Calculating Limits to Productivity in Reactor-Separator

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Calculating Limits to Productivity in Reactor-Separator CALCULATING LIMITS TO PRODUCTIVITY IN REACTOR-SEPARATOR SYSTEMS OF ARBITRARY DESIGN DISSERTATION Presented in Partial Fulfillment of the Requirements for The Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Yangzhong Tang, B.S. * * * * * * The Ohio State University 2005 Dissertation Committee: Approved by Dr. Martin R. Feinberg, Adviser Dr. James F. Rathman Adviser Graduate Program in Dr. Bhavik R. Bakshi Chemical Engineering ABSTRACT This thesis aims to solve the following major problem in the process synthesis area of chemical engineering: Given a network of chemical reactions with its associated kinetics, given certain available resources such as the catalyst mass, given specific feed rates, given permissible temperature and pressure ranges within reactor units, and given certain environmental constraints, what is the maximum production rate that can be achieved for a certain desired species over all possible steady-state reactor-separator systems consistent with those specifications? The most difficult part in solving this problem is the huge varieties of the reactor- separator configurations that can be applied in the process. Besides the classical types of reactors that are widely known (i.e. continuous flow stirred tank reactors or plug flow reactors), there could be reactors that are beyond our imagination. So on top of the complexity already present in consideration of the great variety of already-existent reactor-separator systems, one must also allow for consideration of the as-yet-unknown types of reactors. ii While it seems that it is almost impossible to solve the problem, an idea called the CFSTR Equivalence Principle for Reactor-Separator Systems was provided in 2001 by Feinberg and Ellison as a very important tool. This principle says that to sort out all attainable effluents, it suffices to look at an exceptional design in which the only reactors are continuous flow stirred tank reactors (CFSTRs) whose number is determined by the network of chemical reactions. So the search for the maximum production rate of a certain desired species can be carried out among different variations of this CFSTR-only design rather than among the vast spectrum of different combinations of many types of reactors and separators. However, the CFSTR Equivalence Principle only serves as a theoretical tool for the problem. What this thesis tries to do is to provide concrete implementation methods, based on the principle, for searching the kinetic bounds on productivity for stipulated resources and specified process constraints. Five linear methods and one nonlinear method are explored for this purpose and a software package called Productivity Limit Calculator (PLC) is developed with all these methods imbedded. Case studies are carried out by using the software package both for academic test examples and for more practical industrial processes. It can be seen that in general the nonlinear method is better than the linear methods in performance. The nonlinear method uses a commercial-grade solver for the search of the maximum production rate. It gives good results for both large and small-sized problems. Although linear methods are only iii good for small-sized problems, they do not depend on any commercial-grade solver, and their underlying algorithms are freely available. For this reason, the linear methods are useful in educational settings. Besides searching for the kinetic bounds on productivity in reactor-separator systems of arbitrary design, the software also provides means to examine certain theoretical questions. In particular, it becomes possible to examine how changes in available reactor capacity or how tightening of environmental constraints affect the maximum possible production rate of some desired chemical species. These issues are examined in the context of two examples. iv DEDICATED TO MY PARENTS v ACKNOWLEDGMENTS I would like to express my deepest appreciation to my advisor, Dr. Martin R. Feinberg, for his advice and guidance throughout my research period. I would also like to thank him for his patient criticism during the writing of this thesis. Working with Dr. Feinberg has been the most challenging and rewarding experience in my life. He has inspired me in many different ways. Besides being an advisor, Dr. Feinberg is also like a father to me for all these years with his support and encouragement. My group-mate Thomas Abraham has always been very nice and helpful. It is amazing that he knows so many things besides chemical engineering that I always went to seek answers from him in the first place. Now that he graduated recently and got a job, I wish him and his families all of the best. Finally, I am grateful to Chemical and Biomolecular Engineering Department at The Ohio State University and United States National Science Foundation for their financial supports of my doctoral studies. vi VITA June 25, 1978…………………………… Born – Zhuzhou, Hunan, China 2000…………………………………….. B.S., Control Science and Engineering, Zhejiang University, Hangzhou, Zhejiang, China 2000 – 2004…………………………….. Department Fellow, Chemical Engineering, The Ohio State University, Columbus, OH 2004 – 2005…………………………….. Graduate Research Associate Chemical Engineering, The Ohio State University, Columbus, OH FIELDS OF STUDY Major Field: Chemical Engineering vii TABLE OF CONTENTS Page ABSTRACT........................................................................................................................ ii DEDICATION.................................................................................................................... v ACKNOWLEDGMENTS ................................................................................................. vi VITA................................................................................................................................. vii LIST OF FIGURES .......................................................................................................... xii LIST OF TABLES........................................................................................................... xiv LIST OF ABBREVIATIONS.......................................................................................... xvi NOMENCLATURE ....................................................................................................... xvii Chapters: 1. INTRODUCTION .......................................................................................................... 1 1.1 A Big Question in Chemical Engineering ................................................................ 1 1.2 Current Progress in Process Synthesis...................................................................... 2 1.2.1 Progress in the Pure Reactor Synthesis Area..................................................... 3 1.2.1.1 Geometric Approach................................................................................... 3 1.2.1.2 The Superstructure and Mixed-integer Nonlinear Programming Approach7 1.2.1.3 Target-based Approach............................................................................. 10 1.2.1.4 Stochastic Optimization Approach and Other Approaches ...................... 11 1.2.2 Progress in the Reactor-Separator Synthesis Area........................................... 12 viii 1.3 Finding Kinetic Bounds on Productivity in Reactor-Separator Systems of Arbitrary Design ........................................................................................................................... 16 1.3.1 Addressing the Problem................................................................................... 16 1.3.2 An Important Conceptual Tool The CFSTR Equivalence Principle for Reactor-Separator Systems ....................................................................................... 21 1.3.3 Beyond the Theory One Step Further ......................................................... 24 1.4 Summary of Chapter 1............................................................................................ 25 2. THE CFSTR EQUIVALENCE PRINCIPLE FOR REACTOR-SEPARATOR SYSTEMS......................................................................................................................... 27 2.1 Some Preliminaries................................................................................................. 28 2.1.1 A Few Mathematical Preliminaries ................................................................. 28 2.1.2 Stoichiometric and Kinetic Preliminaries ........................................................ 29 2.2 The CFSTR Equivalence Principle for Reactor-Separator Systems....................... 32 2.3 Applying the CFSTR Equivalence Principle to Find the Kinetic Bounds on Productivity in Reactor-Separator Systems of Arbitrary Design.................................. 37 2.3.1 A Few More Mathematical Preliminaries........................................................ 37 2.3.2 How the CFSTR Equivalence Principle Provides Kinetic Bounds.................. 39 2.3.3 Constraint Set Ω............................................................................................... 40 2.3.4 The Role of the CFSTR Equivalence Principle in Finding the Kinetic Bounds ................................................................................................................................... 44 2.3.4.1 The CFSTR Equivalence Principle Characterizes the Attainable Effluent Rate Vectors.........................................................................................................
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