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Synthesis of integrated distillation systems
European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.
59
Synthesis of Integrated Distillation Systems Jose A. Caballero , Juan A. Reyes-Labarta and Ignacio E. Grossmann *Department of Chemical Engineering. University of Alicante. Ap. Correos 99, E03080 Alicante SPAIN. Department of Chemical Engineering. Carnegie Mellon University. Pittsburg, PA, 15213, USA.
Abstract The paper presents a novel superstructure based optimization procedure for design a sequence of distillation columns for separating a non azeotropic n component mixture. The separation can be performed using from conventional to fully thermally coupled distillation sequences going through all the intermediate possibilities of partial thermal integration. A two stage procedure is proposed, in the first a feasible sequence of tasks is selected, with an approximation to the total annualized cost that, under some considerations, produces a lower bound to the total annualized cost. In the second stage the configuration in actual columns is selected among all the thermodynamically equivalent configurations. A case study is presented in order to illustrate the procedure.
1. Introduction The fully thermally coupled (PC) configuration has been known for over fifty years (Wright, 1949). Different theoretical studies has shown that thermally coupled configurations can save among 10 to 30% in total and operating costs (see for example, Glinos and Malone 1988 or Triantafillou and Smith, 1992). Petlyuk (Petlyuk et al, 1965) was the first in analyzing the PC system and found it thermodynamically attractive due to the reversible mixing of feeds with internal column streams. Consider a mixing consisting of three components A, B and C, where A is the lightest and C the heaviest. Por some mixtures, for instance when B is the major component and the split between A and B is as easy as the split between C and D, this configuration (Pigure 1) has an inherent thermal inefficiency (Schultz et al, 2002).
r ^
Molar
fraction
/r^ 1
AB
ABC
B in column
^ 2 .,-—"'" B in column
V l ^ B /'' ^ - ^
/ / Bottom
Trays
Top
Figure 1. Concentration profile for component B in a sequence AB/C A/B. Remix ofB occurs in column 1.
60 In the first column, the concentration of B reach a maximum at a tray near the bottom. On trays below this point, the amount of C continues increasing, diluting B. Energy has been using to separate B to a maximum purity but, due to B is not removed at this point B undergone a remixing and it is diluted till the concentration at which it is removed in the bottoms. This remixing is inherent to any separation that involve an intermediate boiling component, and the result can be generalized to a N component mixture. Halvorsen and Skogestad (2001) proved that the minimum energy consumption for a sequence of columns is always obtained with the FC configuration. Petlyuk and coworkers generalized the FC system for n number of components. They defined a FC system as a one with n(n-l) sections for a n component mixture, only one condenser and one reboiler for the entire system, all the components (except the most and least volatile) distributing between the top and the bottom of each column, and all of the product column that is composed of (n-1) binary separation columns built on top of each other. This definition has latter extended and generalized (Agrawal, 1996). In an FC system is not needed that all the products are produced by a main column, the number of column sections goes from (4n-6) -the minimum number of column section for a FC system- to n(n-l) and the condenser and reboiler do not necessarily belong to the same column. Although the total energy consumption is always lower in FC systems than in any other configuration, there are some drawbacks: The number of total sections increases with the reduction in the number of heat exchangers, increasing the total number of trays and then the total cost (in some cases compensated by the integration in a single shell). The energy must be supplied in the worst conditions, at the highest temperature in the reboiler and removed at the lowest temperature, preventing in most cases the use of utilities like medium or low pressure steam. Operation is more difficult due to the large number of interconnections among columns. As the knowledge of these systems increases and operational problems are being solved interest in thermally coupled systems is renewed. However, it is clear that from conventional systems (each column with a condenser and a reboiler) to fully thermally coupled systems there are a large number of possibilities, and the optimum is probably among them. Here we present mathematical programming base procedure for screening among these possibilities. It is a two stage procedure, in the first a sequence of tasks is selected, and in the second the best configuration of columns among those thermodynamically equivalent is selected. The problem addressed in this paper can be stated as follows: Given a number of components, that do not form azeotropes, to be separated into a predefined set of products. The objective is to find an appropriate and cost effective separation scheme. This scheme includes conventional columns, partially linked distillation systems -with any number of heat exchangers between 2 and 2(n-l)- that can produce prefractionators, sloppy splits, side columns etc. Without loss of generality, the products are listed in a decreasing order of volatilities.
2. Integrated Distillation Model Due to the nature of the problem there is not a one to one match between separation tasks and columns that perform a given separation. Even more, a given feasible sequence of separation tasks can be performed by different sequences of thermodynamically equivalent columns. In this paper we present a task based superstructure with intermediate characteristics between the pure State Task Network (STN) (Yeomans and Grossmann, 1999) in which all the separation tasks are explicitly enumerated, and a superstructure in which equipment is previously determined. Figure 2 shows the superstructure for a mixture of 5 components. Although the picture by itself
61 is not new (for example it corresponds to the classical Sargent and Gaminibandara structure (1976). Some important aspects must be remarked that are important at the modeling level. First, individual separation tasks are not considered explicitly. For instance, for the mixture ABCD we consider the most general approach "separate A from D" in which intermediate boiling compounds can or cannot distribute. However, at the level of relation among tasks it is important which separation has taken place. Second, if a group of compounds (state) do not exists in the final solution it is considered as a simple bypass in the superstructure See Figure 2. And third, heat exchangers are not explicitly included in the superstructure, but are considered at the modeling level. In particular, they appear in the final cost, the flow transfer among pseudo-columns (tasks) is very different if there is or there is not a heat exchanger and the presence of a heat exchanger associated to a final product is related to the minimum and maximum number of separation sections. These approach has proved very robust and computationally efficient.
'XX: State does not exist: Bypass.
State ABCDE, for instance, can produce the following separation tasks: A/BCDE; AB/BCDE: AB/CDE; ABC/BCDE ABC/CDE; ABC/DE; ABCD/BCDE; ABCD/CDE; ABCD/DE; ABCD/E
Figure 2. Superstructure for a mixture of 5 components. Note that if a state (group of components) do not exist then becomes in a bypass. Very important, and related to second point of previous paragraph is the question of how generating feasible sequences. Logical connectivity relationships are not enough. It is also convenient to forbid that a given separation can be produced twice, or a given state can be produced simultaneously by two rectifying or stripping sections. Although some authors (Rong and Kralawski, 2001) considered these possibilities they are always suboptimal from the point of view of energy, an it increases the total number of tasks. It could be justified if different concentrations of the same split are considered or if we are interested in some kind of multi-effect heat integration (in our approach, these constraints can be easily relaxed in order to allow these possibilities if desired). Other configurations like that proposed by Kaibel (1987) need more energy than other fully or partially thermally coupled, however due to the reduction in the number of sections it could be interesting in some cases. A set of logical relationships among tasks in terms of binary variables can be included in order to fulfill all these conditions. (Caballero and Grossmann, 2001). Operation conditions into the columns was calculated by Underwood, Fenske equations. However, any other set of equations including rigorous tray by tray calculations could be implemented. The conceptual procedure continue being the same and only the numerical performance would be affected. As an objective the total annualized cost (operating cost, annualized capital cost of columns and heat exchangers) is considered. Procedure proposed by Douglas (1988) has been implemented.
62 The conceptual model is conveniently represented using a disjunctive formulation as follows: min total annualized cost = Annualized Capital Cost + Operation costs s.t.
Underwood equations Fenske equations
V
Calculation Column Area
Bypass of Flows Capital Cost = 0
Capital Cost = fiD, P, N^^^y^ ) ^s Calculation of Qreb or Qcond Calculation of Utilities cost
Transfer of Liquid and Vapor
V
among columns.
Heat exchanger cost - f(Area,UyAT)
Qreb = Qcond = 0
Distillate or Bottom liquid at their buble point
Costs =0
^{z„W,)=True Where s is an index set making reference to the states in the superstructure, Zs is a Boolean variable that takes the value True if a given state exists, Ws is a Boolean variable that takes the value of True is a Heat exchanger associated to that state exists. And the last equation makes reference to the logical relationships among states (tasks) and heat exchangers in order to assure feasible separations. Remark that previous model is linear except for Underwood equations and those equations related to costs estimation. The model has proven to be reliable and computational efficient. Due to the task based approach, the total cost of columns is calculated assuming that a task can be considered a pseudo-column (each pseudo-column with their own diameter), this approach produces a lower bound to the total capital cost. The actual capital cost depends on the final configuration in actual columns. If the capital cost is not the dominant factor (and even in some cases if it is) for preliminary design the previous approach is good enough. With the optimal sequence of tasks it is possible to obtain the best possible rearrangement of these tasks in actual columns (Caballero y Grossmann 2002). In this second stage it is possible include control and operational constrains. Although this second part can be integrated in the model previously presented, due to the large number of thermodynamically equivalent configurations that some sequences of tasks can produce the increase of dimensionality of the problem do not justify it but in some special cases.
3. Case Study As an example we present the separation for a mixture of 5 hydrocarbons. In Table 1 basic data are presented.
63 Table 1. Basic data for example. Component n-Hexane n-Heptane n-Octane n-Nonane n-Decane Total flow Pressure
Feed composition (molar fraction) 02 0.1 0.2 0.2 0.3 200 kmol/h 2atm.
U= 800 W/m^ K Steam cost = 5.09 $/GJ Cold water cost= 0.19 $7GJ Recovery: 98% of heavy key and light key in each separation
The best sequence of tasks is presented in Figure 3a. The solution involve three reboilers and three condensers with a total of 12 column sections. If we do not take into account the possibility of divided wall columns, the minimum number of columns in which the different separation tasks can be performed is equal to n-1, in this case four columns. Taking into account that each thermal link (link between states without heat exchanger) produces two different possibilities of rearrangement of these separation tasks (Caballero and Grossmann 2002), for our solution there are 16 thermodynamically equivalent configurations. The best obtained solution is shown in Figure 3b. The total annualized cost of the best configuration obtained assuming that each separation task is pseudo-column was $1457487 that is a lower bound to the total cost. When we calculate the total annualized cost of the actual configuration -Figure 3b- this cost increases to $1571159, which is around 8% higher. /^r^ r - ^ c
^C2>-i^Q)^^ Figure 3. a) best sequence of tasks obtained, b) Best arrangement in actual columns. It is possible start an iterative procedure in which the previous result is an upper bound, and study the possibility of getting other configurations. Although it has not been presented here it is also possible consider the integration of some columns in a single shell with it is likely to produce some reductions in the investment cost. Note that each integration reduced by 4 the number of thermodynamically equivalent configurations. Note also that there are a good number of configurations with similar performance. The proposed procedure is flexible and it allows study in a easy way other configurations. Some final remarks: In the solution presented the vapor flows always from columns at higher to lower pressures in order to facilitate the operational problems associated to vapor transfer between columns. However, if the number of interconnections among columns makes difficult the control it is possible to implement some of the alternatives like those proposed by Agrawal (2000,2001) for reducing the flow transfer among
64 columns, or if possible try some integration of columns. This lasts points can be implemented at any of the two levels depending on the influence in the total cost.
4. References Agrawal, R., 1996; Synthesis of distillation column configurations for multicomponent distillation. Ind. Eng. Chem. Res. 35, 1059-1071. Agrawal, R., 2000. Thermally coupled distillation with reduced number of intercolumn vapor transfers. AIChE J. 46(11) 2198-2210. Agrawal, R., 2001; Multicomponent distillation columns with partitions and multiple reboilers and condensers . Ind. Eng. Chem. Res. 40. 4258-4266. Caballero, J.A.; Grossmann, I.E.; 2001; generalized Disjunctive programming model for the optimal synthesis of thermally linked distillation columns. Ind. Eng. Chem. Res. (40) 10,2260-2274. Caballero, J.A.; Grossmann, I.E.; 2002; Logic based methods for generating and optimizing thermally coupled distillation systems. Procedings ESCAPE 12, J. Grievnik, and J van Schijndel (Editors), 169-174. Douglas, J.M., 1988, Conceptual design of chemical processes. McGraw-Hill Chemical Engineering Series. Glinos, K, Malone, P., 1988; Optimality regions for complex columns alternatives in distillation systems. Trans IchemE, Part A. Chem. Eng. Res. Des. 66, 229. Halvorsen, I.J., 2001; Minimum energy requirements in complex distillation arrangements.; Ph.D. Thesis, under supervision of S. Skogestad. Norwegian Institute of Science and Technology. Kaibel, G.; 1987; Distillation columns with vertical partitions. Chem. Eng. Tech. 10. 92 Petlyuk, F.B; Platonov, V.M. and Slavinskii, D.M.; 1965. Thermodynamically optimal method of separating multicomponent mixtures. Int. Chem. Eng. 5, 555. Rong. B; Kraslawski, A.; 2001. Procedings ESCAPE 12, J. Grievnik, and J van Schijndel (Editors) (10) 319-324. Sargent, R.W.H. and Gaminibandara, K., 1976. Introduction: approaches to chemical process synthesis. In Optimization in Action (Dixon, L.C. ed) Academic Press, London. Schultz, M.A.; Steward, D.G.; Harris, J.M.; Rosenblum, S.P.; Shakur, M.S.; O'Brien, D. 2002; Reduce cost with dividing-wall columns. Chem. Eng. Prog. May, 6470. Triantafillou, C and Smith, R., 1992; The design and optimization of fully thermally coupled distillation columns. Trans IchemE, Part A. Chem. Eng. Res. Des. 70, 118. Wright, R.O., 1949 US Patent 2,471, 134. Yeomans, H.; Grossmann, I.E., 1999; A systematic modeling framework for of superstructure optimization in process synthesis. Comp. Chem. Eng. 23-709.
5. Acknowledgements Financial support provided by the "Ministerio de Ciencia y Tecnologia", under project PPQ2002-01734 is gratefully acknowledged.
59
Synthesis of Integrated Distillation Systems Jose A. Caballero , Juan A. Reyes-Labarta and Ignacio E. Grossmann *Department of Chemical Engineering. University of Alicante. Ap. Correos 99, E03080 Alicante SPAIN. Department of Chemical Engineering. Carnegie Mellon University. Pittsburg, PA, 15213, USA.
Abstract The paper presents a novel superstructure based optimization procedure for design a sequence of distillation columns for separating a non azeotropic n component mixture. The separation can be performed using from conventional to fully thermally coupled distillation sequences going through all the intermediate possibilities of partial thermal integration. A two stage procedure is proposed, in the first a feasible sequence of tasks is selected, with an approximation to the total annualized cost that, under some considerations, produces a lower bound to the total annualized cost. In the second stage the configuration in actual columns is selected among all the thermodynamically equivalent configurations. A case study is presented in order to illustrate the procedure.
1. Introduction The fully thermally coupled (PC) configuration has been known for over fifty years (Wright, 1949). Different theoretical studies has shown that thermally coupled configurations can save among 10 to 30% in total and operating costs (see for example, Glinos and Malone 1988 or Triantafillou and Smith, 1992). Petlyuk (Petlyuk et al, 1965) was the first in analyzing the PC system and found it thermodynamically attractive due to the reversible mixing of feeds with internal column streams. Consider a mixing consisting of three components A, B and C, where A is the lightest and C the heaviest. Por some mixtures, for instance when B is the major component and the split between A and B is as easy as the split between C and D, this configuration (Pigure 1) has an inherent thermal inefficiency (Schultz et al, 2002).
r ^
Molar
fraction
/r^ 1
AB
ABC
B in column
^ 2 .,-—"'" B in column
V l ^ B /'' ^ - ^
/ / Bottom
Trays
Top
Figure 1. Concentration profile for component B in a sequence AB/C A/B. Remix ofB occurs in column 1.
60 In the first column, the concentration of B reach a maximum at a tray near the bottom. On trays below this point, the amount of C continues increasing, diluting B. Energy has been using to separate B to a maximum purity but, due to B is not removed at this point B undergone a remixing and it is diluted till the concentration at which it is removed in the bottoms. This remixing is inherent to any separation that involve an intermediate boiling component, and the result can be generalized to a N component mixture. Halvorsen and Skogestad (2001) proved that the minimum energy consumption for a sequence of columns is always obtained with the FC configuration. Petlyuk and coworkers generalized the FC system for n number of components. They defined a FC system as a one with n(n-l) sections for a n component mixture, only one condenser and one reboiler for the entire system, all the components (except the most and least volatile) distributing between the top and the bottom of each column, and all of the product column that is composed of (n-1) binary separation columns built on top of each other. This definition has latter extended and generalized (Agrawal, 1996). In an FC system is not needed that all the products are produced by a main column, the number of column sections goes from (4n-6) -the minimum number of column section for a FC system- to n(n-l) and the condenser and reboiler do not necessarily belong to the same column. Although the total energy consumption is always lower in FC systems than in any other configuration, there are some drawbacks: The number of total sections increases with the reduction in the number of heat exchangers, increasing the total number of trays and then the total cost (in some cases compensated by the integration in a single shell). The energy must be supplied in the worst conditions, at the highest temperature in the reboiler and removed at the lowest temperature, preventing in most cases the use of utilities like medium or low pressure steam. Operation is more difficult due to the large number of interconnections among columns. As the knowledge of these systems increases and operational problems are being solved interest in thermally coupled systems is renewed. However, it is clear that from conventional systems (each column with a condenser and a reboiler) to fully thermally coupled systems there are a large number of possibilities, and the optimum is probably among them. Here we present mathematical programming base procedure for screening among these possibilities. It is a two stage procedure, in the first a sequence of tasks is selected, and in the second the best configuration of columns among those thermodynamically equivalent is selected. The problem addressed in this paper can be stated as follows: Given a number of components, that do not form azeotropes, to be separated into a predefined set of products. The objective is to find an appropriate and cost effective separation scheme. This scheme includes conventional columns, partially linked distillation systems -with any number of heat exchangers between 2 and 2(n-l)- that can produce prefractionators, sloppy splits, side columns etc. Without loss of generality, the products are listed in a decreasing order of volatilities.
2. Integrated Distillation Model Due to the nature of the problem there is not a one to one match between separation tasks and columns that perform a given separation. Even more, a given feasible sequence of separation tasks can be performed by different sequences of thermodynamically equivalent columns. In this paper we present a task based superstructure with intermediate characteristics between the pure State Task Network (STN) (Yeomans and Grossmann, 1999) in which all the separation tasks are explicitly enumerated, and a superstructure in which equipment is previously determined. Figure 2 shows the superstructure for a mixture of 5 components. Although the picture by itself
61 is not new (for example it corresponds to the classical Sargent and Gaminibandara structure (1976). Some important aspects must be remarked that are important at the modeling level. First, individual separation tasks are not considered explicitly. For instance, for the mixture ABCD we consider the most general approach "separate A from D" in which intermediate boiling compounds can or cannot distribute. However, at the level of relation among tasks it is important which separation has taken place. Second, if a group of compounds (state) do not exists in the final solution it is considered as a simple bypass in the superstructure See Figure 2. And third, heat exchangers are not explicitly included in the superstructure, but are considered at the modeling level. In particular, they appear in the final cost, the flow transfer among pseudo-columns (tasks) is very different if there is or there is not a heat exchanger and the presence of a heat exchanger associated to a final product is related to the minimum and maximum number of separation sections. These approach has proved very robust and computationally efficient.
'XX: State does not exist: Bypass.
State ABCDE, for instance, can produce the following separation tasks: A/BCDE; AB/BCDE: AB/CDE; ABC/BCDE ABC/CDE; ABC/DE; ABCD/BCDE; ABCD/CDE; ABCD/DE; ABCD/E
Figure 2. Superstructure for a mixture of 5 components. Note that if a state (group of components) do not exist then becomes in a bypass. Very important, and related to second point of previous paragraph is the question of how generating feasible sequences. Logical connectivity relationships are not enough. It is also convenient to forbid that a given separation can be produced twice, or a given state can be produced simultaneously by two rectifying or stripping sections. Although some authors (Rong and Kralawski, 2001) considered these possibilities they are always suboptimal from the point of view of energy, an it increases the total number of tasks. It could be justified if different concentrations of the same split are considered or if we are interested in some kind of multi-effect heat integration (in our approach, these constraints can be easily relaxed in order to allow these possibilities if desired). Other configurations like that proposed by Kaibel (1987) need more energy than other fully or partially thermally coupled, however due to the reduction in the number of sections it could be interesting in some cases. A set of logical relationships among tasks in terms of binary variables can be included in order to fulfill all these conditions. (Caballero and Grossmann, 2001). Operation conditions into the columns was calculated by Underwood, Fenske equations. However, any other set of equations including rigorous tray by tray calculations could be implemented. The conceptual procedure continue being the same and only the numerical performance would be affected. As an objective the total annualized cost (operating cost, annualized capital cost of columns and heat exchangers) is considered. Procedure proposed by Douglas (1988) has been implemented.
62 The conceptual model is conveniently represented using a disjunctive formulation as follows: min total annualized cost = Annualized Capital Cost + Operation costs s.t.
Underwood equations Fenske equations
V
Calculation Column Area
Bypass of Flows Capital Cost = 0
Capital Cost = fiD, P, N^^^y^ ) ^s Calculation of Qreb or Qcond Calculation of Utilities cost
Transfer of Liquid and Vapor
V
among columns.
Heat exchanger cost - f(Area,UyAT)
Qreb = Qcond = 0
Distillate or Bottom liquid at their buble point
Costs =0
^{z„W,)=True Where s is an index set making reference to the states in the superstructure, Zs is a Boolean variable that takes the value True if a given state exists, Ws is a Boolean variable that takes the value of True is a Heat exchanger associated to that state exists. And the last equation makes reference to the logical relationships among states (tasks) and heat exchangers in order to assure feasible separations. Remark that previous model is linear except for Underwood equations and those equations related to costs estimation. The model has proven to be reliable and computational efficient. Due to the task based approach, the total cost of columns is calculated assuming that a task can be considered a pseudo-column (each pseudo-column with their own diameter), this approach produces a lower bound to the total capital cost. The actual capital cost depends on the final configuration in actual columns. If the capital cost is not the dominant factor (and even in some cases if it is) for preliminary design the previous approach is good enough. With the optimal sequence of tasks it is possible to obtain the best possible rearrangement of these tasks in actual columns (Caballero y Grossmann 2002). In this second stage it is possible include control and operational constrains. Although this second part can be integrated in the model previously presented, due to the large number of thermodynamically equivalent configurations that some sequences of tasks can produce the increase of dimensionality of the problem do not justify it but in some special cases.
3. Case Study As an example we present the separation for a mixture of 5 hydrocarbons. In Table 1 basic data are presented.
63 Table 1. Basic data for example. Component n-Hexane n-Heptane n-Octane n-Nonane n-Decane Total flow Pressure
Feed composition (molar fraction) 02 0.1 0.2 0.2 0.3 200 kmol/h 2atm.
U= 800 W/m^ K Steam cost = 5.09 $/GJ Cold water cost= 0.19 $7GJ Recovery: 98% of heavy key and light key in each separation
The best sequence of tasks is presented in Figure 3a. The solution involve three reboilers and three condensers with a total of 12 column sections. If we do not take into account the possibility of divided wall columns, the minimum number of columns in which the different separation tasks can be performed is equal to n-1, in this case four columns. Taking into account that each thermal link (link between states without heat exchanger) produces two different possibilities of rearrangement of these separation tasks (Caballero and Grossmann 2002), for our solution there are 16 thermodynamically equivalent configurations. The best obtained solution is shown in Figure 3b. The total annualized cost of the best configuration obtained assuming that each separation task is pseudo-column was $1457487 that is a lower bound to the total cost. When we calculate the total annualized cost of the actual configuration -Figure 3b- this cost increases to $1571159, which is around 8% higher. /^r^ r - ^ c
^C2>-i^Q)^^ Figure 3. a) best sequence of tasks obtained, b) Best arrangement in actual columns. It is possible start an iterative procedure in which the previous result is an upper bound, and study the possibility of getting other configurations. Although it has not been presented here it is also possible consider the integration of some columns in a single shell with it is likely to produce some reductions in the investment cost. Note that each integration reduced by 4 the number of thermodynamically equivalent configurations. Note also that there are a good number of configurations with similar performance. The proposed procedure is flexible and it allows study in a easy way other configurations. Some final remarks: In the solution presented the vapor flows always from columns at higher to lower pressures in order to facilitate the operational problems associated to vapor transfer between columns. However, if the number of interconnections among columns makes difficult the control it is possible to implement some of the alternatives like those proposed by Agrawal (2000,2001) for reducing the flow transfer among
64 columns, or if possible try some integration of columns. This lasts points can be implemented at any of the two levels depending on the influence in the total cost.
4. References Agrawal, R., 1996; Synthesis of distillation column configurations for multicomponent distillation. Ind. Eng. Chem. Res. 35, 1059-1071. Agrawal, R., 2000. Thermally coupled distillation with reduced number of intercolumn vapor transfers. AIChE J. 46(11) 2198-2210. Agrawal, R., 2001; Multicomponent distillation columns with partitions and multiple reboilers and condensers . Ind. Eng. Chem. Res. 40. 4258-4266. Caballero, J.A.; Grossmann, I.E.; 2001; generalized Disjunctive programming model for the optimal synthesis of thermally linked distillation columns. Ind. Eng. Chem. Res. (40) 10,2260-2274. Caballero, J.A.; Grossmann, I.E.; 2002; Logic based methods for generating and optimizing thermally coupled distillation systems. Procedings ESCAPE 12, J. Grievnik, and J van Schijndel (Editors), 169-174. Douglas, J.M., 1988, Conceptual design of chemical processes. McGraw-Hill Chemical Engineering Series. Glinos, K, Malone, P., 1988; Optimality regions for complex columns alternatives in distillation systems. Trans IchemE, Part A. Chem. Eng. Res. Des. 66, 229. Halvorsen, I.J., 2001; Minimum energy requirements in complex distillation arrangements.; Ph.D. Thesis, under supervision of S. Skogestad. Norwegian Institute of Science and Technology. Kaibel, G.; 1987; Distillation columns with vertical partitions. Chem. Eng. Tech. 10. 92 Petlyuk, F.B; Platonov, V.M. and Slavinskii, D.M.; 1965. Thermodynamically optimal method of separating multicomponent mixtures. Int. Chem. Eng. 5, 555. Rong. B; Kraslawski, A.; 2001. Procedings ESCAPE 12, J. Grievnik, and J van Schijndel (Editors) (10) 319-324. Sargent, R.W.H. and Gaminibandara, K., 1976. Introduction: approaches to chemical process synthesis. In Optimization in Action (Dixon, L.C. ed) Academic Press, London. Schultz, M.A.; Steward, D.G.; Harris, J.M.; Rosenblum, S.P.; Shakur, M.S.; O'Brien, D. 2002; Reduce cost with dividing-wall columns. Chem. Eng. Prog. May, 6470. Triantafillou, C and Smith, R., 1992; The design and optimization of fully thermally coupled distillation columns. Trans IchemE, Part A. Chem. Eng. Res. Des. 70, 118. Wright, R.O., 1949 US Patent 2,471, 134. Yeomans, H.; Grossmann, I.E., 1999; A systematic modeling framework for of superstructure optimization in process synthesis. Comp. Chem. Eng. 23-709.
5. Acknowledgements Financial support provided by the "Ministerio de Ciencia y Tecnologia", under project PPQ2002-01734 is gratefully acknowledged.