Calculate δh∘rxn for the reduction for v2o5.

FUEL CELL FUNDAMENTALS

Third Edition

RYAN O’HAYRE Department of Metallurgical and Materials Engineering Colorado School of Mines [PhD, Materials Science and Engineering, Stanford University]

SUK-WON CHA School of Mechanical and Aerospace Engineering Seoul National University [PhD, Mechanical Engineering, Stanford University]

WHITNEY G. COLELLA The G.W.C. Whiting School of Engineering, and The Energy, Environment, Sustainability and Health Institute The Johns Hopkins University Gaia Energy Research Institute [Doctorate, Engineering Science, The University of Oxford]

FRITZ B. PRINZ R.H. Adams Professor of Engineering Departments of Mechanical Engineering and Material Science and Engineering Stanford University

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Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

To the parents who nurtured us.

To the teachers who inspired us.

CONTENTS

PREFACE xi

ACKNOWLEDGMENTS xiii

NOMENCLATURE xvii

I FUEL CELL PRINCIPLES

1 Introduction 3

1.1 What Is a Fuel Cell? / 3 1.2 A Simple Fuel Cell / 6 1.3 Fuel Cell Advantages / 8 1.4 Fuel Cell Disadvantages / 11 1.5 Fuel Cell Types / 12 1.6 Basic Fuel Cell Operation / 14 1.7 Fuel Cell Performance / 18 1.8 Characterization and Modeling / 20 1.9 Fuel Cell Technology / 21 1.10 Fuel Cells and the Environment / 21 1.11 Chapter Summary / 22

Chapter Exercises / 23

v

vi CONTENTS

2 Fuel Cell Thermodynamics 25

2.1 Thermodynamics Review / 25

2.2 Heat Potential of a Fuel: Enthalpy of Reaction / 34

2.3 Work Potential of a Fuel: Gibbs Free Energy / 37

2.4 Predicting Reversible Voltage of a Fuel Cell under Non-Standard-State Conditions / 47

2.5 Fuel Cell Efficiency / 60

2.6 Thermal and Mass Balances in Fuel Cells / 65

2.7 Thermodynamics of Reversible Fuel Cells / 67

2.8 Chapter Summary / 71

Chapter Exercises / 72

3 Fuel Cell Reaction Kinetics 77

3.1 Introduction to Electrode Kinetics / 77

3.2 Why Charge Transfer Reactions Have an Activation Energy / 82

3.3 Activation Energy Determines Reaction Rate / 84

3.4 Calculating Net Rate of a Reaction / 85

3.5 Rate of Reaction at Equilibrium: Exchange Current Density / 86

3.6 Potential of a Reaction at Equilibrium: Galvani Potential / 87

3.7 Potential and Rate: Butler–Volmer Equation / 89

3.8 Exchange Currents and Electrocatalysis: How to Improve Kinetic Performance / 94

3.9 Simplified Activation Kinetics: Tafel Equation / 97

3.10 Different Fuel Cell Reactions Produce Different Kinetics / 100

3.11 Catalyst–Electrode Design / 103

3.12 Quantum Mechanics: Framework for Understanding Catalysis in Fuel Cells / 104

3.13 The Sabatier Principle for Catalyst Selection / 107

3.14 Connecting the Butler–Volmer and Nernst Equations (Optional) / 108

3.15 Chapter Summary / 112

Chapter Exercises / 113

4 Fuel Cell Charge Transport 117

4.1 Charges Move in Response to Forces / 117

4.2 Charge Transport Results in a Voltage Loss / 121

4.3 Characteristics of Fuel Cell Charge Transport Resistance / 124

4.4 Physical Meaning of Conductivity / 128

4.5 Review of Fuel Cell Electrolyte Classes / 132

CONTENTS vii

4.6 More on Diffusivity and Conductivity (Optional) / 153

4.7 Why Electrical Driving Forces Dominate Charge Transport (Optional) / 160

4.8 Quantum Mechanics–Based Simulation of Ion Conduction in Oxide Electrolytes (Optional) / 161

4.9 Chapter Summary / 163

Chapter Exercises / 164

5 Fuel Cell Mass Transport 167

5.1 Transport in Electrode versus Flow Structure / 168

5.2 Transport in Electrode: Diffusive Transport / 170

5.3 Transport in Flow Structures: Convective Transport / 183

5.4 Chapter Summary / 199

Chapter Exercises / 200

6 Fuel Cell Modeling 203

6.1 Putting It All Together: A Basic Fuel Cell Model / 203

6.2 A 1D Fuel Cell Model / 206

6.3 Fuel Cell Models Based on Computational Fluid Dynamics (Optional) / 227

6.4 Chapter Summary / 230

Chapter Exercises / 231

7 Fuel Cell Characterization 237

7.1 What Do We Want to Characterize? / 238

7.2 Overview of Characterization Techniques / 239

7.3 In Situ Electrochemical Characterization Techniques / 240

7.4 Ex Situ Characterization Techniques / 265

7.5 Chapter Summary / 268

Chapter Exercises / 269

II FUEL CELL TECHNOLOGY

8 Overview of Fuel Cell Types 273

8.1 Introduction / 273

8.2 Phosphoric Acid Fuel Cell / 274

8.3 Polymer Electrolyte Membrane Fuel Cell / 275

8.4 Alkaline Fuel Cell / 278

8.5 Molten Carbonate Fuel Cell / 280

viii CONTENTS

8.6 Solid-Oxide Fuel Cell / 282

8.7 Other Fuel Cells / 284

8.8 Summary Comparison / 298

8.9 Chapter Summary / 299

Chapter Exercises / 301

9 PEMFC and SOFC Materials 303

9.1 PEMFC Electrolyte Materials / 304

9.2 PEMFC Electrode/Catalyst Materials / 308

9.3 SOFC Electrolyte Materials / 317

9.4 SOFC Electrode/Catalyst Materials / 326

9.5 Material Stability, Durability, and Lifetime / 336

9.6 Chapter Summary / 340

Chapter Exercises / 342

10 Overview of Fuel Cell Systems 347

10.1 Fuel Cell Subsystem / 348

10.2 Thermal Management Subsystem / 353

10.3 Fuel Delivery/Processing Subsystem / 357

10.4 Power Electronics Subsystem / 364

10.5 Case Study of Fuel Cell System Design: Stationary Combined Heat and Power Systems / 369

10.6 Case Study of Fuel Cell System Design: Sizing a Portable Fuel Cell / 383

10.7 Chapter Summary / 387

Chapter Exercises / 389

11 Fuel Processing Subsystem Design 393

11.1 Fuel Reforming Overview / 394

11.2 Water Gas Shift Reactors / 409

11.3 Carbon Monoxide Clean-Up / 411

11.4 Reformer and Processor Efficiency Losses / 414

11.5 Reactor Design for Fuel Reformers and Processors / 416

11.6 Chapter Summary / 417

Chapter Exercises / 419

CONTENTS ix

12 Thermal Management Subsystem Design 423

12.1 Overview of Pinch Point Analysis Steps / 424

12.2 Chapter Summary / 440

Chapter Exercises / 441

13 Fuel Cell System Design 447

13.1 Fuel Cell Design Via Computational Fluid Dynamics / 447

13.2 Fuel Cell System Design: A Case Study / 462

13.3 Chapter Summary / 476

Chapter Exercises / 477

14 Environmental Impact of Fuel Cells 481

14.1 Life Cycle Assessment / 481

14.2 Important Emissions for LCA / 490

14.3 Emissions Related to Global Warming / 490

14.4 Emissions Related to Air Pollution / 502

14.5 Analyzing Entire Scenarios with LCA / 507

14.6 Chapter Summary / 510

Chapter Exercises / 511

A Constants and Conversions 517

B Thermodynamic Data 519

C Standard Electrode Potentials at 25∘C 529

D Quantum Mechanics 531

D.1 Atomic Orbitals / 533

D.2 Postulates of Quantum Mechanics / 534

D.3 One-Dimensional Electron Gas / 536

D.4 Analogy to Column Buckling / 537

D.5 Hydrogen Atom / 538

D.6 Multielectron Systems / 540

D.7 Density Functional Theory / 540

x CONTENTS

E Periodic Table of the Elements 543

F Suggested Further Reading 545

G Important Equations 547

H Answers to Selected Chapter Exercises 551

BIBLIOGRAPHY 555

INDEX 565

PREFACE

Imagine driving home in a fuel cell car with nothing but pure water dripping from the tailpipe. Imagine a laptop computer that runs for 30 hours on a single charge. Imagine a world where air pollution emissions are a fraction of that from present-day automobiles and power plants. These dreams motivate today’s fuel cell research. While some dreams (like cities chock-full of ultra-low-emission fuel cell cars) may be distant, others (like a 30-hour fuel cell laptop) may be closer than you think.

By taking fuel cells from the dream world to the real world, this book teaches you the science behind the technology. This book focuses on the questions “how” and “why.” Inside you will find straightforward descriptions of how fuel cells work, why they offer the potential for high efficiency, and how their unique advantages can best be used. Emphasis is placed on the fundamental scientific principles that govern fuel cell operation. These principles remain constant and universally applicable, regardless of fuel cell type or technology.

Following this philosophy, the first part, “Fuel Cell Principles,” is devoted to basic fuel cell physics. Illustrated diagrams, examples, text boxes, and homework questions are all designed to impart a unified, intuitive understanding of fuel cells. Of course, no treatment of fuel cells is complete without at least a brief discussion of the practical aspects of fuel cell technology. This is the aim of the second part of the book, “Fuel Cell Technology.” Informative diagrams, tables, and examples provide an engaging review of the major fuel cell technologies. In this half of the book, you will learn how to select the right fuel cell for a given application and how to design a complete system. Finally, you will learn how to assess the potential environmental impact of fuel cell technology.

xi

xii PREFACE

Comments or questions? Suggestions for improving the book? Found a typo, think our explanations could be improved, want to make a suggestion about other important con- cepts to discuss, or have we got it all wrong? Please send us your feedback by emailing us at fcf3@yahoogroups.com. We will take your suggestions into consideration for the next edition. Our website http://groups.yahoo.com/group/fcf3 posts these discussions, fliers for the book, and additional educational materials. Thank you.

ACKNOWLEDGMENTS

The authors would like to thank their friends and colleagues at Stanford University and the former Rapid Prototyping Laboratory (RPL), now the Nano-Prototyping Laboratory (NPL), for their support, critiques, comments, and enthusiasm.Without you, this text would not have been written! The beautiful figures and illustrations featured in this textbook were crafted primarily by Marily Mallison, with additional illustrations by Dr. Michael Sanders—their artistic touch is greatly appreciated!

The authors would like to thank the Deans of the Stanford School of Engineering, Jim Plummer and Channing Robertson, and John Bravman, Vice Provost Undergraduate Educa- tion, for the support that made this book possible.Wewould also like to acknowledgeHonda R&D, its representatives J. Araki, T. Kawanabe, Y. Fujisawa, Y. Kawaguchi, Y. Higuchi, T. Kubota, N. Kuriyama, Y. Saito, J. Sasahara, and H. Tsuru, and Stanford’s Global Climate and Energy Project (GCEP) community for creating an atmosphere conducive to studying and researching new forms of power generation. All members of RPL/NPL are recog- nized for stimulating discussions. Special thanks to Dr. Tim Holme for his innumerable contributions, including his careful review of the text, integration work, nomenclature and equation summaries, and the appendixes. Thanks also to Professor Rojana Pornprasertsuk, who developed the wonderful quantum simulation images for Chapter 3 and Appendix D. The authors are grateful to Professor Yong-il Park for his help in the literature survey of Chapter 9 and Rami Elkhatib for his significant contributions in writing this section. Profes- sor Juliet Risner deserves gratitude for her beautiful editing job, and Professor Hong Huang deserves thanks for content contribution. Dr. Jeremy Cheng, Dr. Kevin Crabb, Professor Turgut Gur, Shannon Miller, Masafumi Nakamura, and A. J. Simon also provided signifi- cant editorial advice. Thanks to Dr. Young-Seok Jee, Dr. Daeheung Lee, Dr. Yeageun Lee,

xiii

xiv ACKNOWLEDGMENTS

Dr. Wonjong Yu, and Dr. Yusung Kim for their contributions to Chapters 6 and 13. Spe- cial thanks to Rusty Powell and Derick Reimanis for their careful editing contributions to the second edition. Finally, thanks to colleagues at the Colorado School of Mines (CSM), including Bob Kee and Neal Sullivan for their helpful discussions and for a decade’s worth of students at CSM for catching typos and identifying areas in need for clarification for this third edition.

We would like to extend our gratitude to Professor Stephen H. Schneider, Professor Terry Root, Dr. Michael Mastrandrea, Mrs. Patricia Mastrandrea, Dr. Gerard Ketafani, and Dr. Jonathan Koomey. We would also like to thank the technical research staff within the U.S. Department of Energy (DOE) complex, including researchers at DOE national lab- oratories [Sandia National Laboratories (SNL), Lawrence Berkeley National Laboratory (LBNL), Argonne National Laboratory (ANL), the National Renewable Energy Laboratory (NREL), and Lawrence Livermore National Laboratory (LLNL), among others]. We would also like to thank research participants within the International Energy Agency (IEA) Sta- tionary Fuel Cell Annex, the American Institute of Chemical Engineers (AICHE) Transport and Energy Processes Division (TEP), and the National Academy of Engineering (NAE) Frontiers of Engineering (FOE) program.

For intellectually stimulating discussions on energy system design, we also would like to thank Dr. Salvador Aceves (LLNL), Dr. Katherine Ayers (ProtonOnsite Inc.), Professor Nigel Brandon (Imperial College London), Mr. Tom Brown (California State University Northridge), Dr. Viviana Cigolotti [Energy and Sustainable Economic Development (ENEA)], Professor Peter Dobson [University of Oxford (Oxon)], Dr. Elango Elangovan (Ceramatec Inc.), Professor Ferhal Erhun, Dr. Angelo Esposito (European Institute for Energy Research), Dr. Hossein Ghezel-Ayagh [FuelCell Energy Inc. (FCE)], Dr. Lorenz Gubler [Paul Scherrer Institut (PSI)], Dr. Monjid Hamdan (Giner Inc.), Dr. Joseph J. Hartvigsen (Ceramatec Inc.), Professor Michael Hickner (The Pennsylvania State University), Professor Ben Hobbs (Johns Hopkins University), Professor Daniel M. Kammen [University of California at Berkeley (UCB)], Professor Jon Koomey, Dr. Scott Larsen (New York State Energy Research and Development Authority), Mr. Bruce Lin (EnerVault Inc.), Dr. Ludwig Lipp (FCE), Dr. Bernard Liu (National Cheng Kung University), Professor V. K. Mathur (University of New Hampshire), Dr. Marianne Mintz (ANL), Professor Catherine Mitchell (University of Exeter), Dr. Cortney Mittelsteadt (Giner Inc.), Dr. Yasunobu Mizutani (ToHo Gas Co. Ltd.), John Molburg (Argonne National Laboratory), Dr. Angelo Moreno [Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA)], Professor Vincenzo Mulone (University of Rome Tor Vergata), Dr. Jim O’Brien (Idaho National Laboratory), Professor Joan Ogden (University of California at Davis), Dr. Pinakin Patel (FCE), Dr. Randy Petri (Versa Power Inc.), Professor Bruno Pollet (University of Ulster), Dr. Peter Rieke [Pacific Northwest National Laboratory (PNNL)], Dr. Subhash C. Singhal (PNNL), Professor Colin Snowdon (Oxon), Professor Robert Socolow (Princeton University), Mr. Keith Spitznagel (KAS Energy Services LLC), Professor Robert Steinberger-Wilckens (University of Birmingham), Dr. Jeffry Stevenson (PNNL), Professor Richard Stone (Oxon), Professor Etim Ubong (Kettering University), Professor Eric D. Wachsman (University of Maryland), Professor Xia Wang (Oakland University), and Professor Yingru Zhao (Xiamen University).

ACKNOWLEDGMENTS xv

Fritz B. Prinz wants to thank his wife, Gertrud, and his children, Marie-Helene and Benedikt, for their love, support, and patience.

Whitney G. Colella would like to thank her friends and family, especially the Bakers, Birchards, Chens, Colellas, Culvers, Efthimiades, Hoffmans, Jaquintas, Judges, Louies, Mavrovitis, Omlands, Pandolfis, Panwalkers, Qualtieris, Scales, Smiths, Spielers, Tepers, Thananarts, Tragers, Wasleys, and Wegmans.

Suk-Won Cha wishes to thank Unjung, William, and Sophia for their constant support, love, and understanding.

Ryan O’Hayre sends his thanks and gratitude to Lisa for her friendship, encouragement, confidence, support, and love. Thanks also to Kendra, Arthur, Morgan, little Anna, and little Robert. Ryan has always wanted to write a book … probably something about dragons and adventure. Well, things have a funny way of working out, and although he ended up writing about fuel cells, he had to put the dragons in somewhere.…

NOMENCLATURE

Symbol Meaning Common Units

A Area cm2

Ac Catalyst area coefficient Dimensionless a Activity Dimensionless ASR Area specific resistance Ω ⋅ cm2 C Capacitance F Cdl Double-layer capacitance F c∗ Concentration at reaction surface mol∕cm2 c Concentration mol∕m3 c Constant describing how mass transport affects

concentration losses V

cp Heat capacity J∕mol ⋅ K D Diffusivity cm2∕s E Electric field V∕cm E Thermodynamic ideal voltage V Ethermo Thermodynamic ideal voltage V ET Temperature-dependent thermodynamic voltage at

reference concentration V

F Helmholtz free energy J, J∕mol F Faraday constant 96, 485 C∕mol Fk Generalized force N f Reaction rate constant Hz, s−1

f Friction factor Dimensionless

xvii

xviii NOMENCLATURE

Symbol Meaning Common Units

G, g Gibbs free energy J, J∕mol g Acceleration due to gravity m∕s2 ΔG‡ Activation energy barrier J∕mol, J ΔGact Activation energy barrier J∕mol, J H Heat J H, h Enthalpy J, J∕mol HC Gas channel thickness cm HE Diffusion layer thickness cm h Planck’s constant 6.63 × 10−34 J ⋅ s ℏ Reduced Planck constant, h∕2𝜋 1.05 × 10−34 J ⋅ s hm Mass transfer convection coefficient m∕s i Current A J Molar flux, molar reaction rate mol∕cm2 ⋅ s Ĵ Mass flux g∕cm2 ⋅ s, kg∕m2 ⋅ s JC Convective mass flux kg∕m2 ⋅ s j Current density A∕cm2 j0 Exchange current density A∕cm2 j00 Exchange current density at reference

concentration A∕cm2

jL Limiting current density A∕cm2 jleak Fuel leakage current A∕cm2 k Boltzmann’s constant 1.38 × 10−23 J∕K L Length m M Molar mass g∕mol, kg∕mol M Mass flow rate kg∕s Mik Generalized coupling coefficient between

force and flux Varies

m Mass kg mcp Heat capacity flow rate kW∕kg ⋅ ∘C N Number of moles Dimensionless NA Avogadro’s number 6.02 × 1023 mol−1 n Number of electrons transferred in the reaction Dimensionless ng Number of moles of gas Dimensionless P Power or power density W or W∕cm2 P Pressure bar, atm, Pa Q Heat J, J∕mol Q Charge C Qh Adsorption charge C∕cm2 Qm Adsorption charge for smooth catalyst surface C∕cm2 q Fundamental charge 1.60 × 10−19 C R Ideal gas constant 8.314 J∕mol ⋅ K R Resistance Ω Rf Faradaic resistance Ω

NOMENCLATURE xix

Symbol Meaning Common Units

Re Reynolds number Dimensionless S, s Entropy J∕K, J∕mol ⋅ K S∕C Steam-to-carbon ratio Dimensionless Sh Sherwood number Dimensionless T Temperature K, ∘C t Thickness cm U Internal energy J, J∕mol u Mobility cm2∕V ⋅ s ū Mean flow velocity cm∕s, m∕s V Voltage V V Volume L, cm3

V Reaction rate per unit area mol∕cm2 ⋅ s 𝑣 Velocity cm∕s 𝑣 Hopping rate s−1, Hz 𝑣 Molar flow rate mol∕s, mol∕min W Work J, J∕mol X Parasitic power load W x Mole fraction Dimensionless x𝑣 Vacancy fraction mol vacancies∕mol sites yx Yield of element X Dimensionless Z Impedance Ω z Height cm

Greek Symbols

Symbol Meaning Common Units

𝛼 Charge transfer coefficient Dimensionless 𝛼 Coefficient for CO2 equivalent Dimensionless 𝛼∗ Channel aspect ratio Dimensionless 𝛽 Coefficient for CO2 equivalent Dimensionless 𝛾 Activity coefficient Dimensionless Δ Denotes change in quantity Dimensionless 𝛿 Diffusion layer thickness m, cm 𝜀 Efficiency Dimensionless 𝜀FP Efficiency of fuel processor Dimensionless 𝜀FR Efficiency of fuel reformer Dimensionless 𝜀H Efficiency of heat recovery Dimensionless 𝜀O Efficiency overall Dimensionless 𝜀R Efficiency, electrical Dimensionless 𝜀 Porosity Dimensionless �̇� Strain rate s−1

xx NOMENCLATURE

Symbol Meaning Common Units

𝜂 Overvoltage V 𝜂act Activation overvoltage V 𝜂conc Concentration overvoltage V 𝜂ohmic Ohmic overvoltage V λ Stoichiometric coefficient Dimensionless λ Water content Dimensionless 𝜇 Viscosity kg ⋅ m/s 𝜇 Chemical potential J, J/mol �̃� Electrochemical potential J, J/mol 𝜌 Resistivity Ω cm 𝜌 Density kg∕cm3, kg∕m3 𝜎 Conductivity S∕cm, (Ω ⋅ cm)−1 𝜎 Warburg coefficient Ω∕s0.5 𝜏 Mean free time s 𝜏 Shear stress Pa 𝜑 Electrical potential V 𝜑 Phase factor Dimensionless 𝜔 Angular frequency (𝜔 = 2𝜋f ) rad/s

Superscripts

Symbol Meaning

0 Denotes standard or reference state eff Effective property

Subscripts

Symbol Meaning

diff Diffusion E, e, elec Electrical (e.g., Pe,Welec) f Quantity of formation (e.g., ΔHf ) (HHV) Higher heating value (LHV) Lower heating value i Species i P Product P Parasitic R Reactant rxn Change in a reaction (e.g., ΔHrxn) SK Stack SYS System

Nafion is a registered trademark of E.I. du Pont de Nemours and Company. PureCell is a registered trademark of UTC Fuel Cells, Inc. Honda FCX is a registered trademark of Honda Motor Co., Ltd. Home Energy System is a registered trademark of Honda Motor Co., Ltd. Gaussian is a registered trademark of Gaussian, Inc.

PART I

FUEL CELL PRINCIPLES

CHAPTER 1

INTRODUCTION

You are about to embark on a journey into the world of fuel cells and electrochemistry. This chapter will act as a roadmap for your travels, setting the stage for the rest of the book. In broad terms, this chapter will acquaint you with fuel cells: what they are, how they work, and what significant advantages and disadvantages they present. From this starting point, the subsequent chapters will lead you onward in your journey as you acquire a fundamental understanding of fuel cell principles.

1.1 WHAT IS A FUEL CELL?

You can think of a fuel cell as a “factory” that takes fuel as input and produces electricity as output. (See Figure 1.1.) Like a factory, a fuel cell will continue to churn out product (electricity) as long as raw material (fuel) is supplied. This is the key difference between a fuel cell and a battery. While both rely on electrochemistry to work their magic, a fuel cell is not consumed when it produces electricity. It is really a factory, a shell, which transforms the chemical energy stored in a fuel into electrical energy.

Viewed this way, combustion engines are also “chemical factories.” Combustion engines also take the chemical energy stored in a fuel and transform it into useful mechanical or electrical energy. So what is the difference between a combustion engine and a fuel cell?

In a conventional combustion engine, fuel is burned, releasing heat. Consider the sim- plest example, the combustion of hydrogen: