Scholars' Mine Doctoral Dissertations Student Theses and Dissertations Fall 2010 Identifying multiple steady states in the design of reactive distillation processes Thomas Karl Mills Follow this and additional works at: https://scholarsmine.mst.edu/doctoral_dissertations Part of the Chemical Engineering Commons Department: Chemical and Biochemical Engineering Recommended Citation Mills, Thomas Karl, "Identifying multiple steady states in the design of reactive distillation processes" (2010). Doctoral Dissertations. 2190. https://scholarsmine.mst.edu/doctoral_dissertations/2190 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. IDENTIFYING MULTIPLE STEADY STATES IN THE DESIGN OF REACTIVE DISTILLATION PROCESSES by THOMAS KARL MILLS A DISSERTATION Presented to the Faculty of the Graduate School of the MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY in CHEMICAL ENGINEERING 2010 Approved by Neil L Book, Coadvisor Oliver C Sitton, Coadvisor Douglas K Ludlow Jee-Ching Wang Mark W Fitch © 2010 Thomas K Mills All Rights Reserved iii PUBLICATION DISSERTATION OPTION This dissertation has been prepared in the style utilized by Computers and Chemical Engineering. Pages 18-32 and 33-47 will be submitted for publication in that journal. Appendices A, B, C, and D have been added for purposes normal to dissertation writing. iv ABSTRACT Global homotopy continuation is used to identify multiple steady states in ideal reactive flash and reactive distillation systems involving a reaction of the form A+B ↔C taking place in the liquid phase. The choice of specifications has an influence on the existence of multiple solutions for both the flash and the column. For the flash, specification of the heat input or withdrawal can give rise to multiplicities while specification of the split fraction does not. Specification of one internal energy balance variable and one external material balance variable does not produce multiplicities in the column; however, specification of two internal energy balance variables can produce multiplicities. This is seen to have implications for the selection of control variables for both the flash and the column. The effects of the relative volatility between the light and heavy components, the forward rate constant, and the reaction equilibrium constant are studied. It is concluded that both the relative volatility spread and the equilibrium constant exhibit threshold values, below which only singular solutions are obtained. Above this threshold, multiplicities are to be found. The rate constant also affects the appearance of multiple solutions, but the multiplicities are found in regions bounded above and below by regions producing only singular solutions. The cause of multiplicities in the idealized system studied is seen to be the interaction between consumption and creation of species by reaction and transfer of material between phases. The reaction rate appears to be the major contributor to this effect because it is able to reverse direction, assuming either positive or negative values. v ACKNOWLEDGMENTS The author is indebted to advisors Dr Neil Book and Dr Oliver Sitton for their advice and guidance during this project, and to committee members Dr Douglas Ludlow, Dr Jee-Ching Wang, and Dr Mark Fitch for their support and encouragement. A debt of thanks is also owed to other members of the Chemical Engineering department, past and present, for their encouragement along the way. Additionally, sincere thanks are due to the author’s wife Janice, son Thomas Jr, and father Horace Mills, whose encouragement and patience have made this project possible. vi TABLE OF CONTENTS Page PUBLICATION DISSERTATION OPTION....................................................................iii ABSTRACT....................................................................................................................... iv ACKNOWLEDGMENTS .................................................................................................. v LIST OF ILLUSTRATIONS...........................................................................................viii LIST OF TABLES............................................................................................................. ix NOMENCLATURE ........................................................................................................... x SECTION 1. INTRODUCTION...................................................................................................... 1 1.1. CHEMICAL / THERMODYNAMIC MODEL ................................................. 1 1.2. COLUMN MODEL AND SOLUTION ALGORITHM .................................... 3 2. LITERATURE REVIEW........................................................................................... 5 2.1. REACTIVE DISTILLATION APPLICATION................................................. 5 2.2. GRAPHICAL AND ALGEBRAIC MODELS................................................... 5 2.3. SIMULATIONS OTHER THAN WITH HOMOTOPY CONTINUATION .. 11 2.4. HOMOTOPY METHOD DEVELOPMENT ................................................... 15 2.5. HOMOTOPY METHOD APPLICATION ...................................................... 17 PAPERS I. MULTIPLE STEADY STATES IN THREE-COMPONENT REACTIVE DISTILLATION: EFFECT OF OPERATING PARAMETERS............................ 18 ABSTRACT............................................................................................................. 18 1. INTRODUCTION............................................................................................ 18 2. THE REACTIVE FLASH................................................................................ 20 3. THE REACTIVE COLUMN ........................................................................... 23 4. CONCLUSIONS.............................................................................................. 29 NOMENCLATURE ................................................................................................ 30 vii REFERENCES ........................................................................................................ 31 II. MULTIPLE STEADY STATES IN THREE-COMPONENT REACTION SYSTEMS: EFFECT OF COMPONENT PHYSICAL PROPERTIES ................ 33 ABSTRACT............................................................................................................. 33 1. INTRODUCTION............................................................................................ 33 2. THE REACTIVE FLASH................................................................................ 35 3. THE REACTIVE COLUMN ........................................................................... 39 4. CONCLUSIONS.............................................................................................. 42 NOMENCLATURE ................................................................................................ 45 REFERENCES ........................................................................................................ 46 SECTION 3. CONCLUSIONS...................................................................................................... 48 APPENDICES A. COMPUTER PROGRAMS USED FOR THIS STUDY....................................... 50 B. REACTIVE DISTILLATION PROGRAM SOURCE CODE............................... 79 C. REACTIVE FLASH PROGRAM SOURCE CODE ........................................... 130 D. HOMOTOPY CONTINUATION SOLVER SOURCE CODE........................... 159 BIBLIOGRAPHY........................................................................................................... 186 VITA .............................................................................................................................. 192 viii LIST OF ILLUSTRATIONS Page PAPER I Figure 1 - Reactive flash ............................................................................................ 20 Figure 2 – Reactive flash with vapor-to-feed ratio specified..................................... 23 Figure 3 – Reactive flash with heat duty specified .................................................... 24 Figure 4 - Reactive column........................................................................................ 24 Figure 5 – Reactive distillation with specified boilup and bottoms rates .................. 26 Figure 6 – Reactive distillation with boilup and reflux rate specified ....................... 27 Figure 7 – Component A liquid compositions with boilup and reflux rate specified 28 Figure 8 – Component B liquid compositions with boilup and reflux rate specified 28 Figure 9 – Component C liquid compositions with boilup and reflux rate specified 29 PAPER II Figure 1 – Reactive flash............................................................................................ 35 Figure 2 - Conversion versus Damkohler number for a range of species A relative volatilities.................................................................................................. 38 Figure 3 - Conversion versus Damkohler number for a range of rate constant values......................................................................................................... 38 Figure 4 - Conversion versus Damkohler number for a