- Email: [email protected]
A General Framework for Process Synthesis, Integration and Intensification
Mario R. Eden, Marianthi Ierapetritou and Gavin P. Towler (Editors) Proceedings of the 13th International Symposium on Process Systems Engineering – PSE 2018 July 1-5, 2018, San Diego, California, USA © 2018 Elsevier B.V. All rights reserved. https://doi.org/10.1016/B978-0-444-64241-7.50069-0
A General Framework for Process Synthesis, Integration and Intensification Salih Emre Demirel, Jianping Li, M. M. Faruque Hasan* Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77845, USA. *Corresponding Author Email: [email protected].
Abstract Block-based superstructure (Demirel et al., 2017; Li et al., 2017) offers advantages over classical unit operation-based process synthesis approaches as it leverages upon building blocks to represent different physicochemical phenomena, processing tasks and equipment configurations. In this work, we extend this approach to demonstrate that the same block superstructure representation can be used to perform simultaneous synthesis, integration and intensification in a unified framework. The block-based representation also enables automatic generation of intensified flowsheets without a priori postulation of connectivity. Moreover, it is generic enough to be reduced to various process integration network problems, such as heat exchanger networks, fuel gas networks, water networks, etc. A literature example is used to demonstrate the benefits of block superstructure for the particular case of flowsheet generation and heat exchanger network synthesis (HENS). Keywords: Block Superstructure, Process Synthesis, Intensification, Integration.
1. Introduction Optimization-based process synthesis provides a systematic pathway for identifying optimal process flowsheets from numerous alternatives. However, most synthesis methods are currently limited in scope for “out-of-the-box” design solutions as they require pre-postulated superstructures. This also prohibits innovative equipment design which plays a critical role in process intensification (Stankiewicz and Moulijn, 2000). To this end, we have proposed building block superstructure (Demirel et al., 2017; Li et al., 2017) which eliminates the need for pre-specified equipment types, and automates the search for intensified process alternatives. In this work, further benefits of the building block superstructure are presented via extending the formulation to include simultaneous heat integration and to form a comprehensive framework for intensified conceptual process design. As the proposed superstructure automatically generates the flowsheet alternatives without any a priori information on the final flowsheet, position and the identity (i.e. hot/cold) of the integrated streams are not known beforehand. Accordingly, proposed formulation is for simultaneous process synthesis and heat integration network synthesis with unclassified process streams. This opens up the potential of utilizing the block superstructure as a general framework for process synthesis, heat integration and intensification. The benefits of the proposed approach is demonstrated via a literature example and it is shown that significant advantages can be obtained by utilizing building block superstructure in conceptual process design.
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2. Block Superstructure in a Grid Formation Block superstructure is shown in Figure 1. Here, each block can be used to represent different chemical phenomena, tasks, materials and equipment. A detailed discussion on how to use building blocks to represent various phenomena are given in Demirel et al. (2017). Each block is connected with neighbouring blocks via bidirectional inter-block streams. Bidirectional flow representation enables incorporation of the recycle connections into the superstructure. Furthermore, heater/cooler and expander/compressor equipment are positioned on each stream so as to quantify the utility requirements in the superstructure and to consider operating and capital costs for these equipment. Each block can also have feed and product streams to facilitate interaction with external environment. j=1
j=2
j=J-1
j=J
i=1
i=2
i=I-1
i=I
Figure 1. A schematic of the block superstructure. With this representation, many process synthesis superstructures can be incorporated into the block superstructure. An example superstructure taken from literature (Kong et al., 2017) and its block superstructure representation are illustrated in Figure 2. Here, reactors are represented as single blocks while separators are represented via block boundaries between two blocks to indicate the position of the separated stream. 9
10
a)
3
2
1
5
CSTR1
CSTR2
6
j=2
1 Feed
SEP1
4
j=1
b)
8
2
CSTR1 CSTR2
i=1
7
10
11
7
12
13
8 SEP1
i=2
CSTR3
j=3
27 Product
9
23 27
22 SEP5
19
14
SEP4
SEP2
21
Heat 12
15
i=3
20 24
16 25
13
18
i=4
26
18
SEP 3
26
SEP3
17
11
CSTR3
13
SEP 2 SEP 4 SEP 5 Waste 25
15 27 15
27 Product
Figure 2. Superstructure representations (a) unit-operation based, (b) block based.
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Different process integration networks can be also included in the same superstructure representation. Each stream contains a heater/cooler and the identity of the stream (i.e. hot or cold) and corresponding utility consumption can be determined via an energy balance around each stream. If the utility requirement of a hot and cold stream at two different positions are the same, then they can be integrated to each other. If no such stream available, then the heating/cooling requirement is satisfied via external utilities. This is illustrated in Figure 3a. Although each stream is allowed to match with any other stream in the superstructure, these matches can be restricted to certain positions to yield the same superstructure with the one given by Yee and Grossmann (1990), in which case, each column represents one stage. In Figure 3b, this is illustrated for 2 hot and 2 cold streams. Stream splitting can also be achieved via increasing the number of rows that a stream can go through. For instance, if all the streams in Figure 3b can go through splitting, then 8×5 superstructure with each stream occupying two rows would be used.
(a)
j=1
j=2
(b)
j=3
j=1
j=2
j=3
j=4
j=5
H1 i=1
i=1
H2 i=2
i=2 C1 i=3
i=3
C2
i=4
Cold utility
Hot utility
Figure 3. Heat exchanger network representation using block superstructure.
3. Superstructure Model for Synthesis, Heat Integration and Intensification The overall model for process synthesis, integration and intensification is based on a single mixed integer nonlinear programming (MINLP) and summarized below. Model contains block superstructure constraints for generating the process flowsheet and HENS constraints for determining the corresponding HEN.
௫ǡ௫ᇱǡ௭ǡ௭ᇱǡ௬ǡ௪
݂ሺݔǡ ݔᇱ ǡ ݖǡ ݖԢሻ ݄ሺݕǡ ݓሻ
(1)
݃ǡ ሺݔǡ ݔԢሻ ൌ Ͳ݅ ܫ אǡ ݆ ܬ אǡ ݃ᇱ ǡǡௗ ሺݔǡ ݔԢሻ ൌ Ͳ݅ ܫ אǡ ݆ ܬ אǡ ݀ ܦ א
(2)
ݍǡ ሺݖሻ Ͳ݅ ܫ אǡ ݆ ܬ אǡ ݍᇱ ǡǡௗ ሺݖԢሻ Ͳ݅ ܫ אǡ ݆ ܬ אǡ ݀ ܦ א
(3)
ݎǡ ሺݔǡ ݔԢǡ ݖሻ Ͳ݅ ܫ אǡ ݆ ܬ אǡ
(4)
ݎԢǡǡௗ ሺݔǡ ݔԢǡ ݖԢሻ Ͳ݅ ܫ אǡ ݆ ܬ אǡ ݀ ܦ א
ܩǡᇱ ሺݔԢǡ ݓሻ ൌ Ͳ݈ǡ ݈ ᇱ ݈ܮ א൏ ݈Ԣ
(5)
ܳ ሺݕሻ Ͳ݈ ܮ א
(6) ᇱ
ܴǡᇱ ሺݓǡ ݕሻ Ͳ݈ǡ ݈ ݈ܮ א൏ ݈Ԣ ݔԢ ݔᇱ ݔᇱ ݔ ݔ ݔ ݓ ݓ ݓ ܴ א ݔூൈ ǡ ݔᇱ ܴ אூൈൈ ǡ ܴ א ݓൈ ݖൌ ሼͲǡͳሽூൈ ݖᇱ ൌ ሼͲǡͳሽூൈൈ ݕൌ ሼͲǡͳሽൈ
(7)
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The overall superstructure model is comprised of objective function, Eq.(1), which minimizes the annualized cost while considering operating and capital cost for the process, i.e. ݂ሺݔǡ ݔᇱ ǡ ݖǡ ݖԢሻ, and corresponding heat exchanger network, i.e. ݄ሺݕǡ ݓሻ, process related constraints Eqs.(2)-(4), and HENS model constraints Eqs.(5)-(7). Each block is designated with its position in the superstructure as ܤǡ , in which ݅ ൌ ͳǡ ǥ ǡ ܫ and ݆ ൌ ͳǡ ǥ ǡ ܬare row and column indices, respectively. There are mainly two type of variables in the superstructure model: block, i.e. ݔǡ ݖ, and boundary, i.e. ݔԢǡ ݖԢ, variables. Block variables, for instance, include ܲǡ and ܶǡ which stands for block pressure and temperature, respectively. Boundary variables, on the other hand, are defined to ௦ in represent flow rate of the interblock streams, ܨǡǡௗ , and stream temperatures, ܶǡǡௗ which ݀ ൌ ሼͳǡʹሽ designates the orientation of the boundary variables as horizontal (݀ ൌ ͳ) or vertical (݀ ൌ ʹ). While block binary variables,ݖ, are used to assign reaction related phenomena to the blocks, boundary binary variables, ݖԢ, are used to assign separation related phenomena or operation to the boundaries in the superstructure. In process related constraints, Eqs.(2) indicate block material and energy balances and stream energy balances, Eqs.(3) designate logical constraints, and Eqs.(4) relate continuous and binary variables. In the HENS model, block indices are mapped into a single index, ݅ǡ ݆ǡ ݀ ՜ ݈ where ݈ ൌ ͳǡ ǥ ǡ ܮis an ordered set and contains all the streams in the superstructure, i.e. ܮൌ ʹ ൈ ܫൈ ܬ. Note that, as the model is posed as a simultaneous synthesis and heat integration model, and the identity of the streams, i.e. hot/cold, in the superstructure are not known beforehand, binary variables are used to determine stream identities. Accordingly, HENS model is similar to the one proposed by Yee and Grossmann (1990) except that it is extended for unclassified process streams. While continuous variables,ݓ, are used to represent the heat duty for each matching stream in the superstructure and determine approach temperatures for these matches, binary variables, ݕ, are used to determine the stream matches within the superstructure, and classifying streams as hot or cold. In HENS model related constraints, Eq. (5) stands for heat balances for each stream, Eq. (6) designates logical constraints for determining the existence of a match and classification of a stream, and Eq. (7) relates HENS model binary variables with continuous variables.
4. Case Study An example problem adapted from Kong et al. (2017) is used to demonstrate the use of block superstructure for automatic flowsheet generation first and, then for determining its corresponding HEN. The original superstructure given by Kong et al. (2017) and its block representation is given in Figure 2. There are four components in the process: A and B are used as raw materials to produce C (R1: A + B ՜ C), which is further utilized in a second reaction to obtain the final product D (R2: C ՞ D). There are two isothermal reactor alternatives for R1: CSTR1 (500 K) and CSTR2 (400 K). R2 is an equilibrium reaction carried out in an isothermal equilibrium reactor: CSTR3 (330-400 K). There are five separator alternatives. While Sep1 (430 K) is used to separate C from R1 reactants, Sep2-5 are used to separate product D from C. Note that Sep1 and CSTR3 requires hot utility. The aim of the problem is to synthesize a process for maximizing the total annual profit considering product revenue, unit capital costs and utility costs. All the equipment parameters along with their cost parameters are taken from Kong et al. (2017). First, the problem is solved via fixing the binary variables related with the unit operations and flow directions, as shown in Figure 2 and the original superstructure
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is obtained. When this fixed superstructure solved with ANTIGONE, it yields the global solution with an objective value of $14,004,425 in 152 CPU s. 306.7 K Feed
Equivalent Flowsheet:
CSTR1
430 K
500 K 300 K
430 K Waste
Heat
SEP1 430 K
Feed
12.2 MW
SEP1 0.7 MW
SEP5
Product
388.1 K
-3.8 MW
306.7 K
350 K
HeatCSTR3 400 K
500 K CSTR1
-3.1 MW 400 K 0.7 MW CSTR3 388K 7.3 MW
350 K
350 K
SEP 5 350 K Waste
Hot utility: 20.9 MW Cold utility: 6.9 MW Annual Profit: $14.0 MM
350 K Product
Figure 4. Solution obtained from the original superstructure. Resulting block superstructure solution and its equivalent flowsheet are shown in Figure 4. Then, the same problem is solved for 22 h with ANTIGONE for automatic flowsheet generation without any fixing and with an initial solution provided by the strategy outlined by Li et al. (2018). The flowsheet identified by block superstructure has an annual profit of $14,171,800 which is $167,300 higher than the process flowsheet obtained via the original superstructure. This result is shown in Figure 5. The improvement is due to the change in the position of the unreacted recycle stream from Sep1. As Sep1 operates a lower temperature than the CSTR1, the recycle stream from top of the Sep1 needs to be heated before entering into CSTR1 (see Figure 4). However, recycling reactor outlet directly facilitates a higher mixing temperature at the feed mixer and decreases the cost associated with the recycle stream. Accordingly, flow rate of the recycle stream can be increased which contributes to higher overall conversion. Note that this structural alternative is not included in the original superstructure and block superstructure could identify this connection without pre-specifying its existence. . Equivalent Flowsheet:
300 K Feed Heat SEP 1 430 K Waste 400 K
355.8 K
355.8 K
500 K 300 K
CSTR1 500 K
500 K
Heat CSTR3 400 K
Feed
Waste H1:-3.6 MW
C1: 12.0 MW CSTR1 355.8 K 350 K
500 K 350 K SEP5
SEP 5 350 K Waste
350 K Product
430 K
H2:-3.2 MW 400 K CSTR3
Product C2:0.7 MW
372.7 K
SEP1
C4: 0.7 MW
400 K C3: 7.4 MW 372.7 K
Hot utility: 20.8 MW Cold utility: 6.8 MW Annual Profit: $14.2 MM
Figure 5. Final block superstructure result. HEN for this result can also be addressed via block superstructure. The final flowsheet contains 4 cold streams (C1-C4 while C3 and C4 are isothermal) and 2 hot streams (H1 and H2). Accordingly, 6×7 block superstructure can be used to represent HEN superstructure as shown in Figure 6. Note that in Figure 6, the resultant block structure and only the matched streams are shown with a heater/cooler symbol. While first two rows are used for two hot streams, other rows are used for cold streams. First and last columns are used to represent hot and cold utility consuming heat exchangers,
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respectively. Isothermal cold streams are handled with 1 K fictitious temperature difference. As the identity of the streams are known, binary variables associated with the stream classification are fixed accordingly. The objective is to synthesize a HEN with minimum annual cost while considering fixed and variable capital costs and operating costs. The optimal block superstructure result is obtained in 7 CPU s with ANTIGONE and corresponding HEN is also shown in Figure 6. Resulting network has a total annual cost of $1,566,440 and contains two heat exchangers (between C1-H1 and C1-H2), four heaters and one cooler. Since the heat content of the hot streams are low, three cold streams (C2, C3, and C4) could not be integrated and, they require hot utility.
i=1
j=1
j=2
j=3
j=4
j=5
j=6
j=7
H1
500
430
430
430
430
430
400
400
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357.1
357.1
500
431
388.4
355.8
355.8
355.8
372.7
350
350
350
350
350
C2
H1: 0.05
350
H2: 0.06
401
400
400
400
400
400
C3
C1: 0.08
400
C2: 0.03
C3
C3: 7.43
430
C4: 0.58
500 H2
i=2
400
i=3
i=4
i=5
i=6
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430
430
430
430
430
400 H2 500 H1 523 HU 500 431 C1 355.8 388.4
297 m2 32.8 m2 57.9 m2 357.1 430 523 CU 293 303 4.0 m2 350 Other heater areas: C1 Fcp C2: 2.1 m2 355.8 (MW/K) 350
C3: 30.3 m2 C4: 3.1 m2 Hot utility: 14.5 MW Cold utility: 0.4 MW TAC: $1,566,440 Heat Exchanger
Heater Cooler
Figure 6. Optimized HEN for the generated flowsheet.
5. Conclusions In this work, block superstructure model is extended to include simultaneous HENS. The use of the model is illustrated via a literature example first for automated flowsheet generation and then constructing the corresponding HEN. Note that superstructure model developed in this work is also applicable for simultaneous HENS. Future work will focus on utilizing the full model and demonstrating the capabilities of block superstructure for simultaneous process synthesis, heat integration and intensification.
References S. E. Demirel, J. Li, M. M. F. Hasan, 2017, Systematic process intensification using building blocks, Computers & Chemical Engineering, 105, 2–38. J. Li, S. E. Demirel, M. M. F. Hasan, 2017, Simultaneous process synthesis and process intensification using building blocks, Computer Aided Chemical Engineering, 40, 1171–1176. J. Li, S. E. Demirel, M. M. F. Hasan, 2018, Process Synthesis using block superstructure with automated flowsheet generation and optimization , Submitted. L. Kong, V. Avadiappan, K. Huang, and C. T. Maravelias, 2017, Simultaneous chemical process synthesis and heat integration with unclassified hot/cold process streams, Computers & Chemical Engineering, 101, 210-225. A. I. Stankiewicz, and J. A. Moulijn, 2000, Process Intensification: Transforming Chemical Engineering. Chemical Engineering Progress, 1, 22–34. T.F. Yee, and I.E. Grossmann, 1990, Simultaneous optimization models for heat integration—II. Heat exchanger network synthesis, Computers & Chemical Engineering, 14(10), 1165-1184.
A General Framework for Process Synthesis, Integration and Intensification Salih Emre Demirel, Jianping Li, M. M. Faruque Hasan* Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77845, USA. *Corresponding Author Email: [email protected].
Abstract Block-based superstructure (Demirel et al., 2017; Li et al., 2017) offers advantages over classical unit operation-based process synthesis approaches as it leverages upon building blocks to represent different physicochemical phenomena, processing tasks and equipment configurations. In this work, we extend this approach to demonstrate that the same block superstructure representation can be used to perform simultaneous synthesis, integration and intensification in a unified framework. The block-based representation also enables automatic generation of intensified flowsheets without a priori postulation of connectivity. Moreover, it is generic enough to be reduced to various process integration network problems, such as heat exchanger networks, fuel gas networks, water networks, etc. A literature example is used to demonstrate the benefits of block superstructure for the particular case of flowsheet generation and heat exchanger network synthesis (HENS). Keywords: Block Superstructure, Process Synthesis, Intensification, Integration.
1. Introduction Optimization-based process synthesis provides a systematic pathway for identifying optimal process flowsheets from numerous alternatives. However, most synthesis methods are currently limited in scope for “out-of-the-box” design solutions as they require pre-postulated superstructures. This also prohibits innovative equipment design which plays a critical role in process intensification (Stankiewicz and Moulijn, 2000). To this end, we have proposed building block superstructure (Demirel et al., 2017; Li et al., 2017) which eliminates the need for pre-specified equipment types, and automates the search for intensified process alternatives. In this work, further benefits of the building block superstructure are presented via extending the formulation to include simultaneous heat integration and to form a comprehensive framework for intensified conceptual process design. As the proposed superstructure automatically generates the flowsheet alternatives without any a priori information on the final flowsheet, position and the identity (i.e. hot/cold) of the integrated streams are not known beforehand. Accordingly, proposed formulation is for simultaneous process synthesis and heat integration network synthesis with unclassified process streams. This opens up the potential of utilizing the block superstructure as a general framework for process synthesis, heat integration and intensification. The benefits of the proposed approach is demonstrated via a literature example and it is shown that significant advantages can be obtained by utilizing building block superstructure in conceptual process design.
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2. Block Superstructure in a Grid Formation Block superstructure is shown in Figure 1. Here, each block can be used to represent different chemical phenomena, tasks, materials and equipment. A detailed discussion on how to use building blocks to represent various phenomena are given in Demirel et al. (2017). Each block is connected with neighbouring blocks via bidirectional inter-block streams. Bidirectional flow representation enables incorporation of the recycle connections into the superstructure. Furthermore, heater/cooler and expander/compressor equipment are positioned on each stream so as to quantify the utility requirements in the superstructure and to consider operating and capital costs for these equipment. Each block can also have feed and product streams to facilitate interaction with external environment. j=1
j=2
j=J-1
j=J
i=1
i=2
i=I-1
i=I
Figure 1. A schematic of the block superstructure. With this representation, many process synthesis superstructures can be incorporated into the block superstructure. An example superstructure taken from literature (Kong et al., 2017) and its block superstructure representation are illustrated in Figure 2. Here, reactors are represented as single blocks while separators are represented via block boundaries between two blocks to indicate the position of the separated stream. 9
10
a)
3
2
1
5
CSTR1
CSTR2
6
j=2
1 Feed
SEP1
4
j=1
b)
8
2
CSTR1 CSTR2
i=1
7
10
11
7
12
13
8 SEP1
i=2
CSTR3
j=3
27 Product
9
23 27
22 SEP5
19
14
SEP4
SEP2
21
Heat 12
15
i=3
20 24
16 25
13
18
i=4
26
18
SEP 3
26
SEP3
17
11
CSTR3
13
SEP 2 SEP 4 SEP 5 Waste 25
15 27 15
27 Product
Figure 2. Superstructure representations (a) unit-operation based, (b) block based.
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Different process integration networks can be also included in the same superstructure representation. Each stream contains a heater/cooler and the identity of the stream (i.e. hot or cold) and corresponding utility consumption can be determined via an energy balance around each stream. If the utility requirement of a hot and cold stream at two different positions are the same, then they can be integrated to each other. If no such stream available, then the heating/cooling requirement is satisfied via external utilities. This is illustrated in Figure 3a. Although each stream is allowed to match with any other stream in the superstructure, these matches can be restricted to certain positions to yield the same superstructure with the one given by Yee and Grossmann (1990), in which case, each column represents one stage. In Figure 3b, this is illustrated for 2 hot and 2 cold streams. Stream splitting can also be achieved via increasing the number of rows that a stream can go through. For instance, if all the streams in Figure 3b can go through splitting, then 8×5 superstructure with each stream occupying two rows would be used.
(a)
j=1
j=2
(b)
j=3
j=1
j=2
j=3
j=4
j=5
H1 i=1
i=1
H2 i=2
i=2 C1 i=3
i=3
C2
i=4
Cold utility
Hot utility
Figure 3. Heat exchanger network representation using block superstructure.
3. Superstructure Model for Synthesis, Heat Integration and Intensification The overall model for process synthesis, integration and intensification is based on a single mixed integer nonlinear programming (MINLP) and summarized below. Model contains block superstructure constraints for generating the process flowsheet and HENS constraints for determining the corresponding HEN.
௫ǡ௫ᇱǡ௭ǡ௭ᇱǡ௬ǡ௪
݂ሺݔǡ ݔᇱ ǡ ݖǡ ݖԢሻ ݄ሺݕǡ ݓሻ
(1)
݃ǡ ሺݔǡ ݔԢሻ ൌ Ͳ݅ ܫ אǡ ݆ ܬ אǡ ݃ᇱ ǡǡௗ ሺݔǡ ݔԢሻ ൌ Ͳ݅ ܫ אǡ ݆ ܬ אǡ ݀ ܦ א
(2)
ݍǡ ሺݖሻ Ͳ݅ ܫ אǡ ݆ ܬ אǡ ݍᇱ ǡǡௗ ሺݖԢሻ Ͳ݅ ܫ אǡ ݆ ܬ אǡ ݀ ܦ א
(3)
ݎǡ ሺݔǡ ݔԢǡ ݖሻ Ͳ݅ ܫ אǡ ݆ ܬ אǡ
(4)
ݎԢǡǡௗ ሺݔǡ ݔԢǡ ݖԢሻ Ͳ݅ ܫ אǡ ݆ ܬ אǡ ݀ ܦ א
ܩǡᇱ ሺݔԢǡ ݓሻ ൌ Ͳ݈ǡ ݈ ᇱ ݈ܮ א൏ ݈Ԣ
(5)
ܳ ሺݕሻ Ͳ݈ ܮ א
(6) ᇱ
ܴǡᇱ ሺݓǡ ݕሻ Ͳ݈ǡ ݈ ݈ܮ א൏ ݈Ԣ ݔԢ ݔᇱ ݔᇱ ݔ ݔ ݔ ݓ ݓ ݓ ܴ א ݔூൈ ǡ ݔᇱ ܴ אூൈൈ ǡ ܴ א ݓൈ ݖൌ ሼͲǡͳሽூൈ ݖᇱ ൌ ሼͲǡͳሽூൈൈ ݕൌ ሼͲǡͳሽൈ
(7)
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The overall superstructure model is comprised of objective function, Eq.(1), which minimizes the annualized cost while considering operating and capital cost for the process, i.e. ݂ሺݔǡ ݔᇱ ǡ ݖǡ ݖԢሻ, and corresponding heat exchanger network, i.e. ݄ሺݕǡ ݓሻ, process related constraints Eqs.(2)-(4), and HENS model constraints Eqs.(5)-(7). Each block is designated with its position in the superstructure as ܤǡ , in which ݅ ൌ ͳǡ ǥ ǡ ܫ and ݆ ൌ ͳǡ ǥ ǡ ܬare row and column indices, respectively. There are mainly two type of variables in the superstructure model: block, i.e. ݔǡ ݖ, and boundary, i.e. ݔԢǡ ݖԢ, variables. Block variables, for instance, include ܲǡ and ܶǡ which stands for block pressure and temperature, respectively. Boundary variables, on the other hand, are defined to ௦ in represent flow rate of the interblock streams, ܨǡǡௗ , and stream temperatures, ܶǡǡௗ which ݀ ൌ ሼͳǡʹሽ designates the orientation of the boundary variables as horizontal (݀ ൌ ͳ) or vertical (݀ ൌ ʹ). While block binary variables,ݖ, are used to assign reaction related phenomena to the blocks, boundary binary variables, ݖԢ, are used to assign separation related phenomena or operation to the boundaries in the superstructure. In process related constraints, Eqs.(2) indicate block material and energy balances and stream energy balances, Eqs.(3) designate logical constraints, and Eqs.(4) relate continuous and binary variables. In the HENS model, block indices are mapped into a single index, ݅ǡ ݆ǡ ݀ ՜ ݈ where ݈ ൌ ͳǡ ǥ ǡ ܮis an ordered set and contains all the streams in the superstructure, i.e. ܮൌ ʹ ൈ ܫൈ ܬ. Note that, as the model is posed as a simultaneous synthesis and heat integration model, and the identity of the streams, i.e. hot/cold, in the superstructure are not known beforehand, binary variables are used to determine stream identities. Accordingly, HENS model is similar to the one proposed by Yee and Grossmann (1990) except that it is extended for unclassified process streams. While continuous variables,ݓ, are used to represent the heat duty for each matching stream in the superstructure and determine approach temperatures for these matches, binary variables, ݕ, are used to determine the stream matches within the superstructure, and classifying streams as hot or cold. In HENS model related constraints, Eq. (5) stands for heat balances for each stream, Eq. (6) designates logical constraints for determining the existence of a match and classification of a stream, and Eq. (7) relates HENS model binary variables with continuous variables.
4. Case Study An example problem adapted from Kong et al. (2017) is used to demonstrate the use of block superstructure for automatic flowsheet generation first and, then for determining its corresponding HEN. The original superstructure given by Kong et al. (2017) and its block representation is given in Figure 2. There are four components in the process: A and B are used as raw materials to produce C (R1: A + B ՜ C), which is further utilized in a second reaction to obtain the final product D (R2: C ՞ D). There are two isothermal reactor alternatives for R1: CSTR1 (500 K) and CSTR2 (400 K). R2 is an equilibrium reaction carried out in an isothermal equilibrium reactor: CSTR3 (330-400 K). There are five separator alternatives. While Sep1 (430 K) is used to separate C from R1 reactants, Sep2-5 are used to separate product D from C. Note that Sep1 and CSTR3 requires hot utility. The aim of the problem is to synthesize a process for maximizing the total annual profit considering product revenue, unit capital costs and utility costs. All the equipment parameters along with their cost parameters are taken from Kong et al. (2017). First, the problem is solved via fixing the binary variables related with the unit operations and flow directions, as shown in Figure 2 and the original superstructure
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is obtained. When this fixed superstructure solved with ANTIGONE, it yields the global solution with an objective value of $14,004,425 in 152 CPU s. 306.7 K Feed
Equivalent Flowsheet:
CSTR1
430 K
500 K 300 K
430 K Waste
Heat
SEP1 430 K
Feed
12.2 MW
SEP1 0.7 MW
SEP5
Product
388.1 K
-3.8 MW
306.7 K
350 K
HeatCSTR3 400 K
500 K CSTR1
-3.1 MW 400 K 0.7 MW CSTR3 388K 7.3 MW
350 K
350 K
SEP 5 350 K Waste
Hot utility: 20.9 MW Cold utility: 6.9 MW Annual Profit: $14.0 MM
350 K Product
Figure 4. Solution obtained from the original superstructure. Resulting block superstructure solution and its equivalent flowsheet are shown in Figure 4. Then, the same problem is solved for 22 h with ANTIGONE for automatic flowsheet generation without any fixing and with an initial solution provided by the strategy outlined by Li et al. (2018). The flowsheet identified by block superstructure has an annual profit of $14,171,800 which is $167,300 higher than the process flowsheet obtained via the original superstructure. This result is shown in Figure 5. The improvement is due to the change in the position of the unreacted recycle stream from Sep1. As Sep1 operates a lower temperature than the CSTR1, the recycle stream from top of the Sep1 needs to be heated before entering into CSTR1 (see Figure 4). However, recycling reactor outlet directly facilitates a higher mixing temperature at the feed mixer and decreases the cost associated with the recycle stream. Accordingly, flow rate of the recycle stream can be increased which contributes to higher overall conversion. Note that this structural alternative is not included in the original superstructure and block superstructure could identify this connection without pre-specifying its existence. . Equivalent Flowsheet:
300 K Feed Heat SEP 1 430 K Waste 400 K
355.8 K
355.8 K
500 K 300 K
CSTR1 500 K
500 K
Heat CSTR3 400 K
Feed
Waste H1:-3.6 MW
C1: 12.0 MW CSTR1 355.8 K 350 K
500 K 350 K SEP5
SEP 5 350 K Waste
350 K Product
430 K
H2:-3.2 MW 400 K CSTR3
Product C2:0.7 MW
372.7 K
SEP1
C4: 0.7 MW
400 K C3: 7.4 MW 372.7 K
Hot utility: 20.8 MW Cold utility: 6.8 MW Annual Profit: $14.2 MM
Figure 5. Final block superstructure result. HEN for this result can also be addressed via block superstructure. The final flowsheet contains 4 cold streams (C1-C4 while C3 and C4 are isothermal) and 2 hot streams (H1 and H2). Accordingly, 6×7 block superstructure can be used to represent HEN superstructure as shown in Figure 6. Note that in Figure 6, the resultant block structure and only the matched streams are shown with a heater/cooler symbol. While first two rows are used for two hot streams, other rows are used for cold streams. First and last columns are used to represent hot and cold utility consuming heat exchangers,
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respectively. Isothermal cold streams are handled with 1 K fictitious temperature difference. As the identity of the streams are known, binary variables associated with the stream classification are fixed accordingly. The objective is to synthesize a HEN with minimum annual cost while considering fixed and variable capital costs and operating costs. The optimal block superstructure result is obtained in 7 CPU s with ANTIGONE and corresponding HEN is also shown in Figure 6. Resulting network has a total annual cost of $1,566,440 and contains two heat exchangers (between C1-H1 and C1-H2), four heaters and one cooler. Since the heat content of the hot streams are low, three cold streams (C2, C3, and C4) could not be integrated and, they require hot utility.
i=1
j=1
j=2
j=3
j=4
j=5
j=6
j=7
H1
500
430
430
430
430
430
400
400
357.1
357.1
357.1
500
431
388.4
355.8
355.8
355.8
372.7
350
350
350
350
350
C2
H1: 0.05
350
H2: 0.06
401
400
400
400
400
400
C3
C1: 0.08
400
C2: 0.03
C3
C3: 7.43
430
C4: 0.58
500 H2
i=2
400
i=3
i=4
i=5
i=6
431
430
430
430
430
430
400 H2 500 H1 523 HU 500 431 C1 355.8 388.4
297 m2 32.8 m2 57.9 m2 357.1 430 523 CU 293 303 4.0 m2 350 Other heater areas: C1 Fcp C2: 2.1 m2 355.8 (MW/K) 350
C3: 30.3 m2 C4: 3.1 m2 Hot utility: 14.5 MW Cold utility: 0.4 MW TAC: $1,566,440 Heat Exchanger
Heater Cooler
Figure 6. Optimized HEN for the generated flowsheet.
5. Conclusions In this work, block superstructure model is extended to include simultaneous HENS. The use of the model is illustrated via a literature example first for automated flowsheet generation and then constructing the corresponding HEN. Note that superstructure model developed in this work is also applicable for simultaneous HENS. Future work will focus on utilizing the full model and demonstrating the capabilities of block superstructure for simultaneous process synthesis, heat integration and intensification.
References S. E. Demirel, J. Li, M. M. F. Hasan, 2017, Systematic process intensification using building blocks, Computers & Chemical Engineering, 105, 2–38. J. Li, S. E. Demirel, M. M. F. Hasan, 2017, Simultaneous process synthesis and process intensification using building blocks, Computer Aided Chemical Engineering, 40, 1171–1176. J. Li, S. E. Demirel, M. M. F. Hasan, 2018, Process Synthesis using block superstructure with automated flowsheet generation and optimization , Submitted. L. Kong, V. Avadiappan, K. Huang, and C. T. Maravelias, 2017, Simultaneous chemical process synthesis and heat integration with unclassified hot/cold process streams, Computers & Chemical Engineering, 101, 210-225. A. I. Stankiewicz, and J. A. Moulijn, 2000, Process Intensification: Transforming Chemical Engineering. Chemical Engineering Progress, 1, 22–34. T.F. Yee, and I.E. Grossmann, 1990, Simultaneous optimization models for heat integration—II. Heat exchanger network synthesis, Computers & Chemical Engineering, 14(10), 1165-1184.