Computer-Aided Design of Catalysts 9781003067115, 0824790030, 9780824790035

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CONIPUTER- AIDED DESIGN OF CATAlrYSTS

CHEMICAL INDUSTRIES A Series of Reference Books and Textbooks

Consulting Editor HEINZ FIEINEMANN

Berkeley, California

Fluid Catalytic Cracking with Zeolite Catalysts, Paul B. Venuto and E. Thomas Habib, Jr. Ethylene: Keystone to the Petrochemical Industry, Ludwig Kniel, Olaf Winter, and Karl Stork The Chemistry and Technology of Petroleum, James G. Speight The Desulfurization of Heavy Oils and Residua, James G . Speight Catalysis of Organic Reactions, edited by William R. Moser Acetylene-Based Chemicals from Coal and Other Natural Resources, Robert J. Tedeschi Chemically Resistant Masonry, Walter Lee Sheppard, Jr. Compressors and Expanders: Selection and Application for the Process Industry, Heinz P. Bloch, Joseph A. Cameron, Frank M. Danowski, Jr., Ralph James, Jr., Judson S. Swearingen, and Marilyn E. Weightman Metering Pumps: Selection and Application, James P. Poynton Hydrocarbons from Methanol, Clarence D. Chang Form Flotation: Theory andApplications, Ann N . Clarke and David J. Wilson The Chemistry and Technology of Coal, James G . Speight Pneumatic and Hydraulic Conveying of Solids, 0. A. Williams Catalyst Manufacture: Laboratory and Commercial Preparations, Alvin B. Stiles Characterization of Heterogeneous Catalysts, edited by Francis Delannay BASIC Programs for Chemical Engineering Design, James H. Weber Catalyst Poisoning, L. Louis Hegedus and Robert W. McCabe Catalysis of Organic Reactions, edited by John R. Kosak Adsorption Technology: A Step-by-Step Approach to Process Evaluation and Application, edited by Frank L. Slejko Deactivation and Poisoning of Catalysts, edited by Jacques Oudar and Henry Wise

Catalysis and Surface Science: Developments in Chemicals from Methanol, Hydrotreating of Hydrocarbons, Catalyst Preparation, Monomers and Polymers, Photocatalysis and Photovoltaics, edited by Heinz Heinemann and Gabor A. Somorjai Catalysis of Organic Reactions, edited by Robert L. Augustine Modern Control Techniques for the Processing Industries, T. H. Tsai, J. W. Lane, and C. S. Lin Temperature-Programmed Reduction for Solid Materials Characterriation, Alan Jones and Brian McNichol Catalytic Cracking: Catalysts, Chemistry, and Kinetics, Bohdan W. Wojciechowski and Avelino Corma Chemical Reaction and Reactor Engineering, edited by J. J. Carberry and A. Varma Filtration: Principles and Practices: Second Edition, edited by Michael J. Matteson and Clyde Orr Corrosion Mechanisms, edited by Florian Mansfeld Catalysis and Surface Properties of Liquid Metals and Alloys, Yoshisada Ogino Catalyst Deactivation, edited by Eugene E. Petersen and Alexis T. Bell Hydrogen Effects in Catalysis: Fundamentals and Practical Applications, edited by Zoltan Padl and P. G. Menon Flow Management for Engineers and Scientists, Nicholas P. Cheremisinoff and Paul N. Cheremisinoff Catalysis of Organic Reactions, edited by Paul N. Rylander, Harold Greenfield, and Robert L. Augustine Powder and Bulk Solids Handling Processes: Instrumentation and Control, Koichi linoya, Hiroaki Masuda, and Kinnosuke Watanabe Reverse Osmosis Technology: Applications for High-Purity-Water Production, edited by Bipin S. Parekh Shape Selective Catalysis in Industrial Applications, N. Y . Chen, William E. Garwood, and Frank G. Dwyer Alpha Olefins Applications Handbook, edited by George R. Lappin and Joseph L. Sauer Process Modeling and Control in Chemical lndustries, edited by Kaddour Najim Clathrate Hydrates of Natural Gases, E. Dendy Sloan, Jr. Catalysis of Organic Reactions, edited by Dale W. Blackburn Fuel Science and Technology Handbook, edited by James G. Speight Octane-Enhancing Zeolitic FCC Catalysts, Julius Scherzer Oxygen in Catalysis, Adam Bielafiski and Jerzy Haber The Chemistry and Technology of Petroleum: Second Edition, Revised and Expanded, James G. Speight

45. Industrial Drying Equipment: Selection and Application, C . M . van't Land 46. Novel Production Methods for Ethylene, Light Hydrocarbons, and Aromatics, edited by Lyle F. Albright, Billy L. Crynes, and Siegfried Nowak 47. Catalysis of Organic Reactions, edited by William E. Pascoe 48. Synthetic Lubricants and High-Performance Functional Fluids, edited by Ronald L. Shubkin 49. Acetic Acid and Its Derivatives, edited by Victor H. Agreda and Joseph R . Zoeller 50. Properties and Applications of Perovskite-Type Oxides, edited by L. G. Tejuca and J. L. G. Fierro 51. Computer-Aided Design of Catalysts, edited by E . Robert Becker and Carmo J. Pereira

ADDITIONAL VOLUMES IN PREPARATION

Models for Thermodynamic and Phase Equilibria Calculations, edited by Stanley I. Sandler Composition and Analysis of Heavy Petroleum Fractions, Klaus H . Altgelt and M. M. Boduszynski Catalysis of Organic Reactions, edited by John Kosak and Thomas A. Johnson

edited by E. Robert Becker Environex, Inc. Wayne, Pennsylvania

Carmo J. Pereira

W. R. Grace & Company Columbia, Maryland

Marcel Dekker, Inc.

New York*Basel* Hong Kong

Library of Congress Cataloging-in-Publication Data

Computer-aided design of catalysts / edited by E. Robert Becker, Carmo J. Pereira. p. cm. — (Chemical industries ; 51) Includes bibliographical references and index. ISBN; 0-8247-9003-0 (acid free) 1. Catalysts. 2. Computer-aided design. I. Becker, E. Robert. II. Pereira, Carmo Joseph. III. Series: Chemical industries ; v. 51. TP159.C3C66 1993 660'.2995—dc20 93-19302 CIP

The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the address below. This book is printed on acid-free paper. Copyright © 1993 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Marcel Dekker, Inc. 270 Madison Avenue, New York, New York 10016 Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA

Preface

The tools and insights required for the design of catalysts have come a long way in the past fifty years. The pioneering calculations relating the interactions of mass transport and chemical reaction led the way and have withstood the test of time. The pioneers could not have imagined the powers of modern surface science and computing which allow the examination of the many facets of catalytic reactions. The advances of surface science have allowed a closer and more detailed inspection of catalytic surfaces, their chemistry, their morphology, and their electronic behavior. At the same time computing power has grown exponentially. The power of a 1960s university computing center now fits comfortably on a desk. The complex relationships between molecular phenomena on a catalyst surface and the output from a chemical reactor can only be quantified by mathematical models. These models form the bridge that relate the chemical and physical processes and properties on the microscopic scale to the behavior of a macroscopic system like a reactor. Models range from those describing the movement of single molecules on a surface to those that describe the behavior of a catalytic reactor. For many, these models isolate specific interactions of selected aspects of the spectrum from molecular motion to reactor engineering. The industrial practitioner needs the tools to understand the importance and influence of a large number of variables in choosing a catalyst for a specific objective. Computer-aided design of catalysts has matured from theory to practice in real industrial applications. First applied successfully Mi

iv

Preface

to petrochemical applications and then to catalytic emission control, computeraided catalyst design has great utility in providing cost-effective catalyst development. The first systematic discussion of this topic was the subject of a 1984 symposium on reaction engineering for catalyst design, later published in a book, Catalyst Design (Wiley), edited by L. L. Hegedus. Our purpose in assembling the chapters from experts in the field of chemical reaction engineering is to illustrate the key role that modeling plays in the development of new catalysts for a variety of commercially important applications. These chapters provide an update to recent advances in the development of computing tools as well as a perspective to past accomplishments. We have aimed to cover the molecular aspects through reactor modeling with the purpose of providing insights into the requirements of catalysts properties. We invite and encourage the practitioners of catalyst science and reaction engineering to apply and refine the techniques illustrated in this book. At the same time we wish to encourage our academic colleagues to further develop the tools that make the practice of catalyst design attractive to practitioners. As practitioners of reaction engineering and catalyst design, we dedicate this book to our teachers, mentors, and colleagues who have inspired and encouraged us through the years. Finally, we express our sincere thanks to our fellow authors for their support and their contributions. E. Robert Becker Carmo J. Pereira

Contents

Preface Contributors 1. Introduction E. Robert Becker and Carmo J. Pereira

Hi vii 1

2.

Microkinetic Analysis and Catalytic Reaction Synthesis for Methane Partial Oxidation Ma.-Guadalupe Cdrdenas-Galindo, Luis M. Aparicio, Dale F. Rudd, and James A. Dumesic

3.

Catalyst-Based Descriptions of Catalytic Cracking Chemistry David T. Allen, Pradeep Marathe, and Robert Harding

4.

Molecular Simulation of Kinetic Interactions in Complex Mixtures Matthew Neurock, Scott M. Stark, and Michael T. Klein

55

5.

Simulation Techniques for the Characterization of Structural and Transport Properties of Catalyst Pellets Sebastian C. Reyes and Enrique Iglesia

89

6.

Optimal Distribution of Catalyst in Pellets 137 Asterios Gavriilidis, Arvind Varma, and Massimo Morbidelli

9

31

Contents

vi

7.

Reaction-Transport Selectivity Models and the Design of Fischer-Tropsch Catalysts Enrique Iglesia, Sebastian C. Reyes, and Stuart L. Soled

199

8.

Catalytic Converter Modeling for Automotive Emission Control Se H. Oh

259

9.

Design of Monolithic Catalysts for Improved Transient Performance Kyriacos Zygourakis

297

10.

Modeling of Polymerization Processes Kyu Yong Choi

11.

Impact of Wetting on Catalyst Performance in Multiphase Reaction Systems Michael P. Harold

12.

Catalytic Membrane Reactors Theodore T. Tsotsis, Ronald G. Minet, Althea M. Champagnie, and Paul K. T. Liu

471

13.

Some Aspects of Modeling in Petroleum Processing Ajit V. Sapre and James R. Katzer

553

Index

335

391

603

Contributors

David T. Allen California

University of California, Los Angeles, Los Angeles,

Luis M. Aparicio Wisconsin

University of Wisconsin-Madison,

E. Robert Becker

Environex, Inc., Wayne, Pennsylvania

Ma.-Guadalupe Cardenas-Galindo Madison, Wisconsin Althea M. Champagnie Kyu Yong Choi Maryland

Wisconsin-Madison,

Simulation Sciences, Inc., Brea, California

University of Maryland at College Park, College Park,

James A. Dumesic Wisconsin

University of Wisconsin-Madison,

Asterios Gavriilidis Robert Harding

University of

Madison,

Madison,

University of Notre Dame, Notre Dame, Indiana

W. R. Grace & Company, Columbia, Maryland vii

Contributors

viii Michael P. Harold Enrique Iglesia New Jersey

University of Massachusetts, Amherst, Massachusetts

Exxon Research and Engineering Company,

James R. Katzer Mobil Research and Development Princeton, New Jersey Michael T. Klein Paul K. T. Liu Pennsylvania

Annandale,

Corporation,

University of Delaware, Newark, Delaware Media and Process Technology Corporation, Pittsburgh,

Pradeep Marathe California

University of California, Los Angeles, Los Angeles,

Ronald G. Minet California

University of Southern California, Los Angeles,

Massimo Morbidelli

Politecnico di Milano, Milano, Jtaly

Matthew Neurock Se H. Oh

University of Delaware, Newark, Delaware

General Motors Research Laboratories, Warren, Michigan

Carmo J. Pereira

W. R. Grace & Company, Columbia, Maryland

Sebastian C. Reyes Exxon Research and Engineering Company, Annandale, New Jersey Dale F. Rudd

University of Wisconsin-Madison,

Ajit V. Sapre Mobil Research and Development Princeton, New Jersey

Madison, Wisconsin Corporation,

Stuart L. Soled Exxon Research and Engineering Company, Annandale, New Jersey Scott M. Stark

University of Delaware, Newark, Delaware

Theodore T. Tsotsis California

University of Southern California, Los Angeles,

ix

Contributors

Arvind Varma

University of Notre Dame, Notre Dame, Indiana

Kyriacos Zygourakis

Rice University, Houston, Texas

COmPUTER- AIDED DESIGN OF CITAhYSTS

1

Introduction E. Robert Becket

Environex, Inc., Wayne, Pennsylvania

Carmo J. Pereira

W. R. Grace & Company, Columbia, Maryland

I.

ROLE OF COMPUTER MODELING IN TECHNOLOGY

Computer-aided design, or CAD as it is commonly called, is used routinely in a variety of industries for developing products that range from large mechanical structures to small electronic components. The role of computer-aided modeling in the nation's critical technologies was recently highlighted in a National Research Council book entitled Mathematical Sciences, Technology and Economic Competition [1]. Examples of technologies that rely on computer-aided modeling include major segments of industry: • Aircraft design and selection of critical wind tunnel tests. The benefits of modeling are lower development costs and reduced time to commercialization. • Design of automobile components from an artist's concept to the generation of detailed shapes; these computer-generated shapes are then transformed into structural elements. • Design and fabrication of the electronic chip, the prediction of electrical characteristics of semiconductor devices, the preparation of masks for fabricating chips, the testing of chips, and even the simulation of structural properties of electronic packaging to predict heatinduced stresses. • Characterization of oil reservoir geology and the prediction of fluid flow patterns in petroleum exploration and production. Such calcu1

Chapter 1

2

lations are used to set the location of future wells. In petroleum refining, CAD techniques are used for process design, optimization, and control. • Studies of the physics and chemistry of materials using supercomputers and visualization systems [2]. Successful analysis of polymeric network behavior under stress, the mechanisms of self-diffusion, and the effects of polymer bending will result in models for designing polymers with specific performance features [3]. • Analysis of structure and thermodynamic properties of molecules. Quantum chemical calculations and new software are expected to provide the scientific basis for new advances in pharmacology [1,4]. Catalysts are important by any measure. They are at the heart of 90% of the processes in the chemical industry, with U.S. sales of over $290 billion, and the petrochemical industry, with U.S. sales of over $140 billion. Catalysis has also been singled out as a vital component of a number of national critical technologies identified by the National Critical Technologies Panel [5]. The development of new and/or improved catalysts will have a positive impact on the nation's economic competitiveness. In traditional areas there are opportunities for developing new catalysts and processes that use cheaper feedstocks, convert methane into desirable chemicals with high conversion and selectivity, and at the same time improve process safety. A large new opportunity is driven by environmental regulations. New and/ or improved catalysts are required for producing environmentally acceptable fuels, minimizing hazardous chemical intermediates and by-products, and for tail-end emission control [6-8]. These opportunities provide a strong incentive for developing and promoting tools such as CAD for the advancement of catalyst technology. II.

CATALYST DESIGN

Catalyst design is the process of selecting catalyst properties that maximize (or minimize, depending on the problem) an objective function. These catalyst properties include surface chemical properties, pore structure, shape and size of the catalyst, impregnation profiles, and crush strength. The objective function is usually related to reactor performance or to the goals of the chemical plant or refinery. An optimization scheme and examples of objective functions are illustrated in a review paper by Hegedus and Pereira [9]. An example of a new refinery objective, mandated by the U.S. 1990 Clean Air Act Amendments, is the production of reformulated gasoline. The regulations specify a minimum gasoline oxygen content and place limits

Introduction

3

on vapor pressure and benzene content. The mandated oxygen level can only be met by making (or purchasing) oxygenates and blending them into the gasoline. Since oxygenates can be made from the C4 and C5 olefins produced by fluid catalytic cracking (FCC), one processing option is to modify FCC catalyst properties to increase olefin yields. However, this increased olefins yield cannot be at the expense of selectivity to primary products such as gasoline and fuel oil. One of the catalyst "designer's1' constraints is that not all properties can be varied independently. For example, changes in pore structure affect catalytic surface area and crush strength. A second constraint is that catalyst properties can be varied only within certain physical limits (e.g., due to thermal and mechanical stability considerations). To optimize the catalyst, the relationships between catalyst properties and reactor or process performance need to be understood. Since reactor performance also depends on other variables (such as operating conditions, the composition of the reactants, the type of reactor, etc.), these relationships are highly nonlinear and are best described by a mathematical model. Mathematical models often contain submodels that describe surface chemical kinetics, inter- and intraparticle diffusion, reactor hydrodynamics, and catalyst deactivation. Submodels can focus on molecular aspects such as surface chemistry on the one hand, and reactor and process models on the other; they span the range from science to technology. Recent developments of sophisticated mathematical models is stimulated by an increased understanding of catalytic surfaces and by the availability of supercomputers. Analytical tools that probe catalyst surfaces, especially under reaction conditions, are providing new molecular-level structure-performance information. An improved understanding of the structure of adsorbed species and the dynamics of surface elementary processes during catalysis is advancing the development of realistic theoretical models (e.g., Refs. 10 and 11). Despite this progress, however, the a priori design of a catalytic surface is not yet possible. Supercomputers provide the power needed to tackle space complex problems. Increased computer speed (time per operation down to 4 ns) a larger number of central processing units (eight and more CPUs), larger memory size (up to 16 megawords per CPU), higher input/output transfer rate (up to 100 megabytes per second), and storage peripherals with gigabyte disks with a 10-megabyte per second transfer rate all make complex computing more practical [3]. With machine speeds of over 1 billion floating-point operations per second, the "designer" can now develop useful models from the simulation and visualization of catalytic processes. CAD of catalysts has proven to be a useful tool in a number of cases [9,12-14]. Optimization calculations point the direction to physically achievable optimum properties. Experimental work is then focused on

Chapter 1

4

achieving the recommended properties. The new catalysts are tested, the model is validated or fine-tuned, and a new set of optimum properties can be determined. Model calculations are used to examine the sensitivity of catalyst performance to key performance parameters. Answers to many of the questions during a development program can be obtained by performing calculations rather than expensive experimentation. The goal is to minimize developmental costs and reduce the time required for product commercialization. III.

MODELING

Some recent advances in modeling diffusion-reaction processes in catalysts from an application perspective are discussed in this book. The chapters are organized, building from microscopic surface kinetics to the macroscopic design of pellets and monolith reactor elements. Kinetics

The development of kinetic models requires an understanding of the elementary steps that occur at the catalytic surface. The Catalyst Design Advisory Program can combine experimental results with existing literature information on thermodynamic properties to determine physically realistic catalyst-adsorbate bonding parameter values and elucidate the reaction mechanism. Such an approach has been used to explain selectivity patterns for molybdena/silica and vanadia/silica catalysts in methane partial oxidation [15]. Further progress in this area is discussed in Chapter 2. Complex Mixtures

The modeling of complex mixtures poses a considerable challenge. The traditional approach has been to use lumped kinetics; recently, however, carbon center approaches are being developed in which the complex mixture is characterized in terms of functional groups similar to those used in thermodynamic property estimation. This method was first used to explain selectivity patterns for cracking over amorphous catalysts; application to the catalytic cracking of heptane over ZSM-5 zeolite is reported in Chapter 3. Monte Carlo Methods The problem of hydrocracking of complex mixtures has been tackled using Monte Carlo calculations. Molecules are first generated on the computer using the available analytical information on the feedstock and then cracking is simulated using the reactivity of the functional groups contained in the molecule. Reasonable information on product composition and quality

Introduction

5

can be obtained after the simulated cracking of several thousand molecules. This approach is amenable to vectorization; algorithms for the efficient use of a parallel supercomputer have been developed. These are described in Chapter 4. Pore Diffusion

Physical models that relate pore structure and diffusion properties are often based on an idealized description of the pore structure. Models in which the pore structure is represented by three-dimensional networks, however, reveal that both morphology (i.e., size and shape) and topology (i.e., interconnectedness) of the pores are important in determining the diffusive properties (and the deactivation rate in the case of deposition in the pores) [16]. Bethe networks and the computer generation of disordered threedimensional porous structures are useful to describe porous networks and to characterize their structural and transport properties; these methods are reviewed in Chapter 5. impregnation Profiles

Impregnation profiles within porous pellets can be optimized to maximize performance. While nonuniform impregnation of pellets has been described in both the open and patent literature for some time, it has now been proved theoretically that the optimum impregnation profile is one in which the catalytic ingredients are located as a sharp concentrated band at a specific location in the pellet. The optimal location depends on the physicochemical parameters and the objective function; work on this topic is discussed in Chapter 6. Fischer-Tropsch Catalysts

The need for clean energy from coal will revive technologies for synthetic fuels manufacture. Pellet properties have long been recognized as important in determining product selectivity for complex Fischer-Tropsch kinetics. Modeling studies on Fischer-Tropsch catalysts show how operating conditions and catalyst structural parameters are important in determining selectivity of gasoline range products. This subject is examined in Chapter 7. Automobile Catalysts

Pore structure optimization calculations that led to the design of the catalyst pellet for automobile exhaust emission control have been reported by Hegedus [12]. Pellets containing platinum and rhodium profiles optimized for poison resistance have been deployed commercially. Over the last decade, washcoated monolith converters have replaced pelleted systems, primarily

6

Chapter 1

because of pressure drop and low-temperature performance. The properties of these catalysts under steady-state conditions have been optimized [13,17]. Despite the high removal efficiencies at normal operating temperatures, a significant fraction of emissions in current-generation automobile exhaust catalysts occur during cold-start conditions. Design considerations for reducing these emissions are discussed in Chapter 8. Catalyst Transient Performance

Tightening environmental standards have required the development of selective catalytic reduction (SCR) catalysts for reducing nitrogen oxides from power and cogeneration plant exhausts [14]. In such applications, pressure drop across the catalyst reduces boiler or turbine efficiency, which represents a considerable economic penalty. Work on modifying monolith substrate properties is ongoing to maximize the external mass-transferlimited performance (which represents the upper limit of performance) for a given pressure drop. Examples of such developments include thinnerwalled ceramic monoliths and metal monoliths [18]. The effect of monolith substrate properties on the transient reactor performance is examined in Chapter 9. Polymerization Catalysts

In some applications, catalyst properties can only be optimized within the context of the reactor or process employed. Two such examples are discussed in this book. Polymerization catalysts are dispersed into the reactants; in this case, product properties depend on the catalyst, the reactor type, and the processing conditions. Polymerization catalysts are discussed in Chapter 10. Multiphase Catalysts

Catalyst effectiveness in gas-liquid reaction systems, such as in hydrotreating and hydrocracking of petroleum feedstocks, depends on what fraction of the external surface of the pellet is exposed to liquid. Pellet performance depends on the reactants, the reactor type (e.g., fixed bed versus ebullated bed), the operating conditions, flow distribution, and on the location of the pellet within the reactor. The impact of wetting is discussed in Chapter 11. Membrane Reactors

Catalysts and reactors are designed for more than only the chemical transformation. New catalysts, which incorporate product separation, include catalytic distillation and membrane catalysts. Membrane catalysts are reviewed in Chapter 12.

Introduction

7

Petroleum Refining

The petroleum refining industry is an important developer of catalytic technologies. The development and application of reaction engineering concepts to industrial practice was to a large extent pioneered at Mobil's research laboratories over 20 years ago. New modeling challenges, particularly in light of impending environmental regulations, will include the development of techniques for the treatment of complex feedstocks and improved reactor models and refinery optimization algorithms. Some historical perspective and the new frontiers in petroleum refining are discussed in Chapter 13. Zeolite modeling is an exciting frontier not discussed in this book. The goal of this zeolite modeling work is to "obtain a description of the reactant-zeolite potential surface, from which it will then be possible to define reaction intermediates and to determine rate coefficients for chemical transformations'7 [5]. A number of interesting papers on this subject have appeared in the recent literature. Examples of progress include Monte Carlo calculations to provide isotherms and heats of adsorption [19], molecular dynamics calculations to determine molecular diffusion coefficients [20], and ah initio quantum chemical techniques to characterize the interaction of the reactant molecules with the acid site in the zeolite [21]. IV.

CONCLUDING REMARKS

This book provides an update on recent developments in computer-aided design and modeling of catalysts for a variety of important industrial applications. Key hurdles in catalyst design are different for each application: The modeling frontiers for methane partial oxidation, automotive catalysis, Fischer-Tropsch synthesis, and polymerization present quite different challenges; ongoing developments on each frontier allow the practitioner to make CAD of catalysts an integral part of the catalyst development process. REFERENCES

1. Glimm, G. J., ed. (1991). Mathematical Sciences, Technology and Economic Competition, National Academy Press, Washington, D.C., pp. 21-24, 28, 68. 2. National Academy. (1989). Materials Science and Engineering for the 1990s: Maintaining Competitiveness in the Age of Materials, National Academy Press, Washington, D.C., p. 269. 3. National Academy. (1989). Supercomputers: Directions in Technology and Applications, National Academy Press, Washington, D.C., pp. 51-55, 84. 4. Borman, S. (1992). New 3-D search and de novo design techniques aid drug development, Chem. Eng. News, August 10, p. 18.

Chapter 1

8 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

16. 17. 18. 19. 20. 21.

National Academy. (1992). Catalysis Looks to the Future, National Academy Press, Washington, D.C., pp. 1, 61. Roth, J. F. (1991). Industrial catalysis: poised from innovation, Chemtech, June, p. 357. Cusumano, J. A. (1992). New technology and the environment, Chemtech, August, p. 482. Hegedus, L. L., and Pereira, C. J. (1992). Catalytic control of automobile and stationary-source emissions, Annual Meeting of the AAAS, Chicago. Hegedus, L. L., and Pereira, C. J. (1990). Reaction engineering for catalyst design, Chem. Eng. Set., 45, 2027. Somorjai, G. A. (1991). Directions of theoretical and experimental investigations into the mechanisms of heterogeneous catalysis. CataL Lett., 9, 311. Bell, A. T. (1990). The impact of catalyst science on catalyst design and development, Chem. Eng. Sci., 45, 2013. Hegedus, L. L. (1980). Catalyst pore structures by constrained nonlinear optimization, Ind. Eng, Chem. Prod. Res. Develop., 19, 533. Pereira, C. J., Kubsh, J. E., and Hegedus, L. L. (1988). Computeraided design of catalytic monoliths for automobile emission control, Chem. Eng. Sri., 43,^2087. Beeckman, J. W., and Hegedus, L. L. (1991). Design of monolith catalysts for power plant NOx emission control, Ind. Eng. Chem. Res., 29, 969. Amiridis, M. D., Rekoske, J. E., Dumesic, J. A., Rudd, D. F., Spencer, N. D., and Pereira, C. J. (1991). Simulation of methane partial oxidation over silica-supported MoO-, and V 2 O 5 , AlChE J., 37, 87. Sahimi, M., and Tsotsis, T. T. (1985). A percolation model for site deactivation and pore blockage, J. CataL, 96, 552. Oh, S. H., and Cavendish, J. C. (1983). Design aspects of poisonresistant automobile catalysts, AIChE J., 22, 509. Gulian, F. J., Rieck, J. S., and Pereira, C. J. (1991). Camet oxidation catalyst for cogeneration applications, Ind. Eng. Chem. Res., 29, 122. June, L. R., Bell, A. T., and Theodorou, D. N. (1990). Prediction of low occupancy sorption of alkanes in silicalite, /. Phys. Chem., 94, 1508. June, L. R., Bell, A. T., and Theodorou, D. N. (1990). Molecular dynamics study of methane and xenon in silicalite, /. Phys. Chem., 94, 8232. Lonsinger, S. R., Chakraborty, A. K., Theodorou, D. N., and Bell, A. T. (1991). The effects of local structural relaxation on aluminum siting within H-ZSM-5, CataL Lett., in press.

Microkinetic Analysis and Catalytic Reaction Synthesis for Methane Partial Oxidation Ma.-Guadalupe Cdrdenas-Galindo, Luis M. Aparicio, Dale F. Rudd, and James A. DumesiC University of Wisconsin-Madison, Madison, Wisconsin I.

INTRODUCTION

A major goal of industrial catalysis is the selection of catalytic materials and reaction conditions that are likely to lead to active and selective catalysis. In principle, this goal can be reached using chemical intuition and experience with related catalytic processes. We suggest that microkinetic analysis can assist by consolidating in a quantitative fashion the experimental, theoretical, and semiempirical information relevant to the catalytic process [1]. We define microkinetic analysis as an examination of catalytic reactions in terms of elementary chemical reactions that occur on the catalytic surface and their relation with each other and with the surface during a catalytic cycle. Moreover, we define catalytic reaction synthesis as the combining of surface chemical information from diverse experimental and theoretical sources to create a coherent description of how the catalyst, catalytic reaction cycles, and reaction conditions may be formulated to achieve high yields of particular desired products. With the definitions above we see that microkinetic analysis deals primarily with the elucidation of existing catalytic chemistry in terms of available experimental data, whereas catalytic reaction synthesis deals mainly with the identification of promising research directions for the discovery of new catalytic materials and processes. The essential link between these two activities is the ability to extrapolate our existing knowledge to new

10

Chapter 2

areas, and this extrapolation is based on the identification of analogies and the formulation of correlations. It is relevant in this book on computer-aided design of catalysts and reactors to note that the role of computers in microkinetic analysis and catalytic reaction synthesis is to assist the researcher in the quantitative consolidation of surface kinetic and thermodynamic data as functions of catalyst structure and composition. The essential role of formulating a serviceable reaction mechanism on which to base the microkinetic analyses is maintained by the researcher. The subsequent task of the computer is to assess the quantitative consequences of the surface chemistry proposed by the researcher. In this respect the computer aids the researcher to generalize experience with proven catalysts and to focus chemical intuition in the search for improved catalysts. In the present chapter we illustrate various applications of microkinetic analysis in heterogeneous catalysis using the example of methane partial oxidation over silica-supported vanadia and molybdena. Subsequently, we introduce the application of correlations in catalytic reaction synthesis for methane oxidation using semiempirical molecular orbital calculations to probe the changes in chemical bonding of vanadia that may be caused by the presence of sodium.

II.

COMPUTER-AIDED MICROKINETIC ANALYSIS AND CATALYTIC REACTION SYNTHESIS

One reason why the microkinetics approach described above has not been widely used to direct experimental research and catalytic reaction synthesis is that the solution of reaction rate expressions for realistic reaction mechanisms cannot often be done analytically; furthermore, the numerical solution of the equations representing the formation and consumption of the reactants, products, and surface intermediates for realistic reaction mechanisms may be difficult. These problems can be overcome, however, by modern numerical methods [2] and the growing accessibility of computers in the laboratory environment. Another important function of computers in microkinetic analysis and catalytic reaction synthesis is the implementation of complex computational methods to correlate surface bonding parameters with surface structure or composition. For example, semiempirical molecular orbital calculations can be used to describe the chemical bonding in various metal and metaloxide clusters. These calculations, although semiempirical in nature compared to more rigorous quantum mechanical calculations, must be carried out numerically. Thus we see that computers play important roles in both

Methane Partial Oxidation Analysis

11

the solution of the microkinetic model and the formulation of correlations used to extrapolate the microkinetic model to new catalytic materials. Finally, we note that an emerging application of computers in catalysis research is in evaluation of the potential economic impact of promising research directions identified by catalytic reaction synthesis. In particular, the general result of microkinetic analysis and catalytic reaction synthesis is the suggestion of directions in the search for new catalytic materials; however, the specific catalyst formulations required to achieve the desired catalyst performance are not typically known with precision. Therefore, before an experimental program is started to pursue the research directions identified by catalytic reaction synthesis, it is useful to assess the feasibility of the new catalytic process in the chemical industry. Computers are used in this respect to generate flow sheets for the new catalytic process, to conduct the subsequent process design, to estimate capital and operating costs of the process, and to assess the advantages of the new process with respect to existing technologies. We anticipate that this computer application will become a significant factor in the planning of experimental catalysis research programs, especially in an era of increased industrial competitiveness. We will not discuss this topic further in this chapter. III.

CORRELATIONS IN MICROKINETIC ANALYSIS AND CATALYTIC REACTION SYNTHESIS

The microkinetics of a catalytic reaction are defined completely when: 1. All of the chemical species on and above the catalyst surface have been identified unambiguously. 2. The elementary reactions involving the formation and cleavage of chemical bonds have been established uniquely. 3. The rate constants for each elementary reaction have been measured independently. Unfortunately, we know of no catalytic reaction for which these conditions have been met. However, a reasonably complete definition of the microkinetics exists for a few simple catalytic reactions. For example, Oh et al. [3] and Fisher et al. [4] were able to describe the kinetics for CO oxidation over a supported Rh catalyst, based on kinetic parameters measured for Rh single-crystal surfaces. Stoltrze and N0rskov [5] and Dumesic and Trevino [6] employed a similar approach to interpret the kinetics of ammonia synthesis over iron. Waletzko and Schmidt [7] have successfully employed low-pressure measurements on polycrystalline Pt to model the kinetics of HCN synthesis over an industrial Pt gauze catalysts. Rekoske

12

Chapter 2

et al. [8] combined the results of extensive steady-state kinetic measurements, isotopic tracing, infrared spectroscopy, and temperature-programmed reaction spectroscopy to quantify the reaction kinetics for ethylene hydrogenation over platinum. For more complex reactions, our understanding is considerably less detailed. Further, if the microkinetic model is to be an exact tool in catalytic reaction synthesis, an additional condition must be met: 4. The rate constants for each elementary reaction must be known functions of the catalyst formulation. Again, we know of no catalytic reaction for which there is a detailed and complete understanding of the effects of the catalyst structure and composition on all of the elementary reactions. Uncertainty, speculation, and empiricism are therefore an essential part of microkinetic analysis and catalytic reaction synthesis. This situation is particularly true for emerging catalytic technologies during the initial stages of microkinetic analysis, where detailed experimental studies are not generally available. In these cases, the strategy of microkinetic analysis is to utilize semiempirical correlations to extrapolate the available experimental data from related catalytic processes for application to the catalytic process of interest. The relationship between microkinetic analysis and catalytic reaction synthesis is outlined schematically in Figure 1. The role of microkinetic analysis is to use fundamental surface chemical concepts to consolidate the available quantitative information from diverse kinetic studies, such as steady-state kinetic studies, transient measurements, and isotopic tracing. Semiempirical correlations are introduced even at this fundamental level of microkinetic analysis because all of the kinetic parameters in the model cannot be measured directly. For example, we require that the microkinetic analysis be consistent with established kinetic theories, such as collision theory and transition-state theory; however, we recognize that these theories introduce parameters into the analysis (e.g., the steric factor in collision theory and the structure of the activated complex in transition-state theory). Importantly, however, these parameters have physical and chemical significance. In some cases it is also necessary to employ further correlations, such as the Evans-Polanyi relation, to relate activation energies for similar reactions. These correlations reduce the number of kinetic parameters in the model, and they serve the important function of ensuring that the values of the kinetic rate constants for the various steps are in accord with available thermodynamic data, such as the thermodynamic properties of the reactants, products, and proposed intermediates, as well as with known or estimated surface bond strengths.

Figure 1. Relation between microkinetic analysis and catalytic reaction synthesis.

Chemical Analogies e.g., analogies with related catalytic systems and organometallic compounds

Spectroscopic Studies e.g., surface species, surface coverages

Descriptive Information

Chemical Concepts e.g., acidity, basicity electro negativity

Macroscopic Bonding Correlations e.g., heats of formation, proton affinities, ionization energies

Macroscopic Concepts

Catalytic Reaction Synthesis

Microkinetic Analysis

Geometric Considerations e.g., ensemble and particle size effects, shape selectivity Microscopic Concepts

Thermodynamic Data e.g., AH and AS for reactants, products and intermediates, surface bond strengths

Microscopic Bonding Correlations e.g., molecular orbital calculations, bond order conservation

Quantitative Information

Catalyst Characterization e.g., bulk and surface structures, nature of surface sites

Kinetic Theories e.g., collision and transition state theories

Kinetic Studies e.g., steady state studies, transient measurements, isotopic tracing

c/>

>

o"

Q

CL

a

(D

Q

14

Chapter 2

In addition to the quantitative considerations noted above, the microkinetic model must be in agreement with descriptive information about the catalytic process. For example, physical techniques are used to determine the bulk structure, surface area, pore structure, surface composition, and morphology of the catalyst. Accordingly, the microkinetic model must employ surface sites that can be justified from characterization studies of the catalyst bulk and surface structures. Furthermore, the surface chemical foundation of the microkinetic model must be based, whenever possible, on reaction intermediates that have been observed spectroscopically or are reasonable in view of analogies with related catalytic systems or organometallic compounds. As noted above, our goal in microkinetic analysis is to interpret, coordinate, and generalize the results available from diverse experimental studies to create a basis for catalytic reaction synthesis. This approach is depicted schematically in Figure 1, where we note that a variety of microscopic and macroscopic concepts may be used to formulate correlations for extrapolation of the microkinetic model to new catalytic materials or processes. Microscopic correlations involve a description of the catalytic process in terms of the geometry of the active sites and the surface species on these sites. It is important to emphasize here that one need not know the surface geometries with precision to use microscopic correlations, but one must simply be willing to propose reasonable geometries and then pursue the research directions suggested by catalytic reaction synthesis based on these geometries. Typical microscopic correlations include molecular orbital calculations and bond-order-conservation correlations to relate two-center bond strengths on metal surfaces for the estimation of surface bond energies. Correlations can also be based on effects related to the number and orientation of surface atoms that comprise the active sites (i.e., ensemble effects) as well as effects resulting from changes in the surface geometry with particle size. Zeolite catalysts are particularly sensitive to the size and shape of the micropore structure, leading to shape selectivity effects. Macroscopic correlations for catalytic reaction synthesis do not involve a detailed description of the active-site geometry and its bonding to adsorbed species. For example, we may estimate the stability of a particular adsorbed species from the heat of formation of a related stable compound, combined with bond-dissociation energies. Similar estimates may be made using proton affinities for reactions on Br0nsted acid sites and using ionization energies for reactions on Lewis acid sites. Other macroscopic correlations that are particularly useful for catalytic reactions over oxides involve chemical concepts based on the acid-base properties of the surface and how these properties vary with the overall electronegativity of the

Methane Partial Oxidation Analysis

15

catalyst. For example, electronegativity scales may be used to correlate the strengths of heterolytic bonds on oxide catalysts, and Drago-Wayland correlations of acid-base interactions may be used to describe the energetics of base molecule adsorption on acidic catalyst surfaces. It is important to indicate that the level of chemical detail that should be incorporated in the microkinetic model involves a compromise between the amount of detail that is accessible to experimental observation and the desirability of writing all reactions as elementary steps. The microkinetic model must be based on physical and chemical parameters that can be measured independently or that can be estimated by theories of chemical bonding. The experimental data base must be sufficiently diverse to probe the active catalytic phenomena. We are more tolerant of minor errors in the analysis of each individual data set than we are tolerant of failures of the analysis to capture the chemical trends observed in the various experiments performed. However, although the microkinetic model must be based on sound experimental evidence, application of the microkinetic model in catalytic reaction synthesis requires that the microkinetic model must include initially untested conjectures concerning the catalytic phenomena. Accordingly, the microkinetic analysis must be conducted at a level that is more detailed than available experimental data can support quantitatively. The need to introduce conjectures into the microkinetic analysis for the purpose of catalytic reaction synthesis has an effect on the nature of the correlations used to guide the search for new catalytic materials and processes. In particular, the level of complexity that can be justified in correlations for catalytic reaction synthesis depends on the level of detail in which the serviceable reaction mechanism of the microkinetic model can be expressed with confidence. For example, catalytic reaction synthesis for a well-studied catalytic processes would justify microscopic bonding correlations based on a thorough description of the chemical bonding at the surface. In contrast, the surface chemistry involved in a newer catalytic technology, where extensive experimental data are not available, would warrant global correlations based on a more empirical description of the chemical bonding believed to be important on the surface. In summary, we note the important role of semiempirical correlations in establishing relationships between microkinetic analysis and catalytic reaction synthesis. These correlations, based on microscopic and macroscopic chemical concepts, are used to extrapolate chemical information for existing catalysts to new catalytic materials or processes. Accordingly, semiempirical correlations allow results from microkinetic analysis to be used for the purpose of catalytic reaction synthesis for existing catalytic processes, and they allow experimental data from related catalysts

Chapter 2

16

to be used in microkinetic analyses of catalytic processes where extensive experimental data are not yet available. In general, by using semiempirical correlations to link microkinetic analysis and catalytic reaction synthesis, we provide an effective approach to guide further experiments in the search for new catalysts or catalytic reaction conditions. In this chapter we illustrate some of these ideas using molecular orbital calculations to provide correlations between chemical bonding and catalyst structure for methane oxidation over molybdena and vanadia. IV.

MICROKINETIC ANALYSIS OF METHANE PARTIAL OXIDATION

We have recently reported the results of a microkinetic analysis of the partial oxidation of methane over MoO3/SiO2 and V2CVSiO2 catalysts [9]. The mechanism employed in these analyses is shown in Figure 2. Because studies of this reaction are relatively recent, critical experimental data on the surface chemistry are not yet available. This is a typical case in the practice of industrial catalysis. A useful strategy for beginning microkinetic analysis without detailed information specific to the reaction of interest is to seek experimental data and theoretical concepts from related or analogous catalytic systems. Importantly, data of a diverse nature are used to increase the chemical basis of the analysis. The result is a serviceable (1)

CH 4 + 2MO

^ ^

MOCH3 + MOH

(2)

MOCH3 + MO

« ^

MOCH2 + MOH

(3)

MOCH2

^=:

HCHO + M

(4)

HCHO + MO

^=^

MOCH2O

(5)

MOCH2O + MO

^=t

CO + 2MOH

(6)

2MOH

*F^

H2O + MO + M

(7)

2M + O2

* ^

2MO

(8)

MOCH3 + 2MO

^=^

MOCH2OM + MOH

(9)

MOCH2OM + 2MO

^=t

CO2 + 2MOH + 2M

(10)

MOCH3 + MOH

^=^

CH3OH + MO + M

(11)

CO + MO

«*:

MCO2

(12)

MCO2

methanol, formaldehyde, carbon monoxide, carbon dioxide, water the microkinetic analysis must also reproduce independent kinetic data for the following subsequent partial oxidations: • methanol, => formaldehyde, carbon monoxide, carbon dioxide, water • formaldehyde = > carbon monoxide, carbon dioxide, water • carbon monoxide ^> carbon dioxide This procedure allowed us to capture as much of the essential catalytic chemistry as was available, and it gives some justification in using microkinetic analysis to explore regions of methane oxidation catalysis that have not yet been studied experimentally. In short, microkinetic analysis of methane partial oxidation suggests that a significant change in the active reaction pathway occurs with changes in the catalyst from MoO3/SiO2 to V2O5/SiO2. This change alerts us to a possibility of identifying the particular causes of this reaction path change, for example, by identifying critical changes in the strengths by which species are held to the active sites on the catalyst surface. This information is fundamental to the identification of improved catalytic materials and catalyst treatments.

Chapter 2

18 V.

MOLECULAR ORBITAL STUDIES OF METHANE PARTIAL OXIDATION

A.

Guiding Principles

It has been observed with silica-supported molybdena catalysts that the presence of sodium, even at low concentrations, leads to an overall decrease in methane conversion and a drop in the selectivity to formaldehyde [10]. In addition, sodium promotes the oxidation of formaldehyde and the conversion of CO to CO2. Even though sodium has a negative effect on the catalytic performance of silica-supported molybdena for the partial oxidation of methane, it has a positive effect on our understanding of the essential chemistry of methane oxidation. We may hope to use this understanding to identify catalyst modifications that may lead to more desirable catalyst performance. Importantly, we do not require a detailed description of the effects of sodium addition to molybdena. Instead, we employ a plausible description of the effects that is consistent with the available experimental data and that we may use to suggest directions for further research in the search for new and improved catalytic materials. Quantum mechanical calculations are useful in describing the chemical bonding in molecules. Although the quantitative calculation of chemical bond strengths is difficult, we may hope to use these methods to capture the essential bonding properties of known molecules and to use this description to estimate the chemical bonding properties of related, unknown species. Accordingly, an effective strategy for the use of quantum mechanical calculations in microkinetic analysis is to calibrate one of these methods (e.g., molecular orbital calculations) for stable molecules that possess structures and chemical bonds believed to be important in the critical reaction intermediates of the catalytic cycle under investigation. In this way we use quantum mechanical calculations to extrapolate known chemical bonding information to situations where the chemical bond strengths are not yet known with precision (i.e., on catalyst surfaces). As will be seen below, the accuracy of some of these calculations is sufficient to predict trends in catalyst performance, allowing possible directions for catalytic reaction synthesis to be explored. In the example presented here, the atom superposition and electron delocalization (ASED) molecular orbital theory was employed, which is based on delocalized states and is an extended Hiickel approximation [11,12]. This theory was used first to describe the chemical bonding properties of vanadia and then to estimate how these properties may be altered by changes in the structure of vanadia catalysts. These calculations require knowledge about the geometric structure of the molecule, values of the Pauling electronegativity, ionization potentials of the valence electrons,

Methane Partial Oxidation Analysis

19

and Slater coefficients and exponents. The last three values can be optimized to predict accurate values for those species whose heats of formation are known (e.g., V2O5, VO2). Once these parameters have been calibrated, it is possible to use them to predict the heats of formation of different types of vanadia compounds (e.g., surface phases of vanadia on various supports) and the stabilities of molecular fragments on vanadia surfaces. B. Chemical Bonding in Vanadia Many authors have used molecular orbital calculations for the estimation of bond lengths by the minimization of the total energy involved in the molecular configuration (e.g., Ref. 13). In particular, Anderson and coworkers have used the ASED method to calculate bond lengths, force constants, and bond energies of diatomic transition metal oxides and sulfides [12,14]. They used the same technique to study and predict the chemical bonding properties of metal oxide clusters, such as MgO and ZnO, in the formation of methyl radicals on the surface and the adsorption of CO andCO 2 [15,16]. In general, it is expected that the bond lengths in vanadia clusters should change with the coordination number and oxidation state of the vanadium cations. Vanadium oxides can be viewed as containing octahedrally coordinated vanadium, which is true for such low oxidation states as VO, and V2O3. For high oxidation states, as in V2O5, the coordination is a distorted octahedral coordination that may be considered fivefold because the bond length between vanadium and the oxygen that completes the octahedron is sufficiently long that their interaction is almost negligible. In the case of V2O5? all valence electrons are located on the 2p band formed from overlapping oxygen anions. The 3d orbitals of vanadium are empty, and as a consequence they will be involved in any reactions where the oxide accepts electrons. Therefore, the energy of these orbitals is an indication of the ease of accepting electrons during adsorption. For example, molecular orbital calculations show that the energy of the lowest d orbital decreases with the increasing length of the shortest V—O bond. Clearly, vanadium oxide becomes a better electron acceptor for structures involving longer V—O bonds. Coordination number affects the electronic structure of the transition metal oxides. These metal oxides show an energy band structure consisting of a nonmetallic band corresponding to the oxygen 2s band, a nonmetallic band corresponding to the oxygen 2p band, and a metallic d band. The major effect of cation coordination number is in the energy of the orbitals in the d band. These orbital are split in various levels. For example, Figure 3 shows this behavior clearly and it can be seen that the number of orbitals

20

Chapter 2

I I

-2

I

-3

I

-4

I I "III

- Ill

"III

II "

-8

l

-7

7 =

"III

-6

l

-5

i

I

5

I

V0

-1

>

0

Figure 3. Effect of coordination number on the d-orbital energies in vanadium oxides.

with high energy increases with the coordination number. These results were obtained assuming clusters with coordination numbers of 4, 5, 6, and 8 and with all the bond lengths equal. Although these ideal configurations are not likely to be found in vanadium oxides, the same trends were observed when the energy levels were calculated for clusters where the vanadium has the coordination numbers and bond lengths found in several vanadium oxide crystals. C. Analysis of Reaction Mechanism A sensitivity analysis of the reaction mechanism for the partial oxidation of methane by Amiridis et al., [9] suggested that only a limited number of rate constants are kinetically important. In the combined cases of molybdena and vanadia, the kinetically important parameters are the equilibrium constant /C4 and the rate constants ku k2, /c5, ks, and ku. The adsorption of methane on the catalyst surface during the methane partial oxidation results in the formation of a methoxy and a hydroxyl species: CH4 + 2MO

MOCH3 + MOH

We assume for simplicity that vanadia is present on the catalyst as tetrahedral clusters of VO4~3 bonded to the silica surface. Molecular orbital calculations show that an active-site MO with this geometry has all the electrons located in orbitals with oxygen 2s and 2p character, while the 3d band is empty. This situation is depicted schematically in Figure 4.

21

Methane Partial Oxidation Analysis

o VO4

-5 • V 3d band

-10 • O2pband

CD LU

-15 ^

Fully Occupied

-25 O 2s band

-30

O

Figure 4. Electronic correlation diagram for VO4

The formation of surface methoxy species on the catalyst can be analyzed by considering the bonding in the VO4CH3 cluster shown in Figure 5. We see that this cluster possesses a full oxygen 2s band, a full oxygen 2p band that is wider compared to VO4, and three orbitals with energies between the 2s and 2/7 oxygen that correspond to the hybrid sp3 orbitals in CH3. The wider 2p band in VO4CH3 is the result of the bonding between an sp3 orbital on C and a 2p orbital orbital in VO4, with the formation of an antibonding orbital that has a binding energy value higher than that of the 3d band. As a consequence, the initially empty 3d band in the VO4 cluster becomes occupied by one electron in the VO4CH3 cluster. The adsorption of atomic H on a VO4 cluster is similar to the case of CH3 adsorption. In particular, a wider 2p oxygen band results from the bonding between the Is orbital in H and a 2p orbital in VO4, with the formation of an antibonding orbital that has a binding energy higher than the 3d band. Accordingly, vanadium undergoes a formal change in oxi-

Chapter 2

22

VO4

VO4-CH3

V 3d band

-10 O 2p band

3-15

V Fully Occupied

-20

-25 O 2s band

-30

r O

Figure 5. Electronic correlation diagram for CH3 adsorption on VO4

dation state, as the initially empty 3d band in the VO4 cluster becomes occupied by one electron in the VO4H cluster. Another species involved in the kinetically important reaction steps is MOCH2, and the bonding in this species is addressed using the VO4CH2 cluster shown in Figure 6. It is interesting to note that the bonding energetics are more favorable in this geometry compared to the situation where

Methane Partial Oxidation Analysis

23

o VO4

VO 4 -CH 2

V 3 d band

-10 O 2p band

> o5 a> c

-15

LU

-20

Fully Occupied

-25 O 2s band

-30 CH2

O

I

O

Figure 6. Electronic correlation diagram for CH2 adsorption on VO4~3.

CH2 is bridge-bonded between two oxygen atoms in the VO4 cluster. In contrast to the VO4CH3 and VO4H clusters, vanadium does not change oxidation state in the formation of the VO4CH2. Again, the 2s and 2p oxygen bands are wider in the VO4CH2 cluster than in VO4; there are two orbitals with energies between the oxygen 2s and 2p bands, and one orbital between the 2p of oxygen and the 3d of vanadium. Since the CH2 group brings six electrons to the cluster, these electrons can be accommodated

Chapter 2

24

by orbitals below the vanadium d band. Therefore, the energetics of reaction steps involving MOCH2 species are insensitive to the energies of the 3d orbitals. Figure 7 shows two VO4CO clusters that may be used to probe the modes and energetics of CO adsorption on vanadia. These factors are of major importance in the methane oxidation reaction network, since they control the selectivity for CO2 production via CO oxidation. In the linear mode of adsorption, CO is bonded to a single oxygen atom of vanadia, and the bonding energetics are controlled by the overlap of 2s and 2p orbitals of carbon with corresponding orbitals of oxygen. The bridged mode of adsorbed CO is bonded to two oxygen atoms of vanadia, and the bonding energetics are controlled by the same factors as those described above for linear-bonded CO, plus an additional contribution resulting from overlap of 2s and 2p orbitals of carbon with 3d orbitals of vanadium. Although the molecular orbital calculations suggest that the linear-bonded mode of adsorbed CO is more stable than the bridged mode of CO on vanadia, the latter species may be an important intermediate for CO2 production. In

-30 -35

jpied

;O2S

vo 4 co

(linear)

^ a--CO 1

1

===

• ; ;"*rt" .. \

LL

1

yI

>,

3 u_

LL

CO

0

o

o

0

1

vo4co

(bridged)

ully

-25

- g \

TTT

gs

co

{MM

'm[2

: O2P

-15 -20

•m}

(linear)

OCCLipied

; V3d

vo 4 co

in

-10

vo 4

ully

-5

ully OCCLipied

0

0

X /

\

Figure 7. Electronic correlation diagram for linear and bridge adsorbed on

Methane Partial Oxidation Analysis

25

particular, CO2 adsorption on metal oxides takes place via the formation of surface carbonate species (i.e., CO3 species). D. Predicted Effects of Sodium on Methane Partial Oxidation In the analysis of the reaction mechanism for methane partial oxidation with respect to effects of Na addition, we must speculate the manner in which sodium enters the structure. Several possibilities may be considered. For example, sodium may be added to the cluster in the neutral state or as a univalent cation. In addition, the coordination of vanadium by oxygen may change or remain the same upon addition of sodium. For purposes of discussion, we assume first that sodium is a neutral interstitial impurity that donates an electron to the 3d orbital band of vanadium, since the energy level of the 3d orbitals is considerably lower than the energy of the Na valence electron. Furthermore, we assume that the coordination of vanadium remains tetrahedral after sodium addition. Accordingly, we conduct molecular orbital calculations for NaVO4, NaVO4CH3, NaVO4H, NaVO4CH2, and NaVO4CO clusters, where sodium is bonded to a single oxygen atom in each cluster. The results of molecular orbital calculations confirm the expectation that the 35 electron of sodium is donated to a 3d orbital in the VO4 cluster. The most significant effect of the overlapping of the vanadium oxide orbitals with the Na 3s orbital is a lowering of the binding energies in the 2s oxygen band, while the energies of the orbitals in the 3d band remain essentially unchanged. The addition of sodium to the VO4CH3, VO4H and VO4CH2 clusters has little effect on the cluster stabilities. Accordingly, sodium does not apparently change to a significant extent the energetics for the adsorption of CH3, H, and CH2 species on vanadia, at least at the level of these simple semiempirical calculations. In contrast to the results of the calculations above, the adsorption of CO appears to be altered considerably by the presence of sodium. The occupied molecular orbitals with highest energy in the linear-bonded VO4CO cluster do not have vanadium 3d character, and they can be considered as arising from bonding between carbon and two oxygen atoms, one oxygen from CO and the other from vanadia. Importantly, the vanadium 3d band is at higher energies than these molecular orbitals resulting from O—C—O bonding. In the presence of sodium, the bonding of CO to vanadia is stabilized, since an electron is transferred from the 3d band to the partially occupied O—C—O bonding orbitals available at lower energies. Another possible effect of sodium is to alter the coordination of vanadia. For example, preliminary experimental evidence suggests that molybdena

Chapter 2

26

is present on silica as MoO4 tetrahedra during methane oxidation reaction conditions, whereas MoO6 octahedra are present for catalysts containing sodium (N. D. Spencer, personal communication, 1991). The effects of sodium on the adsorption of CO in this situation may be assessed by comparing the stabilities of VO6CO and NaVO6CO clusters. The VO6CO and NaVO6CO clusters involving linearly-bonded CO are more stable than the bridge-bonded clusters, as was the case for the VO4 and NaVO4 clusters. The presence of sodium also favors CO adsorption by donation of an electron from the vanadium 3d level to O—C—O bonding orbitals. The new behavior predicted for the octahedral VO6 cluster, however, is the easier formation of bridge-bonded CO. In particular, the overlap between the 2s and 2p orbitals of carbon and the 3d orbitals of vanadium in the octahedral cluster is more favorable than for the tetrahedral cluster. It is important to note that CO2 adsorption on metal oxides is generally believed to form carbonate species (CO3) that resemble the bridgebonded VO4CO cluster. Therefore, if we view the linear- bonded VO4CO species as adsorbed CO and the bridge-bonded VO4CO species as adsorbed CO2, the molecular orbital calculations suggest that an important effect of sodium addition to vanadia should be the promotion of CO conversion to CO2. In summary, the molecular orbital calculations suggest that the most important effects of adding sodium to vanadium may be the stabilization of linearly-adsorbed CO and an enhancement in the formation of bridgebonded CO. Accordingly, sodium addition to vanadia may be expected to favor CO oxidation to CO2 by stabilizing the formation of surface species that are believed to be intermediates in this reaction. VI.

CATALYTIC REACTION SYNTHESIS FOR METHANE PARTIAL OXIDATION

As noted earlier, Spencer et al. [10] observed that sodium exhibits both a poisoning and a promoting action: It poisons the formation of formaldehyde and the direct oxidation of CH4 to CO2, while it promotes the oxidation of HCHO to carbon monoxide and the oxidation of carbon monoxide to carbon dioxide. Of these effects, the promotion of CO oxidation to CO2 is the most important. Since it has been suggested that the reaction mechanisms for partial methane oxidation over molybdena- and vanadiabased catalysts are related through a more general mechanism, it can be expected that sodium produces the same trends over vanadia-based catalysts. It is now apparent that the major prediction of the molecular orbital calculations is in agreement with the most significant experimental effect observed for the addition of sodium to methane oxidation catalysts i.e.,

Methane Partial Oxidation Analysis

27

increased conversion of CO to CO2. Spencer et al. argue that the observed promotion by sodium of HCHO oxidation to CO is related to the enhancement in CO oxidation (e.g., a facilitation of nucleophilic attack by surface oxygen). This idea would be in agreement with the molecular orbital calculations, which suggest that structures involving multiple oxygen atoms surrounding carbon are favored over octahedrally coordinated vanadium clusters, which may be formed upon sodium addition to the catalyst. The observed poisoning effects by sodium of methane oxidation to formaldehyde and to CO2 are smaller than the promotion of CO oxidation. Spencer et al. suggest that these poisoning effects are caused by bonding of sodium to oxygen, which makes it more difficult for oxygen to become multiply bonded to molybdenum. The molecular orbital calculations indicate that sodium has a small stabilizing effect on the oxygen 2s band by forming Na—O bonds, and these bonds could have the effect suggested by Spencer et al. The molecular orbital calculations suggest that the promotion and poisoning of methane oxidation catalysts by Na can be explained consistently by a microkinetic model combined with semiempirical molecular orbital calculations. Future work can now be undertaken to extend these analyses to other promoters and poisons, with the aim of identifying changes in the strength of specific chemical bonds which are likely to lead to superior catalytic performance. The goal of these studies would be to identify the outer limits on the activity and selectivity of catalysts which involve the surface chemistry embodied in our microkinetic analysis. We see from the microkinetic analysis and semiempirical molecular orbital calculations above that changes in kinetic parameters for various steps of the mechanism that may be anticipated by changing the catalyst structure and composition are constrained by the fundamental surface chemistry. For example, it may not be possible to identify a catalyst that shows high methane conversion and maintains high formaldehyde selectivity. At our present level of microkinetic analysis and using simple molecular orbital calculations, we may only speculate that promising transition metal oxide catalysts for this reaction should satisfy the following criteria: 1. The transition metal oxide d band should be empty under reaction conditions; otherwise, CO2 formation from CO oxidation will be excessive. 2. The transition metal d band must be located at sufficiently low energy that it may accept electrons during methane activation to form methoxy and hydroxyl surface species. 3. The transition metal cation should be tetrahedrally coordinated to minimize CO2 formation and maintain methane activation activity.

Chapter 2

28

These criteria suggest directions for research on mixed metal oxide catalysts that may possess these desirable oxidation-reduction and coordination properties. VII.

CONCLUDING REMARKS

We suggest that a coordinated research approach involving experimental studies and microkinetic analysis offers an opportunity for determining the factors that limit catalyst performance and for suggesting strategies that alter these limitations. The combination of these ideas with semiempirical correlations of chemical bonding properties with catalyst structure and composition provides directions in the search for new catalytic materials. The area of catalytic reaction synthesis is in its infancy. We have used some rather simple arguments and calculations in this chapter, however, to present our view of this emerging area. Microkinetic analysis is first used to consolidate the essential surface chemistry of the catalytic process through consideration of results from diverse experimental data. The result of this analysis is a quantitative description of the available chemical information in terms of constitutive surface reactions, their individual rates, and their dependence on the properties of the catalyst. Microkinetic analysis is then used to provide a foundation on which speculations can be based about the synthesis of new catalytic materials and reaction conditions. Catalytic reaction synthesis involves establishing a link between the parameters of the microkinetic model and the structure and/or composition of the catalyst. This link may be based on theoretical calculations or semiempirical correlations. In general, the level of complexity that can be justified in forming this link depends on the level of detail in which the microkinetic reaction mechanism can be formulated. In this respect we have employed simple molecular orbital calculations to illustrate directions for catalytic reaction synthesis, since the surface chemistry involved in our example, methane partial oxidation over silica-supported metal oxides, is not known in detail. More generally, we believe that the procedures outlined in this chapter provide a strategy to extrapolate our existing catalytic experience to suggest new catalytic materials. In particular, we seek to determine the activity and selectivity limits of undiscovered materials which may operate at the theoretical limits of the postulated catalytic surface chemistry. REFERENCES

1. Dumesic, J. A., Rudd, D. F., Aparicio, L. M., Rekoske, J. E., and Trevino, A. A. (1992). The Microkinetic of Heterogeneous Catalysis, American Chemical Society, Washington, D.C.

Methane Partial Oxidation Analysis

29

2. Stewart, W. E., Caracotsios, M., and S0rensen, J. P. (1993). Computational Modelling of Reactive Systems, Butterworth, Stoneham, Mass. 3. Oh, S. H., Fisher, G. B., Carpenter, J. E., and Goodman, D. W. (1986). /. CataL, 100, 360. 4. Fisher, G. B., Oh, S. H., Carpenter, J. E., DiMaggio, C. L., Schmieg, S. J., Goodman, D. W., Root, T. W., Schwartz, S. B., and Schmidt, L. D. (1987). Studies Surface ScL CataL, 30, 215. 5. Stoltze, P., and N0rskov, J. K. (1988). /. CataL, 110, 1. 6. Dumesic, J. A., and Trevino, A. A., (1989). /. CataL, 116, 119. 7. Waletzko, N., and Schmidt, L. D. (1988). AIChEJ., 34, 1146. 8. Rekoske, J. E., Cortright, R. D., Goddard, S. A., Sharma, S. B., and Dumesic, J. A. (1992). /. Phys. Chem,, 96, 1880. 9. Amiridis, M. D., Rekoske, J. E., Dumesic, J. A., Rudd, D. F., Spencer, N. D., and Pereira, C. J. (1991). AIChEJ., 37, 87. 10. Spencer, N. D., Pereira, C. J., and Grasselli, R. K. (1990). /. CataL, 126, 546. 11. Anderson, A. B. (1975). J. Chem. Phys., 62, 1187. 12. Anderson, A. B., Grimes, R. W., and Hong, S. Y. (1987). J. Phys. Chem., 91, 4245. 13. Gibbs, G. V., Finger, L. W., and Boisen, M. B., Jr. (1987). Phys. Chem. Minerals, 14, 327. 14. Anderson, A. B., Hong, S. Y., and Smialek, J. L. (1987). /. Phys. Chem., 91, 4250. 15. Mehandru, S. P., Anderson, A. B., and Brazdil, J. F. (1988). /. Am. Chem. Soc, 110, 1715. 16. Jen, S. F., and Anderson, A. B. (1989). Surface ScL, 223, 119.

Catalyst-Based Descriptions of Catalytic Cracking Chemistry David T. Allen and Pradeep Marathe Angeles, Los Angeles, California Robert Harding I.

University of California, Los

W.R. Grace & Company, Columbia, Maryland

INTRODUCTION

The catalytic cracking of petroleum is a complex process involving a chemically diverse feedstock and catalysts that can be designed with a range of size and shape selectivities. Because of the wide variation in feedstock properties and because of the large number of variable catalyst features, it is impractical to design cracking catalysts using a completely empirical approach. Instead, a framework must be built to approach cracking catalyst design systematically. In this chapter we describe one possible approach to the problem of cracking catalyst design. The approach has three elements. First, a molecular description of the petroleum feedstock is built. Although it is impractical, if not impossible, to identify every molecule present in a petroleum feedstock, it is feasible to identify several hundred molecules that represent the main structural features of the feedstock. The next element in the catalyst design process is the development of methods for predicting the cracking behavior of these representative structures. We show that group contribution methods can be used to reduce the problem of determining multiple reaction rates of hundreds of compounds to a problem of esimating roughly two dozen group contribution parameters. These empirically determined group contribution parameters, used to estimate hundreds of reaction rates, will depend strongly on catalyst properties. Thus the final element in the process of cracking catalyst design is 31

32

Chapter 3

to determine the values of the group contribution parameters as a function of catalyst properties. In the following sections, each of the elements of the cracking catalyst design process is described. The molecular description of petroleum feedstocks and the group contribution methods for estimating cracking rates are only summarized, however. These issues have been discussed at length in previous publications [1-4]. We focus primarily on the issue of obtaining group contributions to reactivity, as a function of catalyst properties. II.

MOLECULAR DESCRIPTIONS OF PETROLEUM FEEDSTOCKS

Petroleum feedstocks contain tens of thousands of individual species. This level of complexity has traditionally forced petroleum refiners to characterize feedstocks using descriptors such as volatility (boiling-point distributions), density (API gravity), or average aromatic content (roughly related to the Watson characterization parameter). These descriptors may be sufficient for predicting properties such as vapor pressures, but they are not nearly detailed enough to predict how a petroleum feedstock will react over a size- and shape-selective cracking catalyst. Fortunately, advances in mass spectroscopy and nuclear magnetic resonance spectroscopy now allow for the identification of hundreds to thousands of molecules that make up a petroleum feedstock. Although analytical methods still do not allow every molecule in a petroleum feedstock to be identified, it is possible to identify the dominant structural features. Allen and Liguras [4] have described methods for identifying and estimating the concentration of representative molecular structures, based on mass spectroscopy, nuclear magnetic resonance spectroscopy, elemental composition, and chromatographic separation data. The structures that are selected to represent a particular feedstock are not unique. Several different sets of structures could be used to represent the analytical data describing a petroleum feedstock. As a case in point, Figure 1 shows two different sets of structures with a carbon number of 12 that equally well represent a petroleum feedstock described by Liguras and Allen [2]. This nonuniqueness in defining the molecular characterization of the petroleum feedstock will clearly lead to uncertainties in the kinetic model of cracking chemistry and the catalyst design procedure. Liguras and Allen [2] compared the importance of this molecular characterization nonuniqueness to the importance of uncertainties in rate parameters for amorphous catalysts. They found that predictions of cracking product distributions were affected far more by 10% changes in the values of key rate parameters than they were by the nonuniqueness of the molecular characterization. Thus at least for amorphous catalysts, a molecular characterization of petroleum consisting of several hundred structures is sufficient for modeling cracking behavior.

33

Descriptions of Catalytic Cracking Chemistry C-C-C-C-C-C-C-C-C-C-C-C

c

C-C-C-C-C-C-C-C-C-C-C C C-C-C-C-C-C-C-C-C-C-C

?

?

?

C-C-C-C-C-C-C-C C C C-C-C-C-C-C-C-C- C

22.00

3.40 0.60 720 1.80

0 _ C -c-C-C-C

5.06

f~ rparaffi n = .. > . . . rparaffin > .. zation .. cracking isomenzation cracking cracking ° That is, the effect of a change in primary paraffin cracking rate (formation of a carbenium ion on a paraffin and subsequent cracking) far exceeded the effect of a change in aromatization rate, which in turn exceeded the effects of secondary paraffin cracking, olefin cracking, and isomerization. For octane number, all pathways were of comparable importance, but the following minor differences were observed: , £primary secondary . r. aromati- ^ olefin ^ ^ «• ^ «• olefi n > . . . > rparaffin > rparaffin = zation isomenzation .. .. cracking& cracking cracking Finally, for the octane-barrel yield (gasoline yield multiplied by motor octane number) we observe the following ordering: . secondaryJ . £. rprimary r£. ^ aromati- ^ --. olefi n paraffin > . > Fparaffin ^ = ^ .. zation ,. cracking cracking cracking °

olefin . . isomerization

This sensitivity analysis reveals that the two most important reaction pathways in catalytic cracking are formation of the initial carbenium ion on paraffins and aromatization. These pathways, particularly the carbenium ion formation, will be the focus of our initial examination of zeolite catalysis. B. Cracking over Y Zeolites

In the preceding section we indicated that for cracking over amorphous catalysts, the rates of the initial cracking reactions of paraffins will have a major impact on product distributions. Thus the reactions of ^-paraffins

Base case Reaction time, 1 s Reaction time, 10 s Primary paraffin cracking rate increased by 50% Reaction time, 1 s Reaction time, 10 s Primary paraffin cracking rate decreased by 50% Reaction time, 1 s Reaction time, 10 s Secondary paraffin cracking rate increased by 50% Reaction time, 1 s Reaction time, 10 s Secondary paraffin cracking rate decreased by 50% Reaction time, 1 s Reaction time, 10 s

Case studv — — + 10.9 + 5.8 -19.5 -15.6 + 0.2 + 0.1 -0.7 + 1.5

26.65 42.07

19.35 33.56

24.08 39.78

23.87 40.37

% Change from base case

24.04 39.75

Gasoline yield (wt %)

-0.8 -0.2

+ 0.7 0.0

67.04 75.04 66.05 74.86

+ 0.5 + 1.7

-1.3 -0.1

65.76 74.98 66.90 76.34

— —

66.60 75.02

RONa

% Change from base case

65.38 72.29

65.86 72.18

1586 2871 1561 2918

-0.4 -0.2

-1.1 + 1.3

+ 0.5 -0.3

-18.5 -14.3

+ 9.3 + 5.5

1724 3039 1286 2467

— —-

% Change from base case 1578 2879

Gasoline yield x MON

+ 0.4 -0.4

+ 1.3 + 1.5

-1.4 -0.3

64.70 72.24 66.48 73.51

— —

% Change from base case

65.62 72.43

MONb

Table 3 Sensitivity of Gasoline Yield and Octane Number to Kinetic Model Parameters

(D

Q

O

ro

Source: Ref. 3. ''Research octane number. b Motor octane number.

Olefin cracking rate increased by 50% Reaction time, 1 s Reaction time, 10 s Olefin cracking rate decreased by 50% Reaction time, 1 s Reaction time, 10s Aromatization rate increased by 50% Reaction time, 1 s Reaction time, 10s Aromatization rate decreased by 50% Reaction time, 1 s Reaction time, 10 s Isomerization rate increased by 50% Reaction time, 1 s Reaction time, 10 s -0.2 -0.5 + 0.3 + 0.3 -3.7 -5.3 + 2.7 + 3.9 + 0.1 + 0.1

23.99 39.56

24.11 39.85

23.14 37.63

24.69 41.29

24.07 39.77

67.68 75.74

65.97 73.74

67.12 76.62

67.09 76.18

66.27 74.54

+ 1.0 + 1.0

-0.9 -1.7

+ 0.8 + 2.1

+ 0.7 + 1.5

-0.5 -0.6

66.78 73.09

65.12 71.49

+ 1.8 + 0.9

-0.8 -1.3

1607 2906

1608 1952

1528 2766

+ 0.7 + 1.5

66.05 73.51

1589 2905

+ 0.5 + 0.7

65.92 72.91

1569 2857

-0.3 -0.3

65.43 72.23

+ 1.8 + 0.9

+ 1.9 + 2.5

-3.2 -3.9

+ 0.7 + 0.9

-0.6 -0.8

&

3

(D

O

o"

—*

scrip

Chapter 3

44 14 12 j 10 '• 8

I

2 I

2

3

4

5

6

7

8

9

10 II

12 13 14 15 16

Carbon Number of Product

Figure 4. Carbon number distribution of the cracking products of n-hexadecane in ultrastable Y zeolite. Dashed line, Experimental data; solid line, model predictions. are a logical place to begin our examination of cracking over zeolites. In this section we examine the reactions of n-hexadecane over a USY zeolite. The first step of our analysis will be to compare the carbon number distributions predicted using the model developed for amorphous catalysts to the experimental results obtained using a USY catalyst. The comparison is shown graphically in Figure 4. While the overall carbon number distribution predicted by the model appears reasonable, a more detailed examination reveals some problems. The model predicts higher concentrations of large olefins than are observed. The opposite effect is observed for the paraffins. The model predicts the formation of smaller paraffinic products than are observed. These discrepancies may indicate that when olefins are formed at the active site of a Y zeolite, they frequently do not desorb, but rather, continue to react to form smaller olefins. Thus the mechanism for the degradation of n-hexadecane over Y zeolite could include not only the primary cracking reactions shown in Table 4 (reactions 1 to 11), but also must include reactions that account for the rapid disappearance of large olefins (reactions 12 to 31). We are currently building group contribution models for predicting the rate parameters for reactions 1 to 31. Group contribution models are also being developed for the hy-

Descriptions of Catalytic Cracking Chemistry

45

Table 4 Cracking Reactions of rc-Hexadecane over USYa nC16^C3(O) nC, 6 - • C4(O) «C16 -» C5(O) «C16 -» C6(O) «C16 -» C7(O) «C16 -» Cg(O) nC16 -> C,(O) nC16^C10(O) «C16-Cn(O)

+ C13(P) + C12(P) + C n (P) + C10(P) + C,(P) + Cg(P) + C7(P) + Q(P) + C5(P) Q(P) C3(P)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

H C 1 6 - * C 3 ( O ) + C10(O) + C3(P)

nC16^C4(O) nC16^C5(O) nC16 -» C6(O) nC16 -> C3(O) nC16 -> C4(O) nC16 - • CS(O) nC16-C6(O) nC 1 6 ->C 3 (O) nC 1 6 -»C 4 (O) «C 1 6 -»C S (O) «C16 -» C,(O) nC16 -» C4(O) nC16 - • CS(O) nC16 - . C,(O) nC16 -* C4(O) nC16 -» C,(O) nC16 -» C4(O) nC16 - • C3(O) nC, 6 - C3(O) a

+ + + + + + + + + + + + + + + + + + +

C9(O) Cg(O) C7(O) C,(O) Cg(O) C7(O) C6(O) Cg(O) C7(O) C6(O) C7(O) C6(O) C,(O) C6(O) C,(O) CS(O) C4(O) C4(O) C3(O)

+ + + + + + + + + + + + + + + + + + +

C3(P) C3(P) Cj(P) C4(P) C4(P) C4(P) C4(P) C5(P) C5(P) C5(P) Q(P) Q(P) C6(P) C7(P) C7(P) Q(P) C8(P) CB(P) C,o(P)

(12)

•

(13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31)

(O), olefin; (P), paraffin.

drogen transfer reactions that play a modest role in paraffin cracking over Y zeolites at high temperatures. These group contributions will be reported in subsequent publications. C. Cracking over ZSM-5 Zeolites In Section IV.B we reported that cracking reactions of n-paraffins over a USY zeolite exhibit different selectivities than cracking reactions over

46

Chapter 3

amorphous catalysts. The products observed in the cracking of n-paraffins over ZSM-5 catalysts reveal even more variation in selectivities. Hydrogen, methane, and C2 products appear to a much larger extent with ZSM-5 zeolites than with Y zeolites. Table 5 reports the product selectivities observed in /7-heptane cracking over four ZSM-5 zeolites at three temperatures (450°C, 500°C, 550°C). The details of the experimental work will be reported in future publications. The goal of this work will be to determine if these cracking rates and selectivities can be modeled using a group contribution approach and to determine the dependence of the group contributions on catalyst properties. Recall from Section III that the rates of reaction over the amorphous catalyst were modeled using an overall rate constant multiplied by product selectivities- The data for ZSM-5 zeolites can be analyzed in a similar manner. Figure 5 shows the dependence of overall cracking rate, at three temperatures, as a function Si/Al ratio. Note that the data at all three temperatures (450°C, 40()°C, 550°C) condense to a single curve. Note also that the selectivities of the cracking reactions, reported in Table 5, are roughly independent of Si/Al ratio. Thus it is possible to model the cracking rates using a function of the form

where R(i) is the rate of reaction i, /C(Si/Al) is the overall cracking rate, which is a function of the Si/Al ratio,and S(i) is the selectivity of reaction /. The reaction rate, R(i), for the cracking of/i-paraffins in ZSM-5 zeolites is the product of the intrinsic rate per isolated site and the effective number of sites.

where £site is the rate per site and N is the number of sites. We might anticipate that the functional form for N should be a linear function of the Al mole fraction in the zeolite. This is, in fact, the case for low levels of Al, as shown by Beamount and Barthomeuf [8,9]. At high Al mole fractions, however, the Al atoms are no longer isolated and the acidity of the sites decreases as the Al loading increases. To account for this phenomenon, we define an "effective" number of sites, which is equal to the product of site efficiency and the number (or mole fraction) of Al sites per unit cell. An estimate of the site efficiency can be based on the thermodynamics of acid solutions, treating zeolite active sites as acids. Zeolites are, in fact, solid acids with the acid sites located and stabilized within the silica framework. The effective number of acid sites in zeolites can be

Descriptions of Catalytic Cracking Chemistry

47

Table 5 Product Selectivities (Moles Product per Mole of Heptane Cracked) for Heptane Cracking over ZSM-5 Zeolites Temperature Product*

450°C

500°C

Temperature 550°C

Product

Si/Al ratio - 19.5 Ci(P) C2(P) C3(P) C4(P) Q(P) H2

C2(O) C3(O) C4(O) C5(O)

0.039 0.170 0.411 0.226 0.022 0.135 0.225 0.763 0.366 0.039

0.066 0.227 0.300 0.202 0.023 0.187 0.292 0.805 0.386 0.030

H,

C2(O) C3(O) C4(O) C5(O)

0.040 0.192 0.315 0.200 0.032 0.208 0.165 0.813 0.388 0.052

0.061 0.232 0.244 0,210 0.025 0.234 0.150 0.705 0.522 0.049

500°C

550°C

Si/Al ratio - 21.25 0.092 0.242 0.251 0.168 0.021 0.217 0.391 0.798 0.374 0.033

C,(P) C2(P) C3(P) C4(P) CS(P) H2

C2(O) C3(O) Q(O) Q(O)

Si/Al ratio = 35.25 Ci(P) C2(P) C3(P) C4(P) Q(P)

450°C 0.052 0.241 0.279 0.202 0.026 0.192 0.122 0.639 0.506 0.090

0.057 0.248 0.259 0.188 0.028 0.229 0.148 0.681 0.515 0.089

0.084 0.244 0.237 0.171 0.032 0.237 0.246 0.684 0.498 0.074

Si/Al ratic) - 63.5 0.069 0.230 0.232 0.178 0.028 0.267 0.201 0.722 0.547 0.039

C,(P) C2(P) C3(P) C4(P) Q(P) H2

C2(O) C3(O) C4(O) Q(O)

0.049 0.223 0.288 0.189 0.021 0.220 0,145 0.706 0.493 0,067

0.081 0.208 0.222 0.078 0.021 0.297 0.260 0.727 0,426 0.072

0.078 0.237 0.241 0.174 0.027 0.191 0.241 0.694 0.413 0.062

), olephin; (P), paraffin.

viewed as analogous to the proton concentration in acid solution. Taking advantage of this analogy, the functional form of Figure 5 can be derived. The selectivities, 5(/), can be approximately modeled using a rule-based approach. Cracking is presumably initiated by the formation of a carbonium ion on the n-paraffin. The protonated paraffin can then react via the three routes shown in Figure 6 [10]. One route results in the formation of hydrogen and a carbenium ion. The second and third routes form a paraffin and a carbenium ion. The carbenium ions formed in these reactions can deprotonate, forming an olefin, which then desorbs, or they can crack to form smaller olefins and smaller carbenium ions. Eventually, the carbenium ion will become so small that it can no longer crack and must deprotonate.

48

Chapter 3

17

a550C * 500 C °450C

16

c|4

13 12 00

O.I

l/CSi/AI + D ^

0.2

03

Figure 5. Overall cracking rate [K in units of heptane converted (g catalyst • h) l ] versus Si/Al ratio for ZSM-5 zeolites; the activation energy (E) for the overall cracking rate is HfiOOR(K), and is independent of Si/Al ratio. These data collected at three temperatures condense to a single curve when ln(/Q + EIRT is plotted versus the Si/Al ratio. This simplistic model of the cracking chemistry, coupled with the selectivity data of Table 5, can serve as the basis for a series of cracking rules. These rules are: 1.

Carbonium ions can be formed on any of the methylene carbons of an Az-paraffin. Ion formation at all positions two or more carbons H

I

H

H

Figure 6. Carbonium ion reaction pathways. The position of the carbenium ions generated by pathways b and c may be primary or secondary. The rule-based model for cracking in ZSM-5 zeolites assumes that secondary carbenium ions are formed. (From Ref. 10.)

Descriptions of Catalytic Cracking Chemistry

49

from the end of the chain (central carbons) is equally likely. Formation of carbonium ions in the position adjacent to the end of the chain is half as likely as formation of an ion on a central carbon. Formation of carbonium ions on terminal methyl groups is excluded. 2. Once formed, the carbonium ion can react via the three pathways shown in Figure 6. By a factor of 2, pathway a is less likely to occur than pathway b or c. Pathways b and c are equally likely to occur. 3. The carbenium ions formed via reactions a, b, and c will deprotonate to form an olefln if the carbon number is less than or equal to 4. If the carbon number is 6 or higher, the carbenium ion will crack before deprotonating, forming fragments of three carbons or larger if possible. If the carbon number is 5, 75% of the carbenium ions will crack; the remainder will deprotonate. In defining these cracking rules we have introduced a number of adjustable parameters. These are the relative rates of formation of the carbonium ions, the relative rates of pathways a, b, and c, and the relative rates of deprotonation and cracking of the carbenium ions. The test of these simple rules will be in predicting product selectivities. To see how the rules define product selectivities, consider Figure 7. According to the cracking rules, heptane protonates to form one of five carbonium ions; three of these are chemically distinct. Carbonium ions in the 1 and 7 positions are not allowed. The ions in the 3, 4, and 5 positions are each twice as likely to occur as ions in either the 2 or 6 position. The relative rates of formation of each ion and the reactions of each ion are given in Figure 7. These relative rates result in the product selectivities listed in Table 6. The data for heptane cracking are in reasonable agreement with the rule-based predictions. Data reported by Abbott [11] for n-hexane cracking also agree reasonably well with the predictions of the rules. To summarize, a few simple rules have been used to predict cracking selectivities for n-hexane and n-heptane. These rules are consistent with accepted rules for carbonium ion and carbenium chemistry and contain a minimal number of adjustable parameters. However, the rules do ignore a number of chemical pathways. For example, the carbenium ions could isomerize or alkylate as suggested by Wielers et al. [12] rather than merely crack. These pathways would lead to isobutane and related products, which were not observed at significant levels in our initial cracking products or Abbott's initial cracking products. Such mechanisms could be important, however, at higher alumina contents than those used in this work. So these results are clearly only a beginning in the long and difficult process of determining reaction rates as a function of catalyst properties. A detailed description of the group contribution approach to modeling these rates will be reported in future work.

50

Chapter 3 0^

.25.

f

H+

05*C (0)+C (0)+H + 3 4

H

J2.CH4

H H

0

C 6 (0) + H +

^ • C 3 ( 0 ) + C 3 (0)+H +

(Carbonium ion on positions 2 and 6)

C5(P) C2+ "

:4(0)tc3(0)+H+

.50 H H

.15

(Carbonium ion on positions 3 and 5)

.05.

H

2

0

C 7 (0)+H + C 2 (P)

.25

04

H

JQ^ C4(0) +• H+

-C-C H

.01

H

(Carbonium ion on position 4)

C 2 (0)+C 2 (0) + H* 10

C3(P)

Figure 7. Heptane reaction pathways; the number associated with each pathway is the selectivity of the reaction. (P), paraffin; (O), olefin; +, a carbenium ion.

Descriptions of Catalytic Cracking Chemistry

51

Table 6 Selectivity Predictions Based on Cracking Rules n-Heptane

n-Hexane

Predicted selectivity based on cracking rules

Observed selectivity"1

0.20 0.10 0.25 0.20 0.20 0.10 0.29 0.74 0.35 0.06

0.22 0.06 0.22 0.27 0.18 0.025 0.22 0.73 0.45 0.06

H2 CH 4

C2(P) Q(P) C4(P) C5(P) C2(O) C3(O) C4(O) Q(O)

Predicted selectivity based on cracking rules

Observed selectivity5

0.20 0.13 0.27 0.27 0.13

0.19 0.09 0.23 0.40 0.10

0.23 0.76 0.27 0.03

0.18 0.82 0.25 0.02

0

0

^Average data at four Si/Al ratios and three temperatures. h Datafrom Ref. 11 (T = 500°C)

V.

CONCLUSIONS

In this chapter we have summarized the development of a new approach to the design of petroleum cracking catalysts. The approach has three elements: (1) molecular representation of petroleum feedstocks, (2) group contribution methods for estimating reaction rate parameters, and (3) relationships between catalyst properties and reaction rate (group contribution) parameters. The first element of the approach is now well established. The second element has been developed for amorphous catalysts. Work is currently under way to extend the group contribution methods to zeolites and to determine the functional relationship between catalyst properties and rate parameters. ACKNOWLEDGMENTS

This work was supported by W.R. Grace & Co. and the National Science Foundation through Presidential Young Investigator Award Number CBT 86 57289. NOTATION Cp Cr CN

product concentration (mol) reactant concentration (mol) carbon n u m b e r

Chapter 3

52 K P PR S S(i) SP, SPN,£ t tc T x

overall cracking rate constant ( s 1 ) number of primary hydrogens carbenium ion relative stability number of secondary hydrogens selectivity of reaction i carbenium ion position probability probability for cracking at neighbor atom k if carbenium is located on carbon / time (s) catalyst residence time (s) number of tertiary hydrogens percent conversion

Greek Symbols

catalyst decay function

REFERENCES 1.

Liguras, D. K., and Allen, D. T. (1989). Structural models for catalytic cracking. 1. Model compound reactions, Ind. Eng. Chem. Res., 28, 665. 2. Liguras, D. K., and Allen, D. T. (1989). Structural models for catalytic cracking. 2. Reactions of simulated oil mixtures, Ind. Eng. Chem. Res., 28, 674. 3. Liguras, D. K., and Allen, D. T. (1990). Sensitivity of octane number to catalytic cracking rates and feedstock structure, AIChE / . , 36, 1707. 4. Allen, D.T., and Liguras, D. K. (1991). Structural models of catalytic cracking chemistry: a case study of a group contribution approach to lumped kinetic modeling, in Chemical Reactions in Complex Mixtures, (A. V. Sapre and F. J. Krambeck, eds., Van Nostrand Reinhold, New York, pp. 101-125. 5. Greensfelder, B. S., Voge, H. H., and Good, G. M. (1949). Catalytic and thermal cracking of pure hydrocarbons: mechanisms of reaction, Ind. Eng. Chem., 41, 2573. 6. Franklin, J. L. (1949). Prediction of heat and free energies of organic compounds, Ind. Eng. Chem., 41, 1070. 7. Greensfelder, B. S., and Voge, H. H. (1945). Catalytic cracking of pure hydrocarbons, Ind. Eng. Chem., 37, 514-520. 8. Beaumont, R., and Barthomeuf, D. (1972). X, Y aluminum deficient

Descriptions of Catalytic Cracking Chemistry

9. 10. 11. 12.

53

and ultrastable faujasite type zeolites. I. Acidic and structural properties,/. CataL, 26, 218. Beaumont, R., and Barthomeuf, D. (1972). X, Y aluminum deficient and ultrastable faujasite type zeolites. II. Acid strength and aluminum site reactivity, J. CataL, 27, 45. Gates, B.C., (1992). Catalytic Chemistry, Wiley, New York, p. 278. Abbott, J. (1990). Cracking reactions of C6 paraffins on HZSM-5, Appi CataL, 57, 105. Wielers, A. F. H., Vaarkamp, M., and Post, M. F. M. (1991). Relation between properties and performance of zeolites in paraffin cracking, J. CataL, 127, 51.

Molecular Simulation of Kinetic Interactions in Complex Mixtures Matthew Neurock, Scott M. Stark, and Michael T. Klein University of Delaware, Newark, Delaware

I.

INTRODUCTION

The clear recent trend for hydrocarbon upgrading reaction models to focus on molecular detail is a result of several forces. First, new questions are being posed to these models, such as those related to produce performance or quality measures. Second, the environmental acceptability of hydrocarbon mixtures is often assessed in discrete molecular terms. Finally, the opportunity to manipulate hydrocarbon conversion processes toward improved product quality and environmental acceptability through catalysis has heightened as the molecular understanding of catalysts and catalysis has developed. Development of a general mathematical framework for describing both molecule-molecule and molecule-catalyst kinetic interactions would therefore be quite useful in the computational design of catalytic hydrocarbon conversion systems. To this end we have developed Monte Carlo simulation techniques to describe the structure, reaction, and properties of complex hydrocarbon feedstocks [1-3]. The key component of the Monte Carlo simulation is the Markov chain, which maps out a molecule's reaction trajectory over time by comparing a series of random numbers with a transition probability, such as that shown in Eq. (1) for a first-order reaction. Pl} = 1 - exp(-* iy A0

(1) 55

Chapter 4

56

Averaging the results of many (ca. 105) Markov chains provides the time dependence of the mixture composition. However, a pure Markovian analysis requires completely independent states to describe system transitions; thus interactions among components in a mixture would be ignored. But there are too many examples of kinetic coupling in mixtures: instances where rAl{Ax) ¥^ rAi{AuA2) to allow the reaction probabilities [Eq. (1)] to be independent of composition. Thus PV] of Eq. (1), which reflects the probability that a system in state / is transformed to state j in a specific time interval, Af, must be revised to incorporate the composition of the entire mixture at each time, f, and during Ar. The objective of this chapter is to describe the reformulation of both the description of the Monte Carlo reaction system and its states in order to model composition-dependent transition parameters and address chemical kinetic coupling. We utilize a simple prototype kinetically coupled reaction model to verify the accuracy of a series of different computational algorithms aimed at handling molecular interactions through the redefinition of system state and state space. The best solution algorithm is then used to explore molecular interactions in an example of the catalytic hydrotreating of a complex heavy oil feedstock. II.

BACKGROUND

A.

Kinetic Coupling

From the point of view of Monte Carlo simulation, kinetic coupling is manifested as composition (time)-dependent transition probabilities. Thus even the simple example of second-order kinetics, where, for Eq. (1), k = k2CA/CA = k2CA, is composition dependent. More traditionally, however, kinetic coupling arises through interactions of mixture components via competition for catalyst sites or cross-reactions involving intermediates, such as free radicals. Analytical rate laws that capture these interactions include the Langmuir-Hinshelwood-Houghen-Watson models for catalysis [4], Rice-Herzfeld expressions for pyrolysis [5], and the Michaelis-Menton formalism for enzyme catalysis [6]. In all of these kinetic systems, rate expressions describing a ''catalytic" cycle have been formalized. Application of these rate laws within the stochastic framework is the starting point for modeling kinetically coupled reaction mixtures in terms of composition-dependent transition probabilities. The form of the transition probability P{j of Eq. (1) was retained in full recognition of its simple pseudo-first-order character. However, the rate constant, kip was redefined as the rate of reaction of component i divided by its concentration,

Kinetic interactions in Complex Mixtures

57

rilCi = kip thus allowing composition-dependent transition probabilities. The challenge then was to address the effects that this had on the various Monte Carlo solution techniques. B. Monte Carlo Simulation The Monte Carlo simulation reaction modeling approach chronicles the discrete transformations of an ^/-component system throughout time. Methods for accounting composition and reaction time in Monte Carlo techniques are outlined in Figure 1 [1-3,7-9]. The rows of the figure represent the computational methods used to define the state of the reaction system. Two limiting-case extremes are shown in Figure 2. The first is the TV-component approach, where all Nmolecules are stored in the computer's random access memory. This is represented in Figure 2a by the highlighting of all molecules at a particular time. In the latter approach, the system is described by single-component reaction trajectories, as shown in Figure 2b, where only one molecule occupies the computer's RAM at any given time. Both methods require information about the full N-component state to address kinetic coupling. In the N-component/full memory technique, all N components are reacted together as a single trajectory, which provides a direct basis for calculation of the composition, and therefore compositiondependent transition probabilities at each reaction time. The second approach, which considers the reaction trajectory of only a single component, used iterative methods. The composition-dependent transition probabilities are determined by self-consistency techniques. Fixed Time Step N-molecules/time Full Momory Approach

n 1-molecule/time SCC Approach

1

3

Variable Time Step

2

4

Figure 1. Four stochastic methods for the incorporation of kinetic coupling. The system state is described by either TV components or a single component, whereas state space is characterized as either time (fixed) or event (variable) based.

Chapter 4

58

(b)

N molecules

— — —

N molecules

— — —I

•

(2)

Time A

t2

A

A

A

B A A

A

B A B

A

Figure 2. Two stochastic state algorithms, (a) The TV-component state, where reaction proceeds by addressing all components (horizontally) before computing any reaction transitions of the system, (b) The single-component state, where the reaction first proceeds in the time direction (vertical) before considering a second species.

The state space of the Monte Carlo simulation is defined by one of the two approaches listed in the column of Figure 1. Thefixed-timeor variabletime approaches refer to a time change between system transitions. Both of these state-space techniques are shown schematically in Figure 3. In the

Kinetic Interactions in Complex Mixtures

59 Fixed-interval Compositions

A A A A A A A A A . . . . A

1.000

0.000

ABAABAAAB....A

0.995

0.005

0.300

0.700

At I

1 BAAABAAAB....B

]

B B A B B A B A B . . . . B

(a) Variable-time Compositions V_^

—H

A.. . . A

1.000

0.000

A|BJA A . . . .A

0.999

0.001

0.998

0.002

B

0.997

0.003

A B A A. . . .B

0.996

0.004

JB. A B A B A B A A . . . . B

0.995

0.005

A A A A A AffiA

At At

A

^A

AQAA

Fixed-interval Compositions ^-^ A

—B

1.000

0.000

0.995

0.005

v

= A AlBJ A A A B A A

ff

At , —A A B A(S)A

B A A

At , At

v

fAlA B AlR

(b) Figure 3. Schematic comparison of state-space methods for the reaction of A to B. (a) Example of the fixed-time algorithm. Many events are allowed to occur within the same time step, ro-f]. (b) Example of the variable-time-step method. The simulation proceeds event by event as denoted by the highlighted steps; a time step, Afw-, is computed and the time composition is updated. This caption refers only to events occurring between tQ and t\.

Chapter 4

60

fixed-time approach the system state is tested for reaction and updated in specified equal-time intervals. Multiple events (e.g., A—» B —> C reactions) are allowed within each time interval [1]. The variable-time approach is an event-space algorithm. The simulation proceeds event by event, whereby the structure is continually updated and the time is implicit [2,8,9] and determined after an event has occurred. The variable-time method typically undergoes many single-event transitions at much smaller time intervals than in a fixed-time procedure. The system-state and system-space methods for Figure 1 provide equivalent, exact matches to deterministic solutions for simple uncoupled reaction systems. Their solution for the case of coupled kinetics approaches the deterministic value with reasonable accuracy only after account is made of the inherently changing transition probability. We illustrate methods for this using prototype examples of kinetically coupled reaction systems.

III.

STOCHASTIC APPROACHES FOR SIMPLE COUPLED REACTION SYSTEMS

Langmuir-Hinshelwood-Hougen-Watson rate laws for the reactions of mixtures provide a convenient instrument with which to develop Monte Carlo techniques for handling coupled kinetics. The kinetically coupled system of A reacting reversibly to B is considered here: A ^=± B

(2)

To fix ideas, the case of surface reaction as the rate-determining step in the catalytic cycle was considered. This led to the rate laws of Eqs. (3) and (4), where the rate of reaction of A is dependent on both CA and CB. ,.R. -dCA kfKA(CA - CB/K) r A (A3) = -%- x + KACA + KBCB ) )

_ g j j _ kfKA(CA - CB/X) dt

0) (4)

In what follows, the stochastic simulations are compared with the deterministic solution subject to the input values given in Table 1.

Kinetic Interactions in Complex Mixtures

61

Table 1 Deterministic and Stochastic Simulation Input Parameters Description

Value

Pseudo-first-order forward rate constant Pseudo-first-order reverse rate constant Adsorption constant for A Adsorption constant for B Overall equilibrium = kfKA/KrKB

9.75 x io- 3 3.75 x 10 3 5.0 1.0 13.0 5000.0 1.0 0.0

Variable kf kr KA K# K

'final C$ Co

Final reaction time Initial concentration of A Initial concentration of B

Units S" 1

s-1 cmVmol cnrVmol — s

mol/cm3 mol/cm3

The transition probabilities for the kinetics of Eqs. (3) and (4) are summarized below.

= 1 - expl - : PAB = 1 - exp

A?

KACA

--

(6) AB -f

BA

^B/CA

BA

BA

AB

BAB

(5)

A—>B—>A. . . . Approximate single-event transition probabilities, P A B [Eq. (5)] and F B A [Eq. (6)], are determined by dividing the irreversible reaction rate, r}rr of component / by its concentration, [i.e., Pij = 1 - exp(-A*;rr/C( At)]. Multiple-event transition probabilities, required in the fixed-time approach, were estimated following the derivations of Libanati [1]. The expressions for PABA and PBAB are given in Eqs. (7)

Chapter 4

62

and (8). Higher-order transitions are generally not necessary to account for because of the ultimate computer round-off for low probabilities. A. 1.

Full-Memory Systems Approach Full Memory, Fixed-Time Step

The most straightforward method of handling the concentration dependence of Eqs. (5) to (8) is to store all N components of the mixture in random access memory throughout reaction time. This "full-memory" algorithm is shown schematically in Figure 4. Initially (f0), N molecules of A are constructed, and a series of N random numbers are drawn and compared with the reaction transition probabilities to determine the fate of each component within the fixed time interval. Each component is updated to the next time tu the mixture composition is updated, and new transition probabilities are computed. This allows for the explicit accounting of composition to be used in the calculation of transition probabilities at tx. The simulation tests each member of each row (tQ) before proceeding to the next time. This is depicted by the gray shading in Figure 4; the simulation proceeds by reacting the entire state of N molecules through F transitions, where F is the final time divided by the fixed-time step, until a final reaction time is reached. The results of the full-memory, fixed-timestep (FMFT) approach are shown in comparison with the deterministic solution in Figure 5. The FMFT temporal composition profiles match the deterministic results. 2.

Full Memory, Variable-Time Step

The combination of the full-memory and variable-time-step approaches (FMVT) is as straightforward as the FMFT method. The transition prob^s.

Molecule

time ^ s . tl t2 \ tF

1

2

3 M

4

A A.

5

6

7

N

Averages A B

A ,A y:- tJJ$k

A B

B A A A A B A B A A A B

A A

0.7-0.3

A

B B A B A A

\ B

0.5 - 0.5

j

J 1I j l1

Figure 4. Full-memory stochastic approach for the incorporation of kinetic coupling. All N components are used to formulate the composition-dependent transition probabilities at each time step t{.

63

Kinetic Interactions in Complex Mixtures l

400 600 time/s

200

800

1000

Figure 5. Comparison of the full memory fixed-time stochastic algorithm and the deterministic solution of A reacting reversibly to B with LHHW kinetics. The curve represents the deterministic solution; the points depict the FMFT stochastic simulation results.

abilities are equivalent to those in the fixed-time method; however, only the primary transitions A —> B and B ^ A are required in this event-byevent simulation. In the FMVT approach, the state is once again defined by N components. The methodology of the solution algorithm was shown in Figure 2a. All N components are constructed and used as the basis for computing compositions and calculating reaction probabilities. Every conceivable event is determined and assigned a transition parameter, k" — rxlCr The selectivity of each event is computed by dividing the individual transition parameters k{ by the overall parameter for transition, SfLi k% as shown in Eq. (9): selectivitv =

k] =l

K

i

(9)

An integration of the selectivity versus event (reaction) distribution provides a cumulative reaction probability distribution function (CRPDF) such as that shown in Figure 6b. The simulation proceeds by drawing two random numbers. The first is used to compute which of the N events occurs and is placed on the ordinate of the CRPDF. Mapping to the abscissa indicates the actual event or reaction that occurred. A second drawn random number (RN) is used to

Chapter 4

64 0.25 0.2 0.15 0.1 0.05 0 (a)

1 2 3

4 5 6 7 8 Event (Reaction)

910

-§ 0.8 0.6 0.4

•f 0.2

a o W

1

2

3

4

5 6 7 8 Event (Reaction)

9

10

Figure 6. Variable-time-approach distributions: (a) instantaneous selectivity, k'l/ifLi k" for each event; (b) the cumulative reaction probability.

compute the time required for this transition (reaction) by substituting into the rearranged general probability equation shown in Eq. (10). A very small random number (~0) would yield a very small reaction time, whereas a value close to 1 would yield a very long reaction time. Note that with all else constant, increasing the sample size N leads to a larger value of JlfLl k" and therefore smaller Af0. This in turn approaches a constant composition and therefore transition probability. - RN)

(10)

65

Kinetic Interactions in Complex Mixtures l

200

400 600 time/s

800

1000

Figure 7. Full-memory variable-time stochastic approach for kinetic coupling. FMVT approach corresponds to the points; the line represents the determinsitic solution.

The FMVT algorithm is shown schematically in Figure 3b, whereby the simulation of reaction occurs event by event, as represented by the shading of the molecular transformation. The time, composition, and compositiondependent transition probabilities are recomputed after each event. The results from the FMVT method are shown in comparison with the deterministic solution in Figure 7. Once again, the full-memory stochastic solution captures the exact results. Both of these easily implemented full-memory approaches provide an accurate match with the deterministic solution for simple coupled systems. The straightforward extension to handle complex kinetically coupled systems is encumbered only by the associated severe memory requirement. For example, the introduction of structural information alone to describe an N-component asphaltene sample required on the order of 0.01 megabyte (MB) per molecule [9]. This corresponds to 100 MB of random access memory (RAM) for the structural description of a 10,000-component mixture. Accounting for reaction requires considerably more memory and will thus exceed the RAM limits on many of the computers currently available. Thus the full-memory approach, although the most straightforward for handling intermolecular interactions, is clearly limited by these severe memory requirements. The limitations of the full-memory approach motivated the development of an iterative self-consistent concentration (SCC) approach, somewhat

Chapter 4

66

akin to the self-consistent field methods in quantum mechanical computations. Essentially, a solution (i.e., a composition versus time profile) is guessed. This provides a mixture composition for a Monte Carlo simulation. The results of one pass through the Monte Carlo simulation provide a new solution (composition versus time), and iteration continues until convergence on a self-consistent composition is achieved. In effect, the N molecules converge kinetically to the environment they create. B. Single-Component System Approaches 1.

Self-Consistent Concentration, Fixed-Time Step

The basics of the self-consistent-concentration fixed-time-step (SCCFT) approach are shown in Figure 8. The approach involves initiation, simulation, and convergence algorithms. In the initiation step an initial composition matrix, C°, composed of the concentration of each component as a function of time, is chosen. The columns of O refer to each component, whereas the rows refer to each of the fixed-time steps (fy). A reasonable initial guess might be the solution of the simple first-order uncoupled case, where the terms KACA and KBCB are negligible. The simulation algorithm uses the transition probabilities of Eqs. (5) to (8). The transition probability vector P' is computed prior to Monte Carlo sampling from the current concentration matrix C and using transition probability equations (5) to (8). The rows of P' correspond to the F fixedtime steps. Initial Averages A

B

'^Molecule

time

1

2

3 4

5

6

7

...

N

N^

Simulation Averages A

B

1.0-0.0

11

A

A A A A A A

A

1.0-0.0

0.9-0.1

t2

A

0.8-0.2

0.7-0.3

t3

A B A A A A B B A B A A A B

A

0.6-0.4

•

• 0.5-0.5

tF

I JI I I I J I A B B A B A B

B

• 0.2-0,8

i

Iteration to Convergence

Figure 8. Self-consistent-concentration fixed-time stochastic approach. (1) An initial composition matrix (C) is chosen and reaction probabilities (/*') computed. (2) Monte Carlo simulation of TV single-component reaction trajectories and the identification of a new composition matrix. (3) Iteration on C until convergence.

Kinetic Interactions in Complex Mixtures

67

The fixed-time step Monte Carlo solution technique is used to generate and react N molecules based on these precomputed transition probabilities. The actual implementation proceeds by assembling and reacting one molecule at a time, as depicted by the shading in Figure 8. The identity (A or B) of each molecule at each time step is the only information retained after each simulation iteration. This information is averaged over all N components to yield a new compositional matrix, C1. Cx is then used to compute a new transition probability vector P \ and the Monte Carlo simulation is repeated. The convergence step involves the comparison C'~l with C. Convergence is achieved when the error E of Eq. (11), calculated as the summation of the squares of the difference for the composition of each component (k) at every time step (/) between the (/ - l)th iteration and the /th iteration, is within a specified tolerance. /2-steps /z-molec

= 2 /=!

2 [CUM - ex/,*),-.,]2 k-]

(11)

The results for this SCCFT method as a function of the number of iterations are compared with the deterministic solution in Figure 9. The initial iteration yielded the uncoupled reaction system, which has a significantly different conversion behavior than that of the coupled system. However, after one or two iterations, the system has converged to the deterministic solution. 0.016 Deterministic Solution

0

200

400 600 800 1000 time/s Figure 9. Results of the SCCFT method for the incorporation of kinetic coupling. The initial guess is the uncoupled simulation. Subsequent iterations are numbered.

Chapter 4

68 2.

Self-Consistent Concentration, Variable-Time Step

The final approach for handling kinetically coupled reactions shown in Figure 1 is the self-consistent-concentration variable-time-step (SCCVT) approach. In this method an initial guess at the mixture composition for specified fixed-time steps is used to compute the composition-dependent transition parameters k[ at each step. Calculation of the reaction trajectory is nearly identical to the FMVT method, except for the critical replacement of terms involving the summation, 2-1! k-', by the single predetermined transition parameter, k{. For example, the time at which reaction occurs computed by Eq. (10) in the FMVT approach is determined by Eq. (12) for the SCCVT method: "

KAAC CA

RN

)

where the denominator isfc".As demonstrated in Eq. (12), k[ is computed from the predefined composition matrix and the intrinsic irreversible firstorder rate constant kh where k{ is equal to kf or kr depending on whether the reactive component is A or B. Each component is individually reacted to the final reaction time. After the reaction of all N components, the concentrations are averaged over the prespecified fixed-time intervals to yield a new compositional matrix. This new matrix provides the next guess for the Monte Carlo simulation. Convergence is determined by computing the error of Eq. (11) with the criterion that changes in E of 0.1 to 1% or less indicate convergence. The results for the SCCVT method applied to the prototype example of A to B are shown in Figure 10 along with the deterministic solution. The SCCVT solution was determined after more than 10 iterations to a convergence within 1%. As was evident in Figure 10, the SCCVT technique overpredicted the conversion of A in this example. The most pronounced deviations between the SCCVT and deterministic approaches result in regimes of non-first-order kinetics. The limitations of the SCCVT approach are directly related to the interrelationship of time and composition. The time-dependent mixture composition is updated only after each event, which is not guaranteed to take place in a short enough time interval to have an accurate representation of the reaction environment. For the simple system described above with the reaction parameters shown in Table 2, the event time steps were on the order of 100 to 1000 s. During this time the mixture environment about each component could have changed considerably. Thus the molecular conversions were subject to potential bias.

69

Kinetic Interactions in Complex Mixtures 1

0

200

400 600 time/s

800

1000

Figure 10. Self-consistent-concentration variable-time-step stochastic approach to kinetic coupling. The curve denotes the deterministic solution; the points are from the SCCVT simulation.

Examination of Eqs. (10) and (12) suggests strategies for minimizing this "overprediction" of Afy, which is inversely proportional to the term 2jli kh By simply introducing more molecules to describe the system state, the size of this term would increase, thereby decreasing the size of the variable-time step obtained via the substitution of a random number into Eq. (10). C. Partial System Approaches This simple notion led to the concept of dividing the Monte Carlo system of N molecules into P pseudo systems of M molecules each: N

/molecules\ _ \ system /

/pseudostates\ \ system /

/ molecules \ \pseudostatey

(13)

Simulation by fixed- or variable-time methods led to the final strategy for simulation of kinetically coupled systems. It is a hybrid of the approaches of Figure 1, which contains two limiting cases for describing the system state: approaches that handled either all N components or only a single component. In this partial system (PS) approach the overall reaction is described by the number of molecules that can be accommodated in RAM. The partial system fixed-time approach uses only the concepts of the FMFT or SCCFT method. The essence is sample size. In the PSVT ap-

70

Chapter 4 State 1

liiii tlipii •:Av::*:;:.*:v»;::.:*

t

4

Stale 2

State 4

State 3

A A A A A

A:::A;:::A A A

B AAA A

J

1 \

I

B A A A A

A A A B

B A A A A

J» A A A B

B A A A A

B A B AB

1 J

I

I

(a) Figure 11. Algorithmic methods for the incorporation of composition in partial systems (PS) stochastic approaches: (a) the PSLC method, where the kinetics of each pseudosystem is governed by the composition determined only by the five molecules of that pseudo system; (b) the PSSCC method, where kinetics is determined by the composition of all 20 components, but iteration to self-consistency is required.

proach, the computed variable-time step, Afy, is reduced by the factor M, which minimizes changes in the environment within this time. This provides a more consistent environment and thus more accurate kinetic results. Two different methods for the actual implementation of this PSVT approach are illustrated in Figure 11, a simple example where a total of 20 molecules represents the system. The two methods differ in their methods for incorporating the composition. 1. Partial System Local Composition Method

The first approach in Figure lla is the partial system local composition (PSLC) method. In this example, M molecules define the pseudosystem, providing a representation of the mixture compositions and thus a basis for calculating the transition probability of Eq. (10). In essence, these M components define a local composition and thus the transition probabilities

Kinetic Interactions in Complex Mixtures

71

Iteration i CA

CB

Iteration i+1 State 1

State 2

State 3

State 4

CA

CB

A A A' A A

A A A A A

A A A A A

A A A A A

1.00 0.00

0.90 0.10

A B A B A

B A A A A

A B B A A

B A A A A

0.75 0.25

0.75 0.25

A B A B A

B A A A A

A B B A B

B B A B A

B A A A A

A B B A B

I

0.65 0.35

0.60 0.40

I

B A A A B

B A A A B

0.45 0.55

0.40 0.60

B B A B B

B A A A A

B B B B B

B A B A B

0.35 0.65

C 1.00 0.00

at each time step. Monte Carlo averaging over the P pseudostate reaction trajectories provides the final time-dependent global composition vector. The results from this PSLC approach for a total system of 5000 molecules are shown in Figure 12, parametric in M, where 5 < M < 50. The PSVT

0.3

200

4 0 0 6 0 0 8 0 0 time/s

1 0 0 0

Figure 12. Effect of M molecules in the local-environment-explicit-composition variable-time stochastic method of coupling. The deterministic solution is represented by the curve, and the stochastic simulation is given by the points. The triangles represent M ~ 5, the unfilled diamonds M ~ 10, the circles M = 20, and the crosses M = 50 molecules.

Chapter 4

72

approach provided an accurate description, but only when M was approximately 50 did the results show acceptable precision. 2.

Partial System SCC Method

The second approach, described in Figure lib, is the partial system SCC (PSSCC) method. This approach utilizes the SCC methodology to provide the composition at fixed-time intervals prior to each simulation run, and the M molecules of each pseudosystem are used only to reduce the magnitude of the computed time steps by a factor of M. The P pseudosystems are reacted independently and averaged after simulation to provide a new compositional matrix O and a new transition probability vector k'. These results provide the input for the next iteration in the simulation. The process is repeated until the convergence criterion is met. The PSSCC results depend on simulation parameters such as the number of molecules per state, the number of states, the number of SCC iterations, and the size of the fixed-time intervals at which compositions are stored [9]. Figure 13 depicts the sensitivity to the most significant of these, the number of molecules per state. Figure 13a illustrates that the temporal variation of the concentration of component A converges after M approximately 20. This is shown more clearly in Figure 13b, a plot of the absolute error between the deterministic and stochastic solutions as a function of the number of molecules, M. Both of the PSVT methods accurately describe the state of the system and composition results provided that M was large enough. In the example of A reacting reversibly to B, M was on the order of 50 molecules. The PSLC method, which utilizes M molecules as a local environment to compute transition probabilities, has the advantage of requiring only a single pass through the simulation, while the PSSCC method requires at least two to three iterations for accurate results. The PSSCC approach, however, may prove to be more useful than the local-composition approach for problems in which M molecules significantly reduce the variable-time interval, Afy, yet are not enough to describe the chemistry statistically. For example, a two-component state may effectively reduce the average variable-time step, yet could be statistically inaccurate at describing the behavior of, say, five interacting components. In this scenario, the global environment described by the SCC approach would provide more accurate results than the local environment of the first approach. In general, the applicability of several system-state and state-space algorithms to simple coupled reaction systems has been demonstrated. The detailed analysis of each system provided significant insight into designing an appropriate stochastic architecture to simulate the reactions of complex systems.

Kinetic Interactions in Complex Mixtures

600 400 time/s

800

73

1000

0.6

100 40 60 80 Number of Molecules Figure 13. Effect of the number of molecules in the local-environment SCC variable-time stochastic approach: (a) temporal variation for the concentration for M = 1, 5, 20, 50, and 100 molecules; (b) error between the deterministic solution and this stochastic method as a function of the number of molecules (M) defining the state. (b)

IV.

20

KINETIC COUPLING IN COMPLEX REACTION MIXTURES

Complex reaction systems such as those in the upgrading of heavy oils, asphaltenes, and coal liquids motivate the issue of stochastic analysis of kinetically coupled reactions well. These systems contain 10,000+ indi-

Chapter 4

74

vidual molecules, and hence interactions are many. Even the individual molecules will in general contain multiple reactive moieties, and may require several kinetic parameters to describe the intrinsic, uncoupled reaction paths. These complexities were modeled using a hybrid molecular/ lumped scheme in which the reactions of each molecule were considered and interactions from the mixture were phrased in terms of lumps of molecules with similar reactivity patterns. The associated reaction rate expressions for the active sites of a complex molecule thus took the following form: n=

fM{Q intrinsic reactivity

/Exl{C,} reaction environment

^ '

where the overall rate is decomposed into an intrinsic (pure component) reactivity, which is only a function of the active centers a molecule i comprises, and an extrinsic term that depends on the lumped composition of the entire mixture The kinetic form of Eq. (14) can be rephrased stochastically in terms of the composition-dependent transition probability parameter. This is shown as Eq. (15). The pseudo-first-order parameter k[ is a detailed function of the specific site reactivity, the molecular makeup (e.g., carbonchain length, size), and the relative composition of the particular molecular type. The second reaction environment term accounts for intermolecular interactions through the coupling of averaged pseudomolecules. (15) The proposed formalism of describing the rate of reaction in terms of a detailed intrinsic component and an averaged coupled component provides a realistic framework for the reduction of the explosive number of terms in exact rate laws [9,10]. This also complements the stochastic approaches described previously. The severe memory limitations associated with maintaining the atomic structure of each component and the multiple reaction path transitions suggested that the PSLC variable-time approach would be most efficient. The example of a Langmuir-HinshelwoodHougen-Watson kinetic analysis for the hydrotreating of a heavy oil mixture serves to illustrate this approach.

Kinetic interactions in Complex Mixtures A.

75

A LHHW Heavy Oil Hyclrogenation Example

A hypothetical reactant oil was constructed as an ensemble of the aromatic constituents shown in Table 2. Ring isomers for structures of the same molecular type, such as anthracene and phenanthrene, were arbitrarily given equal probabilities of occurrence. Five thousand components were randomly constructed from these distributions to create this generic feedstock. The simulation followed the reversible kinetics for each reaction site (aromatic or naphthenic rings) summarized in Figure 14. Aromatic rings were allowed to hydrogenate, whereas saturated rings were allowed to dehydrogenate. Hydrogenation reaction sites were identified in the simulation by the number and arrangement of peripheral aromatic carbon atoms in each aromatic ring, whereas the dehydrogenation sites were identified

Table 2 Initial Generic Heavy Oil Feedstock Composition for LHHW Hydrotreating Simulations Initial Example Structures

Initial mole %

Saturates 0%

Aromatics 1 Ring

O

2 Ring

Q5

20%

20 %

3 Ring

QfO

20 %

4 Ring

SrVV

20 %

5 Ring

03$

20%

100%

Chapter 4

76 Peripheral Aromatics

REACTION

2 across

2 adjacent

4

3H.

O

k (s-1) Forward 3.209

2.637e-03

1.49e-03

9.47e-06

k (s-1) Reverse 0.107

8,79e-05

5.44e-05

3.75e-07

Figure 14. Model aromatic hydrogenation and dehydrogenation rate parameters. Available experimental values [11-13] with the site of the highest iT-electron density in each molecule through a linear-free energy relationship [14]. The values reported were extracted from the LFER. Reverse parameters were scaled from the corresponding experimental values.

by the number and arrangement of saturated carbon atoms in each naphthenic ring. The intermolecular competition for catalytic sites was described through the LHHW kinetics formalism. Whereas reaction sites were characterized by their atom types (number of peripheral standard or unsaturated carbon atoms), molecules were characterized by their ring type and number (i.e., saturates and one, two, three, four, and five aromatic rings). Molecules of the same ring type and number were lumped into the adsorption term groups following the rankings found in the available experimental literature: saturates ) (S/r D )2 ( r D a ) 2 / 2

Figure 7. (a) Schematic representation of stimulated three-dimensional solids. Average number of discrete steps (n) required depend on the structure (4>,T,?P), size of the probed region (5), and molecular mean free path (\). (b) Effect of ?pi k on the average number of discrete steps required for statistical accuracy in diffusivity calculation, (c) Schematic representation of hybrid discrete/continuum simulation of molecular displacements within random pore structures. (From Ref. 1.)

In the simulations, we place tracer molecules randomly within the voids of a porous sample. During the sampling time, we monitor their sequential discrete steps as they collide with neighboring molecules or against solid surfaces. We monitor the trajectory of only one tracer molecule at a time. The presence of other molecules is "felt" by a molecule through a logarithmic distribution of free paths obtained from kinetic theory [15]. This distribution gives the distance traveled by the tracer between collisions with surrounding molecules; it depends on temperature, pressure, and on the molecular collision cross section. The probability that a surface or molecular collision occurs depends on whether the free path (X) is greater or less than the local pore dimensions (rp). If a molecular collision occurs, the tracer molecule is redirected in a random direction. When it collides with a surface, the molecule is randomly reflected (cosine reflection law). As they move, tracer molecules conform to the irregular geometrical and topological details imposed by the solid obstacles in their path. Through

107

Characterization of Properties of Catalyst Peitets 80

Molecular/

C 03 60

3 O

reasonable #- computational effort

X!

requires alternate -* technique

/

40

3

/

a;

Transition

20

a

Knudsen \—i—v—\—i—i—i—i—i—i—i—i—i—i—i—i—

6

7

8

9 10

(W Mean pore radius / Mean free path Molecule Trajectory Within Boundary Layer

L" l

— Boundary Layer Solid

(c)

f~—'" ^—Imaginary Sphere Used for FPT Calculation

108

Chapters

many collisional events, they probe a representative region of the pore structure and lead to an effective diffusivity characteristic of a macroscopic sample. Computational time is proportional to the number of discrete steps (surface or molecular collisions) that we must monitor as molecules probe the structure. The number of discrete steps required for statistical accuracy increases quadratically with both the size of the sampled region (S) and the ratio rp/k (Figure 7a). The results of Figure 7b were obtained for 3> = 0.418, T = 1.8, and S - \0rs, where rs is the initial microsphere radius before porosity modification. In Knudsen diffusion (\ > rp), tracer molecules seldom collide with other molecules; molecules travel large distances (of order rp) between collisions and cover macroscopic distances (several sphere diameters) in a relatively few number of steps. Thus Knudsen diffusion simulations require relatively short computing times. However, in the molecular regime (A. < rp), tracer molecules collide preferentially with other molecules and travel only small distances (of order \) between collisions; therefore, the number of steps required to probe a representative porous region becomes very large. Monitoring individual collisional events also becomes very costly in the transition regime. Therefore, we have developed a more efficient simulation technique that monitors discrete events (molecular and surface collisions) only within a small region near surfaces and uses a continuum firstpassage-time approximation (FPT) [62] away from solid surfaces, where molecular collisions prevail. This is depicted schematically in Figure 7c. Molecules move through the pore space by a sequence of events that depends on whether the molecule is inside or outside a prescribed imaginary boundary layer (8) surrounding all solid surfaces. Within this boundary layer, discrete collisional events are monitored. Outside it, molecules are allowed to advance in a single (computational) step (consisting of many individual collisional events) to a random point on the surface of the imaginary sphere that makes point contact with the nearest solid surface. The elapsed time for this event corresponds to the first-passage-time; such a time is obtained from the solution of the Brownian motion (diffusion) equation of molecules in free space [62]. In our case the FPT is the time required for a molecule to reach the surface of an imaginary sphere of radius R for the first time. Such times are distributed according to a probability distribution function with mean value R2I6Dh. A "protective" boundary layer is required near the solid surfaces because FPT spheres smaller than a certain size R = Nk (N is the number of mean free paths) do not contain a sufficient number of equivalent discrete steps required for the valid application of the continuum diffusion equation. The boundary layer thickness (8) is chosen as a compromise between computational accuracy and speed of the simulations; it equals the radius of the smallest

Characterization of Properties of Catalyst Pellets

109

imaginary sphere allowed in the FPT calculations. This hybrid discrete/ continuum technique is required to probe representative pore regions in the transition and molecular diffusion regimes. IV. RESULTS A.

Characterization of Physical Properties

1. Porosity

Porosities in catalyst supports typically range between 10 and 60%. Inaccessible porosity in compressed/sintered aggregates of microspheres is usually low. Porosity is an important catalyst design variable; it has a major impact on mechanical strength but also affects diffusion rates and internal surface areas. The porosity of sol-gel-derived materials is controlled primarily by the level of compression and sintering of the microspheres that form the solid. In our simulations, the highest porosity level in compressed solids is that of the starting random-loose structure, which is about 0.42 for monosize spheres; it is slightly lower in aggregates of multisize (bidisperse distributions) spheres because smaller spheres can fill interstices between larger ones [55]. It can also be greater than 0.42 in simulated solids with bimodal pore size distributions [1]. The solids discussed here consist of spheres of uniform size unless otherwise noted. The lower porosity limit is theoretically zero in compressed structures because porosity can be totally destroyed simply by growing the radii of the microspheres to large dimensions. The growth process is carried out at random; the level of growth obeys a Gaussian function. The growth process is carried out until a porosity of about 5% is reached, and this also provides a starting material for simulated sintered structures. In the latter, the porosity is created (increased) by simply removing microspheres at random; in our simulations, we set an upper porosity limit of 60%. In both model structures, actual porosities at any stage of compression or sintering are computed by a simple algorithm. It consists of randomly throwing points within a representative porous sample and monitoring how often the points fall within voids. The porosity level is simply the probability that points fall within the voids. A few hundred thousand points within a macroscopic sample (about 20 sphere diameters) are typically required to calculate porosities with an accuracy of 99.95%. 2.

Surface Area

The surface area of the support provides a measure of the amount of active catalyst sites that can be placed within a pore structure. Surface area depends on pore size; thus it affects not only the volumetric activity of the

Chapter 5

110

ultimate catalyst sample but also the diffusivities of molecules within it. Here we report surface areas (per unit volume) for compressed and sintered structures as a function of porosity. We compare such results with those of a simple surface area-porosity relationship that we have used previously to describe the evolution of surface area in dynamic structures described by Bethe networks. We evaluate surface areas in simulated solids using procedures similar to those used in porosity determinations. Here we place points at random over the entire surface of each sphere and we measure the fraction of these points that lie outside the partially overlapped pore surfaces. This procedure is repeated over all spheres within a representative region of space. Adding all fractions of open spherical surfaces and dividing by the total volume of the probed region gives the surface area per unit volume characteristic of the solid material. Figure 8 shows surface areas per unit volume as a function of porosity in compressed and sintered structures. The maximum in surface area at an intermediate porosity ( ~ 0.48) in sintered solids arises from competition between creation and destruction of pore surfaces as porosity increases (Figure 8b). Dynamic structures characterized by reactions that lead to pore growth also exhibit this maximum in surface area because of similar competition between pore enlargement and pore overlap [3,4,27-31], Using Bethe networks, we previously reported surface areas per unit volume (av) in dynamic porous structures using [4-6] av = K[(\ - *) - '(1 - ')]

(12)

where K is a constant and $ 7 is evaluated from Eq. (4). Figure 8 also illustrates trends of this equation. For simplicity we have assumed that • DIDe, where D is given by the Bosanquet approximation [12]. The results of such calculations are presented in Figure 12 (4> = 0.418). We have used a boundary layer thickness (8) equal to five times the mean free path (X) as an effective compromise between simulation accuracy and speed of the simulations. At both extremes in rp/X, where D is rigorously

Chapter 5

116 12

• ^

10

a

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o 3

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(a)

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COMPRESSED SOLID SINTERED SOLID

1

1

0.1

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0.2

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1

1

0.4

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r

o

2 -

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(b)

1—'—i—'—r 0.0

0.2

0.4 Pellet

0-6 porosity,

0-8

1.0

Figure 11. Effect of porosity on tortuosity factors: (a) compressed and sintered solids (from Ref. 1); (b) Bethe networks (solid lines) and Wakao and Smith [34] model (dashed line) (from Ref. 70).

Characterization of Properties of Catalyst Pellets 1.9

u

1.8

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117 1

Transition

j i

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Mean Pore Radius / Mean Free Path Figure 12. Effect of rplk on tortuosity factor for a simulated three-dimensional porous solid having a porosity of 0.418. (From Ref. 1.)

given by Dk or Dh, the tortuosity approaches similar values (about 1.8). Clearly, the tortuosity behaves as an intrinsic geometric property of the porous structure. Also, the hybrid simulation technique estimates effective diffusivities accurately throughout the entire range of diffusion mechanisms. The deviations at intermediate values of rp/\ reflect the inadequacy qf_the Bosanquet equation in describing a transition diffusion coefficient (D) in ensembles of interconnected noncylindrical pores that vary in size, shape, and connectivity. The Bosanquet equation underestimates diffusivities (maximum error about 20% at rpl\ = 3), suggesting that diffusing molecules are able to "detect" and use nearby larger pores in parallel with smaller diffusing channels to a much greater extent than the strictly sequential mechanism implied by the Bosanquet equation. 3. Simulated and Experimental Diffusivities

The ability of structural representations to predict experimental diffusivities is a key requirement for porous solid models; surface area per unit volume must also be predicted. Models must provide diffusivity estimates in terms of measurable quantities only to become useful in catalyst design. The remaining information must arise from the model itself. Diffusivity esti-

Chapter 5

118

mates in sintered and compressed structures require that we specify the porosity and the size of the microparticles in the initial colloidal dispersion; then, sintering/compression processes leading to the specified porosity completely define all other morphological properties of the structure. Simulations with Bethe networks require information about the porosity and the pore size distribution in the porous solid; their connectivity is used as an adjustable parameter or, in some cases, inferred from fragmentation or porosimetry studies [2]. Both approaches are described below. First, we use Bethe networks to predict experimental diffusivities in unimodal and bimodal porous structures; in both cases, the structural inputs are the porosity and the pore size distribution data. The first example describes the diffusivity of carbon monoxide in carbon dioxide within porous graphite electrodes [67]. Experimentally measured diffusivities and values predicted with a five-coordinated Bethe network are in excellent agreement over the entire range of pressure (0.1 to 10 atm) and temperature (18 to 900°C) (Table 1); Bethe networks are therefore capable of describing effective diffusivities in all diffusion regimes. The second case describes diffusivities of He and H2 in N2 within bimodal porous catalysts (1 atm, 296 to 502 K) [63]. The catalysts were formed by compressing microporous grains; the pore space consists of small pores within grains (micropellets) and larger pores between them. This preferential arrangement of the pore space is no longer described by Eq. (9), which applies only to diffusivities within pores of varying size but randomly Table 1 Experimental and Predicted Effective Diffusivities in Porous Electrode Graphite Temperature (°C) 18 500 600 700 700 700 700 700 800 900 Source: Ref. 2.

Pressure (atm)

(cm 2 /s)

Dho-co2h (cm2/s)2

1.0 1.0 1.0 0.1 0.2 0.5 1.0 10.0 1.0 1.0

0.0018 0.0060 0.0072 0.043 0.035 0.018 0.0099 0.0012 0.012 0.014

0.0014 0.0069 0.0083 0.041 0.032 0.019 0.011 0.0014 0.011 0.013

Experimental value [67]. Bethe network simulations (z = 5).

b

Characterization of Properties of Catalyst Pellets

119

interconnected throughout the void space. However, this equation can be modified to account for transport occurring by three types of processes in bimodal structures: diffusion through micropores, through macropores, and through alternating micropore and macropore regions. These segregated structures can be described by a porosity c = 1/(5 - 1)], which matches exactly that of the cubic tessellation. B. A Priori Diffusivity Estimates

Our compressed and sintered solids share special pore space connectivity properties that clearly distinguish them from other types of random pore structures; also, they have little or no dead- end or closed porosity. We show here that these features permit accurate estimates of effective diffusivities in terms of standard pore volume properties that can be accurately measured (porosity and surface area) experimentally or by using the results of our simulations.

o.o-

00

0.2

0.4 Pellet

0.6

0.8

1.

porosity,

Figure 14. Comparison of normalized diffusivity factor between cubic lattice and five-coordinated Bethe network. (From Ref. 70.)

Characterization of Properties of Catalyst Pellets

123

Compressed solids arise from random-loose structures ( = 0.42) with fully accessible void space; initially, all the void space is accessible and interconnected because neighboring spheres make only point contact with each other. The porosity within closed pores or dead ends remains small even after spheres radii are significantly increased to achieve highly overlapped structures. Dead-ends are rare because initially sphere growth processes affect only small-scale dimensions (a fraction of a sphere radius). We have confirmed this low closed porosity by direct probing of the structure with tracer molecules at various porosity levels. In this procedure we placed molecules at random within the voids in representative solid regions and measure the fraction of molecules that remain permanently trapped within the structure (i.e., do not exit the probed region even after very long times). We find that this fraction is negligibly small even for porosities as low as 5%. This is not surprising because a highly overlapped structure ($ = 0.05) requires an average growth in sphere radius of only about 18%, which is not sufficient to create dead ends or to isolate void volume within randomloose structures. Therefore, the initial randomness and the morphological features of random-loose structures are largely preserved during porosity modification procedures. These conclusions also apply to sintered solids, which become gradually more connected as spheres are randomly removed from a highly compressed but still interconnected structure. The absence of isolated pores or dead ends in compressed and sintered structures is also consistent with the results of Figure 10a. Figure 10a shows that by using the correct characteristic pore dimension (obtained from simulations) in the equivalent diffusivity (Z)), both types of solids are described by nearly identical diffusivity factors E. Thus, effective Knudsen diffusivities in our solids can be evaluated from D* = E - ifpv

(14)

where £() is a unique topological quantity for random aggregates of spheres, described entirely by the curve in Figure 10a. A priori estimates require only that the porosity and the mean pore size (?p) of the material be specified. As discussed earlier, rp measurements using standard adsorption or porosimetry techniques may be inaccurate and model dependent. Our simulations suggest that an approximate relation,

h -f

uniform distribution for slab geometry (5un J u n ) and external shell distribution (5ext, / c x t ). Consecutive reactions: At -^ A 2 ^ A3; /i(«i) = (1 + v)2uxi (1 + awO2, / 2 (M,) = M2, cr = 8, 1, the poison deposits preferentially in a thin layer close to the pellet's external surface (i.e., pore-mouth poisoning). In the analysis of Becker and Wei [58], four types of active element distributions in the pellet were considered: uniform, eggshell, egg white, and egg yolk. In the case of uniform poisoning the best performance is provided by an eggshell distribution, similarly to the nondeactivating case for positive-order reactions (Section II.A.I.a). However, under poremouth poisoning conditions a significant improvement in the catalyst performance could be achieved by distributing the active element in the inner region of the pellet. Similar improvement was also demonstrated by Polomski and Wolf [59] for egg-yolk catalysts, in which the outer protective layer was assumed to be comprised of a different support material than the support over which the catalyst was deposited, therefore having different diffusion properties. Pavlou and Vayenas [60] addressed the problem of optimal initial activity distribution, which maximizes the total reactant conversion, accounting for saturation of active sites with poison. In this study, which was limited to the specific case of first-order kinetics and large Thiele modulus values, the deactivation process was simulated by a shell progressive model where the deactivation front, sfn advances toward the pellet interior independently of the concentrations of the catalyst, reactants, or poison, according to the Voorhies equation sp=

I - tw

(38)

where t is dimensionless time and w is an empirical coefficient between 0.5 and 1. The results obtained indicate that, in general, the optimal initial activity distribution tends to exhibit a bimodal behavior, concentrating one portion of the active element near the pellet external surface and another portion close to its center, as illustrated in Figure 24. The specific shape depends on the pellet geometry, on the values of the physicochemical parameters involved, and on the kinetics of the deactivating process through the value of the parameter w. It should be noted that in this particular case, contrary to nondeactivating systems, it was found that the performance of the optimal catalyst pellet was not significantly higher than that of a uniformly active pellet. A similar deactivating process occurring in a fixed-bed reactor was considered by DeLancey [61]. An approximate solution was derived using Pontryagin's principle. This allows one to identify various possible reactor

Optimal Distribution of Catalyst in Pellets

171

10

8 -i

6 4-

2-

0.2

0.4

0.6

0.8

1.0

s

Figure 24. Optimal catalyst distribution for constant velocity of the deactivating front (w = 1) and CH4 + H2O

(39)

was studied, under deactivation resulting from the formation of carbonaceous compounds as well as from poisoning by hydrogen sulfide, added in small concentrations in the feed stream. Substantial differences in the behavior of the three pellets were observed in terms of both product selectivity and catalyst lifetime. However, as noted by the authors, since methanation is a structure-sensitive reaction, its kinetics depend on the active element dispersion, which indeed was quite different for the three pellets examined. This aspect was strong enough to mask the effect of the active element distribution throughout the support, thus preventing any definitive conclusions to be drawn about the effectiveness of the catalyst design itself. The

Optimal Distribution of Catalyst in Pellets i

1

173

1

(a) 0.08

^ — — ^ § = 0.3 0 4 5 ^ ^ 1

^^v -— ^^

0.04 40

[

0.2 --N

-

1

80 120 Dimensionless Time

if O

40

80 120 Dimensionless Time

Figure 25. Objective function versus time dependence for various active-layer locations; p = 10, Da, = 10, (a) (a, - fl2)/fl3 = 0.1, (b) (a, - a2)/a3 = 10. Isothermal first-order reaction, poisoning kinetics first order. Objective function: (cost of products per operating time — cost of raw materials and catalyst per operating time)/operating time. (From Ref. 64.)

same reaction systems was also studied by Wu et al. [67] in step-type catalyst pellets. It was found that when the depth of the active layer was greater than a certain value, the influence of carbon deposition was negligible. C. Special Topics 1. The Three-Way Catalyst

In automotive emission control, a catalyst is required which simultaneously catalyzes three reactions (i.e., oxidation of carbon monoxide and residual hydrocarbons, as well as reduction of nitrogen oxides) in a range of values of the air-fuel ratio centered around the stoichiometric point. This is a rather ambitious goal that needs to utilize various active elements simul-

174

Chapter 6

taneously to perform the various required functions. Also, except under startup conditions when the catalyst is cold, under normal operating conditions the catalyst is at a sufficiently high temperature that the reactions are diffusion controlled, and for this reason the active elements are deposited close to the external surface of the pellet. However, a complication arises from the occurrence of two deactivating processes: poisoning due to the presence of trace quantities of lead and phosphorus in the feed, and thermal sintering. The poisoning process is nonselective (i.e., it involves both the support as well as the active catalyst). Since the poisoning process is diffusion controlled (i.e., pore-mouth poisoning), the poison penetrates the catalyst pellet in the form of a sharp front whose velocity is substantially independent of the local concentration of the active elements. Summers and Hegedus [68] treated the case where only the two oxidizing reactions occur, and comparing several distributions of Pt and Pd, concluded that the best performance is obtained by a catalyst pellet that is impregnated with Pt at the outer shell and Pd in a separate subsurface band, as illustrated in Figure 26. This was attributed to the fact that Pt is more resistant to poisoning, with a nonzero residual activity, while Pd located in the interior provides higher hydrocarbon oxidation activity. The configuration above also guarantees a certain resistance to sintering, which is provided by the Pd band protected from poisoning by the external Pt band. When also the reduction of nitric oxide is desired, it is necessary to include in the catalyst pellet a certain amount of Rh, which catalyzes this reaction even in the presence of traces of oxygen. However, the high cost of Rh as compared to that of Pt and Pd, and its strong sensitivity to phosphorus and lead poisoning, suggest using a small amount of Rh in the pellet and protecting it from poisoning. Based on the considerations reported above, a three-way catalyst was designed by Hegedus et al. [69]. On the whole, the catalyst pellets contained 1.12 g of Pt, 0.44 g of Pd, and 0.06 g of Rh per car. These were located in three separate bands, one underneath the other. The first, at the pellet's external surface, was the Pt band, whose depth was determined so as to contain entirely the expected penetration depth of the poison during the desired catalyst lifetime. Next was located the Rh band, so that diffusional resistances in the nitric oxide reduction process would be minimized and it would also be protected from poisoning. Finally, the Pd band was placed at the deepest location, providing reasonable activity even at relatively low temperatures, typically encountered during engine startup conditions. The three-way catalyst indeed constitutes a remarkable example of catalyst design, despite the fact that because of a lack of detailed expressions

175

Optimal Distribution of Catalyst in Pellets 100 • PVPd o Pd/Pt • Pt-Pd A Pt

90 80

o O

70 60 50 40

i t

Indolene Clear

0

10

20

30

40

Time (hrs)

Figure 26. Hydrocarbon conversion with time, during accelerated poisoning experiments. Pt/Pd: Pt (exterior)/Pd (interior); Pd/Pt: Pd (exterior)/Pt (interior); Pt~Pd: Pt and Pd (both exterior); Pt:Pt (exterior); Pd:Pd (exterior). (From Ref. 68.) for the kinetics of the various reactions involved, the design was based only on experimental observations rather than on quantitative models. 2.

Hydrotreating Catalysts

Hydrotreating catalysts are used in the petroleum industry to remove various compounds (e.g., metals, sulfur) from the bottom fraction of distilled crudes. This is required to prevent these contaminants from poisoning the catalysts used in subsequent processes. In hydrodemetallation, the metals are removed by irreversible adsorption on the catalyst. In contrast to previous situations, this deactivating process is actually desired since the goal is to maximize the amount of metals deposited on the catalyst. Metal deposition usually occurs first at the pore mouth, which prevents the entrance of other reactant molecules, thus leaving a substantial fraction of the catalyst in the internal part of the pellet unutilized. This process is illustrated schematically in Figure 27, where it is shown that when the thickness of the deposit equals the difference between the pore radius Rp and the reactant molecule radius Rm7 the transport through the pore mouth

176

Chapter 6

is inhibited and the pellet becomes inactive. For first-order deposition kinetics, the time t, where such pore-blocking occurs, can be estimated from the relationship t =

(40)

kC

where pd is the deposited layer density, C the reactant concentration, and k the rate constant of the deposition process. To use the catalyst more effectively, various strategies have been explored, involving optimization of the pore size distribution and the catalyst shape. In a detailed theoretical study, Limbach and Wei [70] investigated the use of catalyst pellets with nonuniform activity distributions. The case of deposition rate following first-order kinetics was considered. It was assumed that the intrinsic reaction rate per unit active surface area is not affected by deposition. The change of active surface area with deposition was accounted for by using an empirical relationship and similarly, the decrease of the effective diffusion coefficient with deposition was also taken into account, because as illustrated in Figure 27, the deposited metal decreases the cross-sectional area of the pores available for transport. It was demonstrated that for hydrodemetallation, the overall deposited amount in a uniform pellet could be increased by up to 25% simply by decreasing the amount of catalyst located near the pore mouth, so as to delay its complete blockage. The optimal catalyst activity distributions were also computed numerically, and these exhibit a sharp maximum toward the center of the pellet followed by a decrease toward the external surface, so that the front of the fully deactivated catalyst originates at the center of the pellet and moves to the external surface. This distribution provides

Rp 6 Rm Deposition

- Molecule Pore Mouth Figure 27. Schematic representation of pore-mouth plugging. (From Ref. 70.)

Optimal Distribution of Catalyst in Peliets

177

a good utilization of the catalyst, maximizing the overall amount of metals deposited. For hydrodesulfurization, Asua and Delmon [71] have made a theoretical study for catalysts containing molybdenum and cobalt sulfides. In this case, catalyst performance optimization can be pursued by varying both the overall catalyst concentration (i.e., Mo + Co) as well as its composition (i.e., Mo/Co). They used a detailed kinetic model which accounted explicitly for the catalyst composition, as well as for the concentration of active sites, and showed that the catalyst performance could indeed be improved by using nonuniformly distributed catalyst pellets. 3. Composite Catalysts

Composite catalysts consist of small particles of the active catalyst (e.g., zeolite crystals) embedded in a support (e.g., silica/alumina) that may exhibit some modest catalytic activity itself. The support has much larger pores and therefore the diffusion coefficient is much larger in the support than in the active catalyst. As illustrated by Ruckenstein [72], this is the main advantage of composite catalysts, since the reactants have a much easier access to the active catalyst particles than in the case where the entire pellet is comprised of the active catalyst alone. The advantages of these catalytic systems in the presence of deactivation were studied by Varghese and Wolf [73] with reference to uniformly distributed catalyst pellets and pore-mouth poisoning. In this case the complete plugging of the larger pores of the support is significantly delayed relative to the case of a pellet which contains the active catalyst alone. Accordingly, the catalyst life is longer and allows for a better utilization of the active catalyst located in the inner portion of the pellet. The possibility of further improving the pellet performance through a nonuniform distribution of the active catalyst particles within the support was theoretically investigated by Dadyburjor [74]. In particular, a zeolite/ silica-alumina cracking catalyst was examined. The effect of the deactivation process, mainly due to cooking, was described empirically by simultaneously decreasing the rate constant of the catalytic reaction and the diffusion coefficient in the support. The optimal distributions were computed using an approximate numerical procedure that maximized the overall reaction rate at a given time during the deactivation process—thus leading to different optimal distributions at different times. It was found that the shape of the optimal distribution depended strongly on the size of the pellet as well as on values of the kinetic parameters. However, at least for the parameter values explored, the improvement in pellet performance over the uniform pellet obtained was not very large.

Chapter 6

178 V.

CATALYST PREPARATION CONSIDERATIONS

A.

Adsorption on Powders

The adsorption of metal complexes on oxide surfaces without any diffusional limitations (i.e., when the support is in powder form) can be analyzed in terms of phenomena that occur at the interface between the support and the catalyst precursor. Strong interaction between the support and the metal complex generally leads to high loadings and well-dispersed catalysts. If such an interaction does not exist, the precursor deposits according to a process of crystallization, precipitation, or decomposition during the drying step, typically yielding large crystallites [19,75,76]. The impregnation techniques used for preparation of nonuniform catalyst distributions require strong interaction between the support and the precursor. The substrate should therefore have ion-exchange capabilities, which is true for many inorganic oxides. Protons or surface hydroxyl groups are used to fix the metal compound to the support surface. In principle the interactions are controlled by [75,77,78] (1) the type of the support and state of the surface: number of functional groups, their acidity and/ or basicity, and (2) the impregnating solution: pH, type and concentration of metal compound, and presence of competing ions. When oxide particles are suspended in aqueous solutions a surface polarization results in net electrical surface charges. The nature and magnitude of this charge are a function of the pH of the solution surrounding the particle. In acidic solutions the surface is positively charged (S—OH2+) and will preferentially adsorb anions, while in basic solutions the particles carry a negative surface charge (S—O ) and adsorb cations. In between these two cases, a value of pH exists at which the overall charge of the particle is zero. This value is characteristic of the oxide and corresponds to its zero point of charge (ZPC) or isoelectric point of solid (IEPS). A comprehensive collection of isoelectric points of oxides and hydroxides was published by Parks [79]. It is worth noting that isoelectric points of different samples of the same oxide may vary markedly. This has been attributed to factors such as impurity levels, surface crystallinity, dehydration, and aging. For alumina, Jiratova [80] found isoelectric points in the range 4.5 to 9.7, depending on the type of foreign ions present on the surface. Among the common support materials, zeolites, silica-aluminas, and silicas adsorb cations; aluminas, titanias, and chromia are amphoteric (i.e., they adsorb anions in acidic and cations in alkaline solutions); and magnesia adsorbs anions. Although each individual adsorption process may be different, general rules of anionic adsorption have been demonstrated in a study by D'Aniello [81] on the adsorption of transition metal oxalate and cyanide complexes

Optimal Distribution of Catalyst in Pellets

179

on a ^-alumina surface. The results have been interpreted with an adsorption mechanism of the type Al—OH + H+
Al—

M~n
(Al—

involving simultaneous coadsorption of protons and anions. In the absence of chemical reactions the amounts of anion adsorbed could easily be controlled by the amount of acid present in the impregnating solution. However, not all ion-exchange processes follow the simple scheme outlined above but involve a series of sequential reactions. For example, the adsortion of H2PtCl6 on 7-AUO3 has been associated with an acid attack of the alumina with dissolution of aluminum and subsequent formation of aluminum ions. These ions are finally readsorbed on the support together with the hexachloroplatinic anion [82]. Adsorption characteristics of other systems that have been investigated in detail include calcium [83], nickel [84], chromium, cobalt, molybdenum, tungsten [85,86], and aromatic acids [87] on 7-alumina. Theoretical approaches of phenomena occurring at the oxide-water interface have been developed largely in the colloid and interface science literature. Based on the electric double-layer theory, James and Healy [88] modeled the adsorption of hydrolyzable metal ions on oxide surfaces. Their calculations were based on the total free energy of adsorption being comprised of a Coulombic attraction, representing the energy change favorable for adsorption and a solvation term, representing an energy barrier to adsorption. However, the model required the use of an adjustable parameter that was associated with chemical interaction forces. This model has been employed for fitting experimental data for cobalt, calcium, chromium, and iron adsorption on silica [89], nickel adsorption on silica [90], and the adsorption of ammonium complexes of copper, nickel, and cobalt on alumina, titania, and iron oxide [91]. Due to the relatively large magnitude of the adjustable chemical contribution in the double-layer model above, a site-binding model was developed by Yates and co-workers [92] and Leckie and co-workers [93-95]. This model is based on the premise that the principal mechanism of surface charge development is the reaction of major electrolyte ions with ionizable surface sites. The formation of surface complexes occurs in addition to

180

Chapter 6

simple ionization of surface groups by the association-dissociation reactions of protons and hydroxy ions. This approach requires fitting of experimental adsorption data for the capacitance of the inner layer, from which the adsorption equilibrium constants for each species can be obtained. B. Simultaneous Diffusion-Adsorption in Pellets 1. Theoretical Studies

Nonuniform impregnation profiles usually arise due to complex interaction of intrapellet flow, diffusion, adsorption, electrochemical, and reaction phenomena, depending upon the particular system and the impregnation process employed. Several models reviewed by Lee and Aris [21] have been proposed to explain the distribution of the active ingredients in catalyst supports. Two rate processes are involved in the impregnation step: the transport of solute in the pores of the support and the uptake of solute by the pore walls. In most of the models developed so far, Fickian diffusion is assumed to take place in the liquid-filled pores, either during wet impregnation or in dry impregnation after the initial convective transport has ceased. Different variations of Langmuir type of adsorption (e.g., reversible or irreversible, kinetic or equilibrium, one or more types of adsorption sites) have been considered for the uptake of the solute on the support. The following studies are representative of those which have appeared in the literature. Vincent and Merrill used a simple model of plug flow into a single pore to analyze the time-dependent flow of impregnating solution into a dry pellet and interior dispersal of the impregnant [96]. Two types of resistances at the liquid-solid interface were considered: mass transfer and adsorption kinetics, and were shown to yield similar impregnation profiles in systems where saturation occurred. For the limiting cases where mass transfer or adsorption controls, Lee [97] developed analytical expressions for the intrapellet catalyst concentration at the end of the filling period. Do [98] modeled the impregnation of one adsorbing agent in a wet pellet. The steady-state solution of the diffusion-adsorption equation was obtained analytically, while the transient solution was obtained numerically. It was shown that when the impregnation is diffusion controlled, a sharp eggshell catalyst distribution is obtained, particularly when there is no desorption of the active species, so that there is no chance for redistribution. A higher adsorption capacity of the support results in an increase of the overall loading, but it does not have a significant effect on the activity profile.

Optimal Distribution of Catalyst in Pellets

181

Coimpregnation of pellets with metal precursor solution and a siteblocking agent can be used to manipulate intrapellet distribution of the active ingredient. The model calculations of Vincent and Merrill for dry impregnation were extended for such multicomponent adsorption by Kulkarni et al. [99]. The authors obtained qualitative agreement with the data of Shyr and Ernst [100]. Analytical solutions were obtained by Lee and Aris [101] and Lee [102]. Both models were able to produce a variety of distributions of the active material, such as uniform, sharply defined eggshell, egg white, and egg yolk. The former study [101] also addressed the effect of diffusion after impregnation was complete, as well as the effect of drying. It was shown that the phenomena above had a smoothing effect on the nonuniformities of the catalyst distribution developed at the end of the impregnation step. Hegedus et al. modeled competitive multicomponent adsorption on wet pellets by using adsorption constants determined from separate experiments [103]. The model was used to predict the uptake of Rh in 7-Al2O3 pellets, as well as the Rh distribution inside the pellet, when HF was used as the site-blocking agent, by using the diffusion constants as adjustable parameters. Scelza et al. [104], using a similar model, fitted the data of Castro et al. [105] for coimpregnation of pellets with H2PtCl6 and HC1. However, the adsorption constants as well as the diffusion constants were treated as adjustable parameters. Using a purely competitive Langmuir adsorption model for coimpregnation of chloroplatinic and citric acids, Price [106] was able to predict successfully the location of the platinum layer inside a 7-Al2O? pellet. For the case of sequential impregnation, the solution effect introduced by the competitive adsorbate was considered and the resulting model agreed well with experimental results as illustrated in Figure 28. The models above do not explicitly account for the influence of pH and ionic strength on the catalyst distribution. Ruckenstein and Karpe [107] have conducted a detailed study taking into account electrokinetic and ionic dissociation phenomena and employing the electric double-layer theory. The effects of pH, ionic strength of the impregnating solution, the nature of the support, the effect of coimpregnating species on the distribution profile, and the amount adsorbed were examined within this framework. A comparison of this model with the results of the more commonly used model based on Fickian diffusion and Langmuir adsorption (where both the ionic dissociation and the elecrokinetic phenomena are neglected), and with the case where only the electrokinetic effects are neglected, is shown in Figure 29. It is clear that the profiles of adsorbing agents in the pore can be quite different for the various cases.

Chapter 6

182 1.00-!

0.75-

Citric Acid

0.50-

0.25

0

.0556 M

•

.1111 M

D

2222U

•

.3333 M •

i

15

•

\w

D ^

1

30

\

i

45

60

75

Time (minutes!

Figure 28. Comparison of model predictions and experimental platinum band locations for sequential impregnation with 0.00589 M hcxachloroplatinic acid and various citric acid concentrations. (From Rcf. 106.)

Chu et al. [108] developed a transport-adsorption model for wet impregnation based on the continuity equations for dilute ionic species and on triple-layer electrostatic theory. This model predicted the Ni profile in 7-AI2O3 pellets very well, obtained with a system of NiCl2, NaCl, and HC1, as shown in Figure 30. This system, with appropriate choice of the operating variables, produced a variety of Ni distributions (i.e., eggshell, egg white, and egg yolk). 2.

Experimental Studies

The catalyst precursor deposited on the surface of the pores of a pellet is comprised of two parts: The first is the solute adsorbed on the support during the impregnation process, and the second is from the precipitation of unadsorbed solute from the pore liquid during the drying process. Depending on the transport and adsorption characteristics of the system, catalyst deposition by adsorption can yield uniform or nonuniform distributions.

183

Optimal Distribution of Catalyst in Pellets

.05

.10

.15

.20

Reduced Pore Length

Figure 29. Effect of coimprcgnation on platinum distribution profile with citrate ion as coimpregnant: solid line, electrokinetic and ionic effects considered; dotted line, electrokinetic effects neglected; dashed line, electrokinetic and ionic dissociation effects neglected, (a) Adsorbed impregnant in the absence of coimpregnation; (b) adsorbed impregnant during coimpregnation; (c) adsorbed coimpregnant. Chloroplatinic acid 0.5 x 10 3 M, sodium citrate 0.5 x 10"3 M, pH(, - 3.3, time - 10 h, /0 = 10 3 M. (From Ref. 107.)

When only one component is present during impregnation (which must then be the catalyst precursor), and in the case where drying does not affect distribution of the catalytic material, the relative rates of the transport and adsorption processes determine the type of distribution actually obtained. Fast transport or weak adsorption of the solute yield relatively uniform distributions, while strong adsorption or slow transport yield eggshell distribution [109,110]. The impregnating solution concentration and the impregnation time determine the thickness of the shell [111-113], When

184

Chapter 6

-0.1

- 1.0

-0.8

Figure 30. Nickel profile in a ^-alumina pellet after 26.75 h. Impregnation with 10 3 M NiCl2 and 0.1 M NaCl after acid pretreatment for 120 h, pH. - 5.2. (From Ref. 108.) impregnation with short contact time produces catalysts with decreasing concentration profile toward the pellet center, increasing time of impregnation smoothens catalyst nonuniformities [114]. The effect of the state of the support, dry or wet before impregnation, depends on the adsorptivity of the catalyst precursor and is more pronounced for a short impregnation time, in which case the effect of initial convective transport is significant. In the case of weak adsorption, dry impregnation yields a catalyst with more total loading and relatively more uniform than wet impregnation [115]. For strong adsorption, Summers and Ausen [110] observed that the penetration depth obtained from wet impregnation was slightly less than that from dry impregnation. The drying step that follows the impregnation phase causes the transfer and evaporation of the liquid in the pore volume and in the process redistributes the impregnant remaining in the pore volume. The extent of this redistribution on the impregnation profile depends on the physicochemical parameters of the system, and in certain cases can be significant [cf. 116119]. This process is also affected by the viscosity of the liquid in the pores [120]. The effect of drying is indeed complex and differing conclusions about the consequences of slow and fast drying have been reported in the literature [cf. 21]. Most multicomponent impregnation studies concern platinum supported on a 7-AI2O3 pellet. Shyr and Ernst [100] studied the influence of a large number of acids and salts used as coimpregnants with H2PtCl6, on the

Optimal Distribution of Catalyst in Pellets

185

distribution of Pt within 7-Al2O3 pellets, and obtained profiles shown in Figure 31. If along with chloroplatinic acid, HC1 is used as coimpregnant, uniform platinum distribution is obtained [121,122]. When dibasic organic acids (e.g., citric or oxalic acid) are used instead, the platinum is driven into the pellet interior, forming a subsurface layer with controlled location and width [2,123]. Employing HF as coimpregnant, Hegedus et al. [103] prepared egg-white Rh/7-Al2O3 catalysts. Increase of the impregnation time has been found to increase the local loading, the width, and the distance of the active layer from the external surface, while increase in the coimpregnant concentration pushes the active layer deeper [103,123,124]. When the pellet is impregnated with the catalyst precursor and competitive adsorbate sequentially, in this or the reverse order, similar egg-white catalysts are obtained. The width of the catalytic layer is decreased if the metal precursor is impregnated first, while if the impregnation order is reversed, the resulting catalyst has a thicker active layer [124]. Some platinum catalysts, prepared by using sequential impregnation of chloroplatinic and citric acids, are shown in Figure 32; theoretical predictions of catalyst locations for types (a) to (c) were shown in Figure 28. Maitra et al. studied the effect of pH by carefully monitoring and adjusting it during the impregnation process [125]. In this way, eggshell or uniform tungsten catalysts were prepared. In an attempt to predict catalyst

O 03 CD O

o O

E

13 C

Q_ CD 05

cr

Figure 31. Types of Pt profiles obtained in coimpregnation experiments. (From Ref. 100.)

186

Chapter 6

Figure 32. Step-type platinum catalysts prepared by sequential and coimpregnation. (a) 0.106 M chloroplatinic acid for 15 min, followed by 1.0 M citric acid for 15 min; (b) 0.106 M chloroplatinic acid for 15 min, followed by 1.0 M citric acid for 60 min; (c) 0.106 M chloroplatinic acid for 15 min, followed by 3.0 M citric acid for 60 min; (d) 0.106 M chloroplatinic acid for 15 min; (e) 0.106 M chloroplatinic acid and 1.5 M citric acid coimpregnation for 3 h; (f) 0.106 M chloroplatinic acid and 1.5 M citric acid coimpregnation for 10 h. (From Ref. 124.)

nonuniformities in their impregnation studies, Schwarz and Heise classified the coimpregnants according to their effect on three interfacial phenomena [126]. The first class consists of inorganic salts such as NaCl, NaNO3, and CaCl2, which affect electrostatics at the solution-surface interface. The second class includes simple inorganic acids and bases such as HC1, HNO3, and NaOH, which change the potential difference between the adsorbing ions and the surface. The third class of ingredients, such as acetates, citrates, and phosphates, compete with the metal ion for possible adsorption sites. This competition is similar to a chromatographic process. These ingredients can also alter the electrostatics and potential of the heterogeneous system. ACKNOWLEDGMENTS

We gratefully acknowledge financial assistance from the Union Carbide Chemicals and Plastics Company and a NATO Collaborative Research Grant in support of our research in the area of optimal catalyst activity distributions in pellets. Our earlier work in this area was supported by the National Science Foundation.

Optimal Distribution of Catalyst in Pellets

187

NOTATION

activity activity distribution function cost of products cost of raw materials cost of catalyst surface area of active element per unit catalyst pellet weight (m 2 /g catalyst pellet) At component involved in a reaction b constant defined by Eq. (28) B bCc Bi^ Biot number for heat transfer Bi m Biot number for mass transfer cp fluid heat capacity C reactant concentration C reactant concentration vector Ce weight fraction of active element (g active element/g catalyst pellet) Ce volume average of Ce d number of zones in a reactor Da Damkohler number, L(l - e)r°ivC°f Dj dimensionless effective diffusivity, DeAIDei De, effective diffusivity of component A-x / dimensionless production rate of desired product, integrated over the catalyst pellet //(M(-,G) dimensionless reaction rate, rj(ChT)lrj(CfAlTf), [rj(CnT)l rj(C}A,T}) for reactor] g dimensionless reactant concentration in the external fluid phase, g = Cf/Cf gv volume-averaged catalyst density hj(C,T) concentration- and temperature-dependent portion of the y'th reaction rate, defined by Eq. (17) /0 external ionic strength of impregnating solution (mol/cm 3 ) k(x) local reaction rate constant k volume-averaged reaction rate constant K adsorption equilibrium constant L reactor length m reaction order n integer, characteristic of pellet geometry; = 0 for infinite slab, = 1 for infinite cylinder, = 2 for sphere p specific surface area of active element (rrr/g active element) q(s) dimensionless active element concentration, Ce{s)ICe a a(x,t), a{ a2 a3 A

a(s)

Chapter 6

188 Tj(ChT) r0 R Rg Rm Rp s s 5 t T U; u{ u v Vp w x y Y z

reaction rate reaction rate in a catalyst pellet where the active surface area per catalyst weight is equal to pCe characteristic pellet dimension; half-thickness (n = 0), radius (n - 1, 2) universal gas constant reactant molecule radius pore radius dimensionless distance from center of pellet, x/R dimensionless location of the catalyst selectivity time absolute temperature dimensionless reactant concentration, C-JCjA dimensionless reactant concentration at the catalyst location dimensionless reactant concentration vector velocity of external fluid phase pellet volume empirical coefficient, defined by Eq. (38) distance from center of pellet dimensionless axial coordinate along the reactor, zIL yield axial coordinate along the reactor

Greek Symbols a Py p 7 8 A AH AHa e

upper bound of the dimensionless active element concentration (0 < q(s) < a) dimensionless heat of the yth reaction, (~AHj)DeACfA/(\eTf) external Prater n u m b e r , (-&H)C}/pcpT°f dimensionless activation energy for reaction rate constant, EIRgTf deposition thickness half-thickness of step distribution heat of reaction heat of adsorption bed void fraction or dimensionless heat of adsorption, {~AHa)l

T| 0 6 K ke

effectiveness factor dimensionless t e m p e r a t u r e , TITf dimensionless t e m p e r a t u r e at the catalyst location ratio of Thiele moduli, §y§\ particle thermal conductivity

Optimal Distribution of Catalyst in Pellets

189

j cf)0 ij;

Bi,,,/Bi,, stoichiometric coefficient of the zth component in the y'th reaction DeAIDe2 density of external fluid phase deposited layer density dimensionless adsorption equilibrium constant, KjCfA dimensionless temperature in the external fluid phase, T = TfITJ _ _ _ Thiele modulus, Ry/rfiCfAJf)lDeACfA "clean 11 Thiele modulus, cf>(l + a ) modified Thiele modulus, (J>/\/7?

v\fn

function of the catalyst location; see Eq. (27)

it. vtj k p pti a,T

Subscripts ext / opt p un

external bulk value optimal poison uniform

Superscript °

reactor inlet

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Technology, Vol. 6, J. R. Anderson and M. Boudart, eds., SpringerVerlag, Berlin, p. 227. Parks, G. A. (1965). The isoelectric points of solid oxides, solid hydroxides, and aqueous hydroxo complex systems, Chem. Rev., 65, 177. Jiratova, K. (1981). Isoelectric point of modified alumina, Appl. Catal, 1, 165. D'Aniello, M. J. (1981). Anion adsorption on alumina, J. CataL, 69, 9. Santacesaria, E., Carra, S., and Adami, I. (1977). Adsorption of hexachloroplatinic acid on -y-alumina, hid. Eng. Chem. Prod. Res. Develop., 16, 41. Huang, C.-P., and Stumm, W. (1973). Specific adsorption of cations on hydrous 7-Al2Ov J. Colloid Interface Sci., 43, 409. Huang, Y.-J. R., Barrett, B. T., and Schwarz, J. A. (1986). The effect of solution variables on metal weight loading during catalyst preparation, Appl CataL, 24, 241. lannibello, A., Marengo, S., Trifiro, F., and Villa, P. L. (1979). A study of the chemisorption of chromium(VI), moIybdenum(VI) and tungsten(Vl) onto ^-alumina, in Preparation of Catalysts II, B. Delmon, P. Grange, P. Jacobs, and G. Poncelet, eds., Elsevier, Amsterdam, p. 65. lannibello, A., and Mitchell, P. C. H. (1979). Preparative chemistry of cobalt-molybdenum/alumina catalysts, in Preparation of Catalysts II, B. Delmon, P. Grange, P, Jacobs, and G. Poncelet, eds., Elsevier, Amsterdam, p. 469, Kummert, R., and Stumm, W. (1980). The surface complexation of organic acids on hydrous 7-AUO3, J. Colloid Interface Sci., 75, 373. James, R. O., and Healy, T. W. (1972). Adsorption of hydrolyzable metal ions at the oxide-water interface. 3. A thermodynamic model of adsorption, /. Colloid Interface Sci., 40, 65. James, R. O., and Healy, T. W. (1972). Adsorption of hydrolyzable metal ions at the oxide-water interface. 1. Co(II) adsorption on SiO2 and TiO2 as model systems, J. Colloid Interface Sci., 40, 42. Theis, T. L., and Richter, R. O. (1980). Adsorption reactions of nickel species at oxide surfaces, Adv. Chem. Ser., 189, 73. Fuerstenau, D. W., and Osseo-Asare, K. (1987). Adsorption of copper, nickel, and cobalt by oxide adsorbents from aqueous ammoniacal solutions, /. Colloid Interface Sci., 118, 524. Yates, D. E., Levine, S., and Healy, T. W. (1974). Site-binding model of the electrical double layer at the oxide/water interface, /. Chem. Soc. Faraday Trans. I, 70, 1807. James, R. O., Davis, J. A., and Leckie, J. O. (1978). Computer

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simulation of the conductometric and potentiometric titrations of the surface groups on ionizable latexes, /. Colloid Interface Sci., 65, 331. Davis, J. A., James, R. O., and Leckie, J. O. (1978). Surface ionization and complexation at the oxide/water interface. 1. Computation of electrical double layer properties in simple electrolytes, J. Colloid Interface Sci., 63, 480. Davis, J. A., and Leckie, J. O. (1980). Surface ionization and complexation at the oxide/water interface. 3. Adsorption of anions, /. Colloid Interface Sci., 74, 32. Vincent, R. C , and Merrill, R. P. (1974). Concentration profiles in impregnation of porous catalysts, /. CataL, 35, 206. Lee, H. H. (1984). Catalyst preparation by impregnation and activity distribution, Chem. Eng. Sci., 39, 859. Do, D. D. (1985). Modeling of impregnation kinetics and internal activity profiles: adsorption of HC1, HReO4 and H2PtCl6 onto 7A12O3, Chem. Eng. Sci., 40, 1871. Kulkarni, S. S., Mauze, G. R., and Schwarz, J. A. (1981). Concentration profiles and the design of metal-supported catalysts, J. CataL, 69, 445. Shyr, Y.-S., and Ernst, W. R. (1980). Preparation of nonuniformly active catalysts, /. CataL, 63, 425. Lee, S. Y., and Aris, R. (1983). Theoretical and experimental aspects of catalyst impregnation, in Preparation of Catalysts III, G. Poncelet, P. Grange, and P.A. Jacobs, eds., Elsevier, Amsterdam, P . 35. Lee, H. H. (1985). Catalyst preparation by impregnation and activity distributions. 2. Coimpregnation for nonuniform distribution based on competitive adsorption, Chem. Eng. Sci., 40, 1295. Hegedus, L. L., Chou, T. S., Summers, J. C , and Potter, N. M. (1979). Multicomponent chromatographic processes during the impregnation of alumina pellets with noble metals, in Preparation of Catalysts II, B. Delmon, P. Grange, P. A. Jacobs, and G. Poncelet, eds., Elsevier, Amsterdam, p. 171. Scelza, O. A., Castro, A. A., Ardiles, D. R., and Parera, J. M. (1986). Modeling of the impregnation step to prepare supported Pt/ A12O3 catalysts, Ind. Eng. Chem. Fundam., 25, 84. Castro, A. A., Scelza, O. A., Benvenuto, E. R., Baronetti, G. T., de Miguel, S. R., and Parera, J. M. (1983). Competitive adsorption of H2PtCl6 and HC1 on A12O3 in the preparation of naptha reforming catalyst, in Preparation of Catalysts III, G. Poncelet, P. Grange, and P. A. Jacobs, eds., Elsevier, Amsterdam, p. 47.

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106. Price, D. M. (1988). The preparation of Pt/7-Al2O3 pellets with an internal step-distribution of catalyst: experiments and theory, Ph.D. thesis, University of Notre Dame. 107. Ruckenstein, E., and Karpe, P. (1989). Control of metal distribution in supported catalysts by pH, ionic strength and coimpregnation, Langmuir, 5, 1393. 108. Chu, P., Petersen, E. E., and Radke, C. J. (1989). Modeling wet impregnation of nickel on ^-alumina, /. Catal., 111, 52. 109. Chen, H.-C, and Anderson, R. B. (1976). Concentration profiles in impregnated chromium and copper on alumina, /. Catal., 43, 200. 110. Summers, J. C , and Ausen, S. A. (1978). Catalyst impregnation: reactions of noble metal complexes with alumina, J. Catal., 52, 445. 111. Maatman, R. W., and Prater, C. D. (1957). Adsorption and exclusion in impregnation of porous catalytic supports, Ind. Eng. Chem., 49, 253. 112. Harriott, P. (1969). Diffusion effects in the preparation of impregnated catalysts, /. Catal., 14, 43. 113. Santacesaria, E., Galli, C , and Carra, S. (1977). Kinetic aspects of the impregnation of alumina pellets with hexachloroplatinic acid, Reaction Kinet. Catal Lett., 6, 301. 114. Cervello, J., Hermana, E., Jimenez, J. R, and Melo, R (1976). Effect of the impregnation conditions on the internal distribution of the active species in catalysts, in Preparation of Catalysts /, B. Delmon, R A. Jacobs, and G. Poncelet, eds., Elsevier, Amsterdam, p. 251. 115. Melo, R, Cervello, J., and Hermana, E. (1980). Impregnation of porous supports. 2. System Ni/Ba on alumina, Chem. Eng. Sci., 35, 2175. 116. Van den Berg, G. H., and Rijnten H. Th. (1979). The impregnation and drying step in catalyst manufacturing, in Preparation of Catalysts //, B. Delmon, P. Grange, P. A. Jacobs, and G. Poncelet, eds., Elsevier, Amsterdam, p. 265. 117. Komiyama, M., Merrill, R. P., and Harnsberger, H. R (1980). Concentration profiles in impregnation of porous catalysts: nickel on alumina, /. Catal., 63, 35. 118. Neimark, A. V., Kheifez, L. I., andFenelonov, V. B. (1981). Theory of preparation of supported catalysts, Ind. Eng. Chem. Prod. Res. Develop., 20, 439. 119. Uemura, Y., Hatate, Y., and Ikari, A. (1987). Formation of nickel concentration profile in nickel/alumina catalyst during post-impregnation drying, /. Chem. Eng. Jpn., 20, 117. 120. Kotter, M., and Riekert, L. (1979). The influence of impregnation,

Chapter 6

198

121. 122. 123.

124. 125. 126.

drying and activation on the activity and distribution of CuO on aalumina, in Preparation of Catalysts //, B. Delmon, P. Grange, P. A. Jacobs, and G. Poncelet, eds., Elsevier, Amsterdam, p. 51. Maatman, R. W. (1959). How to make a more effective platinumalumina catalyst, Ind. Eng. Chem., 51, 913. De Miguel, S. R., Scelza, O. A., Castro, A. A., Baronetti, G. T., Ardiles, D. R., and Parera, J. M. (1984). Radial profiles in Pt/A12O3, Re/Al2O3, and Pt-Re/Al2O3, AppL Catal., 9, 309. Becker, E. R., and Nuttall, T. A. (1979). Controlled catalyst distribution on supports by co-impregnation, in Preparation of Catalysts II, B. Delmon, P. Grange, P. A. Jacobs, and G. Poncelet, eds., Elsevier, Amsterdam, p. 159. Papageorgiou, P. (1984). Preparation of Pt/7-Al2O3 pellets with internal step-distribution of catalyst, M.S. thesis, University of Notre Dame. Maitra, A. M., Cant, N. W., and Trimm, D. L. (1986). The preparation of tungsten based catalysts by impregnation of alumina pellets, AppL Catal., 27, 9. Schwarz, J. A., and Heise, M. S. (1990). Preparation of metal distributions within catalyst supports. 4. Multicomponent effects, J. Colloid Interface Sci., 135, 461.

Reaction-Transport Selectivity Models and the Design of Fischer-Tropsch Catalysts Enrique Iglesia, Sebastian C. Reyes, and Stuart L Soled

Exxon Research and Engineering Company, Annandale, New Jersey

I.

INTRODUCTION

The synthesis of hydrocarbons from natural gas involves the intermediate conversion of methane to CO/H 2 and then to a mixture of paraffins, olefins, and oxygenates in Fischer-Tropsch synthesis and related processes. The conversion of methane to synthesis gas (CO/H2) is a challenging and expensive initial step in the overall process scheme; it places selectivity demands on the subsequent synthesis gas conversion processes to minimize recycle to the synthesis gas generation steps. Therefore, high CO hydrogenation selectivity is a critical requirement in such integrated gas conversion schemes. In general, optimum catalysts give high yields of C v products and low selectivity to light components (particularly CH4), which need to be recycled to the synthesis gas generation step. High-molecular-weight hydrocarbons (C2(> -) are desired products because they provide useful feedstocks in downstream processes leading to fuels and petrochemicals. Catalytic CO hydrogenation occurs on metal sites (e.g., Co, Ru, Fe) located within porous solids that frequently contain the liquid hydrocarbon products of the reaction. As a result, the transport of reactants and products to and from catalytic sites is slow and often controls the rate of primary and secondary hydrocarbon synthesis reactions. Diffusion-limited arrival of CO at reaction sites leads to low CO concentrations and high H2/CO ratios within catalyst pellets, conditions that favor formation of light products and secondary reactions of primary products. In contrast, diffusion199

Chapter 7

200

limited removal of reactive products, such as a-olefins, increases their concentration within catalyst pellets and leads to higher rates of readsorption and chain initiation, processes that increase product molecular weight and C5+ yields. Thus intermediate levels of transport restrictions lead to highest yields of desirable products, such as linear high-molecular-weight hydrocarbons, which provide excellent raw materials for the synthesis of clean fuels and petrochemicals. We have experimentally measured the rate and selectivity of hydrocarbon synthesis reactions on Co and Ru catalysts within packed-bed reactors. Concurrently, we have developed reaction-transport models to describe our results and to suggest strategies for the design of catalysts and reactors that maximize C5+ yields or products in a specific carbon number range. In this work we focus on the detailed tailoring of catalyst physical properties such as pellet size, pore size distribution, and the density and location of the active sites within support pellets. The models describe the effects of bed residence time, carbon number, and density of active sites on molecular weight distribution and paraffin content in products. An important finding of our study is that diffusion-enhanced readsorption of a-olefins accounts in a very simple manner for the non-Flory carbon number distributions of highly paraffinic products typically observed in Fischer-Tropsch synthesis on Co and Ru catalysts [1], II.

BACKGROUND

A.

Hydrocarbon Synthesis Reactions

Hydrocarbon synthesis from CO and H2 requires that reactants form monomer species. Several studies [2-4] have suggested that initial steps involve the dissociation of CO to form chemisorbed carbon species that undergo subsequent hydrogenation to surface methylene and methyl groups. Methyl groups act as primary chain initiators that grow by reaction with methylene monomers [3,4]. The chain growth process ends by hydrogen addition, which causes the hydrogenolysis of metal-carbon surface bonds and leads to paraffin products, or by hydrogen elimination to give a-olefins. Internal olefins and branched products are formed by chain growth and termination steps of alkyl chains attached to the surface through nonterminal carbons; they are much less abundant than their linear homologs but are also found among reaction products. A simplified kinetic scheme for chain growth and termination is shown in Figure 1. Secondary reactions occur when primary products desorb from a chain growth site and interact with another catalytic site before exiting the reactor. For example, sites that catalyze hydrogenation, oligomerization, and

201

Design of Fischer-Tropsch Catalysts (Cn) paraffins

(Cn.i*)

(C mi C n . m ) paraffins

K

(Cn*)

(Cn) olefins

(Cn+1 OH)

I

alcohols

(C n + 1*)

paraffins

secondary reactions

J

Figure 1. Chain growth and termination and secondary reactions in FischerTropsch synthesis on Co and Ru Catalysts. acid-type cracking of olefins can influence strongly the type and molecular weight of the hydrocarbon products. Some of these reactions are shown schematically within the boxed area in Figure 1. Hydrogenation (ks) and skeletal or double-bond isomerization merely change the product functionality within a carbon number. Olefin oligomerization (ka) and cracking (kc) change the molecular weight distribution. Many of these reactions are inhibited by CO and H2O. Therefore, their rates tend to be higher near the reactor inlet (low H2O concentrations), near the exit of high-conversion reactors (low CO concentrations), and toward the interior of diffusionlimited pellets (low CO concentrations) [1,5]. In later sections we address the role of these reactions in controlling carbon number distribution and product functionality during Fischer-Tropsch synthesis. Other secondary reactions merely reverse one of the termination steps in the chain growth sequence. Such reactions occur only when termination steps are near equilibrium because only then reverse reaction rates become important. Hydrogen elimination steps leading to olefins are reversible (kr, Figure 1). In contrast, hydrogen addition steps leading to /^-paraffins are not. a-Olefins, and to a much lesser extent internal olefins, readsorb and initiate surface chains that grow and ultimately desorb again as larger molecules; this process is repeated until reactive olefins are removed by diffusion (within pellets) and convection (between pellets) processes from the reactor or until readsorbed a-olefins eventually desorb as unreactive paraffins during chain growth.

202

Chapter 7

Many studies have suggested that a-olefins readsorb and initiate surface chains [6-13]. These reports [8-11] have confirmed that readsorbed olefins act predominantly as chain initiators; less readily, they also incorporate as intact species into other growing chains. These studies [8-11] concluded that secondary hydrogenation of a-olefins also occurs along with readsorption and chain initiation during Fischer-Tropsch synthesis. Recently, we showed that olefin hydrogenation is inhibited strongly by water, an indigeneous product of hydrocarbon synthesis [1,5]; as a result, secondary hydrogenation of a-olefins becomes very slow at CO conversions above 5% and high pressures (>50() kPa) on both Ru and Co catalysts [1]. We have also found that a-olefin hydrogenation rates are strongly inhibited by CO. Hydrogenation rates become fast, however, as CO is depleted either by strong diffusional gradients within pellets or by complete conversion in the reactor. As metal sites become depleted of chemisorbed CO, other reactions, such as hydrogenolysis and cyclization, can also influence product functionality and molecular weight. B. Product Functionality and Molecular Weight Distributions

Hydrocarbon formation requires the initiation of surface chains, their growth by addition of CH2 groups, and their sometimes reversible termination by detachment from the surface as olefins or paraffins (Figure 1). Mathematical treatments of polymerization kinetics are often adequate to describe products of chain growth. This is possible when the growth probability (a) is independent of chain size (n). Then product distributions can be described by a Flory distribution [14], Fn = n{\ - a ) V i !

(1)

where Fn is the fraction of the carbon atoms within chains containing n carbon atoms. Therefore, the slope of a plot of \og(Fn/n) versus n gives the chain growth probability a. Deviations from Flory distributions have been widely reported in the literature [1,7,16-23]. Often, the chain growth probability increases with increasing carbon number, leading to higher-than-predicted yields of highmolecular-weight products. Pichler et al. [7] first reported such deviations on Co catalysts; they suggested that the higher intrinsic readsorption rate of the higher olefins led to surface chains that terminate with increasing difficulty. Non-Flory product distributions were also attributed to the presence of two types of chain growth sites with different probabilities for chain growth and for olefin formation [22,23]. Recently, we have shown that non-Flory distributions can also occur because transport-limited removal

Design of Fischer-Tropsch Catalysts

203

of a-olefins from catalyst pellets enhances readsorption rates on Ru and Co catalysts [1,15]. Here we describe hydrocarbon synthesis products by reporting chain termination probabilities (p 7 „) for each chain size [6]: (2)

In terms of molar fractions, chain termination probabilities can be expressed as (3)

where 4>H is the molar fraction of products containing n carbon atoms and rpn and rtn are the rates of propagation and termination of Cn chains. This approach is more rigorous and general than the Flory treatment and allows chain growth kinetics that depend on carbon number; however, the denominator of Eq. (3) requires that we measure accurately the entire molecular weight distribution. The total termination probability (PT>) is a linear combination of the individual termination pathways described in Figure 1: P7> =

Pt),« + P//,« " Pr,«

(4)

Readsorption (pr^) decreases the total termination probability by reversing the olefin termination step; readsorption can be enhanced by increasing the olefin reactivity (readsorption rate constant kr) or the olefin concentration within pellets and reactors. The corresponding chain growth probability (a,,) is obtained from Eqs. (3) and (4) as =

C.

Transport Effects in Fischer-Tropsch Synthesis

Transport of reactants and products is slow in Fischer-Tropsch synthesis because it occurs predominantly through high-molecular-weight liquid hydrocarbons. The liquid phase is contained within the pore structure and in the outer surface of catalytic pellets in packed-bed reactors. Diffusion through liquids is typically 103 to 104 times slower than through gases [24].

204

Chapter 7

Also, diffusion of large hydrocarbon chains through polymeric melts is very sensitive to molecular size and requires concerted segmental and reptationtype motion to overcome molecular entanglements [25]. The reported benefits of catalyst pellets with sites preferentially located near the outer pellet surface (eggshell) suggest that transport restrictions strongly influence CO hydrogenation rates and selectivity [26-31]. Several experimental studies have addressed the role of transport restrictions on the rate and selectivity of Fischer-Tropsch synthesis processes. Fischer and co-workers [32,33] first reported that small Co/ThO2/kieselghur granules were more active and selective in Q synthesis than larger pellets, which also gave higher CH4 selectivities. Anderson et al. [34,35] observed a decrease in CO hydrogenation rate as the pellet size of Fe catalysts increased and attributed it to diffusional restrictions on the rate of arrival of CO and H2 at reaction sites. Based on a detailed dimensional analysis, Madon et al. [36] reached conclusions similar to those of Anderson et al. [34,35] and showed that pellet diameters of less than about 0.2 mm were required to avoid CO intrapellet gradients for typical synthesis rates (2 |jimol • s" 1 • c m " 3 ) .

Modeling descriptions that attempt to quantify the role of transport limitations on hydrocarbon synthesis processes are also available [1,3743]. These models differ significantly from each other in the type and extent of the controlling transport processes. For example, Zimmerman et al. [41] observed marked transport limitations for Fe catalyst pellets as small as 0.3 mm and developed a reaction-transport model that included first-order kinetics and assumed that H2 is the diffusion-limited reactant. A more detailed transport model with more complex rate equations was also proposed to describe pellet size effects at reaction conditions favoring light hydrocarbons [38,39]. The reported transport models include the rate of reactant arrival to catalytic sites in fixed-bed [37-43] and slurry [44] reactors; they do not include the rate of secondary reactions or detailed descriptions of carbon number distributions. A single-pellet model [37] recently reported describes only H2 diffusion limitations, even though CO becomes the limiting reactant for usual H2/CO feed ratios on Co and Ru catalysts [1]. This model describes well the marked decrease in hydrocarbon synthesis rate observed as the pellet diameter of Co/ZrO2/SiO2 catalysts increased from 1 to 2 mm [37,42]; any accompanying changes in selectivity were not described. These studies clearly show that transport restrictions markedly influence hydrocarbon synthesis rates and selectivity. Two types of transport effects are apparent from our studies: (1) slow removal of reactive products from pellets and reactors, and (2) delayed arrival of reactants to catalytic sites. As we discuss later, both types of diffusional constraints significantly influence Fischer-Tropsch synthesis rate and selectivity.

Design of Fischer-Tropsch Catalysts

205

We have recently described a reaction-transport model of hydrocarbon synthesis selectivity that accounts for slow removal of a-olefins from catalysts and reactors containing Ru sites [1]. Such a model clearly shows how intraparticle (diffusion) and interparticle (convection) processes affect the rate of primary and secondary reactions during Fischer-Tropsch processes on Ru catalysts. Here we extend this model to describe hydrocarbon synthesis product distributions on Co catalysts. We also develop a model that accounts for the diffusion-limited arrival of reactants to catalytic sites. These two models are subsequently used to explore catalyst properties and reactor designs required to increase selectivity to desired products. III.

EXPERIMENTAL METHODS

A.

Catalyst Synthesis and Characterization

Ru catalysts were prepared by impregnation of TiO2 (P25, Degussa, 60% rutile), SiO2 (Davison, grade 62; Shell spheres, S980A-G), and 7-Al2O3 (Catapal SB, Conoco) with Ru nitrate (Engelhard Corp.). The supports were calcined in air at 873 K for 4 h before impregnation. The impregnated samples were dried at room temperature and then evacuated at 373 K overnight. The unsupported Ru powder was obtained from JohnsonMatthey (Puratronic grade). Cobalt catalysts were prepared similarly using an aqueous Co nitrate impregnating solution (Johnson-Matthey, Puratronic grade). Samples were crushed and sieved to retain desired pellet sizes; 80 to 140 mesh size fractions (0.17 mm average pellet diameter) were used in all catalytic tests unless noted otherwise. Co catalysts were calcined in air between 373 and 773 K for 2 to 4 h before reduction. All catalysts were reduced in H2 at 723 K for 4 h and then passivated with a dilute (1%) oxygen stream. The samples were reduced again at 673 K for 1 to 3 h before chemisorption and catalytic measurements. Ru and Co contents were measured by x-ray fluorescence and atomic absorption. Physical surface area and pore size distribution were determined from N2 physisorption and pore filling measurements at 77 K using the BET and Kelvin methods [45]. Ruthenium dispersion, defined as the fraction of Ru atoms located at the surface of the supported metal crystallites, was determined by titration of preadsorbed oxygen with H2 at 373 K [1]. Cobalt dispersions were obtained by hydrogen chemisorption at 373 K7 assuming a 1:1 H:Co surface stoichiometry [46,47]. Co/TiO2 catalysts were recalcined at 573 K for 0.5 h and rereduced at 523 K in H2 before chemisorption experiments. Such treatments were required to avoid strong metal-support interactions (SMSI) that strongly inhibit CO and H2 chemisorption [48]. Hydrogen chemisorption, x-ray diffraction line broadening, and TEM measurements

Chapter 7

206

gave very similar dispersion values; such values were used to calculate rates as site-time yields or turnover rates. B. Catalytic Measurements Steady-state hydrocarbon synthesis rates and selectivities were measured in an isothermal fixed-bed reactor at 453 to 503 K, 100 to 2100 kPa, and H2/CO ratios between 1 and 10 [1,15]. The reactor effluent was analyzed directly (Q to C15, CO, CO2, N2) and after product collection (Cl6+) by gas chromatography using flame ionization, thermal conductivity, and mass spectrometric detection. The carbon number distribution in C35+ products was measured by high-temperature gas chromatography and gel-permeation chromatography [1,15]. Selectivities are reported on a carbon basis as the percentage of converted CO that appears as a given product. Synthesis rates are reported both as a metal-time yield (moles CO converted/gatom metal • s) and as a site-time yield or turnover rate (moles CO converted/g-atom surface metal • s). Bed residence times are reported as inverse space velocity, defined as feed flow rate per total (not void) reactor volume. IV.

MODELING APPROACHES

A.

Reaction Mechanism

Hydrocarbon synthesis on Co and Ru involves stepwise incorporation of CH2 species into growing chains and the removal of O atoms as water. The overall reaction stoichiometry is CO + 2H2 —^ ^CH 2 -> + H2O

(6)

CO hydrogenation and Cn formation rates were found to obey LangmuirHinshelwood kinetics of the form '

1 + K[CO]

K }

The kinetic constants (k) and the reaction orders (a and b) were obtained by measurements of synthesis rates and selectivity over a wide range of pressure (100 to 2100 kPa) and H2/CO ratios (1 to 10). The resulting rate expressions are reported in Table 1; they are very similar on Co and Ru catalysts, suggesting a mechanistic resemblance in reaction pathways. Such rate expressions are consistent with a catalytic sequence of steps involving

Design of Fischer-Tropsch Catalysts

207

Table 1 CO Hydrogenation and CH 4 Formation Kinetics on Co and Ru Catalysts

_

1 + K\CO]

Catalyst*

Ru

Co

kfi a b

CO

CH4

CO

CH4

1.96 x 10 K 0.60 0.65

1.08 x 10~8 1.0 0.05

7.46 x 10-11 1.0 0.6

1.0 x 10" n 1.5 0.0

^Obtained on SiOrsupportcd Ru and Co catalysts at 473 to 483 K, 100 to 3000 kPa, UJCO = 1 to 10, -fCH 2 ^- + H2O > CH4 + H2O

(24) (25)

These reactions simply account for the number of CO and H2 molecules required to form hydrocarbon chains (expressed as CH2 units) and methane, respectively. At steady state, intrapellet CO and H2 mass balances become

" a'Rco = ° —^ =

() at r = 0,

VDIl2 • V ( ^ ^ J

Pco = Pco(z) at r - /?0

" arRH2 = 0

(26) (27)

(28)

- 7 ^ = 0 at r = 0, P Hi - Plu(z) at r = /?0 (29) or where C r is the molar concentration of the liquid phase and Rco and RHl are total rates of CO and H2 consumption in reactions (24) and (25), respectively. P c o , D c o , Hco and PH^ £>Hi, IIUi are virtual pressures (fugacities), effective diffusivities, and Henry's law constants of CO and H2 within the liquid-filled catalyst pores. The corresponding mass balances for CO and H2 within interpellet voids in a plug-flow reactor are u

^

Ul

CO

- ^ - =

/£>

- ap(RC0)

\

p

fn\

rC0(U)

_

p

- 1 co|o

CX(W

(3U)

Chapter 7

212

where (RCo) and (RH) are total rates of CO and H2 consumption within catalyst pellet at an axial position z in the reactor. Pcoio a n d PH2\O a r e CO and H2 pressures at the reactor inlet. Equations (26) to (31) completely define the CO/H 2 reaction-transport model by describing reactant concentrations within catalyst pellets and bed voids at any reactor position. They can be made dimensionless by defining y - ^

x = ^ Po

re

0 -

UPG/RT _

f7n*

y

4 =

P0

(J>2 = — =

—

y() =

~ Ro

Dco/Hco

where RQ0 is a reference CO hydrogenation rate. Substitution of these dimensionless variables and parameters into Eqs. (26) to (31) leads to V 2 * - *fooS C o = 0 ~ =

0 at i = 0,

(32) x = x(\) at £ = 1

V2y - *§SH2 = 0 d

-l = o at £ = 0,

| - ^ < W .

(33) (34)

y = y(k) at 4 = 1

40)-,,,

(35)

(36)

Equations (32) to (37) form a system of coupled equations with unknowns x and y\ its solution is obtained by the same techniques as those described for the olefin readsorption model. Again, these equations contain a Thiele modulus (4>o) an( 3 a Peclet number (Pe()); their definitions resemble those in the olefin readsorption model. Here the Thiele modulus does not reflect a characteristic time for product removal but one based instead on reactant arrival to catalytic sites. Also, these equations contain an additional key dimensionless quantity, y0; it measures the relative transport rates of H2 and CO within liquid-filled catalyst pores. Accordingly, the value of 70 and the reaction stoichiometry determine local H 2 /CO ratios

Design of Fischer-Tropsch Catalysts

213

and the selectivity of reactions (24) and (25) under diffusion-controlled reactant arrival conditions (2(> > 1). For example, for stoichiometric pellet boundary conditions [H2/CO = 2, as in reaction (24)], 70 > 1 causes the intraparticle gradients in CO concentration to exceed those of H2; this leads to CO depletion toward the particle interior and favors methane formation. At typical hydrocarbon synthesis conditions (200°C, 2100 kPa), 7() is about 1.9 [54,55]. Consequently, methane selectivity increases as pellets become diffusion limited in stoichiometric feeds. The parameter y0 varies slightly with temperature (1.8 to 2.0 between 150 to 250°C) [54,55]. As in the olefin readsorption model, the Thiele modulus for reactant diffusion (g) is given by the product of two parameters: (38)

where \\fco characterizes the diffusivity and reactivity properties of CO within the catalyst particles. The second term in Eq. (38) is identical to the structural parameter \ described in Eq. (22); it accounts for the effect of catalyst structural properties on the seventy of diffusional restrictions. Not surprisingly, structural catalyst properties that restrict the removal of a-olefins from catalyst pellets also limit the rate of arrival of reactants at intrapellet catalytic sites. V.

RESULTS AND DISCUSSION

A.

Metal Crystallite Size and Support Effects on Selectivity

Our site-time yields were measured on catalyst granules smaller than 0.2 mm in diameter to ensure that CO hydrogenation rates were not influenced by diffusion-limited CO or H2 arrival at catalytic sites. Product removal is still slow on such small pellets, but this affects only the selectivity of CO hydrogenation reactions, not the rate. The site-time yields were measured on catalysts with more than 90% of the Co and Ru atoms in the reduced state. Specific CO hydrogenation rates increase linearly with Ru dispersion (Figure 2a). Therefore, site-time yields are very similar (about 0.01 to 0.02 s"1) on all Ru catalysts, suggesting that CO hydrogenation rates are proportional to the number of exposed Ru atoms, regardless of crystallite size or of the chemical identity of the metal oxide support. Cobalt catalysts behave similarly. Figure 2b shows that CO hydrogenation rates are also nearly proportional to cobalt dispersion. Site-time yields are 0.015 to 0.03

Chapter 7

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Design of Fischer-Tropsch Catalysts

215

s ! at 2000 kPa and 473 K on these catalysts. At these conditions, site activity is not influenced strongly by metal-support interactions or by the size of the cobalt crystallites in this dispersion range (500 kPa, 473 K) where C5+ products selectivities are well above 80%. We conclude that the Fischer-Tropsch synthesis is a structure-insensitive reaction [68], one that depends only weakly on Co and Ru dispersion and on the chemical identity of the metal oxide support. B. Bed-Resiclence-Time Effects on Chain Growth Probability and Product Functionality

Bed residence time was changed by varying the space velocity of reactants at constant reactor temperature and pressure. CO conversion increased linearly with increasing bed residence time, suggesting that site-time yields are constant over a wide range of CO conversion (5 to 60%). C$> selectivity

o

Bed Residence Time (s)

Figure 3. Bed-residence-time effects on methane and C5. selectivity on Co/Ti0 2 (catalyst: 11.7 wt % Co, 1.5% Co dispersion, 0.022 s"1 site-time yield at 50% conversion) (473 K, 2000 kPa, H2/CO = 2.1, 9.5 to 72% CO conversion)

216

Chapter 7

increases and CH4 decreases with increasing bed residence time (and CO conversion) on Co/TiO2 catalysts (Figure 3). Previously, we reported similar results on Ru catalysts [lj. Chain growth does not obey Flory kinetics (Figure 4a); the selectivity toward high-molecular-weight hydrocarbons increases as bed residence time increases (Figure 3). At all CO conversion levels (9.5 to 72%), the carbon number-distribution (Flory) plots are nonlinear, suggesting that chain growth probability increases with carbon number. Chain growth probabilities, however, become independent of bed residence time and carbon number for C2o- hydrocarbons. Similar trends were reported on Ru catalysts (Figure 4b) [1,15]; such deviations from Flory kinetics can be described by an enhancement of secondary readsorption reactions driven by an increase in the residence time and intrapellet concentration of reactive a-olefins within bed interstices (controlled by convection) and catalyst pellets (controlled by diffusion) [1]. The results shown in Figure 4 suggest that secondary reactions lead to the growth of small molecules and to their ultimate removal from pellets and reactors as larger unreactive paraffins. Such effects are clearly consistent with the decrease in chain termination probability observed with increasing carbon number and bed residence time on Co (Figure 5a) and Ru (Figure 5b) catalysts. Chain termination probabilities decrease with increasing carbon number, showing that large chains become increasingly difficult to terminate because they remain in contact with catalyst sites for a longer period. The trends are similar on Co and Ru catalysts, suggesting that similar processes are responsible for the observed non-Flory hydrocarbon distributions on the two metals. Termination rates become independent of chain size and of bed residence time for hydrocarbon chains greater than about 20 carbon atoms (Figure 5b), because all a-olefins are consumed. The absence of a-olefins from hydrocarbon products leaving pellets and reactors renders such mixtures unreactive; they do not undergo the secondary readsorption and chain initiation reactions that lead to the curvature of the Flory plots and to the observed effects of bed residence time on selectivity. The olefin content becomes negligible in the same carbon number range where chain growth and total termination probabilities reach constant values (Figure 6). Our bed-residence-time studies also show that readsorption and chain growth are the predominant secondary reactions of reactive a-olefins on both Co and Ru catalysts. The paraffin content increases as bed residence time and carbon number increase on Co (Figure 6a) and Ru (Figure 6b) catalysts. It had previously been proposed that secondary hydrogenation reactions of a-olefins account for such effects [5,12]; this is, however, inconsistent with the concurrent effects of carbon number and bed resi-

Design of Fischer-Tropsch Catalysts 100

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Chapter 7

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Design of Fischer-Tropsch Catalysts i

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Figure 6. Bed-residence-time and carbon number effects on a-olefin to n-paraffin ratio: (a) Co/Ti0 2 (catalyst: 11.7 wt % Co, 1.5% Co dispersion) (473 K, 2000 kPa, H2/CO = 2.1, 9.5 to 72% CO conversion); (b) Ru/TiO2 (catalyst: 1.2 wt % Ru! 48% Ru dispersion) (476 K, 560 kPa, H2/CO - 2.1, 5 to 60% CO conversion).

Chapter 7

220

dence time on chain growth probability. Secondary hydrogenation merely converts an a-olefin to a n-paraffin of equal carbon number; it does not affect chain growth. The proposal that a-olefin hydrogenation occurs readily during FischerTropsch synthesis also contradicts the observed effects of bed residence time on light olefin and paraffin selectivity (Figure 7). Our data show that the increasing paraffin content in products reflects the selective disappearance of light a-olefins into higher-molecular-weight fractions and not into the corresponding paraffin of equal carbon number. For example, the selectivity to 1-butene decreases with increasing bed residence and CO conversion on Co/TiO2 (Figure 7). Secondary reactions contribute increasingly to synthesis products as a-olefin concentration and bed residence time increase and clearly account for this behavior. n-Butane selectivity, however, is independent of bed residence time, suggesting that hydrogenation is not responsible for the disappearance of 1-butene. Methane selectivity actually decreases with increasing bed residence time (Figure 3); therefore, 1-butene is not consumed in secondary hydrogenolysis reactions. We have previously reported similar trends for Ru catalysts [1,15]. Our proposal that a-olefin readsorption and chain initiation are the predominant secondary reactions is consistent with the marked decrease

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2-Butenes

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4

6

8

10

12

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Figure 7. Bed-residence-time effects on C4 olefin and paraffin carbon selectivity on Co/TiO2 (catalyst: 11.7 wt % Co, 1.5% Co dispersion) (473 K, 2000 kPa, H2/CO - 2.1, 9.5 to 72% CO conversion).

Design of Fischer-Tropsch Catalysts

221

in chain termination to a-olefins observed as carbon number increases (Figures 8 and 9). Ultimately, chain termination to olefins is totally reversed by the readsorption of such olefins until none are found among reaction products. In contrast, net termination to paraffins, which would include any paraffins formed in secondary olefin hydrogenation reactions, depends only weakly on carbon number and bed residence time. Such data show clearly that n-paraffins are formed predominantly in primary chain termination steps and not in secondary hydrogenation or hydrogenolysis reactions. Therefore, we conclude that a-olefins and paraffins can be formed after one surface sojourn by termination of growing surface chains. They are primary Fischer-Tropsch synthesis products. Additionally, a-olefins readsorb and initiate chains in a secondary reaction step; they reenter the primary chain growth process and appear ultimately as higher-molecularweight hydrocarbons.

C. Carbon Number Effects on Chain Growth Probability and Product Functionality In the preceding section we showed that hydrocarbon synthesis leads to non-Flory product distributions on Ru and Co catalysts (Figure 4). The chain termination probability decreases with increasing chain length; it reaches constant values for molecules larger than about 20 carbon atoms (Figure 5). Here we show that the selective reversal of the step leading to chain termination as a-olefins becomes more important as chain length increases and accounts for the observed effects of chain size on selectivity. The total chain termination probability can be separated into individual contributions from each termination step [Eq. (4)]. The termination probability for a-olefin formation decreases markedly with increasing carbon number on Co (Figure 8) and Ru (Figure 9) catalysts, even at very short bed residence times (> °

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Figure 21. Effect of diffusion-enhanced hydroformylation of a-olefins (simulations: experimental/model parameters as in Figure 15): (a) alcohol selectivity versus Thiele modulus (A: intrapellet reaction, (Vpr = 0.5; B: interpellet reaction, = 1); (b) carbon selectivity versus carbon number (intrapellet reaction, P, = 0.5). Such carbon number dependence reflects the relative reactivity of carboncarbon bonds within a molecule in cracking reactions [76,77]; in this simple model, cracking occurs with zero probability at the three C—C bonds closest to the end of the molecule and with equal probability at all other bonds. These reactivity trends are qualitatively similar to those reported

243

Design of Fischer-Tropsch Catalysts

for carbenium-ion cracking reactions on acid catalysts [42,76,77]. As done previously, we define this probability as a ratio of cracking to readsorption rates (|3°/pr). We also assume that both products of a cracking event are unreactive in subsequent cracking, readsorption, or chain initiation reactions. Diffusion-enhanced intrapellet cracking of a-olefins leads to much higher yields of products in the range C4 to C9 (i.e., it increases from 25.4% to 79.8%) at the expense of C10+ hydrocarbons (Figure 22). The combined effects of a-olefin interception and random reversal of chain growth pathways by cracking lead to C104 product distributions that obey the Flory equation [83]. As in other olefin secondary reactions, cracking sites are most effective when placed within transport-limited pellets where high olefin fugacities provide a strong driving force for chemical reactions. Such a strong kinetic driving force is needed to catalyze olefin cracking at FischerTropsch conditions because cracking reactions usually require higher temperatures [76,77]. Many other secondary reactions of olefins can also influence FischerTropsch synthesis selectivity. For example, olefins can oligomerize and polymerize within bifunctional catalyst pellets; they can also incorporate into chain growth sites, not just initiate them, at higher olefin concentrations and lower temperatures. Finally, a-olefins can be converted into less

-

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4

6

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244

Chapter 7

reactive internal or branched isomers and thus be kept from reentering chain growth pathways steps. These bifunctional pellets share in common an enhancement in secondary reaction rates on a separate catalyst function by the restricted removal of reactive olefins from catalyst pellets. The presence of secondary reaction sites within transport-limited pellets significantly extends our ability to catalyze these reactions at mild conditions required for selective Fischer-Tropsch synthesis. Ultimately, transportlimited bifunctional pellets could eliminate the need for separate processes and reactor for the secondary upgrading of Fischer-Tropsch products [42].

C. Changes in Intrapellet Liquid Composition and in Spatial Distribution of Chain Growth Sites In previous sections we described how transport-limited arrival of reactants and removal of reactive olefin products from catalyst pellets influences Fischer-Tropsch selectivity. Specifically, we described Fischer-Tropsch selectivity in terms of a structural parameter (x), contained within Thiele moduli required to describe both olefin readsorption [Eq. (22)] and reactant transport [Eq. (38)]. In the preceding two sections we described how transport-limited removal of a-olefins from catalyst pellets increases the rate of secondary reactions. Here we show how such transport limitations can be controlled by (1) varying site density and pellet size, (2) changing the composition of the liquid within catalyst pellets, and (3) locating CO hydrogenation sites near the outer surface of pellets (eggshell catalysts). In the discussion that follows we refer to the experimental data and simulation results of Figure 18a, where we show the effects of the structural parameter (x) on C5- selectivity. C$~ selectivity can be controlled by varying the density of sites within catalyst pellets, which determines the required reactant transport requirements, and by changing the pellet size, which controls the path length that molecules must travel to reach catalytic sites. Site density and pellet size change x values and move catalysts along the curve shown in Figure 18a for a catalyst with certain intrinsic readsorption and CO hydrogenation kinetics (|3r). However, site density and pellet size may not be entirely within the control of the catalyst designer. Low site densities may be required to lower x values in catalysts limited by reactant transport, but reactor productivity will also decrease. Smaller pellets can also be used to remove such transport restrictions, but they lead to convective flow restrictions and to unacceptable pressure drops in packed-bed reactors. Thus we must suggest alternative catalyst designs and operating strategies to achieve or to complement changes in x- One strategy is to decrease the

Design of Fischer-Tropsch Catalysts

245

molecular weight of the intrapellet liquid product; another places catalytic sites in a nonuniform manner within catalyst pellets. The diffusivity of CO, H2, and hydrocarbons through catalyst pores increases as the molecular weight of the contained liquid phase decreases or as the liquid is replaced by a gaseous or supercritical phase. Then the parameters \\in and I(JCO that precede \ in Eqs. (22) and (38) decrease. For a given catalyst structure (x), transport restrictions decrease and the reactions become increasingly controlled by kinetics. The net effect is that C5~ versus x curves, such as those in Figure 18a, shift toward lower values of x- As a result, larger pellets and higher site densities can be achieved while maintaining a given level of transport restriction. Thus we can design catalytic materials that avoid CO transport limitations even at the high productivity and large pellet sizes required in fixed-bed reactors. The removal of heavy products from catalyst pores can occur in several ways. The average molecular weight of the product can be lowered by continuous recycle of light hydrocarbons, which shift the vapor-liquid equilibrium composition toward lighter components; also, the liquid phase can be totally removed by operating reactors at temperatures above the boiling point of the liquid, but such temperatures usually lead to the synthesis of very light hydrocarbons. More interestingly, it appears that operation of Fischer-Tropsch synthesis reactors in the presence of supercritical light paraffins (e.g., n-hexane) also decreases the average molecular weight of intrapellet liquids [78,79]. Such studies report an apparent increase in the rate of CO hydrogenation and in the olefin content of products at supercritical conditions. These authors attributed such effects to the removal of waxy liquids from catalyst pores by the supercritical solvent, a process that decreases the rate of secondary hydrogenation of retained a-olefins. Our models would suggest that recycle of light paraffins under supercritical conditions also decreases the intrapellet liquid molecular weight simply by vapor-liquid equilibrium effects, rather than by the supercritical nature of the reactor operation. The shift in vapor-liquid equilibrium point leads to a lighter, perhaps gaseous, product within pellets, to capillary condensation of the recycled light molecules, and to the removal of CO transport limitations. As a result, CO hydrogenation rates and C5 selectivity increase and the products become increasingly olefinic, as found experimentally [78,79]. Our models are in qualitative agreement with the effect of recycle, whether supercritical or not, on Fischer-Tropsch selectivity. A more quantitative analysis of such effects requires more detailed information on the structural and reactive properties of the catalysts used in such studies [78,79] and on the rates of CO, H2, and hydrocarbon diffusion in supercritical hydrocarbons. We propose that such recycle conditions shift the

246

Chapter 7

maximum value of C5 selectivity in Figure 18a toward higher values of x without a significant change in the shape of the curve. Therefore, the net effect of supercritical operation on Fischcr-Tropsch selectivity depends on whether catalysts reside on the olefin readsorption or reactant transport side of the C 5 , selectivity curve (Figure 18a) at reaction conditions. The pellet size term (R()) in the defining equation for x [Eq. (22)] reflects the diffusion pathlength required to reach catalytic sites. Pellet size and diffusion path lengths are identical only when catalytic sites are distributed uniformly within pellets. Pellet size and diffusion path length can be decoupled by placing catalytic sites within specific regions within a pellet. For example, eggshell catalysts [80], where catalytic sites are placed selectively near the outer pellet surface, provide short diffusion paths to reactive sites, irrespective of pellet size. The beneficial use of eggshell catalysts in Fischer-Tropsch catalysis has been reported [26-31,81]; the general concepts have been widely discussed and broadly applied also in automotive exhaust and selective hydrogenation catalysis [80,82]. Eggshell catalysts allow the design of catalyst pellets with values of \ that become independent of pellet size. Thus optimum C5+ selectivities given by a specific value of x (such as in Figure 18a) can be obtained by Table 2 Effect of the Eggshell Thickness on Hydrocarbon Synthesis Selectivity Co/SiO2a

Catalyst Co site density (g-atom Co surface/g catalyst) Pellet size (mm) Impregnated pellet region (average eggshell thickness) (mm) Co dispersion (%) Site-time yield (s ') CH4 selectivity (%) C^-selectivity (%) 1-Butene/n-butane ratio 1-Decene/^-decane ratio

Large pellet

Crushed large pellet

Crushed eggshell pellet

Eggshell pellet

0.207

0.207

0.192

0.192

2.2 2.2

0/17 0.17

0.17 0.17

2.2 0.23

6.3 0.014 12.1 81.5 0.11 0.011

6.3 0.026 5.2 89.6 1.7 0.031

5.5 0.039 4.7 90.5 1.8 0.031

5.5 0.029 7.7 88.0 0.32 —

Source: Ref. 81. Co/SiO 2 , 12.7 to 13.1 wt % Co, 5.5 to 6.3% Co dispersion. Conditions: 473 K, 2000 kPa, H 2 /CO = 2.1, 56 to 65% CO conversion.

a

Design of Fischer-Tropsch Catalysts

247

controlling the thickness of the impregnated area. Our experimental results are consistent with this model. Evenly impregnated catalysts show low sitetime yields and C5« selectivity because of reactant transport limitations; crushing the pellets to much smaller size increases the site-time yield and the C5+ selectivity (Table 2) [81]. Similar effects are observed when Co sites are placed within 0.2 mm of the outer pellet surface; however, crushing eggshell catalysts increases hydrocarbon synthesis rates and C5 selectivity still further, suggesting that such catalysts remain partially limited by the rate of diffusion of CO to catalytic sites (Table 2). The olefin content in products decreases as we remove transport limitations, whether such changes occur as the result of partial impregnation or of decreased pellet size (Table 2) [81]. These eggshell catalysts present challenging tasks by requiring the synthesis of thin uniform catalytic layers. Moreover, they require that we accommodate all metal surface atoms within a very small fraction of the available pellet volume and surface area; thus these catalysts must maintain high metal dispersions at very high local metal loadings. We conclude that structural catalyst changes lead to sizable changes in C5 selectivity. As we have shown, the rigorous modeling of the coupling between reaction and transport provides key insights in the design of improved catalysts for Fischer-Tropsch synthesis. VIII.

CONCLUDING REMARKS

We have developed predictive models of Fischer-Tropsch synthesis selectivity on Co and Ru catalysts. Model simulations agree well with experimental data and accurately describe changes in chain growth probability and olefin content with bed residence time and product molecular size. In particular, they account for an intrinsic coupling between reaction and transport that is difficult to avoid even in small three-phase packed-bed reactors. This coupling enhances the secondary readsorption of a-olefins and leads to non-Flory distributions of paraffinic products; in some cases it also restricts the rate of CO arrival at catalytic sites and lowers reaction rates and C5~ selectivity. Our models combine diffusive and convective transport processes with a kinetic model of primary chain growth and termination. We assume that chain growth and olefin readsorption kinetics do not depend on metal crystallite size, the identity of the support, or the size of the growing chain, consistent with experimental results on these catalysts. The olefin readsorption model describes the diffusive and convective removal of reactive olefins from intrapellet and interpellet voids. Transport-enhanced readsorption leads to an increase in chain growth probability and in paraffin

Chapter 7

248

content with increasing pellet and bed residence time. It also accounts for the increase in C5 ( selectivity as intrapellet olefin concentration gradients become more severe in pellets with larger diameter or higher site density. Deviations from conventional (Flory) kinetics and the increasing paraffin content of higher hydrocarbons are described accurately by the effect of transport on the residence time of reactive olefins, without the requirement for several types of chain growth sites. The CO transport model describes intrapellet and reactor reactant concentration gradients in Fischer-Tropsch synthesis. In general, reactant transport restrictions lower reaction rates and C5 - selectivity by lowering the local concentration of required reactants near active sites. Site density and pellet size increases, which favor olefin readsorption and C s - products, can also lead to CO transport limitations and to lower C5 ( selectivity because the same structural parameters that restrict the removal of reactive olefins ultimately also restrict the arrival of required reactants at catalytic sites. As a result, intermediate levels of transport restriction and of pellet size and site density lead to maximum values of C5+ selectivity. A dimensional analysis of these coupled reaction-transport models identifies critical structural parameters in catalyst pellets and reactor strategies that maximize G^ selectivity. Rigorous simulations using the detailed models can be used in the design of catalytic pellets with tailored selectivity. Some examples illustrated here — diffusion-enhanced bifunctional pellets, eggshell catalysts, and recycle reactors—show the use of these models to suggest strategies for the design of Fischer-Tropsch synthesis pellets and reactors. ACKNOWLEDGMENTS

We thank Rocco A. Fiato, Chang J. Kim, and Rostam J. Madon for many discussions about the concepts described in this chapter and for their many independent contributions to our understanding of Fischer-Tropsch chemistry. We also thank G. D. Dupre and W. W. Schultz, who developed the gas chromatography and gel permeation chromatography methods used for the analysis of high-molecular-weight Fischer-Tropsch products. Finally, we acknowledge the expert technical assistance of Hilda Vroman and Joseph E. Baumgartner and Bruce DeRites in the synthesis and catalytic evaluation of the cobalt catalysts reported here. NOTATION a, b

reaction orders for CO hydrogenation and CH4 formation reactions on Co and Ru catalysts

Design of Fischer-Tropsch Catalysts ap av Cn C* CT Dco DH^ Dn D{) En Fn H Hco HHl ka kc kh kt kp kr ks k{) K n N() Pco ^Y:o|o Pe 0 PH^ P Hi l 0 Pn Pm) Po Qn

Qn{) r R Rco Rco RH^ (Rco)

249

surface area per unit reactor volume surface area per unit volume of catalyst particle olefin and paraffin concentration surface concentration of growing hydrocarbon chains molar concentration of liquid phase effective diffusivity of C O within catalyst particle effective diffusivity of H 2 within catalyst particle effective diffusivity of a-olefins and ^-paraffins reference diffusivity defined by E q . (39) dimensionless effective diffusivity of a-olefins and n-paraffins fraction of carbon atoms contained within chains with rc-carbons reactor length C O Henry's constant H 2 Henry's constant hydroformylation rate constant cracking rate constant hydrogenation rate constant C O hydrogenation or m e t h a n e formation rate constant propagation rate constant readsorption rate constant secondary a-olefin hydrogenation rate constant hydrogen abstraction rate constant adsorption constant carbon n u m b e r Avogadro's number C O partial pressure C O partial pressure at reactor's inlet Peclet n u m b e r H 2 partial pressure H 2 partial pressure at reactor's inlet /i-olefin partial pressure within liquid phase n-olefin partial pressure at reactor's inlet total inlet pressure /7-paraffin partial pressure within liquid phase

/7-paraffin partial pressure at reactor's inlet catalyst pellet radial dimension universal gas constant local rate of CO consumption reference rate of CO consumption local rate of H 2 consumption particle-averaged rate of CO consumption

Chapter 7

250 /?/ rp rpn rtn R[} Sco SH2 Sn 50 T U x Xn x0 y y0 Yn Yn0 z Zn Z n0

particle-averaged rate of H 2 consumption C O hydrogenation or m e t h a n e formation rate m e a n pore radius propagation rate termination rate catalyst pellet radius dimensionless rate of C O consumption dimensionless rate of H 2 consumption surface concentration of growing hydrocarbon chains concentration of catalyst sites absolute temperature interstitial gas velocity dimensionless CO concentration dimensionless concentration of growing n-chains dimensionless inlet CO concentration dimensionless H 2 concentration dimensionless inlet H 2 concentration dimensionless a-olefin concentration dimensionless a-olefin concentration at reactor's inlet axial reactor distance dimensionless ^-paraffin concentration dimensionless n-paraffin concentration at reactor's inlet

Greek Symbols an chain growth probability Pfl probability of hydroformylation of a-olefins pc probability of cracking of a-oleflns P^ reference cracking probability (3// „ probability of chain termination to n-paraffins Pr „ probability of readsorption of a-olefins P, probability of secondary hydrogenation of a-olefins $Tn total chain termination probability Po rt probability of chain termination t o a-olefins 7 () H 2 / C O effective transport ratio 0 catalyst site density X dimensionless reactor position £ dimensionless pellet position pp catalyst pellet density §n mole fraction of n-hydrocarbons $ pellet porosity $^ Thiele modulus of ^-hydrocarbons

Design of Fischer-Tropsch Catalysts

4>o X i|iCO \\fn

reference Thiele modulus structural parameter defined in Eqs. (22) and (38) diffusivity-reactivity parameter defined in E q . (38) diffusivity-reactivity parameter defined in Eq. (22)

REFERENCES 1.

2. 3. 4. 5. 6. 7. 8.

9.

10.

11.

251

Iglesia, E., Reyes, S. C , and Madon, R. J. (1991). Transport-enhanced a-olefin readsorption pathways in Ru-catalyzed hydrocarbon synthesis, / . Catal., 129, 238. Biloen, P., Helle, J. N., and Sachtler, W. M. H. (1979). Incorporation of surface carbon into hydrocarbons during Fischer-Tropsch synthesis: mechanistic implications, J. Catal., 58, 95. Brady, R. C , and Pettit, R. (1980). Reactions of diazomethane on transition-metal surfaces and their relationship to the mechanism of the Fischer-Tropsch reaction, J. Am. Chem. Soc, 102, 6181. Brady, R. C , and Pettit, R. (1981). On the mechanism of the FischerTropsch reaction: the chain propagation step, / . Am. Chem. Soc, 103, 1287. Iglesia, E., and Madon, R. J. (1988). Reducing methane production and increasing liquid yields in Fischer-Tropsch reactions, U.S. Patent 4,754,092 (assigned to Exxon Research and Engineering Co.). Herrington, E. F. G. (1946). The Fischer-Tropsch synthesis considered as a polymerization reaction, Chem. Ind., 65, 346. Pichler, H., Schulz, H., and Elstner, M. (1967). Gesetzmabigkeiten bei der Synthese von Kohlenwasserstoffen aus Kohlenoxid und Wasserstoff, Brennstoff. Chem., 48, 78. Golovina, O. A., Sakharov, M. M., Roginskii, S. Z., and Dokukina, E. S. (1954). Zum Reaktionsmechanismus der Fischer-TropschSynthese. VII. Uber den Aufbau der Kohlenwasserstoffe, Brennstoff. Chem., 35, 161. Golovina, O. A., Sakharov, M. M., Roginskii, S. Z., and Dokukina, E. S. (1959). Isotopic data on the role of two-dimensional chains in the synthesis of hydrocarbons from carbon monoxide and hydrogen, Russ. J. Phys. Chem., 33, 471. Roginskii, S. Z. (1965). Molecular mechanism of some catalytical reactions as revealed by means of isotopic kinetical effects and experiments with tracer molecules, Proc. 3rd International Congress Catalysis, Amsterdam, 1964, Wiley, New York, p. 939. Hall, W. K., Kokes, R. J., and Emmett, P. H. (1960). Mechanism studies of the Fischer-Tropsch synthesis: the incorporation of radioactive ethylene, propionaldehyde and propanol, J. Am. Chem. Soc, 82, 1027.

252

Chapter 7

12. Schulz, H., Rao, B. R., and Elstner, M. (1970). 14C-Studien zum Reaktionsmechanismus der Fischer-Tropsch-Synthese, Erdoel Kohle, 23, 651. 13. Novak, S., Madon, R. J., and Suhl, H. (1982). Secondary effects on the Fischer-Tropsch synthesis, J. Catal., 11, 141. 14. Flory, P. J. (1936). Molecular size distribution in linear condensation polymers, /. Am. Chem. Soc, 58, 1877. Friedel, R. A., and Anderson, R. B. (1950). Composition of synthetic liquid fuels. I. Product distribution and analysis of C5-Q paraffin isomers from cobalt catalysts, J. Am. Chem. Soc, 72, 1212. Friedel, R. A., and Anderson, R. B. (1950). Composition of synthetic liquid fuels. I. Product distribution and analysis of C5-Q paraffin isomers from cobalt catalysts, J. Am. Chem. Soc, 72, 2307. 15. Madon, R. J., Reyes, S. C , and Iglesia, E. (1991). Primary and secondary reaction pathways in ruthenium-catalyzed hydrocarbon synthesis, /. Phys. Chem., 95, 7795. 16. Schulz, H. (1984). Selectivity and mechanism of the Fischer-Tropsch CO-hydrogenation, Izv. Khim., 17, 3. 17. Schulz, H., Beck, K., and Erich, E. (1988). The Fischer-Tropsch CO-hydrogenation, a non-trivial surface polymerization selectivity of chain branching, Proc. 9th International Congress on Catalysis, Calgary, 1988, M. J. Phillips and M. Ternan, eds., Vol. 2, Chemistry Institute of Canada, Ottawa, pp. 829-836. 18. Vanhove, D. (1988). Fischer-Tropsch synthesis in a gas-liquid solid medium: selectivities induced by phase equilibria, Proc. International Meeting of the Societe Fr. Chimie, Division Chimie Physique, pp. 147. Vanhove, D., Zhuyong, Z., Makambo, L., and Blanchard M. (1984). Hydrocarbon selectivity in Fischer-Tropsch synthesis in relation to textural properties of supported cobalt catalysts, Appl. Catal., 9, 327. 19. Tau, L. M., Dabbagh, H. A., and Davis, B. H. (1990). FischerTropsch synthesis: 14C tracer study of alkene incorporation, Energy Fuels, 4, 94. Tau, L. M., Dabbagh, H. A., Bao, S., and Davis, B. H. (1990). Fischer-Tropsch synthesis: evidence for two chain growth mechanisms, Catal. Lett., 1, 127. 20. Madon, R. J., and Taylor, W. R. (1981). Fischer-Tropsch synthesis on a precipitated iron catalyst, /. Catal., 69, 32. 21. Ekerdt, J. G., and Bell, A. T. (1979). Synthesis of hydrocarbons from CO and H2 over silica-supported Ru: reaction rate measurements and infrared spectra of adsorbed species, J. Catal., 58, 170. Ekerdt, J. G., and Bell, A. T. (1980). Evidence for intermediates involved in Fischer-Tropsch synthesis over Ru, /. Catal., 62, 19. 22. Huff, G. A., Jr., and Satterfield, C. N. (1984). Evidence for two

Design of Fischer-Tropsch Catalysts

23. 24. 25. 26.

27.

28. 29.

30.

31. 32.

33.

253

chain growth probabilities on iron catalysts in the Fischer-Tropsch synthesis, J. CataL, 85, 37. Donnelly, T. J., and Satterfield, C. N. (1989). Product distributions of the Fischer-Tropsch synthesis on precipitated iron catalysts, Appl. CataL, 52, 93. Konig, L., and Gaube, J. (1983). Fischer-Tropsch-Synthese. Neuere Untersuchungen und Entwicklungen, /. Chem. Ing. Tech., 55, 14. Reid, R. C , Prausnitz, J. M., and Sherwood, T. K. (1977). The Properties of Gases and Liquids, 3rd ed., McGraw-Hill, New York. deGennes, P. G. (1971). Reptation of a polymer chain in the presence of fixed obstacles, J. Chem. Phys., 55, 572. Everson, R. C , Woodburn, E. T., and Kirk, A. R. M. (1978). Fischer-Tropsch reaction studies with supported ruthenium catalysts. I. Product distributions at moderate pressures and catalyst deactivation,/. CataL, 53, 186. van Erp, W. A., Nanne, J. M., and Post, M. F. M. (1987). Process for preparation of catalyst, U.S. Patent 4,637,993; (1986). Catalyst preparation, Eur. Patent Appl. 178,008 (assigned to Shell Research and Development). Post, M. F. M., and Sie, S. T. (1986). Process for the preparation of hydrocarbons, Eur. Patent Appl. 174,696 (assigned to Shell Research and Development). Post, M. F. M., and Sie, S. T. (1986). Process for the preparation of hydrocarbons, Eur. U.K. Patent 2,161,177; (1986). Process for the preparation of hydrocarbons, Eur. Patent Appl. 167,215 (assigned to Shell Research and Development). Behrmann, W. C , Mauldin, C. H., Arcuri, K. B., and Herskowitz, M. (1988). Surface-supported particulate metal compound catalysts, their preparation and their use in hydrocarbon synthesis reactions, Eur. Patent Appl. 266,898 (assigned to Exxon Research and Engineering Co.). Mauldin, C. H., and Riley, K. L. (1990). Process for the preparation of surface impregnated dispersed cobalt metal catalysts, U.S. Patent 4,977,126 (assigned to Exxon Research and Engineering Co.). Fischer, F., and Tropsch, H. (1926). Die Erdolsynthese bei gewohnlichem Druck aus den Vergasungsprodukten der Kohle, Brennstoff. Chem., 7, 97. Fischer, F., and Koch, H. (1932). Neues uber die Eignung von Kobaltkatalysatoren fur die Benzinsynthese, Brennstoff. Chem., 13, 61. Fischer, F. (1935). Die Synthese der Treibstoffe (Kogasin) und Schmierole aus Kohlenoxid und Wasserstoff bei gewohnlichem Druck, Brennstoff. Chem., 16, 6.

254

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34. Anderson, R. B., Seligman, B., Shultz, J. F., Kelly, R., and Elliott, M. A. (1952), Fischer-Tropsch synthesis: some important variables of the synthesis on iron catalysts, Ind. Eng. Chem., 44, 391. 35. Anderson, R. B. (1956). Kinetics and reaction mechanism of the Fischer-Tropsch synthesis, in Catalysis, P. H. Emmett, ed., Vol. IV, pp. Reinhold, New York, 257-371. 36. Madon, R. J., Bucker, E. R., and Taylor, W. F. (1977). Development of improved Fischer-Tropsch catalysts for production of liquid fuels, ERDA (DOE) Rep. E(46-l)-8008. 37. Post, M. F. M., van't Hoog, A. C , Minderhoud, J. K., and Sie, S. T. (1989). Diffusion limitations on Fischer-Tropsch catalysts, AIChE / . , 3 5 , 1107. 38. Dixit, R. S. (1980). Experimental and theoretical investigations of the Fischer-Tropsch synthesis reactions on supported ruthenium catalysts, Ph.D. dissertation, Illinois Institute of Technology. Dixit, R. S., and Tavlarides, L. L. (1983). Kinetics of the Fischer-Tropsch synthesis, Ind. Eng. Chem. Process Design Develop., 22, 1. 39. Dixit, R. S., and Tavlarides, L. L. (1982). Integral method of analysis of Fischer-Tropsch synthesis reactions in a catalyst pellet, Chem. Eng. ScL7 37,539. 40. Bub, G., and Baerns, M. (1980). Prediction of the performance of catalytic fixed bed reactors for Fischer-Tropsch synthesis, Chem. Eng. Sci., 35, 348. 41. Zimmerman, W. H., Rossin, J. A,, and Bukur, D. B. (1989). Effect of particle size on the activity of a fused iron Fischer-Tropsch catalyst, Ind. Eng. Chem. Res., 28, 406. 42. Sie, S. T., Senden, M. M. G., and Van Wechem, H. M. H. (1991). Conversion of natural gas to transportation fuels via the Shell middle distillate synthesis process (SMDS), CataL Today, 8, 371. 43. Stern, D., Bell, A. T., and Heinemann, H. (1985). A theoretical model for the performance of bubble-column reactors used for Fischer-Tropsch synthesis, Chem. Eng. Sci., 40, 1655. 44. Stern, D., Bell, A. T., and Heinemann, H. (1985). Experimental and theoretical studies of Fischer-Tropsch synthesis over ruthenium in a bubble-column reactor, Chem. Eng. Sci., 40, 1917. 45. Smith, J. M. (1981). Chemical Engineering Kinetics, 3rd ed., McGraw-Hill, New York. 46. Zowtiak, J. M., Weatherbee, G. D., and Bartholomew, C. H. (1983). Activated adsorption of H2 on cobalt and effects of support thereon, J. CataL, 82, 230; (1983). The kinetics of H2 adsorption from cobalt and the effects of support thereon, J. CataL, 83, 107.

Design of Fischer-Tropsch Catalysts

255

47. Beuther, H., Kibby, C. L., Kobylinski, T. P., and Pannell, R. B. (1986). Conversion of synthesis gas to diesel fuel and catalyst therefor, U.S. Patent 4,613,624 (assigned to Gulf). 48. Tauster, S. J., and Fung, S. C. (1978). Strong metal-support interactions: occurrence among the binary oxides of groups IIA-VB, J. Catal., 55, 29. 49. Mims, C. A., Krajewski, J. J., Rose, K. D., and Melchior, M. T. (1990). Residence times and coverage by surface intermediates during the Fischer-Tropsch synthesis, Catal. Lett., 7, 119. 50. Carey, G. G., and Finlayson, B. A. (1975). Orthogonal collocation on finite elements, Chem. Eng. Sci., 30, 587. 51. Hindmarsh, A. C , and Byrne, G. D. (1985). EPISODE: an experimental package for the integration of systems of ordinary differential equations, Report UCID-30112, Lawrence Livermore Laboratory. 52. Froment, G. F., and Bischoff, K. B. (1979). Chemical Reactor Analysis and Design, Wiley, New York. 53. Reyes, S. C , and Iglesia, E. (1991). Effective diffusivities in catalyst pellets: new model porous structures and transport simulation techniques, J. Catal, 129, 457. 54. Matthews, M. A., Rodden, J. B., and Akgerman, A. (1987). Hightemperature diffusion of hydrogen, carbon monoxide and carbon dioxide in liquid n-heptane, n-dodecane, and /i-hexadecane, J. Chem. Eng. Data, 32, 319. 55. Albal, R. S., Shah, Y. T., Carr, N. L., and Bell, A. T. (1984). Mass transfer coefficients and solubilities for hydrogen and carbon monoxide under Fischer-Tropsch conditions, Chem. Eng. Sci., 39, 905. 56. Ho, S. W., Houalla, M., and Hercules, D. M. (1990). Effect of particle size on CO hydrogenation activity of silica supported cobalt catalysts, /. Phys. Chem., 94, 6396. 57. Bartholomew, C. H., and Reuel, R. C. (1985). Cobalt-support interactions: their effects on adsorption and CO hydrogenation activity and selectivity properties, Ind. Eng. Chem. Prod. Res. Develop., 24, 56; (1984). Effects of support and dispersion on the CO hydrogenation activity/selectivity properties of cobalt, J. CataL, 85, 78. 58. Johnson, B. G., Bartholomew, C. H., and Goodman, D. W. (1991). The role of surface structure and dispersion in CO hydrogenation on cobalt, J. Catal., 128, 231. 59. Dalla Betta, R. A., Piken, A. G., and Shelef, M. (1974). Heterogeneous methanation: initial rate of CO hydrogenation on supported ruthenium and nickel, J. Catal., 35, 54. 60. King, D. L. (1978). A Fischer-Tropsch study of supported ruthenium catalysts, /. CataL, 51, 386.

256

61. 62. 63. 64. 65.

66. 67. 68. 69. 70. 71. 72. 73. 74. 75.

Chapter 7

Fu, L., and Bartholomew, C. H. (1985). Structure sensitivity and its effects on product distribution in CO hydrogenation on cobalt/alumina, 7. CataL, 92, 376. Morris, S. R., Moyes, R. B., Wells, P. B., and Whyman, R. (1985). Support effects in the ruthenium-catalyzed hydrogenation of carbon monoxide: ethene and propene addition, /. CataL, 96, 23. Everson, R. C , and Thompson, D. T. (1981). Liquid fuels from coal: developments in the use of ruthenium catalysts for the FischerTropsch reaction, Platinum Met. Rev,, 25, 50. Kellner, C. S., and Bell, A. T. (1982). Effects of dispersion on the activity and selectivity of alumina-supported ruthenium catalysts for carbon monoxide hydrogenation, J. CataL, 75, 251. Morris, S. R., Moyes, R. B., Wells, P. B., and Whyman, R. (1982). Support effects in the ruthenium-catalyzed hydrogenation of carbon monoxide, in Metal-Support and Metal-Additive Effects in Catalysis, B. Imelik et al., eds., Elsevier, Amsterdam. Kikuchi, E., Matsumoto, M., Takahashi, T., Machino, A., and Morita, Y. (1984). Fischer-Tropsch synthesis over titania-supported ruthenium catalysts, Appl. CataL, 10, 251. Stoop, R, Verbiest, A. M. G., and Van der Wiele, K. (1986). The influence of the support on the catalytic properties of Ru catalysts in the CO hydrogenation, Appl. CataL, 25, 51. Boudart, M., and Djega-Mariadassou, G. (1984). Kinetics of Heterogeneous Catalytic Reactions, Princeton University Press, Princeton, NJ. Schulz, H., and Achtsnit, H. D. (1977). Olefin reactions during Fischer-Tropsch synthesis reactions, Rev. Port. Quim., 19, 317. Kobori, Y., Yamasaki, H., Naito, S., Onishi, T., and Tamaru, K. (1982). Mechanistic study of carbon monoxide hydrogenation over ruthenium catalysts, /. Chem. Soc. Faraday Trans. I, 78, 1473. Jordan, D. S., and Bell, A. T. (1986). Influence of ethylene on the hydrogenation of CO over ruthenium, J. Phys. Chem., 90, 4797. Jordan, D. S., and Bell, A. T. (1987). The influence of propylene on CO hydrogenation over silica-supported ruthenium, J. CataL, 107, 338. Jordan, D. S., and Bell, A. T. (1987). The influence of butene on CO hydrogenation over ruthenium, /. CataL, 108, 63. Pichler, H. (1952). Twenty-five years of synthesis of gasoline by catalytic conversion of carbon monoxide and hydrogen, Adv. CataL, 4, 271. Lafyatis, D. S., and Foley, H. C. (1990). Molecular modelling of the shape selectivity for the Fischer-Tropsch reaction using a tri-functional catalyst, Chem. Eng. Sci., 45, 2567.

Design of Fischer-Tropsch Catalysts

76. 77. 78. 79. 80. 81.

82. 83.

257

Coonradt, H. L., and Garwood, W. E. (1964). Mechanism of hydrocracking, Ind. Eng. Chem. Process Design Develop., 3, 38. Weitkamp, J. (1975). The influence of chain length in hydrocracking and hydroisomerization of n-alkanes, ACS Symp. Ser., 20, 1. Yokota, K., Hanakata, Y., and Fujimoto, K. (1990). Supercritical phase Fischer-Tropsch synthesis, Chem. Eng. Sci., 45, 2743. Yokota, K., and Fujimoto, K. (1989). Supercritical phase FischerTropsch synthesis reaction, Fuel, 68, 255. Corbett, W. E., Jr., and Luss, D. (1974). The influence of nonuniform catalytic activity on the performance of a single spherical pellet, Chem. Eng. Sci., 29, 1473. Iglesia, E., Vroman, H., Soled, S. L., Baumgartner, J. E., and Fiato, R. A. (1991). Selective catalysts and their preparation for catalytic hydrocarbon synthesis, U.S. Pat. 5,036,032 (assigned to Exxon Research and Engineering Co.). Maatman, R. W., and Prater, C. D. (1957). Adsorption and exclusion in impregnation of porous catalysts, Ind. Eng. Chem., 49, 253. Iglesia, E., Reyes, S. C , Madon, R. J., and Soled, S. L. (1993). Selectivity control and catalyst design in the Fischer-Tropsch synthesis: sites, pellets, and reactors, Adv. Catal., 39 (Eley, D. D., Pines, H., and Weisz, P. B., eds), p. 239.

8

Catalytic Converter Modeling for Automotive Emission Control SB H. Oh

I.

General Motors Research, Warren, Michigan

INTRODUCTION

U.S. federal regulations of automobile exhaust emissions are based on pollutant emissions measured while driving a vehicle over a prescribed driving schedule referred to as the Federal Test Procedure (FTP). This standardized emission test procedure requires that the vehicle as well as the catalytic converter under test be at room temperature for a minimum of 12 h before the test. For a short period of time after the cold start, the engine usually runs fuel-rich, emitting high concentrations of hydrocarbons and CO. To compound the problem, the catalyst is relatively cold at this time and thus is not fully operational. As a result of the combination of the high engine-out emissions and the low catalyst efficiencies encountered following a vehicle cold start, CO and hydrocarbon emissions from the first few minutes of the FTP constitute a large fraction (up to 75% for latemodel gasoline vehicles) of the total tailpipe emissions [1-4]. Therefore, it is crucial to improve converter warm-up performance to meet the future automotive emission standards, which mandate more stringent control of the pollutants. Since converter performance is a complex function of operating conditions, converter geometries, and catalyst properties, an empirical approach to the problem can be very costly and time consuming; thus mathematical modeling promises to be helpful in the development of catalytic converters with improved warm-up performance. Two general types of catalytic converters are currently used for auto259

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260

mobile exhaust emission control: packed-bed and monolithic converters. Both converter types have perceived advantages and disadvantages with respect to factors such as required converter size and cost, catalyst performance and durability, ease of replacement, and back pressure. The relative merits of the two types of converters are not discussed here; interested readers are referred to review papers by Taylor [1] and Kummer [2]. In this review we focus on the mathematical modeling of both types of converters, with particular emphasis on the experimental verification and practical applications of the model. This chapter is based largely on the converter modeling work done at General Motors over the past decade. A critical survey of the literature on converter modeling is not intended here; instead, references to selected previously published converter modeling studies will be made at appropriate points in the text to put our modeling work in perspective. In view of the importance of cold-start emissions mentioned above, we restrict our attention to the first few minutes of the FTP driving schedule (i.e., converter warm-up period) for modeling purposes. This portion of the FTP is composed of various driving modes (idle, cruise, acceleration, and deceleration), with vehicle speed varying from 0 to 100 km/h. This causes a multitude of highly transient converter inlet conditions with respect to exhaust gas flow rate, composition, and temperature. In addition, the cold-start requirement of FTP tests makes converter temperature transients (i.e., cold converter suddenly exposed to hot exhaust gas) and reaction kinetics (i.e., converter operation at relatively low temperatures) important parts of the problem. In particular, the amount and distribution of noble metals within the converter have been shown to have a strong influence on its performance during the warm-up period. Therefore, converter models of practical value in automotive emission control are those that account for the simultaneous processes of heat transfer, mass transfer, and chemical reaction under transient conditions, and which include enough details about the catalysts. Such considerations led to the development of the mathematical models for packed-bed and monolith converters presented in succeeding sections. II.

PACK-BED CONVERTERS

A cutaway view of a packed-bed catalytic converter used by General Motors is shown in Figure 1. High-surface-area alumina beads (about 3 mm diameter, 100 m2/g) impregnated with noble metals are housed in a container that has a large frontal area and a shallow depth to minimize the pressure drop across the converter. Both the top and bottom of the converter container are insulated to minimize heat loss to the surroundings.

261

Modeling for Automotive Emission Control

Inlet Header"

Inlet Plenum

Retaining Grid &

Sill!

Studs

Figure 1. Cutaway view of GM packed-bed converter. (From Ref. 10.)

A. Development of the Model The model considers the Pt-catalyzed oxidation reactions of CO, hydrocarbons, and H2. A mixture of propylene and methane was used to approximate engine exhaust hydrocarbons, with propylene typifying fastoxidizing hydrocarbons and methane representing slow-oxidizing hydrocarbons [5,6]. It is assumed that the fast-oxidizing hydrocarbons constitute 90% (by volume) and the slow-oxidizing hydrocarbons 10% (by volume) of the total engine-out hydrocarbon concentrations [7]. Additionally, the concentration of H2 in the exhaust gas is assumed to be one-third of the CO concentration [8]. The reaction rate expressions used in the computations are of the bimolecular Langmuir-Hinshelwood type: }2

mol species / cm2 Pt • s

, 2(C 3 H 6 ), 3(CH 4 ), 4(H 2 )

(1)

where G = (1 + KlCco +

K2CC3H6)2(1

+

*:3C2COC2C3H6)(1

+

(2)

We remark that Rt in Eq. (1) is the specific reaction rate for species i (i.e., rate per unit Pt surface area). The preexponential factors of the rate con-

Chapter 8

262

stants kx in Eq. (1) were obtained by adjusting those of Voltz et al. [6], based on the recycle reactor data of Schlatter and Chou [9], without changing the activation energies and adsorption equilibrium constants. Notice that in addition to the inhibition effects of CO and C3H6, the adsorption term G accounts for the inhibition effect of the nonreacting species NO. The kinetic parameter values for the rate expressions for the consumption of the reactive species, given by Eqs. (1) and (2), can be found in Oh and Cavendish [10]. From the stoichiometry, the reaction rate for oxygen is given by mol O2 cm2 Pt • s

ROi = 0.5/?c

co

1.

(3)

Basic Equations and Assumptions

Vehicle-aged automotive catalyst pellets typically have a catalytically active band sandwiched between an unimpregnated inert core and a relatively shallow poisoned layer, as illustrated in Figure 2. For modeling purposes, therefore, individual catalyst pellets are treated as composite porous media composed of concentric shells of differing physical and chemical properties. Such a multilayered configuration, though an idealization of reality, has Inert Core Active

Poisoned

Figure 2. Schematic diagram of the cross section of a typical vehicle-aged catalyst pellet. (From Ref. 18.)

Modeling for Automotive Emission Control

263

been used successfully for the modeling of automotive catalysts [11-13] and, as we will see, provides a convenient means of examining the effects of poison penetration and various noble metal impregnation strategies. The conservation of reactive species / in a spherical catalyst pellet is described by

? Jr {Dej2 Ik) " flM*fr'r') = °

i = 1(CO), 2(C3H6), 3(CH4), 4(H2), 5(O2)

° 225 s, however, the model overpredicts the bed temperature by approximately 40°C. At least part of this discrepancy can be attributed to the fact that our adiabatic converter model does not account for the heat loss from the converter to the surroundings, which becomes significant for t > 225 s as a result of the high converter temperature. As can be seen from Figure 3, however, this does not adversely affect the predictions of converter-out emissions, because converter performance becomes relatively insensitive to temperature at high temperatures due to the increasing effects of mass transfer limitations. Additional comparisons between measured and predicted cumulative tailpipe (i.e., converter-out) emissions of CO are made in Figure 5 for the two surface-impregnated catalysts (Surface-Hi and Surface-Lo). Here again the model provides reasonably good predictions of the cumulative emissions of CO during the first 333 s of the FTP. It should be noted that the predicted curve for the Surface-Hi catalyst was generated by assigning one-twentieth of the fresh activity to the poisoned Pt layer, in view of independent experiments with phosphorus-poisoned platinum catalysts

Chapter 8

270 50 r

3

o

40

30

o

.1 120 3

Measured Predicted

10

0

100

200 FTP Time (s)

300

Figure 5. Comparisons of measured and predicted cumulative CO emissions leaving converter for the Surface-Hi and Surface-Lo catalysts. (From Ref. 18.)

[21]. In accordance with our anticipation, the cumulative CO emission at the end of the 333-s period for the Surface-Hi catalyst is considerably lower (by about 15 g) than that for the Surface-Lo catalyst. (This difference in cold-start CO emission translates into about 0.9 g/mile in the overall FTP emission of CO, compared to the current emission standard of 3.4 g/mile.) This demonstrates that converter warm-up performance is generally sensitive to the amount of active noble metals in the catalyst pellet. (Table 1 shows that the Surface-Hi catalyst contains approximately four times more active Pt than the Surface-Lo catalyst.) Notice, however, that for t > 240 s, where converter temperatures are high, this Pt loading effect disappears and both catalysts gave nearly complete conversion of CO. C. Model Applications 1. Parametric Sensitivity Analysis

The comparisons made in Figures 3 to 5 between the model predictions and experimental data demonstrate that the model developed here provides

271

Modeling for Automotive Emission Control

a computational tool for quantitative predictions of the thermal response and conversion performance of GM packed-bed catalytic converters during the warm-up period of the FTP. Consequently, the model can be used with confidence to investigate the effects of each of the converter design and operating parameters on cold-start exhaust emissions. Such parametric sensitivity analysis is useful because it identifies important design/operating parameters and quantifies the sensitivity of converter warm-up performance to changes in each of those variables. Although there are numerous system parameters affecting converter performance (see Table 2), we discuss only selected results of parametric calculations for illustration purposes. Figure 6 shows how tailpipe CO emissions during the first 333 s of the FTP ("cold-start CO emission") are affected by variations in converter volume for two different active metal loadings of the catalyst pellet. (The Pt loading in fresh catalysts ranges from 0.05 to 0.09 wt %; however, the amount of active metal in the converter generally decreases with vehicle 50 r

_

40

.1 O

r 30 CD

55

5 20

5 10 Converter Depth (cm)

15

Figure 6. Effects of converter volume (frontal area fixed at 516.1 cm2) on coldstart CO emissions for two different active Pt loadings of catalyst pellets. (From Ref. 18.)

272

Chapter 8

use by a factor of 10 to 20 as a result of catalyst sintering and poisoning [22].) For the calculations, it was assumed that the exhaust gas from the 4.1-L V-6 engine was passed through a converter packed with catalyst pellets that have a 25-|xm outer poisoned layer surrounding a 75-(xm catalytically active band. Also, the converter volume was perturbed by varying the depth of the catalyst bed while keeping its frontal area constant at 516.1 cm2. As expected, for each of the two Pt loadings considered, CO emissions at the converter outlet generally decrease with increasing converter volume. Notice, however, that increasing the catalyst volume (while holding its properties constant) beyond a certain value gives only a small reduction in exhaust emissions during converter warm-up. This can be explained based on the finding of our earlier study [10] that the catalyst pellets in the upstream portion of a converter are primarily responsible for converter light-off; the additional catalyst in the rear portion of the bed does not warm up fast enough to contribute significantly during the early portions of the FTP. The difference in the asymptotic emission levels of the two catalysts predicted in Figure 6 reflects the sensitivity of cold-start emissions to the noble metal loading of catalyst pellets. The results of Figure 6 demonstrate the importance of a proper choice of catalyst's noble metal loading in converter design; it determines an upper limit on converter warm-up performance that cannot be overcome simply by increasing the converter volume. The performance of automobile exhaust catalytic converters has been shown to be influenced significantly by diffusion resistances within the catalyst pellets. One convenient way of examining the degree of intrapellet diffusion-reaction interactions is to place a Pt band of fixed thickness subsurface to various depths away from the pellet's outer edge. Figure 7 shows the results of such simulations for two different active Pt loadings (75-|mm Pt band, GM type 160 converter). CO emissions during cycle 1 (first 125 s of the FTP) are dependent on the amount of active Pt in the catalyst pellet but are virtually unaffected by the location of the Pt band, indicating that converter performance during cycle 1 of the FTP is kinetically controlled. Converter performance during cycle 2 (126 to 333 s), on the other hand, is adversely affected by intrapellet diffusion resistances, due primarily to the high-temperature (~400°C) converter operation encountered for t > 200 s (see Figure 4). As a result, the total tailpipe CO emissions during cycles 1 and 2 increase with increasing thickness of the inert outer layer (i.e., as the Pt band is buried deeper), as illustrated in the top portion of Figure 7. In addition to elucidating the nature of converter operation during warm-up, the results of Figure 7 provide guidance in the design of subsurface-impregnated catalysts and in assessing the impact of poison penetration on converter warm-up performance. Notice that the case discussed in Figure 7 is a special case of general

Modeling for Automotive Emission Control 50

273

0.0033 wt % Pt 0.0133 wt%Pt

_ 40 c o

Cycles 1 + 2

(ft (ft

E

LU

O O

_30 .1

Cycle 1 _ __ J — — •

20

0

J I 100 200 Thickness of Inert Outer Layer (^m)

300

Figure 7. Effects of location of Pt band (75 jxm thick) on cold-start CO emissions for two different active Pt loadings of catalyst pellets. (From Ref. 18.) design strategies involving nonuniform distribution of the noble metal within catalyst pellets. Readers interested in the theoretical and experimental aspects of optimal activity profiles in catalyst pellets are referred to Chapter 6 of this book. The parametric sensitivity results discussed so far were based on the inlet exhaust gas conditions of the same vehicle that was used for our model verification studies (4.1-L V-6 engine with automatic transmission). The converter model developed here can also be used to assess the effects of variations in the inlet exhaust gas conditions on the performance of the catalytic converter system at hand. This capability of the model would enable one to predict the impact of possible modifications of engine design and calibration on FTP emissions during converter warm-up. 2.

Optimum Converter Design

In this section we address the following two design questions of practical interest: (1) maximize converter warm-up performance with a given amount

Chapter 8

274

of Pt, and (2) minimize Pt usage for a given performance requirement. An example will be given here which illustrates how the model can be used to answer these optimum converter design questions for a specific vehicle system. The results of design calculation for the vehicle with a 4.1-L engine are summarized in Figure 8, where tailpipe CO emissions during the first 333 s of the FTP are plotted against converter depth (with its frontal area fixed at 516.1 cm2) for three different amounts of active Pt in the converter. Here again, a partially poisoned surface-impregnated catalyst was considered which contains a 75-JJLITI active band surrounded by a 25-|xm poisoned shell. It is important to note that since the total amount of Pt in the converter is fixed in each case, the Pt loading of the catalyst pellet (and

50 r

40

8 30 CD

55

20

10

0.295 g Pt/Converter

_L J_ 4 6 Converter Depth (cm)

10

Figure 8. Dependence of cold-start GO emissions on converter volume (frontal area fixed at 516.1 cm2) for three active Pt contents per converter. (From Ref. 18.)

Modeling for Automotive Emission Control

275

thus the local Pt concentration in the catalyst bed) is inversely proportional to converter volume. Referring to Figure 8, minimum CO emissions are predicted to occur at an intermediate value of converter volume. If the converter volume is larger than the optimum value, the cold-start emissions increase as a result of the concomitant decrease in the Pt loading of the catalyst pellets. As shown in Figure 5, this decrease in the catalyst's Pt loading adversely affects the converter performance during cycle 1 and the early portion of cycle 2. If the converter volume is too small, on the other hand, the beneficial effect of the increased Pt local concentration on the early-time converter performance is more than offset by the performance deterioration (caused by insufficient contact time between the gas and catalyst) in the later portions of the warm-up process, resulting in an increase in the total CO emissions during cycles 1 and 2. This aspect is clearly illustrated in Figure 40 r

100

200 FTP Time (s)

300

Figure 9. Comparison of cumulative tailpipe CO emissions for small and large converters. (From Ref. 18.)

Chapter 8

276

9, which shows cumulative tailpipe CO emissions as a function of time for two different converter volumes (0.169 g active Pt/converter in both cases). The small converter (dotted line) outperforms the large converter (solid line) at early times because the former contains catalyst pellets of a higher Pt loading; however, the ability of the large converter to convert CO nearly completely for t > 205 s results in a lower cumulative emission level at the end of cycle 2. It should be noted that Figure 8 can also be used to determine a minimum amount of Pt required to achieve a specified cold-start tailpipe emission level. It is clear from Figure 8 that for a given amount of Pt per converter, there are, in general, two converter volumes giving the same emission level. A minimum amount of Pt required for a desired emission level can then be determined by ascertaining the Pt content for which the required converter volumes collapse into one value. Once the optimum values of the Pt content and converter volume are established, the corresponding Pt loading of the catalyst pellet is determined automatically. III.

MONOLITHIC CONVERTERS

Monolithic converters have an array of thin-walled parallel channels composed either of cordierite (2MgO • 2A12O3 • 5SiO2) or of stainless steel (more precisely, Fe-Cr-Al-Y alloy). A thin (20 to 50 u.m) washcoat of alumina is applied to the surface of the substrate to provide a high-surfacearea support onto which the noble metals are deposited. Unlike packedbed converters, monolithic converters typically operate in a laminar flow regime, yielding a low-pressure drop. The basic elements of a ceramic monolith catalytic converter are shown in Figure 10. A. 1.

Development of the Model Basic Equations and Assumptions

The major assumptions invoked in the development of the model are (1) a uniform flow distribution at the monolith face, and (2) adabatic operation of the converter (i.e., no heat loss to the surroundings). Under these assumptions, all the channels would behave the same, thus allowing channel-to-channel variations or interactions to be ignored in the calculations. Thus we adopt a transient, one-dimensional single-channel model that predicts the temperature and species concentrations, both in the solid and gas phases, as a function of axial position and time. The uniform flow distribution assumption seems reasonable because our sample calculations show that both the previously developed three-dimensional model of Chen

Modeling for Automotive Emission Control •NSULAT.ON

I N

277

«*J™

MAT

UPPER SHELL SHIELD

LOWER SHELL

MONOLITH CATALYST

Figure 10. Ceramic monolith catalytic converter. (From Ref. 23.)

et al. [23] (where the effects of flow maldistribution are accounted for) and the simpler one-dimensional model adopted here predict very similar converter warm-up performance. Furthermore, our model neglects the radial variations of the gas-phase temperature, concentration, and velocity within the individual channels, so that those variables in the governing equations given below are to be interpreted as cross-sectional averages. Heck et al. [24] have shown that the capability of the model to predict monolith behavior during warm-up is not adversely affected by this simplifying approximation. The material and energy balances for the gas phase are

^ f = ~V^ " kmiS(CsJ ~ Csi) - CrO3/SJIica/Ti(O-iPr)4/(NH4)2SiF6 (1977)

TiCI4/MgCI2ATHF/Si02/AIEt3 (1979)

• BCPC = Bis(cyclopentadienyl) chromate

Table 2 Developments in Heterogeneous Propylene Polymerization Catalysts I. Unsupported Type • Metal comp. ol Group IV-VI & org. metal of Group 1-111(1954)

^ ^ ^

porous - T1CI3/DEAC (Solvay type, 1972)

^ > ^ Transition metal/RMgX/TiCI4 -+(1974)

Tl(OR)nX4_n/RMgXyTiC]4 /Si-OR(1987)

II. Supported Type • TlCI4/MgCI2/EB/TEA - • (Montedison / Mitsui, 1971)

Activated MgX2 - TiCI4/TEA/ Dtamme (1970)

- - * - MgX2/Org acid esters/Si comp./ TiCWTEA (1974)

- ^

—+- Activated MgX2 —*Ti halide-ester/ TEA/Si comp. (1980)

Activated MgX2/E.D. - Ti comp./ TEA/Aromatic carboxylic acid ester (1971) Mg comp. - Ti comp. - H/C solution/ E.D./TEA/Si comp. (1981)

• DEAC = Diethyl aluminum chloride, TEA = Tnethyl aluminum chloride, EB = Ethyl benzoate, E.D = Electron donor

339

Modeling of Polymerization Processes

A-2

A-3

A-4

Figure 1. Scanning electron micrographs of polypropylene particles prepared with 8-TiCl3 catalyst system (average particle size, 19 ^xm; polymerization activity, A2: 108 g polymer/g catalyst, A3: 880 g polymer/g catalyst, A4: 2030 g polymer/g catalyst. (From Ref. 14.) a replica of the original catalyst particle. This implies that the polymer particle morphology can be controlled by the catalyst particle morphology. Recent work by Kakugo and co-workers [12-14] shows, in a most convincing manner, how the polymer particles grow with classical TiCl 3 catalysts and high activity Mg-Ti catalysts in propylene polymerization. Figure 1 shows the polymer globules with diameters of 0.9 to 1.0 |xm observed on the surface of the polymer particles by scanning electron microscopy (SEM). Note that the polymer globules have a broad size distribution, ranging from 0.4 to 1.1 jjim at low polymer yield, but they become round and uniform particles about 1 |xm in diameter at high polymer yield. However, further analysis of the particle interior by transmission electron microscopy (TEM) reveals that those polymer globules observed by SEM are not the primary polymer particles but aggregates of much smaller primary particles with diameters of 0.1 to 0.35 |xm (Figure 2). Moreover, their xray microanalysis shows that these primary particles contain one or sometimes two titanium nuclei with diameters of 50 to 170 A at the core of each of them as represented by A and B (Figure 2). These nuclei have the same dimension as the catalyst crystallites and thus it was concluded that they are the catalyst crystallites. It was also observed that with TiCl 3 catalyst, the catalyst crystallites do not break at least until the polymer yield exceeds

340

Chapter 10

Figure 2. X-ray microanalysis of polypropylene prepared with 8-TiCl3 catalyst system (average particle size, 19 \xm, polymerization activity 1100 g polymer/g catalyst). (From Ref. 13.) 12 g polymer/g catalyst and the initial catalyst crystallites retain their size during the course of polymerization. The growth of polypropylene with Mg-Ti catalyst is similar to that with TiCl3 catalyst except for the number of catalyst crystallites in the primary polymer particle at low polymer yield and the presence of the catalyst crystallites near the boundary at high polymer yield. Figure 3 illustrates a schematic model for a three-level polymer growth [i.e., primary microparticle (about 0.1 |xm), secondary microparticle (about 1 |mm), macroparticle (about 500 |xm)] proposed by Kakuko et al. based on their electron microscopy and x-ray analysis. Controlling the polymer particle morphology during the polymerization is of industrial importance because average particle diameter, particle size distribution, fines content, shape, bulk density, surface roughness, and porosity affect the polymerization rate and the dispersion and good mixing of additives in the finishing stage. Thus there is a strong need to develop a quantitative understanding of polymer particle growth and associated physicochemical and reaction phenomena in each polymer particle during polymerization. Some earlier works on polymer particle modeling have

Modeling of Polymerization Processes Catalyst

341

Polymer particle (Low polymer yield)

(High polymer yield)

Polymer globulePrimary polymer particle Catalyst crystallite

Figure 3. Schematic model for three-level polypropylene growth. (From Ref. 14.) been reviewed in detail by Taylor et al. [11]. Figure 4 illustrates four morphological models stemming from different levels of experimental observation and assumptions [15]. In the following, some highlights of these models are briefly described. 1. Solid core model (SCM): This model is obviously oversimplified. The polymer is assumed to grow at the surface of the original catalyst particle and there is no further catalyst breakup during polymerization. This model will perhaps be ideal to describe the behavior of primary polymer particles observed by Kakugo and co-workers [12-14]. 2. Polymeric core model (PCM): In this model it is assumed that catalyst breakup is instantaneous and that a polymer-catalyst dispersion of fixed radius is formed. The polymer then grows up around this permeable core of the fixed radius. Monomer and hydrogen must diffuse through the outer polymer shell and the inner core. 3. Polymeric flow model (PFM): This model is a generalization of the preceding two models. It assumes that the polymer particle is a dispersion of catalyst fragments in a polymer continuum. This mass grows with time and the catalyst particles move outward in proportion to the local volumetric expansion due to polymerization.

342

Chapter 10

SCM

PCM

original catalyst particle

breakup o f particle

PFM

MGM Figure 4. Polymer particle models. (SCM, solid core model; PCM, polymeric core model; PFM, polymeric flow model; MGM, multigrain model. (From Ref. 15.) 4.

Multigrain model (MGM): This model is a very detailed picture of catalyst breakup in which micrograins of the fractured catalyst particle each behave as small solid core models. Thus there is microdiffusion into each microparticle and macrodiffusion in the macroparticle. Extensive modeling and analysis of polymer particle growth phenomena and associated mass and heat transfer phenomena have been carried out by Ray and co-workers [11,16-19]. Figure 5 depicts a schematic diagram of the multigrain model used in their detailed mathematical analysis. Notice that due to the presence of polymer microparticles and macroparticles there are at least two levels of mass and heat transports within the growing polymer particle. As the polymer particle grows, there is an increasing monomer diffusion resistance, resulting in a spatially nonuniform monomer concentration distribution. The governing equation for the monomer diffusion in the microparticle of radius Rs with rc as a core catalyst particle radius is given as

dM

l a /

,dM\

(1)

343

Modeling of Polymerization Processes

k s (0 b ) Monomer Diffusion

\ \ \ \

ortsiontY Computational porosily) Shell Eme'fnoi

\

film

Figure 5. Multigrain model. (From Ref. 17.)

with the boundary and initial conditions rr-r_ c P

r = Rs t = 0

dM n

rc

- R p, Ds—--R

(2a)

M = Meq(ML) < ML

(2b)

M = Ma

(2c)

where M is the monomer concentration, em the porosity in the micropar-

Chapter 10

344

tide, Ds the monomer diffifusivity in the microparticle, Rps the surface polymerization rate, Meq the monomer concentration at the surface of the microparticle, and ML the monomer concentration in pores of macroparticle. The monomer diffusion equation in the macroparticle is

with the boundary and initial conditions r, = 0 rL = RL r = 0

^ =

0

DL ^ = ML = M/j0

(4a) ks{Mh - ML)

(4b) (4c)

where eL is the porosity in the macroparticle, DL the monomer diffusivity in the macroparticle, RL the radius of macroparticle, RpL the volumetric reaction rate in macroparticle, ks the external film mass transfer coefficient, and Mb the bulk-phase monomer concentration. For the simulation of nonisothermal polymerization, energy balance equations for both the microparticle and macroparticle are added. Furthermore, molecular weight moment equations are also derived and solved with the governing equations above to calculate polymer molecular weight. The total number of microparticle layers in the macroparticle is also a simulation parameter to be specified. It is shown in Ref. 16 using the multigrain model that the monomerdiffusion limitation in the growing polymer particle with single-site low-activity Ziegler-Natta catalyst can cause a broad MWD observed in ethylene and propylene polymerization. However, there are some experimental results which suggest that the MWD broadening observed in heterogeneous olefin polymerization is due to the presence of multiple active sites differing in their reactivities (see Refs. 20 and 21 for review). For example, for stable catalysts of relatively low activity, the polymerization rate remains almost constant, independent of the amount of polymer produced. It has also been shown that for polymerization with high-activity catalyst under quasi-living conditions, the MWD remains constant throughout the polymerization, indicating that the buildup of polymer layers leading to diffusion limitation cannot be the cause for the MWD broadening.

Modeling of Polymerization Processes

345

20,000

EFF

10,000-

Time (hours)

Time (hours)

l. 2

Time (hours)

Time (hours)

Figure 6. Effect of diffusion resistance and site heterogeneity on polymerization rate (Rp), effectiveness factor (EFF), molecular weight (A/J, and polydispersity (Q) with high-activity second-order deactivating catalyst: 1, single-site catalyst; 2, two-site catalyst. (From Ref. 19.)

Figure 6 shows typical multigrain model simulation results for highactivity single-site and two-site catalyst systems [19]. It shows that for a catalyst particle diameter of 30 (xm, intraparticle diffusion resistance is minor and the characteristic activity decay curve is only slightly influenced by diffusion. However, the two-site catalyst system shows much higher polydispersity (Q — Mw/Mn) than does the single-site catalyst. A maximum polydispersity is predicted when the weight fractions of the polymer produced over sites with different activities are roughly equivalent. Broad MWDs are obtained when the polymer fractions of the molecular weights differ by roughly an order of magnitude. From their analysis they conclude that diffusion resistance affects the polymerization rate more strongly than the polymer properties and that active-site heterogeneity offers a convincing explanation of both the polydispersity and the shape of MWD curves. Intraparticle and boundary layer heat and mass transfer effects were also investigated using the multigrain model [17,18]. For slurry polymerization, intraparticle mass transfer effects may be significant at both the macroparticle and microparticle levels; however, for normal gas-phase

346

Chapter 10

polymerization, microparticle mass transfer effects are more important. For slurry polymerization with high-activity catalysts, external film mass transfer effects may also be significant. For gas-phase polymerization, significant particle overheating during the early stage of polymerization occurs, which may explain the particle sticking and agglomeration problems sometimes observed in industrial gas-phase polymerization reactors. Quite often some differences in polymerization behavior are observed even with the same catalyst when the reaction is carried out in various media. Although mass and heat transfer characteristics of gas-phase and liquid slurry processes in the growing polymer particle were found to be different as discussed above, it has been pointed out by Hutchinson and Ray [22] that equilibrium sorption also plays an important role in determining the local concentration of monomers in the polymer phase. In other words, the thermodynamics of monomer sorption in semicrystalline polyolefins control the monomer accessibility to the catalyst surface, and thus the polymerization rate. It was shown that in gas-phase polymerization the monomer condenses during the sorption into the polymer phase, changing from a vapor to a liquid. As a result, the concentration of monomer can actually be higher in the polymer phase than in the bulk gas phase. This theory also provides a qualitative understanding of some unusual rate enhancement phenomena observed in ethylene polymerization with higher a-olefins (e.g., butene, hexene), which sorb an order of magnitude more than ethylene. Moreover, they found that the sorption effects can also affect the observed reactivity ratios in olefin copolymerization processes. Their quantitative analysis of the monomer sorption effects is of practical significance because it suggests that when the kinetic data obtained in liquid slurry polymerizations are used for the design of gas-phase polymerization processes, appropriate corrections should be made in effective monomer concentration(s) at the catalytic sites. B. Modeling of Heterogeneous Olefin Polymerization Reactors With the development of highly active and stereospecific transition metal catalysts, a variety of industrial polymerization reactors have also been developed and commercialized. Olefin polymers are produced primarily in continuous reactors such as stirred tank reactors and loop reactors for liquid slurry and solution polymerizations, fluidized-bed reactors, stirredbed reactors, and horizontal-compartmented reactors for gas-phase polymerizations. Multiple reactors and reactor types are often combined to produce copolymers or elastomers. Some important characteristics of these polymerization reactors are reviewed in [1,2,15,23-26]. Liquid slurry and gas-phase polymerization reactors are operated at 70 to 110°C and 8 to 35

Modeling of Polymerization Processes

347

atm with 1.5- to 5-h residence time, whereas solution polymerization reactors are operated at higher temperature (130 to 250°C) and higher pressure (30 to 200 atm) with very short residence time (5 to 10 min). Higher ct-olefin comonomers (e.g., butene-1, hexene-1, octene-1, 4-methyl-lpentene) are also added to control the degrees of chain branching and bulk densities. In contrast to a plethora of literature on polymerization catalysis, there is a dearth of literature on the modeling of industrial olefin polymerization reactors. Since there is a huge release of reaction heat in olefin polymerizations, heat removal and reactor temperature control are of particular importance in designing and optimizing the polymerization reactors. Moreover, polymer properties are affected not only by the catalysts being used but also the reactor operating conditions. Therefore, mathematical reactor models capable of predicting the macroscopic reactor behavior and resulting polymer properties are useful for the design of more efficient reactor operating conditions. Two of the major gas-phase polymerization reactor systems, fluidized bed and stirred bed, have been modeled and analyzed by Choi and Ray [27,28]. It was shown that for both types of reactors, there exists a range of reactor operating conditions that can cause a strong parametric sensitivity, thermal runaway, and oscillatory dynamics. Figure 7 shows a schematic diagram of the fluidized-bed and stirred-bed polymerization reactors. In the fluidized-bed reactor, the reaction heat is removed by circulating large amounts of cooled monomer gas to the reactor and the polymerization rate is regulated by manipulating the catalyst injection rate. In this process the monomer conversion per pass is quite low because of high recycle ratio. In what follows, nonlinear steady-state and dynamic behaviors of the fluidizedbed polymerization reactor are illustrated. In modeling the fluidized-bed polymerization reactor, the following simplifying assumptions are made: 1. The emulsion phase (dense phase) is perfectly backmixed and is at minimum fluidizing conditions. 2. The flow of gas in excess of minimum fluidization passes through the bed in the form of bubbles. The bubbles are spherical, of uniform size, and flow in plug flow. 3. The bubble phase is always at a quasi-steady state. 4. Polymerization occurs only in the emulsion phase. 5. Mass and heat transfer between the bubble and emulsion phases occur at uniform rates over the bed height. 6. There is negligible mass and heat transfer resistance between the solid polymer particles and the emulsion phase.

Chapter 10

348 unreocted 90s

(a)

Catalyst-polymer particle

Figure 7. (a) Fluidized-bed polymerization reactor; (b) continuous-flow stirredbed polymerization reactor. (From Ref. 15.)

7. 8. 9.

No elutriation of solids occurs and catalyst injection is continuous. The product withdrawal rate is adjusted to maintain the bed height constant. There is no catalyst deactivation.

With these assumptions, the following modeling equations for the twophase bubbling fluidized-bed polymerization reactor model are derived.

349

Modeling of Polymerization Processes

(b)

PKOOUCT REMOVAL

CONDENSER

POLYMER PARTICLE CATALYST

Material balances Bubble phase (monomer); dz*

~

Ub

{

Me

(5)

Mb)

Emulsion phase (monomer): dCMe

Ue

dt

H - — kp(T)ps(l

- 8*) -

cat Me

(-'Me)

A H

^

_

g.j

(6)

Chapter 10

350 Emulsion phase (catalyst):

dt

- 8*)(1 - em/)p.v

AH{\

w

- 8*)

AH{\

Energy balances Bubble phase: \C*,JTu - T A] = rf7* l^Mb\ib

l

refv'J

— (T - Tu) \ie

TJ ^ *

l

(R)

b)

\°)

Emulsion phase: rn LU

>» r* + r r* l ^ e m / j p , C p , + e m / C ^ C ^ j dt

- -

i

i

i

f

i

•

i

i

370

360 •

Tb350-

340x10" 6 2.5" R2.0: A : T1.5 E : 1.0c)

.

.

.

•

I

10

.

>

20

•

i

>

Time, HR

30

1

' ' i ' ' '

40

l

50

Figure 9. Open-loop responses to step changes of fluidized-bed ethylene polymerization reactor to step changes in catalyst injection rate (adiabatic, U0/Umf — 5). (From Ref. 15.)

Modeling of Polymerization Processes

353

erage bubble phase temperature. For a step change in qc larger than 55% from the original steady-state value, runaway will occur. In this process, the polymer production rate is controlled by manipulating the catalyst injection rate. Therefore, when one wants to make any changes in the catalyst injection rate, it is important to ascertain the stability of the reactor with new operating conditions. Under feedback control the reactor can be stabilized provided that there is sufficient cooling capacity of the recycle heat exchanger. However, even in the closed loop, temperature runaway can occur in some situations in which the rate of heat removal by recirculating gas becomes lower than the rate of heat generation in the reactor. The overall dynamic behavior of propylene polymerization is also quite similar to that of ethylene polymerization. But the region of stable steady state is broader for propylene polymerization due to the relatively lower heat of propylene polymerization. More details of reactor analysis can be found in Ref. 27. The stirred-bed olefin polymerization reactor depicted in Figure 7 can be modeled similarly and the modeling equations are presented in [28]. In this process, recirculation and condensation of monomer is used for reactor cooling because of the poor convective heat transfer capacity of the gassolid reaction medium. The heat of polymerization is removed by evaporation of the feed and recycled monomer. Unreacted monomer vapor from the reactor is liquefied by a condenser and liquid monomer is recycled to control the reactor temperature. Figure 10 shows the steady-state temperature profiles for a stirred-bed gas-phase propylene polymerization reactor operating adiabatically at constant volume and constant pressure. Note that a similar steady-state structure to that of the fluidized-bed reactor is seen (e.g., multiple steady states), but there is only a small region of feasible gas-phase operation bounded by reactor phase changes (polymer melting or monomer liquid formation). Thus the only possible steady states are unstable saddles. Also notice that in the region of feasible operating conditions, higher steady-state temperatures are obtained at lower catalyst injection rates {qc). At steady state, the rate of heat removal is the same as the rate of heat generation; however, the rate of heat removal (by monomer evaporation) is relatively constant with increase in catalyst injection rate. Therefore, the steady-state temperature becomes lower at higher catalyst concentration. With appropriate feedback controls, the reactor can be stabilized for normal operations. But for some reactor operating conditions, the stirred-bed polymerization reactor exhibits strong parametric sensitivity. Modeling of other types of olefin polymerization reactors (e.g., loop reactors, stirred reactors) have also been reported in Refs. 29 to 31.

Chapter 10

354

200

700

qc(or£) (Kg/hr) 500

200 0.00

0.05

0.10

0.15

0 20

qc(or£) (Kg/hr) Figure 10. Steady-state reactor temperature profiles in a CSBR under constantvolume, constant-pressure conditions. (From Ref, 28.)

C. Modeling of Homogeneous Olefin Polymerization Reactors Soluble homogeneous Ziegler-Natta catalyst is an important class of olefin polymerization catalysts. Although vanadium-based catalysts (e.g., VC14, VOC13) have long been used in the industry for solution polymerization of ethylene and diens, it is only recently that extremely active soluble Z-N catalysts have been discovered, notably by Kaminsky and co-workers in Germany. It is now well known that titanocene and zirconocene compounds form very active soluble Z-N catalysts when they are used in conjunction with methyl aluminoxane (MAO) as a cocatalyst. These catalysts exhibit

Modeling of Polymerization Processes

355

an ethylene polymerization activity of more than 3500 kg/mol Zr • atm • h [32-35]. High-activity metallocene catalysts offer some unique features: (1) the catalyst system is extremely long-lived; (2) the MWDs of the resulting polymers are very narrow; and (3) high-molecular-weight atactic polymers are obtainable from propylene and higher a-olefins [36]. MAO is synthesized by reacting extremely flammable trimethyl aluminum (TMA) with water contained in hydrated salts. Water has long been considered to be a catalyst poison for many heterogeneous Z-N catalyst systems; however, addition of water to soluble catalyst systems (e.g., Cp2TiEtCl—AlEtCI2) was found to increase the polymerization activity due to an increase of the Lewis acidity [37,38]. Detailed investigations on the influence of water showed that oligomeric aluminoxane formed from water and trimethyl aluminum contains the structure -\-0—Al(Me)^-^ as shown in Figure 11 [39]. The aluminoxane surrounds the transition metal to form a complex , and a ir-bond is formed by the interactions between the transition metal and the cyclopentadienyl groups with the aluminum and the oxygen atoms of the aluminoxanes. Almost every transition metal atom forms an active complex and it produces about 15,000 polymer chains in 1 h. The turnover time is 5 x 10 5 s. Recently, ring-substituted zirconocene dichlorides with oligomeric MAO have been found to have high ethylene polymerization activities but the MWD is much broader than in the Cp2ZrCl2 catalyst [40]. When high-activity soluble Z-N catalysts are used, relatively small reactors with short residence time may be used either in series or parallel to alter molecular weight distribution of the product. The use of small reactors has some advantages in that a broad range of product properties can be obtained in a single-line plant with a short transition time for product grade changes [1,41]. Recently, Kim and Choi [42] analyzed steady-state and transient behavior of a continuous olefin copolymerization reactor with soluble Z-N catalyst. Let us consider an ideal, backmixed, continuous-flow stirred-tank reactor with a cooling jacket. A feedstream consists of ethylene (Mx) and higher a-olefin comonomer (M2) such as butene-1, which is much less reactive than ethylene. A small amount of preactivated catalyst solution is supplied from a separate storage tank and mixed with the monomers near the inlet of the reactor before being injected to the reactor. The feed stream temperature is sufficiently low to prevent a premature polymerization near the reactor inlet. The copolymerization kinetics are characterized by very rapid chain initiation and catalyst deactivation leading to a substantial loss of catalyst activity. However, the overall catalyst activity (kg polymer/g catalyst) is so high that a good yield of copolymers is obtainable in relatively short residence time. In the absence of added chain

356

Chapter 10 CH3 CH,

x

Al

-O'

I

5Al(CH3), + 5H 2 .O-

O

/

Al

Al

CH,

CH,

O

o

CH, ^"3

\

\1-CH3

CH2 CHJ3v \ Cp

H,C-A1

o

o Al-CH,

CH,

CH 3

Figure 11. Active center formation in Cp2Zr(CU^)2 catalyst with aluminoxane.

transfer agents, the polymer chains stop to grow via catalyst deactivation and chain transfers to monomers and aluminum alkyl cocatalyst, and spontaneous chain transfer reactions. Table 3 shows a kinetic scheme for the copolymerization of a-olefins. Here Pnm is the growing polymer chains having n units of Mx and m units of M2 with Mx attached to active transition metal site. Qnm is defined similarly. C* is the active-site concentration and D* is the deactivated catalyst site. Then a dynamic reactor model can be represented as follows: = \ (Mxf - A*,) - {kuP + k2lQ)M,

(13)

Modeling of Polymerization Processes Table 3

357

Kinetic Scheme with a-olefin copolymerization

Chain initiation: C' + M1 — ^ - + P i i 0

(A.I)

Cm + M2

(A.2)

- ^ L H - QO.I

Chain propagation: Pn

m

"f Mi

r P n+ 1

m

(£•!)

Pn,m^M2-^C?n.m+1 ^Cn.m

~T" iWi

Qn

4_ JV/2

m

(£.2)

• J n-t-l,m

\"^'"/

—*• Qn m + l

(5-4)

Chain transfer:

Pn,m + Mi -^~* Mn.m T QoA

(C.2)

Qn.m + Mi — — M n . m -T Pi.o

(C.3)

Qn,m + M2 — ^ M n , m + Qo.J

(C.4)

Pn.m + -4/ - ^ ^ M n . m + C*

(C.O)

^ Mn,m -h C

(C.6)

Qn.m - Al —

^

YI T

m

-* ^* ti, rn

^~ t^

^ O. i j

Catalyst deactivation:

Pn.m -

at

T

^ M n . m -r D*

(D.2)

Q n , m - ^ - M n , m + D'

(D.3)

- M2) - (*12P + ^ 22 Q)M 2

= - ( c ; - p r ) - kdpT T - ^

(14) (is)

PQ k22Q)M2 - - p * - (T ~ Tc)

(16)

Chapter 10

358

where T is the residence time and the subscript/denotes the feed condition. P and Q are the total concentrations of the copolymer species, and PT is the total concentration of active catalytic sites in the reactor. In the model above, the first-order catalyst deaetivation kinetics is used and it is assumed that kdc — kdl — kd2 — kd. For the calculation of copolymer molecular weight, the first three leading moments of dead polymers are used. The /cth molecular weight moments for live polymers (Pn,m and Qnm) and dead polymers (Mnm) are defined as

K =I ^ =

2 K

2 i

n = O m= = 0

+ rnw2fP,um

(17a)

(nw, + mw2yQnjn

(17b)

m

(17c)

E E

where vvt and w2 are the molecular weight of Mx and M2, respectively. The moment equations are derived following the technique described in Ref. 43: dt

T

dt

T

ot2

1

) \?

r2

Figure 14. Thermal decomposition of unsymmetrical bifunctional initiator.

Chapter 10

366 Table 5

Polymeric Species in Bifunctional Initiator System

Symbols Pn :

[—

•

live polymer without peroxides

•

live polymer with undecomposed peroxide A

Qn :

A

Sn :

B————

•

live polymer with undecomposed peroxide B

Tn :

•

•

live diradical

]

dead polymer

Mn :

—

Note

[

Un :

[

A

inactive polymer with undecomposed peroxide A

Vn :

[

B

inactive polymer with undecomposed peroxide B

Wn :

A

B

inactive polymer with undecomposed peroxide A and B

U'n :

A—

A

inactive polymer with undecomposed peroxides A

V^ :

B

B

inactive polymer with undecomposed peroxides B

initiator system. Then the resulting kinetic model comprises component population balance equations and molecular weight moment equations. The kinetic scheme for free-radical homopolymerization of styrene is summarized in Table 6. With this kinetic scheme, one can derive the rate expressions for various reaction steps as follows: For initiator and primary radicals

ljt(Jv) = -(kdA + k^I i j t (RAv) =

/A*4B/

- £ d A R A - A:,RAM

(27) (28)

Modeling of Polymerization Processes

367

Table 6 Styrene polymerization with an Unsymmetrical Bifunctional Initiator Propagation (n > 1)i:

Initiation: +R

^RB

-+

p

QI

RA +R

^ * + R'

RA~

-^ / ?

RB

2Jt p

+ •R'

R + M _!u P,

Chain transfer (n > 1):

M —* 0 i M—

*4 +

Pn + M - ^ Mn + i= fc/m

n

2*.

5n + ^ i ? ^ ^ ^ k

-

i? -4-Tn

(n > 1)

Tn + M

(n>l)

^ i ?

-I~Pn

(n>2)

^

•}-Pn

(n>2)

R

2kfTn

» Pn+P]

Pn + Pm

*(

(n>2)

kt

Wn~ ~^/2 -

Pn + Sm

(n>2)

p 4_ T -* n * •* vn

2k t

2k,

Vn —X/?

(n > 2 )

,-sB

-> Af n +

m

Pn + Qm~^-

wn- ^R -f O n U'n~

1

- ^

Termination ( n , m ->1):

^ ^ k

Vn~

M

p

Qn+Qm

(n > 2))

Q

-j_ 5" m

Qn+Tm

'^2Pl

kt

-Kn +m -Pn+.

- y;+m -

TVB+m

2Jt ( kt 2k,

- j

(R B v) = / B ^ A / " /JBRB " *.-RnA#

- y (Rv) = / R (A: dB + kdA)I v at

+ / R A: dA R A + fRkdB^B

+ U+V

(29) -

k.RM

+ 2U')

+ V + W + 2V)

(30)

Chapter 10

368 ~|

(R'v) = UkdARA

+ / R ^ R B - 2/c,-R'Af

(31)

where/ A ,/ B ,/ R , and/R< are the initiator efficiency factors, which represent the fraction of primary radicals being involved in chain initiation reactions. It is assumed that the initiator efficiencies are constant during the course of polymerization. For growing polymers ljt(Piv) = 2kdMM3 + k,RM + kdAUv + kdBV} - kp + kfmM{P ~P, + Q + S - kf^P (P)

kU

+Q + S + 2T)

+ kV

+

p n

(32)

_ , - Pn)

+ kfmM(2Tn - Pn) - k,Pn(P +Q + S + 2T) + 2k"2Pn-mTm

(«>2)

(33)

k,RAM - kdKQx - kpMQx - kfmMQl - k.Q^P + Q + S + 2T)

(34)

- K&n + kdBWn + 2kdAU'n + kpM(Qn_! - Qn) - kfmMQn - k,Qn(P +Q + S + 2T) + 2k"2Qn-mTm

(n>2)

Q + S + 2T) vdv

n

(35)

(36)

' - ktSn{P + Q + S + 2T) t2Sn,mTm m=l

(n>2)

(37)

Modeling of Polymerization Processes

369

Q, + kmS, - 2kpMTx - 2kfmMTx (38)

- 2k,T1(P + Q + S + 2T) lJt(Tnv) =

kdAQn + kdBSn + 2kpM(Tn__, - Tn) - 2kfmMTn - 2k,Tn(P +Q + S + 2T) (n>2)

(39)

- — (Mv) = - kpM(P 4- Q + S + 2T)

(40)

"^ Tn_mTm

m=l

For monomers and dead polymers

I I jj (Mnv) v at

= kfm f MPn +\k\t l

"2

Pn-mPm

(n * 2)

(41)

m-\

For temporarily inactive polymers (42)

IJUiV)

= - kdAU, + kfmMQx

-j(Unv) vat vat

= - kdAUn + kfmMQn + k, 2 Pn-mQm \

(n^2)

(43)

V.1

1d

m•=.1

V ill

\iSWnV)

=

-—(ir\-

~(ddA + kd»)Wn -7k

ir +-k"y

+ k< o

S i Q-mSm n

rnv) = - 2kdBV'n + \kt 2 Sn.JSm

{n 2)

(n>7^ (n > 2)

-

(46) (AI\ (48)

where P, Q, S, T, U, V, W, U\ and V are the total concentrations of the corresponding polymeric species. Due to the density difference between polymer and monomer, the reaction volume (v) changes during the poly-

Chapter 10

370

merization. Thus the rate of volume change is described by the following equation: Mo + eM dt

v dt

where Mo is the initial monomer concentration and e the volume contraction factor. To compute the molecular weight averages of the polymers, molecular moment equations need to be derived. The A:th molecular weight moments for live and dead polymers are defined as nkYn[Y = P,Q,S,T,U,V(j = 1); W,U',V'(j = 2)] (50a)

n=j

X* = 2 nkMn

(50b)

«=2

The overall number-average chain length (Xn) and weight-average chain length (Xw) of the resulting polymers are defined by X

"

=

Y

J

'

W ' ! W

'2 +

(* = P,Q,S,T,U,V,W,U',V) ^eA^U^.^I/'.V')

(51a) (51b)

The moment equations for all live and inactive polymers can be found in [48]. Figure 15 shows the amounts of undercomposed peroxides A and B in the polymers at four different reaction temperatures computed by using the molecular species model for bulk styrene polymerization with 4-((rerrbutylperoxy)carbonyl)-3-hexyl-[7-((terf-butylperoxy)carbonyl)heptyl]cyclohexene, which is an unsymmetrical bifunctional initiator. Here CA and CB are the mole ratio of undecomposed peroxides A and B to the total peroxide groups present at the beginning of polymerization. The peroxide A has a half-life of 8.0 h at 100°C and the peroxide B has a half-life of 0.7 h at 100°C. Note that the amount of less stable peroxide B is quite small even in the low-conversion regime, indicating that the chain propagation is due mainly to the primary radicals generated by the cleavage of the O—O linkage in peroxide B of the primary initiator. As the monomer conversion increases, the total amount of undecomposed peroxide A in the polymer increases and then gradually decreases with a further increase

371

Modeling of Polymerization Processes 0.6 r

mi

0.02

CR

I

0.0

I

I

;

i

I

0.5 Monomer conversion

I

1.0

0.01

o.oot

0.0

0.5 Monomer conversion

1.0

0.02r

0.4

0.2

0.0

0.0

1.0 M n (x10' 5 )

M n (x10"-

Figure 15. Concentration profiles of undercomposed peroxides A and B in polystyrene as functions of monomer conversion and polymer molecular weight, /0 =

0.0042 mol/L; CA - +O0+ A /+O0+ A , 0 , CB = + 0 + / + 0 4

in monomer conversion as peroxide A attached to the polymers decomposes. The monomer conversion and the molecular weight that yield the maximum concentrations of undecomposed peroxides A and B in the polymer decrease as the reaction temperature is increased. Figure 15c and d also show that the peroxide group concentration distribution in the polymer becomes narrower as the polymerization temperature is increased. The model simulation results shown in Figure 15 show that if one wants to prepare block copolymers by sequential monomer addition technique, the first-stage polymerization condition must be carefully designed so that the peroxide concentration in the polymer is sufficiently high to form block copolymers with second monomers.

372

Chapter 10

The effect of reaction temperature on monomer conversion (X) and number average polymer chain length for three different concentrations of unsymmetrical bifunctional initiator is shown in Figure 16. As the initiator concentration is lowered, the dramatic effect of the bifunctional initiator becomes quite clear. Note that high molecular weight and high polymerization rate are obtained simultaneously by the use of unsymmetrical bifunctional initiators. Moreover, the higher molecular weight is obtained at higher reaction temperature as the monomer conversion increases. Such a

1.0 0.8

/ /oo°

//9 0

°c

0.6 0.4

y

0.2

J

100°C 110 °c

-0.015 mol/l

I

Li

I ,= 0.015 mol/l

*

110 °c

0.0

2000

/1L

I

°c

o°c

1

1

j

2000

1000

1.0 0.8 0.6 0.4 0.2 0.0

110° c/ /1OO C

/

y 100

y *^

c

c

S\90°C

/

^

i

/

y\

80°C

^

4000

TIME (MINI)

1

300

400

^

l

0

100 °c

11O°C

2000 80 °C

i o -0.005 mol/l

200

LL

Ic = 0.005 mol/l

100

- ^

i

200

90°C ^—•

i 300

400

TIME (MIN)

Figure 16. Effect of temperature and initiator concentration on monomer conversion and number-average chain length (NAC1) of polystyrene with unsymmetrical bifunctional initiator.

Modeling of Polymerization Processes

373

phenomenon is not observed when either a single monofunctional initiator or a mixture of monofunctional initiators is used. It is also possible to synthesize polyfunctional initiators where more than two peroxide or azo groups are incorporated in relatively high-molecularweight oligomeric molecules [52-55]. When such initiators are used for free-radical polymerization, very high polymer molecular weight can be obtained and multimodal molecular weight distributions are often observed [52]. The modeling of polymerization kinetics with such polyfunctional initiators will be a challenging computational task and no quantitative modeling that includes various reactions involved and associated physical changes during the polymerization (e.g., diffusion-controlled termination) has yet been reported in the literature. B. Dynamic Modeling of Continuous Free-Radical Polymerization Reactors It is well known that continuous polymerization reactors for vinyl monomer polymerization may exhibit strongly nonlinear steady state and dynamic behavior (e.g., multiple steady states, oscillatory dynamics, parametric sensitivity, and thermal runaway) under certain operating conditions. In what follows some examples of interesting reactor dynamics in free-radical polymerization of styrene with unsymmetrical bifunctional initiators and mixed monofunctional initiators are discussed to illustrate such nonlinear reactor behavior. Let us consider a continuous-flow stirred-tank polymerization reactor in which styrene is polymerized by a symmetrical bifunctional initiator studied by Prisyazhnyuk and Ivanchev [56]. This initiator is structurally symmetric, but once one of the two peroxides decomposes, the thermal stability of the remaining peroxide changes. Thus the resulting kinetic scheme differs slightly from that presented in Table 5 for structurally unsymmetrical initiator. The derivation of molecular species model for this system can be found in Ref. 57. In dimensionless form, the mass and energy balance equations take the following form:

—- = -X, + Da(l - A ^ e x p l ^ =

' > I

(52)

-Jf2 + K • Da(l - Z2) e x p f ^ V )

(53) - 8)

(54)

Chapter 10

374

where Xx is the fractional monomer conversion, X2 the fractional initiator conversion, X3 the dimensionless temperature, Da the dimensionless residence time, Xp = (P + Q + 2S)/(P + Q + 25)/? p the dimensionless heat of reaction, a the dimensionless heat transfer coefficient, 8 the dimensionless coolant temperature, and K the dimensionless initiator decomposition rate constant, y and yx are the dimensionless activation energies. For this symmetrical bifunctional initiator, the following species in Table 5 are absent: Sn, Vny Wny and V'n. For the calculation of polymer molecular weight averages, moment equations are derived. The moment equations for inactive polymers (species MnJ Ufn, Un) take the following form:

dt "

e ^ ( 2 ' p-°

d\d 1 -^ = --K1 + k,kPMkPA d

d\ ^

k

d1

+ k(kkr,2 ^

+ ^

(56) + kj,A)

(57)

Zkk

(58)

(60) at

af

u

where 6 is the reactor residence time. The number-average chain length is represented by the ratio of the first moment to the zeroth moment, and the weight-average chain length by the ratio of the second moment to the first moment. After some algebraic manipulations, the following equation is obtained at steady state:

Da(l - XdXpexp(^^J

- 0

(64)

Modeling of Polymerization Processes

375

where X3 can be expressed as a function of XY. The principal parameters that influence the reactor behavior are Da, a, p, y, yu and 8. In practical situations, we are interested in knowing the steady-state multiplicity pattern existing for a given set of system parameters. With parameters 8, 7} (feed temperature), and If (feed initiator concentration) held fixed, we can construct a diagram that shows the steady-state reactor behavior. Figure 17 is such a diagram in the a - p plane. Note that five unique regions of steadystate behavior are identified: Region Region Region Region Region

I: unique steady state II: multiple steady state (S-shaped curve) III: isola and unique steady state IV: isola and multiple steady state (S-shaped curve) V: mushroom

Here r 2 (r 2 ) represents the hysteresis (isola) variety which defines the parameter space at which a continuous change of the parameter causes the appearance or disappearance of hysteresis (isola) type multiplicity. The criteria for the hysteresis variety are

- 0

(65)

— (*,,Da,p) = 0

(66)

| | (*,,Da,P) = 0

(67)

F(Xl9Da£)

in which F represents a steady-state manifold obtained by combining the three modeling equations (52) to (54) into one by eliminating X2 and X3 for fixed value of a. Across the hysteresis variety the number of solutions increases by two for increasing value of a. The criteria for the isola variety are given by Eqs. (65) and (66) and ^

(XuDa#) = 0

(68)

In regions III and IV, isolated branches (isola) are observed. Since regions IV and V are so small, it will be practically very difficult to confirm these tiny regions experimentally. This means that most of the reactor behavior will be represented by regions I, II, and III for practical operating conditions. Note that unique steady-state behavior is never expected in bulk

Chapter 10

376 1.25

inadequate for CSTR model

1.00 —

0.75 —

0.50 —

0.25

0.00

100

0.540 0.460

27.5

00.450-

0.440 17.5

18 .0

18.5

19.0 3 0.725 50.0

51.0

Figure 17. Steady-state behavior regions for styrene solution polymerization in a CSTR with bifunctional initiator, 5 = 0.01, IfB = 0.025 mol/L.

Modeling of Polymerization Processes

377

free-radical polymerization reactors (i.e., solvent volume fraction/s = 0.0). For adiabatic operation (i.e., a = 0.0), only type I and II steady-state profiles will appear. Figure 18 shows the steady-state profiles of monomer conversion (X{) and number-average polymer chain length (XN), with an unsymmetrical diperoxy ester initiator having two peroxides of differing thermal stabilities. These peroxides have a 100°C half-life of 7.4 and 13.2 min, respectively. First notice that multiple steady states exist when the reactor residence time (6) is varied. Here B is the bifunctional initiator and Al and A2 represent the corresponding monofunctional initiators (hypothetical) with a half-life of 7.4 and 13.2 min, respectively. It is seen that the highest monomer conversion at temperatures below 348 K is obtainable when the slow initiator (A2) is used; however, it is the bifunctional initiator (B) which gives rise to both high monomer conversion and high molecular weight simultaneously at higher reaction temperatures. The high molecular weight obtained by the use of the bifunctional initiator at high temperatures is due to the extended lifetime of peroxide groups which reside in various polymeric species (e.g., Qn, Ufl, U!n) that are created by repeated reinitiation, chain transfer, and chain termination reactions. Mixed monofunctional initiators are often used in industrial free-radical polymerization processes. Let us consider a continuous-flow-stirred-tank reactor in which styrene is solution polymerized with a binary mixture of monofunctional initiators having different thermal stabilities. Here the two monofunctional initiators used are rm-butyl perbenzoate (initiator A, slow initiator) and benzoyl peroxide (initiator B, fast initiator). The effect of initiator feed composition on the steady-state behavior of the reactor is illustrated in Figure 19. yAf is the mole fraction of tert-butyl perbenzoate in the feedstream. The analysis of steady-state and periodic bifurcation branches has been carried out with the numerical package AUTO [58]. This software package is designed for the semi-interactive determination of bifurcation branches and their display in graphical form. Starting from a known or calculated steady-state value, AUTO can trace the associated steady-state branch, determine any steady-state or Hopf bifurcation points, and follow the branches emanating from those bifurcation points. On branches of periodic orbits, it can identify period-doubling bifurcation points and follow branches emanating from them. Therefore, one can obtain a complete picture of both steady-state and periodic bifurcation characteristics of the dynamic systems. In Figure 19, steady-state branches are exhibited as lines and periodic branches as circles. Solid lines and circles demark asymptotically stable orbits (as determined by a local eigenvalue analysis at steady state and by

Chapter 10

378

9 (hr)

0.0

Figure 18. Steady-state profiles of monomer conversion (Xx) and number-average polymer chain length (XN) in a continuous-flow stirred-tank styrene polymerization reactor: B, unsymmetrical bifunctional initiator; Al, A2, monofunctional initiators.

0.8

0.0

XA.-0.4

1.0 8(hr)

0.0

0.2

0.4

0.6

08

y u - 0.690

o.o

VAI-1-0

y.,= 0.8

r

i

(

1

1.0 8{hr)

^

J ^

_ _

^

2.0

0

Figure 19. Steady-state profiles of monomer conversion in solution polymerization of styrene in a CSTR: (i), period-doubling bifurcation point; (ii), second period-doubling bifurcation point; (iii), homoclinic bifurcation point.

0.0

0.2

0.4

0.6

0.0 1.0

0.2

0.2

0.0 1.0

0.4

0.6

0.4

06

0.8

0.2

08

O unstable lima cycle

0.4

0.0 1.0

yyw-0 2

Hop! bifurcation point

stable limit cyde

•

•

0.0 1.0

0.2

0.4

0.6

stable steady state unstable Heady slate

06

—

1.0 0.8

vo

0.8

380

Chapter 10

Floquet exponents at periodic orbits), and dashed lines and open circles demark unstable solutions. For any periodic orbit, the maximum value on that orbit is exhibited. Notice in Figure 19 that as the content of the initiator A in the initiator feed mixture (yAf) is increased, oscillatory dynamics and isolated solution branches (isola) appear. It is also seen that period-doubling bifurcation (i), second period-doubling bifurcation (ii), and homoclinic bifurcation (iii) occur as yAf\% increased. In Figure 19c for yAf = 0.4, two Hopf bifurcation points connected by stable periodic branches are present. As yAf is increased to 0.5, these branches become disconnected and they terminate in homoclinic orbits. For this value ofyAf, all the orbits on the right periodic branches are stable. The left branch bifurcates almost vertically, either subcritically (to the left) and orbits near the left Hopf bifurcation point are unstable, or else supercritically, but switches back to the right, and stability is gained. There is then a period-doubling bifurcation point. The periodic branch loses its stability, and a second periodic branch bifurcates from it. Orbits on this branch have period about twice that of those on the first periodic branch. This branch also terminates in an unstable homoclinic. Figure 20 shows phase-plane portraits of the bifurcation phenomena such as Hopf bifurcation, period-doubling limit cycles, and homoclinic limit cycles. These figures represent the reactor transients to the pulse disturbance in yAf during steady-state operation of the reactor with yAf = 0.5 at each bifurcation point. Figure 20a exhibits a limit cycle on the left periodic branch of Figure 19d. The value of 0 is set near the value at the left Hopf point (i). The orbit is a small-amplitude oscillation around the steady-state value. In Figure 20b, an approximation to a homoclinic orbit is shown. The system relaxes to a very long-period orbit. Along the branch of periodic orbits, the period is unbounded, and the limiting orbit is asymptotic in both forward and backward times to an unstable stationary point. The times between the spikes in Figure 20b 1 becomes infinite in the limit. The unstable stationary point is approximately at the lower left of the trajectories in Figure 20b2. The system spends most of its time near that point, making quick excursions through the rest of its orbit. With a further increase in yAf, the isola appears as a breaking-off of a portion of the steady-state branch. At a slightly larger value of yAf, the right periodic branch reattaches to the steady-state branch (Figure 19g). As yAfis increased further, the two Hopf points come closer together, the period-doubling behavior collapses and disappears, and finally, the two Hopf points coalesce and the period branch itself disappears (Figure 19h). Eventually, at yAf = 0.8, the steady-state branch straightens out and loses its saddle-node switchback. The example above illustrates how the reactor dynamics can be affected by the presence of more than one initiator in the reactor. Although not

381

Modeling of Polymerization Processes

~ pufso in y A | : 0.525 for 30 min i

407 0.850

0.860

°0.25

.

.

i

I

0.50

i

i

•

.

0.75

1.00

450

500

800

478

600 —

X n 476 400 — 474

iHopf bifurcating limit cycle

407

408

T(°K)

409

410

200,

350

400

T(°K)

Figure 20. Transient response and phase-plane portraits to the pulse disturbance in the initiator feed composition during the steady-state operation of styrene polymerization reactor with mixed initiator: a = 210.5, fs = 0.1, If = 0.025 mol/L, yAf = 0.5, 7} = 343 K, Tc = 363 K.

shown, polymer molecular weight properties are also affected by the variations in the feed initiator composition. When more than one reactor is used for continuous polymerization, the second reactor dynamics are more complex and strongly dependent on the dynamic behavior of the first reactor. Figure 21 illustrates the bifurcation diagrams for the second reactor (V2 = v^) with yAf (initiator A mole fraction in the feed to the first reactor) = 0.5. Note that up to five steady states are present for a certain range of reactor residence time. The overall qualitative bifurcation behavior is

Chapter 10

382

quite similar to that shown in Figure 19 for a single reactor system. There is one pair of Hopf bifurcation points and the branches of periodic orbits are disconnected and they terminate in homoclinics (point iii), where the period of orbits becomes unbounded. Figure 21 shows that the amplitudes of oscillations in monomer conversion (X12) on the periodic branches are quite small; however, the initiator concentrations, the number-average degree of polymerization (Xn2), and the polydispersity (PD2) oscillate with much larger amplitudes. Figure 22 shows the transient behavior of the two reactors when the initiator feed composition is changed from 0.5 to 0.35 (30% less slow initiator in the feed). The first reactor moves smoothly toward a new stable steady state in less than 3 h; however, the second reactor, after about 17 h, runs away to upper unstable steady state in an oscillatory manner. The

1.0 0.8 0.6 0.4 0.2 0.0

x10'

r ,

| a

= 0.5, v =1.0

v.....--.. / /

• •

o

Hopl bifurcation stable limit cycle unstable cycle

1.25 1.00 0.75

(mol/l) Q.50 0.25 0.00

stable steady state unstable steady state

x10';

9(hr)

Figure 21. Bifurcation diagrams for the second reactor: yAf = 0.5, bx and 52 = 0.058 (i, period doubling; ii, second period doubling; iii, homoclinic limit cycle).

383

Modeling of Polymerization Processes 0.10

{mot/I)

1.60 t (hr)

Figure 22. Transient response of the two CSTRs to a step change in the initiator feed composition during the steady-state operation: yAf = 0.5, h^ - 0.0, 82 = 0.05, 6 = 1.0 h.

temperature surge is as large as 75°C and the polymer molecular weight varies with a large amplitude of oscillation. Such a reactor behavior, as illustrated in Figure 22, can lead to a potentially very dangerous situation. More details of reactor dynamics under other operating conditions can be found from [59,60]. Although only a few examples were shown in the above,

Chapter 10

384

it is now clear that understanding nonlinear reactor dynamics through modeling and analysis will be very important in designing stable reactor controls. IV.

CONCLUDING REMARKS

In this chapter an attempt has been made to illustrate polymerization reactor modeling techniques for a few selected polymerization systems. As shown in various examples presented, mathematical modeling is a powerful tool in developing an improved understanding of both microscopic and macroscopic phenomena in polymerization processes. In transition metalcatalyzed olefin polymerization processees, it is crucial to understand not only the catalytic reaction mechanisms and kinetics but also complex physical transport phenomena that affect the reaction rate and resulting polymer properties. When more than one type of active sites are present in the solid phase, the reaction kinetics become extremely complicated and estimating relevant kinetic parameters is a quite formidable task. Continuous olefin polymerization reactors may also exhibit strongly nonlinear dynamic behaviors, which must be fully understood in designing reactor controls. The discussion of free-radical polymerization process modeling has been limited to the systems where nonconventional inititators such as bifunctional initiators and mixed monofunctional initiators are used. A primary incentive for using such initiator systems is to better control radical concentrations and resulting polymer properties without major modification of existing polymerization process facility. It has been illustrated that the presence of an additional labile group in the bifunctional initiator significantly increases the degree of complexity of reaction kinetics. The molecular species modeling approach has been used to quantify the reaction kinetics. There are some reports on the use of polyfunctional initiators in the literature; however, no quantitative modeling that includes various reactions involved and associated physical changes during the polymerization has yet been reported. Also presented in this chapter are some examples of continuous polymerization reactor dynamics. There are many process parameters that may cause reactor instability, oscillations, and parametric sensitivity. In view of the fact that these continuous reactors are used to produce polymers in large quantity, it is of significant importance to develop a quantitative understanding of steady-state and transient reactor behaviors for a wide range of reactor operating conditions and avoid undesirable reactor dynamics. Finally, it should be pointed out that detailed reactor models are becoming more important in designing on-line process estimation and control systems for accurate on-line control of polymer properties.

Modeling of Polymerization Processes

385

REFERENCES

1.

Choi, K. Y., and Ray, W. H. (1985). Recent developments in transition metal catalyzed olefin polymerization: a survey. I. Ethylene polymerization, J. MacromoL Sci. Rev. Macromol. Chem. Phys., C25(l), 1. 2. Choi, K. Y., and Ray, W. H. (1985). Recent developments in transition metal catalyzed olefin polymerization: a survey. II. Propylene polymerization, J. MacromoL Sci. Rev. MacromoL Chem. Phys., C25(l), 57. 3. Kissin, Y. V. (1985). Isospecific Polymerization of Olefins, SpringerVerlag, New York. 4. Karol, F. J. (1985). Studies with high activity catalysts for olefin polymerization, CataL Rev. Sci. Eng., 26(3-4), 557. 5. Hsieh, H. L. (1984). Olefin polymerization catalysis technology, CataL Rev. Sci. Eng., 26(3-4), 631. 6. McDaniel, M. P. (1985). Supported chromium catalysts for ethylene polymerization, Adv. CataL, 33, 47. 7. Barbe, P. C , Cecchin, G., andNoristi, L. (1987). The catalytic system Ti-complex/MgCl2, Adv. Polym. Sci., 81, 1. 8. Seppala, J. V., and Auer, M. (1990). Factors affecting kinetics in slurry type coordination polymerization, Prog. Polym. Sci., 15, 147. 9. Pino, P., and Rotzinger, B. (1984). Recent developments in the polymerization of olefins with organometallic catalysts, Makromol. Chem. SuppL, 7, 41. 10. Nowlin, T. E. (1985). Low pressure manufacture of polyethylene, Prog. Polym. Sci., 11, 29. 11. Taylor, T. W., Choi, K. Y., Yuan, H., and Ray, W. H. (1983). Physicochemical kinetics of liquid phase propylene polymerization, in Transition Metal Catalyzed Polymerizations, R. P. Quirk, ed.? Harwood Academic Publishers, New York, p. 191. 12. Kakugo, M., Sadatoshi, H., and Sakai, J. (1989). Morphology of nascent polypropylene produced by MgCl2 supported Ti catalyst, presented at the International Symposium on Research and Development in Olefin Polymer Catalyst, Tokyo, October 23-25. 13. Kakugo, M., Sadatoshi, H., Yokoyama, M., and Kojima, K. (1989). Transmission electron microscopic observation of nascent polypropylene particles using a new staining method, Macromolecules, 22, 547. 14. Kakugo, M., Sadatoshi, H., Sakai, J., and Yokoyama, M. (1989). Growth of polypropylene particles in heterogenous Ziegler-Natta polymerization, Macromolecules, 22, 3172.

386

Chapter 10

15. Choi, K. Y. (1984). The reaction kinetics, modeling and control of solid catalyzed gas phase olefin polymerization reactors, Ph.D. thesis, University of Wisconsin-Madison. 16. Nagel, E. J., Kirillov, V. A., and Ray, W. H. (1980). Prediction of molecular weight distributions for high-density polyolefins, Ind. Eng. Chem. Prod. Res. Develop., 19, 372. 17. Floyd, S., Choi, K. Y., Taylor, T. W., and Ray, W. H. (1986). Polymerization of olefins through heterogeneous catalysis. III. Polymer particle modeling with an analysis of intraparticle heat and mass transfer effects, /. AppL Polym. Sci., 32, 2935. 18. Floyd, S., Choi, K. Y., Taylor, T. W., and Ray, W. H. (1986). Polymerization of olefins through heterogeneous catalysis. IV. Modeling of heat and mass transfer resistance in the polymer particle boundary layer, J. AppL Poly. Sci., 31, 2231. 19. Floyd, S., Heiskanen, T., and Ray, W. H. (1988). Solid catalyzed olefin polymerization, Chem. Eng. Prog., November, p. 56. 20. de Carvalho, A. B., Gloor, P. E., and Hamielec, A. E. (1989). A kinetic mathematical model for heterogeneous Ziegler-Natta copolymerization, Polymer, 30, 280. 21. de Carvalho, A. B., Gloor, P. E., and Hamielec, A. E. (1990). A kinetic model for heterogeneous Ziegler-Natta (co)polymerization. 2. Stereochemical sequence length distributions, Polymer, 31, 1294. 22. Hutchinson, R. A., and Ray, W. H. (1990). Polymerization of olefins through heterogeneous catalysis. VIII. Monomer sorption effect, /. AppL Polym. Set., 41, 51. 23. Short, J. N. (1983). Low pressure ethylene polymerization processes, in Transition Metal Catalyzed Polymerizations, R. P. Quirk, ed., Harwood Academic Publishers, New York, p. 651. 24. Brockmeier, N. F. (1983). Latest commercial technology for propylene polymerization, in Transition Metal Catalyzed Polymerizations, R. P. Quirk, ed., Harwood Academic Publishers, New York, p. 671. 25. Ray, W. H. (1988). Some issues in the design and control of copolymerization processes, presented at the AIChE Meeting, Washington, D.C. 26. Choi, K. Y. (1989). Overview of polymerization reactor technology, in Handbook of Polymer Science and Technology, N. P. Cheremisinoff, ed., Vol. 1, Marcel Dekker, New York, p. 67. 27. Choi, K. Y., and Ray, W. H. (1985). The dynamic behavior of fluidized bed reactors for solid catalyzed gas phase olefin polymerization, Chem. Eng. Sci., 40(12), 2261. 28. Choi, K. Y. and Ray, W. H. (1988). The dynamic behavior of con-

Modeling of Polymerization Processes

29. 30.

31. 32. 33. 34. 35.

36.

37. 38. 39. 40.

387

tinuous stirred bed reactors for the solid catalyzed gas phase polymerization of propylene, Chem. Eng. Sci., 43(10), 2587. Ferrero, M. A., and Chiovetta, M. G. (1990). Preliminary design of a loop reactor for bulk propylene polymerization, Polym. Plast. Technol Eng., 29(3), 263. Brockmeier, N. F., and Lin, C. H. (1979). Continuous gas phase polymerization of propylene: relationship between residence time and particle size distribution, presented at the AIChE Meeting, April, Houston, Tex. Brockmeier, N. F., and Lin, C. H. (1979). Continuous gas phase polymerization kinetics in gas phase reactors using titanium trichloride catalyst, ACS Symp. Ser., 104, 201. Kaminsky, W. (1988). Stereocontrol with new soluble catalysts, in Transition Metal Catalyzed Polymerizations, R. P. Quirk, ed., Cambridge University Press, Cambridge, p. 37. Sinn, H., and Kaminsky, W. (1980). Ziegler-Natta catalysis, Adv. Organomet. Chem., 18, 99. Ewen, J. S. (1984). Mechanisms of stereochemical control in propylene polymerizations with soluble group 4B metallocene/methyalumoxane catalysts, /. Am. Chem. Soc, 106, 6355. Kaminsky, W., and Buschermdhle, M. (1987). Stereospecific polymerization of olefins with homogeneous catalysts, in Recent Advances in Mechanistic and Synthetic Aspects of Polymerization, F. Fontanille and A. Guyot, eds., D. Reidel, Dordrecht, The Netherlands, p. 503. Giannetti, E., Ninoletti, G. M., and Mazzocchi, R. (1985). Homogeneous Ziegler-Natta catalysis. II. Ethylene polymerization by IVB transition metal complexes/methyl aluminoxane catalyst systems, J. Polym. Sci. Polym. Chem. Ed., 23, 2117. Reichert, K. H., and Meyer, K. R. (1973). Zur Kinetik der Niederdruckpolymerisation von Athylene mit loslichen Ziegler-Katalysatoren, Makromol. Chem., 169, 163. Cihlav, J., Mejzlik, J., and Hamrik, O. (1978). Influence of water on ethylene polymerization catalyzed by titanocene systems, Makromol. Chem., 179,2553. Kaminsky, W., Kulper, K., and Niedoba, S. (1986). Olefin polymerization with highly active soluble zirconium compounds using aluminoxane as cocatalyst, Makromol. Chem. Makromol. Symp., 3, 377. Kaminsky, W. (1983). Polymerization and copolymerization with a highly active, soluble Ziegler-Natta catalyst, in Transition Metal Catalyzed Polymerizations, R. P. Quirk, ed., Harwood Academic Publishers, New York, p. 225.

388 41. 42. 43. 44. 45. 46.

47. 48. 49. 50. 51. 52. 53. 54. 55.

Chapter 10 Choi, K. Y. (1985). Control of molecular weight distribution of polyethylene in continuous stirred tank reactors with high activity soluble Ziegler-type catalysts, J. Appl Polym. Sci., 30, 2707. Kim, K. J., and Choi, K. Y. (1991). Continuous olefin copolymerization with soluble Ziegler-Natta catalysts, AIChE J., 37(8), 1255. Ray, W. H. (1972). On the mathematical modeling of polymerization reactors,/. Macromol. Sci. Rev. Macromol. Chem., C8(l), 1. Piirma, I., and Chou, L. P. H. (1979). Block copolymers obtained by free radical mechanism. I. Methyl methacrylate and styrene, /. Appl Polym. Sci., 24, 2051. Gunesin, B. Z., and Piirma, I. (1981). Block copolymers obtained by free radical mechanism. II. Butyl acrylate and methyl methacrylate, /. Appl Polym. Sci., 26,3103. Zherebin, Y. L., Ivanchev, S. S., and Domareva, N. M. (1974). Preparation of block copolymers using oligoperoxide initiators containing peroxide groups of different heat stabilities, Polym. Sci. USSR, 16(4), 1033. Oppenheimer, C , and Heitz, W. (1981). The synthesis of block copolymers by radical polymerization, Angew. Makromol Chem., 98, 167. Kim, K. J., and Choi, K. Y. (1989). Modeling of free radical polymerization of sytrene catalyzed by unsymmetrical bifunctional initiators, Chem. Eng. Sci., 44(2), 297. Choi, K. Y., and Lei, G. D. (1987). Modeling of free radical polymerization of styrene by bifunctional initiators, AIChE J., 33(12), 2067. Choi, K. Y., Liang, W., and Lei, G. D. (1988). Kinetics of bulk styrene polymerization catalyzed by symmetrical bifunctional initiators, /. Appl Polym. Sci., 35, 1547. Kim, K. J., Liang, W., and Choi, K. Y. (1989). Bulk free radical polymerization of styrene with unsymmetrical bifunctional initiators, Ind. Eng. Chem. Res., 28, 131. Ivanchev, S. S. (1979). New views on initiation of radical polymerization in homogeneous and heterogeneous system: Review, Polym. Sci USSR, 20, 2157. Walz, R., Bomer, B., and Heitz, W. (1977). Monomeric and polymeric azoinitiators, Makromol Chem., 178, 2527. Simionescu, C , Kim, G. S., Comanita, E., and Dumitriu, S. (1984). Bifunctional initiators, Eur. Polym. J., 20(5), 467. Simionescu, C , Comanita, E., Pastravanu, M., and Dumitriu, S. (1986). Progress in the field of bifunctional and polyfunctional free radical polymerization initiators, Prog. Polym. Sci., 12, 1.

Modeling of Polymerization Processes

56.

57. 58. 59. 60.

389

Prisyazhnyuk, A. I., and Ivanchev, S. S. (1970). Diperoxides with differing thermal stabilities of the peroxide groups as initiators of radical polymerization and block copolymerization, Polym. Sci. USSR, 12, 514. Kim, K. J., and Choi, K. Y. (1988). Steady state behavior of a continuous stirred tank reactor for styrene polymerization with bifunctional free radical initiators, Chem. Eng. Sci.7 43(4), 965. Doedel, E. J. (1986). Auto: Software for Continuation and Bifurcation Problems in Ordinary Differential Equations, California Institute of Technology, Pasadena, Calif. Kim, K. J., Choi, K. Y., and Alexander, J. C. (1990). Dynamics of a CSTR for styrene polymerization initiated by a binary initiator system, Polym. Eng. Sci., 30(5), 279. Kim, K. J., Choi, K. Y., and Alexander, J. C (1991). Dynamics of a cascade of two continuous stirred tank polymerization reactors with a binary initiator mixture, Polym. Eng. Sci., 31(5), 333.

11

Impact of Wetting on Catalyst Performance in Multiphase Reaction Systems

Michael P. Harold Massachusetts

I.

University of Massachusetts, Amherst,

INTRODUCTION

An important class of catalytic reactions involve gas and liquid components (i.e., multiphase catalytic reactions). Table 1 lists some of the many types of multiphase reactions carried out in the petroleum and chemical industries [1-6]. Most involve reaction between highly volatile (e.g., hydrogen, oxygen) and less volatile species (e.g., olefins, sulfur- and nitrogen-containing hydrocarbons) and are of the general form A(g) + D(g) O products(g)

T|

t i

Tj

A(/) 4- D (/) O products(/) This form emphasizes that reaction may occur as a gas- or liquid-phase catalytic reaction due to vaporization, condensation, solution, and dissolution processes. Multiphase catalysts span the spectrum from supported noble metals used for olefin hydrogenation [1-12,18-37], to multicomponent metal oxides used for hydrodesulfurization [1,3,7-9,12-17], to supported noble metal complexes used for hydroformylation and carbonylation [38-40]. Both economic factors (e.g., energy costs) and chemical considerations (e.g., boiling points of the reactants and products, liquid reactant stability, catalyst durability) determine if a particular reaction should be 391

Chapter 11

392

Table 1 Some Industrially Important Multiphase Catalytic Reactions Liquid reactant (or reaction medium)

Gaseous reactant

Product(s)

Petroleum Processing Sulfur-containing species

Hydrogen

Desulfurized compounds,

Nitrogen-containing species

Hydrogen

Denitrogenated compounds,

Long-chain paraffins Acetylinic species

Hydrogen Hydrogen

Short-chain alkane products Olefins

H2S

NH 3

Chemicals Production Olefins Esters Carboxylic acids Aldehydes, ketones Aromatics Solvent Water Solvent

Hydrogen Hydrogen Hydrogen Hydrogen Hydrogen Olefins, oxygen SO2, oxygen CO,H 2

Hydrogenated species Alcohols Alcohols Alcohols Saturated cyclic species Partial oxidation species Sulfuric acid Methanol

Food Processing Unsaturated fatty oils

Hydrogen

Sugars

Hydrogen

Partially or fully saturated species Polyols

carried out in a multiphase rather than a purely gas-phase environment [1,8]. Many types of multiphase catalytic reactors are used in industry. Several reviews have classified the various types of multiphase reactors and have discussed their respective advantages and disadvantages [1,5,6,8,11,12]. The reactors can be classified in various ways, such as whether the solid moves or remains stationary, or whether the continuous fluid phase is the gas or the liquid. The presence of both gas and liquid phases makes the design of multiphase catalysts and reactors inherently more difficult than that of their single-phase counterparts. The principal complication is the multiphase hydrodynamics. Understanding the hydrodynamics is essential, as the nature of the contacting of the two phases with the solid catalyst

Impact of Wetting on Catalyst Performance

393

can have a significant impact on the mass and heat transport processes, and hence on the catalyst performance. In single fluid-phase catalytic systems one can assess the influence of diffusional limitations with the use of well-established tests and criteria [2,62,63]. On the other hand, with the possible exception of reaction on finely divided catalyst in a stirred threephase (slurry) reactor, evaluation of transport-reaction interactions in multiphase reactors is a nontrivial task. The main reason is that the catalyst may be only partially contacted (wetted) by the liquid on its surface or within its pores. Transport and reaction occurs in both phases. Moreover, the rate of reaction, the extent of wetting, and the spatial distribution of the two phases are interdependent variables. The focus of this chapter is on catalyst performance in the various types of multiphase environments that are encountered in the reactors. We are not so much interested in the reactor type but in the local interactions between the reaction and multiphase transport processes. This focus demands a classification that is based on the features of the local state of the multiphase catalyst. In the next section we identify eight states which differ from one another by virtue of the existence and location of the liquid and gas phases. Depending on the reactor type, one or more of these states may be relevant. The main premise of this approach is that it provides a starting point for rationally evaluating multiphase catalysts under the local conditions expected in a particular reactor. It also provides a framework for multiphase catalytic reactor analysis and design based on detailed treatment of crucial local phenomena. The success of this approach relies on a synergism between experiments and modeling focused at the local level. This chapter is organized as follows. In Section II eight states of the multiphase catalyst are classified and described. Whenever possible, experimental observations are highlighted which serve to identify the reactor type(s) and conditions for which each state is expected to occur. The observations also illustrate typical catalyst behavior in each state. In Section III some dynamic phenomena are discussed which underscore features of some of the key reaction-transport interactions. In Section IV we review the current state of mathematical models in simulating the performance of catalysts in the different states. Results of recently developed models are described which help to elucidate previous observations of multiphase catalyst performance. In Section V two models are described which illustrate how a detailed picture of local events can form the basis for simulating an entire reactor. Described in Section VI are recent attempts of exploiting the improved understanding of multiphase reaction-transport interactions in the development of new multiphase catalysts and reactors. Finally, in Section VII some remarks are made about future directions.

Chapter 11

394 II.

STEADY STATES OF THE CATALYTIC PELLET IN MULTIPHASE ENVIRONMENTS

1.

Different States of the Catalytic Pellet: Identification

Catalytic pellets in the multiphase reactor may be exposed to a number of different environments. Figure 1 depicts eight, qualitatively different states of a pellet: State 1: pellets that are completely wetted both externally and internally by the liquid phase State 2: pellets that are entirely devoid of liquid both externally and internally State 3: pellets that are partially wetted externally by a single film or rivulet and have void volumes that are completely filled with liquid State 4: pellets that are partially wetted externally by two or more films or rivulets and have void volumes that are completely filled with liquid State 5: pellets that are completely contacted on the external surface by liquid but which have pores that are partially filled with gas due to vaporization State 6: pellets that are not wetted on the external surface but that are partially filled with liquid due to capillary condensation State 7: pellets that are partially wetted externally and are flooded with liquid in a fraction of the void volume while the remaining pores are filled with gas State 8: pellets that are partially wetted externally and have void volumes containing of both gas and liquid More states could be added to this list of eight if more detailed descriptions are desired. However, the eight identified states have combinations

Liquid film or rivulet Capillary condensation Liquid-filled pores Partially-filled pores

Figure 1. Eight different identified states of the catalyst pellet in multiphase reactors.

Impact of Wetting on Catalyst Performance

395

of features that cover most situations in multiphase reactors. A large number of factors determine which of the states are encountered within the the reactor. These include (1) the bulk conditions, (2) the component properties, (3) the reaction characteristics, (4) the catalyst properties, and (5) the reactor features. A summary of these factors with examples of each is provided in Figure 2. The eight states are not restricted to a single multiphase reactor type. However, all are encountered in the commonly used multiphase fixed- or trickle-bed reactor. A brief review of the flow features in this reactor is helpful in identifying the hydrodynamic factors that contribute to the formation of the different local environments within the reactor. 2.

Multiphase Flow Features in the Trickle-Bed Reactor

The trickle-bed reactor can operate in several flow modes, including cocurrent downflow, cocurrent upflow, or countercurrent flow (with liquid downflow). We discuss here the most common of these, the cocurrent downflow mode. The hydrodynamics and transport features of the cocurrent downflow trickle-bed reactor have been the subject of a large number of studies, as summarized in a number of reviews, monographs, and other key papers [1,5,7,11,14,28,41,52,55,60,64-98]. The flow type that is encountered depends on the relative magnitudes of the gas and liquid fluxes. The flow types are partially wetted trickling flow, fully wetted trickling

BULK CONDITIONS Flow rate v Composition Temperature Total Pressure

,x

,.

Gas

\

..

Liquid

REACTION CHARACTERISTICS Intrinsic kinetics of reaction

/

Heat

^ /

State of the

Catalytic Pellet

COMPONENT PROPERTIES

mornhnim.v.

CATALYST PROPERTIES

/

Vapor-liquid equilibrium Transport parameters

^"L^L*^

\

Heat exchange

I1™ distributor

Bed

p r0SltV ° REACTOR FEATURES

Figure 2. Factors that determine the state of the catalyst pellet in the multiphase reactor.

396

Chapter 11

flow, spray flow, foaming flow, foaming/pulsing flow, bubble flow, and pulsing flow. In Table 2 the relative gas and liquid flow rates for which each flow type is encountered are listed. The exact locations of the transitions between each flow type depend on the packing features and the liquid and gas physical properties. A major focus of previous trickle-bed studies has been on prediction of transport variables, such as pressure drop, static and dynamic liquid holdup, contacting efficiency, dispersion, and transport coefficients. These variables have a significant effect on reactor performance. This is especially true for exothermic reactions which are rate-limited by transport processes. Of pertinence to this chapter are the fine features encountered at the local level in the trickling flow regime. The liquid contacts the catalyst in several different forms; these include films, rivulets, filaments, drops, pockets, and pendular structures. The liquid distributor design, the pellet size and shape, and the flow rates of each stream all affect the degree of wetting. Any given catalyst particle may be completely wetted on its external surface (states 1 and 5 in Figure 1), completely nonwetted (states 2 and 6), or partially wetted by one or more liquid forms (states 3,4,7, and 8). Complete wetting is encountered within the bed if the liquid flux is sufficiently large and the liquid feed is well distributed. Complete nonwetting results from a poorly distributed feed or from liquid-phase evaporation. Partial external wetting may occur for the same reasons. It may also occur if the liquid flux is simply insufficient to wet the entire external solid surface or if the interfacial tension is too high. In some cases pellets may be contacted by stagnant liquids, and hence are termed inactively wetted. Several correlations have been developed for predicting the extent of contacting in the trickle bed. These are summarized by Dudukovic and Mills [74]. The use Table 2 Flow Types Encountered in the Cocurrent Downflow Trickle-BedReactor

Flow ratea

Flow type

Continuous phase

Liquid

Gas

Partially wetted trickling Fully wetted trickling Spray Foaming Foaming/pulsing Bubble Pulsing

Gas Gas Gas Gas, liquid Gas, liquid Liquid Gas, liquid

VL L L H H H H

L-I L-I H L I I-H H

a

VL, very low; L, low; I, intermediate; H, high.

Impact of Wetting on Catalyst Performance

397

of these correlations in analyzing reactor performance data is discussed later. Notably, several recent studies have experimentally characterized local flow structure and transitions in the different macroscopic flow regimes under nonreaction conditions. Christensen et al. [68] observed pressuredrop hysteresis during cocurrent downflow of air and water through a bed of rectangular cross section containing nonporous particles. Visualization of the liquid flow near the transparent walls indicated that two qualitatively different flows, film and filament, correspond to the multiple hydrodynamic states. Lutran et al. [83] used tomography to characterize liquid (water) structure and flow in a circular cross-section column. The gas (air) was quiescent in the experiments. The existence of a given flow pattern was shown to depend on the flow history; (e.g., whether or not a bed is prewetted). In general, film flow occurs in a prewetted bed, whereas filament flow occurs in initially dry beds. These findings appear to corroborate the observations of Christensen et al. [68]. Moreover, film flow predominated in a bed with larger particles. A plausible explanation is the inability of the liquid to span the wider-pore throats. Finally, Melli et al. [85] have used visualization to identify four microscale flow regimes during cocurrent downflow in a two-dimensional, unconnected network. Their observations indicate that the various macroscopic flows have "microscale roots/' which are a consequence of the local competition between the gas and liquid for the void space. Recent theoretical work has also focused on the link between the microscale and the macroscale, and of stability analysis of macroscopic flow models. Ng [87] derived several criteria from microscale pictures which predict the transitions between the different flow regimes. For example, one criterion predicts the transition between partial and complete wetting in the trickling flow regime. The criterion applies the dry patch model of Hartley and Murgatroyd [99], which predicts the critical liquid film flow rate per perimeter length of wetted planar surface above which complete wetting occurs. The available perimeter in a reactor cross section is calculated given the bed porosity and spherical particle size. The criterion shows good agreement with the data of Gianetto et al. [76], who located the transition experimentally. Grosser et al. [77] performed a linear stability analysis of a macroscopic two-phase flow model which is based on a relative permeability formulation. The loss of stability of the steady-state solution was identified as the transition from trickling to pulsing flow. Good agreement was found between the Grosser et al. model and experiments of others. Finally, de Santos et al. [72] have developed a microscale flow theory to predict the observations of Melli et al. [85].

398 3.

Chapter 11 Different States of the Catalytic Pellet: Classification and Experimental Observations

Next, the eight states encountered in multiphase reactors are described in more detail. The reactor types and conditions for which each state is typically encountered are identified. Given that some of the states are more complex than others, the current level of understanding of each is also assessed. In Section IV several mathematical models and simulation results are described which help to elucidate the performance of catalysts that exist in the more complex states 3 to 8. A.

Pellets in Contact With a Single Phase (States 1 and 2)

Catalytic pellets in state 1 (completely wetted and liquid filled) are encountered in all of the liquid-continuous multiphase reactors and in several flow regimes of the fixed-bed reactor. Reactants supplied from the bulk liquid diffuse through the pores to the catalytic sites where they react. Reaction products traverse the reverse path. Unless the reaction is sufficiently exothermic or the reactants and/or products are sufficiently volatile, the combination of the strong capillary forces and effective heat removal by the flowing liquid results in a pellet that is completely liquid filled and isothermal. State 1, like state 2 below, is well understood. A distinguishing feature of reactions in liquid-filled catalysts is their propensity to be rate limited by the pore diffusion process. For example, for hydrodesulfurization reactions in cobalt-molybdate catalysts, diffusion limitations can be severe despite the comparatively low catalytic activity because of the low diffusivities (10 ~7 to 10~9cm2/s) of the sulfur-containing species [3,13,101]. To illustrate, Figure 3 shows the data of Papayannakos and Marangozis [13], who measured the dependence of catalyst effectiveness (TJ) on a generalized Thiele modulus for the hydrodesulfurization of a petroleum residuum in a fully wetted and completely filled commercial cobalt-molybdate catalyst. The data reveal that only for the particles of 0.34 mm diameter are pore diffusion limitations eliminated (i.e., t] —> 1). Catalytic pellets in state 2 (completely dry externally and internally) are encountered within dry zones of the multiphase reactor. Two mechanisms lead to dry zones in the multiphase fixed-bed reactor, for example. First, liquid channeling and poorly designed liquid distributors prevent the contacting of all the pellets in the reactor. If the liquid reactant is nonvolatile, the local rate on nonwetted pellets is obviously zero. This clearly provides an incentive for designing effective liquid distributors. Second, if the reaction is sufficiently exothermic and the liquid reactant has a finite volatility, reaction may occur in catalyst pellets that are entirely devoid of liquid.

Impact of Wetting on Catalyst Performance

399

a>

Thiele Modulus Figure 3. Measured dependence of catalyst effectiveness on the Thiele modulus for the hydrodesulfurization of petroleum residua on a commercial cobalt-molybdate catalyst. Solid circle, 0.34-mm-diameter particles; open circles, iWn.-diameter extrudates; open triangles, Hn.-diameter extrudates; open squares, data of de Bruijn et al. [15]. (From Ref. 13.)

State 2 is distinguished from state 6 described below. In state 6 partial pore filling of the smallest pores may occur in the externally nonwetted pellet because of condensation of a less volatile reactant or product. As is the case for state 1 pellets, state 2 pellets are in a single-phase, essentially uniform environment. The reader is referred to the large number of books and monographs that treat isothermal diffusion and reaction interactions in this more conventional situation (e.g., Refs 2,63, and 100, and references within). However, there is an important difference between states 1 and 2: rates, and temperatures are typically higher in gas-filled catalysts. There are two primary reasons. First, mass transport is more rapid in gas-filled pores than in liquid-filled pores. This can lead to higher rates. Second, exothermic reaction heat is removed much less effectively by a flowing gas than by a flowing liquid external to the catalyst. The higher rates and temperatures make reaction in gas-filled pellets particularly dangerous in the multiphase reactor. Such a gas-phase reaction may be sustained in a section of the reactor that is devoid of the liquid stream. This hot spot is undesirable because of the possible initiation of side reactions and destruction of the catalyst. Of crucial importance is the potential for the deleterious reactor runaway [102,103], a situation in which a localized hot spot may

400

Chapter 11

grow unchecked by a gradual consumption (vaporization) of the liquid reactant. This is another incentive for achieving good liquid distribution. Experiments carried out by Hanika et al. [24,25] illustrate some of these points. The hydrogenation of the volatile cyclohexene (normal boiling point = 83°C) was carried out in a lab-scale fixed bed of 3% Pd on activated carbon cylindrical pellets. Figure 4 shows the dimensionless axial temperature (0; normalized by feed temperature, Tf) profile for three different feed temperatures. The liquid feed consisted of 12 wt% cyclohexene in cyclohexane. The hydrogen gas flow rate was maintained at a value of 11 times the stoichiometric requirement (i.e., JV = 11, where N = H2 gas molar flow rate/cyclohexene liquid molar flow rate). For the lowest feed temperature (290 K) there is a negligible temperature rise. A much higher temperature rise is evident at higher feed temperatures. The sharp increase in the temperature in the latter cases to levels exceeding the normal boiling points of cyclohexene and cyclohexane provides evidence of a phase transition within the reactor. The simplest explanation is that there is an abrupt depletion of the liquid phase within the reactor. This implies the coexistence of pellets in state 1 upstream of a phase transition point and state 2 pellets downstream of this point. Figure 5 shows that a counterclockwise hysteresis dependence of the cyclohexene conversion on the hydrogen gas flow rate was observed for a 35 wt% cyclohexene feed. (The points are measurements

1.17

0.5

1

Distance from Inlet

Figure 4. Axial temperature profiles observed during cyclohexene hydrogenation on a Pd/charcoal catalyst in a lab-scale trickle-bed reactor for three different feed (gas and liquid) temperatures. The open circles correspond to a 290-K feed, the half-open circles to a 325-K feed, and the closed circles to a 364-K feed. Other conditions: N hydrogen molar gas flow rate/cyclohexene molar liquid flow rate = 11, 12 wt% cyclohexene in cyclohexane liquid feed. (From Ref. 25.)

Impact of Wetting on Catalyst Performance

401

1.0 Dry catalyst

^ - Data •

0.8"

o u

*

\ \

0.6-

VLE Model

0.2

HYDROGEN FED/CYCLOHEXENE FED,

N

Figure 5. Observed (points) and predicted (solid lines) dependence of the cyclohexene conversion on the stoichiometric excess of hydrogen (N). Other conditions: feed temperature = 310 K, 35.5 wt% cyclohexene in cyclohexane liquid feed. (Data are from Hanika et al. [25] and predictions are from the dewetting model described in Section V.B.)

and the lines are predictions of a model described in Section V.B.) Thus the two regimes of the low-temperature liquid-phase catalytic reaction and the high-temperature gas-phase catalytic reaction may overlap for some conditions. The key feature to note at this point is the significantly higher rates and conversions obtained if vaporization occurs. B. Partial Wetting of Completely Filled Pellets (States 3 and 4)

Catalytic pellets in state 3 (completely filled pellet externally partially wetted by single film or rivulet) and state 4 (completely filled pellet externally partially wetted by multiple films or rivulets) are typically encountered within the trickle bed when the liquid flow rate is sufficiently low or reactorscale maldistribution occurs. Multiple rivulets can result from liquid being supplied to the pellet from several higher pellets via the contact points. The key simplifying feature of states 3 and 4 is that the pellet is completely filled with liquid. This feature is not expected to hold for a reaction that is sufficiently exothermic and/or that involves a sufficiently volatile liquid phase (i.e., states 5 to 8 below). The impact of partial external wetting on overall rate has been indirectly estimated in lab-scale trickle-bed reactors. By "indirectly estimated" it is

Chapter 11

402

meant that the standard measure of the extent of wetting, appropriately called the degree of wetting (or contacting efficiency, wetting efficiency), which is the fraction of external catalyst surface contacted by the liquid, is not directly measured under reaction conditions. Several experimental techniques have been used to develop correlations of contacting efficiency on the relevant hydrodynamic parameters (e.g., gas and liquid flow rates) and packing characteristics (e.g., size, shape, porous/nonporous). These are reviewed by Shah [7] and Dudukovic and Mills [74]. The dependence of the contacting efficiency (Ew) on the liquid flow rate (qL) generally follows the form Ew ccqi

n C occurring in a spherical pellet. The gaseous atmosphere surrounding the pellet contains the condensible species A and C and the sparingly soluble (i.e., in condensate) species B. The pellet has an assumed bimodal pore distribution. Intraparticle species transport and reaction occurs in the gas-filled macropores. The key model feature is contained in the vapor-liquid equilibrium relationship. A straightforward application of Kelvin's equation to an ideal multicomponent mixture yields Raoult's law modified by the reduction in vapor pressure in a small pore [145,148]:

where yi(Xi) = species i gas (liquid) mole fraction pT = total pressure pit = pure component vapor pressure of species i 75 = surface tension V( = molar volume of species / 8 = contact angle of the liquid meniscus with an assumed spherical shape R* = critical pore radius Note that p°vi represents the Henry's law constant for sparingly soluble species B. The gaseous transport is handled using the dusty-gas model for the case of negligible bulk viscous flow with an appropriate integration over all pore sizes exceeding/?*. Transport in liquid-filled pores is ignored; the liquid-filled micropores are assumed in local equilibrium with the vapor (i.e., no liquid phase concentration gradients). This, together with the

Impact of Wetting on Catalyst Performance

429

assumption that the reaction is controlled by the surface reaction, guarantees equal gas-phase and liquid-phase reaction rates [145]. Finally, the pellet is assumed isothermal with all heat transport resistance concentrated in an external boundary layer. The model calculations show that the extent of pore filling is a sensitive function of pore-size distribution, gas-phase concentration of condensible species, heat of reaction, and external heat transfer coefficient. As expected, pore filling becomes more significant if the heat of reaction decreases or the heat transfer coefficient increases. The analyses that reveal these trends are restricted to conditions where the pellet temperature rise is not significant (T/TbG < 1.02). The simulations presented reveal that the critical pore size is highest near the pellet surface and decreases monotonically toward the center of the pellet. At a sufficiently low heat of reaction or high concentration of the condensible reactant in the bulk concentration, the pore filling is sufficient to cause a detrimental drop in the effectiveness. Since transport (diffusive or capillary-driven convection) in the liquid-filled pores is ignored, the predicted effectiveness drops to zero. This model feature and the neglect of liquid-phase concentration gradients are probably questionable under such conditions. In the third study, Jaguste and Bhatia [108] demonstrate good agreement between model prediction and the single-pellet experiments of Kim and Kim [105] discussed in Section II.D. The model contains some additional features that help to explain the complex experimental multiplicity features. One key addition differentiates between the shape of the meniscus during vaporization and condensation. During vaporization, the liquid menisci assume a perfect hemispherical shape and the vapor-liquid equilibrium relation follows the Kelvin formulation [Eq. (10)]. However, during condensation the liquid menisci assume a cylindrical shape. As a result, the argument of the exponential term is one-half that in Eq. (11); the result is the Cohan equation [149]. This modification results in a multivalued dependence of the critical pore radius on the pellet temperature (i.e., condensation-evaporation hysteresis). The main impact of the hysteresis is an expansion in the range of parameter values for which the rate is multivalued. A comparison of the data of Kim and Kim [105] with the model fit of Jaguste and Bhatia [108] is shown in Figure 10. The effectiveness was estimated as the actual rate normalized by the rate obtained with a completely gas-filled pellet at the bulk conditions. In their analysis, Jaguste and Bhatia used parameters (transport and kinetic) and conditions provided by Kim and Kim and estimated other physical properties. The tortuosity (T*) is an assumed linear function of the degree of pore filling (eL) [i.e., T* = TL,(1 + 3'€/,), where TV is the tortuosity for a vapor-filled pellet and P' is a constant]. Adjustment of TW, 3 \ and the external film heat transfer

430

Chapter 11

coefficient enabled a good fit of the data. Without describing the details of the model solution, the low branch L'L corresponds to a state where the pellet void volume is about 85% filled with liquid, while the highbranch QST corresponds to a state in which the void volume is completely filled with gas. The two intermediate branches MNV and MBV correspond to a state of incomplete filling of the mesopores. These branches bound a region where the exact path traversed (experimental or numerical) depends on the degree of pore filling. For example, if one starts at point B and proceeds to decrease the hydrogen mole fraction, the dashed path BM is followed. Along this path of decreasing pellet temperature the degree of pore filling remains constant at 75%. Further condensation does not occur until a critical temperature (or hydrogen mole fraction) is reached such that condensate can form with cylindrical menisci in even larger pores (i.e., the critical pore size satisfying the Cohan equation). On the other hand, if one were to begin the decrease in hydrogen mole fraction at another point along the BV branch, a different path would be traversed. The models of Bhatia and co-workers elucidate the complex behavior during exothermic reaction in a pellet with capillary condensation. It is apparent that the impact of this process is expected to be most significant for a pellet with a sufficiently broad (or even bimodal) pore size distribution exposed to a sufficiently high gas-phase concentration of a condensible component. 1. Implementation of State 6 Model The parameter requirements of the state 6 model are similar to those for a catalytic gas-phase reaction in a catalytic pellet. These include: Pellet size and shape, porosity, tortuosity, and pore size distribution Intrinsic gas-phase catalytic kinetics and heat of reaction Effective diffusivities Bulk gas flow rate, composition, and temperature Vapor-liquid equilibrium data Liquid mixture surface tension 2. Modifications of State 6 Model Improvements in the state 5 model involve the relaxation of a few key assumptions. These include: 1. Account for diffusional limitations in liquid condensed in pores. 2. Account for capillary-driven convective liquid flow in macropores and corresponding nonisobaric gas transport.

Impact of Wetting on Catalyst Performance

431

Relaxation of these assumptions is a nontrivial exercise. However, such modifications would probably enable the prediction of a smooth transition to a primarily liquid-filled, diffusion-controlled reaction state, for example. This and other model modifications are needed to link the state 6 model with the state 7 and 8 models discussed below. C. Partial Pore Filling by Vaporization in the Partially Wetted Pellet (States 7 and 8) We now return to the case in which the pellet is contacted on its surface by a flowing liquid. Thus, in addition to capillary condensation, liquid can fill the pore structure by a capillary-driven imbibition process. The distribution of gas and liquid phases in the porous body depends on the catalyst morphology, the reaction kinetics and associated heat effects, the heat and mass transport phenomena, and the species volatilities. A flooded region will exist near the actively wetted surface unless the heat generation and gas evolution are sufficiently intense to create a gas sheath between the liquid and the catalyst surface, as encountered in film boiling [150]. At some point sufficiently removed from the wetted surface, a two-phase zone emerges. Qualitative estimates by Pismen [151] indicate that continuous liquid filaments can be maintained by sufficiently strong capillary forces in a porous body with a distribution of pore sizes. That is, the positions of the gas-liquid interfaces withstand typical pressure gradients occurring in the medium. Generally, it is anticipated that the volume fraction of liquid will decrease as one moves away from the flooded zone because of an increased rate of reaction and heat generation in vapor-filled pores. In the case of a porous body with a sufficiently narrow pore size distribution, regions of complete flooding and pore emptying are likely. As one moves toward the nonwetted exterior surface the volume fraction of liquid may increase due to condensation of the less volatile reactant. Pismen has shown that even without reaction or heat effects, countercurrent gas-liquid flow may occur inside a catalyst due to the coupling of diffusion, capillarity, and evaporation/condensation [151]. It is clear that the complexity of this system demands some simplifying assumptions to permit a tractable analysis. Some pioneering modeling efforts have appeared which have followed the lead of Pismen [151]. Several studies have treated the degree of pore filling as an independent parameter [34,117,124,126]. This approach allows one to examine the impact of reaction and transport in gas-filled pores. However, these models oversimplify the problem by ignoring the key causative physical processes of heat generation, capillarity, and vaporization. Hu and Ho [152] found that the simple model of an exothermic reaction in a partially wetted, completely filled pellet which employs the weighted

432

Chapter 11

average formulation [e.g., Eq. (8)] has multiple solutions for some conditions. Drobyshevich et al. [147] studied the exothermic reaction system A(g/) —» R(8j) + C(£) in a partially wetted and filled slab catalyst; phase transition was considered only to occur by reaction. Unfortunately, no mention was made about the pore size distribution, and capillary condensation was not considered. Kuzin and Stegasov [153] developed a model to describe the behavior of a nonporous pellet during an exothermic multiphase reaction with phase transition. It is reported that the model predicts the existence of periodic oscillations in the pellet temperature [154]. In a typical period, vaporization of the wetting liquid is induced by the exothermic reaction. This leads to a partly wetted state. At a critical surface temperature a completely gas-phase surface reaction occurs. For unspecified reasons, the granule temperature then decreases, leading to a rewetting of the surface. Details of the model are needed for a critical evaluation of these simulations. Harold [155] considered the exothermic reaction A(gj) -» vB(g) *n a half-wetted slab catalyst consisting of a single pore size. The model system shown in Figure 15 is one-dimensional [i.e., gradients in the direction (z) normal to the downward film flow] and may be viewed as a simplified case of a more complicated system, such as the partially wetted spherical pellet. Following earlier discussion, such a simple morphology validates the model picture of continuous liquid-filled (flooded) and gas-filled zones. The simple geometry, reaction, and other simplifying assumptions (e.g., no reaction in liquid-filled pores, isobaric gas-filled pores) permit efficient numerical and analytical examination of the interacting processes. The results reveal that the position of the single distinct interface depends on the many factors identified above. 1. The Half-Wetted Catalytic Slab

It is instructive to examine in some detail the more realistic bimolecular reaction A + vDD -» vBB, which occurs in the completely liquid-filled and gas-filled zones of the half-wetted slab. The simplified one-dimensional geometry can be appreciated by considering the number and complexity of even the one-dimensional model equations provided in Tables 5 and 6. The parameter requirements for this model is essentially a union of the state 3, 4, and 6 model requirements presented earlier. A detailed presentation and analysis of this state 7 model are presented elsewhere [156]. The gas zone (0 < z < 8*) is described by differential mass balances for the three components [Eqs. (12) and (13)], three dusty gas constitutive flux relations [nonisobaric with bulk diffusion control, following Jackson [157]; Eqs. (14) and (15)] and an energy balance [Eq. (16)]. The reaction kinetics approximate those of a noble metal-catalyzed olefin hydrogenation [Eq. (12)]; the rate is positive order in D (hydrogen) with the de-

Impact of Wetting on Catalyst Performance Flowing liquid film

/I

433

Catalytic pellet

ACTUAL PICTURE

Cross-section representation

MODEL PICTURE

Liquid film

Wetted

face

Nonwetted face

Figure 15. The half-wetted slab catalyst is an idealized representation of a partially wetted pellet of spherical or cylindrical shape. (From Ref. 155.)

pendence on A having a Langmuir chemisorption form (i.e., a reaction order between 0 and 1, depending on the extent of species A binding; see Kiperman [142]). The energy balance [Eq. (16)] includes conduction, convection, and heat generation terms. The liquid zone (8* < z < 8) is described by differential mass balances for the less volatile component (A) and sparingly soluble component (D) [Eqs. (17) and (18)]. The three-component mixture is treated as a pseudoideal binary liquid with dissolved component D [i.e., CL = CAL + CBL + C&L = constant; CDL ^D

KD(Tf)CL

YbD~ °- 8

" p ~ - J- 0 0 1

3

k cA 5

1J

3

Am

K aAG (T bG )p bC y bA « 1

fT^^p

,

^ A B ^ b G ' PbG^ C b T ^A

-250

p°vi PbG

7^~ ~

10

YbD

C pDL

4

^Am

§^-1

^Arn

PbG

Af C p A L Svo _

4

^ = 10

f

A

C

^•eL

K ]

^B

A

hw5

= ^- 10

*r

«

i^pS ^Dm

4

hn5

kc; S R T ^

4

^ A B ^ ^ b G ' PbG-'

^eG

= 0.003

A B ^ b G ' PbG>

_ J

= 5

.

10

^

C

==

pAG

55 =

k^CTbc) K^ G (T b G ) pgc y b p

DABtTbG,

Y/2

PbG)

1Q

( - AHG) D AH (T hC ,

PhG)

C hT

multiphase system. Consider the p = 0.05 and 0.15 cases. The pellet remains in the mostly liquid-filled state over a wide range of catalytic activities (). For the two more exothermic cases (p = 0.05 and 0.15), as the catalytic activity (i.e., 4>) is increased from a sufficiently low ( 0) to gasfilled (5* -* 1) state. In contrast, for the almost-isothermal case ((3 = 0.01), there is little pore emptying over a large range of activity. This underscores

Chapter 11

438

c 10 -

PG

= 0.15

e \ \ \

1 ;

a .11

d

(a)

\

V\

\f 0 05

\

\

\ / 0 .01

b)

.01'

\

101 -

.1

10

-

©

0 100

1000

0.15

.1-

O

.01:

J

0.01

(b)

.001

.1

10

100

1000

Thiele Modulus Figure 16. (a) Dependence of the catalyst effectiveness on the Thiele modulus (O) for the half-wetted slab. The dimensionless heat of reaction (p) is varied as a parameter, (b) Corresponding dependence of the gas-liquid interface position (s*) on

Impact of Wetting on Catalyst Performance

439

the significance of the exothermic reaction heat on inducing the phase transition. In the limiting regime of low activity (), the imbibing liquid is continuously removed by evaporation from the nonwetted surface to the bulk. The capillarity is sufficient to fill most of the pellet under these conditions (s* ** 0.004). Under these conditions, over 99% of the reaction occurs in the liquid-filled pores of the pellet. The pellet temperature is nearly uniform and actually slightly below the bulk (liquid and gas) temperature because of the endothermic vaporization process. An effectiveness based on a liquidphase reaction reference, T\L = Ti/(R^G/y6A^6D), is close to unity under these conditions. This indicates minimal liquid-phase transport limitations. In the limiting regime of high activity (4>), the pellet is nearly devoid of liquid and, correspondingly, most of the reaction occurs in gas-filled pores. The decreasing dependence of T] on $ in this regime signifies a rate that is limited by transport in the gas-filled pores. For intermediate catalytic activities between these two extremes multiple solutions and several extrema in the effectiveness exist. The multiplicity pattern is of the 1-3-1 counterclockwise variety. The multiplicity and extrema signal the existence of several rate-controlling regimes. As ,K?i) - 0 (10)

r * / exp(2a W ) exp | --yf ^— - 1 I I ^ f ( V f ,e™,/C2) = 0 (11)

Catalytic Membrane Reactors ym

485

XF

_

at

(lla)

a) = 0

aw

Yf = Xf ^

at

Jon

a exp(aw)Nup(9"1 - 9P) = - —

co =

1

(lib)

In the tube side:

x sf(yf,ef,A:j)

(12)

(13) with the initial conditions at

The tubeside Ergun equation becomes

e

^

with the initial condition, V' = 1

at ^ - 0

and/given by an equation like (7a) or similar.

(14a)

Chapter 12

486

In the shell side:

dyp

08/ \dY? a

x p{Yf,%p,Kpei) P

\ "

U

V

nPn

(15) P

P

L

1

y/V,) "^r - S PfDaf exp | - - y f ( - - 1 ^ - H:z:^

+ ^ ^ ( e 5 - ep)

(16)

with the initial conditions

at £ = 0

A.

(16a)

PBMR with a Pd Membrane

A model for the PBMR using a Pd membrane was first presented by Itoh [18]. The findings of the model were also compared with experimental data. The model assumes isothermal conditions [i.e., Eqs. (11), (13), and (16) are replaced by a single equation: 0m = 0/J = QF = 1], that the catalyst is packed only in the tube side (i.e., Da/J = 0), and that there is no pressure drop on either the shell side or the tube side. A single reaction was studied (i.e., cyclohexane dehydrogenation to benzene), and the reaction rate &pF is given as (in terms of partial pressures rather than concentrations; since the PBMR is assumed isothermal and assuming that the ideal gas law applies, one can easily interconvert between partial pressures and concentrations simply by dividing with RT) Pc/Pi, - PB/K*' where C stands for cyclohexane, H for hydrogen, and B for benzene. KF and KF are functions of temperature [18]. Obviously, Eqs. (10) and (11) do not apply in this case. Instead, the following equation was used by Itoh

Catalytic Membrane Reactors

487

to describe the permeation rate of H2, Q H (in mol/s), through the cylindrical Pd membrane: (18)

QH = a H [

with a H = [27rL/ln(/?2/#i)] (CjVK) D> wh ^re PQ is a pressure of 101.3 kPa, Co the concentration of H2 in Pd in equilibrium with H2 at a partial pressure of Po, and D is the diffusivity of H2 through the Pd membrane. The model assumes that cyclohexane in argon (an inert) was fed in the feed side and argon only fed in the shell side. Figure 2 shows the conversion as a function of the shell-side inlet molar flow rate vA of argon, which is used as purge gas. The solid lines represent the results of the numerical integration of the model equations. The points are the experimental results. Note that conversions significantly higher than equilibrium are obtained. Increasing vA, furthermore, increases the conversion and so does decreasing u°c (the inlet feed-side flow rate of cyclohexane) for a constant value oft£. In a more recent paper Itoh et al. [140] have studied the effect on the behavior of a Pd PBMR of the flow conditions prevailing in the shell and tube sides of the membrane. Five different situations were investigated. These are shown schematically in Figure 3. Case (1), the cocurrent model, is similar to the case discussed previously. The catalyst is packed in the interior of the membrane, adiabatic isothermal

1.0

^

^

/0.29

X

I 0.5 o o

/

/

/ /

/

/

1/

•

—

—

•

—

-—p

^-——

0.80 _ - — - •

•

cole

^

-

^

1.64 o uc° x 106 [mol-sH] ^

473K 1 atm

(— Equilibrium conversion (0.187) i

5 10 Flow rate of purge gas

15

VK x 10s [mol-s"1] Figure 2. Experimental and calculated results. (From Ref. 18.)

488 sweep feed

Chapter 12 separation side reaction side (a) cocurrent model

Pd membrane

sweep

feed (b) countercurrent

model

sweep feed (c) plug - mixing model

sweep feed (d) mixing - plug model

sweep feed (e) mixing - mixing model Figure 3. 140.)

Ideal flow models in the palladium membrane reactor. (From Ref.

489

Catalytic Membrane Reactors

conditions prevail, the H2 permeation rate is again given by Eq. (18), and the reaction studied is cyclohexane dehydrogenation. Once more cyclohexane in an inert stream is fed in the tube side and pure inert in the shell side. The countercurrent model (see Figure 3) is similar to the cocurrent model except that the sweep gas flows in a direction opposite to the feed (i.e., the known initial conditions for the shell-side equations occurs at z — L). As already mentioned, a rather straightforward modification is needed to account for the fact that the sweep gas flows in the opposite direction to the feed gas. The resulting problem, however, is now a split boundary value problem since the conditions in the shell side at z = 0 are unspecified and it is the conditions at z = L instead that are specified. The plugmixing, mixing-plug, and mixing-mixing models are models for which the plug-flow conditions in the feed or shell side are replaced by well-mixed conditions (i.e., the concentrations of the various species are assumed to be uniform everywhere). Figures 4 to 6 compare conversions of the various models as a function of yfo/(l - yfQ) (V° in the figures) (i.e., the ratio of inlet molar flow rate of inert in the shell side to the cyclohexane inlet molar flow rate in the feed side). The parameters are Da F and Q {Tu in the figures). Note that generally the countercurrent model is superior to the

100

r

countercurrent

cocurrent & plug-mixing mixing-plug

mixing-mixing

|

o o Equilibrium

10

conversion (18.2%)

50

100

500

Figure 4. Comparison of reactor performance calculated for the five models (Da - 300, Tu = 300, U°f - 4). (From Ref. 140.)

490

Chapter 12

100 countercurrent

cocurrent & plug-mixing

mixing-plug mixing-mixing

Equilibrium

t

10

i

conversion (18.2%) i

I

50

i

i

i i I

100

500

Figure 5. Comparison of reactor performance calculated for the five models (Da = 50, Tu = 150, U°j = 4). (From Ref. 140.) 100

plug-mixing

o 50 0)

mixing-mixing

o O

Equilibrium conversion (18.2%)

10

50

100

500

Figure 6. Comparison of reactor performance calculated for the five models (Da = 20, Tu = 30, U°j - 4). (From Ref. 140.)

Catalytic Membrane Reactors

491

other models, with the exception of low Daf and Q values and for small values of V°l7 for which the cocurrent model becomes superior to the countercurrent model. This is due to the fact that under these conditions in the entrance of the reactor there is back permeation of H2 from the permeate side to the feed side, which tends to lower the permeation rate at the entrance conditions. In a more recent study Itoh and Xu [141] have applied their isothermal Pd/PBMR model to the ethylbenzene dehydrogenation reaction. They consider the following reaction scheme (B stands for benzene, E for ethylbenzene, S for styrene, and T for toluene): E ^ ^ S + H2 lK})

(19)

PF{\ + KPS)2

E —> B + C2H4

I'

E + H2 —-» T + CH4

]

l

(21)

22

(23)

P -P hH

(24)

The Pd/PBMR was shown to perform better than the conventional PFR reactor. The countercurrent and cocurrent reactors gave approximately the same conversion and yield. The Pd PBMR in the absence of a sweep gas in the shell side but in the presence of a pressure gradient was analyzed by Itoh [142]. The maximum conversion attained in this reactor was found to depend only on the shell side H2 pressure. For a broad range of conditions the reactor gave conversions higher than the static equilibrium. A model similar to that of Itoh for a Pd/PBMR was used by Uemiya et al. [38] to model their PBMR. Their reactor used a membrane consisting of a glass cylinder covered by a Pd thin film (ca. 20 u,m thick) to study the water-gas shift reaction: CO + H2O ; = ± CO2 + H2

(25)

In the reactor of Uemiya et al. the catalyst (commercial Fe/Cr2O3 catalyst) was packed in the shell side. The rate expression used was

Chapter 12

492 uu

90

80

f -!

^j

Q

U__ equi l i b r i u m

^ ^ ' "

1

70

60

7 1

t

i

l

l

H20/C0 Molar Ratio

Figure 7. Effect of molar ratio of steam to carbon monoxide on conversion of carbon monoxide. Circles represent experimental results; solid curve represents calculated results. Experimental conditions: temperature, 673 K; H2O/CO molar ratio, 1; flow rate of sweep argon, 400 cm3(STP) min"1. (From Ref. 38.) The results of the model compare very favorably with the experimental results, as can be seen in Figure 7. A model for an adiabatic nonisothermal Pd/PBMR was presented by Itoh and Govind [143]. Plug-flow conditions were assumed in the tube and shell sides and the catalyst was packed in the tube side. The equations describing the tube side are similar to Eqs. (12) and (13). The H2, which is the product of the reaction on the tube side (assumed to be the dehydrogenation of 1-butene), diffuses through the membrane and reacts on the shell side with O2. Although the oxidation reaction is assumed to be catalyzed by the Pd surface itself, the dimensionless equations describing the shell side are the same as Eqs. (15) and (16). Negligible pressure drops are assumed for both the shell and tube sides. The permeation of H2 through the membrane is assumed to follow Eq. (18). The H2 permeability is assumed, furthermore, to have an exponential dependence on the temperature. The reaction rate on the tube side is assumed to be (in terms of partial pressures) 1/2

(PFyl2(l

+ \.2lP\l2 + 1.263PU2)2

with C being 1-butene, D butadiene, and H hydrogen.

(27)

Catalytic Membrane Reactors

493

The oxidation reaction on the shell side is assumed to follow a rate expression of the form (O means oxygen) (28)

Since the Pd membrane is nonporous, Eq. (10) is inapplicable and Eq. (11) is presumably accounted for by an overall heat transfer coefficient between shell and tube sides, which should include the gas-phase heat transfer coefficients and the thermal conductivity of the membrane. The temperature of the membrane surface on the shell side is assumed equal to the gas-phase temperature on the shell side. Itoh and Govind have analyzed their model under both isothermal (with the energy equations neglected) and adiabatic conditions. Figure 8 shows the dimensionless feed- and shell-side temperatures (0r and 05 in the figure, equivalent to 9F and 0P) and conversion versus the dimensionless reactor length (L in the figures, equivalent to £) with F (equivalent to HF) as a parameter. As F increases, the difference in temperature between the shell and feed sides decreases. Note that complete conversion is attained in a very short time in the adiabatic reactor. For a broad range of conditions the adiabatic reactor gives better conversions than the isothermal reactor. A countercurrent isothermal Pd/PBMR reactor with a dehydrogenation reaction occurring on one side and an oxidation reaction on the other was analyzed in a subsequent paper by Itoh and Govind [144] and its conversion compared to a cocurrent reactor under similar operating conditions. It turns out that for the conditions studied the countercurrent reactor performed much better than the cocurrent one. An effort to verify the theoretical adiabatic Pd/PBMR model of Itoh and Govind [143,144] experimentally was made by Zhao et al. [20]. Unfortunately, due to heat losses on the permeation side, the experimental data showed significant deviations from the theoretical calculations. A further analysis of the Pd/PBMR model of Itoh and Govind [143] was presented by Itoh [145], this time applied to the cyclohexane dehydrogenation reaction [which means that the rate on the reaction side is given by Eq. (17) rather than Eq. (27)]. An interesting result is presented in this paper, pertaining to the effect of the dimensionless heat transfer coefficient (y in the model of Itoh, equivalent to H) on reactor conversion. Note that as shown in Figure 9, as 7 decreases the reactor length required to attain 100% conversion decreases (i.e., the reaction appears to proceed at a faster pace with a decreasing heat transfer coefficient). This appears to be unusual but can be explained based on the following arguments. As the heat transfer coefficient decreases it becomes progressively more difficult to transfer heat from the permeation (oxida-

494

Chapter 12

Figure 8. Conversion and temperature profiles calculated for the adiabatic reactor model. (From Ref. 143.)

tion) side to the feed side (dehydrogenation reaction side). The resulting excess heat is then used to increase the temperature of the permeate side. This makes the oxidation reaction faster and in turn results in an additional increase in the temperature of both the permeate and reaction sides. So, in fact, for smaller heat transfer coefficients, Itoh [145] calculates permeateand reaction-side temperatures, which are higher than those corresponding to the higher heat transfer coefficients (see Figure 9). This trend continues until 7 = 5. Below this 7 value the heat transfer between the permeate and reaction sides becomes so small that the heat evolved by the oxidation reaction is not capable of maintaining the endothermic dehydrogenation reaction on the tube side. Figure 10 shows the reactor length required for

Catalytic Membrane Reactors

495

1.6

Y=r 100

1 /1 Y-500 / . . . .

O 50

35 ccui >

/

z o o

Air used i

0.2

0.4

0.6

Figure 9. Conversion and temperature profiles when 7 is large (Da° — 100, Da; - 5 x 10\ Tu° = 45, U°M - 4, V°sw - 5). (From Ref. 145.)

100% conversion as a function of 7 with the Damkohler number of the oxidation side as a parameter. Notable in this figure is the presence of a minimum in 7, as just discussed. Verification of the isothermal version of the model was presented by Itoh by applying the model to data reported previously [19] with the cyclohexane oxidative dehydrogenation reaction. The agreement between model and experiments is shown in Figure 11 and appears to be good. A nonisothermal PBMR model was developed by Oertel et al. [146] and used for the methane steam reforming reaction. Synthesis gas is produced from hydrocarbons such as methane by reaction with steam at high tem-

Chapter 12

496 0.6 -

1

Da°s 5X103

_

— 0.4 j

0.2

5X104 5X10 5

n 1

i

10

i

i

102

103

y

i

104

105

106

[-i

Figure 10. Reactor length required to attain 100% conversion (Da° = 100, Tu° = 45, U°j = 4, V°sw = 5). (From Ref. 145.)

100

-o

— O - 10.1% Oxygen — D— No Oxygen

EQUILIBRIUM

50

Isothermal

w0

100

150

Vsw Figure 11. Example of application of the isothermal model to experimental results (Da? = 107, Tu° = 45.1, U? = 4.05, 473 K). (From Ref. 145.)

Catalytic Membrane Reactors

497

peratures over a suitable catalyst according to the reactions CH4 + H2O CO + H2O

> CO + 3H2 > CO 2 + H2

(29) (30)

The rate expression was of the form 9'{P,) = PCH4 - y

2

—

(31)

where K^ is the equilibrium constant for the reaction given by Eq. (29). A schematic of the cross section of the multitube PBMR reactor suggested by Oertel et al. is shown in Figure 12. A single tube of the reactor consists of a reformer tube packed with Ni-coated Raschig rings, inside which are placed a number of Pd tubular membranes (ca. 50 jxm thick). A porous-walled product tube is situated on the inside of the reformer tube, while a heating jacket pipe surrounds the reformer tube. Heating for the endothermic reaction is provided by a helium gas stream flowing in the jacket pipe countercurrent to the reformer gas flow. The helium is cooled from 950°C to 700°C while heating the reformer gas to a maximum 850°C. The PBMR was modeled by assuming that heat was transferred between the jacket tube and reformer tube by a combination of convection and radiation. Heat transfer between the reformer and membrane tubes was assumed to be by convection alone, while heat transfer between the reformer and product tubes was neglected. Equations (15) and (16) therefore applied, with the addition of a radiative heat transfer term. The permeation of hydrogen through the Pd membrane tubes was assumed to follow a Sievert-type law such as Eq. (1) (with n = 0.5), with an exponential dependence on the reactor temperature. Negligible pressure drops were assumed in both the tube side (Pd tube) and shell side (reformer tube). Figure 13 shows the conversion of methane, CCH4, as a function of normalized tube length L/LmRX (equivalent to Q for Pd tubes of thickness 50 (Jim. The solid line is the calculated PBMR conversion, and the dashed line shows the conversion in a conventional reactor without the Pd tubes, operated under the same conditions. The methane conversion in the PBMR reactor is up to 36% higher than that obtained in the conventional reactor due to the separation of H 2 from the product gas. By reducing the thickness of the Pd membrane tubes, the conversions obtained can be increased even further. Calculations using Pd tubes with thicknesses of 20 jxm show that methane conversions 43% higher than conversions in a conventional reactor can be obtained.

Chapter 12

498

helium

Figure 12. (a) Balance element of a single tube; (b) section through a single tube without packing. (From Ref. 146.)

B. Microporous PBMR

The first model of a PBMR utilizing a microporous Vycor membrane was also presented by Itoh et al. [147]. A single reaction, again cyclohexane dehydrogenation, was assumed to take place this time following a rate expression of the form

9F(Pf) =

(32)

with C signifying cyclohexane, B benzene, and H hydrogen. The catalyst bed was placed in the interior volume of the membrane. The reactor was assumed to be isothermal and adiabatic, plug-flow behavior was assumed for both the tube and shell sides and the pressure drop in the tube side was assumed negligible. Equations (11), (13), and (16) are therefore not applicable, replaced instead by a single equation (i.e., 0m = 6^ = 6P = 1). Equation (10) with = 0 can be integrated analytically to express the flux of various species through the membrane.

Catalytic Membrane Reactors

499

return tube membranes (b)

reformer tube jacket pipe

Figure 12.

Continued.

Figure 14 shows the calculated mole fraction profiles of the various species in the shell side (separation side) and tube side (reaction side) along the (dimensionless) reactor length. Note that the shell-side concentrations of cyclohexane, benzene, and hydrogen all increase, while the tube-side concentrations of benzene and hydrogen pass through a maximum. Itoh et al. [147] studied in detail the effect of membrane thickness on reactor performance. Figure 15 shows the total molar flow rate of cyclohexane at the outlet of the reactor as a function of membrane thickness (F'Cout is the molar flow rate in the tube side and Q'Coui in the shell side). Note that the total outlet molar flow rate of cyclohexane goes through a minimum at a

500

Chapter 12

max

Figure 13. Methane conversion against normalized tube length. (From Ref. 146.)

given membrane thickness. This means that the reactor conversion itself goes through a maximum as a function of membrane thickness, as can be seen in Figure 16. The model of Itoh et al. [147] was subsequently studied in greater detail by Mohan and Govind [148]. Figure 17 shows the reactor conversion as a function of h, which is the ratio of permeation rate to the reaction rate (equivalent to Q/DaF) with Z (proportional to DaF) as a parameter. Note again (as noted previously by Itoh et al. [147]) that for a constant Z (i.e., constant DaF) the conversion passes through a maximum as a function of Q. For all other parameters constant, this is equivalent to saying that the conversion passes through a maximum as a function of the thickness of the permselective membrane layer. Mohan and Govind [149] also presented an isothermal PBMR model with a single reversible reacton (A ^± bB + cC) taking place on the tube side of the membrane and with negligible pressure drop. They examined the behavior of various membrane reactor flow configurations (i.e., cocurrent, countercurrent), the presence of feed- or permeate-side recycle streams and feeds at intermediate locations. They also studied the effect of various operating variables such as feed- and shell-side flow rates, reactor length, and component permeabilities on conversion. Figure 18 shows the

Catalytic Membrane Reactors

501

0.02 • Separation side

H2j

o o

0.01

o E

Reaction side 0.15

0.5

1.0

LH Figure 14. Profiles of molar composition in the inner and outer tubes. (From Ref. 147.)

effect on conversion of 8, which is defined as the ratio of the permeation rate to the reaction rate (equivalent to Q/DaF) with the inert flow rate on the permeate side, Q inert (equivalent to yf) as a parameter. The reaction studied is of the form A ^ 4B. There is an optimum value of Q inert beyond which the conversion decreases due to an increased reactant loss in the permeate stream and back permeation of product.

Chapter 12

cm ]

Figure 15. Molar rate of flow of cyclohexane at the outlet of the tube as a function oitv. (FromRef. 147.) Mohan and Govind also discuss the effect of 8 on the membrane reactor's separation efficiency. As noted previously, one advantage of membrane reactors, over their conventional counterparts, is that they provide for in situ separation of reactants and products, thus potentially reducing the need for expensive downstream separation equipment. For a three-component system (i.e., for a reaction of the form A ^ bB + cC), one defines the extent of separation, £,y, between components i and/ as the absolute value of the determinant of a matrix written in terms of four segregation factors, = abs det

(33)

where Yih the segregation factor, is given by

Y

ij 1

—

when ; = 1 when 7 = 2

(34)

503

Catalytic Membrane Reactors \ 0.6

maximum conversion

04

I X 02

kn rate constant

0.1

0.2

0.3

tm [ cm ]

Figure 16. Maximum conversion for different values of the frequency factor k0. (From Ref. 147.)

where F^^ is the dimensionless flow of i on the feed side (equivalent to yf) and Qitop is the dimensionless flow of i on the permeate side (equivalent to yf). Figure 19 shows the effect of the rate ratio 8 on the conversion x and separation efficiencies £iy. The separation efficiency increases as 8 increases due to the increased permeation of product(s), until a maximum efficiency is obtained at an optimum rate 8. Above this value of 8, the separation efficiency decreases due to increasing permeation of the reactant(s) from the reaction side to the permeate side, combined with increasing backpermeation of product. Mohan and Govind also presented a nonisothermal microporous PBMR model [150]. The model was written for a single reaction of the form A ^ B with first-order forward and reverse reactions. They write no temperature or concentration equations for the membrane. Instead, the influence of the membrane is lumped into a single linear flux equation and an overall heat transfer coefficient. The reactor is assumed adiabatic. Figure 20 shows

504

Chapter 12 GO Pr = 0.00 P, = 1.00

C t - 5.24 C, = 7.30

.80

160

240

3.20

4.00

Permeation Rate/Reaction Rate. h

Figure 17. Effect of permeation rate/reaction rate ratio on perm-reactor conversion. (From Ref. 148.)

the effect of feed-side inlet temperature Tf (equivalent to TF) on conversion. Note that for exothermic reactions an optimum 7} exists, which maximizes conversion. The same is not true, however, for endothermic reactions, for which increasing 7} always increases conversion. The parameter 5 on this figure is again the ratio of permeation rate to reaction rate and is equivalent to Q/DSLF (5 = 0 corresponds to the reactor with impermeable walls). Mohan and Govind also studied a PBMR for which both the shell and feed sides are under well-mixed conditions (defined by them as CSTMR). The behavior of the PBMR with plug-flow conditions prevailing in the tube and shell sides (defined as PFMR by Mohan and Govind) is compared in Figure 21 to the behavior of a PBMR with well-mixed conditions on both sides. In this figure the conversion is plotted as a function of 8 with 1/p (equivalent to \I$F) and 7} as parameters. Note that isothermal operation (i.e.., 1/p -» oo) favors the PFMR over the CSTMR (although for small 7} values the differences are rather small). For exothermic reactions there is a critical value of 8 beyond which the CSTMR gives better conversion than

Catalytic Membrane Reactors

•8 r

505 Qinert = 50

cocurrent flow

Qin«rt=100

( W r t = 20

Da sSO.O Pr«1-0 0.01

a A «1.5, Xmax « 0.35 0.5, Xmax « 0.675

0

1

2

3

4

rate ratio,


-

N

-

I

-

o , 3 c /r , o .'

o

it

0

\

CBC

\

CAC

y

/

i. ?•••

\

/

''

i

N

...1 \

\\

: 1

.1

/

> «A »0.2

aa = 3.0 OC • 1.0 Pr = 0.0 Da# * 5.0 K£ « 0.065 B+C

\

/

J/

/ / /

1

I .2 .1

i

y f

i

X

u

X

\ \ \ \

\

\

\ \ \\ \

>

\

\

1

.2

.3

.4

.5

rate ratio, < Figure 19. Separation efficiency of a membrane reactor as a function of rate ratio when PE reactant < PE product(s) . (From Ref. 149.)

where Xt are mole fractions of the various species (A stands for ethylbenzene, B for styrene, C for hydrogen) and T* is equal to TF/T0, with To being an unspecified reference temperature. Although the general mathematical equations account for heat exchange between the reactor and its surroundings through a reactor wall heat transfer coefficient, numerical examples of the solution of the complete nonisothermal model are not presented in the chapter. Figure 22 shows the conversion as a function of 8 with the molar flow of inerts [i.e., steam (equivalent to the dimensionless quantity yf)] as a parameter. Superimposed on this figure are the results of the analysis of a Pd/PBMR, which is permeable only to H2. Note again that an optimum 5 exists for the microporous PBMR, something that is not true for the Pd/PBMR. The effect of feed temperature on reactor performance is shown in Figure 23. In a subsequent study Mohan and Govind [151] applied their isothermal microporous PBMR model to two additional equilibrium-limited reactions:

Catalytic Membrane Reactors

507

Exothermic. Er = 2.0. Kr = 8 0 . 0 , 6 = 0.8 E n d o t h e r m i c . Er = 0.5, Kr = O S , 6 = -0.8

0.0 200

600

1000

1400

1800

feedtemperature. Tf (K) Figure 20. Effect of permeation rate on the performance of a PFMR. (From Ref. 150.) HI decomposition described by 2HI ^ = ± H 2 + I 2

(37)

with a rate expression in terms of mole fractions (38) and propylene disproportionation described by 2C 3 H 6 ? = ± C 2 H 4 + C 4 H 8

(39)

508

Chapter 12

02

0.1

X I

5 £

X CO + 2H 2

(47)

&S(Pj) = Pu2aPc2u4 CH4 + H2O n(P}) =

W H

CO + H2O

(48)

> CO + 3H2 2

(49)

O

(50)

> CO2 + H2

(51)

F

(52)

d = (PcoPu2o)P

With the exception of reaction (41) all other reactions are assumed to be far removed from equilibrium, so that the reverse reactions can be neglected. The various gases are assumed to diffuse by Knudsen diffusion, and the Ergun equation is used to describe the pressure drop in the tube side. Wu and Liu have studied the effect of the various dimensionless reactor parameters. The yield to styrene was shown to increase as Da F and A (equivalent to Q) increased. Wu and Liu also studied a hybrid reactor system consisting of a combination of a packed bed and a membrane reactor. Under some conditions the hybrid reactor system appears to give a better yield. For example, in Figure 25 the hybrid packed bed/membrane reactor system is compared to a system consisting of two packed-bed reactors in series. Note that in the latter system, the toluene yield (toluene is an undesired by-product) increases while in the packed bed/membrane hybrid system it levels off. The same is also true for the benzene yield, another undesirable by-product. Song and Hwang [152] have used an isothermal microporous PBMR to study the partial oxidation of methanol to formaldehyde. Their reactor uses a Vycor glass porous membrane and has a double-pipe configuration, with the Vycor glass tube connected in the one end to an ordinary Pyrex glass tube, while its other end is fused. Their reactor is therefore very similar to the reactor of Sun and Khang (see Figure 30b and the discussion that follows). The catalyst is packed in the shell side. Song and Hwang use a PBMR model similar to that of Itoh et al. [147], the only difference being that Da F (rather than Dap) = 0. Since one end of the membrane tube is closed, the feed flow rate into the tube side is always zero. For the reaction rate in the shell side they use a kinetic equation QfP(pP\ 1 i}

p

J

^

(1 + KMPM + KHPH)

O

l

P05 "

(1 + KoP°o?)

where PM and Pu are the partial pressures of methanol and hydrogen and POi is the pressure of oxygen at the inlet of the reactor. Song and Hwang

Chapter 12

512 Steam Feed

Products

10.00

T=640 C P= 1.15 ami Pr=1.0 GHSV = 3560 hi-t H20/EB= 10 Add-on Stage with Steam Shell Purge

5.00 -

— Packed

Bed

— Membrane

o

0.00

\

0.0

10.0

20.0

30.0

40.0

50.0

Reactor Length (cm)

Figure 25. Hybrid packed bed/membrane reactor versus packed-bed reactors in series. (From Ref. 55.)

carried out a series of independent experiments to calculate the reaction rate constants. In the membrane reactor experiments they studied the effect of space time and of the membrane surface area (by using four membranes of different lengths, ranging from 8 to 21 cm). As expected, increasing the space time and membrane area generally increases the conversion (see Figure 26). The model performs generally well, but the gains in conversion were usually modest over the packed-bed reactor (i.e., the membrane reactor operating with the tube-side exit closed). Song and Hwang calculate that additional improvements in conversion can be attained by using a membrane with higher permeability or permselectivity or by using recycle reactors.

Catalytic Membrane Reactors

513

Membrane Reactor (Simulation)

°^ C o

60 Packed Bed

vt

a> C

o O

50 Equilibrium Conversion

Space Time (sec)

Figure 26. Effect of space time on conversion at 60% air (350°C, 10 mm OD, length = 12 cm, porous Vycor glass membrane). (From Ref. 152.)

Tsotsis et al. [62] presented an isothermal PBMR model applicable to their experiments with the reaction of ethane dehydrogenation to ethylene in an alumina microporous membrane (Membralox®) shell-and-tube reactor. The reactor was operated isothermally, with the shell-side flow being cocurrent to that on the tube side, and the catalyst (Pt/7-Al2O3) packed in the tube side. Equations (11), (13), and (16) do not apply, replaced instead by 0m = 0F = 0P = 1. In the model, plug flow was assumed in both the tube side and shell side. Equations (10), (12), and (15) then all apply, with - 0 and Dap = 0. Tsotsis et al. [62] assumed that there was no pressure drop in the shell side (il^ = \\tPF = constant) and that the pressure drop on the tube side was accounted for by an Ergun equation likeEq. (14). Figures 27 and 28 show the experimentally observed (points) and calculated (solid line) conversions as a function of the sweep ratio Fr for two different feed compositions, a dilute feed mixture containing < 10% of ethane in argon and hydrogen and a dense mixture containing > 80% of

Chapter 12

514

o

i 2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Figure 27. Conversion versus sweep ratio for dilute feed, T = 550°C, T — 2 s, PS = 30 psi, tyPF = 0.5. (From Ref. 62.)

ethane in argon and hydrogen. The thickness of the permselective layer, e, was used as the fitting parameter. The results in both Figures 27 and 28 show that the reactor conversions obtained were higher than the equilibrium conversion values (Xcq in figures), corresponding to the tube- and shell-side pressure conditions and the feed-side composition. As can be seen in these figures, increasing Fr (by increasing the shell-side inert flow rate while keeping the feed-side flow rate constant) produces an increase in conversion. This is due to the decreased partial pressures of hydrogen in the shell side and the corresponding increase in the permeation rate of hydrogen out of the reaction side. For comparison purposes, furthermore, they have calculated in Figure 28 the conversion Xdn of the reactor operating with the shell-side inlet and outlet closed (i.e., operating as a plug-flow reactor). The pressure conditions for the Xdil line are those prevailing in the shell side and the composition results from mixing the feed- and shell-side gas streams at the shell-side pressure conditions. The membrane reactor conversions are, again, significantly higher than the corresponding Xdii conversion values.

Catalytic Membrane Reactors

515

12

o

10 -

o

-

> O

6 :-

-

^ ^ ^ ^

00

u

shell

x d i ,...

o

PC

3

^ ^ ^

X

4 --

eq, tube

w a!

2 --

0.2

-

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

SWEEP RATIO, Fr

'maidedlyde ( c>/o)

Figure 28. Conversion versus sweep ratio for dense feed, T = 550°C, T = 2 s, PS = 30 psi, VF - 0.5. (From Ref. 62.)

o

j_

o >

100 PFR RSCMR

80 60 40 20

CD

0

1

2 3 4 Conversion of Methane (%)

5

6

Figure 29. Comparison of the performance of a RSCMR and a PFR for V2O5/ SiO3 catalyzed partial oxidation of methane at 773 K. (From Ref. 154.)

516

Chapter 12 Catalytic

(a)

Direction of Diffusion

r=0

(In the Membrane)

Catalyst

(b)

Bed

r=0

Figure 30. Single-cell model: (a) catalytic membrane reactor; (b) inert membrane reactor with catalyst in the feed side, (c) Experimental setup: 1, mass flow meter; 2, regulating valve; 3, metering valve; 4, temperature indicator; 5, syringe pump; 6, heating lamp; 7, membrane (reactor) cell; 8, electric furnace; 9, temperature controller; 10, sampling ports; 11, condenser; 12, bubble flowmeter; 13, pressure gauge; 14, adjustable check valve; 15, plug valve; 16, liquid collector. (From Ref. 51.)

A PBMR in which a consecutive catalytic reaction occurs, B

(54)

with B being the desirable product, has been modeled by Agarwalla and Lund [153] and by Lund [154]. The model assumes isothermal and plugflow conditions in the tube and shell sides. Two flow configurations have been examined: one in which an inert sweep gas is used in the shell side

Catalytic Membrane Reactors

517

Gases in (Air.Hj.0rN3)

(C)

Figure 30.

Continued.

(defined as ISCMR) and another (defined as RSCMR) in which the reactant A is first fed in the shell side and after the product species B is removed; it is subsequently fed (together with any product C) into the tube side. The performance of both reactor configurations was compared to that of a regular plug-flow reactor (PFR). For membranes permselective to B, both configurations for cocurrent conditions were shown to have comparable conversion to the PFR but with a better selectivity. For nonpermselective membranes, the ISCMR did not perform particularly well, but the RSCMR still gave better selectivities than the PFR without significant losses in conversion. The CH4 partial oxidation reaction was used as an example and shown to give better formaldehyde selectivities, as can be seen in Figure 29. C. Microporous CMR Sun and Khang [51] presented a model for an isothermal CMR. The model was used to fit their experimental data with the cyclohexane dehydrogenation reaction utilizing a Vycor microporous membrane impregnated with Pt. The equation describing the membrane is the same with Eq. (10). Since the model is isothermal and adiabatic, Eqs. (11), (13), and (16) are not applicable; instead, one assumes that 0m = 9F = 8F = 1. Sun and Khang assumed that the tube- and shell-side volumes of the membrane are well

518

Chapter 12

mixed, so Eqs. (12) and (15) must be replaced by their corresponding modified versions used to describe well-mixed conditions. The model of Sun and Khang is somewhat specific to their experimental setup, shown in Figure 30. Well-mixed conditions might prevail in the shell side of the membrane, but it is unlikely that they will prevail on the tube side, as Sun and Khang themselves admit. The reactant stream (cyclohexane in a H2 stream) is fed in the shell side. There was no inlet port for the tube side (permeate side of the membrane). The rate expression used for the cyclohexane dehydrogenation is Eq. (32). Figure 31 shows the overall CMR conversion (indicated as YbT or XT) and what is defined as the benzene molar fraction in organics in the feed side, Ybf [equivalent to y^l{yc + y^)] a n d sne U side YbP [equivalent to y^l{yc + y^)\ a s a function of the CMR's feed-side space time (equivalent to iF). Conversions higher than the equilibrium conversions corresponding to the feed-side conditions are observed both theoretically and experimentally. In Figure 32, the behavior of the CMR is compared with the behavior of a PBMR (called an inert membrane reactor by Sun and Khang), both containing the same amount of catalyst. Note that for large space times the CMR shows a higher conversion than the PBMR. Both show conversions higher than equilibrium. The same is not true, however, for smaller space times. Note that for a region of temperatures the conversion

0.0

10

15

20

25

30

SPACE TIME, s

35

40

45

Figure 31. Effect of space time on the benzene molar fraction in organics (Yh) (T = 573 K, Pf = 191 kPa, Pp = 99 kPa, X\ = 0.49, X\ = 0, and X% - 0.51). (From Ref. 51.)

Catalytic Membrane Reactors 1

519

ic -membrane

Inert-membrane Reactor yr

.8

t

510

520

530

540

a

( )

550

560

570

560

1

590

600

TEMPERATURE, K

Catalytic-membrane Reactor Inert-membrane Reactor

510

(b)

520

530

540

650

560

570

580

590

600

TEMPERATURE, K

Figure 32. (a) Conversion versus temperature for high-space-time operations (T = 31.22 to 36.62 s, Pf - 191 kPa, Pr - 0.5, X\ = 0.5, X\ - 0, X% - 0.5, and Qf - 2.5 x 10" 9 kmol/s). (b) Conversion versus temperature for low-space-time operations (r = 9.73 to 11.44 s, Pf - 191 kPa, Pr - 0.5, X\ = 0.5, X°2 = 0, X? = 0.5, and Q; = 8.0 x 10" 9 kmol/s). (From Ref. 51.)

520

Chapter 12

of the CMR is lower than the conversion of the PBMR and the corresponding equilibrium conversion. In a follow-up paper, Sun and Khang [155] compared the behavior of a CMR to that of PBMR, a regular PFR, and a CSTR reactor, all of them containing the same amount of active catalyst. Three types of reaction were studied: a reaction with an overall increase in the number of moles (i.e., Ax > A2 + 3A3) following a rate expression of the form 9F(P,) = Pi

(55)

a reaction with an overall decrease in the number of moles (i.e., Ax 3A2 ~» A3 + A4) following a rate expression of the form 9F(P,) = P,Pl -

(56)

and a reaction of the form A1 + A 2 -> A 3 + A 4 following a rate expression of the form

9F(Pj) = P,P2 -

0.0

0.3

P3P4

(57)

KF

0.6

0.9

1.2

1.5

Figure 33. Total conversion of the CMR, IMRCF, PFR, and MFR vs the dimensionless diffusional space time () for the case of AAZ > 0 [n = 3, v = ( —1, 1, 3), a - (1, 1, 6), X° = (0.5, 0, 0.5), 4> - 10.0, Pf = 191 kPa, Pp = 95.5 kPa! and Kp - 4.471 x 106 kPa 3 ]. (From Ref. 155.)

Catalytic Membrane Reactors

521

Figures 33 to 35 show the overall conversion for the various reactors for the three different reactions above as a function of $ (equivalent to Q), defined as the dimensionless diffusional space time. Obviously, for the PFR or the CSTR (which Sun and Khang call MFR) 4> is of no real relevance. Based on the definition, one can, of course, calculate values of 4> corresponding to the input flow rates to these reactors and the transport properties of the Vycor membrane utilized by Sun and Khang in the CMR and PBMR. Note from Figure 33 that for the most part, the CMR performs better than the PBMR (IMRCF in the figure) for reactions with a net mole increase. For the range of conditions studied by Sun and Khang, both perform worse than either the CSTR or PFR operated at the permeate pressure conditions. For reactions with no net increase or decrease in the number of moles, Figure 34 indicates that the PBMR performs better than the CMR and both perform better than either the PFR or CSTR. Note that for this case the overall total pressure has no effect on conversion or the calculated equilibrium conversions. Finally, for reactions with a net decrease in the number of moles, the PBMR performs better than the CMR (see Figure 35). Based on these and similar numerical calculations, Sun and Khang developed the reactor selection guide shown in Table 2. 1.0

0.8

PFR (P, or /

PP)

IMRCF _____—.——

*.f = X..P

0.6

_

_

0

1. 2. 3. 4. 5. 6. 1. 2. 3. 4. 1. 2. 3. 4. 5. 6.

1. 2. 3. 4. 5. 6. 1. 2. 3. 4. 1. 2. 3. 4. 5. 6.

An « 0

An < 0

Source: Ref. 155.

PFR (at P J MFR (at Pp) PFR (at Pf) IMRCF MFR (at Pf) CMR PFR (at P,) IMRCF MFR (at Pf) CMR PFR (at P,) IMRCF MFR (at Pf) PFR (at Pp) MFR (at P J CMR

PFR (at Pp) MFR (at Pp) CMR IMRCF PFR (at Pf) MFR (at Pf) IMRCF CMR PFR (at Pr) MFR (at Pr) IMRCF PFR (at P,) MFR (at Pf) CMR PFR (at Pp) MFR (at Pp)

Catalytic Membrane Reactors

523

Champagnie et al. [60] utilized a CMR model to fit their experimental data with the ethane dehydrogenation reaction in a cocurrent isothermal shell-and-tube reactor utilizing a Pt-impregnated ceramic (Membralox®) membrane. They examined the effect of operating variables such as reactor temperature, shell- and tube-side gas flow rates, tube-side total pressure, and residence times. In terms of partial pressures, the rate expression used was of the form (58)

K'e

As the reactor is isothermal, Eqs. (11), (13), and (16) do not apply, replaced instead by 6m = 0^ = 0P — 1. There was no pressure drop in either the tube or shell sides (*\jF = 1 and typ = \\fPF = constant) and plugflow behavior was assumed for both the tube and shell sides of the membrane. Equations (10), (12), and (15) therefore apply, with DaF = Da p = 0 for Eqs. (12) and (15). Figure 36 shows the experimentally observed (points) and calculated (solid line) reactor conversions as a function of temperature. As expected,

o O V

B< 500

510

520

530

540

550

560

570

580

590

TEMPERATURE, C

Figure 36. Conversion versus temperature for the dilute feed; Fr - 1, T = 2.15 s, PF - 2 atm, Pf - 1 atm. (From Ref. 60.)

524

Chapter 12

the CMR conversion increases as the temperature increases. Figure 37 shows the reactor conversion as a function of the sweep ratio. As the sweep ratio increases, the overall conversion increases. Figure 38 shows the effect of varying the permselective membrane layer thickness on the conversion. As seen in the figure, a maximum conversion is obtained at an optimum thickness. This is similar to the behavior observed by Itoh et al. [147] for the microporous (Vycor glass) PBMR. D.

Microporous PBCMR

Tsotsis et al. [61] presented a model for a PBCMR, which they also applied to the ethane dehydrogenation reaction. The PBCMR was operated cocurrently, isothermally, and was modeled under the assumption that there was no pressure drop on the shell side (\\fp = \\sPF = constant). The equations describing the temperature changes in the membrane [Eq. (11)], tube side [Eq. (13)], and shell side [Eq. (16)] then do not apply and 0m = 0F = 6P = 1. Also, as there are two reaction zones, one in the membrane and

0.4

0.6

0.8

1

1.2

1.4

1.6

SWEEP RATIO

Figure 37. Conversion versus sweep ratio for the dilute feed; T = 550°C, T = 2.15 s, Pf = 2 atm, Pf = 1 atm. (From Ref. 60.)

Catalytic Membrane Reactors

525

16.5

MEMBRANE THICKNESS, microns

Figure 38. Reactor conversion versus membrane thickness for dilute feed conditions. the other in the tube side, Eqs. (10), (12), and (15) apply, with Da7* = 0. The pressure drop in the tube side was accounted for by an Ergun correlation like Eq. (14). Figure 39 shows the effect of reactor temperature on reactor conversion for the dense feed conditions. Note that the theoretical and experimental PBCMR conversions are greater than the corresponding equilibrium conversions calculated at the tube- and shell-side pressures and temperatures. The conversions shown in Figure 39, already higher than equilibrium, can be further improved by increasing the sweep ratio or residence time, or by decreasing the tube-side pressure. E. CNMR Reactor

An interesting membrane reactor system, a schematic of which is shown in Figure 40, was suggested by Sloot et al. [64] and applied to the Claus reaction and most recently to the reaction between NO and NH3 [65,69]. In this reactor the reaction takes place inside the catalytically active membrane, but in contrast to the membrane reactors discussed so far the perm-

Chapter 12

526

520

540

560

580

600

620

640

TEMPERATURE, C

Figure 39. Conversion versus temperature: dense feed, sweep ratio = 1.0, T = 2.0 s, PFT = 30 psi, PPT = 15 psi. (From Ref. 61.) selective properties of the membrane are not important. As shown in Figure 40, in the CNMR reactor of Sloot et al. the reactants are fed to different sides of the membrane. If the reaction is fast compared to mass transport, a reaction zone will form inside the membrane. For instantaneous, irreversible reactions the reaction zone will shrink into a reaction plane. The position of the reaction zone/plane is adjusted inside the membrane so that the molar fluxes of the various reactants are stoichiometric and the slip of one of these reactants to the opposite side is prevented. In that sense the CNMR is, at least in principle, ideally suited for processes requiring strict stoichiometric ratios, such as NH 3 + NO or SO2 + H 2 S, where slip of one of the reactants is of serious concern. Sloot et al. [64] have studied the fast reversible reaction of the general form (59)

2 vAiAt = 0

with vAi < 0 for reactants, vAi > 0 for products, and vAi = 0 for inerts. A special case of Eq. (59) is the Claus reaction 2H,S + SO,

|S 8

2H2O

(60)

Catalytic Membrane Reactors

527

c

gas

gas -f B

gas

gas + B+C

B

C

Figure 40. Schematic representation of the membrane reactor. (From Ref. 64.)

At steady state one writes a mass balance for each component, dJA

(61)

where / A is the molar flux of each component A, and r(X) is the reaction rate, dependent on the concentration of the various reactants (X is the vector of the mole fractions with components XAi, XAi, XAj, XAAJ and XA the mole fraction of inerts). Sloot et al. [64] recast Eq. (61) as vA dJAx

dJA

v

dZ

dZ

(62)

with JA. consisting of a viscous component and a diffusive contribution as (63) with

^ - ) J

A(,dif

-

DA , -

1 RT

Atef

T z

d(XAP) dZ 1 1/(€/T)DA,,AS

with

* -= £

(64)

Chapter 12

528

where P is the total pressure, DAk the Knudsen diffusivity, and DA A the bulk diffusion coefficient of A,, with e, T, and dp being the porosity, tortuosity, and mean pore diameter of the membrane, respectively. Equations (62) to (64), together with the overall equilibrium equation (65) and the appropriate set of boundary conditions, were integrated numerically (further details can be found in the original publication [64]). Figure 41 shows calculated values for concentrations of the various species in the membrane for the Claus reaction under conditions for which the reaction can be considered instantaneous and irreversible. Note that the reaction zone is very narrow and the slip of each reactant to the other side is less than 1%. In contrast, Figure 42 shows a situation where the Claus reaction is still instantaneous but reversible. Note that the reaction zone is broader and there is considerable reactant slip. Further design aspects of this interesting reactor concept can be found in the original publication [64]. A more general model for the CNMR reactor was recently published by Sloot et al. [156], based on the dusty-gas model of transport of Mason and Malinauskas [157] extended to account for surface diffusion. In this model Eqs. (59) to (63) and (65) again apply. Instead of Eq. (64), which

stagnant gas film

stagnant gas film

0.0

0.2

0,4

0.6

location (x/L)

0.8

1.0 &-

Figure 41. Molar fraction profiles at 200°C in absence of pressure difference over the membrane. (From Ref. 64.)

Catalytic Membrane Reactors

529 stagnant gas film

stagnant gas film

D.O

0.2

0.4

0.6

location (x/L)

0.8

1.0 •

Figure 42. Molar fraction profiles at 300°C in absence of pressure difference over the membrane. (From Ref. 64.)

uses Fick's law with effective binary diffusivity coefficients to describe diffusion, the following equation is used: i

XA jJ

Bo PDAUK

1 dXAI RT dZ

RT\P

i = 1, . . . . 5

dP dZ (66)

The effective binary diffusion coefficients Dtj are equal to (e/r)Z)°7 where D°j are the gas-phase binary diffusivities. Dt K is equal to (e/T)D A , KJ where D°AiK - (d P /3)V8/?r/irAf,. The total molar flux through the membrane of component A, (i.e., JAi) is given by the equation

dP

/ — 1, . . . , 5

(67)

where JAiS is the flux due to surface transport. Equation (67) assumes that the membrane pores are cylindrical. JAis is given by i = 1, . . . , 5

(68)

Chapter 12

530

DAis is the surface diffusion coefficient for A,, Cs the total concentration of adsorption sites, and 0A/ the surface coverage of A,-. 6A, is assumed to obey a Langmuir isotherm of the form btXAlP *

i

1

5

Mass transfer resistances outside the membrane are taken into account by applying the Stefan-Maxwell diffusion equation to the stagnant gas film adjacent to either membrane side (see the original paper for further details [156]). The equations for the general model were solved numerically. The solutions were first applied to simplified versions of the model for dilute mixtures, for which multicomponent diffusion is described by Fick's law with pressure-independent diffusion coefficients and for which analytical (or approximately analytical) solutions exist. The numerical scheme appeared to perform well. Even in the absence of a pressure difference across the membrane, the model shows that the total pressure inside the membrane exhibits a minimum at the location of the reaction zone, attributed to the fact that the total number of moles is reduced by the chemical reaction (i.e., the Claus reaction). This introduces a pressure gradient within the membrane, which induces a viscous flow and as a side effect an opposite diffusive flux of inert to maintain a mass balance. The pressure minimum in the membrane is also found in the absence of reaction but in the presence of surface diffusion from the various species. A pressure maximum is instead formed in the presence of an instantaneous reaction and surface diffusion for H2S. The application of this model was tested with experimental data using the Claus reaction as a model reaction. The ratio of the molar flux of H2S to the molar fraction of H2S (i.e., Ju2s^u2s) a s measured experimentally (data points) and as predicted theoretically by the model (lines) using parameters that have been measured independently are plotted as a function of ^ H 2 S ^ S O , in Figure 43. The experimental data lie systematically below the theoretical lines. According to Sloot et al. [156], this happens because their model assumes the reaction to be instantaneous, although experimentally this might not be true and due to the uncertainty in measurement of the surface diffusivities of H2S and SO2. In another paper the same group studied the CNMR reactor for the case for which the reaction occurring in the membrane is irreversible [158]. In this paper attention was paid to developing the conditions for which the slip of reactants in either membrane side vanishes and the rate reaches a maximum value asymptotically. The results of the model were compared

Catalytic Membrane Reactors 301

I0

m s

531

D data at 220 kPa A data at 500 kPa - theoretically predicted

20

10-

0

1.0

2.0

3.0

4.0

5.0

*so

Figure 43. Conversion measurements at a temperature of 542 K and pressures of 220 and 500 kPa. (From Ref. 156.) with preliminary experimental results with the CO oxidation reaction in a CNMR reactor. More recently, Harold et al. [159] have investigated the application of a similar reactor concept to partial oxidation reactions. In their analysis they considered a general reaction scheme A A +

b >R —

>r,R

(70)

PJ

(71)

A + b 3B -^p3P

q3Q

(72)

where A and B represent the oxygen and hydrocarbon, respectively; R the desired product of the partial oxidation; and P and Q the total oxidation products. The membrane is flat and thought to consist of a macroporous inactive support layer with a microporous active film on its top surface. Harold et al. investigated in detail a simpler reaction scheme, A A

(73) VpP

(74)

Under isothermal, isobaric conditions assuming that Fick's law of diffusion prevails and for differential reactor operation they analyzed two reactionorder combinations (otA1 = 0, a A2 = 1) and (a A 1 = 1, a A2 = 1) for which the problem is amenable to analytical solution. For a range of conditions,

Chapter 12

532

feeding two different mixtures of A and B on either side of the membrane seemed to give better yields to the desired product R when compared to the mixed-feed case (i.e., with both sides of the membrane exposed to the same feed mixture of A and B). Their theoretical results are in qualitative agreement with their experimental studies with the ethylene oxidation reaction to produce acetaldehyde and carbon oxides. In their experiments they used an asymmetric 7-Al2O3/a-Al2O3 membrane in which the active 7-Al2O3 layer was impregnated with V2O5. Experiments under segregated feed conditions in which the active layer was exposed to a C2H4 4- He mixture and the support to an O2 + He mixture gave significantly better selectivities to acetaldehyde over the mixed feed experiments, in which the active layer was exposed to a C2H4 + O2 + He mixture and the support side to a pure He feed. Harold and Cini [70] have also proposed the use of nonpermselective ceramic membranes in multiphase reactor applications. In their reactor (see Figure 44 for a schematic) the catalyticaly impregnated membrane serves primarily as a gas-liquid conducting device, in which the gaseous reactant flows through the tube side and the liquid reactant in the shell side. The liquid wets and fills the pores of the membrane within which the reaction occurs. Harold and Cini report that this multiphase membrane reactor provides for reduced transport limitations, better temperature control, and a well-controlled and defined reactant interface. They have presented a model for this reaction both for the case where axial concentration Liquid

Ga5 In .

I

•

In

Gas Filled Tube Core \ \ Liquid Filled Tube Wall

/ Liquid Filled Annul TL5

I

•+

—»

Figure 44. Schematic of the catalytically impregnated tube contacted cocurrently by the gas in tube core and the liquid on the shell side. (From Ref. 70.)

Catalytic Membrane Reactors

533

gradients exist in the liquid phase in the shell side and for the case for which the liquid in the shell-side volume is well mixed. The reactor behavior was compared with the behavior of a prototype trickle-bed reactor which consists of a string of suspended particles (see Figure 45), which are contacted by a cocurrent downflow of a gas and a liquid film. For catalytic reactions, whose rate is limited by the concentration of the volatile reactant, they find that for an identical catalyst volume the efficiency of the multiphase membrane reactor exceeds that of the prototype trickle bed by as much as an order of magnitude. The primary reason for this is that the liquid film in the membrane pores always remains exposed to the gas phase, and the additional mass transfer resistance one encounters with completely wetted catalyst particles is eliminated. The model development is based on prior models by Harold and Ng [160] and Ng [161] for multiphase catalytic reactors and its detailed description goes beyond the scope of this brief chapter. The complete set of equations can be found in the appendix of the paper by Harold et al. [70] and in the paper by Harold and Ng [160]. The reactors are assumed isothermal and the reaction is given by products,*(/)

Hs) + B,

(75)

with the rate of the reaction equal to /:CB/CA3^(CB), where CA and CB are the intraparticle concentrations of A and B, C B/ is the bulk liquid-phase Liquid In

Gas In

Gas

v

In

e

1

I Catalytic Pellet

1

cl

1

pi mm

L Liquid

/

111 (

X

Liquid Film

4

S X T~

/

1-Ew)S

2

Non wetted Surface

Film

Rs—-

Figure 45. (a) Schematic of the string of suspended spherical catalytic pellets contacted cocurrently by the gas and a liquid film; (b) catalytic slab model. (From Ref. 70.)

534

Chapter 12

concentration and ^(C B ) the Heaviside function. The prototype, string of pellets, trickle-bed reactor is treated as a catalytic wall of thickness 8 (see Figure 45), where 8 is the characteristic diffusion length of the catalyst sphere. This problem was studied by Harold and Ng and the model (see Ref. 160) consists of a mole balance for species A, and a momentum balance in the gas phase and mass balances for A and B in the liquid and catalyst phases. Quantities of interest include the fractional conversions of A and B, XA and XB defined in the customary way, and the overall reactor efficiency defined as the overall rate with respect to A divided by a hypothetical rate in the absence of transport limitations (i.e., with CB/everywhere equal to its inlet value, and CA the liquid-phase concentration everywhere equal to its inlet value in equilibrium with the inlet gas-phase concentration). The model for the multiphase membrane reactor (very similar to the CMR models discussed so far) contains momentum and mass balance terms for the tube side, reaction and radial diffusion terms in the membrane, and mass and momentum balance equations in the shell side, when axial gradients are assumed (the cocurrent flow catalytic tube reactor, CF as defined by Harold and Cini) or the modified equations for describing completely stirred conditions (this reactor is defined as WS by Harold and Cini). Figure 46 shows the efficiency of the CF reactor in comparison with the string of pellets for a constant value of catalytic material and as a function of liquid flow rate. The string of pellets curves are solid and for the CF reactor dashed (corresponding to a membrane thickness of 0.1 cm) or dotted (corresponding to a membrane thickness of 0.05 cm). Note that the CF membrane reactor (this is also true for the WS reactor) outperforms the prototype trickle-bed reactor. This is generally true as long as the nonvolatile reactant B is in short supply. In a subsequent paper [71] Harold and Cini have reported experimental results with their catalytic multiphase membrane reactor. The reaction studied was a-methylstyrene (AMS) hydrogenation to cumene and the ceramic membrane consisted of a thin -y-Al2O3 layer (ca. 50 |xm thick) deposited on an a-Al2O3 tube and impregnated with Pd. The authors report that the multiphase membrane reactor performed better than a single pellet reactor did under similar experimental conditions. F. FBMR System

Two different design options utilizing a Pd membrane FBMR for methane steam reforming have been suggested by Adris et al. [162] (see Figure 47). The designs differ in the stream that is used as sweep gas in the tube side of the Pd membrane tubes. In the first design, one uses the reaction product

Catalytic Membrane Reactors

-

/

-

/

-

*

•

535

-

5*

1

2

3

4

Liquid Flowrate, qr (cc/scc)

Figure 46. Comparison of the overall rate as a function of the liquid flow rate for the pellet string and two different catalytic tubes contacted by cocurrent gasliquid flow. The catalyst volume and overall length are fixed and the catalytic activity (kf) assumes three different values. The feed liquid is saturated with A and contains a large supply of B (CB/ = 103 gmol/cm3). Catalyst dimensions and other parameter values are provided in Table 4 from Ref. 70.

stream after it passes through a cyclone and a pressure-reducing valve. In the second design, part of the feed is allowed to pass through the membrane tubes and the rest through the reactor. The two feedstreams are then mixed to create the product stream. The development of the model proceeds along lines similar to that of the Pd/PBMR models, allowance being made for the fact that the shell side is a fluidized-bed reactor and the appropriate equations must be used. Adris et al. [162] assume that two-phase theory holds, the emulsion phase is well mixed, the bubble phase is in plug flow, and that one can use an average bubble size. The reactor is adiabatic and in the Pd membrane tubeside isothermal plug flow prevails for configuration I and nonisothermal plug flow for configuration II. One then proceeds by writing mass and heat balance equations for the bubble and dense phases in the fluidized bed on the shell side and by accounting for the hydrogen permeation through the Pd membrane wall. Development of the exact detailed equations can be found in the original publication by Adris et al. [162] and follows classical treatises on the subject of fluidized beds, allowance being made for the presence of Pd membranes. The authors, unlike the majority of fluidized bed reactor models, take into account the change in the total number of moles due to reaction and permeation.

Figure 47.

CONFIGURATION J

REACTOR FEED

ORIFICE PLATE

HEAT PIPE

PALLADIUM TUBE 8UNOLE

)

Figure 2. Relationship of catalyst effectiveness factor and Thiele modulus with first-order reaction in a spherical nonisothermal catalyst pellet.

558

Chapter 13

is plotted for a first-order reaction for several values of (3 for a spherical pellet with y - 20; they also presented graphs for other values of y. One of the most interesting features of Figure 2 is that for (3 > 0 (exothermic reaction), there are regions where the effectiveness factor is greater than 1. This behavior is based on the physical reasoning that with sufficient temperature rise, caused by intraparticle heat transfer limitations, the increase in reaction rate more than compensates for the decrease in concentration throughout the particle. The other interesting feature of Figure 2 is that for large p, multiplicity of effectiveness factor values exists. Of the three possible solutions, only the highest or lowest values of effectiveness factor are actually attained, depending on the direction of approach. The center value represents an example of physicochemical instability. Thus a catalytic reactor may operate at one of two stable-steady states, depending on the direction of approach to this region. The particle effectiveness factors show complex behavior for many different forms of kinetics under both isothermal and nonisothermal conditions. The relationships between effectiveness factors and Thiele modulus have been worked out for industrially important Langmuir-Hinshelwood reaction kinetics by Roberts and Satterfield [13,14]. These early results are extended to reactions for which diffusional gradients are beneficial by Varma and co-workers [15] and Harold and Luss [16]. A generalized method for analysis of multicomponent diffusion and complex reaction networks in porous catalysts was first proposed by Sorensen and Stewart [17]. Significantly more complex kinetic behaviors occur in biochemical and biological processes. A theoretical description of complex autocatalytic reaction mechanisms such as the Brusselator and the Oregonator, which describe these biochemical and biological processes for distributed parameter systems, is described by Nicolis and Prigogine [18]. Some complex periodic and chaotic results for the Brusselator model are summarized in Figure 3. Industrial practice over the years indicates that the usual order of events, as transport limitations occur in catalyst particles, is first internal pore diffusion, followed by external heat transfer resistance. For extremely rapid reactions, there is the possibility of external mass transfer resistance and then finally intraparticle temperature gradients. Only for unusual situations are the multiplicity features and instabilities predicted theoretically actually observed. The literature is full of fascinating nonlinear effects for complex kinetics coupled with transport limitations as shown in Figure 3. An excellent review of multiplicities and instabilities in chemically reacting systems is given by Razon and Schmitz [19]. As an illustrative example, here we consider some interesting features observed commercially for autocatalytic reactions reported recently by

Aspects of Modeling in Petroleum Processes Complex periodic Concentration of X

Time Concentration of X

Concentration of Y

559 Chaos

Concentration of X

Time Concentration of X

Concentration of Y

Figure 3. Dynamical behavior of chemical systems can take many different forms: plots of concentration versus time (top row) and phase portraits (bottom row).

Sapre [20], and Hu and Sapre [21]. Figure 4 shows calculated effectiveness factors as a function of Thiele modulus for an isothermal quadratic autocatalytic reaction. As shown in Figure 4, over a certain parameter range there is a significant enhancement in apparent catalyst activity. The effectiveness factor initially increases with increasing Thiele modulus, contrary to the expected effect of decreasing effectiveness factors for an isothermal catalyst particle. This behavior is based on the physical reasoning that the

Chapter 13

560 500 200 100

10

s p = i.o

Thiete Modulus ($)

Figure 4. Particle effectiveness factor as a function of Thiele modulus: quadratic autocatalysis. reaction rate of the primary reaction is increased due to the increased concentration of rate-enhancing autocatalytic species inside the particle because of intraparticle mass transport limitations. This behavior for autocatalytic reactions suggests that larger catalyst particles would lead to higher catalyst effectiveness factors for the conversion of the primary reactant and is opposite to the normal direction of reducing particle size to minimize mass transport limitations. Thus larger particles would allow higher space velocity operation for a flow reactor, reducing the amount and cost of catalyst. One could either increase the capacity of a given reactor by increasing catalyst size, or design a smaller reactor for the fixed capacity. The lower pressure drop with larger particles is a further practical benefit. Many biochemical, biological, and photochemical reactions are autocatalytic in nature. In the petroleum industry, methanol conversion over zeolite catalysts is reported to be autocatalytic [22,23]. A significant body of literature now exists in the field of transport processes coupled with heterogeneous reactions which has extended the earlier concepts. For a thorough review of this literature, readers are referred to many books on this subject (e.g., Aris [24], Satterfield [25], and FrankKamenetskii [26]). Above we discussed several aspects of intraparticle transport phenomena, in macroscopic catalyst particles. We now want to discuss the more molecular or microscopic aspects of transport and reaction. Here we focus primarily on the zeolites as catalytic materials.

Aspects of Modeling in Petroleum Processes

561

Zeolites have been studied since about 1756, but they gained little practical significance until zeolite A and zeolite X (Y) were commercially synthesized. Initially, these materials were used as commercial sorbents (desiccants) and for molecular size separations, such as the separation of nparaffins from isoparaffins [27]. The latter separation is based on the fact that zeolites have unique pore structures in that their pores are uniform in size and in the same size range as small molecules, Figure 5 [28]. Thus zeolites act as molecular sieves admitting those molecules that are smaller and screening out those that are too large. With the introduction of catalytic activity by ion exchange in the late 1950s, the potential for molecular shape-selective catalysis became a reality. Weisz and Frilette [2] were the first to demonstrate molecular shape selective catalysis. They demonstrated that Ca zeolite A, having an effective pore diameter of 4 to 5 A, selectively cracked straight-chain n-paraffins that could enter the pore structures and did not crack isoparaffins which were excluded based on molecular size. Weisz and co-workers [29] also demonstrated product selectivity by showing that of the multiplicity of products that could be formed, only those product molecules that can exit from the pores based on their size appear among the products. The discovery of ZSM-5 [30] having a pore diameter (5 to 6 A) intermediate in size between that of zeolite A (4 to 5 A) and that of zeolite X(Y) (8 to 9 A effective pore diameter), greatly increased the potential for molecular shape-selective catalysis (Figure 5). Since then, tremendous progress has been made in the understanding and application of molecular shape-selective catalysis. Chen et al. [31] provide an excellent review of molecular shape-selective catalysis and of its industrial application. In addition to molecular size-exclusion catalytic phenomena in zeolites, the interaction of diffusion rates and catalytic reaction is extremely important in determining their catalytic behavior. Furthermore, the diffusional rates for molecules as they approach the size of the zeolite pores is very complicated. Weisz [32] termed this region configurational diffusion. Its relation to diffusion in gases, Knudson diffusion is larger pores, and diffusion in liquids is shown in Figure 6. Figure 7 illustrates the strong dependence on unidirectional diffusion rate that the six carbon paraffins and methylbenzenes exhibit in ZSM-5 at elevated temperatures as a function of their critical molecular diameter [33]. This extreme dependence of diffusion rate on molecular size and shape indicates the complexity of configurational diffusion. Under reaction conditions, counterdiffusion must occur to accommodate the required fluxes of reactants and of products. Figure 8 again shows the extreme dependence of diffusion rate on critical molecular diameter for aromatic hydrocarbons counterdiffusing into a cyclohexane-saturated NaY

Chapter 13

562 Effective Diameter, A

VPI-5

AIPO4-5

AIPO4-H

NaX

ZSM-5

CaA

a(A)

Figure 5. Correlation between pore size of molecular sieves and the diameter (a) of various molecules. zeolite at room temperature [34]. Activation energies (10 to 20 kcal/mol) are markedly higher than those for counterdiffusion in liquids indicating the role played by steric factors [35]. Cations present (Na+ versus H + ), nature of the diffusing molecule (1,3,5-triisopropyl benzene versus 1,2,5triisopropylcyclohexane), and nature of the counterdiffusing molecule all have profound effects on diffusion rate. The impact of the presence of a second counterdiffusing species on the observed diffusion rates is also very pronounced as illustrated by the observation that the cumene unidirectional adsorptive diffusion rate is greater than 2000 times faster than for cumene counterdiffusion [35]. An anomalous cage effect for the diffusion of n-paraffins as a function of carbon number in potassium zeolite T was observed by Gorring [36]. The results are summarized in Figure 9. Rather than decreasing with carbon number, diffusivities exhibit a local minimum at C8 followed by a twoorder-of-magnitude increase to a maximum at C12. This appears to be due to a close fit between molecular length and cage dimension. Recently, Nitsche and Wei [37] presented a theoretical analysis of the window effect based on analogy of the configurational diffusion process with an "equivalent" one-dimensional Brownian motion of a rod through a periodic se-

563

Aspects of Modeling in Petroleum Processes Regular

mini

latm 10 atm

i

Gases

Liquids

1

10

100

1000

1

10

Pore Diameter/Angstroms

Figure 6. Diffusivity and size of aperture (pore); the regions of regular, Knudsen, and configurational diffusion. quence of potential barriers. Numerical calculations are in reasonable agreement with Gorring's experimental results. n-Alkanes longer than C8 are too large to fit entirely within the potential wells formed by the erionite cages and therefore experience smaller energy barriers to diffusion. When n-C22 and n-C23 paraffins are cracked over erionite, which has a pore structure similar to zeolite T, the product distribution has two distinct maxima at about C4 and C12 and a distinct minimum at C8 (Figure 10) [38]. This distribution is drastically different from any produced by other acidcracking catalysts and illustrates a strong interplay between reaction and diffusion; C8 cannot diffuse out rapidly enough and undergoes further cracking. Much progress has been made in the area of molecular dynamics simulation of sorbate molecules in zeolites, which can provide quantitative analysis of configurational diffusivities and other transport and reaction

564

Chapter 13

10

10

10"10

10

-12

(j) Aromatics 315°C •

Aliphatics 500°C

2

I

!

4

6

8

10

Critical Diameter of Molecule, A

Figure 7. Diffusion coefficients in HZSM-5 for hexane isomers (at 500°C) and aromatics (at 315°C).

parameters. A classic study in this field is by June et al. [39]. They report good quantitative agreement between the theoretical molecular dynamics estimates and NMR pulsed field gradient measurements for methane, xenon, and propane in low-Al ZSM-5. The challenges in computational dynamics are to extend these principles to industrially relevant and significantly more complex systems. Recent examples of this involve NMR measurements and molecular dynamics modeling of reactions occurring over ZSM-5 in the methanol to gasoline (MTG) reaction. The first direct evidence of both specific reaction pathways and of diffusion-related shape selectivity has recently been reported. In this case, the use of 13C magic-angle-spinning NMR shows promise to identify the mechanism of formation of the first carbon-carbon bond and the nature of reaction intermediates in the catalytic conversion of

Aspects of Modeling in Petroleum Processes

565

100.00 D

vToulene

A 1,3-diethyl benzene

Symbol

effat

= 0.60

10.00 — \

p-xylene

1.00 —

-

A) naphthalene 2 - ethyl naphthalene

1,3diisopropyl benzene 1 - ethyl naphthalene

1 - methyl naphthalene

0) Q

1,3,5-trimethyl benzene

pure

0.01

0.001

r

m-xylene

_L 7

8

9

Critical Molecular Diameter, A

Figure 8. Dependence of effective diffusion coefficient on critical diameter of diffusate, adsorptive counterdiffusion into cyclohexane saturated NaY at 298 K.

methanol to hydrocarbons over ZSM-5 zeolite catalyst [40]. Several organic species were identified in the adsorbed phase which were not present in measurable quantities in the bulk phase, and their fate was monitored during the course of the reaction using this technique. This direct observation of product shape selectivity and ability to distinguish unequivocally between mobile and adsorbed species should provide a better understanding of catalytic processes in the intracrystalline space of zeolites and assist the design of improved shape-selective catalysts. Molecular dynamics calculations of the van der Waals interaction energy between methyl-substituted aromatics and the ZSM-5 pore structure pro-

Chapter 13

566

o o

10

-12

\

i

L

\

- \

i

1 \

\ \ \

10

-13

0

1

2

3

4

5

6

KJ 7

8

alkane

Figure 9. Diffusion coefficients of «-alkanes in potassium T zeolite at 300°C.

vides further insight into factors controlling product molecular shape selectivity. Results are summarized in Table 1 [41]. p-Xylene has a low, shallow energy minimum and diffuses about a thousand times faster than either o- or m-xylene. Of the trimethyl aromatics the 1,2,4-trimethylbenzene has the lowest energy, should diffuse more rapidly than the other isomers, and is the predominant product, exceeding equilibrium, whereas the others, which are more sterically limited, appear at only very low levels (Figure 11). Similarly for the tetramethylbenzenes, which represent about 4% of the product, only the 1,2,4,5-tetramethylbenzene appears in significant quantities and in strong preference to the equilibrium preferred 1,2,3,5-tetramethylbenzene (Figure 11). Here the energy minima suggest that the 1,2,4,5-species should be favored, but also that the 1,2,3,5-species

Aspects of Modeling in Petroleum Processes

567

30

20 5?

10

0

1 2 3 4

5

6 7

8 9 10 11 12 13 14

Product Carbon Number Figure 10.

Carbon number distribution of cracked products over erionite at 340°C.

Table 1 Minimum van der Waals Interaction Energy for Aromatic Hydrocarbon in ZSM-5 Hydrocarbon Xylenes o-xylene m-xylene p-xylene Trimethylbenzenes 1,2,3-TrMeB 1,3,5-TrMeB 1,2,4-TrMeB Tetramethylbenzenes 1,2,3,4-TrMeB 1,2,3,5-TrMeB 1,2,4,5-TrMeB Source: Ref. 41.

Min. van der Waals energy, kcal/mol 16 -4 -13 56 45 16 54 450 21

Chapter 13

568 100

Equilibrium Experimental

80 *

60

S

40 20 0

1,2,3

1,2,4

1,3,5

Trimethylbenzenes 100

Equilibrium Experimental

80 55

60

S

40 20 0

1,2,3,5

1,2,4,5

1,2,3,4

Tetramethylbenzenes

Figure 11. Polymethylbenzene reaction selectivity of ZSM-5 in methanol to gasoline reaction. may be severely sterically hindered from forming in the pores, suggesting a transition-state selectivity as proposed for other reactions [42,43], Although there is much left to be done, predictive techniques are beginning to bear fruit. The knowledge gained from such studies, combined with information on the structure of the catalyst surface, and macroscopic reaction kinetics should lead to critical understanding of both the steric and chemical requirements of active sites essential for improved activity and selectivity. The net result is that catalyst development will become less empirical and more predictive and, perhaps, will allow us to reach the elusive goal of developing solid catalysts with enzymelike specificity. The power of chemical reaction engineering principles and modern surface science techniques to develop a step-out catalyst is illustrated by the development of selective catalytic reduction (SCR) catalysts. Specifically,

Aspects of Modeling in Petroleum Processes

569

a reaction engineering model showed that the optimum balance between surface-catalytic activity and diffusivity is provided by a bimodal pore structure with a substantial component of macropores [44]. Such pore structures are not physically stable for conventional vanadia on titania SCR catalysts. Whereas silica can be engineered to satisfy the calculated pore structure requirement, the intrinsic activity of vanadia dispersed on silica is poorer than vanadia dispersed on titania. This superior performance of vanadia on titania can be explained by the Raman spectra, which show a higher proportion of noncrystalline vanadia with titania. Temperatureprogrammed reduction and 18O/16O isotopic exchange studies revealed significantly more labile oxygen with this highly dispersed, noncrystalline species of vanadia [45]. Since NO reduction by NH3 proceeds by a redox mechanism, more facile oxygen correlates with higher catalyst activity. Therefore, an ideal catalyst would have a silica support to achieve the optimum physical characteristic of porosity and pore size distribution, and a surface that is coated first with titania to provide the desired chemical properties to achieve high vanadia dispersion. The optimized vanadia/ titania/silica catalyst shows 50% higher NO conversion activity than the currently available conventional commercial catalyst. This higher activity is expected to reduce SCR reactor volume by about 33%, with associated gains in reduced operating cost and capital requirements, and increased time between catalyst change-outs as reported by Beeckman and Hegedus [44]. 11.

REACTION KINETICS

Reaction kinetics often play a key role in helping synthesizing improved catalysts with the desired balance between activity and selectivity for the catalyst particles. Furthermore, knowledge of the kinetics of a process allows one to design and operate commercial reactors and optimize the processes that employ those reactors. The most widely used industrial process models in the late 1940s and early 1950s were, typically, graphical representations of plant data in easy-to-use nomograph form. One such model, a run-around chart for commercial TCC units, is shown in Figure 12. Such nomographs were purely correlative with no fundamental basis built into them. As a result, extrapolation beyond the range of data used for their development could be quite hazardous. The pioneering work by Weisz and co-workers on kinetics of coke burning in the mid-1950s lead to the first successful kinetic model used commercially in Mobil and perhaps in the industry. This model included such effects as fast- and slow-burning coke, intrinsic carbon-burning kinetics and its relation to oxygen utilization, and the impact of diffusion on coke burning in TCC beads. Quantitative

Chapter 13

570 Space Velocity V/HR/V 20 30 40 15'

465

Catalyst to Oil Ratio V/V

Figure 12. Runaround chart for commercial TCC unit. predictions of resulting "fish-eye" phenomenon observed commercially in TCC beads and intrinsic kinetics are well documented in a series of papers by Weisz and Goodwin [46,47]. Experimental data on average burning rates as a function of temperature are plotted for TCC beads and groundup catalyst in Figure 13. It is evident that the beads suffer from significant diffusional resistance for temperatures greater than 475°C, and these observations are consistent with criterion stated in Eq. (1). The observed coke profiles range from homogeneous burning at low temperatures to the sharp-boundary-shell progressive situation resulting in fish-eyes at high temperatures as depicted in Figure 13. The first successful so-called "cold turkey model" was the TCC kiln model developed in the mid-1950s and used extensively to optimize TCC kilns. This classic work has been reviewed in detail by Prater et al. [48]. Below we review advances in the reaction kinetics of hydrocarbon cracking and reforming. Before we review advances in catalytic kinetics, we review the kinetics of thermal cracking to illustrate the level of fundamental detail captured in modern-day reaction kinetics. Advancements in analytical chemistry and computational techniques are allowing us to describe events in microscopic detail. Such fundamental kinetic descriptions will

Aspects of Modeling in Petroleum Processes

571

Powder (R = 0.01 cm)

10" CO CO

Beads (R 3 2.0 cm) o

10" Low Temperature

I 450

I 500

Intermediate Temperature

I I I 550 600 650

High Temperature

w

Vc Figure 13. Average observed burning rates of cracking catalyst versus temperature.

help synthesize improved catalysts in the future, design better processes, and more effectively optimize their operation. IV.

HYDROCARBON CRACKING

Cracking large hydrocarbon molecules to smaller hydrocarbons to produce fuels and petrochemicals is one of the most significant developments of this century. Both thermal and catalytic processes evolved to produce small olefins such as ethylene and propylene, which are major building blocks of the petrochemical industry and midrange hydrocarbons for gasoline manufacture. A. Steam (Thermal) Cracking Stream cracking is the dominant process to produce ethylene and propylene. Although the steam cracking has gradually evolved into a short-contract-time (millisecond furnace residence time) and high-temperature (800

572

Chapter 13

to 1100°C) process, the fundamental chemical reaction sequence and product selectivities have changed very little. Over the years, the process chemistry and reaction kinetics have been studied very carefully. Today, advanced fundamentally based reaction kinetic models have been developed and are applied successfully commercially. A key factor in modern olefin plant design and operation for maximum flexibility and feedstock utilization is accurate, detailed yield and furnace performance predictions, including run-length predictions, for feedstocks ranging from ethane to heavy gas oil or mixtures thereof (co-cracking). Modern steam cracking kinetic modeling employs a homogeneous freeradical reaction scheme involving several hundred reactions [49,50]. The current status has evolved from over three decades of fundamental research. The completeness and complexity of the current models is in part due to advanced analytical and particularly advanced computation facilities that permit handling large numerical computations. Steam cracking kinetics evolved as follows: 1. Empirical modeling, regression of yields and operating parameters 2. Stoichiometric or global molecular (apparent reaction kinetic) models 3. Mechanistic models, based on detailed description of main radicals and elementary molecular reaction paths With the empirical modeling methods, only the overall material and thermal balances around the furnace were possible. In general, a pilot steam cracking unit was used, and the resulting data were regressed to develop empirical or semitheoretical scale-up rules to translate laboratory results to commercial applications. Although such models were useful over a narrow range of operation and were often used for control purposes, they were unreliable outside the range of data from which they were derived and could not predict the effects of changing feedstocks. As the technology advanced, much effort went into global molecular or stoichiometric modeling. Only the apparent global chemical reactions were accounted for in this approach. A large set of high-quality experimental data was always necessary to estimate the kinetic parameters and to discriminate between rival apparent reaction kinetic schemes through nonlinear optimization programs [51,52]. This global molecular reaction approach has been quite successfully applied to the pyrolysis of ethane, propane, butanes, and their mixtures. However, the modeling of complex feed mixture such as naphthas and gas oils was intractable with this approach. Therefore, simplified, lumped kinetic models evolved for handling such feeds. Although global molecular lumped models suggest a fundamental

Aspects of Modeling in Petroleum Processes

573

approach, such a conclusion is misleading because apparent frequency factors and activation energies are not typically real constants but are functions of reactant concentration and operating variables as shown by Van Damme et al. [53]. As a result, anomalous paradoxical behavior occurs for the same reaction depending on whether a pure component or a mixture is used as feedstock. In 1970, Benson proposed that "there is now sufficient understanding and both kinetic and thermochemical data available to describe the behavior of the most complex pyrolysis reaction in terms of a finite number of elementary-step reactions. On this basis it might be expected that hydrocarbon pyrolysis is a ripe candidate for quantitative modeling" [56]. In the early 1970s Ranzi et al. [54], Sundaram and Froment [55] and others recognized the shortcomings of the global molecular models and undertook developing fundamental mechanistic models. As a result of these activities, Benson's prediction is now a commercial reality. Pyrolysis models are the most fundamental kinetic models that have been developed to date and are used routinely in the commercial operation of steam pyrolysis furnaces. An excellent review of this field is given by Ranzi et al. [54] and Dente et al. [57-59]. A commercial simulation package called SPYRO includes a comprehensive mechanistic kinetic model [59], and there are several other competitive commercial products that match the complexity and rigor of SPYRO. Mechanistic models allow significant extrapolation beyond the original data base in terms of feed composition, and operating conditions. After characterization of the reactions and their associated intrinsic kinetic parameters, the proper use of structural and mechanistic analogies allows a priori modeling of the conversion of previously untested hydrocarbons and feed mixtures. Development of such mechanistic models is expensive since they require a large amount of up-front experimental and analytical work. However, the payoff associated with their accuracy and resulting potential to improve commercial operation typically far outweighs their initial cost. Main pyrolysis reaction classes are summarized in Figure 14. Most reactions involve radicals, but some purely molecular reactions also play a significant role. Figure 15 represents the radical reaction scheme for the thermal cracking of 3-methylpentane, one of the many components of naphtha [60]. Such reaction networks can be generated automatically using rule-based systems reflecting the structure of the hydrocarbon reactant and fundamental radical chemistry as illustrated by Hillewaert et al. [61]. Classification of elementary reactions allows use of group contribution methods and the analogies for reactions of the same class, which significantly reduce the number of independent rate parameters that need to be obtained from experimental data. Importance of group contribution methods in ther-

Chapter 13

574 1. Chain-initiation reactions unimolecular: R - R1 -> R • + R' •

(example: C 2 H 6 -* 2 CH3)

or bimolecular (R'H in an unsaturated hydrocarbon): RH + R'H - R • + R'H •

(example: C 2 H 6 + C 2 H 4 - 2 O , ^ )

2. Hydrogen-abstraction (metathetical) reactions R • + R'H -> RH + R1 •

(example: CH 3 + C 2 H 6 - CH 4 + C2Hg)

3. Radical-decomposition reactions R • - RH + Rl •

(example: n-C3H'7 - C 2 H 4 + CH3)

4. Radical-addition reactions to unsaturated molecules R • + R'H - R" •

(example: CH3* + C 2 H 4 - n-C3H7)

5. Chain-termination reactions by recombination of radicals: R • + R' • -> R - R'

(example: CH 3 + C ^ -> C3H8)

by disproportionation of radicals: R • + R' • -» RH + R"H

(example: CgHg + C2Hs - 2 C2H4)

6. Purely molecular reactions RH + R'H - R"H + R'"H e.g., "four-center11 concerted reactions "six-center" concerted reactions

(example: C 2 H 6 ~* C 2 H 4 + H2) (example: pentene-1 — C 2 H 4 + C 3 H 6 or hexadienes 1-3 -• hexadienes 2*4 isomerization)

Diels-Alder type dissociations (cyclohexene -+ C 2 H 4 + C4H6) 7. Radical-isomerization reactions R1 • - R" •

(example: CH 3 CH 2 CH 2 CH 2 - CH3CH2CHCH3)

Figure 14. Thermal-cracking main reaction classes.

modynamic calculations is well known [62]. Use of such concepts in chemical kinetics has advanced rapidly in recent years. Use of group contribution methods to estimate frequency factors and activation energy for thermal pyrolysis is described by Willems and Froment [49,50]. Starting from a detailed mechanism for every elementary reaction, a structure is proposed for the corresponding activated complex. The standard entropy of the activated complex is estimated from statistical thermodynamics, the frequency factor is calculated from transition-state theory and the activation

575

Aspects of Modeling in Petroleum Processes

/AAA

k

ls,ps

k

D(p)

o®//+/W k

K

k

k

//\

*

A

ls.s P ||k, s , p s

ls,sp

k

D(p)

, / W

Ab< H s

• CH3

CH3

/V *ls,ss

k

ls,:ss k

K

ls,sp

D(p)A + CH3

Is.ps

\A k

Ab Catalyst A Catalyst B Catalyst C

63 65 68

0.53 0.38 0.42

66 62 67

Catalyst A-REY Catalyst B-USY Catalyst C-RE-USY Source: Ref. 65.

B A C

C C A c

rv

"

Cr -

A B B

Conv.,

Kc

1.39 0.95 1.04

70 64 67

Kc

1.47 1.20 1.33

Ranking for Coke Selectivity

Ranking for Activity FFB Ranking MAT Ranking Riser Ranking

Riser Results

MAT Test

B B B

C C

c

A A A

Coke Cr x

1 - x

catalyst ranking is a function of the catalyst characteristization test. The true ranking is reflected by the riser data. For a heat-balanced FCC operation, coke conversion selectivity, or the dynamic activity as it is termed in the petroleum industry, is far more important and is also shown in Table 2. The second-order kinetics coupled with accurate description of transport phenomena and transient operation can accurately translate measurements from one reactor to another. Experimental data and model predictions for MAT and FFB reactors for USY and REY catalysts using this approach are summarized in Figure 19. The agreement between model predictions (the lines) and experimental data (the points) is excellent. The simple second-order reaction kinetics model could easily sort out these potential pitfalls in catalyst ranking. For catalyst screening, therefore, this simple model is adequate. This approach is used even today to translate catalyst performance among different reactor types, as summarized by Sapre and Leib [66]. The second-order kinetics approach has been extended to the entire boiling range as a continuous function by Krambeck [67]. For a given

Chapter 13

580 100

§ o

E

50

75

100

MAT Conversion

Figure 19. Comparison of MAT and FFB conversions. Second-order kinetics can accurately translate test results (lines represent model predictions). feedstock and catalyst, this approach is excellent and can be used reliably to interpolate the experimental yields. However, the resulting kinetic parameters are feedstock and catalyst dependent. The inherent difficulty with this continuum approach is that not enough chemistry is included in the kinetic description. A complete description of the system in terms of individual compounds is impractical for complex feedstocks typically processed in FCCs. It is impossible to characterize and describe kinetics at a molecular level. Thus lumping many individual compounds into a smaller number of groups is necessary. Lumping of similar chemical species greatly reduces the complexity of kinetic formulation. Considerable use has been made of this technique in commercial reactor modeling. The theoretical background for lumped mono-molecular reactions was provided by Kuo and Wei [68,69]. This work showed that it is possible to lump a number of species together and still have the lumped kinetics accurately describe the overall reaction behavior of the system. The first such successful commercially important lumped model is the 10-lump Mobil FCC model described by Jacob et al. [70]. The structure of the 10-lump Mobil FCC model is shown in Figure 20. The rate constants in this model were invariant with respect to the original crude source. It did an excellent job for vacuum gas-oils typically processed in Mobil at

Aspects of Modeling in Petroleum Processes

= Wt.% paraffinic molecules, (mass spec analysis), 430°- 650T = Wt.% naphthenic molecules, {mass spec analysis), 430°- 650°F ~ Wt.% carbon atoms among aromatic rings, (n-d-M method), 430°- 650°F A/ = Wt.% aromatic substituent groups (430°- 650°F) P h = Wt.% paraffinic molecules, (mass spec analysis), 650°F+ Nn

- Wt.% naphthenic molecules, (mass spec analysis), 650°F+

C ^ n = Wt.% carbon atoms among aromatic rings, n-d-M method, 650°F+ An

- Wt.% aromatic substituent groups (650°F+)

G = G lump (C 5 - 430°F) C = C lump (C1 to C 4 + COKE) C A / + p / + N/+ A/= LFO (430°- 650T) C A h + Ph + N h + A h =

Figure 20.

H F 0

(650°F+)

Ten-lump FCC kinetic model.

581

Chapter 13

582 80

Conversion 70

60

50

40

1/2

Actual Predicted

JL

1/30

3/6

4/3

5/1

5/29

Time ———

6/26

7/24

JL

8/21

9/25

»

Figure 21. Mobil FCC model accurately tracks commercial performance. the time of its development and further improvements to the model have been made over time. Significant additional delumping has become necessary to represent the much wider variety of feedstocks being processed in FCCs today. FCC feeds can vary from hydrotreated heavy gas-oils to atmospheric resids, and can include significant portions of nonvirgin stocks such as lube extracts, coker gas-oils, and other cracked stocks. The FCC kinetic model forms the heart of the FCC process model or process simulator. In the process simulator, all components of the FCC process, including the reactor, the regenerator, the main column, and the unsaturated gas plant, are typically included. For refinery use, this type of process simulator can be integrated into a refinery-wide simulator and can also feed data into the refinery management information systems. The process simulator is typically customized for each refinery to reflect the actual equipment in the plant. Accuracy of the model to reflect commercial plant performance is shown in Figure 21. Both conversion and gasoline yield are accurately predicted. V.

REFORMING

In FCC, although important, catalyst deactivation does not significantly affect product selectivities and is a secondary effect when compared with

Aspects of Modeling in Petroleum Processes

583

catalyst type. However, in other processes, such as catalytic reforming, catalyst deactivation significantly impacts product selectivity. Therefore, a fundamental catalyst deactivation model must be an integral part of a reforming kinetic model. Some of the earliest work on dual-functional catalysis, which is typical of reforming reactions, is summarized by Weisz and Prater [71]. This fundamental work on how re-forming catalysts function formed a basis of the later kinetic modeling efforts at Mobil. In attempting to understand the complex network of reactions involved in reforming, Wei and Prater [72] did a comprehensive study of complex systems of mono-molecular and pseudo-mono-molecular reactions using the methods of linear algebra. A first attempt to abandon the global kinetics approach and apply lumped kinetics to naphtha reforming was undertaken by Smith [73]. His lumped reaction sequence distinguished between n- and /-paraffins, naphthenes, and aromatics. This lumped model is akin to the three-lump model described previously for catalytic cracking, and the rate constants were a function of feedstock. This lumped representation is closely tied to what the analytical chemist could reliably measure at that time. In fact, the history of lumped kinetics is closely tied to the advances in analytical chemistry. In the late 1950s, crude PIONA (n-paraffins, isoparaffins, olefins, naphthenes, aromatics) analysis allowed only such coarse characterization of naphthas. As gas chromatography advanced, the component analysis of naphthas became possible, and models were developed to reflect the components and lumps associated with the measurements. Kmak [74] published aspects of Exxon's reforming model containing 22 lumped species, which is summarized in Figure 22. Whereas many of the lower-molecular-weight species are pure components, the seven- and eight-carbon systems lump many different species. Kmak's model considers dealkylation of the naphthenes with seven or more C atoms, but all components above C8 are still lumped. Kmak's comparison of the predicted product selectivity with the observed data was excellent. Mobil developed a reforming model in the early 1970s, which was similar to Exxon's reforming model. Details of Mobil's reforming kinetics model are summarized by Ramage et al. [75]. Two of the rules laid down in the development of this model were that it contain no adjustable parameters and that it predict the performance of commercial units from laboratory measurements of the rate parameters in special experiments. This goal was achieved and has been maintained since. In this reforming model reaction rates for the start of cycle are described by 13 pseudo-mono molecular kinetic lumps. On the other hand, there are 22 deactivation kinetic lumps to describe the aging phenomena. Therefore, whereas the 13 hydrocarbon lumps represent the hydrocarbon conversion kinetics, they

584

Chapter 13

Figure 22. Reforming lump reaction network. (From Ref. 74.)

had to be delumped to describe the deactivation kinetics. Additional delumping is necessary to estimate many of the product properties, such as octane and RVP. There are 34 lumps to characterize the product properties completely. The different lumps in the reforming model are summarized in Figure 23 and Tables 3 and 4. Paraffins, five- and six-ring naphthenes, and aromatics for each carbon number are the critical lumps to describe the yield patterns, as summarized in Figure 23. The four dominant reaction types are dehydrogenation, isomerization, ring closure, and cracking to C5— lighter products. Catalyst aging is a strong function of feedstock and increases with increasing amounts of C 8 + species in the feed. Therefore, there are 22 deactivation kinetic lumps, which are summarized in Table 3. Furthermore, catalyst aging affects the four reaction types differently. Therefore, there

Aspects of Modeling in Petroleum Processes

585

Table 3 Aging Components in Reforming Kinetic Model Component number 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Component name

Component abbreviation

Hexanes Methylcyclopentane Cyclohexane Benzene C 7 Paraffins C 7 Cyclopentanes QCyclohexanes Toluene QParaffins QCyclopentanes QCyclohexanes C 8 Aromatics QParaffins C 9 Cyclopentanes QCyclohexanes C 9 Aromatics C10Paraffins C 10 Naphthenes C 10 Aromatics C n Paraffins C n Naphthenes C n Aromatics

QP QN5 QN6 QA QP QN, C7N6 QA QP QN5 QN6 QA QP QN5 QN fi QA C10P C10N C10A Q,P CnN QiA

Source: Ref. 74.

are four deactivation rate parameters, each corresponding to dehydrogenation, isomerization, ring closure, and cracking reactions. However, these are independent of carbon number but are a function of local hydrocarbon composition, temperature, and time. Additional delumping was necessary to estimate product properties and process conditions critical to an effective process model, the C 5 - kinetic lump is delumped into C1 to C5 light-gas components; the paraffin kinetic lumps into isoparaffin and n-paraffin components; and the C8+ kinetic lumps into C8, C9, C1(), and C n components by molecular type, as summarized in Table 4. The paraffin distribution is constrained by known equilibria. The accuracy of this model to predict pilot plant and commercial data is illustrated in Figure 24. Gasoline yield versus octanes for a variety of feedstocks, catalysts, and operating conditions is shown in Figure 24a. This large variation in the gasoline yield at a given octane (as much as 25%) results from the wide range of process conditions and feed quality. As

Table 4 Delumped Components Required to Predict Product Properties Component Number

Component Lump

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

Hydrogen Methane Ethane Propane Isobutane n-Butane Isopentane n-Pentane Isohexane n-Hexane Methylcyclo C5 Cyclohexane Benzene Isoheptane n-Heptane C7 Cyclo C5 Methylcyclo C6 Toluene Isooctane n-Octane C8 Cyclo C5 C8 Cyclo Q CH Aromatic Isononane n-Nonane C9 Cyclo C5 C9 Cyclo C6 C9 Aromatic C10 Paraffin C10 Naphthene C10 Aromatic C n Paraffin C n Naphthene C n Aromatic Additional paraffin distribution lumps 2-Methyl Pentane 3-Methyl Pentane Dimethyl Butane 2-Methyl Hexane 3-Methyl Hexane Dimethyl Pentane Monomethyl C7 +. Dimethyl C 6+ Normal C3 +.

Source: Ref. 74.

Aspects of Modeling in Petroleum Processes

587 C5-

C7 Lumps:

C5-

C6 Lumps:

C5-

p

*

* N5 «

*- N6'

Figure 23. Mobil reforming lump reaction network. shown in Figure 24b when these data are normalized using the model, the model predictions are shown to be quite accurate. The prediction of cycle length also closely matches the commercial plant performance as shown in Figure 25. This demonstrates the strength of the aging kinetics. The first version of the model was developed for fixed-bed semiregenerative reformers. The model has now been extended to the latest generation of continuous reformers as well. Having a fundamental kinetic basis made this task easier. The gasoline octane predictions from the model are summarized in Figure 26. This is one of the earliest composition-based octane models developed. More than 6000 runs went into validating the model, of which only a small fraction of the data are presented in Figure 26 along with the form of the octane correlation. In this model, ONi is pure component octane number, and Vi is the volume fraction of that component in the gasoline. This model recognizes nonlinear blending of octanes, and blending octane numbers are a function of the absolute octane level. The standard error of perditions is 0.7 octane number. Froment and co-workers [76] recently delumped the Kmak reaction network; their model is summarized in Figure 27. Specifically, the C8 fraction is delumped. Furthermore, in fitting the rate data the problem was partitioned by studying first C6 reforming, then C7 reforming, before proceeding to the full-range naphtha. This current trend in kinetic modeling continues to reflect the increasing detail and accuracy with which chemical compositions can be determined with modern analytical methods as well as the relative ease of tracking more difficult computational problems with modern computers. More detailed composition-based modeling advances are expected even for the proven reforming kinetics.

Chapter 13

588 95 • Pilot Plant Data D Commercial Data

D DD

90 85

£

-

* D

n

*£l

80

D

D

j_Dp

75 -70

D D D

\ D

\

D

B 88

-

•

D

•

P i

•

_

i

•

100 102 104 106 Octane Number, C5+ R+3

108

(a)

•Q

1 Q

10 8 6 4 2 0 -2 -4 -6

-10

Average Deviation of KINPtR

Pilot Plant Data Commercial Data 98

100

102

104

106

108

+

Octane Number, C 5 R+3

(b)

Figure 24. KINPtR yield comparisons: (a) actual reformate yield—octane data; (b) KINPtR normalized data.

500

2. 9 300 -

200 ~

1 0

100

200

300

400

500

Actual Cycle Length, days

Figure 25. KINPtR accurately predicts commercial cycle lengths. 150 ON

ZVi (1 - ai) ONi

1-XViai

125

100

50

25

-

1

^1

........Ill 2

-

1

0

hi...

1

2

(Observed R+O)-(Predicted R+O)

Figure 26. Accuracy of composition-based octane number model. 589

Chapter 13

590

i

6N 9 + -

r

V-

— nPD«—-6NO

-SBP 8 S=^5N-—

nP,

r

5N7 nP 6

SBP, 6

't!

OIN

6

Figure 27. Reforming lump reaction network. (From Ref. 76.)

Aspects of Modeling in Petroleum Processes VI.

591

RECENT TRENDS IN PETROLEUM KINETICS

There is significant renewed excitement in the petroleum research community today in kinetic modeling. This is due primarily to the new directions being taken in dealing with the kinetics of complex mixtures, such as petroleum fractions. A recent workshop organized by Mobil captures some of the latest trends as summarized by Sapre and Krambeck [77], More fundamentals of reaction chemistry are now being integrated with the kinetics, and the trend is clearly toward further delumping. The types of mechanistic models developed for thermal cracking in homogeneous media are a good indication of future directions for heterogeneous catalytic reactions. Modern analytical chemistry provides the ability to characterize feedstocks at essentially the molecular level of detail. Thus a wealth of new information is now available for inclusion in kinetic modeling. Molecularlevel feedstock characterization is now possible due to advances in analytical techniques, such as high-performance liquid chromatography (HPLC), gas chromatography (GC), mass spectrometry (MS), field ionization mass spectrometry (FIMS), nuclear magnetic resonance (NMR), and so on. Such detailed feedstock description allows deeper understanding of reaction networks for each characterized molecular lump. For each reaction type, such as cracking, isomerization, and so on, elementary reaction steps and single event kinetics can be incorporated into kinetic models. For example, in catalytic cracking, carbenium ion theory, stability and reactivity of primary, secondary, and tertiary carbenium ions, beta-scission rules, and so on, are applied at the pseudomolecular level. When appropriate feedstock molecular detail and elementary reactions are incorporated into sufficiently detailed kinetic expressions, the resulting product distribution also has molecular-level detail. This capability will allow accurate calculation of product composition and accurate prediction of product properties. Fuels are typically complex mixtures of hydrocarbons prepared to meet certain physical properties. However, this is changing rapidly. Fuels are being viewed more as mixtures of chemicals having constrained composition ranges driven by environmental and other regulations. Mechanistic kinetic models provide the necessary composition detail on the products formed as well as on extent of conversion, which has been the focus in the past. Reaction engineers are taking advantage of the increased compositional information provided by modern analytical methods to revolutionize kinetic modeling. Reaction networks can be generated for each molecular type using rule-based systems. In the past, reaction pathways were identified by doing experiments with model compounds representing initial feed and

Chapter 13

592

several intermediates. The detailed reaction pathways were identified for each reactant molecule. Such fundamental information from model compound studies is valuable in developing the rules. In addition, incorporation of fundamental laws of reaction chemistry allows accurate description of reaction pathways. A new method, called structure oriented lumping (SOL), for describing the reactions, product composition, and properties of complex hydrocarbon mixtures has been developed as described by Quann and Jaffe [78]. The kinetics are developed by the application of simple principles. The types of reaction that a particular molecule undergoes and their rates are a function of its molecular structure, reaction conditions, and catalyst type. Molecules are represented as a collection of structural increments, and group contribution methods can be applied to estimate the kinetics. Group contribution methods have been used successfully in thermodynamics for many years. These methods have been applied successfully to the kinetics of homogeneous pyrolysis reactions more recently, and their use in describing heterogeneous kinetics offers new opportunities for describing the catalytic conversion of complex feedstocks. The SOL approach provides a foundation for molecular-based modeling of all refinery processes.

S

0.99

1.00

1.01 1.02 n - Electron Density

1.03

1.04

Figure 28. Linear-free-energy relationship for the hydrogenation of aromatic compounds. (From Ref. 79.)

593

Aspects of Modeling in Petroleum Processes

Group contribution methods allow unknown reaction rates of compounds to be estimated from measured reaction rates on similar compounds. This concept of molecular structure and reactivity is illustrated by a simple example in Figure 28. Figure 28 shows a good correlation of experimentally measured kinetics for the hydrogenation of aromatic compounds with the ir-electron density of the ring undergoing hydrogenation [79]. Thus two parameters, the slope of the line and intercept, allow estimation of hydrogenation rates of compounds in a homologous series. The power of this methodology is in the implied predictive ability. For example, the rate of hydrogenation of a molecule not studied experimentally can be determined by performing molecular orbital calculations to determine the 7T-electron density and then utilizing the linear relationship of Figure 28. The key element in this approach is the correlation of kinetic parameters as a function of substructures or functional groups. Work of Allen and co-workers [80,81] represent the state of the art in catalytic cracking kinetics following the group contribution approach. Their results for gas-oil cracking over an amorphous catalyst are shown in Figure 29, which gives the carbon number distributions as a function of reaction time. Time equal to zero corresponds to feed composition. For each carbon number, approximately 20 to 35 molecular structures are included. As the reaction proceeds, hundreds of molecular species are produced as heavy

250 -i

Time (sec) 10

15

25

Carbon Number

Figure 29. Carbon number distributions of the cracking products of gas-oil.

Chapter 13

594

hydrocarbons are converted to light products with increasing reaction times. This approach shows great potential to predict product composition and properties such as gasoline octanes [82]. The challenge in this area is clearly to extend this approach to heavier feedstocks such as resids and to the current-generation zeolite catalysts. With zeolites, shape selectivity will play an important role in modifying the product selectivity. A structurally based model for diffusivity of hydrocarbons in zeolites coupled with transition state selectivities will be required. Developing structural models for size and transition state selectivities is in itself a challenging problem, but examples of significant progress are already appearing. VII.

PROCESS, PLANT, AND SYSTEM OPTIMIZATION

Fundamental kinetics apart from guiding catalyst development also form the basis of reactor modeling. Accurate reactor modeling allows detailed process and plant simulations to improve design and operation of commercial plants. Since the final product sold in the market place has roots at the microscopic fundamentals, there is a need for closer integration of modeling at catalyst, reactor, process, plant, and total system level. The frontier areas in process engineering today are on-line optimization and advanced control, which supplement traditional engineering design. An accurate and detailed description of different processes allows their efficient integration to maximize product quality and uplift within the existing constraints of an operating plant. In the area of process simulation, the trend is toward rigorous description of material and energy balances, tray-to-tray calculations for separations equipment with many components and simultaneous solution methodology. The simultaneous simulation and optimization approach allows an accurate description of complex heat integration, recycle flows, and description of hydraulic, thermodynamic, and other constraints in operating plants. The open-equations approach allows efficient on-line tuning of models, data reconciliation, and optimal setpoint prediction for advanced control applications. Furthermore, mathematical algorithms have enhanced over the years that allow efficient solution of resulting large-scale nonlinear-programming problems. For a typical process (reactors, several flash drums, compressors, and distillation towers), up to 100,000 simultaneous nonlinear equations result. Such problems with large degrees of freedom for optimization are being solved today with considerable savings and improvements in design and operation of plants. Such large-scale computation problems are now amenable to practical solution because of the unrelenting advances in computer technology.

595

Aspects of Modeling in Petroieum Processes

As a single resource, computer technology is now and will continue to have a tremendous impact on the process industries. VIII.

ADVANCES IN COMPUTER TECHNOLOGY

Advances in speed, memory size, vectorization, and massively parallel processing are significantly enhancing the effectiveness of the computer each year. Figure 30 is a score card of what has been accomplished in the last 40 years, computing cost has been halved approximately every 3 years, as indicated in this graph of the most powerful commercial machines of each era [83]. Furthermore, massively parallel computing is expected to change the slope of the relative cost curve dramatically. The change in 100 ^ ^

IBM 650

10 " ^ g ^ IBM 704 V//Zu IBM 7090 ^9/% IBM 7094 '//%% IBM 360/50 / %m'/ IBM 360/67

oi

IBM 360/91 mCDC640 3>

dimensionless t e m p e r a t u r e rise, ratio of Thiele modulii for autocatalytic reactions dimensionless activation energy effectiveness factor t e m p e r a t u r e sensitivity p a r a m e t e r electron density dimensionless concentration, diameter of molecules Thiele modulus Thiele modulus (observable)

Subscripts

eff / obs s

effective ith component observed surface

REFERENCES

1.

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Index

Acetyl alkylsulfonyl peroxides, 363 Adsorption in nonuniform catalyst preparation on powders, 178-180 simultaneous diffusionadsorption in pellets, 180-184 on vanadia/silica, 21-25 Aging, of catalysts, 584-585 monoperoxycarbonates, 363 hydroperoxides, 363 tert-A\ky\ peroxyesters, 363 y-Alumina, adsorption on, in catalyst preparation, 178-179, 181-185 Alumina, isoelectric point, 178 Alumina membranes, 475-476, 513-517 Aluminum alkyl compounds, as cocatalysts for Ziegler-Natta catalysts, 337 Amorphous silica alumina (see Silica alumina, amorphous)

Anionic adsorption, 178 Aromatics catalytic cracking, group contributions, 35 van der Waals interaction energy in ZSM-5, 565-568 yield in heavy oil hydrogenation simulation, 78-80, 82-85 Atom superposition and electron localization (ASED) theory, 18-19 Autocatalytic processes, 558-560 Automobile catalysts (see Catalytic converters) Automobile exhaust emissions testing, 259 AUTO numerical package, 377 Bang-bang control systems, 158 Benzene hydrogenation, Monte Carlo simulation, 80, 81 Bethe networks, 5, 90-91, 96-97, 101-105 for diffusivity estimation, 115-116, 121-122 603

604 [Bethe networks] for optimal structural properties selection, 127-129 BET techniques, 92 Bifunctional catalysts, for FischerTropsch synthesis, 240-244 Bifunctional initiators, 363-373 reactor modeling, 373-384 Bimodal porous catalysts, diffusivity, 118-120 Bismuth oxides, in membrane reactors, 476 Bosanquet equation, 104 underestimation of diffusivity in supports, 117 Brownian motion, 105 Brusselator mechanism, 558, 559 Bubble flow, 396 Bulk diffusion, 93 Butene-1, copolymerization with ethylene, 359-360 CAD (computer-aided design) (see Computer-aided design) Cage effect, in zeolites, 562-563, 566 Capillary condensation, 92 in externally wetted pellets, 408-409,427-431,443 Carbon, for membrane reactors, 477 Carbon center approaches, 4 Carbonium ions, role in catalytic cracking, 47-49 Carbon monoxide emissions (see also Catalytic converters) from monolithic catalytic converters, 280-281 from packed-bed catalytic converters, 268-270, 271-273,274-276 Carbon monoxide hydrogenation model, for Fischer-Tropsch synthesis, 210-213, 237-238 selectivity, 199 sites for, 199-200

Index Carbon monoxide methanation, on nonuniform catalysts, 161, 172-173 Carbon monoxide oxidation, on nonuniform catalysts, 160-161, 163, 164, 167-168 Catalyst activity decay function, 35 Catalyst aging, 584-585 Catalyst deactivation (see Deactivation) Catalyst design, 2-4 activity/diffusivity tradeoff, 89-90 of catalytic surface, 3 pore models (see Pore models) Catalyst Design Advisory Program, 4 Catalysts, 2 diffusion in (see Diffusion) Fischer-Tropsch (see FischerTropsch catalysts) intraparticle transport phenomena (see Intraparticle transport phenomena) multiphase (see Multiphase catalytic systems) nonuniform (see Nonuniform catalysts) physical characterization, 92-93 for polymerization (see also Initiators), 335-336 Catalyst supports, 5 Bethe networks (see Bethe networks) diffusivity in (see Diffusivity, in catalyst supports) isoelectric points, 178 multiphase wetting phenomena (see Multiphase catalytic systems) nonuniform catalyst distribution (see Nonuniform catalysts) optimal design, 95-96 optimal structural properties selection, 126-129 pore size distribution, 110-113 porosity, 109

Index [Catalyst supports] structure effects on activity/ selectivity, 125-126 structure simulation (see Pore models) surface area, 109-110 tortuosity factor, 93, 115, 116 transport property characterization Knudsen diffusion regime, 113-115 simulation vs. experiment, 117-121 transition/molecular diffusion regime, 115-117 Catalytic converters, 5-6 deactivation, 173-175 engine misfiring and, 290-291 monolithic (see Monolithic converters) packed-bed (see Packed-bed converters) summary of types, 259-260 Catalytic cracking, 3, 31, 577-582 catalyst design approach, 31-32 group contributions, 593-594 amorphous silica alumina, 34-40 zeolites, 40-51 reaction pathways, 41 Catalytic membrane reactors (CMR), 472, 517-524 Catalytic nonpermselective membrane reactors (CNMR), 472, 525-534 Catalytic reaction synthesis, 9-11 relationship to microkinetic analysis, 12-16 Cationic adsorption, 178 Ceramic membranes, 532 future use, 537-538 Chain-initiation reactions, 574 Chain-termination reactions, 574 Chaotic reaction behavior, 558-559 Chemical vapor deposition, for creation of membranes, 477

605 Chromia, isoelectric point, 178 Chromium-based catalysts, 337, 338 Claus reaction, in membrane reactors, 525-528 Clean Air Act Amendments of 1990, 2-3 Cobalt, for Fischer-Tropsch synthesis (see FischerTropsch synthesis, experimental studies over Co and Ru) Cobalt/molybdate, for hydrodesulfurization, 398, 399 Cobalt/thoria/kieselghur, for Fischer-Tropsch synthesis, 204 Cobalt/zirconia/silica, for FischerTropsch synthesis, 204 Co-cracking, 572 Coimpregnation, for nonuniform catalyst preparation, 181 Coke combustion kinetics, 569-571 formation, group contribution modeling, 38 Competitive adsorption, in nonuniform catalyst preparation, 181-182 Complex feedstocks, modeling, 7 Complex mixtures kinetic interactions in (see Monte Carlo simulations, of complex mixtures) modeling, 4 Complex periodic reaction behavior, 558-559 Composite catalysts, deactivation, 177 Compressed solids, 99, 101 Compressed support structures (see also Catalyst supports) diffusivity, 118-120 Bethe networks for estimation, 115-116, 121-122 a priori estimation, 122-125

606 [Compressed support structures] pore size distribution, 112-113 surface area, 110-111 tortuosity factor, 115-116 Computer-aided design (see also various computer-intensive methods, such as Lumping methods or Monte Carlo simulation) advances in, 595-596 of catalysts (see also Catalyst design), 3-4 examples, 1-2 for microkinetic analysis, 10-11 in petroleum processing, 594-596 Configurational diffusion, 561, 563 Connectivity, 96, 97, 126 Consecutive-parallel reactions, and nonuniform catalyst distribution, 153, 154 Consecutive reactions, and nonuniform catalyst distribution, 148-149, 152-153 Continuous-flow stirred-tank reactors, for olefin polymerization, 355-361 Converters, catalytic (see Catalytic converters) Copolymerization, 335, 357, 359-360 Copper oxide/a-alumina, in nonuniform catalysts, 160 Counterdiffusion, 561-562 Coupled reaction systems (see Monte Carlo simulation, simple coupled systems) Cracking (see Catalytic cracking; Thermal cracking) Crank-Nicholson method, 305-308 Cubic tessellation, 95, 122 Cumulative reaction probability density function, 63, 64 Cyclization, group contribution modeling, 38

Index Cyclohexane dehydrogenation, in membrane reactors, 486-487 microporous CMR reactors, 517-522 microporous PBMR reactors, 498-500 Cyclohexene hydrogenation, 400-401,451-452 dynamic behavior in, 412-413 1,5-Cyclooctadiene hydrogenation, 449 Danckwerts boundary condition, 312-313 Deactivation composite catalysts and, 177 hydrotreating catalysts and, 175-177 in monolithic converters, 173-175,328-332 nonuniform catalysts and experimental studies, 172-173 nonselective poisoning, 169-171 selective poisoning, 171-172 three-way catalysts and, 173-175 Dealkylation, group contribution modeling, 38 Dehydrogenation (see also dehydrogenation of specific compounds) group contribution modeling, 38 in membrane reactors, 473-474, 475 Diacyl peroxides, 363 Di-terf-alkyl peroxides, 363 Dialkyl peroxydicarbonates, 363 Di-OA-f-alkyl)per(oxy) ketals, 363 Dibenzothiophene, hydrodesulfurization, 403 Diffusion (see also Transport properties) in catalysts, 89, 93-94 and nonuniform catalyst preparation, 180-184

607

Index [Diffusion] in pores, 5, 555-556, 561-563 regions, 561, 563 Diffusional falsification, 555 Diffusivity, in catalyst supports Bethe networks for estimation, 115-116, 121-122 Knudsen regime, 113-115 a priori estimation, 122-125 simulation vs. experiment, 117-121 transition/molecular diffusion regime, 115-117 2,7-Dimethyloctane, catalytic cracking, 36-38 Dirac delta function catalyst distribution, 138 isothermal fixed-bed reactor, 166 multiple isothermal reactions, 148-149, 150 multiple nonisothermal reactions, 153-156 and selective poisoning, 171-172 single isothermal reactions, 139, 142-143 single nonisothermal reactions, 146 Dual-function catalysis, 583 Dynamic reaction behavior and intraparticle transport, 558, 559

oscillations, 168, 351-353, 380-383, 559 Effectiveness factor, 555-558 Eggshell catalyst distribution, 139 deactivation and, 170, 172 experimental studies of, 160-161, 167 for Fischer-Tropsch synthesis, 246-247 preparation, 180, 181, 184, 185 Egg white catalyst distribution, 139 deactivation and, 170

[Egg white catalyst distribution] experimental studies of, 167 preparation, 181, 185 Egg yolk catalyst distribution, 139 deactivation and, 170, 172 experimental studies of, 160, 167 preparation, 181 Electric double-layer theory, 179 Electrode graphite, diffusivity in, 118 Emissions testing, 259 Engine misfiring, and converter performance, 290-291 Environmental regulations, 2 Ergun equation, 482, 485 Ethane dehydrogenation, in membrane reactors microporous CMR, 523-524 microporous PBCMR, 524-526 microporous PBMR, 513-517 Ethylbenzene dehydrogenation, in membrane reactors, 491-492, 505-506, 510-511 Ethylene production in thermal cracking, 571-577 readsorption probability, in Fischer-Tropsch synthesis, 232 Ethylene epoxidation, on nonuniform catalysts, 153, 161-163 Ethylene hydrogenation, on nonuniform catalysts, 160-161 Ethylene polymerization copolymerization with butene-1, 359-360 dynamic behavior in fluidizedbed reactors, 351-353 monomer diffusion limitation, and MWD broadening, 344-345 Ziegler-Natta catalysts for, 338

608 Federal Test Procedure, 259 Feedstock characterization, new techniques for, 591 Fischer-Tropsch catalysts, 238 bifunctional, 240-244 eggshell, 246-247 intrapellet liquid composition and, 244-247 modeling, 5 preparation: ruthenium and cobalt, 205-206 site distribution, 244-247 surface reactions modification, 238-240 Fischer-Tropsch synthesis, 199-202 chain growth and termination, 200-202 experimental studies over Co and Ru, 205-207 bed-residence time effects (on chain growth), 215-221 carbon monoxide hydrogenation model, 210-213, 237-238 carbon number effects (on chain growth), 221-225 CO pressure effects (on secondary rxns/selectivity), 225-227 metal crystallite size effects (on selectivity), 213-215 model simulations, 232-238 olefin readsorption model, 207-210, 232-237 pellet size effects (on selectivity), 227-232 rate expressions, 207 reaction mechanism, 206-207 secondary reactions, 216, 220-221,225-227 site density effects (on selectivity), 227-232 structural parameter effects (on selectivity), 230-232

Index [Fischer-Tropsch synthesis] support effects (on selectivity), 215 intrapellet cracking, 243 molecular weight distribution, 216 Flory, 202, 216, 239 non-Flory, 202-203 olefin readsorption, 238-240 product functionality, 202-203 recycle, 245-246 secondary reactions, 239, 241-244 selectivity, 204-205 transport effects, 203-205 Fish-eyes, 570 Fixed-bed reactors, with nonuniform catalyst distribution, 163-169 Fixed-time step stochastic methods, 58-60 Flory distribution, 216, 239 from Fischer-Tropsch synthesis, 202-203 Flow types, in trickle-bed reactors, 395-396 Fluid catalytic cracking (see Catalytic cracking) Fluidized-bed catalytic membrane reactors (FBCMR), 473 Fluidized-bed membrane reactors (FBMR), 473, 534-537 Fluidized-bed reactors, olefin polymerization in, 347-353 Foaming flow, 396 Free-radical addition reactions, 574 Free-radical decomposition reactions, 574 Free-radical isomerization reactions, 574 Free-radical polymerization with bifunctional initiators, 363-364 modeling, 364-373 reactor modeling, 373-384

Index [Free-radical polymerization] vinyl monomers (see Vinyl polymerization) Full memory, fixed-time step (Monte Carlo) approach, 62 Full memory, variable-time step (Monte Carlo) approach, 62-66 Fully-wetted trickling flow, 396-397

Galerkin's method, 265, 279 Gas-oil catalytic cracking group contribution methods for, 593-594 lumping models, 577-578, 580-582 thermal cracking group contribution model, 576 Gasoline yield, 41-43 Gauss quadrature techniques, 319 GEAR codes, 279 GEARIB subroutine code, 265 Group contributions, 573-574, 576-577, 592-594 for amorphous silica alumina, 34-40 sensitivity analysis, 40-41 product distribution calculation, 36-39 for zeolites, 40 Y zeolite, 41-45 ZSM-5 zeolite, 45-51 Heat of reaction parameter (p), and optimal catalyst distribution, 145-146 Heat transfer, intraparticle limitations, 557-558 Heavy oil hydrogenation, Monte Carlo simulation, 75-86

609

n-Heptane catalytic cracking, 46-51 /i-Heptane isomerization, 556 Heterogeneous catalytic reaction systems, industrially important, 392 H-Hexadecane, catalytic cracking, 44-45 n-Hexane, catalytic cracking, 49, 51 High-temperature membrane reactors (see Membrane reactors) Hollow-tube multiphase reactors, 455 Hopf bifurcation, 380-382 Hougen, O. A., role in early history of petroleum processing, 554 Hougen-Watson rate laws (Langmuir-HinshelwoodHougen-Watson), 60-61, 75-86 Hydrazine decomposition, 408, 411-412 Hydrocarbon cracking catalytic cracking kinetics, 31, 34-51, 577-582 thermal cracking kinetics, 571-577 Hydrocarbon emissions from monolithic catalytic converters, 280-281 from packed-bed catalytic converters, 268-273, 274-276 Hydrocarbon pyrolysis, 573-577 Hydrocarbons, aromatic (see Aromatics) Hydrocarbon synthesis reactions, Fischer-Tropsch (see Fischer-Tropsch synthesis) Hydrodemetallation, 175-177 Hydrodesulfurization, 177 diffusion limitations in, 398, 399 partial wetting in multiphase reactors, 402-403

610 Hydroformylation, in Fischer Tropsch synthesis, 240-241 Hydrogen-abstraction reactions, 574 Hydrogenation (see also hydrogenation of specific compounds) in membrane reactors, 473-474 partial wetting in multiphase reactors, 402, 403, 404-407, 419-420 Hydrotreating catalysts, deactivation, 175-177 Hydroxides, isoelectric points, 178 Impregnation for nonuniform catalyst preparation, 178-186 dry vs. wet, 184 profiles, modeling, 5 Inactive wetting, 396 Initiators, 335-336 bi- and polyfunctional, 363-373 in high-molecular-weight oligomers, 373 reactor modeling, 373-384 generation of free-radicals by, 363 Inorganic membranes (see Membrane reactors) Inorganic oxides, for nonuniform catalyst preparation, 178 Intraparticle transport phenomena diffusional falsification, 555-556 effectiveness factor concept, 555-558 heat transfer resistance, 557-558 order of importance of effects, 558 Thiele modulus, 556-558 in zeolites, 555,561-569 Iridium-based catalysts, for hydrazine decomposition, 408, 411-412 Iron, for Fischer-Tropsch synthesis, 204

Index Isoelectric point, and nonuniform catalyst preparation, 178 Isomerization free-radical isomerization, 574 group contribution modeling, 38 Isoparaffins, catalytic cracking, group contributions, 35-36

Ketone peroxides, 363 Kinetic coupling (see also Monte Carlo simulation), 56-57 complex mixtures, 73-74 simple coupled systems, 60-61 Kinetics (see also Microkinetic analysis) of catalytic cracking (see Catalytic cracking) of coke combustion, 569-571 of complex mixtures (see Monte Carlo simulation, complex mixtures) group contribution models (see Group contributions) history of developments in, 569-570 LHHW kinetics, 60-61, 75-86 lumping models (see Lumping models) modeling, 4 reaction trajectory, 56 recent trends in petroleum processing models, 591-594 of reforming, 582-590 of thermal cracking, 571-577 Knudsen diffusion, 93, 561, 563

Langmuir-Hinshelwood-HougenWatson rate laws, 60-61 and Monte Carlo simulation of heavy oil hydrogenation, 75-86 Liquid maldistribution, in tricklebed reactors, 446-449

Index Lumping methods basic description of, 580 for gas-oil catalytic cracking, 577-578 10-lump Mobil FCC model, 580-582 for reforming Exxon model, 583, 584, 587, 590 Mobil model, 583-587, 588-589 structured oriented lumping, 592 for thermal cracking, 572-573 Magic-angle-spinning NMR, 564-568 Magnesia, isoelectric point, 178 Magnesium-titanium catalysts, 338-340 Markov chains (see also Monte Carlo simulation), 55-56 Mathematical models (see Modeling) Mean free path, 93 Mean molecular velocity, 93 Mean pore size, effect on firstorder reaction rate, 126-129 Membralox® membrane, 475, 513, 523 Membrane reactors, 471-477 asymmetric nature of commercial membranes, 480 catalytic membrane reactors (CMR), 472 comparison with other reactors, 518, 520-522 models, 517-524 catalytic nonpermselective membrane reactor (CNMR), 472 models, 525-534 factors for enhancing equilibrium shift, 540-541 fluidized-bed catalytic membrane reactor (FBCMR), 473

611

[Membrane reactors] fluidized-bed membrane reactor (FBMR), 473 models, 534-537 future developments, 537-538 high-temperature applications, 473-477 low-temperature applications, 471-472 modeling, 6 packed-bed catalytic membrane reactor (PBCMR), 473 model, 477-486 microporous PBCMR, 524-525, 526 packed-bed membrane reactor (PBMR), 473 models with microporous membranes, 498-517 models with palladium membranes, 486-498, 500 requirements for successful scaleup, 538-539 selection guide: high vs. low space times, 522 types of, 472-473 Mercury porosimetry, 92 Metallocene catalysts, for homogeneous olefin polymerization, 354-355 Metathetical reactions, 574 Methane partial oxidation, 4 catalytic reaction synthesis for, 26-28 criteria for successful catalysts, 27-28 mechanism, 16-17, 20-25 molecular orbital studies, 1826 Methane steam reforming, in membrane reactors, 495, 497-498, 499, 534-537 Methanol conversion to gasoline (MTG), in ZSM-5, 564-568 Methanol partial oxidation, in membrane reactors, 511-512

612 Methyl aluminooxane (MAO), as cocatalyst for soluble Ziegler-Natta catalysts, 354-356 Methylbenzenes, van der Waals interaction energy in ZSM-5, 566-568 3-Methylpentane pyrolysis, 573575 ct-Methylstyrene hydrogenation, 403, 404-407, 419-420 dynamic behavior in, 412, 413 in hollow-tube reactor, 455-456 liquid maldistribution in, 447-448 in membrane reactors, 534 Michaelis-Menton kinetics, 56 Microactivity test (MAT), 578-580 Microkinetic analysis, 9-10 computer-aided, 10-11 conditions for success of, 11-12 of methane partial oxidation (see Methane partial oxidation) relationship to catalytic reaction synthesis, 12-16 of simple catalytic reactions, 11-12 Microsphere aggregates, diffusivity, 120-121 Mixtures, kinetic interactions in (see Monte Carlo simulation, complex mixtures) Modeling (see also specific reactions, i.e., Olefin polymerization), 3, 4-7 lumping (see Lumping methods) Monte Carlo simulation (see Monte Carlo simulation) Molecular dynamics simulation for sorbate molecules in zeolites, 563-564 in zeolites design, 7 of ZSM-5, 564-568 Molecular orbital calculations, of methane partial oxidation, 18-27

Index Molecular weight distribution in Fischer-Tropsch synthesis, 202-203 in olefin polymerization broadening of, with heterogenous catalysis, 344-345 narrow, with homogenous catalysis, 355 Molybdena/silica, 4 methane partial oxidation on, 16-18, 25-26 sodium effects on activity/ selectivity, 18 Molybdenum/silica, for dibenzothiophene hydrodesulfurization, 403 Monolithic converters, 260, 297-299 basic model equations, 276-279 equivalent continuum models of transient operation adiabatic, nonuniform flow distribution, 323-326 adiabatic, uniform flow distribution, 320-322 catalyst deactivation, 328-332 diabatic operation, 326-328 flow maldistribution effects, 314-315 model equations, 315-319 numerical solution, 319-320 pinwheel flow distribution, 315, 323-326, 328 "quenching" stage, 321-322, 326 experimental model verification, 280-281 model applications, 282-291 numerical solution, 279-280 overtemperature prediction, 285-289 single-passage models of transient operation, 299-301 with insulated leading edge, 313-314

Index [Monolithic converters] numerical solution, 305-308 with pre-entrance region, 301-304 pre-entrance region effects, 308-313 transient performance, 298-299 light-off stage, 298-299, 311, 328, 330-332 upstream concentration of catalyst, 284-285 warm-up behavior, 282-285 washcoated, 5-6 Monte Carlo simulation in catalyst design, 4-5 of catalyst diffusion, 93-94 of catalyst pores, 90, 91, 98-101, 105-109 complex mixtures, 55-56, 57-60 comparison of approaches, 86-87 heavy oil hydrogenation example, 75-86 kinetic coupling, 73-74 memory (RAM) requirements, 65 fixed- vs. variable-time methods, 58-60 full memory approach, 57, 58 kinetic coupling, 56-57, 60-61, 73-74 simple coupled systems, 60-62 full memory, fixed-time step approach, 62 full memory, variable-time step approach, 62-66 kinetic coupling, 60-61 partial system approaches, 69-73, 77 self-consistent concentration(SCC), fixedtime step approach, 66-67 self-consistent concentration(SCC), variable-time step approach, 67-69

613

[Monte Carlo simulation] single component approach, 57, 58 in zeolites design, 7 Multifunctional initiators, 363-373 Multigrain model, of olefin polymerization, 342-346 Multiphase catalytic reactors, 392-393 hollow-tube design, 455-456 new reactor designs for, 454-456 trickle-bed, 395-397 Multiphase catalytic systems, 6, 391-393 capillary condensation in externally nonwetted pellets, 408-409 modeling, 427-431 exploiting partial wetting, 453-456 new reactor designs for, 454-456 guide to modeling single pellets, 441-445 inactive wetting in, 396 multipellet modeling, 445 catalyst dewetting by external liquid film vaporization, 449-453 liquid maldistribution, partial wetting, and reaction, 446-449 multiphase flow in trickle-bed reactors, 395-397 nonsteady-state wetting phenomena, experimental observations, 410-413 partial wetting of completely filled pellets, 401-407 modeling, 414-427 modeling studies: table of, 415-417 single-pellet reactors and, 404-407 pellets in contact with a single phase, 398-401

614

[Multiphase catalytic reactors] steady states of pellets: summary, 394-395 vaporization in externally completely wetted pellets, 407-408 vaporization in externally partially wetted pellets, 410 half-wetted catalytic slab, 432-441 modeling, 431-442 Multiple steady states, in nonuniform catalyst reactions, 166-167 Naphtha, thermal cracking group contribution model, 576 Naphthalene catalytic cracking, group contributions, 35 Naphthalene hydrogenation, Monte Carlo simulation, 80-82 National Critical Technologies Panel, 2 Neutral oil hydrotreating, 79-80 Newton-Raphson method, 305-308, 319 Nickel/alumina, in nonuniform catalysts, 161 NMR, 13C magic-angle-spinning, 564-568 Non-Flory molecular weight distribution, 202-203 Nonlinear reaction dynamics and intraparticle transport, 558, 559 in olefin polymerization, 351-353 over nonuniform catalysts, 168 in styrene polymerization, 380-383 Nonselective poisoning, nonuniform catalysts, 169-171 Nonuniform catalysts Dirac delta function distribution (see Dirac delta function catalyst distribution) for Fischer-Tropsch synthesis, 246-247

Index [Nonuniform catalysts] fixed-bed reactor studies, 163-169 isothermal plug flow, 163-166 isothermal with axial dispersion, 166-167 nonselective poisoning, 169-171 optimal distribution overview, 137-138 preparation adsorption on powders, 178-180 experimental studies, 184-186 simultaneous diffusionadsorption in pellets, 180-184 selective poisoning, 171-172 single-pellet optimization, 138-139 experimental studies, 159-163 multiple isothermal reaction, 147-150 multiple nonisothermal reaction, 150-156 single isothermal reaction, 139-143 single nonisothermal reaction, 143-147 step function distribution, 141-143 surface area effect, 156-159 step distribution, 138, 141-143, 157-158 Objective function, 2 Octane number, 41-43 Olefin catalytic cracking in Fischer-Tropsch synthesis, 201 group contributions, 35 Olefin hydrogenation, in FischerTropsch synthesis, 201, 202 Olefin oligomerization, in FischerTropsch synthesis, 201 Olefin polymerization, 336 Ethylene polymerization); (see also Propylene polymerization

Index [Olefin polymerization] heterogeneous, 336 gas-phase vs. slurry, 345-346 growth of polymer particles, 339-340 heat and mass transfer effects, 345-346 monomer diffusion limitation, and MWD broadening, 344 morphological models, 340-346 multigrain (morphological) model, 342-346 reactor modeling, 346-354 shape of polymeric particles, 337, 339 Ziegler-Natta catalysts for, 337-340 homogeneous copolymerization kinetic model, 357 reactor modeling, 355-362 Ziegler-Natta catalysts (soluble) for, 354-355 Olefin readsorption, in FischerTropsch synthesis, 216, 220-221,225,227,238-240 model, 207-210, 232-237 Olefin yield, 3 On-line optimization, 594 Oregonator mechanism, 558 Oscillatory reaction dynamics in olefin polymerization, 351-353 over nonuniform catalysts, 168 in styrene polymerization, 380-383 Overtemperature, monolithic catalytic converters, 285289 Oxides, isoelectric points, 178 Oxygenates, blending, 3

Packed-bed catalytic membrane reactors (PBCMR), 473, 477-486, 524-526

615 Packed-bed converters, 260 basic model equations, 261-264 experimental model verification, 265-270 model applications, 270-276 numerical solution, 264-265 optimum design, 273-276 parametric sensitivity analysis, 270-273 warm-up behavior, 271-272 Packed-bed membrane reactors (PBMR) (see Membrane reactors, packed-bed membrane reactor (PBMR)) Palladium/alumina for cyclohexene hydrogenation, 412, 413 for a-methylstyrene hydrogenation, 403, 404-407, 419-420, 448-449 dynamic behavior in, 412, 413 in hollow-tube reactor, 455-456 in nonuniform catalysts, 161 Palladium/charcoal, for cyclohexene hydrogenation, 400-401, 451-452 Palladium membranes for dehydrogenation, 474 disadvantages, 474, 537 for hydrogenation, 473-474 hydrogen permselectivity, 474 for methane steam reforming, 534-537 model of, in PBMR, 486-498, 500 Palladium/platinum, poisoning in automobile catalysts, 174-175 /z-Paraffins, catalytic cracking group contributions, 35 over Y zeolites, 43-45, 563, 567 over ZSM-5, 45-51 Parallel reactions, and nonuniform catalyst distribution, 147-148, 151-152

616 Partially-wetted trickling flow, 396, 397 Partial system (Monte Carlo) approaches, 69-70 partial system local composition method, 70-72, 77 partial system self-consistent concentration method, 72-73 Pellets (see Catalyst supports) Pendant pores, 93 Percolation theory, 95 Percolation threshold, 102-103, 113 Peroxides, as initiators, 363-365, 370-371 Petroleum characterization, 32 molecular description, 32-34 pseudocomponents, 33-34 Petroleum processing catalytic cracking (see Catalytic cracking) feedstock characterization advances, 591 historical aspects, 553-554 modeling, 7 recent trends in kinetic models, 591-594 reforming, 582-590 thermal cracking, 571-577 Petroleum residua, hydrodesulfurization diffusion limitations in, 398-399 partial wetting in multiphase reactors, 402-403 Phosphorus poisoning, 330-331 Physical properties, catalyst supports, 109-113 Pinwheel converter flow distributer, 315, 323-326 PIONA analysis, 583 Platinum, in catalytic converters (see Catalytic converters) Platinum/alumina capillary condensation in, 408-409

Index [Platinum/alumina] in membrane reactors, 474, 475 in nonuniform catalysts, 160-161, 167-169 preparation, 184-185 Platinum-palladium, poisoning in catalytic converters, 174-175 Platinum/silica, surface area in nonuniform catalysts, 156-157, 159 Poisoning (see also Deactivation) in automobile catalysts, 173-175 nonuniform catalysts, 169-172 pore-mouth, 170 uniform, 170 Polydispersity, 345 Polyfunctional initiators, 363-373 in high-molecular-weight oligomers, 373 reactor modeling, 373-384 Polymeric core model, of olefin polymerization, 341 Polymeric flow model, of olefin polymerization, 341-342 Polymerization basic concepts, 335-336 free-radical (see Free-radical polymerization) of olefins (see Olefin polymerization) Polymerization catalysts, modeling, 6 Polyphosphazene membranes, 477 Polystyrene manufacture (see Styrene polymerization) Pore diffusion (see also Intraparticle transport phenomena) modeling, 5 and reaction, 555-556 Pore models, 89-90, 94-95 Bethe networks, 90-91, 96-97, 101-105 importance of for successful optimization, 130 percolation theory, 95

Index [Pore models] three-dimensional (Monte Carlo) approaches, 90, 91, 98-101, 105-109 transport properties calculation using Bethe networks, 101-105 using Monte Carlo simulation, 105-109 Pore-mouth poisoning, 170 Pore size determination, 92 effect on first-order reaction rate, 126-129 Pore size distribution, 110-113 Pore volume determination, 92-93 Porosimetry, mercury, 92 Porosity catalyst supports, 109 correction factor, 93 effect on first-order reaction rate, 126-129 Porous materials, physical characterization, 92-93 Porous pellets (see Catalyst supports) Preparation Fischer-Tropsch catalysts: ruthenium and cobalt, 205-206 nonuniform catalysts (see Nonuniform catalysts, preparation) Pressure-drop hysteresis, in cocurrent downward flow trickle-bed reactors, 397 Product distribution, calculation using group contributions, 36-39 Propane oxidation, on nonuniform catalysts, 167 Propene partial oxidation, 160 Propylene, production in thermal cracking, 571-577 Propylene polymerization dynamic behavior in fluidizedbed reactors, 353

617 [Propylene polymerization] growth of polymer particles, 339-340 monomer diffusion limitation, and MWD broadening, 344-345 Ziegler-Natta catalysts for, 338 Pseudocomponents, for petroleum feedstocks, 33-34 Pulsing flow, 396 Pycnometry, 92 Pyrolysis kinetics, 573-577, 592 reactions of, 574 Quantum chemical techniques, in zeolites design, 7 Quantum mechanical calculations, use in microkinetic analysis, 18 Quasi-steady-state approximation, 358-359 Radical reactions (see Free-radical reactions) Random packing arrangements, 98-101 Reaction kinetics (see Kinetics) Reaction trajectory, 56 Reactors and reactor modeling bifunctional catalysts, 373-384 heterogeneous olefin polymerization CFSTR for, 355-361 membrane (see Membrane reactors) modeling, heterogeneous olefin polymerization, 346-354 multiphase catalytic, 392-393, 395-397, 454-456 nonuniform catalyst distribution (see Nonuniform catalysts) single-pellet, 404-407 trickle-bed (see Trickle-bed reactors) vinyl polymerization, 373-384

618 Readsorption model, 207-210, 232-237 Refining {see Petroleum processing) Reforming kinetics, 582-590 lumping models Exxon model, 583-584, 587, 590 Mobil model, 583-589 Reformulated gasoline, 2-3 Rhodium, in three-way catalysts, 174-175 Rhodium/alumina, preparation, 185 Rice-Herzfeld mechanism, 56 Ring opening, group contribution modeling, 38 Run-around charts, 569-570 Ruthenium {see Fischer-Tropsch catalysts) Selective catalytic reduction (SCR) catalysts, 6, 568-569 Selective poisoning, nonuniform catalysts, 171-172 Selectivity, and nonuniform catalyst distribution, 147-150 Self-consistent concentration, fixedtime step (Monte Carlo) approach, 66-67 Self-consistent concentration, variable-time step (Monte Carlo) approach, 67-69 Silica compressed, 100-101 isoelectric point, 178 Silica-alumina, amorphous, group contributions for catalytic cracking, 34-41 Silica-alumina, isoelectric point, 178 Silver, in membrane reactors, 476 Silver/a-alumina in nonuniform catalysts, 161-163 surface area in nonuniform catalysts, 156-157 Single-pellet optimization, nonuniform catalysts {see

Index [Single-pellet optimization] Nonuniform catalysts, singlepellet optimization) Single-pellet reactors, 404-407 Sintered solids, 99, 101 Sintered support structures {see also Catalyst supports) diffusivity in Bethe networks for estimation, 115-116, 121-122 a priori estimation, 122-125 pore size distribution, 112, 113 surface area, 110-111 tortuosity factor, 115-116 Site density, 95 Small-angle neutron scattering (SANS), 92 Small-angle x-ray scattering (SAXS), 92 Sodium effects on molybdena/silica activity/selectivity, 18 effects on vanadia/silica activity/ selectivity, 18, 27 Sol-gel techniques, 94, 98 for creation of membranes, 477 diffusivity produced, 120-121 porosity resulting from, 109 Solid core model, of olefin polymerization, 341 Solid oxide fuel cells, 477 Sorbates, in zeolites, molecular dynamics simulation, 563-564 Spray flow, 396 SPYRO simulation package, 573 Steam cracking kinetics, 571-577 Step catalyst distribution, 138, 141-143, 157-158 and selective poisoning, 171 Stirred-bed reactors, olefin polymerization in, modeling, 353-354 Stochastic methods {see Monte Carlo simulation) Structure oriented lumping, 592

619

Index Styrene polymerization, with bifunctional initiators, 366-373 kinetic scheme, 367 nonlinear dynamic behavior, 380-383 reaction temperature effects, 372-373 reactor modeling, 373-384 steady-state regions, 375, 376 symmetrical initiator decomposition, 373 unsymmetrical initiator decomposition, 365 vs. mixed monofunctional initiators, 377-380 Supercomputers, 3 Supercritical fluids, in Fischer Tropsch synthesis, 245 Supports (see Catalyst supports; specific support materials) Surface area catalyst supports, 109-110 effect in nonuniform catalysts, 156-159 Surface area per unit volume, 95 Synthesis, Fischer-Tropsch (see Fischer-Tropsch synthesis) Synthesis gas production, 199 Temperature runaway, 399-400 in ethylene polymerization, 353 Tessellation, 95, 122 Thermal cracking kinetics, 571-577 reactions of, 574 Thermochemical data, use in kinetic analysis, 573 Thermoformer catalytic cracking (TCC) kinetics, 569-570 Thiele modulus, 125, 556, 557-558 carbon-number dependent, 210 and nonuniform catalyst distribution isothermal reactions, 143 nonisothermal reactions, 146, 147

[Thiele modulus] poison, 169 Three-way catalysts, deactivation, 173-175 Titania, isoelectric point, 178 Titanium-based Ziegler-Natta catalysts, 337-340 Titanium-magnesium catalysts, 337-338 Titanocene compounds, for homogeneous olefin polymerization, 354-355 Tortuosity factor, 93, 115, 116 Transient performance, modeling, 6 Transition metal catalysts (see Ziegler-Natta catalysts) Transition probabilities, 55-56 complex mixtures, 74 simple coupled systems, 61-62 Transport phenomena, intraparticle (see Intraparticle transport phenomena) Transport properties (see also Diffusion), 113-121 calculation using Bethe networks, 101-105 calculation using Monte Carlo simulation, 101-105 Trickle-bed reactors liquid maldistribution in, 446-449 multiphase flow in, 395-397 periodic on-off liquid flow operation, 411 pulsing flow operation, 411 Turnover rate, 95 Uniform poisoning, 170 Vanadia/silica, 4 carbon monoxide adsorption on, 24-25 CH2 adsorption on, 22-23 chemical bonding in, 19-20

620 [Vanadia/silica] hydrogen adsorption on, 21-22 methane partial oxidation on, 16, 17, 19-26 methoxy adsorption on, 21, 22 sodium effects on activity/ selectivity, 25-27 Vanadia/titania SCR catalysts, 569 Vanadium-based catalysts, for homogeneous olefin polymerization, 354 van der Waals interaction energy, in ZSM-5, 565-568 Variable-time step stochastic methods, 58-60 Vinyl polymerization (see also Styrene polymerization), 362-364 with bifunctional initiators, 363-364 modeling, 364-373 reactor modeling, 373-384 Volumetric activity, 95-96 Voronoi tessellations, 95 Vycor membranes, 475, 498-500, 511,517 disadvantages, 537 Warm-up behavior monolithic catalytic converters, 282-285 packed-bed catalytic converters, 271-272 Washcoated monolith catalytic converters, 5-6 Water-gas shift reaction, in membrane reactors, 491-492 Watson, role in early history of petroleum processing, 554 Wei and Prater method, 583 Wetting, in multiphase catalytic reaction systems (see Multiphase catalytic systems) Xylenes, van der Waals interaction energy in ZSM-5, 566-568

Index Yitria-stabilized zirconia, in membrane reactors, 476 Zeolite A, 561 Zeolite REY (rare-earth Y), 578-580 Zeolites acids sites, 46-47 cage effect, 562-563, 566 configurational diffusion in, 561, 563 group contributions for catalytic cracking, 40-41 history of use and development, 555, 561 intraparticle transport behavior in, 555, 561-569 (see also Intraparticle transport phenomena) isoelectric point, 178 laboratory tests for activity, 578-580 for membrane reactors, 477 modeling, 7 molecular dynamics simulation, 7, 563-568 shape-selective behavior, 555, 561, 562 Zeolite/silica-alumina, deactivation, 177 Zeolite T, 562-563 Zeolite USY (ultrastable Y), 578-580 group contributions for catalytic cracking, 44-45 Zeolite Y, group contributions for catalytic cracking, 41-45 Ziegler-Natta catalysts (see also Olefin polymerization, heterogenous), 336 active site multiplicity, 344-345, 361-362 description, 337-340 for ethylene, 338 for propylene, 338 soluble, for homogeneous catalysis, 354-355

Index

Zirconia, yitria-stabilized, in membrane reactors, 476 Zirconocene compounds, for homogeneous olefin polymerization, 354-355, 356

621

ZSM-5, 561 group contributions for catalytic cracking, 45-51 molecular dynamics simulation, 564-568