Thermodynamically Efficient Systems for Ternary ... - ACS Publications

Ind. Eng. Chem. Res. 1999, 38, 2065-2074

2065

Thermodynamically Efficient Systems for Ternary Distillation Rakesh Agrawal * and Zbigniew T. Fidkowski Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, Pennsylvania 18195-1501

In an earlier work (Agrawal, R.; Fidkowski, Z. T. Eng. Chem. Res. 1998, 37, 3444) it was shown that for the distillation of a ternary liquid mixture into pure component product streams the modified direct or indirect split configurations can have higher thermodynamic efficiencies than the conventional thermally coupled configurations. In this paper, thermally coupled column configurations are modified by incorporating intermediate temperature reboilers and condensers to accept/reject heat at the temperatures of boiling/condensing binary mixtures. The modified side rectifier or side stripper configurations retain the low vapor flow of the unmodified configurations. They have the same total number of reboilers and condensers as do the direct or indirect split but they provide higher thermodynamic efficiencies than the corresponding direct or indirect split. These new configurations also provide an additional degree of freedom to shift heat (cold) duty between the intermediate temperature reboiler (condenser) and the reboiler at the warmest temperature (condenser at the coldest temperature). Finally, a more complete ternary and quarterary superstructure is suggested that contains these new configurations as well as all earlier known superstructures and configurations. Introduction An extremely important issue in the synthesis of an optimum system for performing a given task is the completeness of the set of all alternative systems (synthesis domain). The set of alternative systems can sometimes be generated by a synthesis algorithm, usually of a combinatorial nature. For simpler problems, such as ternary distillation, the complete set of alternative column configurations is believed to be known from exhaustive research over the last 5 decades.2-14 Classic configurations described there (e.g., King 15) include direct sequence (DS), indirect sequence (IS), column with side rectifier (SR), column with side stripper (SS), single column with side draw, system with a prefractionating column and fully coupled columns (FC, Petlyuk et al.4). However, the completeness of the set of column configurations has never been proven. The heat demand of these known distillation configurations to separate ternary mixtures into nearly pure components is well-studied in the literature.4,16-22 From these studies, it is well-known that the schemes with thermal coupling (SR, SS, and FC) require less heat input than the ones without thermal coupling (DS and IS). However, lower heat duty does not necessarily translate into higher thermodynamic efficiency.1,22 Finn22 compared the SR with the DS for a specific example and concluded that thermally coupled side column systems can reduce both energy consumption and capital cost, even though their thermodynamic efficiency is similar to conventional column systems. Recently, Agrawal and Fidkowski1 compared the thermodynamic efficiency of the three thermally coupled columns with modified direct and indirect column sequences for ideal feed mixtures over a wide range of feed compositions and relative volatilities. A striking result of this study is that, for the FC configuration, which is known to have the lowest heat demand for ternary distillation, the range of values of feed composition and relative volatili* Corresponding author. Fax: [email protected].

610-481-8803. E-mail:

ties for which it is the most thermodynamically efficient configuration is quite limited. Among the three thermally coupled column configurations, the SR and the SS configurations tend to provide the most efficient configuration more often than does the FC configuration. Generally, a selection from the modified direct and indirect split configurations provides the most thermodynamically efficient configuration for more feed compositions than do any of the three conventional thermally coupled column configurations. The high thermodynamic efficiency of the modified direct and indirect split configurations results primarily from their ability to either accept or reject heat at the intermediate temperatures of binary mixtures. In the FC system, all the energy has to be supplied at the highest temperature (to boil the heaviest component) and it is removed at the lowest temperature (to condense the most volatile component). This can make this system unattractive despite its lower total heat duty. The SS and the SR have lower energy requirements than the direct and indirect split configurations, but their temperature distribution of utilities is not totally beneficials they use either more heating mediums at the highest temperature or more cooling mediums at the lowest temperature than conventional systems (DS or IS). It seems that there is a tradeoff between the first law duty and the second law ∆T’s (Westerberg13). Eventually, what matters in industrial practice is the total annual cost of a plant. A distillation plant with a lower heat demand (or vapor flow) has smaller heat exchangers, smaller column diameters, and potentially lower operating costs. Benefits of a distillation configuration with just higher thermodynamic efficiency but overall higher heat duty are not so obvious. In a case where there is only one heating utility and one cooling utility, available savings with a higher efficiency distillation configuration may be not very important. For example, for a binary distillation using only one heat source but with an intermediate reboiler one can somewhat decrease the total heat exchange area because the temperature difference will be bigger in the

10.1021/ie980531k CCC: $18.00 © 1999 American Chemical Society Published on Web 03/25/1999

2066 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999

Figure 1. (a) Modified direct split (DSLV); (b) modified indirect split (ISLV) configuration.

intermediate reboiler than in the bottom reboiler. The total heat duty is the same as that for the binary distillation without the intermediate reboiler. The use of an intermediate reboiler will also lead to a reduction in the diameter of the column bottom section. These savings are offset by an increased number of stages in the distillation column. However, in a case where there are multiple utilities to choose from (of different temperature and cost), or in a case where the necessary utilities are created within the process using electricity or work (like in cryogenic distillation), the thermodynamic efficiency directly impacts the plant economics. The primary aim of this paper is to seek new ternary distillation schemes that not only have lower heat demand (vapor flow) but also simultaneously achieve higher thermodynamic efficiencies. In this paper, a search is made for ternary separation configurations that retain the lower overall heat duty benefits of the thermally coupled systems and at the same time do not require more high-temperature heating utility (nor a low-temperature cooling medium) than the conventional direct/indirect split systems. An often used technique to arrive at the optimum configuration is to start from a superstructure.23,24 A superstructure is a general system containing all possible (known) configurations. Any particular configuration may be obtained from the superstructure simply by the deletion of a certain part of the flowsheet (stream or column section). It has proven to be a very useful concept for use with mixed integer nonlinear programming techniques, although the mathematical methods used to generate the optimal structure from a superstructure are not yet completely reliable. At least in principle, the use of a superstructure eliminates the necessity to generate all the possible configurations up front, which can be very convenient. However, if a superstructure is incomplete, then it can lead to suboptimal solutions. The first superstructure for ternary distillation was proposed by Sargent and Gaminibandara.23 Subsequently, Glinos17 proposed several new structures of distillation columns for ternary separation, with multiple interconnecting streams (of various compositions) between the columns. In recent publications,25-27 emphasis seems to have shifted from ternary separation to mixtures containing four or more components. However, a general proof for the completeness of the

synthesis domain of ternary mixtures is not yet available, so the completeness of known superstructures for ternary separation cannot be presumed. In this paper we propose some other, new distillation configurations for the separation of ternary mixtures, also without the general proof that all the possible combinations are taken into account. This leads us to a new and more complete superstructure for the separation of ideal to near-ideal ternary mixtures. In the final part of this paper, an attempt is made to extend these new concepts for ternary separation to mixtures containing more components, specially to fourcomponent mixtures. More Efficient Ternary Distillation Schemes In this section, a search is made for more efficient schemes to distill a near-ideal ternary feed mixture ABC (with A being the most volatile and C the least volatile) into pure product streams. The conventional direct and indirect sequences have only one transfer stream from the first distillation column (the one receiving the ternary feed) to the second distillation column. It has been shown,28 however, that it is thermodynamically more beneficial to have two interconnecting streams between the columnssone liquid and one vapor. For example, in the direct split sequence, the liquid feed to the second column is the BC mixture withdrawn from the bottom of the first column, and the vapor feed is withdrawn as a portion of the first column boil-up (sequence DSLV in Figure 1a). A similarly modified indirect split sequence ISLV is shown in Figure 1b. All the three known thermally coupled configurations are shown in Figure 2. As stated earlier, the choice between the DSLV and the ISLV configurations provide the most thermodynamically efficient configuration for more feed compositions than the choice between the three thermally coupled column configurations.1 Since DSLV and ISLV are found to provide the most thermodynamically efficient configuration more often, it is natural that a search for even more efficient configurations starts by a close inspection of either of these homologous configurations. A close examination of the DSLV configuration in Figure 1a reveals that a major source of inefficiency resides at the bottom of the first column. The vapor from the reboiler BC has the same composition as the liquid from the bottom stage

Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 2067

Figure 2. Conventional thermally linked column configurations: (a) side rectifier (SR); (b) side stripper (SS); (c) fully coupled (FC).

Figure 3. First method of efficiency improvement for direct split: first column’s bottom vapor created by side liquid draw and its vaporization.

of the first column. When both B and C are present in significant amounts, this leads to significant exergy loss on the bottom stage of the first column. This happens because there is a substantial mismatch between the composition of the vapor which would be in equilibrium with the liquid leaving the bottom stage and the vapor that is fed to this stage. The first step in improving the efficiency of the DSLV configuration is to reduce or eliminate this exergy loss. There are at least two possible methods for achieving this objective. The first method is shown in Figure 3. In this method, a liquid stream is drawn from an intermediate location of the first column, vaporized, and fed to the bottom of this column. The composition of this vapor stream is such that it is nearly in equilibrium with the liquid stream leaving from the bottom of the first column. This will reduce the mixing losses in the bottom section of the first column in Figure 1a. It is worth noting that, for a given feed when pure streams are to be produced, the composition of the liquid steam BC that is transferred from the first to the second column in Figure 3 is fixed. As a result, the composition of the vapor that is in equilibrium with this liquid is also fixed. This prespecifies the composition of the side liquid draw from the first column. Therefore, the success of the method

Figure 4. Second method of efficiency improvement for direct split: all the vapor from the bottom reboiler of the first column is fed to the second columnsside rectifier with feed reboiler (SRFR).

in Figure 3 will depend on the availability of a liquid draw from an intermediate location with the required composition. This will generally limit the utility of this configuration. Of course, a similar solution exists for the indirect split, where a vapor draw from an intermediate location of the first column is to be condensed and fed to the top of this column as reflux. In the second method, a portion of the liquid from the bottom of the first column is fed to a reboiler and another portion is sent to the second column as shown in Figure 1a. However, no portion of the vapor from this reboiler is returned directly to the bottom of the first column and all of this vapor is sent to the stripping section of the second column (Figure 4). As a result, as compared to Figure 1a, more vapor is sent to the second column. In return, a side vapor stream is withdrawn from the second column at a location where the liquid from the bottom of the first column is fed. This side vapor stream is then fed to the bottom of the first column. For a pinched column, this ensures that the vapor entering and liquid leaving the bottom of the first column are in thermodynamic equilibrium. This eliminates the unnecessary mixing loss in the bottom section


VA )

zARA RA - φ1

(2)

where φ1 is the root of Underwood’s equation:29

RBzB RCzC RAzA + + )0 RA - φ RB - φ RC - φ

(3)

RB < φ1 < RA

(4)

satisfying

Next, vapor flow to condenser B at minimum reflux is calculated from the quadratic equation

a VB2 + bVB + c ) 0

(5)

as Figure 5. Second method of efficiency improvement for indirect split: all the liquid from the top condenser is fed to the second columnsside stripper with feed condenser (SSFC).

of the DSLV configuration in Figure 1a and should result in a more efficient configuration. The corresponding solution for the ISLV configuration is shown in Figure 5. In this solution, no portion of the vapor from the top of the first column after condensation is returned to the first column; instead, all of it is sent to the second column. The reflux to the first column is provided by a side-draw liquid stream from the second column, as shown in Figure 5. Sample calculations were done to check the thermodynamic efficiency improvement for the new configuration in Figure 4 as compared to DSLV in Figure 1a. These calculations were done with the simplifying assumptions and the method described in the earlier papers.1,28 The simplifying assumptions used in the method are ideal vapor phase, ideal liquid solution, equal latent heats for all three components A, B, and C, no pressure drop losses, latent heat independent of temperature (within the operating temperature range of the distillation column), and vapor pressures of the components given by the Clausius-Clapeyron equation. The following definition of distillation thermodynamic efficiency is used:

η)

minimum work of separation (1) minimum work of separation + exergy loss

Exergy loss is calculated by the exergy balance, taking into account all the streams entering and leaving a control volume containing the distillation column system, but excluding the reboiler and condenser heat exchangers. Equations were derived for a saturated ternary liquid feed, with a unit flow rate (e.g., 1 kmol/ s), which is distilled into pure products A, B, and C. All the thermodynamic efficiency and minimum vapor flow equations for the pinched columns for the known distillation systems in Figures 1 and 2 can be found in the two earlier references.1,28 Total reboilers and condensers were assumed, although if needed, then based on the previous work,30 the present analysis could be extended to efficient configurations with partial reboilers and condensers. The corresponding equations for the new configuration in Figure 4 are derived as follows. First, vapor flow to condenser A at minimum reflux is calculated as

VB )

-b + x∆ 2a

(6)

where

a ) RB - RC b ) VAa - zBRB - zCRC

(7)

c ) -VAzBRB ∆ ) b2 - 4ac

The mole fraction of component B in the feed to the second column (xM B ) is then determined as

xM B )

zBRC

(8)

(VB - zB)(RB - RC)

Then, the composition of the liquid phase in equilibrium with the vapor feed to the second column is calculated as

x* ) x*(y)xM B) )

xM B /RB

(9)

M xM B /RB + (1 - xB )/RC

and vapor flow from reboiler C at minimum reflux is

VC )

zCx* xM B

(10)

- x*

Finally, thermodynamic efficiency of this configuration is calculated as:

ηSRFR )

-zA ln RA - zB ln RB - zC ln RC

VA ln RA + VB ln RB - (VA + VB - VC)

[ ]

1 ∫01ln KC,BC

dq

(11)

Detailed derivation of eqs 2-8. is given in the work of Fidkowski and Krolikowski.18 A unique feature of this derivation is that the final expression for thermodynamic efficiency is found to be a function of the feed composition and relative volatilities only; temperatures of the reboilers and condensers do not appear explicitly in the final expression.

Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 2069 Table 1. Thermodynamic Efficiencies for the Three Configurations (Basis: Feed Flow ) 1; zA ) zB ) zC; rA ) 10 and rB ) 5) configuration DSLV (Figure 1a) SRFR (Figure 4) SR (Figure 2a)

vapor from vapor from total thermodynamic reboiler BC reboiler C vapor efficiency (%) 1.35 1.10 0

0.17 0.36 1.46

1.52 1.46 1.46

53.2 64.7 35.9

Consider the calculations for an equimolar feed (zA ) zB ) zC) with relative volatility of A with respect to C (RA) equal to 10 and relative volatility of B with respect to C (RB) equal to 5. Calculations were done for a feed flow of unity and the results are summarized in Table 1. For the DSLV configuration, the minimum vapor flow in the first column is 1.02, the amount of vapor transferred from the first column’s reboiler to the second column is 0.33, and the minimum vapor flow in the bottom section of the second column is 0.17. Therefore, the total vapor flow requirement for the pinched columns is found to be 1.52 and the corresponding thermodynamic efficiency is calculated to be 53.2%. Calculations were then done for the same feed conditions for the new configuration in Figure 4. While the minimum vapor flow for the first column remained the same as that for the DSLV case, the minimum vapor flow at the bottom of the second column increased to 0.36. All the vapor flow of 1.10 from the bottom reboiler of the first column is sent to the second column, and in exchange as shown in Figure 4, a vapor flow of 1.02 is returned from the second column to the bottom of the first column. The total vapor flow generated in the reboilers of the pinched column adds to 1.46 and the corresponding thermodynamic efficiency is found to be 64.7%. This is indeed exciting because the new configuration when compared to the original DSLV not only decreased the first law heat requirement (from 1.52 to 1.46) but also substantially improved the overall thermodynamic efficiency. This happens because of the reduced irreversibility of distillation in the bottom of the first column. Because of the use of a total reboiler, the compositions of liquid and vapor streams that are transferred from the first column to the second column in DSLV are identical, in our example xB ) yB ) 0.5. These two streams are far from equilibrium. In the improved configuration shown in Figure 4, liquid and vapor streams in the bottom of the first column are in equilibrium (i.e., from eq 8: xM B ) 0.77 and the corresponding composition of vapor entering in the bottom of the first column is yB ) 0.94. The improved performance in the total vapor flow of the new configuration is not as surprising when the configurations in Figures 4 and 5 are compared to the SR and the SS configurations. The scheme in Figure 4 can be seen as a side rectifier where a portion of the binary liquid feed from one column to the other is vaporized and fed at the proper location. Thus, it is appropriate to think of this configuration as a side rectifier with a binary feed reboiler (SRFR). Similarly, the configuration in Figure 5 may be called a side stripper with the binary feed condenser (SSFC). Indeed, the calculations for the example problem when done for the SR configuration confirm the equivalence between the SR and the SRFR configurations. The minimum vapor flow generated in the reboiler of the SR configuration is found to be 1.46, which is the same as the total vapor flow for the SRFR configuration. The minimum vapor flow in the rectifying section of the column

receiving the ternary feed is the same for both the configurations. The thermodynamic efficiency of the SR configuration is, however, only 35.9%. Clearly, the improvement in the thermodynamic efficiency of the SRFR configuration as compared to that of the SR configuration results from the fact that only a fraction of the overall heat duty is supplied in the warmest reboiler (0.36 vs 1.46) and most of the heat duty is provided at a lower intermediate temperature. This efficiency improvement comes at the expense of additional (intermediate) reboiler, although total heat exchange area did not increase. Both the SRFR and the DSLV configurations use the same number of reboilers, condensers, and distillation column sections. Therefore, the reduced heat duty and the higher thermodynamic efficiency of the SRFR configuration make it quite attractive. However, as is shown by the example problem, the SRFR configuration requires more heat at the higher temperature of the bottom reboiler of the second column than the DSLV configuration (0.36 vs 0.17). In return, the SRFR requires less heat at the intermediate temperature than the DSLV configuration (1.10 vs 1.35). This may prompt one to conclude that the reduction in the total vapor flow for the SRFR configuration is achieved at the cost of additional higher temperature heat utility. However, a closer examination is required before any conclusion can be drawn. By writing a mass balance for the net amount of B which is transferred from the first column to the second column for each of the DSLV and SRFR configurations, it can be readily shown that the mole fraction of B in the liquid stream to the reboiler at the bottom of the first column is always higher for the SRFR configuration than for the DSLV configuration. For the example problem, the mole fraction of B in the liquid to the intermediate reboiler BC for the DSLV configuration is 0.5 and for the SRFR configuration it is 0.77. This implies that a lower temperature intermediate heat utility can be used for the SRFR configuration than for the DSLV configuration. Thus, as compared to the DSLV configuration, the SRFR configuration not only requires a lower amount of heat at the intermediate temperature but also does so at a lower temperature. The next logical step is to search for a scheme that would require the same amount of heat at the highest temperature of the bottom reboiler of the second column as for the DSLV configuration but where total heat duty would be the same as for the SR or the SRFR configuration. This could be useful when the highest temperature utility is quite expensive or if only limited quantities of it are available. The search for a successful scheme is satisfied by examining the use of an intermediate reboiler in the binary distillation column. It is well-known15 that in a conventional binary distillation column, the heat requirement in the bottom reboiler can be reduced by exactly the same amount of heat as that supplied to an intermediate reboiler; that is, with the use of an intermediate reboiler the total heat demand is unchanged but less of it is needed at the higher temperature of the bottom reboiler. In the SRFR configuration, the second column is a binary distillation column. This suggests that rather than vaporizing a portion of the liquid feed to the second column, an intermediate reboiler could be used. This leads to the side rectifier with intermediate reboiler (SRIR) scheme shown in Figure 6a. There are also other methods of


Figure 6. (a) Side rectifier with intermediate reboiler (SRIR); (b) side stripper with intermediate condenser (SSIC).

intermediate heat addition to a binary distillation column that could be applied to the SR.31,32 For the SRIR configuration in Figure 6a, the total heat duty is independent of the intermediate reboiler location and is the same as that for the SR configuration. However, the split of heat duty between the two reboilers depends on the location of the intermediate reboiler. As the location of the intermediate reboiler is moved down, the required quantity and the temperature of the intermediate heat utility go up and the amount of heat needed in the bottom reboiler decreases. This provides a degree of freedom to better match the available heat utilities with the heat supply to the distillation columns while maintaining the total heat requirements unchanged. Thus, with the SRIR configuration, it is now possible to have the same heat requirement at the highest temperature as that for the DSLV configuration while maintaining the total heat requirement at the SR level. However, it should be noted that there is only one location of the intermediate heat supply to the second column that would give the maximum thermodynamic efficiency. Whether that location corresponds to the vaporization of a portion of the liquid feed, as in the SRFR configuration, or an appropriately chosen intermediate reboiler location, as in the SRIR configuration, will depend to a large extent on the feed composition to the second column and the relative volatility between B and C. Recently, Agrawal and Herron32,33 developed heuristics for a conventional binary distillation column to answer questions such as when is an intermediate reboiler thermodynamically attractive and what is the proper location for the intermediate heat addition to maximize the thermodynamic efficiency? The heuristics could be applied to help in the selection between the SR, SRFR, and SRIR configurations. Following the evolution of the SRIR configuration, the SS configuration can be modified with an intermediate condenser. The side stripper with intermediate condenser (SSIC) configuration is shown in Figure 6b. An efficient choice will now have to be made between the SS, SSFC, and the SSIC configurations. Since the total heat requirement for the FC configuration is lowest of all the configurations, it may be attractive to improve its thermodynamic efficiency. A FC configuration with binary feed treatment (FCFT), that is, with binary vapor condensation and binary

liquid vaporization, is shown in Figure 7a. The FC configuration with the intermediate heat treatment (FCIT) is shown in Figure 7b. In the FCIT configuration, heat is removed from an intermediate location of the rectifying section producing A and heat is added at an intermediate location of the stripping section producing C. In both the configurations of Figure 7, heat is added at an intermediate temperature of a binary mixture BC and heat is removed at another intermediate temperature of a binary mixture AB. This will generally lead to a very efficient configuration; however, an efficiency higher than all the configurations in Figures 4-6 cannot be guaranteed. The reason being that, in all the configurations of Figures 4-6, heat is either added or removed at the temperature of the intermediate component B and this feature is missing from the FCFT and FCIT configurations. Therefore, an intermediate reboiler or a condenser must be added to the second column at the level where B is produced to guarantee the highest thermodynamic efficiency of all the configurations discussed so far. This will increase the total number of reboilers and condensers from four to five. However, through simulations it should be generally possible to identify the intermediate reboilers and condensers that contribute the most to the thermodynamic efficiency and eliminate one or two of the less valuable or more expensive reboilers and condensers. A Ternary Superstructure A superstructure is a general system containing all possible (known) configurations. Any particular configuration can be obtained from the superstructure by simple deletion of certain streams and/or distillation column sections. This concept was introduced by Sargent and Gaminibandara.23 They also introduced a superstructure for ternary distillation. However, the highly efficient configurations of Figures 4-7 are missing from their superstructure. Since the total number of reboilers and condensers in these configurations are no different than those of the configurations considered in earlier studies, it is important that a superstructure be developed which is capable of generating these configurations along with the earlier well-known structures. A new ternary superstructure is proposed in Figure 8. This superstructure contains not only as substruc-


Figure 7. Modification of the FC configuration by intermediate heat addition and intermediate heat removal: (a) FC system with feed treatment; (b) FC system with intermediate heat treatment.

Figure 8. Superstructure for ternary mixture separation.

tures all the new configurations discussed in Figures 4-7 but also the conventional structures of direct split, indirect split, and thermally coupled columns. The general system for ternary mixtures proposed by Sargent and Gaminibandara23 is also a substructure of this

superstructure. Any of these substructures can be easily obtained by eliminating appropriate column sections and/or streams. For example, the SRFR configuration can be derived by eliminating condenser AB and all the associated streams, section 4 and reboiler B of the AB column and section 6 of the BC column along with streams 30 and 40. Alternatively, feed to the reboiler BC could be stream 30 rather than a liquid stream from the BC column; this will be particularly needed when there is a mismatch between the composition of the liquid stream from the bottom of the prefractionating column and the liquid in the BC column with which it is mixed. In the ternary superstructure of Figure 8, the dotted streams 10, 20, 30, and 40 are not needed to derive the thermodynamically efficient structures discussed in Figures 4-7. However, some of them are needed to derive the conventional and the modified direct and indirect split configurations. For example, the conventional indirect split column arrangement is obtained by sending a portion of the vapor stream AB from the top of the prefractionator to the AB column, while the rest of this stream is sent as stream 10 to condenser AB where it is totally condensed and all of it is returned to the prefractionating column via stream 20. No liquid or vapor stream is withdrawn from the intermediate locations of the AB column. The AB column sections 1, 2, and 3 are combined into one section. Streams 30 and 40, reboiler BC and section 5 of the BC column, are also eliminated. There is no interconnecting stream between the AB and BC columns, and condenser B does not exist. Similarly, the modified indirect and direct split column schemes can also be derived.28 A potentially useful substructure of the ternary superstructure is shown in Figure 9. This structure is composite of the earlier discussed modified direct and indirect split configurations. The condenser AB is now a total condenser and reboiler BC is a total reboiler (with some possible purge stream if needed). The stream connections between the


Figure 9. Substructure from the ternary superstructure of Figure 8.

top of the prefractionating and the AB columns are the same as those in the modified indirect split configuration. Similarly, the stream connections between the bottom of the prefractionating and BC columns are the same as those in the modified direct split configuration. In this configuration, all of the vapor and liquid traffic between the prefractionating column and the AB and BC columns is in one direction and therefore should be easier to operate than the FC system. Furthermore, as both vapor and liquid streams are transferred from both ends of the prefractioning column to the next columns, it is expected that this configuration would provide good thermodynamic efficiency while retaining a reasonably low heat requirement. It is interesting to note that the ternary superstructure of Figure 8 also suggests some new modifications to the direct and indirect split configurations. These correspond to the use of partial reboiler BC or partial condenser AB. For example, in a direct split configuration, a portion of the liquid BC from the bottom of the prefractionating column can be sent to the BC column, while the other portion (stream 30) is sent to the partial reboiler BC. Some or all of the vapor phase of the twophase stream exiting reboiler BC is sent to the bottom of the prefractionating column (stream 40). The remaining portion of the two-phase stream is fed to the BC column. In this arrangement, it is possible to have two liquid feeds of different composition to the BC column. Analogous changes can be made for the indirect split using partial condenser AB. Such schemes are generally attractive when the relative volatility between the AB pair or the BC pair is sufficiently large; these are discussed in detail in another publication.30

There are some options that are not present in the superstructure of Figure 8. This is done to keep the superstructure simple; however, if needed, the missing options can be easily incorporated. The option in Figure 3, where the vapor at the bottom of the prefractionating column is provided by vaporizing a liquid from a couple of stages above the bottom, is not included. The multiple interconnecting streams (of different compositions) from the prefractionator to column AB or to column BC, as proposed by Glinos,17 are not shown. For a ternary liquid feed, the possibility of vaporizing a portion of this liquid feed by heat exchange against the vapor stream in condenser B or by a side vapor stream from section 5 of the BC column and then returning the vaporized stream as a separate feed to the prefractionating column is not included. Thus, the commercial configuration of the side rectifier with a low-pressure column to distill argon from air cannot be obtained from the superstructure of Figure 8. Incorporation of all these options would make the superstructure quite complex. While more intermediate reboilers and condensers can be used in the superstructure of Figure 8 to further improve the thermodynamic efficiency, it is usually difficult to justify them economically. In the proposed superstructure scheme, reboiler C at the bottom of the BC column and condenser A at the top of the AB column are always to be retained. However, the selection between reboiler BC, reboiler B, condenser B, and condenser AB will be situation-specific. Generally, one or two of these should be justifiable. Among the parameters influencing the decision are availability of proper utilities, capital and operating costs, and ease of operation. Extension to More Than Three Components The concepts discussed for ternary separation can be easily applied to four-component or more component mixtures. Several schemes to separate a four-component mixture into pure components are known.34 A fourcomponent superstructure with sequential distillation columns was suggested by Sargent and Gaminibandara.23 Recently, a superstructure using satellite columns has been proposed by Agrawal.25 It is equally easy to modify either of these superstructures. As an example, Figure 10 shows the modifications to the satellite column system. All the reboilers and condensers associated with mixtures are modified according to the ideas used in Figure 8 for a ternary mixture. While the modified reboilers and condensers associated with binary mixtures eliminate or minimize unnecessary mixing losses, the same is not true for the ternary mixtures encountered in Figure 10. For example, the chances that the composition of the vapor stream from the reboiler vaporizing the ternary liquid stream BCD would match the vapor composition at its feed point to the main column is quite remote. This would lead to mixing losses. It should be mentioned that the earlier distillation column schemes with boiling and condensing of ternary mixtures also have such mixing losses. Despite these mixing losses, the generalized four-component distillation scheme in Figure 10 is expected to provide more efficient substructures than the earlier satellite columns superstructure because the mixing losses due to vaporization and condensation of binary mixtures can be minimized. An alternative four-component distillation scheme derived by modification of the satellite columns super-


the ternary liquid stream containing B, C, and D from the B-producing satellite column is vaporized by the method shown in Figure 3. A portion of the descending liquid from this satellite column is vaporized and fed to the bottom of this column. The success of this method will depend on the availability of a side liquid draw with the required composition. It is hoped that such a vaporization would minimize the mixing loss due to mismatch in the compositions of the vapor exiting the reboiler and the vapor stream in the column that mixes with this vapor stream. However, as for the ternary scheme in Figure 3, the utility of such a method will be quite limited. Similarly the condenser for the vapor stream containing A, B, and C at the top of the C-producing satellite column is modified. Even though all the reboilers and condensers handling binary mixtures could also be similarly changed, they have been left unchanged. No detailed calculations were done to check the relative advantages/disadvantages of either of the schemes in Figures 10 and 11. Clearly, much more work is needed to derive any generalized conclusions. Conclusions

Figure 10. General system for four-component distillation.

Figure 11. Alternate general system for four-component distillation.

structure is shown in Figure 11. The only difference between Figures 10 and 11 is in the method of vaporization/condensation of the ternary streams. In Figure 11,

For distillation column schemes for the separation of ternary mixtures, incorporation of intermediate heat addition/removal at the intermediate temperatures of the binary mixtures improves their thermodynamic efficiency. Modifications by introducing these additional reboilers/condensers to the thermally coupled side column (SR and SS) configurations are suggested such that the total number of reboilers and condensers are the same as those in a direct or indirect split configuration. These modified schemes not only require the same lower total vapor flow rates as those for the original thermally coupled side column configurations but also provide higher thermodynamic efficiency (although at the expense of an additional reboiler). It is expected that their thermodynamic efficiency will always be higher than that of a corresponding direct or indirect split configuration. These new configurations also provide an additional degree of freedom to shift heat (cold) duty between the intermediate temperature reboiler (condenser) and the reboiler at the warmest (condenser at the coldest) temperature by changing the location of the intermediate reboiler (condenser). For a given application, this will allow the efficient use of an intermediate temperature heat (cold) utility whose temperature may be lower or higher than the corresponding intermediate heat (cold) utility needed for a direct (indirect) split configuration. The concepts are also extended to modify the fully coupled (FC) configuration (the FCFT and FCIT configurations) that should yield the lowest total vapor flow along with improved thermodynamic efficiencies. Finally, a new ternary superstructure that contains the thermodynamically more efficient structures as substructures is also proposed. This superstructure contains all the conventional as well as the new structures, including the modified direct and indirect split schemes. An attempt is also made to extend these concepts to distillation schemes separating four-component mixtures. Notation DS ) direct split FC ) fully coupled system

2074 Ind. Eng. Chem. Res., Vol. 38, No. 5, 1999 FCFT ) fully coupled system with feed treatment FCIT ) fully coupled system with intermediate heat treatment IS ) indirect split KB,BC ) equilibrium coefficient of component B in mixture BC V ) vapor flow rate, kmol/s q ) liquid fraction SR ) side rectifier SRFR ) side rectifier with feed reboiler SRIR ) side rectifier with intermediate reboiler SS ) side stripper SSFC ) side stripper with feed condenser SSIC ) side stripper with intermediate condenser z ) mole fraction in feed R ) relative volatility φ ) root of Underwood’s equation, eq 3 η ) thermodynamic efficiency, defined by eq 1 Subscripts A, B, C ) component A, B, C, or when used with V, section of the column where A, B, or C is produced L, V ) liquid and vapor connection between the columns Superscripts M ) feed to second column of SRFR * ) equilibrium

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Received for review August 11, 1998 Revised manuscript received February 10, 1999 Accepted February 11, 1999 IE980531K

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