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Masters Thesis: Control of Reactive Batch Distillation Columns Via Control of Reactive Batch Distillation Columns via Extents Transformation Carlos Samuel Méndez Blanco Master of Science Thesis Delft Center for Systems and Control Control of Reactive Batch Distillation Columns via Extents Transformation Master of Science Thesis For the degree of Master of Science in Systems and Control at Delft University of Technology Carlos Samuel Méndez Blanco June 13, 2017 Faculty of Mechanical, Maritime and Materials Engineering (3mE) · Delft University of Technology The work in this literature survey was done jointly with the Eindhoven University of Tech- nology Control Systems Department. Their cooperation is hereby gratefully acknowledged. Copyright c Delft Center for Systems and Control (DCSC) All rights reserved. Table of Contents Acknowledgements vii 1 Introduction 1 2 Reactive and Distillation Processes 5 2-1 DistillationandReactiveProcesses . ......... 5 2-2 ReactiveDistillationProcess . ....... 7 3 Extents Transformation for Reaction Systems 17 3-1 ExtentsofReaction ............................... 17 3-2 Variant and Invariant Spaces of Chemical Processes . ............ 20 3-2-1 InclusionofEnergyBalance. 24 3-2-2 SensitivityAnalysis . 27 3-3 Limitations of the extent transformation approach . ............. 29 3-3-1 Spanofthechemicalspeciesspace . .... 30 ⊺ 3-3-2 Rank deficiency of [N Win n0] ...................... 31 3-4 Linear Parameter-Varying (LPV) state space model . ........... 32 3-4-1 First Approach: Model with Disturbance . ...... 33 3-4-2 Second Approach: Change of variable Z .................. 35 3-5 ControlbasedontheLPVmodels . 38 3-5-1 Case 1: Control based on model with external disturbance ........ 38 3-5-2 Case 2: Control with change of variable Z ................. 42 4 Extension of the Extent Transformations to Multiphase Reaction Systems 49 4-1 Continuous Gas-LiquidReaction Systems. ......... 49 4-2 BatchGas-LiquidReactionSystems . ...... 52 4-3 Casestudy...................................... 55 Master of Science Thesis Carlos Samuel Méndez Blanco ii Table of Contents 4-3-1 Development of the model for control . .... 58 4-3-2 State-feedbacklinearization . ...... 61 4-3-3 Linear Model Predictive Control for the Reactive Batch Distillation Process 64 4-3-4 Nonlinear Model Predictive Control for the Reactive Batch Distillation Pro- cess ..................................... 74 5 Conclusions and Future Work 79 ListofAcronyms................................... 85 Carlos Samuel Méndez Blanco Master of Science Thesis List of Figures 1-1 Thesisstructuringflowchart. ...... 3 2-1 Schematic diagram of a continuous distillation column. (Skogestad, 2008) . 6 2-2 Different types of reactors. (Skogestad, 2008) . ........... 7 2-3 Traveling concentration fronts in a nonreactive distillation column after a stepwise increase of the reflux. (Grüner and Kienle, 2004) . ....... 8 2-4 Stage equilibrium model (Perry and Green, 2008) . .......... 9 3-1 Three-way decomposition (linear transformation) (Amrhein et al., 2010) . 23 3-2 Evolution of number of moles per species in the CSTR . ......... 24 3-3 ExtentsofreactionsintheCSTR. ..... 25 3-4 ExtentsofinletintheCSTR . 26 3-5 Evolution of number of moles per species in the CSTR . ......... 27 3-6 Evolution of internal temperature in the CSTR . ......... 28 3-7 ExtentsofreactionsintheCSTR. ..... 29 3-8 ExtentsofinletintheCSTR . 30 3-9 ∂f gradient surface to changes in T and x with x = 1 kmol and x = 1 kg 31 ∂xr in,b r in,a 3-10 ∂f gradient surface to changes in T and x with x = 1 kmol and x = 20 kg 32 ∂xr in,b r in,a 3-11Extentsofinlet ................................. 33 3-12 Reconstructedmoles. .... 34 3-13Extentsofinlet ................................. 35 3-14 Reconstructedmoles. .... 36 3-15 Comparison of nonlinear model and LPV system response to reference changes . 37 3-16 Control based on model with external disturbance . ............ 40 3-17 LPV-model-based LQR controllers for reference tracking ............. 42 3-18 LPV-model-based LQR controllers control actions . ............. 43 Master of Science Thesis Carlos Samuel Méndez Blanco iv List of Figures 3-19 LPV-model-based LQR controllers for reference tracking ............. 45 3-20 LPV-model-based LQR controllers control actions . ............. 46 3-21 LPV-model-based LQR controllers for reference tracking ............. 48 3-22 LPV-model-based LQR controllers control actions . ............. 48 4-1 Representation of the gas-liquid reaction system (Bhatt et al., 2010) . 50 4-2 Representation of the reactive distillation column (Shah et al., 2011) . 56 4-3 Comparision between the formulations of Z .................... 60 4-4 Comparision between the nonlinear plant dynamics and the reproduction done by theLPVmodel ................................... 63 4-5 Reference trajectories of the distillate composition and reactor temperature . 68 4-6 Block diagram of the reactive batch distillation column control loop . 70 4-7 Controlled response of the distilled water composition at the accumulator stage (blue solid line) vs. Distilled water composition reference trajectory (red dashed line). Left to right: 1. Full view, 2. Transient response, 3. Tracking over optimal reference composition, 4. Final composition . ........ 70 4-8 Controlled response of the reactor temperature (blue solid line) vs. Temperature reference trajectory (red dashed line). Left to right: 1. Full view, 2. Transient response, 3. Tracking over optimal reference temperature, 4. Final temperature . 71 4-9 Control actions generated by the linear model-predictive controller. Left side of the dashed line: P controller action. Right side of the dashed line: MPC controller action. ........................................ 71 4-10 Moles of water and propylene glycol in the distillate accumulator . 72 4-11 Moles of reactants and products in the reactor . ........... 73 4-12 Scheme of nonlinear optimization procedure assuming piecewise constant inputs . 75 4-13 Controlled response of the distilled water composition at the accumulator stage (blue solid line) vs. Distilled water composition reference trajectory (red dashed line).......................................... 76 4-14 Controlled response of the reactor temperature (blue solid line) vs. Temperature reference trajectory (red dashed line). ....... 77 4-15 Control actions generated by the nonlinear model-predictive controller. 77 4-16 Moles of water and propylene glycol in the distillate accumulator . 78 4-17 Moles of reactants and products in the reactor . ........... 78 Carlos Samuel Méndez Blanco Master of Science Thesis List of Tables 2-1 Mostcommonequilibriummodels . .... 10 2-2 Summary of control of reactive distillation of Poly(polypropylene/hexylene)- terephthalate .................................... 11 2-3 Summary of control of reactive distillation of Methyl Tert-Butyl Ether (MTBE) 11 2-4 Summary of control of reactive distillation of Ethyl Acetate ........... 12 2-5 Summary of control of reactive distillation of Ethyl Tert-Butyl Ether (ETBE) . 13 2-6 Summary of control of reactive distillation of Methyl Acetate .......... 14 2-7 Summary of control of reactive distillation of Ethylene Glycol .......... 14 2-8 Summary of control of reactive distillation of Methacrylic Anhydride ...... 15 4-1 Change of input bound with respect to the parameters of theplant. 67 Master of Science Thesis Carlos Samuel Méndez Blanco vi List of Tables Carlos Samuel Méndez Blanco Master of Science Thesis Acknowledgements I would like to thank to Dr. L. Özkan for giving me the opportunity to come to TU Eindhoven to work on this project. For her interest and valuable input throughout the development of this thesis. I would also would like to thank Dr. A. Márquez, my daily supervisor, for his unconditional support and help with his advice and encouraging attitude; for having shown me the beauty of control engineering and awaken in me the taste for research and innovative ideas. To parents and my sister, who always stood by me, pushing me to follow my passion. To my family, who was always there supporting me along the way. To my best friend Camila, with whom I had several interesting debates about the content of this thesis. And to all of those who remained by my side knowing I was pursuing my dream. Gracias totales. Delft, University of Technology Carlos Samuel Méndez Blanco June 13, 2017 Master of Science Thesis Carlos Samuel Méndez Blanco viii Acknowledgements Carlos Samuel Méndez Blanco Master of Science Thesis Chapter 1 Introduction Nowadays in large-scale process industry, high purity of products is not only desired but crucial. Products must meet high-purity standards to conform with market and customers’ requirements. Attaining such quality standards, and at the same time, produce sufficiently to satisfy the demand, are typical challenges chemical industry faces. These processes allow the manufacturing of new materials in timely and efficient manner. In process industry, reaction and distillation processes are essential to achieve these objectives. The former transforms raw material into added-value products that can serve a myriad of purposes. The latter, on the other hand, separates and purifies the products obtained through reaction to conform to the quality requirements. Generally, these two processes are carried out in different units. However, there are production schemes where it is convenient and possible to combine both of them. This is done to overcome certain disadvantages and/or limitations that each operation unit possess. The combination of a reactor and a distillation column results in a
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