lighter than nitrogen, is taken to represent all the lights. Thus, all computer simulations were done as if feed air were composed of neon (18.2 ppm), nitrogen (78.12%), argon (0.93%), oxygen (20.95%), and methane (2 ppm). Before discussing how the configuration in Figure 4 can be used to separate this mixture, it is desirable to have a brief description of the conventional air separation process for producing standard-grade products. Separation of air to produce standard-grade oxygen by cryogenic methods is a well-established industrial process (Latimer, 1967; Agrawal and Yee, 1994). A conventional double column process to produce standardgrade oxygen of about 99.5% purity is shown in Figure 9. In this process, feed air is compressed to about 6 atm and is passed through a bed of 13X molecular sieves. Contaminants such as water, carbon dioxide unsatur-

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Figure 9. Conventional process for oxygen and nitrogen production.

ated hydrocarbons-acetylene, ethylene, propylene, and C4 and heavier hydrocarbons are totally adsorbed on the molecular sieves. Even though some ethane and propane are retained by the molecular sieve bed, most of these and virtually all of the methane flow with the feed air to the cryogenic process. Light contaminants helium, hydrogen, and neon are also not adsorbed on the molecular sieves. This purified air is cooled in a main heat exchanger against the returning cold product nitrogen and oxygen streams. Nitrogen and oxygen are separated by distillation of the cold air in a two-stage distillation process. In the high-pressure (HP) column, which operates at about 6 atm, the air is separated into a nitrogen vapor stream and an oxygen-enriched liquid stream. This oxygen-enriched liquid stream, often called crude LOX, is fed to the low-pressure (LP) column. The LP column, which operates close to ambient pressure, produces standard-grade oxygen and nitrogen streams. Liquid nitrogen reflux for both columns is generated at the top of the HP column. Some of the nitrogen vapor at the top of the HP column is condensed against boiling liquid oxygen at the bottom of the LP column by heat exchange between the two streams in a reboiler/condenser. The pressure difference between the two columns ensures a proper temperature difference between the condensing and boiling fluids. A portion of the nitrogen vapor from the top of the HP column is warmed and expanded in a turbo-expander to provide the needed refrigeration for the plant. All the trace components in the feed air to the HP column which are much more volatile than oxygen, such as helium, hydrogen, and neon, leave in the nitrogen stream, while all the other trace components such as methane, ethane, propane, krypton, xenon, and nitrous oxide which are less volatile than oxygen concentrate in the oxygen product. Notice that no argon column is shown in Figure 9, and therefore argon distributes itself between the nitrogen and oxygen product streams. The objective chosen for the current example is to be able to produce a fraction of the total oxygen as UHP oxygen and a fraction of the total nitrogen as lightsfree nitrogen without adding additional reboiler/condensers to the conventional process shown in Figure 9. For this purpose, it is appropriate to consider the LP column as the main column and crude LOX as the main feed containing almost all the components of the feed air. There is no condenser at the top of the main (LP) column, but in its place a condensed nitrogen stream is fed as reflux from the HP column. This reflux stream contains a large fraction of the light trace components present in the air. Consequently, the low-pressure gaseous nitrogen stream leaving the top of the LP column will also contain these trace lights. The objective is to coproduce a fraction of the total nitrogen which

is free of lighter impurities and to coproduce a fraction of the total oxygen product as UHP oxygen. Even though, as discussed earlier, air could be treated as a five-component mixture for this problem, calculations were done using the four-component schemes of Figures 4 and 5a. In these examples the four streams A-D are defined as follows: A is a nitrogen stream containing all the light impurities, B is the lights-free nitrogen, C is the UHP oxygen, and D is the heaviescontaminated liquid oxygen stream. Also, a standard gaseous oxygen stream with a composition similar to that of D is coproduced. A major fraction of the argon in the air feed is an acceptable component of the nitrogen product streams, A and B. A five-component configuration would use a distillation column to produce argon, however, for simplicity only the results from the simulation of the four-component configurations are presented here. The modified cryogenic distillation scheme based on the configuration of Figure 4 together with some calculated results is shown in Figure 10. The air feed contained 18.2 ppm neon and 2 ppm methane. When comparing this figure with Figure 4, notice that a crude LOX stream from the HP column forms the feed ABCD to the main or LP column. The lights-free nitrogen stream 25 is equivalent to stream B produced from one of the satellite columns, and the UHP oxygen stream 17 is equivalent to stream C produced from the other satellite column. The liquid oxygen purge stream 11 from the bottom of the LP column is equivalent to stream D. Notice that no stages of separation are used below the withdrawal of stream 12 from the LP column. This is done to ensure that the concentration of hydrocarbons in the liquid oxygen at the bottom of the LP column is not further increased. A liquid stream 11 containing all the hydrocarbons in the feed air is withdrawn as shown. However, a standard gaseous oxygen stream 9 is withdrawn from a tray location which is intermediate between withdrawal stream 23 and 12 for the two satellite columns. This is done to decrease the concentration of argon in stream 12 to extremely low levels while also decreasing the number of trays in this section of the LP column. Also notice that, unlike Figure 4, no tray section at the top of the LP column is used to increase the concentration of lights in the nitrogen. Instead the nitrogen streams from the top of the LP column and from the satellite column producing lights-free nitrogen are combined to yield a nitrogen stream which is contaminated with light impurities. The liquid nitrogen reflux stream 107 from the HP column is split into two streams and fed to the top of each of these columns. The process of Figure 10 does not use extra boilup as compared to the process of Figure 9. Yet, a large fraction of the total oxygen is produced in ultrahigh purity. The total oxygen recovery of the process is 19.39 mol/100 mol of air feed, and of this amount 12.5 mol is produced as UHP oxygen containing heavier impurities less than 10 ppb and argon less than 1 ppm. The standard-grade oxygen in stream 9 comprises 6.83 mol of 99.5% oxygen, with the rest being primarily argon. The lights-free nitrogen (stream 25) produced is 16.3 mol/100 mol of air feed, and it contains less than 1 ppb of the light impurities. However, the concentration of oxygen in the lights-free nitrogen is relatively high. There are several known solutions to this problem, and they will not be discussed here (Agrawal and Yee, 1994).


Figure 10. Modified cryogenic air distillation process according to Figure 4 to coproduce UHP oxygen and lights-free nitrogen.

Figure 11. Modified cryogenic air distillation process according to Figure 5 to coproduce UHP oxygen and lights-free nitrogen. The figure in the inset shows a redrawn configuration of Figure 5.

Such large recoveries of UHP oxygen and lights-free nitrogen are remarkable. Calculations were also done for a scheme derived from that of Sargent and Gaminibandra shown in Figure 5a. The modified distillation configuration along with some calculated results is shown in Figure 11. The distillation column configuration of Figure 5a is redrawn in the inset of Figure 11 to help one understand its adaptation to the conventional double column air distillation configuration. For convenience, the HP column is not shown in Figure 11. The total numbers of stages of separation used in the simulations of the LP columns depicted in Figures 10 and 11 are the same. However, the total number of separation stages used in the other two columns in Figure 11 is 125, which slightly exceeds the total of 115 used in Figure 10. As described earlier, the total number of sections used for the three distillation columns of the process of Figure 11 is two more than

that of Figure 10 (11 vs 9). This implies some extra cost for the additional redistribution of liquid and vapor streams. While both the flowsheets produced the same 12.5 mol of UHP oxygen/100 mol of air feed, the total oxygen recovery for the process of Figure 11 is slightly lower (19.10 vs 19.39). Furthermore, this process produces less lights-free nitrogen product (14.8 mol vs 16.3 mol/100 mol of air feed). Since both the flowsheets were not highly optimized, the differences in the product recoveries may not be very significant. Furthermore, the example is not a perfect one in that all the constituents of the mixture are not produced as pure products and other minor differences exist between the flowsheets of Figures 10 and 11 and Figures 4 and 5a. This comparison does illustrate, however, that new distillation configurations such as the one shown in Figure 4 can be useful and should be included in a search for an optimized multicomponent distillation scheme.

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Figure 13. Four-component superstructure with one reboiler and one condenser.

upper main branch and also with the mixture CDE on the lower main branch. Therefore, from observation no. 5 or 7, mixture BCD undergoes a sharp split to produce either B directly (assuming BCD is created from ABCD) as in Figure 12b or D directly (assuming BCD is created from BCDE) as in Figure 12c. In both these configurations, the number of column sections increased to 18 from the minimum of 14. This shows that it is possible to draw distillation column configurations with one reboiler and one condenser containing sections greater than the minimum number of 4n - 6 and up to n(n - 1). An Alternate Superstructure

Figure 12. Five-component distillation configurations using more than the minimum of 14 column sections: (a) 20 column sections (Hu et al., 1991); (b and c) 18 column sections.

Some Other Schemes with One Reboiler and One Condenser It is interesting to further pursue the discussion of performing an n-component separation with one reboiler and one condenser but without restricting acceptable solutions to be those with the minimum number of column sections. Distillation column configurations using n(n - 1) column sections are known (Sargent and Gaminibandra, 1976). An example for a five-component distillation configuration is given in Figure 12a. Notice that all possible binary mixtures are transferred from one column section to another. All the splits in the separation steps prior to the creation of binary mixtures are non-sharp splits. This configuration uses 20 column sections, which is greater than the minimum number of 14. For n > 3, distillation column configurations easily can be drawn with less than n(n - 1) but more than 4n - 6 column sections. Such configurations are drawn by violating observation nos. 7 and 8 and performing a non-sharp split when a sharp split is needed. Two example configurations for a five-component mixture are given in Figure 12b-c. In both of these configurations, observation no. 5 or 7 for the minimum number of column sections requires that mixtures ABCD and BCDE be further separated by sharp splits. Instead, a non-sharp separation is done to create an intermediate mixture BCD. This intermediate mixture has two common components, with the mixture ABC on the

It is clear from the proceeding discussion that, for n > 3, the possible number of distillation configurations is quite large. For a process engineer, the task of finding the most optimum configuration from all the available configurations can be quite tedious. A superstructure containing all possible configurations can facilitate the optimization task. In this section, a superstructure for distillation column configurations using one reboiler and one condenser is derived first. This is then followed by a generalized superstructure with multiple reboilers and condensers. A superstructure can be easily drawn from the inspection of earlier figures. For example, a comparison of Figure 4 with Figure 5a shows that in Figure 4 an intermediate mixture BC is not transferred between any two columns. However, this intermediate mixture is potentially present in both satellite columns and can be transferred from one column to another. This transfer is shown in Figure 13. Vapor and/or liquid streams, predominantly composed of B and C, are transferred from (to) the stripping section of the satellite column producing component C to (from) the rectifying section of the satellite column producing component B. This “communication” between the satellite columns provides the basis for a four-component superstructure with only one reboiler and one condenser. Not only the configurations of Figures 4 and 5a are embedded in the configuration of Figure 13 but also there are several other configurations. For example, the other two fourcomponent configurations with 10 four-component sections are drawn in the inset of Figure 13. Configuration a in the inset results from the superstructure configuration of Figure 13 when the vapor and liquid flows in the bottommost section of the satellite column producing component B are zero. In this case, this bottommost section and its associate lines transferring mixture BCD


Figure 14. Separation configuration of Figure 6a redrawn with distillation columns.

Figure 15. Five-component superstructure with one reboiler and one condenser.

are eliminated. Similarly, configuration b in the inset is derived by eliminating the topmost section and its associated transfer streams of mixture ABC from the satellite column producing component C. (Note that configuration a also results when the earlier discussed exercise of thermal linking and the elimination of intermediate reboilers and condensers is applied to configuration IV of Figure 1 and similarly configuration b results from configuration V.) By following the procedure for the four-component superstructure, one can draw a five-component superstructure with one reboiler and one condenser. For this purpose, one starts with the configuration shown in Figure 6a. This configuration is obtained by having n - 2 components common between the first two separated streams ABCD and BCDE and using observation no. 5 thereafter. This configuration is shown in Figure 14. Notice that each satellite column produces a component of intermediate volatility. These satellite columns communicate with only the main column and do not have any communication with each other. In order to create this communication, missing subgroups composed of only the components of intermediate volatility are identified. Of the total possible n(n + 1)/2 subgroups, 3(n - 1) are already in use. This means three subgroups are missing. Although there are other methods available to identify these missing subgroups, they can be readily identified by comparing the network of Figure 6a with that of Figure 12a. The missing subgroups are BCD, BC, and CD. Each of these subgroups can be found in the rectifying section of one satellite column and in the stripping section of another column. For example, in Figure 12a subgroups BCD and BC exist on the line segment joining BCDE and B; therefore, these subgroups can be found in the rectifying section of the B-producing satellite column. Similarly, subgroups BCD and CD exist on the line segment joining ABCD and D and can be found in the stripping section of the D-producing satellite column. Once the two corresponding locations for a subgroup such as BCD are known, communication between these two locations can easily be created. A vapor and a liquid stream, primarily composed of BCD, can flow either in the same or opposite direction from one of the two satellite columns to another satellite column. Communication for other subgroups is similarly created. The resulting five-component superstructure with one reboiler and one condenser is shown in Figure 15. Procedures for the four- and five-component superstructures, shown in Figures 13 and 15, can easily be generalized for any n greater than 3. The first step is

to draw a network representation of a configuration according to observation no. 5 with n - 2 components common between the initially separated two streams from the feed. This configuration is redrawn with distillation columns and is found to consist of a main column communicating with the satellite columns. The satellite columns produce components of intermediate volatility. At this stage there is no communication between the satellite columns. This communication is created by identifying the missing [n(n + 1)/2 - 3(n 1)] subgroups from this configuration. The missing subgroups and their locations in the satellite columns are identified by drawing the network representation of the configuration containing all feasible subgroups as proposed by Sargent and Gaminibandara (1976) and Hu et al. (1991). Communication is then created between the locations of the two satellite columns containing the same subgroup. All such communications are created for each of the missing subgroups. This yields the needed superstructure with one reboiler and one condenser. A superstructure using only one reboiler and one condenser is not adequate for all situations. Depending on the relative volatilities of the constituent components in a given mixture and the needed separation, the most optimal solution can often require multiple reboilers and condensers. An n-component superstructure with one reboilers and one condenser can easily be modified to incorporate multiple reboiler and condensers. One method of modification is to put either a reboiler or a condenser at the appropriate end of each column section (Sargent and Gaminibandara, 1976; Hu et al., 1991). An example of a four-component superstructure thus derived is shown in Figure 16. The basis for adding either a reboiler or a condenser to each column section can be easily explained. Generally, a distillation column can have multiple intermediate reboilers and condensers, and it is possible to use heat exchangers transferring heat from one distillation column to another (Agrawal and Yee, 1994). Therefore, in theory, a superstructure should truly have a large number of reboilers and condensers distributed throughout any of its distillation columns. However, for simplicity, the case generally considered is the one where at least simple distillation sequences using 2(n - 1) column sections and 2(n - 1) reboilers and condensers (such as the ones shown in Figures 1 and 2a) must be embedded in the superstructure (Henley and Seader, 1981). In order to ensure that all simple distillation sequences with 2(n - 1) column sections and 2(n - 1)

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present as substructures of a superstructure drawn by the current method, and, therefore, the current method provides a more complete superstructure for the optimization of distillation systems. Conclusions

Figure 16. Four-component superstructure.

reboilers and condensers are present as substructures in a superstructure, some observations are first made through the examination of such simple distillation sequences. A column section producing a subgroup containing the most volatile component A always requires a condenser. For an n-component feed, there are n - 1 such subgroups. Similarly a column section producing a subgroup containing the heaviest subgroup always requires a reboiler; there are n - 1 such subgroups. The other subgroups containing only the components of intermediate volatility may require a reboiler in one sequence and a condenser in another sequence. There are (n - 1)(n - 2)/2 such subgroups. It implies that, in an n-component superstructure, there should be at least (n - 1)(n - 2)/2 reboilers and the same number of condensers associated with the subgroups containing only the components of intermediate volatility. Therefore, in order to incorporate all the simple distillation sequences, the superstructure must have at least a total of (n - 1) + (n - 1)(n - 2)/2 reboilers and the same number of condensers. This adds to a total of n(n - 1) reboilers and condensers which must be used in a superstructure with multiple reboilers and condensers. It is interesting to note that this total number of reboilers and condensers is the same as the total number of column sections in a superstructure with one reboiler and one condenser such as the ones shown in Figures 13 and 14. Since, in the simple column sequences, either a section has a reboiler or a condenser associated with it, the modification of one reboiler and one condenser superstructure requires that either a reboiler or a condenser be associated with each column section. Therefore, a condenser is added to a section in the rectifying zone of a distillation column and a reboiler to a section in the stripping zone. It is through this procedure that the reboilers and condensers were added to generate Figure 16 from Figure 13. The four-component superstructure of Figure 16 is somewhat different from the corresponding superstructure proposed earlier in the literature (Sargent and Gaminibandara, 1976). The earlier methods draw a superstructure by arranging the distillation columns in a sequential manner, while the current method arranges the n - 2 columns as satellite columns around a central distillation column. This leads to a superstructure which not only has the earlier superstructure embedded in it but also contains other new configurations. For example, the four-component distillation configuration of Figure 4 is not present in the earlier superstructure, while it is embedded in the superstructure of Figure 16. In short, more configurations are

Distillation column configurations for the separation of a near-ideal mixture into constituent product streams are considered. For an n-component mixture with n g 4, a stepwise procedure is developed to draw distillation column configurations using only one reboiler and one condenser. Through the development of this procedure, it is found that the minimum number of column sections used in these configurations is 4n - 6, rather than n(n - 1). Such column configurations can be drawn by following the proposed method. Nine observations are made to help in the generation of these configurations. As expected, the number of possible configurations increases rapidly with the number of components in the feed. When an n-component feed is separated in the initial step into two subgroups each containing n - 1 components, then the use of observation no. 5 leads to distillation column configurations with one reboiler and one condenser which cannot be derived from superstructures known in the literature. The example of air distillation shows that, in certain cases, these new configurations have a potential to give distillation results which are at least similar to, if not better than, the configurations derived from n(n - 1) column sections. This demonstrates that these new configurations are relevant in the search for an optimum distillation configuration. An alternative method to draw an n-component distillation superstructure is suggested. This method does not arrange distillation columns in any known sequential manner. Instead, n - 2 satellite distillation columns in communication with a central distillation column are initially configured and then all these satellite distillation columns are linked with each other through all feasible communications. This creation leads to a superstructure which contains all earlier known configurations and also has the missing configurations as substructures. This provides a more complete superstructure for the optimization task. Acknowledgment Mr. Donald W. Woodward of Air Products and Chemicals provided the simulation results for the example discussed in this paper, and this help is acknowledged with gratitude. Dr. Keith B. Wilson’s comments in the preparation of this manuscript are gratefully acknowledged. Nomenclature n ) number of components in the feed mixture A, B, C, ... ) components in the feed mixture where A is the most volatile component and volatility decreases in successive alphabetical order l ) number of internal subgroups containing n - l - 1 components, 1 e l e n - 3 Rj ) total number of sequences to produce pure products from a j-component subgroup i, j, k ) running indexes lC ) total number of possible combinations containing i i internal subgroups from a total of l internal subgroups (defined by eq 2)

Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1071 Sn ) total number of sequences containing 4n - 6 sections drawn by following observation nos. 6 and 7

Appendix 1 Let Rj be the number of different configurations which can be drawn to separate a j-component stream into pure products. In order to calculate this number, consider the case when in the first step of separation a (j - 1)-component subgroup is created on the upper main branch. This subgroup can be further separated by Rj-1 configurations. If in this first step of separation the subgroup on the lower main branch has i components then it can have Ri configurations. So for this case the total number of possibilities is Rj-1Ri. For a given (j - 1)-component subgroup on the upper main branch, the number of components in the subgroup on the lower main branch can vary from one to j - 1. Therefore, the total number of possible configurations j-1 for this case is ∑i)1 Rj-1Ri. Similarly, if in the first step of separation the subgroup on the upper main branch has j - 2 components, then the total number of j-1 configurations will be ∑i)2 Rj-2Ri. Accounting for all the sizes of subgroups on the upper main branch (from j - 1 to 1), the total number of possible configurations j-1 j-1 is given by Rj ) ∑k)1 ∑i)k Rj-kRi. In this recursive equation, R1 ) 1 and R2 ) 1. The calculated value of R3 is 3 and R4 is 22. Appendix 2 A recursive formula is derived to calculate the number of sequences using observation no. 7 where the required sharp separations are done immediately. Let Si be the number of configurations for the separation of an i-component mixture using 4i - 6 column sections, one reboiler, and one condenser. For a given n-component mixture, the first separation is done such that m components are common between the two separated streams. Furthermore, assume that the light fraction (on the upper main branch of the network representation) has j components; then the heavy fraction (on the lower main branch) has n + m - j components. According to observation nos. 6 and 7, the sequence of separation steps for the next m - 1 steps are fixed. After these m - 1 steps, the multicomponent light mixture to be separated will have j - (m - 1) components and similarly the heavy mixture to be separated will have n + 1 - j components. For these particular values of j and m, the possible number of configurations is Sj-(m-1)Sn+1-j. With j components in the light fraction, the value of m can vary from 1 to j - 1. Also in the first step of distillation, the value of j can vary from 2 to n - 1. Therefore, the total number of possible configurations is given by:

∑ ∑ Sj-(m-1)Sn+1-j j)2 m)1

Received for review May 31, 1995 Revised manuscript received October 12, 1995 Accepted October 30, 1995X IE950323H

n-1 j-1

Sn )

Literature Cited Agrawal, R.; Yee, T. F. Heat Pumps for Thermally Linked Distillation Columns: An Exercise for Argon Production from Air. Ind. Eng. Chem. Res. 1994, 33, 2717-2730. Carlberg, N. A.; Westerberg, A. W. Temperature-Heat Diagrams for Complex Columns. 3. Underwoods Method for the Petlyuk Configuration. Ind. Eng. Chem. Res. 1989, 28, 13861397. Fidkowski, Z.; Kro´likowski, L. Minimum Energy Requirements of Thermally Coupled Distillation System. AIChE J. 1987, 33 (4), 643-653. Freshwater, D. C.; Henry, B. D. The Optimal Configuration of Multicomponent Distillation Trains. Chem. Eng. 1975, 301, 533-536. Glinos, K. A. Global Approach to the Preliminary Design and Synthesis of Distillation Trains. Ph.D. Thesis, University of Massachusetts, Amherst, Amherst, MA, 1985. Hendry, J. E.; Hughes, R. R. Generating Separation Process Flowsheets. Chem. Eng. Prog. 1972, 68 (6), 71-76. Henley, E. J.; Seader, J. D. Equilibrium-Stage Separation Operations in Chemical Engineering; John Wiley and Sons: New York, 1981; pp 529-547. Hohmann, E. C.; Sander, M. T.; Dunford, H. A New Approach to the Synthesis of Multicomponent Separation Schemes. Chem. Eng. Commun. 1982, 17, 273-284. Hu, Z.; Chen, B.; Rippin, D. W. T. Synthesis of General DistillationBased Separation System. Paper presented at the AIChE annual meeting, Los Angeles, CA, Nov 17-22, 1991; Paper 155b. Isalski, W. H. Separation of Gases; Oxford University Press: Oxford, U.K., 1989, p 53. Latimer, R. E. Distillation of Air. Chem. Eng. Prog. 1967, 63 (2), 35-59. Novak, Z.; Kravanja, Z; Grossmann, I. E. Simultaneous Optimization Model for Multicomponent Separation. Comput. Chem. Eng. 1994, 18, S125-S129. Petlyuk, F. B.; Platonov, V. M.; Slavinskii, D. M. Thermodynamically Optimal Method for Separating Multicomponent Mixtures. Int. Chem. Eng. 1965, 5 (3), 555-561. Rathore, R. N. S.; Van Wormer, K. A.; Powers, G. J. Synthesis Strategies for Multicomponent Separation Systems with Energy Integration. AIChE J. 1974, 20 (3), 491-502. Rodrigo, F. R.; Seader, J. D. Synthesis of Separation Sequences by Ordered Branch Search. AIChE J. 1975, 21 (5), 885894. Sargent, R. W. H.; Gaminibandara, K. Optimum Design of Plate Distillation Columns. Optimization in Action; Dixon, L. W. C., Ed.; Academic Press: London, 1976; pp 267-314. Seader, J. D.; Westerberg, A. W. A Combined Heuristic and Evolutionary Strategy for Synthesis of Simple Separation Sequences. AIChE J. 1977, 23 (6), 951-954. Thompson, R. W.; King, C. J. Systematic Synthesis of Separation Scheme. AIChE J. 1972, 18 (5), 941-948. Triantafyllou, C.; Smith, R. The Design and Optimization of Fully Thermally Coupled Distillation Columns. Trans. Inst. Chem. Eng. 1992, 70A, 118-132. Westerberg, A. W. The Synthesis of Distillation-Based Separation Systems. Comput. Chem. Eng. 1985, 9 (5), 421-429.

(A2.1)

The above equation is only valid for n g 3 and should be used with S2 ) 1.

X Abstract published in Advance ACS Abstracts, February 15, 1996.

Synthesis of Distillation Column Configurations for a Multicomponent

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