Modeling, simulation and control of periodic reactor systems

MODELING, SIMULATION AND CONTROL OF PERIODIC REACTOR SYSTEMS Sukumar Balaji (B.Tech, Anna University, Chennai, India) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CHEMICAL AND BIOMOLECULAR ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2007 ii ACKNOWLEDGMENTS Well, I really not know how to start with. Through out my research period, whenever I faced difficulty, the almighty was with me in the form of my supervisor, parents, sisters, other professors, friends and sometimes even in the form of myself. So, at first, I thank the almighty for His help and consideration. I am very much indebted to uncountable number of people for their help, advice, support etc. Primarily, I would like to thank my supervisor, Prof. Lakshminarayanan Samavedham for his excellent guidance and remarkable patience. He has substantially contributed to my personal and professional development. I must thank him for many insightful conversations on the project, helpful comments on my writing, presentation and teaching skills. In simple words, I incurred all the necessary qualities for a Ph.D. student only through my supervisor. Apart from technical matters, I have also enjoyed our numerous discussions on vedas, carnatic music, many philosophical topics etc. I think if I start expressing my gratitude towards him, I will have to write one more thesis. Undoubtedly, he is my best teacher and best well-wisher. I would like to thank Prof. Fraser Forbes and Prof. Bob Hayes for giving me an opportunity to visit their research group at the University of Alberta. I thank both of them for spending their time with me in clarifying some intricate concepts in spite of their busy schedule. Also, many fruitful discussions and group seminars with Prof. Sirish Shah, Prof. Nandakumar and Prof. Biao Huang furnished me an excellent exposure in various fields of process systems engineering. I sincerely thank Prof. Krantz for teaching me scaling analysis. I really admire his enthusiasm in teaching and in trouble shooting difficult scaling problems. Many useful comments and suggestions from my panel members Prof. Farooq, Prof. M. S. Chiu and Prof. A. K. Ray helped me a lot throughout the journey of my research. I am very much indebted to Prof. Krishna, Prof. Rangaiah, Prof. Jim Yang Lee and Prof. M. P. Srinivasan for giving me an opportunity to teach undergraduate iii modules. Their feedback and the achievements of Prof. Laksh and Prof. Nandakumar in teaching inspired me extremely in improving my teaching skills. I also thank my school teachers and undergraduate teachers for inculcating strong fundamental concept and confidence. I also would like to thank the reviewers for my published papers for their constructive comments. I thank all Informatics & Process Control group members (my labmates) and my flatmates for being so friendly and for creating a conducive environment. I would like to express my deep appreciation to all my beloved friends. Altogether, my special friends from University of Alberta (Canada), Anna University (Chennai) and National University of Singapore sum up to more than hundred. If I start mentioning about each and everyone, few hundred episodes of a new television show about friends can be directed. Hence, in short, I would like to thank all my beloved and true friends from the bottom of my heart. I would like to thank the undergraduate students for those I taught (tutor) MATLAB, Process Control, Chemical Reaction Engineering and Probability & Statistics and my lab FYP (Final Year Project) students for their interesting and thought provoking questions through which I learnt numerous things. In addition, special thanks to postgraduate students for those I taught (tutor) Numerical Methods. I thank COMSOL representatives for their prompt help whenever I encountered any problem with the software. Last, but not the least, I sincerely thank all the GSA (Graduate Students Association) office bearers for their team spirit in conducting the symposium for the academic year when I was in capacity as the president of the association. Most importantly, I would like to thank my parents (Mr. T. V. Sukumar, Mrs. S. Kousalya), sisters Padma & Prema and my niece Sreevarshini for their love and support which made me to come to this extent in life. It is said that in everyone’s success, there must be an important person. But in my case, I have six people. The list follows like this - my parents, my sisters, my niece and Prof. Laksh. I dedicate this thesis to them with all my love and affection. iv TABLE OF CONTENTS Page LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Global warming - a weapon of mass destruction . . . . . . . . . . . . 1.2 Fugitive methane emissions . . . . . . . . . . . . . . . . . . . . . . . 1.3 Catalytic combustion of methane . . . . . . . . . . . . . . . . . . . . 1.4 Autothermal operation . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Conventional autothermal reactor . . . . . . . . . . . . . . . . . . . . 1.6 Forced Unsteady-State Reactor Operation . . . . . . . . . . . . . . . 1.7 Reverse Flow Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.8 Loop Reactor or Multi Port Switching Reactor . . . . . . . . . . . . . 12 1.9 Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . . 13 1.10 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 19 LITERATURE REVIEW, MODELING AND SIMULATION . . . . . . . . 21 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Heat trap effect in the Reverse Flow Operation . . . . . . . . . . . . 34 2.3 Schematic of the experimental setup . . . . . . . . . . . . . . . . . . 37 2.4 Modeling a Reverse Flow Reactor . . . . . . . . . . . . . . . . . . . . 38 2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.4.2 Model equations . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.4.3 Fluid and solid properties . . . . . . . . . . . . . . . . . . . . 45 2.4.4 Rate of reaction and effectiveness factor . . . . . . . . . . . . 46 2.4.5 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 48 2.4.6 Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . 50 Numerical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.5 v Page 2.5.1 Coupling logically distinct domains . . . . . . . . . . . . . . . 53 2.5.2 Meshing and grid resolution . . . . . . . . . . . . . . . . . . . 54 2.5.3 Schematic of the simulated model and mesh statistics . . . . . 56 2.6 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.7 Post-processing of the simulated data . . . . . . . . . . . . . . . . . . 58 2.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 SCALING AND SENSITIVITY ANALYSIS OF THE REVERSE FLOW REACTOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2 Literature review on the effect of heat front in the reactor system . . 63 3.3 Introduction to scaling analysis . . . . . . . . . . . . . . . . . . . . . 67 3.3.1 Scaling analysis - minimum parametric representation of a system 67 3.3.2 Scaling procedure . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.3.3 Versatile nature of the analysis . . . . . . . . . . . . . . . . . 69 3.3.4 Scaled equations and scale factors . . . . . . . . . . . . . . . . 72 Deriving useful analytical expressions through scaling analysis . . . . 73 3.4.1 Heat transfer process time constant (tp ) . . . . . . . . . . . . 73 3.4.2 Maximum temperature attained in the reactor . . . . . . . . . 74 3.4.3 Reaction rate time scale . . . . . . . . . . . . . . . . . . . . . 78 3.4.4 Minimum length of the hot zone for sustainability . . . . . . . 78 Analysis of scaled equations and parameters . . . . . . . . . . . . . . 80 3.5.1 Final scaled equations . . . . . . . . . . . . . . . . . . . . . . 80 3.5.2 Proof of heterogeneity/homogeneity . . . . . . . . . . . . . . . 81 3.5.3 Time scale analysis . . . . . . . . . . . . . . . . . . . . . . . . 84 3.6 Stepwise model reduction and validation using scaling procedure . . . 85 3.7 Sensitivity analysis of various parameters . . . . . . . . . . . . . . . . 86 3.7.1 Effect of reactor length . . . . . . . . . . . . . . . . . . . . . . 87 3.7.2 Effect of switching time . . . . . . . . . . . . . . . . . . . . . 89 3.7.3 Mass transfer effects . . . . . . . . . . . . . . . . . . . . . . . 93 3.8 Effective RFR operation . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.4 3.5 vi Page HEAT REMOVAL FROM REVERSE FLOW REACTORS USED IN METHANE COMBUSTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.2 Reverse Flow Reactor with side feed 99 4.3 Overview of control strategies . . . . . . . . . . . . . . . . . . . . . . 100 4.4 Modeling assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.5 Relatively simplified mathematical model . . . . . . . . . . . . . . . . 103 4.6 Simple logic based control . . . . . . . . . . . . . . . . . . . . . . . . 104 4.7 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.8 . . . . . . . . . . . . . . . . . . 4.7.1 Possibility of heat extraction . . . . . . . . . . . . . . . . . . . 107 4.7.2 Optimal heat extraction from best possible location . . . . . . 111 4.7.3 Effect of heat removal on temperature profile . . . . . . . . . . 111 4.7.4 Effect of heat removal on concentration profile . . . . . . . . . 115 4.7.5 Maximum possible heat that can be extracted . . . . . . . . . 118 4.7.6 Effects of heat removal on exit concentration . . . . . . . . . . 120 4.7.7 Sustainability along with heat extraction . . . . . . . . . . . . 124 4.7.8 Reactor operation under rich feed conditions . . . . . . . . . . 127 4.7.9 RFR with side feed arrangement . . . . . . . . . . . . . . . . 129 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 PERFORMANCE COMPARISON OF AUTOTHERMAL REACTOR CONFIGURATIONS FOR METHANE COMBUSTION . . . . . . . . . . . . . 135 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.2 Literature review on different types of autothermal reactors . . . . . . 136 5.3 Overview of the present study . . . . . . . . . . . . . . . . . . . . . . 139 5.4 Reactor configurations . . . . . . . . . . . . . . . . . . . . . . . . . . 140 5.5 5.4.1 Reverse Flow Reactor . . . . . . . . . . . . . . . . . . . . . . . 141 5.4.2 General Multi Port Switching Reactor . . . . . . . . . . . . . 141 5.4.3 MPSR with more than one path line (2 or 3) in one flow direction144 5.4.4 MPSR with only one path line in each flow direction . . . . . 144 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.5.1 Comparison of different MPSR operations . . . . . . . . . . . 146 vii Page 5.6 5.5.2 Comparing MPSR with RFR based on reactant concentration 151 5.5.3 Comparing MPSR with RFR based on flow rate . . . . . . . . 161 5.5.4 New design (A combination of RFR and MPSR) . . . . . . . . 163 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 REPETITIVE MODEL PREDICTIVE CONTROL OF A REVERSE FLOW REACTOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 6.2 Literature review on the control of the Reverse Flow Reactor . . . . . 174 6.3 Repetitive Model Predictive Control for periodic systems . . . . . . . 178 6.4 Overview of the present control study . . . . . . . . . . . . . . . . . . 179 6.5 Reduced order model . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 6.6 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 6.7 Main control problems for the RFR operation . . . . . . . . . . . . . 185 6.8 Feasible operational approaches . . . . . . . . . . . . . . . . . . . . . 185 6.9 6.8.1 Under rich feed conditions . . . . . . . . . . . . . . . . . . . . 185 6.8.2 Under lean feed conditions . . . . . . . . . . . . . . . . . . . . 187 Repetitive Model Predictive Control . . . . . . . . . . . . . . . . . . 188 6.9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 6.9.2 Preferred manipulated variables . . . . . . . . . . . . . . . . . 188 6.9.3 RMPC formulation . . . . . . . . . . . . . . . . . . . . . . . . 191 6.9.4 Periodic errors and periodic disturbances . . . . . . . . . . . . 194 6.9.5 Discrete time state space representation of the model . . . . . 195 6.10 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 198 6.11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 CONTRIBUTIONS AND FUTURE WORKS . . . . . . . . . . . . . . . . 212 7.1 Summary of contributions . . . . . . . . . . . . . . . . . . . . . . . . 212 7.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 7.2.1 Learning control strategy for Reverse Flow Reactors . . . . . . 214 7.2.2 Robust control for periodic systems . . . . . . . . . . . . . . . 218 7.2.3 Alternate heat and mass extraction for better control performance218 7.2.4 Micro Reverse Flow Reactors . . . . . . . . . . . . . . . . . . 219 viii Page LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 A Appendix: Reactor properties . . . . . . . . . . . . . . . . . . . . . . . . . 245 B Appendix: Scaling procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 250 LIST OF PUBLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 VITAE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 ix LIST OF TABLES Table Page 1.1 Examples of processes with improved performance under Forced UnsteadyState Operations (Boreskov and Matros, 1984). . . . . . . . . . . . . . . 2.1 Review of various types of reactions carried out using reverse flow concept and the corresponding journal publications. . . . . . . . . . . . . . . . . 23 2.2 Expressions for various parameters of the packed bed, inert monolith and open sections in the reactor (Salomons et al., 2004). . . . . . . . . . . . . 51 2.3 Mesh statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.1 Characteristic dimensionless numbers and their significance. . . . . . . . 83 6.1 Maximum temperature predicted by the reduced and detailed models for varying inlet methane concentration (at 30th second in the forward direction).186 6.2 RMPC formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 x LIST OF FIGURES Figure Page 1.1 Reactor with feed effluent heat exchanger. . . . . . . . . . . . . . . . . . 1.2 Temperature profiles for two different feed concentrations given in terms of the adiabatic temperature rise(∆Tad ). Taken from Nieken et al., 1994a. 1.3 Illustration of Reverse Flow Reactor concept (Balaji and Lakshminarayanan, 2005). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Illustration of the Loop Reactor concept. . . . . . . . . . . . . . . . . . . 13 1.5 Comparison of methane and carbon monoxide conversion between the reverse flow operation and the unidirectional flow operation. Taken from Liu et al. (2001). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.6 Flowchart representing the nature of work in each chapter and the flow and connection between chapters. . . . . . . . . . . . . . . . . . . . . . . 20 2.1 Illustration of the heat trap effect for the reverse flow operation. . . . . . 36 2.2 Schematic of the reactor and the associated piping. Thermocouple locations are also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.3 Schematic of the reactor, including valves, thermocouples, and thermocouple locations, heat exchanger and gas withdrawal set-up. Radial thermocouple locations are shown in the circles. . . . . . . . . . . . . . . . . 40 2.4 Schematic of the model simulated in COMSOL (the small sections with red lines are open sections). . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.5 Model validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.6 Two-dimensional plot of the temperature distribution simulated in COMSOL after 180s of the start up. . . . . . . . . . . . . . . . . . . . . . . . 59 2.7 Concentration profile simulated from the model at the end of forward and reverse cycle (180s and 360s respectively). . . . . . . . . . . . . . . . . . 60 3.1 Reverse Flow Reactor without inert monolith sections. . . . . . . . . . . 71 3.2 Sensitivity of dimensionless maximum temperature at cyclic-steady-state to changes in the reactor length for varying velocity. . . . . . . . . . . . . 88 3.3 Dimensionless temperature attained in the reactor at every switching time for both forward and reverse flow with nominal bed length (till cyclicsteady-state is attained). . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.4 Dimensionless temperature attained in the reactor at every switching time for both forward and reverse flow with increased bed length (till cyclicsteady-state is attained) . . . . . . . . . . . . . . . . . . . . . . . . . . 91 249 Reaction kinetics HR = −806.9 + 1.586 ∗ 10−2 Tc − 8.485 ∗ 10−6 Tc2 − 3.963 ∗ 10−9 Tc3 +2.16 ∗ 10−12 Tc4 KJmol−1 Physical properties δ = 0.00322 + 0.28 m Fluid properties Cpg = a + bTg + cTg2 + dTg3 Jmol−1 K −1 a= b= c= d= Cg Cg Cg Cg                      19.86cM + (22.22 + ∗ 32.19) (cM o − cM ) +25.44 ((1 − 0.2095cM o) − (cM o − cM )) + 28.85 (1 − cM o ) 0.7808 5.016 ∗ 10 cM + (5.9711 + ∗ 0.1920) ∗ 10 −2 −2     (cM o − cM ) +1.518 ∗ 10−2 ((1 − 0.2095cM o) − (cM o − cM )) − 0.1569 ∗ 10−2 (1 − cM o ) 0.7808       1.267 ∗ 10−5 cM + (−3.495 + ∗ 1.054) ∗ 10−5 (cM o − cM ) −0.7144 ∗ 10−5 ((1 − 0.2095cM o) − (cM o − cM )) − 0.8067 ∗ 10−5 (1 − cM o ) 0.7808 −10.99 ∗ 10 cM + (7.457 − ∗ 3.589) ∗ 10 −9 −9 (cM o − cM ) +1.310 ∗ 10−9 ((1 − 0.2095cM o) − (cM o − cM )) − 2.868 ∗ 10−9 (1 − cM o ) 0.7808 The Nusselt number for heat transfer was calculated from the correlation of Groppi and Tronconi (2000) with an assumption of square shaped channels for the monolith sections (Table 2.2).          250 B. Appendix: Scaling procedure Scaling factors Tc∗ = cM ∗ co Tc − Tcr ∗ Tg − Tgr ∗ ; Tg = ; cM = ; cM = oM Tcs Tgs cM s cM s z∗ = h∗ = z ∗ r t ; r = ; t∗ = zs rs ts h (−R) ∗ ρg Cpg ∗ u HR ∗ km ; (−R)∗ = ; ρg = ; Cp∗g = ; u = ; HR∗ = ; km = hs (−Rs ) ρgs Cpgs us HRs kms Note: For the variables that are not referenced to zero in the initial, boundary, and auxiliary conditions, an unspecified reference factor is also included. The scale and reference factors are substituted in the various expressions used to calculate the system parameters. The reaction rate expression is given by (−R) = 1.35 ∗ 105 e− 6543 Tc coM − T ∗ T6543 +T (−R)∗ (−R)s = 1.35 ∗ 105 e c − (−R)∗ = coM s cs o (co∗ M cM s ) 6543 T Tcs Tc∗ + cr Tcs ( 1.35 ∗ 10 e (−R)s cr ) (co∗ M) (B.1) HR = 806.9 − 1.586 ∗ 10−2 Tc + 8.485 ∗ 10−6 Tc2 ∗ 1000 H∗R HRs = 806.9 − 1.586 ∗ 10−2 Tcs Tc∗ + H∗R Tcr Tcr + 8.485 ∗ 10−6 Tcs2 Tc∗ + Tcs Tcs Tcr Tcr = 806.9 − 1.586 ∗ 10−2 Tcs Tc∗ + + 8.485 ∗ 10−6 Tcs2 Tc∗ + HRs Tcs Tcs ∗ 1000 ∗1000 (B.2) 251 MP Rg Tg ρg = ρ∗g ρgs = MP Rg Tg∗ Tgs + Tgr MP ρ∗g = ρgs Rg Tgs Tg∗ + (B.3) Tgr Tgs Cpg = a + bTg + cTg2 + dTg3 Cp∗g Cpgs = a + b Tg∗ Tgs + Tgr + c Tg∗ Tgs + Tgr   Tgr Cp∗g = a + bTgs Tg∗ + Cpgs Tgs + cTgs u∗ = Tgr Tg∗ + Tgs + d Tg∗ Tgs + Tgr + dTgs Tgr Tg∗ + Tgs   Tg∗ Tgs + Tgr Tg0 6543 (−R)s = coM s ∗ 1.35 ∗ 105 e− Tcs MP Rg Tgs Cpgs = a + bTgs + cTgs + dTgs us = Tg Tg0 uin Tgs Tgr Tg∗ + Tg0 us Tgs ρgs = (B.4) u = uin u∗ us = uin uin Tgs Tg0 HRs = 806.9 − 1.586 ∗ 10−2 Tcs + 8.485 ∗ 10−6 Tcs2 ∗ 1000 (B.5) Catalyst Temperature: The model equation representing the energy balance of the catalyst is ρc Cpc ∂Tc ∂ ∂Tc = kc r ∂t r ∂r ∂r + kc ∂ ∂z ∂Tc ∂z + hap (Tg − Tc ) + HR η (−R) Introducing the scale factors in the above equation results in ∗ ρc Cpc Tcs ∂Tc∗ kc Tcs ∂ ∗ ∂Tc = r ts ∂t∗ rs2 r ∗ ∂r ∗ ∂r ∗ + kc Tcs ∂ zs2 ∂z ∗ ∂Tc∗ ∂z ∗ + hs ap Tcs h∗ Tg∗ Tgs Tgr Tcr + − Tc∗ − Tcs Tcs Tcs + HR∗ HRs η (−R)∗ (−R)s Dividing throughout by the dimensional coefficient of one term (preferably one that must be retained) in each of the describing equations results in the following equation. ∗ kc Tcs ∂ kc Tcs ∂ ρc Cpc Tcs ∂Tc∗ ∗ ∂Tc = r + ∗ ∗ ∗ ∗ ts HRs η (−R)s ∂t rs ηHRs (−R)s r ∂r ∂r zs ηHRs (−R)s ∂z ∗ ∂Tc∗ ap hs Tcs Tgs Tgr − Tcr + h∗ Tg∗ + − Tc∗ +HR∗ (−R)∗ ∗ ∂z ηHRs (−R)s Tcs Tcs (B.6) Applying similar procedure (as was done for catalyst temperature), we can arrive at the scaled form of all the governing equations. Fluid Temperature: ερg Cpg ∂Tg ∂ ∂Tg =ε rkg ∂t r ∂r ∂r +ε ∂ ∂Tg kg ∂z ∂z ∂Tg∗ ερgs Cpgs Tgs ∗ ∗ ∂Tg∗ εTgs ∂ ρg Cpg ∗ = ∗ ∗ r ∗ kg ∗ ts ∂t rs r ∂r ∂r + ∂Tg + hap (1 − ε) (Tc − Tg ) ∂z ∂Tg∗ εTgs ∂ k g zs2 ∂z ∗ ∂z ∗ − Tgr Tcs Tcr + − Tg∗ − Tgs Tgs Tgs us ρgs Cpgs Tgs ∗ ∗ ∗ ∂Tg∗ u ρg Cpg ∗ zs ∂z 252 + (1 − ε) hs ap Tgs h∗ Tc∗ − uρg Cpg ∗ εzs ∗ ∗ ∂Tg∗ εkg zs ∂ εkg ∂ ∗ ∂Tg ρg Cpg ∗ = r + ∗ ∗ ∗ ts us ∂t rs us ρgs Cpgs r ∂r ∂r zs us ρgs Cpgs ∂z ∗ ∗ ∂Tg∗ hs ap (1 − ε) zs ∗ Tcs Tcr − Tgr ∗ ∗ ∗ ∂Tg − u ρ Cp + h Tc∗ + − Tg∗ g g ∗ ∗ ∂z ∂z us ρgs Cpgs Tgs Tgs (B.7) Fluid Concentration: ε ∂cM ∂ ∂cM =ε rDr ∂t r ∂r ∂r ∗ εcM s ∂c∗M εDr cM s ∂ ∗ ∂cM = r ts ∂t∗ rs2 r ∗ ∂r ∗ ∂r ∗ + +ε ∂ ∂cM Dz ∂z ∂z εDz cM s ∂ zs2 ∂z ∗ ∗ εzs ∂c∗M εzs Dr ∂ ∗ ∂cM r = ts us ∂t∗ us rs2 r ∗ ∂r ∗ ∂r ∗ + ∂c∗M ∂z ∗ εDz ∂ zs us ∂z ∗ −u − ∂c∗M ∂z ∗ ∂cM − km ap (1 − ε) (cM − coM ) ∂z o us cM s ∗ ∂c∗M co∗ M cM s ∗ ∗ u − k k a (1 − ε) c c − Ms m ms p M zs ∂z ∗ cM s − u∗ o ∂c∗M kms ap (1 − ε) zs ∗ ∗ co∗ M cM s − k c − m M ∂z ∗ us cM s (B.8) km ap (cM − coM ) = η (−R) ∗ ∗ o km kms ap (c∗M cM s − co∗ M cM s ) = η (−R) (−R)s kms ap cM s ∗ ∗ coM s km cM − co∗ M η (−R)s cM s = (−R)∗ (B.9) 253 −Dz ε − −kg ε − h= 0.017+0.000051Tg Dc      ∂cM ∂z = u (cM − cM ) Dz ε ∂c∗M us zs ∂z ∗ ∂Tg ∂z = u∗ cM − c∗M cM s at z ∗ = 0 ≤ t∗ ≤ = ρg uCpg Tg0 − ρg uCpg Tg ∂Tg∗ kg ε ρgs us Cpgs zs ∂z ∗ + 1.1 at z = 0 ≤ t ≤ tf = ρ∗g u∗ Cp∗g tf ts (B.10) at z = 0 ≤ t ≤ tf Tg0 − Tgr − Tg∗ Tgs at z ∗ = 0 ≤ t∗ ≤ tf ts (B.11) ((28.09+0.1965∗10−2 Tg +0.4799∗10−5 Tg2 )∗28−1 ∗1000)(0.77∗10−5 +0.42∗10−7 Tg −0.75∗10−11 Tg2 ) uDc M P Rg Tg (0.77∗10−5 +0.42∗10−7 Tg −0.75∗10−11 Tg2 )  9.86 ∗ 10−10 Tg1.75   km =   0.0075 0.017+0.000051Tg 3/5 7.701∗10−6 +4.166∗10−8 Tg −7.531∗10−12 Tg2 Rg Tg + 1.1 9.86∗10−10 Tg1.75 MP 3/5 uDc M P Rg Tg (0.77∗10−5 +0.42∗10−7 Tg −0.75∗10−11 Tg2 ) 1/3 1/3           (B.12) (B.13) The scaling and reference factors for different parameters considered in the model were determined based on the procedure given in Krantz (2006). zs = L; rs = Rc ; ts = tf hs =     0.017+0.000051Tgs Dc + 1.1 ∗28−1 ∗1000 ((28.09+0.1965∗10−2 Tgs +0.4799∗10−5 Tgs ) )(0.77∗10−5 +0.42∗10−7 Tgs −0.75∗10−11 Tgs ) u s Dc M P Rg Tgs (0.77∗10−5 +0.42∗10−7 Tgs −0.75∗10−11 Tgs ) 0.017+0.000051Tgs 3/5 1/3      254  255 kms 1.75 9.86 ∗ 10−10 Tgs = 0.0075       + 1.1 7.701∗10−6 +4.166∗10−8 Tgs −7.531∗10−12 Tgs Rg Tgs 1.75 9.86∗10−10 Tgs MP u s Dc M P Rg Tgs (0.77∗10−5 +0.42∗10−7 Tgs −0.75∗10−11 Tgs ) 3/5 1/3       Tgr − Tcr = ⇒ Tgr = Tcr Tcs Tgs = ⇒ Tgs = Tcs Tcs cM r − coM r = ⇒ cM r = coM r cM s The reference factors for both the concentrations are naturally referenced to zero and hence not included in calculating the corresponding scale factors. coM s = ⇒ cM s = coM s cM s coM r = 0; cM r = cM − cM r = ⇒ cM s = cM ⇒ coM s = cM cM s Tg0 − Tgr = ⇒ Tgr = Tg0 ⇒ Tcr = Tg0 Tgs Tcs and Tgs are the maximum temperature in the catalyst and gas phase respectively. The different expressions derived in section 3.4.2 give the expression for both Tcs and Tgs . LIST OF PUBLICATIONS 256 LIST OF PUBLICATIONS Journal Publications 1. Balaji, S., Lakshminarayanan, S. Heat Removal from Reverse Flow Reactors used in Methane Combustion, Canadian Journal of Chemical Engineering, 2005, pp. 695704. 2. Balaji, S., Lakshminarayanan, S. Performance Comparison of Autothermal Reactor Configurations for Methane Combustion, Industrial & Engineering Chemistry Research, 2006, 45 (11), pp. 3880-3890. 3. Balaji, S., Lakshminarayanan, S. Novel Design of Microchannel Plate Geometry for Uniform Flow Distribution, Canadian Journal of Chemical Engineering, 2006, 84, pp. 715-721. 4. Balaji, S., Fuxman, A., Lakshminarayanan, S., Forbes, J.F., & Hayes, R. E. Repetitive Model Predictive Control of a Reverse Flow Reactor, Chemical Engineering Science, 2007, 62, pp. 2154-2167. 5. Balaji, S., Lakshminarayanan, S., Krantz, W. B. Scaling and Sensitivity Analysis of a Reverse Flow Reactor, Chemical Engineering Science, accepted for publication. 257 Conference Proceedings 1. Balaji, S., Lakshminarayanan, S., (2007). Control Oriented Scaling Analysis and Reduced Order Modeling of a Polymer Electrolyte Fuel Cell, to be presented at PSE Asia, Xi’an, China, Aug. 15-18. 2. Balaji, S., Lakshminarayanan, S., (2007). Control of Reverse Flow Reactors used for Methane Combustion: an overview, International Conference on Cleaner Technologies and Environmental Management, Pondicherry, India, Jan. 4-6. 3. Lakshminarayanan, S., Balaji, S., Raghuraj Rao, K., (2007). Role of Process Systems Engineering in Sustainable Development. International Conference on Cleaner Technologies and Environmental Management, Pondicherry, India, Jan. 4-6. 4. Balaji, S., Lakshminarayanan, S., Krantz, W. B., (2006). Scaling and Sensitivity Analysis of Simulated Moving Bed Reactors, American Institute of Chemical Engineers Conference (AIChE), San Francisco, Nov. 12-17. 5. Lakshminarayanan. S, Krantz, W. B., Balaji, S., (2006). Pedagogical and Learning Advantages Realizable Through Scaling and Non-Dimensionalization, American Institute of Chemical Engineers Conference (AIChE), San Francisco, Nov. 12-17. 6. Balaji, S., Lakshminarayanan, S., (2006). Learning Control for Periodic Systems with Unknown Periods, Asian Pacific Confederation of Chemical Engineering Congress, Kualalumpur, Malaysia, Aug. 27-30. 7. Lakshminarayanan, S., Raghuraj Rao, K., Balaji, S., (2006). ‘CONSIM’, MS Excel Based Student Friendly Simulator for Teaching Process Control Theory, Asian Pacific Confederation of Chemical Engineering Congress, Kualalumpur, Malaysia, Aug. 27-30. 8. Lakshminarayanan, S., Balaji, S., Raghuraj Rao, K., (2005). Impact of Process 258 Design on Achievable Control Loop Performance, CHEMCON, 58th annual Indian session of the Institute of Chemical Engineers, New Delhi, India, Dec. 14-17. 9. Balaji, S., Lakshminarayanan, S., Forbes, J. F., & Hayes, R. E., (2005). Repetitive Model Predictive Control for Reverse Flow Reactors, CSChE (Canadian Society for Chemical Engineers) conference, Toronto, ON, Oct. 16-19. 10. Balaji, S., Zheng Suni, Lakshminarayanan, S., Nandakumar, K., (2005). Generation of Desired Concentration Profiles in Micro-fluidic Networks, 2nd Annual Graduate Student Symposium, National University of Singapore, Oct. 6. VITAE 259 BALAJI SUKUMAR 5806, Hobart Street Pittsburgh Pennsylvania PA-15217 Tel: +1 901 619 5968 (HP) Tel: +1 412 268 3039 (Office) Email: sukumarbalaji@gmail.com CAREER OBJECTIVE To make interesting and useful contributions to the area of Process Systems Engineering PERSONAL INFORMATION Nationality Resident of Birth date Gender : Indian : United States of America : 25 January 1982 : Male EDUCATION July 2007 – Present: Postdoctoral Candidate Department of Chemical Engineering Carnegie Mellon University Supervisor: Prof. Erik Ydstie Research Area: Design and Control of Multi-Phase Reactor Systems July 2003 – March 2007: Doctor of Philosophy Department of Chemical & Biomolecular Engineering National University of Singapore Supervisor: Prof. Lakshminarayanan Thesis Area: Modeling, Simulation & Control of Periodic Systems June 1999 – June 2003: Bachelor of Technology (Chemical) Anna University, India CGPA (Cumulative Grade Point Average) - 9.1/10 PROFESSIONAL EXPERIENCE Research experience: July 2003 – March 2007: Research Scholar, National University of Singapore Obtained an excellent exposure in: Computational and theoretical studies of complex systems such as Reverse Flow Reactors, Multi Port Switching Reactors, Micro Reactors Data Analysis, System Identification and subsequent application of advanced control methods like Model Predictive Control, Iterative Learning Control on Periodic (Hybrid) Systems - Reverse Flow Reactor, Multi Port Switching Reactor Modeling various systems from first principles (using the multiphysics modeling software - COMSOL) and Scaling Analysis of such systems Population Balance Modeling of tumor cells using Finite Elements Method Generation of desired concentration gradients in Micro Channels and designs to ensure uniform flow distribution in Micro Channel plate geometry 260 August 2005 – Research Assistant, University of Alberta September 2005: Gained experience in System Identification and Repetitive Nonlinear Model Predictive Control of Reverse Flow Reactors January 2007 – June 2007: Applications Engineer, i-Math Pvt Ltd, Singapore Worked as technical (computationally) assistant in solving research problems for Chartered Semiconductors, Acoustics Research Laboratories, Nanyang Technological University and Singapore Polytechnic Continuing the assistance for the company till date as a virtual support (emails) January 2007 – Present: Co-Supervisor, Nanyang Technological University, Singapore Co-supervising an undergraduate student on a final year project in collaboration with Prof. Vinay Kariwala at Nanyang Technological University Project title: Modeling and Sensitivity Analysis of Reverse Flow Reactors Teaching experience: July 2003 – March 2007: Teaching Assistant/ Lab Demonstrator, National University of Singapore Tutored the following courses: CN5010: Mathematical Methods in Chemical & Environmental Engineering CN3121: Process Dynamics & Control CN2116: Chemical Reaction Engineering CN2108 / EV2108: MATLAB / SIMULINK TC3412: Probability & Statistics TC4109: Design Project Obtained Best Tutor Award for teaching Process Dynamics & Control; AY: 2004-2005; Class size: 118; Response Rate: 91.53%; Avg. Score: 4.37 out of 5. RESEARCH OUTCOMES Journal publications: 1. Balaji, S., Lakshminarayanan, S. Heat Removal from Reverse Flow Reactors used in Methane Combustion, Canadian Journal of Chemical Engineering, 2005, pp. 695- 704. 2. Balaji, S., Lakshminarayanan, S. Performance Comparison of Autothermal Reactor Configurations for Methane Combustion, Industrial Engineering & Chemistry Research, 2006, 45 (11), pp. 3880-3890. 3. Balaji, S., Lakshminarayanan, S. Novel design of Microchannel plate geometry for Uniform Flow Distribution, Canadian Journal of Chemical Engineering, 2006, 84, pp. 715-721. 4. Balaji, S., Lakshminarayanan, S., Forbes, J.F., & Hayes, R. E. Repetitive Model Predictive Control of a Reverse Flow Reactor, Chemical Engineering Science, 2007, 62, pp. 2154-2167. 5. Balaji, S., Lakshminarayanan, S., Krantz, W. B. Scaling and Sensitivity Analysis of a Reverse Flow Reactor, Chemical Engineering Science, 2007, accepted for publication. Obtained Best Paper Award at CHEMCON 2005, New Delhi, India (Advances in Process Control). 261 Conferences: 1. Balaji, S., Lakshminarayanan, S., (2007). Control of Reverse Flow Reactors used for Methane Combustion: an overview, International Conference on Cleaner Technologies and Environmental Management, Pondicherry, India, Jan. 4-6. 2. Lakshminarayanan, S., Balaji, S., Raghuraj Rao, K., (2007). Role of Process Systems Engineering in Sustainable Development. International Conference on Cleaner Technologies and Environmental Management, Pondicherry, India, Jan. 4-6. 3. Balaji, S., Lakshminarayanan, S., Krantz, W. B., (2006). Scaling and Sensitivity Analysis of Simulated Moving Bed Reactors, American Institute of Chemical Engineers Conference (AIChE), San Francisco, Nov. 12-17. 4. Lakshminarayanan. S, Krantz, W. B., Balaji, S., (2006). Pedagogical and Learning Advantages Realizable Through Scaling and Non-Dimensionalization, American Institute of Chemical Engineers Conference (AIChE), San Francisco, Nov. 12-17. 5. Balaji, S., Lakshminarayanan, S., (2006). Learning Control for Periodic Systems with Unknown Periods, Asian Pacific Confederation of Chemical Engineering Congress, Kualalumpur, Malaysia, Aug. 27-30. 6. Lakshminarayanan, S., Raghuraj Rao, K., Balaji, S., (2006). “CONSIM”, MS Excel Based Student Friendly Simulator for Teaching Process Control Theory, Asian Pacific Confederation of Chemical Engineering Congress, Kualalumpur, Malaysia, Aug. 27-30. 7. Lakshminarayanan, S., Balaji, S., Raghuraj Rao, K., (2005). Impact of Process Design on Achievable Control Loop Performance, CHEMCON, 58th annual Indian session of the Institute of Chemical Engineers, New Delhi, India, Dec. 14-17. 8. Balaji, S., Lakshminarayanan, S., Forbes, J. F., & Hayes, R. E., (2005). Repetitive Model Predictive Control for Reverse Flow Reactors, CSChE (Canadian Society for Chemical Engineers) conference, Toronto, ON, Oct. 16-19. 9. Balaji, S., Zheng Suni, Lakshminarayanan, S., Nandakumar, K., (2005). Generation of Desired Concentration Profiles in Micro-fluidic Networks, 2nd Annual Graduate Student Symposium, National University of Singapore, Oct. 6. GUEST LECTURES - Workshop on Multiphysics Modeling using Finite Elements Method at the Penang Skills Development Centre (PSDC), Penang, Malaysia, Nov. 28, 2006 - A two day workshop on COMSOL Multiphysics Modeling at the Institute of High Performance Computing (IHPC), Singapore, Aug. 10 & 11, 2006 - MATLAB for Numerical computing, IEEE Student chapter, National University of Singapore, 2005 - Simulation & Modeling of Catalytic Reverse Flow Reactor, Presented at the i-MathA*Star Seminar on Multi-physics Modeling: FEMLAB and Grid-enabled FEMLAB, Singapore, Jan. 2005 - Transport in an Electrokinetic Valve, Presented at the i-Math Biomedical Conference, Singapore, June 2004 INTERNSHIP EXPERIENCES - In-plant Training, Malar Solvent Extraction Pvt. Ltd., Tamil Nadu, India (5/2002) - In-plant Training, Aranthangi Chemicals Pvt. Ltd., Tamil Nadu, India (11/2002) COMPUTER SKILLS - MATLAB, SIMULINK, FEMLAB (COMSOL), MAPLE, C, C++ 262 EXTRA CURRICULAR ACTIVITIES REFERENCES - Chair person, Engineering session in 7th Association of Pacific Rim Universities Doctoral Students Conference, 2006, July 17-21, Singapore - President, Graduate Students’ Association, National University of Singapore, Singapore 2006 - 2007 - Treasurer, Graduate Students’ Association, National University of Singapore, Singapore 2004 - 2005 - President, Association of Chemical Engineers, Anna University, India. 2002 - 2003 Prof. Lakshminarayanan Samavedham, E5-02-23, Department of Chemical & Biomolecular Engineering, National University of Singapore, Singapore, 117576 Ph: (65) 6516-8484 Email: chels@nus.edu.sg Prof. Fraser Forbes, 536A, Chemical and Materials Engineering Building, University of Alberta, Edmonton, Alberta, T6G 2G6 Ph: (780) 492 0873 Email: fraser.forbes@ualberta.ca Prof. R. E. Hayes, 530, Chemical and Materials Engineering Building, University of Alberta, Edmonton, Alberta, T6G 2G6 Ph: (780) 492 3571 Email: bob.hayes@ualberta.ca Prof. Krishnaswamy Peruvemba R., E5-03-02, Department of Chemical & Biomolecular Engineering, National University of Singapore, Singapore, 117576 Ph: (65) 6516-2177 Email: chekrish@nus.edu.sg [...]... the distribution of molecular weights Effect Concentration of Increase of yield styrene and initiator Concentration of acetic Decrease of catalyst deactiacid vation Space velocity of the ini- Increase of productivity tial mixture Initial mixture composition Concentration decane Temperature cooling agent of of Increase of selectivity n- Change in selectivity the Increase of the rate of chemical conversion... Flow Reactor Figure 1.3 illustrates the concept of a Reverse Flow Reactor (RFR) It consists of a packed bed reactor in which the flow direction is reversed periodically During startup, the reactor section is preheated (using an external heat source) to the ignition temperature The control valves A and D are open (valves B and C are closed) for the forward flow (Figure 1.3(a)) and the control valves B and. .. inlet and the outlet valves are switched along the direction of the flow and hence there is no flow reversal The loop reactor can be thought of in many forms like triangular, rectangular etc 13 1 2 3 8 4 7 6 5 Fig 1.4 Illustration of the Loop Reactor concept 1.9 Motivation and Objectives The focus of this research is to devise suitable operational and control strategies for periodic autothermal reactors... in periodically operated reactors with a view to substantially reduce the global warming potential Considering the advantages of the previously mentioned autothermal reactors (RFR and MPSR) for fugitive methane emissions, a comprehensive study has been done to establish the feasibility of such systems for methane combustion and to gain a better understanding in the operation and control of such systems. .. Network of Reactors (NR) has been introduced (Haynes and Caram, 1994; Balaji and Lakshminarayanan, 2006) 12 1.8 Loop Reactor or Multi Port Switching Reactor The concept of the loop reactor is shown in Figure 1.4 The feed and the product withdrawal ports are switched periodically such that no heat is allowed to go out of the system (Brinkman et al., 1999) In Figure 1.4, the shaded areas represent the reactor. .. novel Repetitive Model Predictive Control (RMPC) strategy, that combines the basic concepts of Iterative Learning Control (ILC) and Repetitive Control (RC) along with the concepts of MPC, is proposed for such systems The above mentioned control strategy and the heat extraction strategy discussed earlier for RFR can be easily extended for MPSR and also for the proposed new reactor configuration 1 1 INTRODUCTION... Dispersion Reverse Flow Reactor ILC Iterative Learning Control LQR Linear Quadratic Regulator LR Loop Reactor MIMO Multiple Input Multiple output MPC Model Predictive Control MPSR Multi Port Switching Reactor NR Network of Reactors PDE Partial Differential Equation PLC Programmable Logic based Control RC Repetitive Control RFR Reverse Flow Reactor RMPC Repetitive Model Predictive Control SCR Selective... (Renken et al., 1976) Chlorination of n-decane in two phase adiabatic reactor with a stirrer (Ding et al., 1974) Ethanol dehydrogenation in the catalyst bed (Denis and Kabel, 1970 a and b) Oxidation of butane, cyclohexane on platinum nets (Wandrey and Renken, 1973 and 1977) Oxidation of SO2 on vanadium catalyst (Boreskov et al., 1983) Initial mixture composition Increase of conversion Hydrogen concentration... characteristics will help in efficient operation of waste treatment processes Thus, detailed theoretical and numerical studies have to be carried out to explore the characteristics of these systems Also, controlling such reactors (with high operational complexity) is often cumbersome Control strategies for these complex systems still remains a relatively unexplored area and warrants further investigation 15... et al., 1998) Switching of the direction of the reaction mixture flow in the catalyst bed Reduction of capital investment; possibility to process gases with variable and low initial concentration; increase of conversion Reduction of capital investment; possibility to process gases with variable and low initial concentration; increase of conversion 1.7 Switching of the direction of the reaction mixture . MODELING, SIMULATION AND CONTROL OF PERIODIC REACTOR SYSTEMS Sukumar Balaji (B.Tech, Anna University, Chennai, India) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR O F PHILOSOPHY DEPARTMENT OF. Rang aiah, Prof. Jim Yang Lee and Prof . M. P. Srinivasan for giving me an opportunity to teach undergraduate iii modules. Their feedback and the achievements of Prof. Laksh and Prof. Nandaku- mar. and suggestions from my panel members Prof. Farooq, Prof. M. S. Chiu and Prof. A. K. Ray helped me a lot throughout the journey of my re- search. I am very much indebted to Prof. Krishna, Prof.