Membrane Cascade Schemes for Multicomponent Gas Separation

Ind. Eng. Chem. Res. 1996, 35, 3607-3617

3607

Membrane Cascade Schemes for Multicomponent Gas Separation Rakesh Agrawal Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, Pennsylvania 18195-1501

A procedure to draw membrane cascade schemes to separate an n-component gaseous mixture into n product streams, each enriched in one of the components, is presented. These n-component membrane cascade schemes are drawn by simple analogy with multicomponent distillation schemes for ideal mixtures. This procedure yields some interesting membrane cascade schemes with two-way communication between various subcascades present within the cascade structure. It also leads to n-component gas separation membrane cascade superstructures which have several n-component cascade schemes embedded within as substructures. Introduction A majority of the work available in the literature for gas separation using membranes relates to binary separation. Membrane cascade theory to separate a binary feed mixture is well-developed (Brigoli, 1979). Many membrane schemes for binary mixture separation are available and some have been extensively studied (Ohno et al., 1978a,b; Hwang and Thorman, 1980; McCandless, 1985; Agrawal and Xu, 1996a). However, only a few schemes have been proposed for separating a mixture containing three or more components into three or more product streams (LaGarza, 1963; Hwang and Ghalchi, 1982; Sengupta and Sirkar, 1984). Sengupta and Sirkar (1987) and Kothe et al. (1989) provide lists of commercially available multicomponent gas mixtures which could potentially be separated into multiple product streams using membrane schemes. Included in these lists are streams which contain CO, CO2, H2, N2, and CH4 in varying proportions, such as coke oven gas, synthesis gas, re-former off-gas, and methanol purge gas. Some other examples are natural gas containing He and N2 and ammonia purge gas containing H2, N2, CH4, Ar, and NH3. With all of these opportunities for multicomponent gas separation, and with the rapid advancements in the fabrication of membranes and membrane modules for gas separation in the past 2 decades, it is possible that membrane based processes for multicomponent gas separation could become commercially attractive. The calculation methods to describe permeation of a multicomponent gas stream across a membrane are well-developed (Stern and Wang, 1980; Shindo et al., 1985; Narinskii et al., 1989; Bansal et al., 1995). However, only a few studies are available for the separation of a multicomponent gas stream into multiple product streams, each enriched in one of the components. In one of the early studies, LaGarza (1963) suggested a membrane cascade system for an “end component” and a “middle component” separation from a multicomponent uranium or tungsten isotope mixture. An “end” component is either a component with the highest or the least permeability. It can be recovered by using a conventional binary mixture cascade. For recovery of an isotope of intermediate permeability, the use of two cascades is suggested. From the first cascade, all isotopes of higher permeability than the desired isotope and the desired isotopes are collected in its tops; they are then fed to another cascade where the desired isotope is concentrated in the tails. This method is restricted to the production of only one component and needs to be extended to simultaneous production of all of the components as product streams. Furthermore, S0888-5885(96)00160-1 CCC: $12.00

synergies which can exist between multiple subcascades for a multicomponent separation were not explored. In another study, Hwang and Ghalchi (1982) suggested combining two continuous membrane columns in order to separate a ternary mixture. In this ternary system, either the most permeable or the least permeable component is recovered as the first product stream from the first continuous membrane column and the second stream from this column is fed to the next continuous membrane column to recover the remaining two components as product streams. The authors found an excellent agreement between the calculated and experimental results for the separation of a CO2-CH4N2 mixture. However, the attractiveness of the continuous membrane columns, in comparison with simple countercurrent recycle cascades, has been in question. For most of the binary and multicomponent gas separations studied, the continuous membrane column has been found to consume more energy and require more membrane area than a simple countercurrent recycle cascade with a limited number of recycle compressors (McCandless, 1985; Rani and Gangiah, 1994; Xu and Agrawal, 1996). Furthermore, all possible methods of linking the two continuous membrane columns for a ternary mixture and the extension of the technique to separate a mixture containing more than three components was not reported by the authors. Sirkar (1980) made an elegant suggestion to use a two-membrane permeator for the separation of a ternary mixture. A single stage permeator with two membranes of reverse selectivities; i.e., one of the components is most permeable through one membrane, while a second component is most permeable through the second membrane is used. Such a permeator separates a ternary feed into three streams, two permeate streams, and one nonpermeate stream. Each stream is enriched in one of the components. Sengupta and Sirkar (1984, 1987) have published both theoretical and experimental results for the separation of He, CO2, and N2 mixtures using such a two-membrane permeator. Even though the use of a two-membrane permeator for a ternary separation is a novel idea, its use is limited by the availability of two commercially feasible membranes of reverse selectivities and desired permeabilities for a given application. The purpose of this paper is to explore and present a systematic procedure for drawing an array of feasible membrane cascade schemes for the separation of an n-component gaseous mixture into n product streams, each enriched in one of the components. The number of components, n, in the gaseous mixture is 3 or more. While membrane stages with different values of perme© 1996 American Chemical Society

3608 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996

Figure 1. Ternary distillation schemes. A and C are the most and least volatile components, respectively.

ability and selectivity could be used at different locations in the cascade structure, the objective is to draw structures which could accomplish the desired task when the same membrane is used in all of the membrane stages of the cascade scheme. This would allow the use of commercially available membrane modules. The only constraint is that the components to be separated should have different values of permeability through the membrane used; i.e., the ratio of any two permeabilities should be a value other than unity. This paper concentrates on the methods for drawing cascade structures and does not include a detailed analysis of any cascade scheme for any given application. Therefore, no heuristics are provided on the applicability and the limitation of any resulting cascade scheme. Multicomponent Membrane Cascade Schemes In contrast to membrane literature, separation of simple n-component mixtures into n product streams, each enriched in one of the components, has been extensively discussed in the distillation literature (King, 1980; Henley and Seader, 1981; Westerberg, 1985). Distillation schemes to separate a ternary mixture, ABC, are reproduced in Figure 1. Direct split configuration is shown in Figure 1a and indirect split configuration in Figure 1b. The configuration in Figure 1c uses a prefractionating column where feed ABC is split into two mixtures AB and BC. Parts e-g of Figure 1 show thermally linked columns with side-enricher, sidestripper, and Petlyuk configuration, respectively. Parts d and h of Figure 1 show configurations where only one distillation column is used and impure B product is produced. Distillation sequences for feed mixtures containing more than three components can be drawn similarly (Henley and Seader, 1981). Distillation superstructures for separating a multicomponent mixture have also been suggested in the literature (Sargent and Gaminibandara, 1976; Hu et al., 1991; Agrawal, 1996). The utility of such superstructures lies in the concept that all other structures are substructures of the superstructure and, therefore, one should be able to derive the optimum structure for a given application by optimization of the superstructure.

There are qualitative similarities between the distillation of a multicomponent mixture in a section of a distillation column and the separation of a multicomponent feed by a simple one stage membrane. The vapor leaving the top of a distillation section is always enriched in the most volatile component, and depleted in the least volatile component while components of intermediate volatility may be enriched or depleted, depending on the operating conditions. The same can be said with regard to the least volatile component in the liquid leaving a distillation section. Bansal et al. (1995) have studied a similar phenomenon when a multicomponent gaseous mixture such as H2, CH4, CO, and CO2 or H2, N2, O2, and CH4 is fed to a single membrane stage. In this case, for all flow geometries in the membrane module, the permeate stream is always enriched in the most permeable component, and depleted in the least permeable component while the components of intermediate permeability may be enriched or depleted, depending on the operating conditions. The authors studied the effect of operating parameters such as pressure ratio, membrane area, and stage cut. The concentration of the least permeable component in the nonpermeate stream will always increase. Qualitative similarities also exist between a distillation column with a multicomponent feed and production of two products and the binary separation membrane cascade of Figure 2 with a multicomponent feed. In a distillation column, depending on the operating conditions, the concentration of a component of intermediate volatility can go through a maximum. That is, its concentration within a distillation section can exceed its concentration at the ends of the section. The magnitudes and locations of the maxima in concentration in the stripping and the enriching sections of the distillation column depends to some extent on the boilup and reflux to the distillation column. Similar behavior is observed with respect to a multicomponent feed to a binary separation membrane cascade. LaGarza (1963) showed that a maximum in the concentration of a component of intermediate permeability can easily exist in an intermediate membrane stage of a membrane cascade. He also described a method for manipulating

Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3609

Figure 2. Symmetrical cascade for a binary separation.

Figure 3. Ternary separation with direct split cascade scheme. An analogous distillation scheme is shown in Figure 1a.

the location of this maximum in the concentration by changing the operating conditions. As a matter of fact, in his separation scheme, all of the components in the feed which have lower permeabilities than the permeability of any desired component of intermediate permeability can be rejected by the proper choice of the operating parameters in the nonpermeate product stream from the cascade. Similarly, an internal maximum in the concentration of a component of intermediate permeability has been reported by Hwang and Ghalchi (1982) for the continuous membrane column. On the basis of the similarities between a distillation column and a membrane cascade such as the one in Figure 2, it is possible to synthesize multicomponent gas separation membrane cascade schemes. This is achieved by translating the known multicomponent distillation schemes to membrane separation. This will be first demonstrated by extending the ternary separation schemes of Figure 1. The separation of mixtures containing more than three components will then be addressed. Membrane Cascades for Ternary Mixtures. Membrane schemes for ternary separation are easily drawn by replacing each of the distillation columns in Figure 1 with the binary membrane cascade scheme of Figure 2. Separation of a ternary feed mixture ABC using a membrane cascade scheme analogous to the direct split distillation sequence of Figure 1a is shown in Figure 3. Throughout this paper, components in a mixture are ranked according to their relative permeability; i.e., for feed mixture ABC, A is the most permeable component and permeability decreases in successive order with C being the least permeable. This is similar to the ranking for distillation where A is the most volatile component and volatility decreases in successive order with C being the least volatile. The ternary mixture ABC is fed to the first membrane subcascade, where it is separated into a product stream enriched in the most permeable component A and a mixture BC. This mixture is then fed to another subcascade where it is separated into two product streams, one enriched in B, the other in C. It is worth noting that depending on the desired purity of product streams, mixture BC can contain some quantities of component A.

Before proceeding further, two terms which are frequently used in the rest of this paper need to be explained. The term “subcascade” will refer to any portion of the total cascade scheme where all the membrane stages are connected in a series similar to the one shown in Figure 2. A subcascade will generally have one or more feed streams which are split into two or more product streams. For example, in Figure 3 the portion of the cascade scheme which splits feed ABC into A and BC is referred to as a subcascade. The term “cascade section” is defined to be a portion of a subcascade which is not interrupted by an entering feed stream or an exiting product stream. Thus, in Figure 3, the portion of the subcascade between feed ABC and product stream A constitutes a cascade section, and in all there are four cascade sections in the ternary cascade scheme of this figure. It is important to note that in all the cascade sections having more than two components, it will be difficult to match the composition of a recycle stream with the high-pressure stream with which it is mixed. This will result in mixing losses. In Figure 3, such mixing losses are likely to exist in cascade sections of the first subcascade. The indirect split cascade scheme, analogous to the distillation scheme of Figure 1b, is shown in Figure 4. Now the least permeable component C is produced from the first subcascade, and the second subcascade splits mixture AB into two product streams, each enriched in one of the components. Unlike mixture BC in the direct split cascade, mixture AB is recovered from the first subcascade at a lower pressure. Therefore, one has multiple options of introducing this as a feed to the second subcascade. Agrawal and Xu (1996b) have identified at least ten ways of introducing a low-pressure feed to a subcascade; and any one of those could be used to introduce low-pressure mixture AB to the second subcascade. However, for simplicity only three options are shown in Figure 4. Mixture AB is compressed and fed to the high-pressure side of a membrane stage. Optionally, either all or a portion of it could be directly fed to the low-pressure side of a membrane stage or to the inlet of a recycle-compressor. It is worth pointing out that the two schemes studied by Hwang and Ghalchi (1982) using two continuous membrane columns to


Figure 4. Ternary separation with indirect split cascade scheme. An analogous distillation scheme is shown in Figure 1b.

Figure 5. Ternary separation with a prefractionator cascade scheme. An analogous distillation scheme is shown in Figure 1c.

separate a ternary mixture were based on the distillation schemes of Figure 1a,b. The prefractionator cascade scheme, analogous to the distillation scheme of Figure 1c, is shown in Figure 5. This scheme is obtained by joining the two second subcascades of direct and indirect split cascade schemes. Notice that this cascade scheme uses six cascade sections and has an option to produce component B as a high-pressure or a low-pressure product stream. If it is decided to produce both the high- and low-pressure B streams as products, then most likely they will be of different purity. Membrane cascade schemes analogous to thermally linked columns in Figure 1e-g can also be drawn. In a thermally linked distillation column arrangement, one or more reboilers and/or condensers are eliminated by allowing both liquid and vapor mass exchange between the two distillation columns. These liquid and vapor flows are in opposite directions. Thus, a distillation column providing a liquid flow to another distillation column gets a vapor flow in return from this other distillation column. The question is how to create the analogous two-way communication in ternary membrane cascade schemes. There are several ways of creating this two-way communication between subcascades within a ternary membrane cascade scheme. The method proposed in this paper is demonstrated in Figure 6a. This membrane cascade scheme is drawn in analogy to the side enricher distillation configuration of Figure 1e. Three membrane stages M1, M2, and M3 are “introduced” in the cascade scheme to allow two-way communication between the main subcascade which receives the feed

ABC and the side enricher subcascade which produces B. The nonpermeate stream from the side enricher subcascade is sent to the main subcascade, and in turn it receives a portion of the permeate stream from the main subcascade as a sweep stream to the low-pressure side of the membrane stage M3. In order to create alternate two-way communication configurations, the three introduced membrane stages M1, M2, and M3 can be eliminated from the structure in Figure 6a in any desired combination. There are options for removing any one or two and even all three introduced membrane stages. This results in seven additional configurations from Figure 6a. In all there are eight (including the original one in Figure 6a) possible side enricher membrane cascade schemes which can be drawn from the proposed method. One of these, when all three introduced membrane stages are eliminated, is shown in Figure 6b. In this figure, if the pressures on the high-pressure side of the two membrane stages Si and E1 are the same, then the two recycle compressors CSi and CE1 can be combined into a single compressor. For a given application, the choice of the best candidate from the available eight configurations will depend on the results of economic optimizations. The availability of methods for two-way communications between subcascades, enables one to draw membrane cascade schemes which are analogous to the two other thermally linked distillation column schemes of Figure 1f,g. Figure 7 shows the side stripper configuration. The introduced membrane stages M4, M5, and M6 serve the same purpose as membrane stages M1, M2, and M3 in Figure 6. The prefractionator cascade scheme


Figure 6. Ternary separation with side enricher cascade schemes based on analogy to the distillation scheme of Figure 1e. Cascade schemes in a and b are with and without the three introduced membrane stages M1, M2, and M3.

Figure 7. Side stripper cascade scheme for ternary separation based on analogy to the distillation scheme of Figure 1f.

Figure 8. Prefractionator cascade scheme with two-way communication for ternary separation based on analogy to the distillation scheme of Figure 1g.

with two-way communication is shown in Figure 8. For this case, there are two sets of introduced membrane stages, one set is M1, M2, and M3, and the other is M4, M5, and M6. It is interesting to note that this leads to 64 distinct possibilities of connecting the prefractionator subcascade to the main subcascade! The membrane cascade schemes analogous to the distillation arrangements of Figure 1d,h have not been drawn because they can easily be obtained from the binary cascade scheme of Figure 2 by producing the impure product stream enriched in component B from either the enriching or the stripping cascade sections. It is apparent that once a ternary cascade scheme using a large number of recycle-compressors has been synthesized, cascade schemes using a limited number

of recycle-compressors are contained as substructures. Selection of such substructures can be easily accomplished by applying any of the procedures discussed by Agrawal and Xu (1996b) and Agrawal (1997). These procedures will not be described here, but some of the resulting one- and two-compressor cascade schemes from Figures 3 and 4 are shown in Figure 9a-d. A three-compressor cascade scheme derived from Figure 5 is shown in Figure 9e. In Figure 9e, the subcascade producing A and high-pressure B can be kept separate from the subcascade producing low-pressure B and C. If the two are joining, as shown by the dotted line in the figure, then the composition of two product streams B are likely to be different. While cascade schemes in Figure 9a,c,e can produce product streams of any


Figure 9. (a and b) Two- and one-compressor substructures from the side enricher membrane cascade scheme of Figure 3. (c and d) Substructures from the side stripper configuration of Figure 4. (e) Substructure from Figure 5.

desired purity, the cascade schemes in Figure 9b,d will be more suitable when one or more product streams are desired to be less pure. The purity of certain product streams from cascade schemes in Figure 9b,d may be improved in some cases by using two-way communication. Thus, in Figure 9b, a portion of the permeate stream from membrane stage S1 (shown as a dotted line) can be directed as a sweep stream to the low-pressure side of the membrane stage E1. Similarly in Figure 9d, a portion of the nonpermeate stream from membrane stage E1 could be mixed with the feed stream to membrane stage S1. These structures with two-way communications are easily generated as substructures from the cascade schemes of Figures 6 and 7, respectively. Many other ternary cascade schemes with a limited number (generally one, two, or three) of recyclecompressors for both high-pressure and low-pressure feed streams can be easily synthesized as substructures of the cascade schemes shown in Figures 3-8. The potential for cascades with a small number of compressors to be commercially attractive is much higher. Not only the capital cost associated with recycle-compressors is decreased, but also there is a reduction in the number of recycle streams which leads to a reduction in the number of potential points for mixing losses. For a given application, the optimum configuration with the proper number of recycle-compressors should be found through an optimization exercise. Membrane Cascades for n > 3. Once ternary gas separation schemes using membranes are available, they can be extended to n-component separation when the number of components, n, in a feed mixture is greater than 3. This can be achieved in ways similar to those used to extend ternary distillation schemes.

Three general techniques will be discussed in this section: simple separation sequencing, the superstructure of Sargent and Gaminibandara (1976), and the superstructure scheme of Agrawal (1996). The simple separation sequence of an n-component mixture using distillation requires n - 1 distillation columns. 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). In any given distillation column, separation between two components of adjacent volatility is made. The direct and indirect split sequences in Figure 1a,b are examples of simple separation sequences. Henley and Seader’s (1981) book provides a detailed discussion of such separation sequences, and equations to calculate the number of possible sequences and the total number of different subgroups for a given n-component mixture are also given. Due to the similarity between the membrane cascade schemes of Figures 3 and 4 and the distillation schemes of Figure 1a,b, it is clear that all of the equations derived for distillation schemes can be valid for the n-component membrane cascades. Thus, the separation of an ncomponent mixture will require n - 1 membrane subcascades and 2(n - 1) cascade sections. Each subcascade will have one feed and produce one product stream from the enriching cascade section and another product stream from the stripping cascade section. In any given membrane subcascade, separation between two components of adjacent permeability values is to be made. As an example, simple separation sequences for a fourcomponent mixture, ABCD, are reproduced in Figure 10. With the help of this figure and Figures 2-4, the


Figure 10. Simple separation sequences for the separation of a four-component feed mixture ABCD.

actual membrane cascade schemes with membrane stages and recycle-compressors can easily be drawn. An alternative method for creating n-component gas separation membrane cascade schemes is to create a superstructure which would not only have all the simple sequences but would also contain more complex ones with two-way communications between various subcascades as substructures. Such a superstructure has a large number of possible configurations embedded in it, and any particular configuration may be obtained by eliminating appropriate cascade sections or interconnecting streams from the superstructure. The first superstructure for an n-component separation by distillation was suggested by Sargent and Gaminibandara (1976). The use of superstructures to find optimum distillation configurations has received renewed attention (Hu et al., 1991; Novak et al., 1994). It is definitely of interest to extend the concept of an n-component superstructure for separations using multiple membrane stages and recycle-compressors. To illustrate the extension of Sargent and Gaminibandara’s method to membrane cascade schemes, consider the separation of a four-component mixture. Their four-component distillation superstructure is shown in Figure 11, together with an inset network representation. For convenience, multiple reboilers and condensers used in the original superstructure are not shown here. The corresponding membrane cascade scheme is proposed in Figure 12. Network representations, such as that in the inset of Figure 11, are quite useful in synthesizing actual membrane cascade schemes. In any given network, the feed mixture 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 membrane subcascade to another membrane subcascade to be further separated into two subgroups. A line connecting a node with a successive node represents a section of a membrane subcascade. A configuration

such as the one in Figure 11 has n(n - 1) lines connecting different nodes, and therefore, the number of cascade sections used is also n(n - 1). The total number of subgroups including feed and product streams is n(n + 1)/2. The four-component cascade scheme in Figure 12 has ten subgroups and requires twelve cascade sections. A network representation for a mixture with number of components greater than four can be easily drawn (Hu et al., 1991; Agrawal, 1996). Therefore, corresponding membrane cascade superstructures for any value of n can also be drawn by following the steps analogous to the one used to generate Figure 12 from the network representation of Figure 11. There is two-way communication between the subcascades of the membrane cascade superstructure of Figure 12. A subcascade receiving a high-pressure nonpermeate stream from another subcascade sends back a portion of the low-pressure permeate stream and vice versa. However, simple separation sequences can be easily obtained from such a superstructure by eliminating some cascade sections and certain streams and thereby retaining only one-way communication between subcascades. For example, the simple separation sequence shown in Figure 10a can be generated from Figure 12 by eliminating cascade sections 4, 8, and 10 and by removing the low-pressure permeate flow from cascade section 6 to cascade section 2 and from cascade section 12 to cascade section 6. This results in combining cascade sections 1, 3, and 7 into one section producing A and combining cascade sections 5 and 9 into one section producing B. Similarly, other simple separation sequences in Figure 10 can be obtained by elimination of appropriate cascade sections and streams from the superstructure of Figure 12. In addition to simple separation sequences, there are clearly several more separation sequences embedded as substructures in the superstructure. The task of an optimization exercise will be to find the most useful substructure. It must be cautioned that such an optimization exercise is far from trivial using currently available tools.


Figure 11. Four-component distillation superstructure drawn according to Sargent and Gaminibandara’s (1976) scheme. The corresponding network representation is shown in the inset.

Figure 12. Four-component gas separation membrane cascade superstructure drawn by analogy to Sargent and Gaminibandara’s distillation superstructure (1976).

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. For an n-component distillation with values of n greater than 3, it has been shown that certain configurations are missing from the distillation superstructure of Sargent and Gaminibandara. Agrawal (1996) has proposed an alternate distillation superstructure which is more complete. This n-component superstructure consists of a main distillation column and n - 2 satellite columns with mass communication between the main and each of the satellite columns and also between each of the satellite columns. The creation of an analogous n-component membrane superstructure for values of n greater than 3 will now be illustrated. The first step is to generate a scheme whereby each of the satellite subcascades communicate only with the main subcascade. The corresponding four-component distillation scheme is reproduced in Figure 13. The analogous membrane cascade scheme is proposed in Figure 14. Notice that in this scheme no subgroup composed of only the components of intermediate permeabilities, such as BC, is transferred from one subcascade to another subcascade. Such subgroups are

missing from the network representation shown in the inset of Figure 13. This network is created by initially splitting the feed such that n - 2 components are common between the first two separated subgroups containing n - 1 components; for example, components B and C are common between the two separated streams ABC and BCD. Then each subgroup is separated such that in each subsequent step a product stream enriched in one of the components is produced directly. A subgroup containing the most permeable component A should produce components by a sharp split, starting from the least permeable component in the subgroup. Similarly, the subgroup containing the least permeable component from the feed mixture should produce components by sharp split, starting from the most permeable component in the subgroup. A total of 3(n - 1) subgroups including feed and product streams are used. In analogy with distillation, there are 4n - 6 cascade sections used in such membrane cascade schemes. Thus, the four-component cascade scheme in Figure 14 requires ten cascade sections, which is two fewer than that for the scheme in Figure 12.


Figure 13. Four-component distillation scheme according to Agrawal (1996). Each of the satellite columns have mass transfer communication only with the main distillation column.

Figure 14. Four-component gas separation membrane cascade scheme drawn by analogy to the distillation scheme of Figure 13.

Even though an n-component membrane cascade scheme such as the one in Figure 14 is capable of producing the desired product streams from a given feed mixture, there are other cascade schemes which are missing from its structure. To create a membrane cascade superstructure, it is essential that all feasible subgroups from a complete network such as the one shown in the inset of Figure 11 be transferred from one cascade section to another cascade section. In the structure of Figure 14, the satellite subcascades communicate only with the main subcascade and not with each other. In order to create this communication, [(n + 1)/2 - 3(n - 1)] subgroups composed of only the components of intermediate permeability must be identified (Agrawal, 1996). These missing subgroups are readily apparent by comparing networks, such as the ones in the inset of Figures 11 and 13. Each of these missing subgroups can be found in the enriching section of one satellite subcascade and in the stripping section of another satellite subcascade. For example, for the

four-component case, subgroup BC exists on the line segment joining BCD and B; this subgroup can be found in the enriching section of the B-producing satellite subcascade. Similarly, subgroup BC exists on the line segment joining ABC, and C and can be found in the stripping section of the C-producing satellite subcascade. Once the two corresponding locations for a subgroup such as BC are known, communication between these two locations can easily be created. A nonpermeate and a permeate stream, composed primarily of BC, can flow either in the same or opposite direction from one of the two satellite subcascades to another satellite subcascade. The resulting fourcomponent superstructure is shown in Figure 15. By following the steps discussed for a four-component superstructure, it is possible to draw n-component membrane cascade superstructures for higher values of n. If needed, additional relevant information is available elsewhere (Agrawal, 1996).


Figure 15. Four-component gas separation membrane cascade superstructure drawn by analogy to a distillation superstructure suggested by Agrawal (1996).

Once an n-component membrane cascade superstructure has been created, the simpler substructures can be obtained by the elimination of unwanted cascade sections and streams. Schemes with fewer membrane stages and recycle-compressors are synthesized by applying the procedures described to draw membrane cascades with a limited number of compressors to one or more cascade sections or subcascades (Agrawal and Xu, 1996b; Agrawal, 1997). This completes the discussion on the synthesis of n-component gas separation membrane cascade superstructures. The substructures of interest may be drawn from these superstructures. A few miscellaneous comments will now be made. A component of intermediate permeability, such as component B in Figure 8, can be drawn either directly from a nonpermeate stream as it exits the membrane (as shown) or subsequently after the nonpermeate stream is mixed with the recycle stream from a previous membrane stage. The same is also true when a nonpermeate stream from an enriching section of a subcascade is sent to the enriching section of another subcascade. For example in Figure 8, if the introduced membrane stage M6 were to be eliminated, then the high-pressure stream enriched in A and B sent to membrane stage M4 could be drawn after the nonpermeate stream from M5 had been mixed with the recycle stream from a previous membrane stage. If a given feed is at a lower pressure and needs compression before it can be fed to the higher pressure side of a membrane stage, as is shown in all the figures, then an alternative in which it is introduced directly to the lower pressure side should be explored. Agrawal and Xu (1996b) have described ten alternative methods of introducing a low-pressure feed to a binary membrane cascade; all of these options are also applicable for the multicomponent case. Furthermore, all of the multicomponent cascade schemes in this paper are described by using a symmetrical binary cascade scheme. If needed, the method described here could also be used with unsymmetrical subcascades to generate unsymmetrical multicomponent membrane cascade schemes. Unsymmetrical cascades are described in detail by Pratt (1967) and Brigoli (1979). Even though in this paper, multicomponent cascade structures are synthesized to work with the same membrane in all of the membrane stages, for some applications, it may be possible to enhance the performance by utilizing membranes with different permselective properties in different cascade sections or subcascades. For example, the direct split ternary separation cascade scheme in Figure 3 could benefit a great deal by having membranes in the first subcascade

which have high permeability of A relative to B and C, whereas the second subcascade would require a membrane having a good permselective value of B relative to C with little effect of the permeability values of A. When membranes with different values of permselectivities are available for an application, a careful optimization will have to be performed to determine the proper choice of membrane stages in different cascade sections. Some words of caution must be added at this point. The analogy with distillation column structures to draw n-component membrane structures is an imperfect one. The physical-chemical phenomena responsible for gas separation are quite different between a distillation column and the countercurrent membrane cascade, so the thermodynamic distinctions between the two processes must be considered. The advantage of the suggested analogy is that it allows one to draw alternate membrane structures. The usefulness of such derived membrane structures must then be independently gauged, first through calculations and then through experimental demonstrations. This paper suggests and uses the analogy to draw several membrane structures, but the usefulness of these membrane structures for any given application needs to be evaluated. Conclusion A procedure for drawing membrane cascade schemes to separate n-component gaseous mixtures, with values of n greater than 2, into n product streams each enriched in one of the components is presented. These n-component membrane cascade schemes are developed by drawing a simple analogy with multicomponent distillation schemes for ideal feed mixtures. The only constraint is that no two components to be separated should have the same value of permeability through the membrane. Membrane cascade schemes to separate ternary gaseous mixtures are discussed first. Six configurations to produce each product stream with relatively good purities are developed. By analogy with thermally linked distillation columns, two-way communication between two subcascades may result. A subcascade receiving a nonpermeate stream from another subcascade returns a permeate stream to the first subcascade or vice versa. This two-way communication is created by introducing three introduced membrane stages between the two subcascades. It is then possible to eliminate one or more of these introduced membrane stages to obtain a desired cascade scheme; this leads to eight possible alternative ways to create two-way com-


munication. It is also demonstrated that multiple ternary cascade schemes with fewer membrane stages and recycle-compressors can be generated from the six original cascade schemes. The method for ternary separation is then extended to separation of mixtures with more than three components. First a procedure is suggested to draw simple separation sequences. Then n-component membrane cascade superstructures based on two different methods are presented. These superstructures contain the simple separation sequences as substructures. These superstructures also contain several other n-component cascade schemes as embedded substructures. Substructures with fewer membrane stages and recyclecompressors can be drawn from any of these multicomponent membrane cascade schemes. The availability of these n-component superstructures should make the task of finding the optimum scheme for the separation of n-component mixtures a little easier. Acknowledgment Helpful discussions with Dr. Jianguo Xu of Air Products and Chemicals are highly appreciated. Literature Cited Agrawal, R. Synthesis of Distillation Column Configurations for a Multicomponent Separation. Ind. Eng. Chem. Res. 1996, 35, 1059. Agrawal, R. A Simplified Method for the Synthesis of Gas Separation Membrane Cascades with Limited Numbers of Compressors. Chem. Eng. Sci. 1997, in press. Agrawal, R.; Xu, J. Gas Separation Membrane Cascades II. TwoCompressor Cascades. J. Membr. Sci. 1996a, 112, 129. Agrawal, R.; Xu, J. Gas Separation Membrane Cascades Utilizing Limited Numbers of Compressors. AIChE J. 1996b, 42 (8), 2141. Bansal, R.; Jain, V.; Gupta, S. K. Analysis of Separation of Multicomponent Mixtures Across Membranes in a Single Permeation Unit. Sep. Sci. Technol. 1995, 30 (14), 2891. Brigoli, B. Cascade Theory. In Uranium Enrichment; Vilani, S., Ed.; Springer-Verlag; Berlin/ Heidelberg, 1979; pp 13-54. Henley, E. J.; Seader, J. D. Equilibrium-Stage Separation Operations in Chemical Engineering; Wiley: New York, 1981; pp 529547. Hu, Z.; Chen, B.; Rippin, D. W. T. Synthesis of General DistillationBased Separation System. AIChE Annual Meeting, Los Angeles, CA, Nov 17-22, 1991; Paper 155b. Hwang, S. T.; Ghalchi, S. Methane Separation by a Continuous Membrane Column. J. Membr. Sci. 1982, 11, 187. Hwang, S. T.; Thorman, M. The Continuous Membrane Column. AIChE J. 1980, 26 (4), 558. King, C. J. Separation Processes, 2nd ed.; McGraw-Hill: New York, 1980; pp 710-721.

Kothe, K. D.; Chen, S.; Kao, Y. K.; Hwang, S. T. A Study of the Separation Behavior of Different Membrane Columns with Respect to Ternary Gas Mixtures. J. Membr. Sci. 1989, 46, 261. LaGarza, A. De. A Generalization of the Matched Abundance Ratio Cascade for Multicomponent Isotope Separation. Chem. Eng. Sci. 1963, 18, 73. McCandless, F. P. A Comparison of Some Recycle Permeators for Gas Separations. J. Membr. Sci. 1985, 24, 15. Narinskii, A. G.; Chekalov, L. N.; Talakin, O. G. Calculations for Symmetric Membrane Cascades for Separating Multicomponent Mixtures. Theor. Found. Chem. Eng. 1989, 23 (6), 478. Novak, Z.; Kravanja, Z.; Grossmann, I. E. Simultaneous Optimization Model for Multicomponent Separation. Comput. Chem. Eng. 1994, 18 (suppl), S125. Ohno, M.; Morisue, T.; Ozaki, O.; Miyauchi, T. Comparison of Gas Membrane Separation Cascades Using Conventional Separation Cell and Two-Unit Separation Cells. J. Nucl. Sci. Technol. 1978a, 15 (5), 376. Ohno, M.; Heki, H.; Ozaki, O.; Miyauchi, T. Radioactive Rare Gas Separation Performance of a Two-Unit Series-Type Separation Cell. J. Nucl. Sci. Technol. 1978b, 15 (9), 668. Pratt, H. R. C. Countercurrent Separation Processes; Elsevier: New York, 1967, pp 28-68. Rani, K. Y.; Gangiah, K. Evaluation of Various Countercurrent Recycle Membrane Cascades for Multicomponent Gas Separation. Indian Chem. Eng. A 1994, 36 (3), 101. Sargent, R. W. H.; Gaminibandara, K. Optimum Design of Plate Distillation Columns. In Optimization in Action; Dixon, L. W. C., Ed.; Academic Press: London, 1976, pp 267-314. Sengupta, A.; Sirkar, K. K. Multicomponent Gas Separation by an Asymmetric Permeator Containing Two Different Membranes. J. Membr. Sci. 1984, 21, 73. Sengupta, A.; Sirkar, K. K. Ternary Gas Mixture Separation in Two-Membrane Permeators. AIChE J. 1987, 33 (4), 529. Shindo, Y.; Hakuta, T.; Yoshitome, H. Calculation Methods for Multicomponent Gas Separation by Permeation. Sep. Sci. Technol. 1985, 20 (5 and 6), 445. Sirkar, K. K. Asymmetric Permeator-A Conceptual Study. Sep. Sci. Technol. 1980, 15, 1091. Stern, S. A.; Wang, S. C. Permeation Cascades for the Separation of Krypton and Xenon from Nuclear Reactor Atmospheres. AIChE J. 1980, 26 (6), 891. Westerberg, A. W. The Synthesis of Distillation-Based Separation Systems. Comput. Chem. Eng. 1985, 9 (5), 421. Xu, J.; Agrawal, R. Membrane Separation Process Analysis and Design Strategies Based on Thermodynamic Efficiency of Permeation. Chem. Eng. Sci. 1996, 51 (3), 365.

Received for review March 19, 1996 Revised manuscript received June 10, 1996 Accepted June 10, 1996X IE960160C

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

Membrane Cascade Schemes for Multicomponent Gas Separation

Recommend Documents