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Simultaneous Optimization Model for Multicomponent Separation
0098-1354/94 $6.00+0.00 Copyright © 1993 Pergamon Press Ltd
Computers chem. Engng. Vol. 18. 8uppl.. pp. 8125-8129. 1994 Printed in Great Britain. All rights reserved
Simultaneous Optimization Model for Multicomponent Separation
Zorka Novak 1, Zdravko Kravanja 1 and Ignacio E. Grossmann 2 1 Dept. of Chern. Eng., University of Maribor, Slovenia 2 Dept. of Chern. Eng., Carnegie Mellon University, Pittsburgh, USA
ABSTRACT This paper describes the general optimization model for the simultaneous synthesis of heat integrated separation sequences and their heat exchanger networks (HEN). The model enables an optimal selection of the separation sequence, type of separation units, heat matches, operating conditions and design parameters. The synthesis of the separation sequence can be either homogeneous (the same type of separators) or heterogeneous (different types of separators) allowing sharp and/or nonsharp separations. The synthesis can be carried out either for a separation problem only or for a separation system together with its flowsheet. The model is formulated as a mixedinteger nonlinear problem (MINLP). The approach is illustrated by two examples: one of them presents the homogeneous synthesis of a sharp distillation sequence using a network separation superstructure and a more compact superstructure. The second example presents the application of the general optimization model in the synthesis of the heterogeneous separation system together with its flowsheet when the compact separation superstructure is used. KEYWORDS
Process synthesis; separation sequence optimization; structure; heat integration; MINLP optimization.
separation
super-
INTRODUCTION Although substantial progress in the synthesis of separation sequences has been recorded in the near past, it is clear that the general separation problem has not yet been solved. In addition, simultaneous optimization models for the synthesis of the separation problem have not been developed in the way which would allow efficient simultaneous flowsheet optimization. Al though recent work exhibits a considerably high level of simul tanei ty (e.g., Aggarwal and Floudas, 1990) and incorporates the heat integration option into model formulations (e.g., Andrecovich and Westerberg, 1985), the optimization models are based on several assumptions such as fixed feed condi tions or very poor or no pressure relations which make the models unsuitable for simultaneous flowsheet optimization. Besides, in most of the models only the homogeneous type of separation problems have been considered, usually as distillation-based separation problems. In this article the recent development of a simultaneous optimization model for the synthesis of the mul ticomponent separation sequence is presented. S125
S126
European Symposium on Computer Aided Process Engineering-3
The proposed model comprises a more general separation superstructure in which mathematical formulations of alternative separator units are embedded. The superstructure is proposed to be either homogeneous or heterogeneous allowing sharp and/or nonsharp separations. The superstructure is constructed by the network rather than by the tree representation. In addition, a more compact representation of the separation superstructure has been derived. The model is formulated as a mixed-integer nonlinear problem (MINLP). It enables simultaneous topology and parameter optimization of a separation problem. The former corresponds to the selection of the optimal separation sequence and the optimal type of separation units. The latter corresponds to the selection of optimal operating conditions (flow rates, compositions, temperatures and pressures) and design parameters. When the synthesis is carried out only for a separation problem, the objective is to find minimum total annual costs, whilst when it is performed for the separation system together with its flowsheet, the objective is to find maximum annual revenue of the overall process flowsheet. In order to reduce utility consumption, simultaneous heat integration including HEN costs can be performed. The general heat integration superstructure (Yee et ai., 1990) can be embedded into the separation and/or process flowsheet superstructure to optimize the combined superstructure simultaneously. The proposed approach has been implemented by the user friendly computer package PROSYN an MINLP process synthesizer (Kravanja and Grossmann, 1992). PROSYN is an implementation of the modelling and decomposition (M/D) strategy by Kocis and Grossmann (1989) and the outer approximation and equality relaxation algorithm (OA/ER) by Kocis and Grossmann (1987).
EXAMPLES The proposed approach is illustrated by several examples. To accomplish the task a short cut simultaneous model for a distillation unit is proposed. Light and heavy key components are allowed to distribute in the top and bottom products of the column. Feed conditions and key component recoveries are treated as the optimization variables. It should be noted that the operating pressure of the column is also treated as an optimization variable to achieve a higher degree of heat integration. Trade offs among component flow rate distribution, the operating pressure, actual reflux ratio, actual number of trays, and heat integrated condenser and reboiler duties are determined simultaneously. The model can be used for sharp or nonsharp separation tasks. The network superstructure of the sharp four-component separation is shown in Fig. 1. The network consists of 10 separators while fi ve different separation sequences are embedded into it. Six pumps are added to the superstructure to increase the inlet pressures of the columns. 10 binary variables are assigned to the distillation columns to denote their potential existence in MINLP formulation. The compact representation for the same separation task is shown in Fig. 2. It consists of 3 columns while 13 binary variables need to be assigned to the input streams of single choice mixers. In that way the selections of separation paths for sharp separation become possible. When the number of components exceeds 6 the number of binary variables needed for compact representation becomes smaller than for the network superstructure. To reduce significantly the NLP subproblems in the network superstructure the general modeling and decomposition scheme (Kravanja and Grossmann, 1990) is applied to decompose the initial NLP substructure problem. The NLP subproblems for the compact representation are considerably smaller, therefore the OA/ER algorithm can be applied directly without the decomposition scheme. In the second example the compact separation superstructure is embedded into the hydrodealkylation of toluene (HDA) process flowsheet followed by the simultaneous optimization of the combined superstructure.
European Symposium on Computer Aided Process Engineering-3
S127
A
B A
B C
D
c
o Fig. 1. The network superstructure for four-component mixture (D - distillation column, P - pump, S - splitter, M - mixer)
A
A
B C D
c
D
Fig. 2. The compact superstructure for four-component mixture Example 1
Synthesis of separation sequence without heat integration. The first example is a four component separation involving a multicomponent feed of: A (benzene), B (toluene), C (o-xylene) and D (diphenyl). It is desired to design an optimal distillation sequence that will provide four pure product streams at a minimum total annual cost composed of investment cost for the separators and HEN plus the operating cost based on utility consumption. The problem is formulated as an MINLP and solved with PROSYN on VAX-3100 The problem size for the network (compact) superstructure is: 10 (13) 0-1 variables, 811 (759) continuous variables and 881 (773) constraints of which 146 (45) are nonlinear equations. The optimal sequence is found in the second iteration after 270 s of CPU time for the network superstructure and in the first iteration after 95 s of CPU time for the compact superstructure. The solution yields a cost of 8,46 M$/yr and is shown in Fig.3. The abbreviations in Fig.3 are referred to the compact superstructure in Fig. 2. CACE 18 Suppl-K
SI28
European Symposium on Computer Aided Process Engineering-3
Synthesis of heat integrated separation sequence simultaneously with its HEN. In this example, both the network and the compact superstructures are merged with the general superstructure for heat integration and HEN synthesis (Yee et aI., 1990) followed by the optimization of the combined superstructures. In that way the synthesis of the heat integrated distillation sequence and corresponding HEN is performed simultaneously. 10 additional binary variables are needed for the network superstructure when the heat integration model is included into synthesis to denote the potential existence of heat matches. By using the compact superstructure the number of additional binary variables is only 18. The optimal topology is found in the fifth iteration after 145 min of CPU time for the network superstructure and in the tenth iteration after 210 min of CPU time for the compact representation. The optimal heat integrated sequence has the total annual cost of 1,40 M$/yr and is shown in Fig.4. The operating pressure of column AB/CD is raised from 1 bar to 3 bar while the pressures of the other two columns are kept at the level of 1 bar. It is obvious that the compact superstructure yields a much smaller optimization problem than the network superstructure. However, the convergence of the OAiER algorithm during the optimization of the compact superstructure is slower because its initialization scheme is weaker and nonconvexities involved are more severe than in the case of the network superstructure.
A
B C D
' - - -...... D
Fig. 3. Optimal distillation sequence without heat integration (C - condenser, R - reboiler, CW - cooling water, LPS - low pressure steam, MPS - medium pressure steam, HPS - high pressure steam)
A B C D
Fig. 4. Optimal heat integrated distillation sequence Example 2 In this example, the simultaneous optimization of the entire process together with its heterogeneous separation system is performed through an MINLP model. The base process flowsheet selected is the optimal HDA process flowsheet structure found by Kocis and Grossmann (1989). This flowsheet is extended with the generalized separation superstructure (Fig. 5). At this stage the separation units for particular separation tasks are selected using heuristics. The problem is solved using the compact representation of the distillation superstructure for three components. The objective function by Kocis and Grossmann (1989) is extended with the HEN investment cost and utility cost for condensers and reboilers. The optimal distillation sequence has the separation of benzene from toluene and diphenyl (01) followed by the separation of toluene from diphenyl (02). The annual revenue of the overall
S129
European Symposium on Computer Aided Process Engineering-3
process flowsheet without heat integration and with sequentially evaluated HEN cost is found to be at 2,87 M$/yr. The synthesis is repeated with simultaneous consideration of heat integration and HEN cost (Yee et al., 1990). MINLP problem size is: 18 0-1 variables, 1093 continuous variables and 1073 constraints of which 95 are nonlinear equations. Annual revenue is increased to 4,98 M$/yr. All the heating requirements for the reactor feed, the reboiler of 01 and the reboiler of stabilizing column are supplied by the quenched reactor outlet stream. It should be noted, that in the suboptimal solution (4,97 M$/yr) the hot utility for the reboiler of 02 is further reduced by heat integration with the reactor outlet and condenser of 01. Thus, the consumption of hot utilities is reduced to zero.
Membrane separator Flash stabilizing column Distillation column H2 / eH, •
Benzene / Toluene / Unit Diphenyl Task
Fig. 5. Flowsheet structure for HOA process extended with the generalized separation superstructure CONCLUSIONS
The example problems show very clearly the importance of optimizing separation systems simultaneously with heat integration systems as well as with the synthesis of the overall flowsheets. The proposed approach is an attempt to develop an advanced and more general separation model that can represent real and complex engineering problems. It is also an attempt to find out how to systematically build a separation superstructure as part of a more general flowsheet superstructure. REFERENCES
Aggarwal A. and C.A. Floudas (1990). Synthesis of general distillation sequences - nonsharp separations. Computers chem. Engng, 14, 631-653. Andrecovich M.J. and A.W. Westerberg (1985). An MILP formulation for heatintegrated distillation sequences synthesis. AIChE Journal, 31, 1461-1474. Kocis G.R. and I.E. Grossmann (1987). Relaxation strategy for the structural optimization of process flowsheets. Ind. Eng. Chem. Res., 26, 1869-1880. Kocis G.R. and I.E. Grossmann (1989). A modelling and decomposition strategy for the MINLP optimization of process flowsheets. Computers chem. Engng, 13, 797-819. Kravanja 2. and I.E. Grossmann (1990). PROSYN-an MINLP process synthesizer. Computers chem. Engng, 14, 1363-1378. KravanJa 2. and I.E. Grossmann (1992). PROSYN - an automated topology and parameter process synthesizer. ESCAPE-2, 5-7 October 1992, Touluse, France, Supplement to Computers chem. Engng, 17, S87-S94. Vee T.F., I.E. Grossmann and 2. Kravanja (1990). Simultaneous optimization models for heat integration-III. Process and heat exchanger network optimization. Computers chem. Engng, 14, 1185-1200.
Computers chem. Engng. Vol. 18. 8uppl.. pp. 8125-8129. 1994 Printed in Great Britain. All rights reserved
Simultaneous Optimization Model for Multicomponent Separation
Zorka Novak 1, Zdravko Kravanja 1 and Ignacio E. Grossmann 2 1 Dept. of Chern. Eng., University of Maribor, Slovenia 2 Dept. of Chern. Eng., Carnegie Mellon University, Pittsburgh, USA
ABSTRACT This paper describes the general optimization model for the simultaneous synthesis of heat integrated separation sequences and their heat exchanger networks (HEN). The model enables an optimal selection of the separation sequence, type of separation units, heat matches, operating conditions and design parameters. The synthesis of the separation sequence can be either homogeneous (the same type of separators) or heterogeneous (different types of separators) allowing sharp and/or nonsharp separations. The synthesis can be carried out either for a separation problem only or for a separation system together with its flowsheet. The model is formulated as a mixedinteger nonlinear problem (MINLP). The approach is illustrated by two examples: one of them presents the homogeneous synthesis of a sharp distillation sequence using a network separation superstructure and a more compact superstructure. The second example presents the application of the general optimization model in the synthesis of the heterogeneous separation system together with its flowsheet when the compact separation superstructure is used. KEYWORDS
Process synthesis; separation sequence optimization; structure; heat integration; MINLP optimization.
separation
super-
INTRODUCTION Although substantial progress in the synthesis of separation sequences has been recorded in the near past, it is clear that the general separation problem has not yet been solved. In addition, simultaneous optimization models for the synthesis of the separation problem have not been developed in the way which would allow efficient simultaneous flowsheet optimization. Al though recent work exhibits a considerably high level of simul tanei ty (e.g., Aggarwal and Floudas, 1990) and incorporates the heat integration option into model formulations (e.g., Andrecovich and Westerberg, 1985), the optimization models are based on several assumptions such as fixed feed condi tions or very poor or no pressure relations which make the models unsuitable for simultaneous flowsheet optimization. Besides, in most of the models only the homogeneous type of separation problems have been considered, usually as distillation-based separation problems. In this article the recent development of a simultaneous optimization model for the synthesis of the mul ticomponent separation sequence is presented. S125
S126
European Symposium on Computer Aided Process Engineering-3
The proposed model comprises a more general separation superstructure in which mathematical formulations of alternative separator units are embedded. The superstructure is proposed to be either homogeneous or heterogeneous allowing sharp and/or nonsharp separations. The superstructure is constructed by the network rather than by the tree representation. In addition, a more compact representation of the separation superstructure has been derived. The model is formulated as a mixed-integer nonlinear problem (MINLP). It enables simultaneous topology and parameter optimization of a separation problem. The former corresponds to the selection of the optimal separation sequence and the optimal type of separation units. The latter corresponds to the selection of optimal operating conditions (flow rates, compositions, temperatures and pressures) and design parameters. When the synthesis is carried out only for a separation problem, the objective is to find minimum total annual costs, whilst when it is performed for the separation system together with its flowsheet, the objective is to find maximum annual revenue of the overall process flowsheet. In order to reduce utility consumption, simultaneous heat integration including HEN costs can be performed. The general heat integration superstructure (Yee et ai., 1990) can be embedded into the separation and/or process flowsheet superstructure to optimize the combined superstructure simultaneously. The proposed approach has been implemented by the user friendly computer package PROSYN an MINLP process synthesizer (Kravanja and Grossmann, 1992). PROSYN is an implementation of the modelling and decomposition (M/D) strategy by Kocis and Grossmann (1989) and the outer approximation and equality relaxation algorithm (OA/ER) by Kocis and Grossmann (1987).
EXAMPLES The proposed approach is illustrated by several examples. To accomplish the task a short cut simultaneous model for a distillation unit is proposed. Light and heavy key components are allowed to distribute in the top and bottom products of the column. Feed conditions and key component recoveries are treated as the optimization variables. It should be noted that the operating pressure of the column is also treated as an optimization variable to achieve a higher degree of heat integration. Trade offs among component flow rate distribution, the operating pressure, actual reflux ratio, actual number of trays, and heat integrated condenser and reboiler duties are determined simultaneously. The model can be used for sharp or nonsharp separation tasks. The network superstructure of the sharp four-component separation is shown in Fig. 1. The network consists of 10 separators while fi ve different separation sequences are embedded into it. Six pumps are added to the superstructure to increase the inlet pressures of the columns. 10 binary variables are assigned to the distillation columns to denote their potential existence in MINLP formulation. The compact representation for the same separation task is shown in Fig. 2. It consists of 3 columns while 13 binary variables need to be assigned to the input streams of single choice mixers. In that way the selections of separation paths for sharp separation become possible. When the number of components exceeds 6 the number of binary variables needed for compact representation becomes smaller than for the network superstructure. To reduce significantly the NLP subproblems in the network superstructure the general modeling and decomposition scheme (Kravanja and Grossmann, 1990) is applied to decompose the initial NLP substructure problem. The NLP subproblems for the compact representation are considerably smaller, therefore the OA/ER algorithm can be applied directly without the decomposition scheme. In the second example the compact separation superstructure is embedded into the hydrodealkylation of toluene (HDA) process flowsheet followed by the simultaneous optimization of the combined superstructure.
European Symposium on Computer Aided Process Engineering-3
S127
A
B A
B C
D
c
o Fig. 1. The network superstructure for four-component mixture (D - distillation column, P - pump, S - splitter, M - mixer)
A
A
B C D
c
D
Fig. 2. The compact superstructure for four-component mixture Example 1
Synthesis of separation sequence without heat integration. The first example is a four component separation involving a multicomponent feed of: A (benzene), B (toluene), C (o-xylene) and D (diphenyl). It is desired to design an optimal distillation sequence that will provide four pure product streams at a minimum total annual cost composed of investment cost for the separators and HEN plus the operating cost based on utility consumption. The problem is formulated as an MINLP and solved with PROSYN on VAX-3100 The problem size for the network (compact) superstructure is: 10 (13) 0-1 variables, 811 (759) continuous variables and 881 (773) constraints of which 146 (45) are nonlinear equations. The optimal sequence is found in the second iteration after 270 s of CPU time for the network superstructure and in the first iteration after 95 s of CPU time for the compact superstructure. The solution yields a cost of 8,46 M$/yr and is shown in Fig.3. The abbreviations in Fig.3 are referred to the compact superstructure in Fig. 2. CACE 18 Suppl-K
SI28
European Symposium on Computer Aided Process Engineering-3
Synthesis of heat integrated separation sequence simultaneously with its HEN. In this example, both the network and the compact superstructures are merged with the general superstructure for heat integration and HEN synthesis (Yee et aI., 1990) followed by the optimization of the combined superstructures. In that way the synthesis of the heat integrated distillation sequence and corresponding HEN is performed simultaneously. 10 additional binary variables are needed for the network superstructure when the heat integration model is included into synthesis to denote the potential existence of heat matches. By using the compact superstructure the number of additional binary variables is only 18. The optimal topology is found in the fifth iteration after 145 min of CPU time for the network superstructure and in the tenth iteration after 210 min of CPU time for the compact representation. The optimal heat integrated sequence has the total annual cost of 1,40 M$/yr and is shown in Fig.4. The operating pressure of column AB/CD is raised from 1 bar to 3 bar while the pressures of the other two columns are kept at the level of 1 bar. It is obvious that the compact superstructure yields a much smaller optimization problem than the network superstructure. However, the convergence of the OAiER algorithm during the optimization of the compact superstructure is slower because its initialization scheme is weaker and nonconvexities involved are more severe than in the case of the network superstructure.
A
B C D
' - - -...... D
Fig. 3. Optimal distillation sequence without heat integration (C - condenser, R - reboiler, CW - cooling water, LPS - low pressure steam, MPS - medium pressure steam, HPS - high pressure steam)
A B C D
Fig. 4. Optimal heat integrated distillation sequence Example 2 In this example, the simultaneous optimization of the entire process together with its heterogeneous separation system is performed through an MINLP model. The base process flowsheet selected is the optimal HDA process flowsheet structure found by Kocis and Grossmann (1989). This flowsheet is extended with the generalized separation superstructure (Fig. 5). At this stage the separation units for particular separation tasks are selected using heuristics. The problem is solved using the compact representation of the distillation superstructure for three components. The objective function by Kocis and Grossmann (1989) is extended with the HEN investment cost and utility cost for condensers and reboilers. The optimal distillation sequence has the separation of benzene from toluene and diphenyl (01) followed by the separation of toluene from diphenyl (02). The annual revenue of the overall
S129
European Symposium on Computer Aided Process Engineering-3
process flowsheet without heat integration and with sequentially evaluated HEN cost is found to be at 2,87 M$/yr. The synthesis is repeated with simultaneous consideration of heat integration and HEN cost (Yee et al., 1990). MINLP problem size is: 18 0-1 variables, 1093 continuous variables and 1073 constraints of which 95 are nonlinear equations. Annual revenue is increased to 4,98 M$/yr. All the heating requirements for the reactor feed, the reboiler of 01 and the reboiler of stabilizing column are supplied by the quenched reactor outlet stream. It should be noted, that in the suboptimal solution (4,97 M$/yr) the hot utility for the reboiler of 02 is further reduced by heat integration with the reactor outlet and condenser of 01. Thus, the consumption of hot utilities is reduced to zero.
Membrane separator Flash stabilizing column Distillation column H2 / eH, •
Benzene / Toluene / Unit Diphenyl Task
Fig. 5. Flowsheet structure for HOA process extended with the generalized separation superstructure CONCLUSIONS
The example problems show very clearly the importance of optimizing separation systems simultaneously with heat integration systems as well as with the synthesis of the overall flowsheets. The proposed approach is an attempt to develop an advanced and more general separation model that can represent real and complex engineering problems. It is also an attempt to find out how to systematically build a separation superstructure as part of a more general flowsheet superstructure. REFERENCES
Aggarwal A. and C.A. Floudas (1990). Synthesis of general distillation sequences - nonsharp separations. Computers chem. Engng, 14, 631-653. Andrecovich M.J. and A.W. Westerberg (1985). An MILP formulation for heatintegrated distillation sequences synthesis. AIChE Journal, 31, 1461-1474. Kocis G.R. and I.E. Grossmann (1987). Relaxation strategy for the structural optimization of process flowsheets. Ind. Eng. Chem. Res., 26, 1869-1880. Kocis G.R. and I.E. Grossmann (1989). A modelling and decomposition strategy for the MINLP optimization of process flowsheets. Computers chem. Engng, 13, 797-819. Kravanja 2. and I.E. Grossmann (1990). PROSYN-an MINLP process synthesizer. Computers chem. Engng, 14, 1363-1378. KravanJa 2. and I.E. Grossmann (1992). PROSYN - an automated topology and parameter process synthesizer. ESCAPE-2, 5-7 October 1992, Touluse, France, Supplement to Computers chem. Engng, 17, S87-S94. Vee T.F., I.E. Grossmann and 2. Kravanja (1990). Simultaneous optimization models for heat integration-III. Process and heat exchanger network optimization. Computers chem. Engng, 14, 1185-1200.