Optimal operation of multiproduct batch plants [Elektronische Ressource] / Brahmdatt Vijaykumar Mishra
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English
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Optimal operation of multiproduct batch plants [Elektronische Ressource] / Brahmdatt Vijaykumar Mishra

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138 pages
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Optimal Operation of Multiproduct BatchPlantsBrahmdatt Vijaykumar Mishrafrom Kalyan, Maharashtra, IndiaAdvisor: Prof. Dr.-Ing. Joerg RaischCo-Advisor: Prof. Dr.-Ing. Achim KienleMax Planck Institute for Dynamic Complex Technical SystemsMagdeburg, Germany2005AcknowledgmentsThough this dissertation is in my name, the credit for this work is not con nedonly upto me. There were many other people involved in making this work possible.First of all, I would like to thank my advisors Prof. Joerg Raisch and Prof. AchimKienle for their continuous guidance and support throughout my work. Without theirin-depth knowledge in this area, this work would have never reached this far. Besidestheir professional support, they also came across as very kind and social people. I amtruly indebted to them for all their support and cooperation. I would also like to thankmy colleagues Dmitry Gromov and Eckart Mayer for all their support, not only on theacademic level but also on the personal level. A special thanks to Dr. Erik Stein forhelping me out during the initial phase of my research. Thank you very much Erik forgiving me a wonderful start. I would like to thank all my other group members as well fortheir moral support and wonderful company during my stay in Magdeburg.I owe an enormous debt of gratitude to the group secretaries Christiane Pueschel andJanine Holzmann for helping me out with everything.

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Publié le 01 janvier 2005
Nombre de lectures 72
Langue English

Exrait

Optimal Operation of Multiproduct Batch
Plants
Brahmdatt Vijaykumar Mishra
from Kalyan, Maharashtra, India
Advisor: Prof. Dr.-Ing. Joerg Raisch
Co-Advisor: Prof. Dr.-Ing. Achim Kienle
Max Planck Institute for Dynamic Complex Technical Systems
Magdeburg, Germany
2005Acknowledgments
Though this dissertation is in my name, the credit for this work is not con ned
only upto me. There were many other people involved in making this work possible.
First of all, I would like to thank my advisors Prof. Joerg Raisch and Prof. Achim
Kienle for their continuous guidance and support throughout my work. Without their
in-depth knowledge in this area, this work would have never reached this far. Besides
their professional support, they also came across as very kind and social people. I am
truly indebted to them for all their support and cooperation. I would also like to thank
my colleagues Dmitry Gromov and Eckart Mayer for all their support, not only on the
academic level but also on the personal level. A special thanks to Dr. Erik Stein for
helping me out during the initial phase of my research. Thank you very much Erik for
giving me a wonderful start. I would like to thank all my other group members as well for
their moral support and wonderful company during my stay in Magdeburg.
I owe an enormous debt of gratitude to the group secretaries Christiane Pueschel and
Janine Holzmann for helping me out with everything. Without their constant cooperation,
my stay in Magdeburg would not have been very pleasant. A special thanks to our library
staff member Cornelia Trieb for her prompt response to my literature needs. She has
been one of the most friendliest and cooperative person that I have come across at the
Max Planck Institute. I would also like to express my gratitude to our IT staff members,
especially Robert Rehner, for always sorting out my IT related problems so ef ciently
and quickly.
Further, I owe a lot to all my Indian friends in Magdeburg. It is only because of them that
Magdeburg still feels like a second home to me. Though all my Indian friends here have
been very very special, I would especially like to mention Ayan Dada, Jitu Bhai and Nikki
Bhabhi, Jignesh, Mohan, Shyam, Fahad Bhai and Ambrin Bhabhi, Dr. K.P. Chary and his
family, Dr. Suhel Parvez and last but not the least, my lovely sister-in-law Rita Raithore.
These people have really come so close to my heart in all these many years that a thank
you would be too small a term to express my feeling towards them.
Finally, a special thanks to my wife Priya for enduring me during all these years of hard
work. Her support, tolerance and patience towards me has been amazing. Thank you
very much sweetheart for your love and support and of course, also for our little wonders
Pooja and Piyush. I could have never managed to reach this far without you and hence, I
dedicate this dissertation to you my love.Contents
1 Introduction 1
1.1 The Control Problem Statement . . . . . . . . . . . . . . . . . . . . . . 3
1.2 General Structure of the Control Problem . . . . . . . . . . . . . . . . . 3
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 A Comparative Study of Different Approaches 8
2.1 Mathematical formulation of the control problem . . . . . . . . . . . . . 8
2.2 Illustrative examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 An Improved Approach for the Control of Multiproduct Batch Plants 42
3.1 Control of MBPs via the Improved Approach . . . . . . . . . . . . . . . 43
3.1.1 Determination of suitable recipe functions . . . . . . . . . . . . . 43
3.1.2 Control problem formulation . . . . . . . . . . . . . . . . . . . . 46
3.2 Illustrative examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
i4 An Application Example 71
4.1 Control via the improved approach . . . . . . . . . . . . . . . . . . . . . 81
4.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 Conclusions and Perspectives 102
A The State Task Network 1
B Transformation of Dynamic Optimization problem into Nonlinear Program-
ming Problem. 5
B.1 The dynamic optimization problem . . . . . . . . . . . . . . . . . . . . . 5
B.2 Transformation of the dynamic optimization problem into the NLP problem 6
B.2.1 Time discretization . . . . . . . . . . . . . . . . . . . . . . . . . 6
B.2.2 The NLP formulation . . . . . . . . . . . . . . . . . . . . . . . . 6
iiList of Figures
1.1 An example multi-product batch plant. . . . . . . . . . . . . . . . . . . . . . . 2
1.2 State-task-network representation of the process shown in Figure 1.1. . . . . . . . . . 4
1.3 Schematic representation of the standard recipe approach (SRA). . . . . . . . . . . . 6
1.4 Schematic of the overall optimization approach (OOA). . . . . . . . . 6
2.1 Flow sheet of the process in example 1. . . . . . . . . . . . . . . . . . . . . . . 16
2.2 State-task-network representation of the process in example 1. . . . . . . . . . . . . 17
2.3 Optimal control pro les for the reaction in example 1. . . . . . . . . . . . . . . . 20
2.4 Optimal schedule obtained by the SRA for example 1. . . . . . . . . . . . . . . . 22
2.5 Optimal schedule obtained by the OOA for example 1. . . . . . . . . . . . . . . . 23
32.6 Control pro les for the reaction task (batch size 3.69 m ) in example 1. . . . . . . . . 24
2.7 Optimal control pro le for the reaction in alternative recipe case. . . . . . . . . . . . 26
2.8 Optimal schedule obtained via the SRA using the alternate recipe. . . . . . . . . . . 26
2.9 Optimal schedule obtained via the SRA using the rst recipe (25 hours makespan). . . . 27
2.10 Optimal schedule obtained via the SRA using the alternate recipe (25 hours makespan). . 27
2.11 Optimal schedule obtained via the OOA (25 hours makespan). . . . . . . . . . . . . 28
2.12 Optimal schedule obtained by the SRA for example 2. . . . . . . . . . . . . . . . 38
2.13 Optimal schedule obtained by the OOA for example 2. . . . . . . . . . . . . . . . 38
3.1 An improved approach for the control of MBPs. . . . . . . . . . . . . . . . . . . 42
iii3.2 An illustration of the polynomial tting used for obtaining Equation 3.2. . . . . . . . 45
3.3 Optimal control pro le corresponding to the minimum processing time for the reaction
in example 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4 Optimal control pro les (u) corresponding to different processing durations for a batch-
3size of 2.5 m in example 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 Plot of the third order polynomial given in Equation 3.10. . . . . . . . . . . . . . . 50
3.6 Optimal schedule obtained via the IA for example 1. . . . . . . . . . . . . . . . . 51
33.7 Control pro les for the reaction task with batch size 2.4809 m in example 1. . . . . . 52
3.8 Optimal control pro les (u) corresponding to the minimum processing durations for
different batch sizes for reaction 1 in example 2. . . . . . . . . . . . . . . . . . . 54
3.9 Optimal control pro les (F ) corresponding to the minimum processing durations forA
different batch sizes for reaction 1 in example 2. . . . . . . . . . . . . . . . . . . 54
3.10 Optimal control pro les (u) corresponding to the minimum processing durations for
different batch sizes for reaction 2 in example 2. . . . . . . . . . . . . . . . . . . 55
3.11 Optimal control pro les (F ) corresponding to the minimum processing durations forA
different batch sizes for reaction 2 in example 2. . . . . . . . . . . . . . . . . . . 55
3.12 Optimal control pro les (u) corresponding to the minimum processing durations for
different batch sizes for reaction 3 in example 2. . . . . . . . . . . . . . . . . . . 56
3.13 Optimal control pro les (F ) corresponding to the minimum processing durations forA
different batch sizes for reaction 3 in example 2. . . . . . . . . . . . . . . . . . . 56
3.14 Plot of the polynomial given in Equations 3.14 and 3.15. . . . . . . . . . . . . . . 58
3.15 Plot of the polynomial given in Equations 3.16 and 3.17. . . . . . . . . . . . . . . 59
3.16 Plot of the polynomial given in Equations 3.18 and 3.19. . . . . . . . . . . . . . . 59
3.17 Optimal control pro les (u) corresponding to different processing durations for a batch
3size of 1.0 m and for reaction 1 in example 2. . . . . . . . . . . . . . . . . . . . 60
3.18 Optimal control pro les (F ) corresponding to different processing durations for a batchA
3size of 1.0 m and for reaction 1 in example 2. . . . . . . . . . . . . . . . . . . . 60
3.19 Optimal control pro les (u) corresponding to different processing durations for a batch
3size of 1.0 m and for reaction 2 in example 2. . . . . . . . . . . . . . . . . . . . 61
iv3.20 Optimal control pro les (F ) corresponding to different processing durations for a batchA
3size of 1.0 m and for reaction 2 in example 2. . . . . . . . . . . . . . . . . . . . 61
3.21 Optimal control pro les (u) corresponding to different processing durations for a batch
3size of 1.0 m and for reaction 3 in example 2. . . . . . . . . . . . . . . . . . . . 62
3.22 Optimal control pro les (F ) corresponding to different processing durations for a batchA
3size of 1.0 m and for reaction 3 in example 2. . . . . . . . . . . . . . . . . . . . 62
3.23 Plot of the third order polynomial given in Equations 3.21 and 3.24. . . . . . . . . . 66
3.24 Plot of the third order polynomial given in Equations 3.27 and 3.30. . . . . . . . . . 66
3.25 Plot of the third order polynomial given in Equations 3.33 and 3.36. . . . . . . . . . 67
3.26 Optimal schedule obtained via the IA for example 2. . . . . . . . . . . . . . . . . 68
4.1 Flow sheet of the application example. . . . . . . . . . . . . . . . . . . . . . . 71
4.2 A schematic of the batch reactors in the application example. . . . . . . . . . . . . 72
4.3 A schematic of the batch puri cators in the application example. . . . . . . . . . . . 76
4.4 State-task-network representation of the application example. . . . . . . . . . . . . 79
4.5 Plot of the polynomial given in Equation 4.26. . . . . . . . . . . . . . . . . . . . 83
4.6 Plot of the polynomial given in Equation 4.27. . . . . . . . . . . . . . . . . . . . 83
4.7 Plot of the polynomial given in Equation 4.28. . . . . . . . . . . . . . . . . . . . 84
4.8 Plot of the polynomial given in Equation 4.29. . . . . . . . . . . . . . . . . . . . 84
34.9 Optimal coolant pro le corresponding to a batch size of 0.8 m over a processing dura-
tion of 4.0 h for reaction 1 on reactor 1. . . . . . . . . . . . . . . . . . . . . . . 87
34.10 Optimal coolant pro le corresponding to a batch size of 0.4 m over a processing dura-
tion of 4.0 h for reaction 1 on reactor 2. . . . . . . . . . . . . . . . . . . . . . . 87
34.11 Optimal coolant pro le corresponding to a batch size of 0.8 m over a processing dura-
tion of 4.0 h for reaction 2 on reactor 1. . . . . . . . . . . . . . . . . . . . . . . 88
34.12 Optimal coolant pro le corresponding to a batch size of 0.4 m over a processing dura-
tion of 4.0 h for reaction 2 on reactor 2. . . . . . . . . . . . . . . . . . . . . . . 88
4.13 Plot of the third order polynomial given in Equation 4.31. . . . . . . . . . . . . . . 90
v4.14 Plot of the third order polynomial given in Equation 4.34. . . . . . . . . . . . . . . 91
4.15 Plot of the third order polynomial given in Equation 4.37. . . . . . . . . . . . . . . 91
4.16 Plot of the third order polynomial given in Equation 4.40. . . . . . . . . . . . . . . 92
4.17 Plot of the polynomial given in Equations 4.44 - 4.46. . . . . . . . . . . . . . . . . 94
4.18 Plot of the polynomial given in Equations 4.47 - 4.49. . . . . . . . . . . . . . . . . 94
34.19 Optimal hot water pro le corresponding to a batch size of 0.4 m over a processing
duration of 2.0 h for puri cation 1. . . . . . . . . . . . . . . . . . . . . . . . . 95
34.20 Optimal hot water pro le corresponding to a batch size of 0.4 m over a processing
duration of 2.0 h for puri cation 2. . . . . . . . . . . . . . . . . . . . . . . . . 95
4.21 Plot of the third order polynomial given in Equations 4.51, 4.54 and 4.57. . . . . . . . 99
4.22 Plot of the third order polynomial given in Equations 4.60, 4.63 and 4.66. . . . . . . . 99
4.23 Optimal schedule obtained obtained via the IA for the application example. . . . . . . 100
A.1 An example state task network. . . . . . . . . . . . . . . . . . . . . . . . . . 2
A.2 State task networks representing two different processes, one with a recycle stream and
the other involving an intermediate state production and consumption. . . . . . . . . 2
A.3 An example plant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
A.4 State task network representation of the example plant. . . . . . . . . . . . . . . . 3
B.1 Consideration of control-intervals within the makespan. . . . . . . . . . . . . . . . 7
B.2 of time-points within each control-interval. . . . . . . . . . . . . . . 7
viList of Tables
2.1 Data for example 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Results of the SBO of the reactor in example 1. . . . . . . . . . . . . . . 20
2.3 Comparison of the SRA and the OOA results for example 1. . . . . . . . 23
32.4 Optimization results for the reaction task (batch size 3.69m ) in example 1. 24
2.5 Results of the SBO for the alternate recipe. . . . . . . . . . . . . . . . . 25
2.6 Comparison of scheduling solutions for different reactor operation costs. . 29
2.7 Kinetic parameters for the reactions in example 2. . . . . . . . . . . . . . 31
2.8 Data for example 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.9 SBO results for reaction 1 in example 2. . . . . . . . . . . . . . . . . . . 34
2.10 SBO results for reaction 2 in example 2. . . . . . . . . . . . . . . . . . . 34
2.11 SBO results for reaction 3 in example 2. . . . . . . . . . . . . . . . . . . 35
2.12 Comparison of the SRA and the OOA results for example 2. . . . . . . . 39
2.13 of the reactor operation cost followed by the OOA schedul-
ing model and that obtained via SBO for example 2. . . . . . . . . . . . . 40
2.14 OOA scheduling model statistics for example 2 with 5 event points. . . . 40
3.1 Minimum processing durations for different batch sizes for a given task
in a given unit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2 Data corresponding to optimal control pro les for different batch sizes
and a given task on a given unit. . . . . . . . . . . . . . . . . . . . . . . 44
vii3.3 Minimum processing durations for different batch sizes for the reaction
in example 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Data corresponding to optimal control pro les for different batch sizes
and for the reaction in example 1. . . . . . . . . . . . . . . . . . . . . . 48
3.5 The tted and the trueQr for the batch sizes shown in Figure 3.6. . . . . 51
3.6 Comparison of the SRA, the OOA and the IA results for example 1. . . . 52
33.7 Optimization results for the reaction task with batch size 2.4809 m in
example 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.8 Minimum processing durations for different batch sizes for the reactions
in example 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.9 Data corresponding to the optimal control pro les for different batch sizes
and for the reaction 1 in example 2. . . . . . . . . . . . . . . . . . . . . 63
3.10 Data corresponding to the optimal control pro les for different batch sizes
and for the reaction 2 in example 2. . . . . . . . . . . . . . . . . . . . . 63
3.11 Data corresponding to the optimal control pro les for different batch sizes
and for the reaction 3 in example 2. . . . . . . . . . . . . . . . . . . . . 64
3.12 The tted and the trueQr for the batch sizes shown in Figure 3.26. . . . . 68
3.13 Comparison of the SRA, the OOA and the IA results for example 2. . . . 69
4.1 Data used for the reactors in the application example. . . . . . . . . . . . 75
4.2 Data used for the puri cators in the application example. . . . . . . . . . 79
4.3 Data for example 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4 Minimum processing durations for different batch sizes for reaction 1 on
reactors 1 and 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.5 Minimum processing durations for different batch sizes for reaction 2 on
reactors 1 and 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.6 Data corresponding to optimal coolant pro les for different batch sizes
and for reaction 1 on reactor 1. . . . . . . . . . . . . . . . . . . . . . . . 85
4.7 Data corresponding to optimal coolant pro les for different batch sizes
and for reaction 1 on reactor 2. . . . . . . . . . . . . . . . . . . . . . . . 85
viii